**Part 2**

## **Cardiovascular and Skeletal Systems**

164 Finite Element Analysis – From Biomedical Applications to Industrial Developments

Tanaka, M; Naito, T; Yokota, M & Kohno, M. (2003). Finite element analysis of the possible

Ueti, H; Todescan, R & Gil, C. (1997). Study of the thickness enamel/dentin in function of

Weinstein, AM; Klaawitter, JJ & Cook, SD. (1980). Implant-bone interface characteristics of

Whitworth, JM; Walls, AWG & Wassell, RW. (2002). Crowns and extra-coronal restorations:

Yamamoto, M. (1985). *Metal-ceramics: Principles and methods of Makoto Yamamoto* (1st ed.),

Zhi-Yue, L; Yu-Xing, Z. (2003). Effects of post-core design and ferrule on fracture resistance

bioglass dental implants. *J Biomed Mater Res*, Vol. 14, pp. 23-29.

crown. *Rev Pós-Grad da USP*, Vol 4, pp. 153-9.

*Dental J*, 2002, Vol. 192, pp. 315-27.

Quintessence, Chicago.

60-67.

73.

mechanism of cervical lesion formation by occlusal force. *J Oral Rehabil*, Vol. 30, pp.

age, group of teeth and distance in relation to the external portion of the clinical

Endodontic considerations: the pulp, the root-treated tooth and the crown. *Br* 

of endodontically treated maxillary central incisors. *J Prosthet Dent*, Vol. 89, pp. 368-

**7** 

*UK* 

**Finite Element Analysis to Study** 

Silvia Schievano, Claudio Capelli, Daria Cosentino,

Percutaneous valve implantation is an innovative, successful alternative to open-heart surgery for the treatment of both pulmonary and aortic heart valve dysfunction (Bonhoeffer et al., 2000; Cribier et al., 2002; Leon et al., 2011; Lurz et al., 2008; McElhinney DB et al., 2010; Rodes-Cabau et al., 2010; Smith et al., 2011; Vahanian et al., 2008). However, this minimallyinvasive procedure still presents limitations related to device design: stent fracture, availability to a limited group of patients with very specific anatomy and conditions, and positioning and anchoring issues (Delgado et al., 2010; Nordmeyer et al., 2007; Schievano et al., 2007a). Computational simulations (Taylor & Figueroa, 2009), together with advanced cardiovascular imaging techniques can be used to help understand these limitations in order to guide the optimisation process for new device designs, to improve the success of percutaneous valve implantation, and ultimately to broaden the range of patients who could

In this Chapter, we review the applications of finite element (FE) analyses to study percutaneous heart valve devices. The current percutaneous pulmonary valve implantation (PPVI) device is first presented: FE analyses were used to understand stent fractures in the patient specific setting and to study a potential solution to this problem. The shortcomings of the present PPVI stent have created a need for the next generation device. The optimisation study performed on this device using FE analyses, together with the first-inman clinical application are described. The last part of this Chapter focuses on transcatheter aortic valve implantation (TAVI) and the innovative use of FE analyses to model patient specific implantation procedures. Computational analyses were used as a tool to assess the feasibility and safety of TAVI in patients who are currently considered unsuitable for this

In the late 1990's, Professor Philipp Bonhoeffer developed a new technique of heart valve replacement that avoided the need for surgery (Bonhoeffer et al., 2000). This was based on the concept that a heart valve sewn inside a stent could be reduced in size, by crimping it onto a balloon catheter, and then introduced through a peripheral vessel to the desired

**1. Introduction** 

benefit from these procedures.

**2. Percutaneous pulmonary valve implantation** 

procedure.

**Percutaneous Heart Valves** 

Giorgia M. Bosi and Andrew M. Taylor *UCL Institute of Cardiovascular Science, London* 

## **Finite Element Analysis to Study Percutaneous Heart Valves**

Silvia Schievano, Claudio Capelli, Daria Cosentino, Giorgia M. Bosi and Andrew M. Taylor *UCL Institute of Cardiovascular Science, London UK* 

#### **1. Introduction**

Percutaneous valve implantation is an innovative, successful alternative to open-heart surgery for the treatment of both pulmonary and aortic heart valve dysfunction (Bonhoeffer et al., 2000; Cribier et al., 2002; Leon et al., 2011; Lurz et al., 2008; McElhinney DB et al., 2010; Rodes-Cabau et al., 2010; Smith et al., 2011; Vahanian et al., 2008). However, this minimallyinvasive procedure still presents limitations related to device design: stent fracture, availability to a limited group of patients with very specific anatomy and conditions, and positioning and anchoring issues (Delgado et al., 2010; Nordmeyer et al., 2007; Schievano et al., 2007a). Computational simulations (Taylor & Figueroa, 2009), together with advanced cardiovascular imaging techniques can be used to help understand these limitations in order to guide the optimisation process for new device designs, to improve the success of percutaneous valve implantation, and ultimately to broaden the range of patients who could benefit from these procedures.

In this Chapter, we review the applications of finite element (FE) analyses to study percutaneous heart valve devices. The current percutaneous pulmonary valve implantation (PPVI) device is first presented: FE analyses were used to understand stent fractures in the patient specific setting and to study a potential solution to this problem. The shortcomings of the present PPVI stent have created a need for the next generation device. The optimisation study performed on this device using FE analyses, together with the first-inman clinical application are described. The last part of this Chapter focuses on transcatheter aortic valve implantation (TAVI) and the innovative use of FE analyses to model patient specific implantation procedures. Computational analyses were used as a tool to assess the feasibility and safety of TAVI in patients who are currently considered unsuitable for this procedure.

#### **2. Percutaneous pulmonary valve implantation**

In the late 1990's, Professor Philipp Bonhoeffer developed a new technique of heart valve replacement that avoided the need for surgery (Bonhoeffer et al., 2000). This was based on the concept that a heart valve sewn inside a stent could be reduced in size, by crimping it onto a balloon catheter, and then introduced through a peripheral vessel to the desired

Finite Element Analysis to Study Percutaneous Heart Valves 169

cylindrical tubes. However, the final shape of the PPVI stent *in situ* is a long way away from

In order to better understand and predict the stent mechanical performance and durability, the implantation site morphology has to be included into *in-vitro* testing. To demonstrate this concept, and to test that computational analysis can indeed predict where stent fractures

Five patients (I to V) who underwent PPVI and experienced fracture between 1 and 6 months after implantation were selected (Cosentino et al., 2011). Biplane, orthogonal, fluoroscopy images (Axiom Artis Flat Detector system, Siemens Medical Systems, Germany) from the actual PPVI procedures of these patients were used to reconstruct the 3D geometry of the stents *in-situ* (Rhinoceros CAD software, McNeel, WA, USA; Schievano et al., 2010b) at the end of balloon inflation, and at early systole and diastole (Fig. 2). From these reconstructions, the displacements of every strut junction of the stent from the end of balloon inflation through systole and diastole were calculated. Circumferential, radial and longitudinal asymmetries were measured for each time step and every patient. The stent expanded into the patients' implantation sites resembled the outline of their arterial walls, resulting in asymmetry in all directions (Fig. 3top). In particular, some of the stent struts were at an early stage of expansion, while others were over-deployed compared to a uniformly deployed stent in a cylinder. The most expanded cells were located in correspondence to the fracture positions as detected from x-rays images in the patients. Furthermore, in all studied patients, the stents were non-circular in cross-section and the

Fig. 2. Superimposition of the stent fluoroscopy reconstructions for one patient at the end of balloon inflation, systole, and diastole compared to the initial crimped configuration (lateral

will occur, we reproduced patient-specific procedures using computational analysis.

terminal rings were more expanded if compared to the central portions.

being uniformly cylindrical.

and top views)

implantation site in the heart (Fig. 1). Inflation of the balloon deployed the valved stent and anchored it within the old dysfunctional valve. Over the last 11 years, this simple technique has shown a marked learning curve with safety and efficacy improvements that have led to CE mark in 2006, Food and Drug Administration (FDA) approval in 2010, and successful, worldwide clinical use of this procedure in the pulmonary position (>2,000 implants to date) and thousands of implants in the aortic position.

Fig. 1. a) Current PPVI device: Melody™, Medtronic, MN USA. Pulmonary angiograms b) pre- and c) post-PPVI in a patient. In this patient significant pulmonary regurgitation (contrast in the anterior right ventricle in b) has been completely abolished

#### **2.1 Current device**

The current PPVI device (Melody™, Medtronic, MN, USA) is constructed with a valve from a bovine jugular vein, sewn into a balloon-expandable, platinum-10%iridium stent (Fig. 1a). The stent is created by 6 wires, formed into a zig-zag shaped pattern, and welded together. Since the platinum welds were prone to fracture, this component of the PPVI was modified during the early clinical experience by introducing a gold braising process to reinforce the crowns. The bovine vein is attached to the stent by sutures around the proximal and distal rings and at each strut intersection. Bovine jugular venous valves are available only up to 22 mm of diameter, thus limiting the use of this minimally-invasive technique to those patients who have a small implantation site. During the procedure in the catheterisation laboratory, the valved stent assembly is hand-crimped to a size of 6 mm onto a custom made delivery system, before being re-expanded inside the patient's implantation site.

#### **2.1.1 Understanding and predicting stent fractures**

During the development phases of the current PPVI device, simple bench and animal experiments were performed as part of routine preclinical testing. These *in-vitro* and *in-vivo* experiments predicted valve degeneration with no stent fracturing. However, in our clinical practice, the opposite occurred – good valve function, ~20% stent fractures (Nordmeyer et al., 2007). These discrepancies were most likely due to the fact that in patients, the *in-vivo* loading conditions could not be correctly reproduced with experimental set-ups, where the boundary conditions are simplified and not representative of the real situation. For example, in the bench experiments for fatigue assessment, PPVI stents were placed in distensible

implantation site in the heart (Fig. 1). Inflation of the balloon deployed the valved stent and anchored it within the old dysfunctional valve. Over the last 11 years, this simple technique has shown a marked learning curve with safety and efficacy improvements that have led to CE mark in 2006, Food and Drug Administration (FDA) approval in 2010, and successful, worldwide clinical use of this procedure in the pulmonary position (>2,000 implants to date)

Fig. 1. a) Current PPVI device: Melody™, Medtronic, MN USA. Pulmonary angiograms b) pre- and c) post-PPVI in a patient. In this patient significant pulmonary regurgitation

The current PPVI device (Melody™, Medtronic, MN, USA) is constructed with a valve from a bovine jugular vein, sewn into a balloon-expandable, platinum-10%iridium stent (Fig. 1a). The stent is created by 6 wires, formed into a zig-zag shaped pattern, and welded together. Since the platinum welds were prone to fracture, this component of the PPVI was modified during the early clinical experience by introducing a gold braising process to reinforce the crowns. The bovine vein is attached to the stent by sutures around the proximal and distal rings and at each strut intersection. Bovine jugular venous valves are available only up to 22 mm of diameter, thus limiting the use of this minimally-invasive technique to those patients who have a small implantation site. During the procedure in the catheterisation laboratory, the valved stent assembly is hand-crimped to a size of 6 mm onto a custom made delivery

During the development phases of the current PPVI device, simple bench and animal experiments were performed as part of routine preclinical testing. These *in-vitro* and *in-vivo* experiments predicted valve degeneration with no stent fracturing. However, in our clinical practice, the opposite occurred – good valve function, ~20% stent fractures (Nordmeyer et al., 2007). These discrepancies were most likely due to the fact that in patients, the *in-vivo* loading conditions could not be correctly reproduced with experimental set-ups, where the boundary conditions are simplified and not representative of the real situation. For example, in the bench experiments for fatigue assessment, PPVI stents were placed in distensible

(contrast in the anterior right ventricle in b) has been completely abolished

system, before being re-expanded inside the patient's implantation site.

**2.1.1 Understanding and predicting stent fractures** 

and thousands of implants in the aortic position.

**2.1 Current device** 

cylindrical tubes. However, the final shape of the PPVI stent *in situ* is a long way away from being uniformly cylindrical.

In order to better understand and predict the stent mechanical performance and durability, the implantation site morphology has to be included into *in-vitro* testing. To demonstrate this concept, and to test that computational analysis can indeed predict where stent fractures will occur, we reproduced patient-specific procedures using computational analysis.

Five patients (I to V) who underwent PPVI and experienced fracture between 1 and 6 months after implantation were selected (Cosentino et al., 2011). Biplane, orthogonal, fluoroscopy images (Axiom Artis Flat Detector system, Siemens Medical Systems, Germany) from the actual PPVI procedures of these patients were used to reconstruct the 3D geometry of the stents *in-situ* (Rhinoceros CAD software, McNeel, WA, USA; Schievano et al., 2010b) at the end of balloon inflation, and at early systole and diastole (Fig. 2). From these reconstructions, the displacements of every strut junction of the stent from the end of balloon inflation through systole and diastole were calculated. Circumferential, radial and longitudinal asymmetries were measured for each time step and every patient. The stent expanded into the patients' implantation sites resembled the outline of their arterial walls, resulting in asymmetry in all directions (Fig. 3top). In particular, some of the stent struts were at an early stage of expansion, while others were over-deployed compared to a uniformly deployed stent in a cylinder. The most expanded cells were located in correspondence to the fracture positions as detected from x-rays images in the patients. Furthermore, in all studied patients, the stents were non-circular in cross-section and the terminal rings were more expanded if compared to the central portions.

Fig. 2. Superimposition of the stent fluoroscopy reconstructions for one patient at the end of balloon inflation, systole, and diastole compared to the initial crimped configuration (lateral and top views)

Finite Element Analysis to Study Percutaneous Heart Valves 171

Patient-specific stent deployments were replicated in Abaqus/Standard (Simulia, RI, USA) using nodal displacement boundary conditions (Fig. 3bottom). These displacements were those previously calculated from fluoroscopy reconstructions and were applied to the central node of each stent strut junction. Three displacement steps were performed to account for the full loading history of the stent and potential residual stresses: the first step resulted in the stent deployment from its initial crimped status to the end of balloon inflation; the second and the third steps replicated a cardiac cycle from systole to diastole. The elements surrounding the nodes of displacement application were subtracted from the model in the analysis of stress outcomes because they resulted distorted due to the type of displacement condition adopted. This was considered acceptable as fractures at the strut junctions have not been reported for the current stent after golden reinforcements were

Fig. 4. Comparison of the stress distribution and Goodman diagrams between the stent deployed in a cylindrical configuration, as performed during conventional preclinical testing, and the stent deployed according to individual *in-situ* geometry from 1 of the studied patients. Goodman diagrams are a graphical representation of fatigue analysis (σm and σa = mean and alternating stresses, while Sult and Se = material ultimate and fatigue

introduced.

endurance strengths)

Fig. 3. Stent fluoroscopy reconstructions for the analysed patients at diastole (top panel) and corresponding FE deployed configurations (bottom panel)

A FE model of the crimped stent in the catheter was created, with a structured hexahedral mesh of 119,360 elements to model the platinum-iridium wires. To reproduce the golden coverings, an additional set of elements was modelled around the junctions and a structured hexahedral mesh was generated using 36,320 elements. Stent geometrical and material properties were provided by the manufacturer (Table 1; Schievano et al., 2007c).


Table 1. Stent geometrical and material properties

Fig. 3. Stent fluoroscopy reconstructions for the analysed patients at diastole (top panel) and

A FE model of the crimped stent in the catheter was created, with a structured hexahedral mesh of 119,360 elements to model the platinum-iridium wires. To reproduce the golden coverings, an additional set of elements was modelled around the junctions and a structured hexahedral mesh was generated using 36,320 elements. Stent geometrical and material

properties were provided by the manufacturer (Table 1; Schievano et al., 2007c).

Wire diameter 0.33 mm Crimped configuration internal diameter 4.00 mm Crimped configuration overall length 34.32 mm Central zig-zag segment length 5.78 mm Terminal zig-zag segment length 5.62 mm

Young modulus 224 GPa Poisson ratio 0.37 Yield stress 285 MPa Ultimate strength 875 MPa Fatigue endurance strength 263 MPa

Young modulus 80 GPa Poisson ratio 0.42

corresponding FE deployed configurations (bottom panel)

Table 1. Stent geometrical and material properties

PPVI stent *Geometry* 

*Gold* 

*Platinum-10% Iridium* 

Patient-specific stent deployments were replicated in Abaqus/Standard (Simulia, RI, USA) using nodal displacement boundary conditions (Fig. 3bottom). These displacements were those previously calculated from fluoroscopy reconstructions and were applied to the central node of each stent strut junction. Three displacement steps were performed to account for the full loading history of the stent and potential residual stresses: the first step resulted in the stent deployment from its initial crimped status to the end of balloon inflation; the second and the third steps replicated a cardiac cycle from systole to diastole. The elements surrounding the nodes of displacement application were subtracted from the model in the analysis of stress outcomes because they resulted distorted due to the type of displacement condition adopted. This was considered acceptable as fractures at the strut junctions have not been reported for the current stent after golden reinforcements were introduced.

Fig. 4. Comparison of the stress distribution and Goodman diagrams between the stent deployed in a cylindrical configuration, as performed during conventional preclinical testing, and the stent deployed according to individual *in-situ* geometry from 1 of the studied patients. Goodman diagrams are a graphical representation of fatigue analysis (σm and σa = mean and alternating stresses, while Sult and Se = material ultimate and fatigue endurance strengths)

Finite Element Analysis to Study Percutaneous Heart Valves 173

occurred in the patients (Fig. 5). The Sines criterion predicted fractures in every case, with the most stressed regions in 3 cases close to the strut intersections between the first and the second ring from the proximal end; in one case it was at the lowest terminal crown and in

Reproducing patient-specific FE analysis with more realistic loading conditions can provide more accurate information regarding the stent mechanical performance and prediction of fatigue life compared to the conventional bench methodologies/FE analyses/ of free/cylindrically constrained expansion. Indeed, this computational analysis predicted failure and the locations of fractures were similar to the sites where the patients ultimately

FE analysis can also give insight into improved clinical management. This is demonstrated by a FE analysis of stent mechanical performance for various combinations of stent designs. Inserting a separate stent into the pulmonary artery prior to the PPVI device (stent-in-stent technique, Nordmeyer et al., 2008) may reduce valved stent fractures. An optimised combination of different stent mechanical properties can help increase the strength of the device structure while at the same time reduce the stresses. This was computationally tested by expanding 2 PPVI stents 1 inside the other (Schievano et al, 2007c). The mechanical performance of the coupled device was compared with that of a single valved stent, expanded and cyclic loaded at the same conditions. The stresses in the outer stent of the coupled device were similar to those of the single valved stent. However, the stresses in the coupled device inner stent, which holds the valve, were lower when compared to the stresses in the single

the last patient it was detected between the second and the third crown.

**2.1.2 Stent-in-stent as a potential solution to stent fractures** 

valved stent (Fig. 6), thus decreasing the risk of fracture for the valved stent.

Fig. 6. Stress distributions in the single valved stent and in the inner valved stent when 2

devices are coupled together (stent-in-stent)

had stent damage.

Stresses in the stents after deployment in patients' configurations were higher if compared to the same stent uniformly expanded in a cylindrical geometry as done during conventional preclinical testing, and, therefore, the risk of reaching the endurance limit of the material was higher (Fig. 4). The highest stresses occurred close to the strut junctions, which were the most highly bent portions of the device. The peak σVM was reached during diastole in every patient, and its values ranged between 516.1 and 612.8 MPa.

A fatigue analysis was performed by applying the Goodman method (Beden et al., 2009; Marrey et al., 2006) and the Sines criterion (Sines & Ohgi, 1981). The first uses a graphical approach to relate alternating stress (σa) and mean stress (σm) during the cardiac cycle with the material strength limits (Fig. 4), where σa and σm are calculated as follows:

2 *sys dia m* and 2 *sys dia a* with σsys and σdia equal to the maximum principal

stresses at the end of the systolic and diastolic phases respectively.

The second is a multi-axial fatigue criterion that uses the equivalent Von Mises stress as control parameter. To evaluate the fatigue resistance with the Sines criterion, the equivalent Sines stress, for the comparison with the material fatigue endurance strength Se, was calculated as in the first member of the following disequation: 2 , 3 3 *<sup>e</sup> Hm e <sup>a</sup> ult <sup>S</sup> J S <sup>S</sup>* 

where <sup>2</sup> *<sup>a</sup> <sup>J</sup>* and σH,m are the amplitude of the mean square root of the second deviatoric stress invariant and the hydrostation pressure, respectively.

During the cyclic loading condition, the stent in the patients worked at high σm and σa, if compared to a uniformly deployed stent, thus indicating a high number of areas at risk of fatigue failure as shown by the Goodman distributions (Fig. 4). The portions at highest potential for fracture were non-uniformly distributed amongst the different studied cases, with highest values in the areas close to the strut junctions, where indeed such fractures

Fig. 5. X-ray image of the stent *in-vivo* in 1 of the analysed patients at 3 months follow-up compared to the Sines stress map in the corresponding patient FE simulation with areas at highest risk for fracture highlighted in red

Stresses in the stents after deployment in patients' configurations were higher if compared to the same stent uniformly expanded in a cylindrical geometry as done during conventional preclinical testing, and, therefore, the risk of reaching the endurance limit of the material was higher (Fig. 4). The highest stresses occurred close to the strut junctions, which were the most highly bent portions of the device. The peak σVM was reached during

A fatigue analysis was performed by applying the Goodman method (Beden et al., 2009; Marrey et al., 2006) and the Sines criterion (Sines & Ohgi, 1981). The first uses a graphical approach to relate alternating stress (σa) and mean stress (σm) during the cardiac cycle with the material strength limits (Fig. 4), where σa and σm are calculated as follows:

The second is a multi-axial fatigue criterion that uses the equivalent Von Mises stress as control parameter. To evaluate the fatigue resistance with the Sines criterion, the equivalent Sines stress, for the comparison with the material fatigue endurance strength Se, was

calculated as in the first member of the following disequation: 2 , 3 3 *<sup>e</sup> Hm e <sup>a</sup> ult*

where <sup>2</sup> *<sup>a</sup> <sup>J</sup>* and σH,m are the amplitude of the mean square root of the second deviatoric

During the cyclic loading condition, the stent in the patients worked at high σm and σa, if compared to a uniformly deployed stent, thus indicating a high number of areas at risk of fatigue failure as shown by the Goodman distributions (Fig. 4). The portions at highest potential for fracture were non-uniformly distributed amongst the different studied cases, with highest values in the areas close to the strut junctions, where indeed such fractures

Fig. 5. X-ray image of the stent *in-vivo* in 1 of the analysed patients at 3 months follow-up compared to the Sines stress map in the corresponding patient FE simulation with areas at

with σsys and σdia equal to the maximum principal

*<sup>S</sup> J S <sup>S</sup>* 

diastole in every patient, and its values ranged between 516.1 and 612.8 MPa.

2 *sys dia*

stresses at the end of the systolic and diastolic phases respectively.

 

*a*

highest risk for fracture highlighted in red

stress invariant and the hydrostation pressure, respectively.

2 *sys dia*

 

and

*m*

occurred in the patients (Fig. 5). The Sines criterion predicted fractures in every case, with the most stressed regions in 3 cases close to the strut intersections between the first and the second ring from the proximal end; in one case it was at the lowest terminal crown and in the last patient it was detected between the second and the third crown.

Reproducing patient-specific FE analysis with more realistic loading conditions can provide more accurate information regarding the stent mechanical performance and prediction of fatigue life compared to the conventional bench methodologies/FE analyses/ of free/cylindrically constrained expansion. Indeed, this computational analysis predicted failure and the locations of fractures were similar to the sites where the patients ultimately had stent damage.

#### **2.1.2 Stent-in-stent as a potential solution to stent fractures**

FE analysis can also give insight into improved clinical management. This is demonstrated by a FE analysis of stent mechanical performance for various combinations of stent designs. Inserting a separate stent into the pulmonary artery prior to the PPVI device (stent-in-stent technique, Nordmeyer et al., 2008) may reduce valved stent fractures. An optimised combination of different stent mechanical properties can help increase the strength of the device structure while at the same time reduce the stresses. This was computationally tested by expanding 2 PPVI stents 1 inside the other (Schievano et al, 2007c). The mechanical performance of the coupled device was compared with that of a single valved stent, expanded and cyclic loaded at the same conditions. The stresses in the outer stent of the coupled device were similar to those of the single valved stent. However, the stresses in the coupled device inner stent, which holds the valve, were lower when compared to the stresses in the single valved stent (Fig. 6), thus decreasing the risk of fracture for the valved stent.

Fig. 6. Stress distributions in the single valved stent and in the inner valved stent when 2 devices are coupled together (stent-in-stent)

Finite Element Analysis to Study Percutaneous Heart Valves 175

as biocompatibility, fatigue resistance, and magnetic resonance (MR) compatibility, with the peculiar mechanical behaviour to undergo large completely recoverable deformations (Petrini et al., 2005). The valve is made of porcine pericardium and is sutured in the central portion of the stent-graft. Conventional animal testing and bench testing had been undertaken for this device and demonstrated a good performance in the animal model (Bonhoeffer et al., 2008). This stent-graft design should guarantee a greater adaptability of the device to the wide range of possible implantation site morphologies, with long-term

During the final stages of the preclinical testing of the new device, a patient presented to our Institution requiring pulmonary valve replacement (Schievano et al., 2010a). This patient (42-year-old man with congenital heart disease) had previously undergone 4 open-heart operations and 2 additional thoracic procedures, and remained highly symptomatic with severe pulmonary insufficiency. A further cardiothoracic surgery was considered too high risk. In addition, the pulmonary artery was too dilated for the current PPVI device. Therefore, the patient was considered for implantation of the new device. An integrated strategy to pre-clinical testing, using patient imaging data, computer modelling and biomedical engineering was developed to influence the final device design for implantation. 4D cardiovascular computed tomography (CT) was performed to acquire 3D volumes of the implantation site over 10 frames of the cardiac cycle (CT-SOMATOM Definition, Siemens Medical Systems) according to previously described methodologies (Schievano et al., 2007a), and to measure the 3D deformations in terms of diameter changes at different sections (Fig. 8a; Schievano et al., 2011). Based on the CT implantation site reconstructions (Mimics, Materialise, Belgium), FE models (Fig. 8b) and 3D rapid prototyping (Fig. 8c) models were created (Schievano et al., 2007b; Schievano et al., 2010b). Multiple device shapes and sizes with varying wire stiffness and configurations were tested in the rapid prototyping models and using FE analysis to optimise the anatomical results in the specific patient: the FE analysis identified definitive areas of contact between the computer simulated stent-graft struts of the customized device and implantation site, predicting likely stability and safe anchoring in-vivo. The rapid prototyping models enabled simulation of the clinical implantation procedure and helped the implanters decide the approach for optimal device

The final device (40 mm diameter in the distal and proximal ring, 22 mm diameter in the central portion holding the valve) underwent acute and chronic animal tests and bench testing. Based on these results, the UK Medicines and Healthcare products Regulatory Agency (MHRA), and the local ethical and industrial committees granted approval for the use of this device on humanitarian grounds. The patient gave informed consent for the

PPVI was successfully carried out in this patient with the new device in January 2009. During the catheterisation procedure, angiographic studies and balloon sizing of the pulmonary trunk were performed and confirmed that the CT and model dimensions were a true representation of the patient's anatomy. The delivery strategy developed from the preprocedural trial implantation in the rapid prototyping models was followed and proved safe

procedure and for the anonymous use of his data and images for research.

fatigue behaviour that dramatically outperforms conventional metals.

**2.2.1 First-in-man application** 

delivery.

The implantation of a previous device before the valved one acts functionally to bolster the vessel and reduce the stresses on the stent. This information, in combination with the computational modelling described above, suggests that pre-stenting may ensure the integrity of the valved device, thus enhancing the success of the percutaneous procedure. Indeed this is the case when we look at patients who undergo pre-stenting, where the risk of developing a stent fracture is reduced (Nordmeyer et al., 2011). However, this solution is still limited to those patients with suitable implantation sites and the current device does not fit all the sizes of patients requiring pulmonary valve treatment. New devices have to be developed to offer this minimally invasive procedure to the entire patient population.

#### **2.2 Next generation device**

Despite the success of the PPVI device, <15% of patients requiring pulmonary valve replacement can be treated with the current PPVI device, with the remaining 85% requiring open-heart surgery (Schievano et al., 2007a). The majority of these patients are those with dilated, dynamic pulmonary arteries in whom the current percutaneous device is too small. Importantly, for this morphological problem, animal testing is of very limited use, as there are no models that encompass the wide variations of anatomy seen in these patients with congenital heart disease. Hence development of a new device to deal with the clinical problem and its translation into man is difficult using the conventional pathway of bench followed by animal testing.

Over the last 5 years, a new PPVI device for implantation into the dilated pulmonary artery has been developed in collaboration with Medtronic Cardiovascular. The device is made from self-expandable nitinol zig-zag rings, held together by a polyester graft in an hourglass shape (Fig. 7). The extremities of the stent, with larger diameters, would ensure the anchoring of the device against the pulmonary artery, while the central rings, with smaller diameter, would act as supporting structures for the valve. Nitinol is a shape memory alloy regularly used in bioengineering applications because it combines important qualities such

Fig. 7. New PPVI device and dimensions

as biocompatibility, fatigue resistance, and magnetic resonance (MR) compatibility, with the peculiar mechanical behaviour to undergo large completely recoverable deformations (Petrini et al., 2005). The valve is made of porcine pericardium and is sutured in the central portion of the stent-graft. Conventional animal testing and bench testing had been undertaken for this device and demonstrated a good performance in the animal model (Bonhoeffer et al., 2008). This stent-graft design should guarantee a greater adaptability of the device to the wide range of possible implantation site morphologies, with long-term fatigue behaviour that dramatically outperforms conventional metals.

#### **2.2.1 First-in-man application**

174 Finite Element Analysis – From Biomedical Applications to Industrial Developments

The implantation of a previous device before the valved one acts functionally to bolster the vessel and reduce the stresses on the stent. This information, in combination with the computational modelling described above, suggests that pre-stenting may ensure the integrity of the valved device, thus enhancing the success of the percutaneous procedure. Indeed this is the case when we look at patients who undergo pre-stenting, where the risk of developing a stent fracture is reduced (Nordmeyer et al., 2011). However, this solution is still limited to those patients with suitable implantation sites and the current device does not fit all the sizes of patients requiring pulmonary valve treatment. New devices have to be developed to offer this minimally invasive procedure to the entire patient population.

Despite the success of the PPVI device, <15% of patients requiring pulmonary valve replacement can be treated with the current PPVI device, with the remaining 85% requiring open-heart surgery (Schievano et al., 2007a). The majority of these patients are those with dilated, dynamic pulmonary arteries in whom the current percutaneous device is too small. Importantly, for this morphological problem, animal testing is of very limited use, as there are no models that encompass the wide variations of anatomy seen in these patients with congenital heart disease. Hence development of a new device to deal with the clinical problem and its translation into man is difficult using the conventional pathway of bench

Over the last 5 years, a new PPVI device for implantation into the dilated pulmonary artery has been developed in collaboration with Medtronic Cardiovascular. The device is made from self-expandable nitinol zig-zag rings, held together by a polyester graft in an hourglass shape (Fig. 7). The extremities of the stent, with larger diameters, would ensure the anchoring of the device against the pulmonary artery, while the central rings, with smaller diameter, would act as supporting structures for the valve. Nitinol is a shape memory alloy regularly used in bioengineering applications because it combines important qualities such

PROXIMAL END DISTAL END

**2.2 Next generation device** 

followed by animal testing.

Fig. 7. New PPVI device and dimensions

During the final stages of the preclinical testing of the new device, a patient presented to our Institution requiring pulmonary valve replacement (Schievano et al., 2010a). This patient (42-year-old man with congenital heart disease) had previously undergone 4 open-heart operations and 2 additional thoracic procedures, and remained highly symptomatic with severe pulmonary insufficiency. A further cardiothoracic surgery was considered too high risk. In addition, the pulmonary artery was too dilated for the current PPVI device. Therefore, the patient was considered for implantation of the new device. An integrated strategy to pre-clinical testing, using patient imaging data, computer modelling and biomedical engineering was developed to influence the final device design for implantation.

4D cardiovascular computed tomography (CT) was performed to acquire 3D volumes of the implantation site over 10 frames of the cardiac cycle (CT-SOMATOM Definition, Siemens Medical Systems) according to previously described methodologies (Schievano et al., 2007a), and to measure the 3D deformations in terms of diameter changes at different sections (Fig. 8a; Schievano et al., 2011). Based on the CT implantation site reconstructions (Mimics, Materialise, Belgium), FE models (Fig. 8b) and 3D rapid prototyping (Fig. 8c) models were created (Schievano et al., 2007b; Schievano et al., 2010b). Multiple device shapes and sizes with varying wire stiffness and configurations were tested in the rapid prototyping models and using FE analysis to optimise the anatomical results in the specific patient: the FE analysis identified definitive areas of contact between the computer simulated stent-graft struts of the customized device and implantation site, predicting likely stability and safe anchoring in-vivo. The rapid prototyping models enabled simulation of the clinical implantation procedure and helped the implanters decide the approach for optimal device delivery.

The final device (40 mm diameter in the distal and proximal ring, 22 mm diameter in the central portion holding the valve) underwent acute and chronic animal tests and bench testing. Based on these results, the UK Medicines and Healthcare products Regulatory Agency (MHRA), and the local ethical and industrial committees granted approval for the use of this device on humanitarian grounds. The patient gave informed consent for the procedure and for the anonymous use of his data and images for research.

PPVI was successfully carried out in this patient with the new device in January 2009. During the catheterisation procedure, angiographic studies and balloon sizing of the pulmonary trunk were performed and confirmed that the CT and model dimensions were a true representation of the patient's anatomy. The delivery strategy developed from the preprocedural trial implantation in the rapid prototyping models was followed and proved safe

Finite Element Analysis to Study Percutaneous Heart Valves 177

technology into early clinical practice, this approach would not be necessary, or sustainable, for each patient in routine clinical practice. Ultimately, the aim for this new PPVI technology would be to have a small number of 'off-the-shelf' devices with varying sizes and shapes, which would be suitable for the vast majority of patients. In order to optimise the number of devices necessary to cover the whole range of patients' morphologies, we used FE analysis

FE modelling is a powerful tool to optimise device design without the need for many prototypes to be created and tested. In pulmonary valve dysfunction, each patient anatomy is completely individual in terms of size, shape and dynamics. FE can help select the most appropriate prosthesis for any individual patient taking into account their specific anatomy, thus enhancing the safety and success of the procedure. Furthermore, FE analysis can help predict how many devices may be needed to cover the whole range of patient morphologies. Three different potential designs for the new stent-graft were considered, with equivalent central ring diameters (22 mm), but different proximal and distal strut dimensions (Fig. 10; Capelli et al, 2010a): the first stent-graft (SG1) resembled the device that had already been successfully tested in animals (Bonhoeffer et al, 2008). The second stent-graft (SG2) was symmetrical, similar to the device implanted into the patient described in the previous paragraph (Schievano et al, 2010a). The third stent-graft (SG3) was similar to SG2, but with larger proximal and distal diameters. 1D beam elements were chosen to mesh the stent wires (696, 696 and 912 elements for SG1, SG2 and SG3, respectively). Surfaces were created in between the struts to model the polyester fabric, which was meshed using membrane elements that offer strength in the plane of the element, but have no bending stiffness (3850, 3408 and 3909 elements for SG1, SG2 and SG3, respectively). A tight, rigid contact was assumed to simulate the suture between the stent and the graft. The shape memory alloy model implemented in Abaqus code was used to describe the nitinol behaviour of the stent wires. A hyperelastic, isotropic constitutive model based on a reduced polynomial strain

Fig. 10. Models of the 3 stent-grafts SG1, SG2 and SG3 designed and tested using FE analysis

45 mm

45 mm

**SG2 SG3**

40 mm

taking into account patient specific anatomies (Capelli et al, 2010a).

**2.2.2 Optimisation of the next generation device** 

33 mm

**SG1**

40 mm 40 mm

Fig. 8. a) 3D volume reconstruction of the patient's implantation site from 4D CT and diameter change measurements over the cardiac cycle measured in the 8 selected planes (C-L). Examples of b) FE model, and c) plastic rapid prototyping model (guidewire in place) of the patient anatomy with the new PPVI device "implanted" to test different positions, anchoring, and delivery approaches

and successful (Fig. 9a). The patient was symptomatically improved following the procedure. A post-implantation 4D CT confirmed that the device had the position, shape and safe anchoring as predicted by the FE models (Fig. 9b). These post implantation CT images were used to reconstruct the stent geometry *in-situ* and to assess the 3D displacements of the device rings over the cardiac cycle. This information was inputted in a FE analysis as explained above to predict the likelihood of stent fracture. The patient remains well 3 years following the procedure, with no fractures of the stent struts detected to date, as predicted by the FE study.

Fig. 9. Lateral view of a) x-ray fluoroscopy, and b) 3D volume CT reconstruction of the new PPVI device, 2 days after implantation in the patient

Whilst such a labour intensive method, which resulted in modifications in the device design prior to this first human case, was essential to enable us to safely transfer this new

Fig. 8. a) 3D volume reconstruction of the patient's implantation site from 4D CT and diameter change measurements over the cardiac cycle measured in the 8 selected planes (C-L). Examples of b) FE model, and c) plastic rapid prototyping model (guidewire in place) of the patient anatomy with the new PPVI device "implanted" to test different positions,

a) b)

and successful (Fig. 9a). The patient was symptomatically improved following the procedure. A post-implantation 4D CT confirmed that the device had the position, shape and safe anchoring as predicted by the FE models (Fig. 9b). These post implantation CT images were used to reconstruct the stent geometry *in-situ* and to assess the 3D displacements of the device rings over the cardiac cycle. This information was inputted in a FE analysis as explained above to predict the likelihood of stent fracture. The patient remains well 3 years following the procedure, with no fractures of the stent struts detected

Fig. 9. Lateral view of a) x-ray fluoroscopy, and b) 3D volume CT reconstruction of the new

Whilst such a labour intensive method, which resulted in modifications in the device design prior to this first human case, was essential to enable us to safely transfer this new

anchoring, and delivery approaches

to date, as predicted by the FE study.

PPVI device, 2 days after implantation in the patient

technology into early clinical practice, this approach would not be necessary, or sustainable, for each patient in routine clinical practice. Ultimately, the aim for this new PPVI technology would be to have a small number of 'off-the-shelf' devices with varying sizes and shapes, which would be suitable for the vast majority of patients. In order to optimise the number of devices necessary to cover the whole range of patients' morphologies, we used FE analysis taking into account patient specific anatomies (Capelli et al, 2010a).

#### **2.2.2 Optimisation of the next generation device**

FE modelling is a powerful tool to optimise device design without the need for many prototypes to be created and tested. In pulmonary valve dysfunction, each patient anatomy is completely individual in terms of size, shape and dynamics. FE can help select the most appropriate prosthesis for any individual patient taking into account their specific anatomy, thus enhancing the safety and success of the procedure. Furthermore, FE analysis can help predict how many devices may be needed to cover the whole range of patient morphologies.

Three different potential designs for the new stent-graft were considered, with equivalent central ring diameters (22 mm), but different proximal and distal strut dimensions (Fig. 10; Capelli et al, 2010a): the first stent-graft (SG1) resembled the device that had already been successfully tested in animals (Bonhoeffer et al, 2008). The second stent-graft (SG2) was symmetrical, similar to the device implanted into the patient described in the previous paragraph (Schievano et al, 2010a). The third stent-graft (SG3) was similar to SG2, but with larger proximal and distal diameters. 1D beam elements were chosen to mesh the stent wires (696, 696 and 912 elements for SG1, SG2 and SG3, respectively). Surfaces were created in between the struts to model the polyester fabric, which was meshed using membrane elements that offer strength in the plane of the element, but have no bending stiffness (3850, 3408 and 3909 elements for SG1, SG2 and SG3, respectively). A tight, rigid contact was assumed to simulate the suture between the stent and the graft. The shape memory alloy model implemented in Abaqus code was used to describe the nitinol behaviour of the stent wires. A hyperelastic, isotropic constitutive model based on a reduced polynomial strain

Fig. 10. Models of the 3 stent-grafts SG1, SG2 and SG3 designed and tested using FE analysis

Finite Element Analysis to Study Percutaneous Heart Valves 179

According to these criteria, successful implantation was achieved in 37% of the patients with SG1. 42% of the patients would be suitable for the SG2 device and 63% for the SG3 device (Fig. 11). Therefore, 37% of those patients who are currently still treated with surgery would potentially be suitable for PPVI with a new device. Furthermore, if the dimensions of this new device are theoretically increased at the distal end (SG2, as done for the first-in-man case) or both proximal and distal ends (SG3), the number of percutaneous procedures would increase by a further 5% and 36%, respectively. Importantly, these dimensions would be difficult to test in animals because of lack of relevant sizes in these settings. Although animal testing remains important, FE modelling could be integrated into preclinical testing to

With the introduction in clinical practice of the new device in 3 sizes, the total number of patients requiring pulmonary valve replacement who could benefit from a percutaneous approach (current device + 3 sizes of the new device) would be approximately 70%. This would potentially have a big impact on the cost benefit for healthcare, by reducing hospital stay and improving the speed at which patients can get back to normal daily activities.

In the past decade, TAVI has been shown to be a feasible and effective option for treatment of patients with symptomatic severe aortic stenosis and high operative risks (Leon et al., 2011; Rodes-Cabau et al., 2010; Smith et al., 2011; Vahanian et al., 2008; Zajarias & Cribier, 2009). Since the first-in-man experience in 2002 (Cribier et al., 2002), several advances in TAVI techniques have led to improved success rates, with acceptable procedure-related complication rates (Delgado et al., 2010). To date, 2 different devices have received CE mark approval – the balloon-expandable Edwards-Sapien® XT Valve (Edwards Lifesciences, CA, USA) and the self-expandable CoreValveReValving System® (Medtronic) – with many other devices emerging into the market (Fig. 12). The encouraging mid- and long-term results of

Fig. 12. TAVI Edwards-Sapien® Valve and the self-expandable Medtronic CoreValve

(http://mail.c2i2.org/web10-06/transcatheter\_aortic\_valve\_implantation.asp)

predict how such devices behave when implanted into the human situation.

**3. Transcatheter aortic valve implantation** 

ReValving System®

energy density function (C10 = 0.38, C20 = 4.36, C30 = 80.56, C40= -134.72, C50 = 86.24, C60= -19.74) was used for the fabric graft material. The material FE models were validated using experimental tensile tests carried out for the nitinol wires and fabric samples. The valve was neglected in the FE analyses.

Pre-operative 3D MR data (1.5 T Avanto, Siemens Medical Systems) from 62 patients who were morphologically or dimensionally unsuitable for the current Melody™ device were used to reconstruct rigid FE models of the implantation sites – rigid 3D shell elements with number of elements varying between 7,172 and 13,104 according to the complexity of the patient implantation site geometry (Capelli et al, 2010a).

The 3 stent-grafts' FE models were placed inside each patient's outflow tract model, as close as possible to the bifurcation, without obstructing the pulmonary arteries. The implantation of the devices was carried out by crimping the stent-grafts down to 7 mm diameter (catheter dimensions) and then releasing them inside the patients' outflow tract models (Abaqus/Explicit). A general contact algorithm was defined to allow interaction between the devices and the arterial wall. The stent-grafts adapted their shape to the implantation site of each specific patient (Fig. 11). The diameters after deployment were quantified in the proximal, central and distal sections of the stents to judge the safe anchoring of the device inside the artery, which was considered optimal if the proximal and distal diameters measured less than 80% of the original diameters, according to manufacturer's specifications. Furthermore, the central portion of the device should be >18 mm so that the valve sewn inside can be fully deployed.

Fig. 11. Percentage of suitable and not suitable patients for SG1, SG2, and SG3 and examples of patients in which device SG2 was virtually implanted. Unsuitable patients are subdivided according to the regions of the stent that did not respect the criteria of safe implantation

energy density function (C10 = 0.38, C20 = 4.36, C30 = 80.56, C40= -134.72, C50 = 86.24, C60= -19.74) was used for the fabric graft material. The material FE models were validated using experimental tensile tests carried out for the nitinol wires and fabric samples. The valve was

Pre-operative 3D MR data (1.5 T Avanto, Siemens Medical Systems) from 62 patients who were morphologically or dimensionally unsuitable for the current Melody™ device were used to reconstruct rigid FE models of the implantation sites – rigid 3D shell elements with number of elements varying between 7,172 and 13,104 according to the complexity of the

The 3 stent-grafts' FE models were placed inside each patient's outflow tract model, as close as possible to the bifurcation, without obstructing the pulmonary arteries. The implantation of the devices was carried out by crimping the stent-grafts down to 7 mm diameter (catheter dimensions) and then releasing them inside the patients' outflow tract models (Abaqus/Explicit). A general contact algorithm was defined to allow interaction between the devices and the arterial wall. The stent-grafts adapted their shape to the implantation site of each specific patient (Fig. 11). The diameters after deployment were quantified in the proximal, central and distal sections of the stents to judge the safe anchoring of the device inside the artery, which was considered optimal if the proximal and distal diameters measured less than 80% of the original diameters, according to manufacturer's specifications. Furthermore, the central portion of the device should be >18 mm so that the

Fig. 11. Percentage of suitable and not suitable patients for SG1, SG2, and SG3 and examples of patients in which device SG2 was virtually implanted. Unsuitable patients are subdivided according to the regions of the stent that did not respect the criteria of safe implantation

Suitable NO Proximal NO Central NO Distal

SG1 SG2 SG3

neglected in the FE analyses.

patient implantation site geometry (Capelli et al, 2010a).

valve sewn inside can be fully deployed.

0

10

20

30

40

50

60

70

According to these criteria, successful implantation was achieved in 37% of the patients with SG1. 42% of the patients would be suitable for the SG2 device and 63% for the SG3 device (Fig. 11). Therefore, 37% of those patients who are currently still treated with surgery would potentially be suitable for PPVI with a new device. Furthermore, if the dimensions of this new device are theoretically increased at the distal end (SG2, as done for the first-in-man case) or both proximal and distal ends (SG3), the number of percutaneous procedures would increase by a further 5% and 36%, respectively. Importantly, these dimensions would be difficult to test in animals because of lack of relevant sizes in these settings. Although animal testing remains important, FE modelling could be integrated into preclinical testing to predict how such devices behave when implanted into the human situation.

With the introduction in clinical practice of the new device in 3 sizes, the total number of patients requiring pulmonary valve replacement who could benefit from a percutaneous approach (current device + 3 sizes of the new device) would be approximately 70%. This would potentially have a big impact on the cost benefit for healthcare, by reducing hospital stay and improving the speed at which patients can get back to normal daily activities.

#### **3. Transcatheter aortic valve implantation**

In the past decade, TAVI has been shown to be a feasible and effective option for treatment of patients with symptomatic severe aortic stenosis and high operative risks (Leon et al., 2011; Rodes-Cabau et al., 2010; Smith et al., 2011; Vahanian et al., 2008; Zajarias & Cribier, 2009). Since the first-in-man experience in 2002 (Cribier et al., 2002), several advances in TAVI techniques have led to improved success rates, with acceptable procedure-related complication rates (Delgado et al., 2010). To date, 2 different devices have received CE mark approval – the balloon-expandable Edwards-Sapien® XT Valve (Edwards Lifesciences, CA, USA) and the self-expandable CoreValveReValving System® (Medtronic) – with many other devices emerging into the market (Fig. 12). The encouraging mid- and long-term results of

Fig. 12. TAVI Edwards-Sapien® Valve and the self-expandable Medtronic CoreValve ReValving System®

Finite Element Analysis to Study Percutaneous Heart Valves 181

models of the selected patients' implantation sites (Fig. 13). The aortic roots were assumed to be 2 mm thick, with density equal to 1,120 kg/m3 (Conti et al., 2010) for all models and meshed with 3D triangular shell general-purpose elements (Table 2). To describe the mechanical behaviour of the aortic roots, Mooney-Rivlin hyperelastic behaviour was adopted incorporating experimental stress-strain data for the ascending aorta (Okamoto et al., 2002) and taking into account the pre-stretching of the aortic root due to the aortic

Fig. 13. CT image reconstruction of the selected patients' aortic wall with previously implanted bioprosthetic valves. FE models of the deployment balloon and TAVI stent are

**Part Elements** 

 A 6,875 B 8,675 C 11,325 D 8,347

 Perimount Magna 44,048 + 29,021 Soprano 51,372 + 28,667 Perimount 44,048 + 29,021 Epic 51,372 + 28,667

 Sapien stent 192,920 Balloon 8,160

Table 2. Number of mesh elements for the different parts involved in the FE simulations

The metal frames of the 4 bioprosthetic valves were reconstructed from the CT images to identify their position inside the patients' outflow tracts. The bioprosthetic valve geometries were re-drawn using CAD software (Rhinoceros) to recreate a complete model of the corresponding commercial device used in the patients, and then placed in the same position as that identified from CT images. Connector elements were used to link the bioprosthetic

pressure during the cardiac circle.

placed inside the implantation site models

*Patient-specific model* 

*TAVI device* 

*Bioprosthesis (stent + leaflets)* 

this technique, together with increased patient comfort, shortened intensive care and hospital stay, and the avoidance of cardiopulmonary bypass, make this non-surgical technique extremely appealing (Ussia et al., 2009).

Accurate multidisciplinary pre-procedural evaluation of patients who are considered candidates for TAVI is mandatory to plan the most adequate treatment and to minimise peri- and post-procedural complications (Smith et al., 2011; Vahanian et al., 2008). However, in this emerging field, several issues remain a source of debate. Device sizing and positioning are the main challenges, but vascular complications, electrical conduction abnormalities and post-procedural aortic regurgitation still remain major safety concerns. In addition, according to the current position statement, TAVI is indicated only in patients with severe symptomatic aortic stenosis, and who are considered at high or prohibitive risk for conventional surgery (Ussia et al., 2009, Leon et al., 2011).

Extending TAVI to patients who still undergo conventional surgery poses new challenges, both for clinicians and device manufacturers, but "within 10 years, with further improvement of the devices and procedures, and depending on the long-term results of upcoming controlled trials in a broad population, TAVI may become the treatment of choice in a majority of patients with degenerative aortic stenosis" (Cribier, 2009). Indeed, highly experienced centres have already demonstrated the feasibility of TAVI in failed bioprosthetic heart valves (valve-in-valve procedure) in patients considered at very highrisk or ineligible for surgery (Webb et al., 2010). Previous surgical valve implantations represent a well-defined landmark with rigid boundaries that increase ease of positioning and anchoring, thus making patients with bioprosthetic valves ideal candidates for TAVI (Walther et al., 2011). Conversely, younger patients, with less severe aortic valve stenosis or with valve insufficiency, often present implantation sites with different anatomical and dynamic characteristics that generate procedural and device related hurdles, which means that such patients are currently not suitable for or offered TAVI.

Combining patient-specific imaging data and computational modelling offers a new method to obtain additional, predictive information about responses to cardiovascular device implantation in individual patients (Schoenhagen et al., 2011; Taylor & Figueroa, 2009). FE analyses were performed to explore the feasibility of TAVI using a model of the Edwards-Sapien® device in specific patient morphologies which are currently borderline cases for a percutaneous approach. This method can help in both refining patient selection and characterising device mechanical performance, overall impacting on procedural safety and success in the early introduction of TAVI devices in new patient populations.

#### **3.1 Patients with previously implanted bioprosthetic valves**

Four patients with different stenotic bioprosthetic valves previously implanted (patients A – 23 mm Carpentier-Edwards Perimount Magna valve, Edwards Lifesciences; B – 23 mm Soprano™ valve, Sorin Biomedica Cardio, Italy; C – 25 mm Carpentier-Edwards Perimount valve, Edwards Lifesciences; D – 25 mm Epic™ valve, St Jude Medical, MN, USA) and who were referred for surgical replacement of their failing bioprosthetic valve were analysed (Bosi et al., 2010; Migliavacca et al., 2011). Data about the anatomy of the aortic root, coronary arteries, AV leaflets and bioprostheses were acquired using CT imaging (CT-SOMATOM Definition) and these data were used to reconstruct 3D geometries for FE

this technique, together with increased patient comfort, shortened intensive care and hospital stay, and the avoidance of cardiopulmonary bypass, make this non-surgical

Accurate multidisciplinary pre-procedural evaluation of patients who are considered candidates for TAVI is mandatory to plan the most adequate treatment and to minimise peri- and post-procedural complications (Smith et al., 2011; Vahanian et al., 2008). However, in this emerging field, several issues remain a source of debate. Device sizing and positioning are the main challenges, but vascular complications, electrical conduction abnormalities and post-procedural aortic regurgitation still remain major safety concerns. In addition, according to the current position statement, TAVI is indicated only in patients with severe symptomatic aortic stenosis, and who are considered at high or prohibitive risk

Extending TAVI to patients who still undergo conventional surgery poses new challenges, both for clinicians and device manufacturers, but "within 10 years, with further improvement of the devices and procedures, and depending on the long-term results of upcoming controlled trials in a broad population, TAVI may become the treatment of choice in a majority of patients with degenerative aortic stenosis" (Cribier, 2009). Indeed, highly experienced centres have already demonstrated the feasibility of TAVI in failed bioprosthetic heart valves (valve-in-valve procedure) in patients considered at very highrisk or ineligible for surgery (Webb et al., 2010). Previous surgical valve implantations represent a well-defined landmark with rigid boundaries that increase ease of positioning and anchoring, thus making patients with bioprosthetic valves ideal candidates for TAVI (Walther et al., 2011). Conversely, younger patients, with less severe aortic valve stenosis or with valve insufficiency, often present implantation sites with different anatomical and dynamic characteristics that generate procedural and device related hurdles, which means

Combining patient-specific imaging data and computational modelling offers a new method to obtain additional, predictive information about responses to cardiovascular device implantation in individual patients (Schoenhagen et al., 2011; Taylor & Figueroa, 2009). FE analyses were performed to explore the feasibility of TAVI using a model of the Edwards-Sapien® device in specific patient morphologies which are currently borderline cases for a percutaneous approach. This method can help in both refining patient selection and characterising device mechanical performance, overall impacting on procedural safety and

Four patients with different stenotic bioprosthetic valves previously implanted (patients A – 23 mm Carpentier-Edwards Perimount Magna valve, Edwards Lifesciences; B – 23 mm Soprano™ valve, Sorin Biomedica Cardio, Italy; C – 25 mm Carpentier-Edwards Perimount valve, Edwards Lifesciences; D – 25 mm Epic™ valve, St Jude Medical, MN, USA) and who were referred for surgical replacement of their failing bioprosthetic valve were analysed (Bosi et al., 2010; Migliavacca et al., 2011). Data about the anatomy of the aortic root, coronary arteries, AV leaflets and bioprostheses were acquired using CT imaging (CT-SOMATOM Definition) and these data were used to reconstruct 3D geometries for FE

technique extremely appealing (Ussia et al., 2009).

for conventional surgery (Ussia et al., 2009, Leon et al., 2011).

that such patients are currently not suitable for or offered TAVI.

**3.1 Patients with previously implanted bioprosthetic valves** 

success in the early introduction of TAVI devices in new patient populations.

models of the selected patients' implantation sites (Fig. 13). The aortic roots were assumed to be 2 mm thick, with density equal to 1,120 kg/m3 (Conti et al., 2010) for all models and meshed with 3D triangular shell general-purpose elements (Table 2). To describe the mechanical behaviour of the aortic roots, Mooney-Rivlin hyperelastic behaviour was adopted incorporating experimental stress-strain data for the ascending aorta (Okamoto et al., 2002) and taking into account the pre-stretching of the aortic root due to the aortic pressure during the cardiac circle.

Fig. 13. CT image reconstruction of the selected patients' aortic wall with previously implanted bioprosthetic valves. FE models of the deployment balloon and TAVI stent are placed inside the implantation site models



The metal frames of the 4 bioprosthetic valves were reconstructed from the CT images to identify their position inside the patients' outflow tracts. The bioprosthetic valve geometries were re-drawn using CAD software (Rhinoceros) to recreate a complete model of the corresponding commercial device used in the patients, and then placed in the same position as that identified from CT images. Connector elements were used to link the bioprosthetic

Finite Element Analysis to Study Percutaneous Heart Valves 183

Mechanical performance of the stent and the impact of the TAVI device into patients' implantation sites were evaluated by analysing: stent configurations at the end of balloon inflation, stent recoil after balloon deflation, stent and arterial stress distribution and peak values at the end of the expansion and recoil phases, degree of aortic valve stenosis assessed according to the post-TAVI geometrical orifice area, and evaluation of coronary artery

At the end of all simulations, the TAVI stent was virtually implanted inside the bioprostheses of the patient-specific aortic root model, with a position that was found in good agreement with available images from a TAVI follow-up case (Fig. 14, Webb et al.,

Fig. 14. Result from the FE simulation of TAVI stent in a Carpentier-Edwards bioprosthesis, resembling the CT image reconstruction of a patient's TAVI in the same bioprosthetic valve

After deployment, the stent assumed an asymmetrical configuration in the longitudinal direction, more expanded in the distal part. There was no contact with the native aortic wall and/or other cardiac structure. This was also demonstrated by the low stresses (<0.1 MPa) measured in the aortic wall, showing how the previously implanted bioprostheses act as a scaffold for the TAVI stent. After balloon deflation, the bioprosthetic valve leaflets partially recoiled forcing the TAVI stent to a more symmetrical shape, which could be defined almost cylindrical in all cases (Fig. 15). Maximum recoil was measured in the distal sections for all patients (A = 17.0%; B = 13.2%; C = 11.7%; D = 10.8%) with absent or low recoil at the level

obstruction.

published by Webb et al., 2010

of the bioprosthetic valves' annulus.

2010).

valves with the aortic vessels to mimic the suture between the ring and the aortic root. Each prosthesis included different frame structures, sewing rings and artificial valve leaflets. The frames (metallic and polymeric) were meshed with 8-node linear hexahedral elements with reduced integration (Table 2), and modelled using an elasto-plastic constitutive behaviour obtained from the manufacturer's data. Bovine and porcine valve leaflets were meshed with 4-node, quadrilateral, shell elements with reduced integration and large-strain formulation (Table 2), while the material properties were simplified using a linear, elastic model (Lee et al., 1984; Zioupos et al., 1994). Calcification of the leaflets was created by increasing Young's modulus and thickness in the region of the commissures (Loree et al., 1994), where a weld constraint was also applied (Schievano et al., 2009): 16 connector elements per commissure were added. An axial, rigid behaviour was assigned to the connectors, allowing them to maintain a fixed distance between the 2 nodes until a threshold force was reached – equal to 0.92 N (Loree et al., 1994) along the direction joining the 2 nodes – and then fail after this threshold value was reached, mimicking calcification failure. The thickening and welding of the failing valve leaflets produced aortic valve geometric orifice areas equal to those measured in the selected patients (1.2 cm2 for A and B, and 1.4 cm2 for C and D).

The Edwards-Sapien® stent is characterised by 12 units, each formed by 4 zigzag elements (Fig. 12). A vertical bar divides each unit and a perforated bar is positioned every 4 units. The CAD geometry of this stent was reproduced with a height, internal diameter and thickness of the expanded stent equal to 16.0, 25.4 and 0.3 mm, respectively. The stent was mashed with hexahedral elements, following mesh sensitivity analysis. It is made of stainless steel which was modelled using Von Mises plasticity behaviour from manufacturer data.

A semi-compliant balloon was designed to resemble the commercial balloon used in clinical practice (Z MED II™, NuMed Inc, NY, USA) and placed inside the TAVI stent in order to deploy the device (Capelli et al, 2010b; Gervaso et al., 2008). The balloon was meshed with 0.03 mm thick membrane elements, and a homogeneous, isotropic, linear-elastic Nylon11 was adopted according to manufacturer data. The stent was crimped down onto the balloon, from its original configuration to catheter dimension (8 mm diameter), using a coaxial cylindrical surface.

The stent-balloon system was placed into the aortic root models according to the judgment of 2 clinicians (Fig. 13). Large deformation analysis of stent deployment in the patients' implantation sites, performed with Abaqus/Explicit, was divided in 2 different steps: balloon pressurisation with resulting stent expansion in the aortic root, and balloon deflation with subsequent stent recoil. In all patients, the implantation site model extremities (upper and lower aortic sections and coronary terminal sections) were constrained in all directions (circumferential, radial and longitudinal) in order to mimic the connection with biological structures. Boundary conditions on the balloon were placed to mimic the bond with the catheter.

Contact properties were defined to describe the interactions encountered in these multi-part analyses. Interactions included contact between surfaces belonging to balloon and TAVI stent, balloon and bioprosthetic aortic valve leaflets, TAVI stent and bioprosthetic aortic valve, bioprosthetic aortic valve and aortic wall. Friction between Nylon and stainless steel was included in the model with coefficient equal to 0.25 (De Beule et al., 2008).

valves with the aortic vessels to mimic the suture between the ring and the aortic root. Each prosthesis included different frame structures, sewing rings and artificial valve leaflets. The frames (metallic and polymeric) were meshed with 8-node linear hexahedral elements with reduced integration (Table 2), and modelled using an elasto-plastic constitutive behaviour obtained from the manufacturer's data. Bovine and porcine valve leaflets were meshed with 4-node, quadrilateral, shell elements with reduced integration and large-strain formulation (Table 2), while the material properties were simplified using a linear, elastic model (Lee et al., 1984; Zioupos et al., 1994). Calcification of the leaflets was created by increasing Young's modulus and thickness in the region of the commissures (Loree et al., 1994), where a weld constraint was also applied (Schievano et al., 2009): 16 connector elements per commissure were added. An axial, rigid behaviour was assigned to the connectors, allowing them to maintain a fixed distance between the 2 nodes until a threshold force was reached – equal to 0.92 N (Loree et al., 1994) along the direction joining the 2 nodes – and then fail after this threshold value was reached, mimicking calcification failure. The thickening and welding of the failing valve leaflets produced aortic valve geometric orifice areas equal to those

measured in the selected patients (1.2 cm2 for A and B, and 1.4 cm2 for C and D).

data.

cylindrical surface.

mimic the bond with the catheter.

The Edwards-Sapien® stent is characterised by 12 units, each formed by 4 zigzag elements (Fig. 12). A vertical bar divides each unit and a perforated bar is positioned every 4 units. The CAD geometry of this stent was reproduced with a height, internal diameter and thickness of the expanded stent equal to 16.0, 25.4 and 0.3 mm, respectively. The stent was mashed with hexahedral elements, following mesh sensitivity analysis. It is made of stainless steel which was modelled using Von Mises plasticity behaviour from manufacturer

A semi-compliant balloon was designed to resemble the commercial balloon used in clinical practice (Z MED II™, NuMed Inc, NY, USA) and placed inside the TAVI stent in order to deploy the device (Capelli et al, 2010b; Gervaso et al., 2008). The balloon was meshed with 0.03 mm thick membrane elements, and a homogeneous, isotropic, linear-elastic Nylon11 was adopted according to manufacturer data. The stent was crimped down onto the balloon, from its original configuration to catheter dimension (8 mm diameter), using a coaxial

The stent-balloon system was placed into the aortic root models according to the judgment of 2 clinicians (Fig. 13). Large deformation analysis of stent deployment in the patients' implantation sites, performed with Abaqus/Explicit, was divided in 2 different steps: balloon pressurisation with resulting stent expansion in the aortic root, and balloon deflation with subsequent stent recoil. In all patients, the implantation site model extremities (upper and lower aortic sections and coronary terminal sections) were constrained in all directions (circumferential, radial and longitudinal) in order to mimic the connection with biological structures. Boundary conditions on the balloon were placed to

Contact properties were defined to describe the interactions encountered in these multi-part analyses. Interactions included contact between surfaces belonging to balloon and TAVI stent, balloon and bioprosthetic aortic valve leaflets, TAVI stent and bioprosthetic aortic valve, bioprosthetic aortic valve and aortic wall. Friction between Nylon and stainless steel

was included in the model with coefficient equal to 0.25 (De Beule et al., 2008).

Mechanical performance of the stent and the impact of the TAVI device into patients' implantation sites were evaluated by analysing: stent configurations at the end of balloon inflation, stent recoil after balloon deflation, stent and arterial stress distribution and peak values at the end of the expansion and recoil phases, degree of aortic valve stenosis assessed according to the post-TAVI geometrical orifice area, and evaluation of coronary artery obstruction.

At the end of all simulations, the TAVI stent was virtually implanted inside the bioprostheses of the patient-specific aortic root model, with a position that was found in good agreement with available images from a TAVI follow-up case (Fig. 14, Webb et al., 2010).

Fig. 14. Result from the FE simulation of TAVI stent in a Carpentier-Edwards bioprosthesis, resembling the CT image reconstruction of a patient's TAVI in the same bioprosthetic valve published by Webb et al., 2010

After deployment, the stent assumed an asymmetrical configuration in the longitudinal direction, more expanded in the distal part. There was no contact with the native aortic wall and/or other cardiac structure. This was also demonstrated by the low stresses (<0.1 MPa) measured in the aortic wall, showing how the previously implanted bioprostheses act as a scaffold for the TAVI stent. After balloon deflation, the bioprosthetic valve leaflets partially recoiled forcing the TAVI stent to a more symmetrical shape, which could be defined almost cylindrical in all cases (Fig. 15). Maximum recoil was measured in the distal sections for all patients (A = 17.0%; B = 13.2%; C = 11.7%; D = 10.8%) with absent or low recoil at the level of the bioprosthetic valves' annulus.

Finite Element Analysis to Study Percutaneous Heart Valves 185

such devices, the maximum stress reached in the stent deployed in the patients was significantly higher than the stress in the stent deployed in the cylinder (443 vs 270 MPa). In addition, the stent was uniformly deployed in the cylinder during the entire simulation: recoil between the steps of balloon inflation and deflation was low (1.5%) and uniform along the stent length. The non-uniform shape of the deployed configuration in the patients and, therefore, the asymmetric stress distribution might cause long-term stent failure due to the pulsatile loading conditions during the cardiac cycle that are not seen during conventional

After simulated TAVI, the connectors modelling calcification of the leaflet commissures were all broken, thus increasing the aortic valve geometrical orifice area to 3.43, 3.60, 3.72, and 3.73 cm2 for patient A, B, C and D respectively. Minimum distances between implanted TAVI device and coronary arteries (right and left) after the deflation of the balloon were 10.9, 11.4, 10.5, and 5.5 mm for patient A, B, C and D respectively, with no direct obstruction

In all cases, the virtual implantation of the TAVI device predicted a successful procedural outcome with an orifice area larger than the pre-implantation stenotic area, and no interference with other cardiac structures. Furthermore, patient-specific FE analyses showed no fractures of the stent immediately post-implantation. These methodologies might help engineers to better understand the mechanical behaviour of the stent when interacting with a wide variety of potential anatomies and, therefore, to optimise the device design for

A patient (E) diagnosed with congenital, moderate aortic valve stenosis, which was treated after birth with aortic balloon valvuloplasty, was selected. At 21 years of age, this patient was referred for surgical repair of her severe aortic valve regurgitation. FE model of TAVI in this patient specific native aortic root and valve leaflets was performed using the same TAVI

CT image data (CT-SOMATOM Definition) from the patient corresponding to mid-systole (i.e. open aortic valve leaflets) were elaborated in the image post-processing software Mimics. A 3D model of the aortic root, coronary arteries and valve leaflets was obtained for the patient (Fig. 17). The native structures were meshed with 3D triangular shell generalpurpose elements (18,890 elements). Aortic wall and native valve leaflets were assumed to be respectively 2 and 0.5 mm thick (Conti et al., 2010) with density equal to 1,120 kg/m3, and Mooney-Rivlin hyperelastic constitutive law was adopted to describe the material

In model E, the TAVI stent/balloon was placed in 3 different positions within the aortic root to test the influence of the landing zone into safe anchoring, the interference with other cardiac structures, such as the mitral valve and the atrioventricular node, and potential occlusion of the coronary arteries. First, the central section of the stent was placed aligned to the leaflet commissures (EM; Fig 17), then it was moved 4.2 mm proximally towards the left

ventricle (EP; Fig. 17), and 4.2 mm distally towards the aortic arch (ED; Fig. 17).

different potential clinical applications before actual procedures are performed.

pre-clinical tests (Schievano et al., 2010b).

**3.2 Patients with aortic incompetence** 

stent model described above.

behaviour.

of the ostia.

Fig. 15. TAVI stent final configuration (end of balloon deflation) in the patients' models

At the end of both the expansion and recoil phases, for all models, non-uniform stress distribution was recorded on the stent struts with the highest Von Mises stresses occurring at the strut junctions with the vertical bars (Fig. 16). At the same locations material plasticisation was reached that guaranteed final open configurations. If we compare the results from the patient-specific simulations with those of a stent uniformly deployed in a cylinder, which is the idealised implantation site used in conventional preclinical testing of

Fig. 16. Von Mises stress distribution in the TAVI stent after balloon deployment and deflation in a cylindrical configuration and in patient C

Fig. 15. TAVI stent final configuration (end of balloon deflation) in the patients' models

Fig. 16. Von Mises stress distribution in the TAVI stent after balloon deployment and

deflation in a cylindrical configuration and in patient C

At the end of both the expansion and recoil phases, for all models, non-uniform stress distribution was recorded on the stent struts with the highest Von Mises stresses occurring at the strut junctions with the vertical bars (Fig. 16). At the same locations material plasticisation was reached that guaranteed final open configurations. If we compare the results from the patient-specific simulations with those of a stent uniformly deployed in a cylinder, which is the idealised implantation site used in conventional preclinical testing of

such devices, the maximum stress reached in the stent deployed in the patients was significantly higher than the stress in the stent deployed in the cylinder (443 vs 270 MPa). In addition, the stent was uniformly deployed in the cylinder during the entire simulation: recoil between the steps of balloon inflation and deflation was low (1.5%) and uniform along the stent length. The non-uniform shape of the deployed configuration in the patients and, therefore, the asymmetric stress distribution might cause long-term stent failure due to the pulsatile loading conditions during the cardiac cycle that are not seen during conventional pre-clinical tests (Schievano et al., 2010b).

After simulated TAVI, the connectors modelling calcification of the leaflet commissures were all broken, thus increasing the aortic valve geometrical orifice area to 3.43, 3.60, 3.72, and 3.73 cm2 for patient A, B, C and D respectively. Minimum distances between implanted TAVI device and coronary arteries (right and left) after the deflation of the balloon were 10.9, 11.4, 10.5, and 5.5 mm for patient A, B, C and D respectively, with no direct obstruction of the ostia.

In all cases, the virtual implantation of the TAVI device predicted a successful procedural outcome with an orifice area larger than the pre-implantation stenotic area, and no interference with other cardiac structures. Furthermore, patient-specific FE analyses showed no fractures of the stent immediately post-implantation. These methodologies might help engineers to better understand the mechanical behaviour of the stent when interacting with a wide variety of potential anatomies and, therefore, to optimise the device design for different potential clinical applications before actual procedures are performed.

#### **3.2 Patients with aortic incompetence**

A patient (E) diagnosed with congenital, moderate aortic valve stenosis, which was treated after birth with aortic balloon valvuloplasty, was selected. At 21 years of age, this patient was referred for surgical repair of her severe aortic valve regurgitation. FE model of TAVI in this patient specific native aortic root and valve leaflets was performed using the same TAVI stent model described above.

CT image data (CT-SOMATOM Definition) from the patient corresponding to mid-systole (i.e. open aortic valve leaflets) were elaborated in the image post-processing software Mimics. A 3D model of the aortic root, coronary arteries and valve leaflets was obtained for the patient (Fig. 17). The native structures were meshed with 3D triangular shell generalpurpose elements (18,890 elements). Aortic wall and native valve leaflets were assumed to be respectively 2 and 0.5 mm thick (Conti et al., 2010) with density equal to 1,120 kg/m3, and Mooney-Rivlin hyperelastic constitutive law was adopted to describe the material behaviour.

In model E, the TAVI stent/balloon was placed in 3 different positions within the aortic root to test the influence of the landing zone into safe anchoring, the interference with other cardiac structures, such as the mitral valve and the atrioventricular node, and potential occlusion of the coronary arteries. First, the central section of the stent was placed aligned to the leaflet commissures (EM; Fig 17), then it was moved 4.2 mm proximally towards the left ventricle (EP; Fig. 17), and 4.2 mm distally towards the aortic arch (ED; Fig. 17).

Finite Element Analysis to Study Percutaneous Heart Valves 187

At balloon deflation, the interaction with the native aortic valve and wall caused high recoil in the proximal section of the stent for all 3 tested positions EM = 14.9%; model EP = 20.2%; model ED = 11.4%. This may be considered a potential cause for obstruction of the left ventricular outflow tract and result in potential dislodgment of the TAVI device from its original position. However, the final geometric orifice areas for the analysed patient in the 3 positions EM, EP, and ED – 4.7, 3.7 and 5.3 cm2 respectively – were same size or larger that the

Direct interaction of TAVI stent with native tissue had impacts both on the device and on the implantation site. After recoil, the geometrical configuration of the stent was not uniform, with an asymmetrical stress distribution (max 477 MPa for EP). The ultimate stress value for the stent material (stainless steel AISI 316L ultimate strength = 515 MPa) was not reached; this means that no stent fractures were seen immediately after deployment. However, pulsatile compressions during cardiac cycle could affect the long-term performance of this stent due to the dynamic nature of the native, non-calcified implantation site. This may be particularly relevant for model EP where the distal portion of the device was in direct contact with the active muscular portion of the left ventricular outflow tract. The expansion of the TAVI stent within native tissue also caused high maximum principal stresses (1 MPa) in the arterial wall, in particular in the region of the leaflets for model ED, at commissure level (Fig. 19). This might induce damage or stimulate remodelling (e.g.

A careful balance between interrelated and sometimes contradictory requirements has to be achieved for optimal TAVI positioning and outcomes such as relief of valve dysfunction and safe anchoring with no tissue damage, no coronary obstruction, no interference with other cardiac structures and no device failure in both short- and long-term. Patient specific FE analysis can be used to help in this process of optimisation and represent an additional

Fig. 19. Maximum principal stress distribution in the native aortic valve leaflets and aortic

Engineering and computational methodologies, together with state of the art imaging technologies, can be used to replicate patient specific patho-physiological conditions in virtual models. Combining patient specific imaging data and computational modelling can improve our understanding of heart structures and the way devices interact with them.

assessment tool for the selection of patients for TAVI.

root after balloon deflation in models EP, EM and ED.

initial orifice area = 3.7 cm2.

stenosis).

**4. Conclusion** 

Fig. 17. Balloon and TAVI stent in the 3 analysed positions inside the native aortic valve: in correspondence of the leaflet commissures (EM); moved 4.2 mm proximally towards the left ventricle (EP); and, 4.2 mm distally towards the aortic arch (ED).

The same loading and boundary conditions as those described above for the study of TAVI in bioprosthetic valves were adopted. Also, the same quantities of interests were measured.

In this patient, at the end of stent deployment and balloon deflation, the device assumed an asymmetrical configuration for all tested positions, more open distally than proximally (Fig. 18). In all 3 cases, the interaction between the TAVI device and the native implantation site was well confined within the left ventricular outflow tract and aortic root portion of the patient's morphology, thus reducing the potential risk of heart block and mitral valve leaflet entrapment. The stent implanted in this patient in the most distal position was the closest to the right coronary artery (3.1 mm). The TAVI device caused no direct obstruction of the coronary orifice; however, further fluid-dynamic studies could enhance our understanding of the effects of the TAVI device placement to the coronary flow.

Fig. 18. TAVI stent final configuration (end of balloon deflation) in the 3 simulated positions.

Fig. 17. Balloon and TAVI stent in the 3 analysed positions inside the native aortic valve: in correspondence of the leaflet commissures (EM); moved 4.2 mm proximally towards the left

The same loading and boundary conditions as those described above for the study of TAVI in bioprosthetic valves were adopted. Also, the same quantities of interests were measured. In this patient, at the end of stent deployment and balloon deflation, the device assumed an asymmetrical configuration for all tested positions, more open distally than proximally (Fig. 18). In all 3 cases, the interaction between the TAVI device and the native implantation site was well confined within the left ventricular outflow tract and aortic root portion of the patient's morphology, thus reducing the potential risk of heart block and mitral valve leaflet entrapment. The stent implanted in this patient in the most distal position was the closest to the right coronary artery (3.1 mm). The TAVI device caused no direct obstruction of the coronary orifice; however, further fluid-dynamic studies could enhance our understanding

Fig. 18. TAVI stent final configuration (end of balloon deflation) in the 3 simulated positions.

ventricle (EP); and, 4.2 mm distally towards the aortic arch (ED).

of the effects of the TAVI device placement to the coronary flow.

At balloon deflation, the interaction with the native aortic valve and wall caused high recoil in the proximal section of the stent for all 3 tested positions EM = 14.9%; model EP = 20.2%; model ED = 11.4%. This may be considered a potential cause for obstruction of the left ventricular outflow tract and result in potential dislodgment of the TAVI device from its original position. However, the final geometric orifice areas for the analysed patient in the 3 positions EM, EP, and ED – 4.7, 3.7 and 5.3 cm2 respectively – were same size or larger that the initial orifice area = 3.7 cm2.

Direct interaction of TAVI stent with native tissue had impacts both on the device and on the implantation site. After recoil, the geometrical configuration of the stent was not uniform, with an asymmetrical stress distribution (max 477 MPa for EP). The ultimate stress value for the stent material (stainless steel AISI 316L ultimate strength = 515 MPa) was not reached; this means that no stent fractures were seen immediately after deployment. However, pulsatile compressions during cardiac cycle could affect the long-term performance of this stent due to the dynamic nature of the native, non-calcified implantation site. This may be particularly relevant for model EP where the distal portion of the device was in direct contact with the active muscular portion of the left ventricular outflow tract.

The expansion of the TAVI stent within native tissue also caused high maximum principal stresses (1 MPa) in the arterial wall, in particular in the region of the leaflets for model ED, at commissure level (Fig. 19). This might induce damage or stimulate remodelling (e.g. stenosis).

A careful balance between interrelated and sometimes contradictory requirements has to be achieved for optimal TAVI positioning and outcomes such as relief of valve dysfunction and safe anchoring with no tissue damage, no coronary obstruction, no interference with other cardiac structures and no device failure in both short- and long-term. Patient specific FE analysis can be used to help in this process of optimisation and represent an additional assessment tool for the selection of patients for TAVI.

Fig. 19. Maximum principal stress distribution in the native aortic valve leaflets and aortic root after balloon deflation in models EP, EM and ED.

#### **4. Conclusion**

Engineering and computational methodologies, together with state of the art imaging technologies, can be used to replicate patient specific patho-physiological conditions in virtual models. Combining patient specific imaging data and computational modelling can improve our understanding of heart structures and the way devices interact with them.

Finite Element Analysis to Study Percutaneous Heart Valves 189

Conti, C.A., Votta, E., Della Corte, A., Del Viscovo, L., Bancone, C., Cotrufo, M., & Redaelli,

De Beule, M., Mortier, P., Carlier, S.G., Verhegghe, B., Van Impe, R., & Verdonck, P. (2008).

Delgado, V., Ewe, S.H., Ng, A.C.T., van der Kley, F., Marsan, N.A., Schuijf, J.D., Schalij, M.J.,

Gervaso, F., Capelli, C., Petrini, L., Lattanzio, S., Di Virgilio, L., & Migliavacca, F. (2008). On

Lee, J.M., Boughner, D. R., & Courtman, D.W. (1984). The glutaraldehyde-stabilized porcine

Leon, M.B., Piazza, N., Nikolsky, E., Blackstone, E.H., Cutlip, D.E., Kappetein, A.P., Krucoff,

Loree, H.M., Grodzinsky, A.J., Park, S.Y., Gibson, L.J., Lee, R.T. (1994). Static circumferential

Lurz, P., Coats, L., Khambadkone, S., Boudjemline, Y., Schievano, S., Muthurangu, V., Lee,

Marrey, R.V., Burgermeister, R., Grishaber, R.B., & Ritchie, R.O. (2006). Fatigue and life

McElhinney, D.B., Hellenbrand, W.E., Zahn, E.M., Jones, T.K., Cheatham, J.P., Lock, J.E., &

Migliavacca, F., Baker, C., Biglino, G., Bosi, G., Capelli, C., Cerri, E., Corsini, C., Cosentino,

Vol.36, Part 4, (01 January 2011), pp. 288-293

*Biomechanics*, Vol.41, No.2, pp. 383-389

Vol.18, No.1, (January 1984), pp. 79-98

January 2011), pp. 253-269

No.2, (February 1994), pp. 195-204

Vol.117, No.15, (15 April 2008), pp. 1964-1972

*Circulation*, Vol.122, No.5, (3 August 2010), pp. 507-516

Vol.27, No.9, (March 2006), pp. 1988-2000

2010), pp. 643-652

A. (2010). Dynamic finite element analysis of the aortic root from MRI-derived parameters. *Medical Engineering & Physics*, Vol.32, No.2, (March 2010), pp. 212-221 Cosentino, D., Capelli, C., Pennati, G., Díaz-Zuccarini, V., Bonhoeffer, P., Taylor, A.M.,

Schievano, S. (2011). Stent Fracture Prediction in Percutaneous Pulmonary Valve Implantation: A Patient-Specific Finite Element Analysis. *International Conference on Advancements of Medicine and Health Care through Technology*, *IFMBE Proceedings*,

Realistic finite element-based stent design: The impact of balloon folding. *Journal of* 

& Bax, J.J. (2010) Multimodality imaging in transcatheter aortic valve implantation: Key steps to assess procedural feasibility. *Eurointervention*, Vol.6, No.5 (November

the effects of different strategies in modelling balloon-expandable stenting by means of finite element method. *Journal of Biomechanics*, Vol.41, No.6, pp. 1206-1212

aortic-valve xenograft .2. Effect of fixation with or without pressure on the tensile viscoelastic properties of the leaflet material. *Journal of Biomedical Materials Research*,

M.W., Mack, M., Mehran, R., Miller, C., Morel, M.A., Petersen, J., Popma, J.J., Takkenberg, J.J.M., Vahanian, A., van Es, G.A., Vranckx, P., Webb, J.G., Windecker, S., & Serruys, P.W. (2011). Standardized endpoint definitions for transcatheter aortic valve implantation clinical trials a consensus report from the valve academic research consortium. *Journal of the American College of Cardiology*, Vol.57, No.3, (18

tangential modulus of human atherosclerotic tissue. *Journal of Biomechanics*, Vol.27,

T.Y., Parenzan, G., Derrick, G., Cullen, S., Walker, F., Tsang, V., Deanfield, J., Taylor, A.M., & Bonhoeffer, P. (2008). Percutaneous pulmonary valve implantation - Impact of evolving technology and learning curve on clinical outcome. *Circulation*,

prediction for cobalt-chromium stents: a fracture mechanics analysis. *Biomaterials*,

Vincent, J.A. (2010). Short- and medium-term outcomes after transcatheter pulmonary valve placement in the expanded multicenter US melody valve trial.

D., Hsia, T.Y., Pennati, G., & Schievano, S. (2011). Numerical simulations to study

Therefore, advanced FE analyses can become a fundamental tool during preclinical testing of new biomedical devices that could shorten the time for device development, minimise animal experimentation, and ensure greater patient safety during the delicate phase of testing clinical feasibility of novel cardiovascular technologies.

#### **5. Acknowledgments**

This work has been supported by grant funding from the British Heart Foundation (BHF) (Dr. Schievano & Mr. Capelli – PhD Studenships), the Royal Academy of Engineering and the Engineering and Physical Sciences Research Council (EPSRC) (Dr. Schievano – Postdoctoral Fellowship), the National Institute of Health Research (NIHR) (Professor Taylor – Senior Research Fellowship), the European Union (Ms. Cosentino – MeDDiCA PhD Studentship 7th Framework Programme, grant agreement 238113) and the Fondation Leducq.

#### **6. References**


Therefore, advanced FE analyses can become a fundamental tool during preclinical testing of new biomedical devices that could shorten the time for device development, minimise animal experimentation, and ensure greater patient safety during the delicate phase of

This work has been supported by grant funding from the British Heart Foundation (BHF) (Dr. Schievano & Mr. Capelli – PhD Studenships), the Royal Academy of Engineering and the Engineering and Physical Sciences Research Council (EPSRC) (Dr. Schievano – Postdoctoral Fellowship), the National Institute of Health Research (NIHR) (Professor Taylor – Senior Research Fellowship), the European Union (Ms. Cosentino – MeDDiCA PhD Studentship 7th Framework Programme, grant agreement 238113) and the Fondation

Beden, S.M., Abdullah, S., Ariffin, A.K., AL-Asady, N.A., & Rahman, M.M. (2009). Fatigue

loading. *European Journal of Scientific Research*, Vol.29, No.1, pp. 157-169 Bonhoeffer, P., Boudjemline, Y., Saliba, Z., Merckx, J., Aggoun, Y., Bonnet, D., Acar, P., Le

dysfunction. *Lancet*, Vol.356, No.9239, (21 October 2000), pp. 1403-1405 Bonhoeffer, P., Huynh, R., House, M., Douk, N., Kopcak, M., Hill, A., & Rafiee, N. (2008).

Bosi, G.M., Cerri, E., Capelli, C., Migliavacca, F., Bonhoeffer, P., Taylor, A.M., & Schievano,

*Engineering Sciences*, Vol.368, No.1921, (28 June 2010), pp. 3027-3038 Capelli, C., Nordmeyer, J., Schievano, S., Lurz, P., Khambadkone, S., Lattanzio, S., Taylor,

*EuroIntervention,* Vol.6, No.5, (November 2010), pp. 638-642

Innovations in Cardiovascular Interventions (ICI) Meeting 2009. http://www.paragon-conventions.net/ICI\_PDF/Alain%20Cribier.pdf

stent with tissue valve. *Circulation*. Vol.118, pp. S\_812

life assessment of different steel-based shell materials under variable amplitude

Bidois, J., Sidi, D., & Kachaner, J. (2000). Percutaneous replacement of pulmonary valve in a right-ventricle to pulmonary-artery prosthetic conduit with valve

Transcatheter pulmonic valve replacement in sheep using a grafted self-expanding

S. (2010). Patient-specific study of transcatheter aortic valve implantation. Endocoronary Biomechanics Research Symposium, Marseille, France, May 2010 Capelli, C., Taylor, A.M., Migliavacca, F., Bonhoeffer, P., & Schievano, S. (2010a). Patient-

specific reconstructed anatomies and computer simulations are fundamental for selecting medical device treatment: application to a new percutaneous pulmonary valve. *Philosophical Transactions of the Royal Society A: Mathematical, Physical and* 

A.M., Petrini, L., Migliavacca, F., & Bonhoeffer, P. (2010b). How do angioplasty balloons work: a computational study on balloon expansion forces.

Anselme, F., Laborde, F., & Leon, M.B. (2002). Percutaneous transcatheter implantation of an aortic valve prosthesis for calcific aortic stenosis - first human case description. *Circulation*, Vol.106, No.24, (10 December 2002), pp. 3006-3008 Cribier, A. (2009). Transcatheter Aortic Valve Implantation: What are the perspectives? at

Cribier, A., Eltchaninoff, H., Bash, A., Borenstein, N., Tron, C., Bauer, F., Derumeaux, G.,

testing clinical feasibility of novel cardiovascular technologies.

**5. Acknowledgments** 

Leducq.

**6. References** 


Finite Element Analysis to Study Percutaneous Heart Valves 191

Schievano, S., Kunzelman, K., Nicosia, M.A., Cochran, R.P., Einstein, D.R., Khambadkone,

Schievano, S.; Taylor, A.M.; Capelli, C.; Coats, L.; Walker, F.; Lurz, P.; Nordmeyer, J.;

Schievano, S., Taylor, A.M., Capelli, C., Lurz, P., Nordmeyer, J., Migliavacca, F., &

Schievano, S., Capelli, C., Young, C., Lurz, P., Nordmeyer, J., Owens, C., Bonhoeffer, P., &

Schoenhagen, P., Hill, A., Kelley, T., Popovic, Z., & Halliburton, S.S. (2011). In vivo imaging

Sines, G., & Ohgi, G. (1981). Fatigue criteria under combined stresses or strains. *Journal of Engineering Materials and Technology*, Vol.103, No.2, (April 1981), pp. 82-90 Smith, C.R., Leon, M.B., Mack, M.J., Miller, D.C., Moses, J.W., Svensson, L.G., Tuzcu, E.M.,

*England Journal of Medidcine*, Vol.364, No.23, (9 June 2011), pp. 2187-2198 Taylor, C.A., & Figueroa, C.A. (2009). Patient-specific modeling of cardiovascular mechanics. *Annual Review of Biomedical Engineering*, Vol.11, pp. 109-134 Ussia, G.P., Mulè, M., Barbanti, M., Cammalleri, V., Scarabelli, M., Immè, S., Capodanno, D.,

Vahanian, A., Alfieri, O., Al-Attar, N., Antunes, M., Bax, J., Cormier, B., Cribier, A., De

*Research*, Vol.4, No. 4, (August 2011), pp. 459-469

No.1, (January 2009), pp. 28-34

750

36-45

1790-1796

S., & Bonhoeffer, P. (2009). Percutaneous mitral valve dilatation: single balloon versus double balloon. A finite element study. *Journal of Heart Valve Disease*, Vol.18,

Wright, S.; Khambadkone, S.; Tsang, V.; Carminati, M., & Bonhoeffer, P. (2010a). First-in-man implantation of a novel percutaneous valve: a new approach to medical device development. *Eurointervention,* Vol.5, No.6, (January 2010), pp. 745-

Bonhoeffer, P. (2010b). Patient specific finite element analysis results in more accurate prediction of stent fractures: Application to percutaneous pulmonary valve implantation. *Journal of Biomechanics*, Vol.43, No.4, (3 March 2010), pp. 687-93

Taylor, A.M. (2011). Four-dimensional computed tomography: a method of assessing right ventricular outflow tract and pulmonary artery deformations throughout the cardiac cycle. *European Radiology*, Vol.21,No.1, (January 2011), pp.

and computational analysis of the aortic root. Application in clinical research and design of transcatheter aortic valve systems. *Journal of Cardiovascular Translational* 

Webb, J.G., Fontana, G.P., Makkar, R.R., Williams, M., Dewey, T., Kapadia, S., Babaliaros, V., Thourani, V.H., Corso, P., Pichard, A.D., Bavaria, J.E., Herrmann, H.C., Akin, J.J., Anderson, W.N., Wang, D., Pocock, S.J., & Investigators PT (2011) Transcatheter versus surgical aortic-valve replacement in high-risk patients. *New* 

Ciriminna, S., & Tamburino, C. (2009). Quality of life assessment after percutaneous aortic valve implantation. *European Heart Journal*, Vol.30, No.14, (July 2009), pp.

Jaegere, P., Fournial, G., Kappetein, A.P., Kovac, J., Ludgate, S., Maisano, F., Moat, N., Mohr, F., Nataf, P., Piérard, L., Pomar, J.L., Schofer, J., Tornos, P., Tuzcu, M., van Hout, B., Von Segesser, L.K., Walther, T. & European Association of Cardio-Thoracic Surgery; European Society of Cardiology; European Association of Percutaneous Cardiovascular Interventions. (2008). Transcatheter valve implantation for patients with aortic stenosis: a position statement from the European Association of Cardio-Thoracic Surgery (EACTS) and the European Society of Cardiology (ESC), in collaboration with the European Association of

aortic arch pathologies: application to hypoplastic left heart syndrome, aortic coarctation and aortic valve diseases. In "New endovascular technologies: from bench test to clinical practice". Eds. Chakfé N, Durand B and Meichelboeck W. Europrot, Strasbourg, France, 9-22, 2011


Nordmeyer, J., Khambadkone, S., Coats, L., Schievano, S., Lurz, P., Parenzan, G., Taylor,

Nordmeyer, J., Coats, L., Lurz, P., Lee, T.Y., Derrick, G., Rees, P., Cullen, S., Taylor, A.M.,

Nordmeyer, J., Lurz, P., Khambadkone, S., Schievano, S., Jones, A., McElhinney, D.B.,

Okamoto, R., Wagenseil, J.E., Delong, W.R., Peterson, S.J., Kouchoukos, N.T., & Sundt, T.M.

Petrini, L., Migliavacca, F., Massarotti, P., Schievano, S., Dubini, G., & Auricchio, F. (2005).

*American College of Cardiology*, Vol.55, No.11, (16 March 2010), pp. 1080-1090 Schievano, S.; Coats, L.; Migliavacca, F.; Norman, W.; Frigiola, A.; Deanfield, J.; Bonhoeffer,

Schievano, S.; Migliavacca, F.; Coats, L.; Khambadkone, S.; Carminati, M.; Wilson, N.;

Schievano, S., Petrini, L., Migliavacca, F., Coats, L., Nordmeyer, J., Lurz, P., Khambadkone,

*Biomedical Engineering*, Vol.30 No.5, (May 2002), pp. 624–635

Europrot, Strasbourg, France, 9-22, 2011

*Journal,* Vol. 29, No.6 (March 2008), pp. 810-815

Vol.97, No.2, (January 2011), pp. 118-123

No.4, (February 2007), pp. 687-695

490-497

546-554

1392-1397

aortic arch pathologies: application to hypoplastic left heart syndrome, aortic coarctation and aortic valve diseases. In "New endovascular technologies: from bench test to clinical practice". Eds. Chakfé N, Durand B and Meichelboeck W.

A.M., Lock, J.E., & Bonhoeffer, P. (2007). Risk stratification, systematic classification and anticipatory management strategies for stent fracture after percutaneous pulmonary valve implantation. *Circulation*, Vol.115, No.11 (20 March 2007), pp.

Khambadkone, S., & Bonhoeffer, P. (2008). Percutaneous pulmonary valve-in-valve implantation: a successful treatment concept for early device failure. *European Heart* 

Taylor, A.M., & Bonhoeffer, P. (2011). Pre-stenting with a bare metal stent before percutaneous pulmonary valve implantation: Acute and one-year outcomes. *Heart*,

(2002). Mechanical Properties of Dilated Human Ascending Aorta. *Annals of* 

Computational studies of shape memory alloy behavior in biomedical applications. *Journal of Biomechanical Engineering*, Vol.127, No.4 (August 2005), pp. 716-725 Rodes-Cabau, J., Webb, J.G., Cheung, A., Ye, J., Dumont, E., Feindel, C.M., Osten, M.,

Natarajan, M.K., Velianou, J.L., Martucci, G., DeVarennes, B., Chisholm, R., Peterson, M.D., Lichtenstein, S.V., Nietlispach, F., Doyle, D., DeLarochelliere, R., Teoh, K., Chu, V., Dancea, A., Lachapelle, K., Cheema, A., Latter, D., & Horlick, E. (2010). Transcatheter aortic valve implantation for the treatment of severe symptomatic aortic stenosis in patients at very high or prohibitive surgical risk acute and late outcomes of the multicenter canadian experience. *Journal of the* 

P., & Taylor, A.M. (2007a). Variations in right ventricular outflow tract morphology following repair of congenital heart disease: implications for percutaneous pulmonary valve implantation. *Journal of cardiovascular magnetic resonance,* Vol.9,

Deanfield, J.E.; Bonhoeffer, P., & Taylor, A.M. (2007b). Percutaneous pulmonary valve implantation based on rapid prototyping of right ventricular outflow tract and pulmonary trunk from MR data. *Radiology,* Vol.242, No.2, (February 2007), pp.

S., Taylor, A.M., Dubini, G., & Bonhoeffer, P. (2007c). Finite element analysis of stent deployment: understanding stent fracture in percutaneous pulmonary valve implantation. *Journal Interventional Cardiology*, Vol.20, No.6, (December 2007), pp.


**8**

*Hungary* 

**Finite Element Modeling and**

**Degenerated Human Lumbar Spine** 

Numerical analyses are able to simulate processes in their progress that are impossible to measure experimentally, like aging and spinal degeneration processes. 3D finite element (FE) simulations of age-related and sudden degeneration processes of compression-loaded human lumbar spinal segments and their weightbath hydrotraction treatment are presented here. The goal is to determine the effect of the main mechanical degeneration parameters on the deformation and stress state of the lumbar functional spinal units (FSU) during longand short-term degeneration processes. Moreover, numerical analysis of the effect of the special underwater traction method, the so-called weightbath hydrotraction therapy (WHT)

About 60-85 % of the human population is afflicted by lumbar disc diseases, by low back pain (LBP) problems, most of them the young adults of 40-45 years, due to the degeneration of the lumbar segments. Degeneration means an injurious change in the structure and function of FSU, caused by normal aging or by sudden accidental, often unexpected effects yielding mechanical overloading. Degeneration starts generally in the intervertebral discs: in the central kernel of it, in the nucleus pulposus. Aging degeneration of the disc is manifested in loss of hydration, a drying and stiffening procedure in the texture of nucleus, and a hardening of annulus as well, accompanied by the appearance of buckling, lesions, tears, fiber break in the annulus or disruption in the endplates, collapse of osteoporotic vertebral cancellous bone (Adams et al., 2002). Sudden accidental degeneration of overload yields the instant loss of hydrostatic compression in nucleus, accompanied or due to some other failures mentioned above. Several recent studies concluded that light degeneration of young discs leaded to instability of lumbar spine and the stability restored with further aging (Adams et al., 2002; Rohlmann et al., 2006), however, sudden accidental degeneration may be also dangerous in young age, thus, the present study aims to understand the

The first goal of this study was to obtain numerical conclusions for the mechanical effects of age-related and sudden degeneration processes of the lumbar spine under compression. The

for treating degenerated lumbar segments is also presented in this chapter.

biomechanical function of these degeneration processes.

**1. Introduction** 

**Simulation of Healthy and**

Márta Kurutz1 and László Oroszváry2 *1Budapest University of Technology and Economics,* 

*2Knorr-Bremse Hungaria Ltd, Budapest,* 

Percutaneous Cardiovascular Interventions (EAPCI). *European Heart Journal,* Vol.29, No.11, (June 2008), pp. 1463-1470


### **Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine**

Márta Kurutz1 and László Oroszváry2 *1Budapest University of Technology and Economics, 2Knorr-Bremse Hungaria Ltd, Budapest, Hungary* 

#### **1. Introduction**

192 Finite Element Analysis – From Biomedical Applications to Industrial Developments

Walther, T., Dehdashtian, M.M., Khanna, R., Young, E., Goldbrunner, P.J., & Lee, W. (2011).

Webb, J.G., Wood, D.A., Ye, J., Gurvitch, R., Masson, J.B., Rodés-Cabau, J., Osten, M.,

Zajarias, A., & Cribier, A.G. (2009). Outcomes and safety of percutaneous aortic valve

Zioupos, P., Barbenel, J.C., & Fisher, J. (1994). Anisotropic elasticity and strength of

No.11, (June 2008), pp. 1463-1470

pp. 1120-1126

2009), pp. 1829-1836

1857

57

Percutaneous Cardiovascular Interventions (EAPCI). *European Heart Journal,* Vol.29,

Trans-catheter valve-in-valve implantation: in vitro hydrodynamic performance of the SAPIEN+cloth trans-catheter heart valve in the Carpentier-Edwards Perimount valves. *European Journal of Cardio-thoracic Surgery*, Vol.40, No.5, (November 2011),

Horlick, E., Wendler, O., Dumont, E., Carere, R.G., Wijesinghe, N., Nietlispach, F., Johnson, M., Thompson, C.R., Moss, R., Leipsic, J., Munt, B., Lichtenstein, S.V., & Cheung, A. (2010). Transcatheter valve-in-valve implantation for failed bioprosthetic heart valves. *Circulation*, Vol.121, No.16, (27 April 2010), pp. 1848-

replacement. *Journal of the American College of Cardiology*, Vol.53, No.20, (19 May

glutaraldehyde fixed bovine pericardium for use in pericardial bioprosthetic valves. *Journal of Biomedical Materials Research*, Vol.28, No. 1, (January 1994), pp. 49-

Numerical analyses are able to simulate processes in their progress that are impossible to measure experimentally, like aging and spinal degeneration processes. 3D finite element (FE) simulations of age-related and sudden degeneration processes of compression-loaded human lumbar spinal segments and their weightbath hydrotraction treatment are presented here. The goal is to determine the effect of the main mechanical degeneration parameters on the deformation and stress state of the lumbar functional spinal units (FSU) during longand short-term degeneration processes. Moreover, numerical analysis of the effect of the special underwater traction method, the so-called weightbath hydrotraction therapy (WHT) for treating degenerated lumbar segments is also presented in this chapter.

About 60-85 % of the human population is afflicted by lumbar disc diseases, by low back pain (LBP) problems, most of them the young adults of 40-45 years, due to the degeneration of the lumbar segments. Degeneration means an injurious change in the structure and function of FSU, caused by normal aging or by sudden accidental, often unexpected effects yielding mechanical overloading. Degeneration starts generally in the intervertebral discs: in the central kernel of it, in the nucleus pulposus. Aging degeneration of the disc is manifested in loss of hydration, a drying and stiffening procedure in the texture of nucleus, and a hardening of annulus as well, accompanied by the appearance of buckling, lesions, tears, fiber break in the annulus or disruption in the endplates, collapse of osteoporotic vertebral cancellous bone (Adams et al., 2002). Sudden accidental degeneration of overload yields the instant loss of hydrostatic compression in nucleus, accompanied or due to some other failures mentioned above. Several recent studies concluded that light degeneration of young discs leaded to instability of lumbar spine and the stability restored with further aging (Adams et al., 2002; Rohlmann et al., 2006), however, sudden accidental degeneration may be also dangerous in young age, thus, the present study aims to understand the biomechanical function of these degeneration processes.

The first goal of this study was to obtain numerical conclusions for the mechanical effects of age-related and sudden degeneration processes of the lumbar spine under compression. The

Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 195

semi-fluid mass, an incompressible sphere that exerts pressure in all directions. The *annulus fibrosus* consists of 15-25 concentric laminated layers of collagen lamellae tightly connected to each other in a circumferential form around the periphery of the disc. Each lamella consists of ground substance and collagen fibers. Within each lamella the collagen fibers are arranged in parallel, running at an average direction of 30° to the discs horizontal plane. In adjacent lamellae they run in opposite directions and are therefore oriented at 120° to each other. The *cartilaginous endplates* separate the nucleus and annulus from the vertebral bodies, they cover almost the entire surface of the adjacent vertebral bony endplates. The plates

Seven types of *ligaments* are distinguished in the lumbar spine. The *anterior longitudinal ligament* covers the anterior surfaces of the vertebral bodies and discs, attached strongly to the vertebral bone and weakly to the discs. The *posterior longitudinal ligament* covers the posterior aspects of the vertebral bodies and discs, attached strongly to the discs and weakly to the bone. The *ligamentum flavum*, the most elastic ligament of the spine connects the lower and upper ends of the internal surfaces of the adjacent laminae. The *intertransverse ligaments* connect the transverse processes by thin sheets of collagen fibers. The *interspinous ligaments* connect the opposing edges of spinous processes by collagen fibers, while the *supraspinous ligaments* connect the peaks of adjacent spinous processes by tendinous fibers. The *capsular ligaments* connect the circumferences of the joining articular facet joints, being perpendicular

The *muscles* of the lumbar spine can be distinguished by their location around the spine. The *postvertebral muscles* can be divided to deep, intermediate and superficial categories. The *prevertebral muscles* are the abdominal muscles. The postvertebral deep muscles consist of short muscles that connect the adjacent spinous and transverse processes and laminae. The intermediate muscles are more diffused, arising from the transverse processes of each vertebra and attaching to the spinous process of the vertebra above. The superficial postvertebral muscles collectively are called the *erector spinae*. There are four *abdominal muscles*, three of them encircle the abdominal region, and the fourth is located anteriorly at

A *motion segment* or *functional spinal unit* (FSU) is the smallest part of the spine that represents all the main biomechanical features and characteristics of the whole spine. Thus the entire spinal column can be considered as a series of connecting motion segments. The motion segment is a three dimensional structure of six degree of statical/kinematical freedom, consisting of the two adjacent vertebrae with its posterior elements and facet joints, and the intervertebral disc between them, moreover the seven surrounding ligaments,

The spinal column is the *main load bearing structure* of the human musculoskeletal system. It has three fundamental biomechanical functions: *to guarantee the load transfer* along the spinal column without instability; *to allow sufficient physiologic mobility* and flexibility; and *to protect* 

**3. Biomechanics of the lumbar spine and spine segments** 

*the delicate spinal cord* from damaging forces and motions.

have a mean thickness of 0.6 mm.

to the surface of the joints.

the midline.

without muscles.

question is answered also why the young adults of 40-45 years have the most vulnerable lumbar discs, and why increases the stability of lumbar segments with further aging.

On the other hand, for the degenerated lumbar spine, for the LBP problems, traction might be an effective treatment. Traction treatments have been well-known for a long time, however, as often happens, instead of stress relaxation, the compression increases in the discs due to the muscle activity (Andersson et al., 1983; White and Panjabi, 1990; Ramos and Martin, 1994). These observations verify the importance of the special Hungarian traction method, the so-called weightbath hydrotraction therapy (WHT), introduced by Moll (1956, 1963), indications and contraindications described by Bene (1988). In WHT patients are suspended in water on a cervical collar for a period of 20 minutes, loaded by extra lead weights on ankles, when the patients are practically in sleeping position in the lukewarm water with completely relaxed muscles. WHT consists of instant elastic and viscous creeping phases. In this study the elastic phase will be analyzed. As far as the authors know, finite element analyses of lumbar FSUs in pure axial tension without the effect of muscles cannot be found in the literature. As White and Panjabi (1990) and Bader and Bouten (2000) established, tensile stresses and deformations are analyzed associated with flexion and extension only, without mentioning axial tension as a dominating loading effect.

Thus, in this study, the latter case will be analyzed. By means of this study of WHT, the beneficial clinical impacts of the treatment are supported by numerical mechanical evidences.

#### **2. Short structural anatomy of the lumbar spine and spine segments**

The lumbar spine is the section of spinal column between the thorax and the sacrum. It consists of five *vertebrae* named L1 to L5 with their *posterior elements* and *articular facet joints*, of *intervertebral discs*, *ligaments* and the surrounding *muscles*. The clinical anatomy of the lumbar spine can be studied in the books of Bogduk and Twomey (1987), White and Panjabi (1990), Dvir (2000), Benzel (2001) and Adams et al. (2002).

The lumbar *vertebrae* are quasi cylindrical with a lateral width of 40-50 mm and sagittal depth of 30-35 mm. The height of a lumbar vertebra is about 25-30 mm. The lumbar vertebrae are thicker anteriorly than posteriorly resulting in anteriorly convex curvature of the spine known as the lumbar lordosis. The *vertebral body* consists of an outer shell of high strength *cortical bone* and of the internal *cancellous bone* as a network of vertical and horizontal bone struts called trabeculae. The superior and inferior surface of the vertebral body is covered by the *bony endplates* of thin cortical bone perforated by many small holes as the passage of metabolites from bone to the discs. Towards the upper end of the posterior surface of the vertebral body the pedicles support the posterior elements, the lamina the neural arch, the vertebral foramen, the spinous process, the transverse processes, the superior and inferior articular processes, the synovial joints called articular facet joints.

The *intervertebral discs* separate the adjacent vertebrae. They are quasi cylindrical with a lateral width of 40-45 mm and sagittal depth of 35-40 mm. The height of the lumbar disc is about 10 mm. The disc consists of three components: the nucleus pulposus, the annulus fibrosus and the superior and inferior endplates. The *nucleus pulposus* is a hydrated gel, a

question is answered also why the young adults of 40-45 years have the most vulnerable

On the other hand, for the degenerated lumbar spine, for the LBP problems, traction might be an effective treatment. Traction treatments have been well-known for a long time, however, as often happens, instead of stress relaxation, the compression increases in the discs due to the muscle activity (Andersson et al., 1983; White and Panjabi, 1990; Ramos and Martin, 1994). These observations verify the importance of the special Hungarian traction method, the so-called weightbath hydrotraction therapy (WHT), introduced by Moll (1956, 1963), indications and contraindications described by Bene (1988). In WHT patients are suspended in water on a cervical collar for a period of 20 minutes, loaded by extra lead weights on ankles, when the patients are practically in sleeping position in the lukewarm water with completely relaxed muscles. WHT consists of instant elastic and viscous creeping phases. In this study the elastic phase will be analyzed. As far as the authors know, finite element analyses of lumbar FSUs in pure axial tension without the effect of muscles cannot be found in the literature. As White and Panjabi (1990) and Bader and Bouten (2000) established, tensile stresses and deformations are analyzed associated with flexion and

lumbar discs, and why increases the stability of lumbar segments with further aging.

extension only, without mentioning axial tension as a dominating loading effect.

**2. Short structural anatomy of the lumbar spine and spine segments** 

(1990), Dvir (2000), Benzel (2001) and Adams et al. (2002).

evidences.

Thus, in this study, the latter case will be analyzed. By means of this study of WHT, the beneficial clinical impacts of the treatment are supported by numerical mechanical

The lumbar spine is the section of spinal column between the thorax and the sacrum. It consists of five *vertebrae* named L1 to L5 with their *posterior elements* and *articular facet joints*, of *intervertebral discs*, *ligaments* and the surrounding *muscles*. The clinical anatomy of the lumbar spine can be studied in the books of Bogduk and Twomey (1987), White and Panjabi

The lumbar *vertebrae* are quasi cylindrical with a lateral width of 40-50 mm and sagittal depth of 30-35 mm. The height of a lumbar vertebra is about 25-30 mm. The lumbar vertebrae are thicker anteriorly than posteriorly resulting in anteriorly convex curvature of the spine known as the lumbar lordosis. The *vertebral body* consists of an outer shell of high strength *cortical bone* and of the internal *cancellous bone* as a network of vertical and horizontal bone struts called trabeculae. The superior and inferior surface of the vertebral body is covered by the *bony endplates* of thin cortical bone perforated by many small holes as the passage of metabolites from bone to the discs. Towards the upper end of the posterior surface of the vertebral body the pedicles support the posterior elements, the lamina the neural arch, the vertebral foramen, the spinous process, the transverse processes, the superior and inferior articular processes, the synovial joints called articular facet joints.

The *intervertebral discs* separate the adjacent vertebrae. They are quasi cylindrical with a lateral width of 40-45 mm and sagittal depth of 35-40 mm. The height of the lumbar disc is about 10 mm. The disc consists of three components: the nucleus pulposus, the annulus fibrosus and the superior and inferior endplates. The *nucleus pulposus* is a hydrated gel, a semi-fluid mass, an incompressible sphere that exerts pressure in all directions. The *annulus fibrosus* consists of 15-25 concentric laminated layers of collagen lamellae tightly connected to each other in a circumferential form around the periphery of the disc. Each lamella consists of ground substance and collagen fibers. Within each lamella the collagen fibers are arranged in parallel, running at an average direction of 30° to the discs horizontal plane. In adjacent lamellae they run in opposite directions and are therefore oriented at 120° to each other. The *cartilaginous endplates* separate the nucleus and annulus from the vertebral bodies, they cover almost the entire surface of the adjacent vertebral bony endplates. The plates have a mean thickness of 0.6 mm.

Seven types of *ligaments* are distinguished in the lumbar spine. The *anterior longitudinal ligament* covers the anterior surfaces of the vertebral bodies and discs, attached strongly to the vertebral bone and weakly to the discs. The *posterior longitudinal ligament* covers the posterior aspects of the vertebral bodies and discs, attached strongly to the discs and weakly to the bone. The *ligamentum flavum*, the most elastic ligament of the spine connects the lower and upper ends of the internal surfaces of the adjacent laminae. The *intertransverse ligaments* connect the transverse processes by thin sheets of collagen fibers. The *interspinous ligaments* connect the opposing edges of spinous processes by collagen fibers, while the *supraspinous ligaments* connect the peaks of adjacent spinous processes by tendinous fibers. The *capsular ligaments* connect the circumferences of the joining articular facet joints, being perpendicular to the surface of the joints.

The *muscles* of the lumbar spine can be distinguished by their location around the spine. The *postvertebral muscles* can be divided to deep, intermediate and superficial categories. The *prevertebral muscles* are the abdominal muscles. The postvertebral deep muscles consist of short muscles that connect the adjacent spinous and transverse processes and laminae. The intermediate muscles are more diffused, arising from the transverse processes of each vertebra and attaching to the spinous process of the vertebra above. The superficial postvertebral muscles collectively are called the *erector spinae*. There are four *abdominal muscles*, three of them encircle the abdominal region, and the fourth is located anteriorly at the midline.

A *motion segment* or *functional spinal unit* (FSU) is the smallest part of the spine that represents all the main biomechanical features and characteristics of the whole spine. Thus the entire spinal column can be considered as a series of connecting motion segments. The motion segment is a three dimensional structure of six degree of statical/kinematical freedom, consisting of the two adjacent vertebrae with its posterior elements and facet joints, and the intervertebral disc between them, moreover the seven surrounding ligaments, without muscles.

#### **3. Biomechanics of the lumbar spine and spine segments**

The spinal column is the *main load bearing structure* of the human musculoskeletal system. It has three fundamental biomechanical functions: *to guarantee the load transfer* along the spinal column without instability; *to allow sufficient physiologic mobility* and flexibility; and *to protect the delicate spinal cord* from damaging forces and motions.

Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 197

generally to a part of the discs only as a side effect of other internal forces, however, the aim of

The range of *spinal movements* can be measured both in vivo and in vitro. The spinal movement has six components: three deflections and three rotations. The physiologic movements are the flexion and extension in the sagittal plane, the lateral bending in the frontal plane and the rotation around the long axis of the spine. The spinal motions are generally characterized by three parameters: the *neutral zone* in which the spine shows no resistance, the *elastic zone* in which the spinal resistance works, and the *range of motion,* the

The mobility of the spine depends on several factors. It depends first of all on the state of the intervertebral discs: the geometry, the stiffness, the fluid content, the degeneration and aging of it. The lumbar region of the spine has greater mobility than the thoracic spine. The range of motion is influenced also by the state of ligaments, the articular facet joints and the posterior bony elements. Viscoelastic properties of discs and ligaments also have an effect

The three-dimensional FSU has six force and six motion components that depend highly on the mechanical properties, stiffness or flexibility, load bearing capacity of each structural component of the motion segment, that all depend on the age and degeneration state of

Lumbar *vertebral bodies* resist most of the compressive force acting along the long axis of the spine. Most of this load must resisted by the dense network of trabeculae, and less by the cortical shell. The state of the cancellous bone is the main factor of compressive failure tolerance of vertebrae (McGill, 2000). Moreover, the cancellous bone of vertebrae acts as shock absorber of the spine in accidental injurious effects. The load bearing capacity of vertebrae depends on the geometry, mass, bone mineral density (BMD) and the bone architecture of the vertebra, which all are in correlation with aging sex and degeneration. Mosekilde (2000) demonstrated that age is the major determinant of vertebral bone strength, mass, and micro-architecture. The posterior elements of vertebrae have also important role in the load bearing capacity and mobility of segments. Facet joints work as typical contact structures, by limiting the spinal movements. They stabilize the lumbar spine in compression, and prevent excessive bending and translation between adjacent vertebrae, to

The *intervertebral discs* provide the compressive force transfer between the two adjacent vertebrae, and at the same time they allow the intervertebral mobility and flexibility. The arrangement of the collagen fibers in the annulus fibrosus is optimal for absorbing the stresses generated by the hydrostatic compression state nucleus pulposus in axial loading of the disc, and they play an important role in restricting axial rotation of the spine. Axial compressive stiffness is higher in the outer and posterior regions than in the inner and anterior regions. Tensile stiffness is higher in the anterior and posterior part than in the

traction therapies is even to apply pure tensional force to the lumbar spine.

**3.4 Biomechanics of the lumbar functional spinal units** 

**3.3 Mobility of the lumbar spine** 

sum of the two latter zones.

protect the disc and the spinal cord.

on the mobility.

them.

The lumbar spine is the most critical part of the spine in aspect of instability and injury since this part is the maximally loaded part of spine and this part has the maximal mobility at the same time, moreover, this part has the minimal stiffening support from the surrounding organs.

#### **3.1 Loads acting on the lumbar spine**

The spinal loads based on biomechanical studies are summarized by Dolan and Adams (2001). The loads acting on the spine can be physiologic and traumatic loads. The *physiologic loads* due to the common, normal activity of the spine have further classes: short-term loads (in flexion, extension), long-term loads (in sitting, standing), repeated or cyclic loads (in gait, walk), dynamic loads (in running, jumping). The *traumatic loads* generally occur suddenly, unexpectedly with great amplitude (impact, whiplash).

Each part of the body is subjected to *gravity load*, proportionally to its mass. The compressive gravity load increases towards the support of the body. This load can be multiplied in acceleration, during a fall, or other effects with acceleration or deceleration.

*Muscle loads* depend on the muscle activity. The muscles are active tissues, they can contract, and their ability of contraction is governed by the nervous system. The back and abdomen muscles stabilize the spine in upright standing; moreover, they prevent the spine from extreme movements. At the same time, the muscle contraction causes high compressive forces to the lumbar spine. Nachemson (1981) and Sato et al. (1999) classified the muscle forces in different body postures.

The *intra-abdominal pressure* decreases generally the spinal compression due to the abdominal muscle activity. Wide abdominal belts help to reduce the spinal compressive forces.

*Ergonomic loads* afflict mostly the lumbar spine. By lifting and holding weights the lumbar spine is subjected to high compressive load, depending on the horizontal distance of the load from the lumbar spine. Long-term vibration and cyclical effects may increase the compression in the lumbar spine leading to structural changes and fatigue effects in the tissue of discs and vertebrae.

*Traumatic overload* of the spine may cause damage in the discs and facet joints. Although muscles can save the spine from excessive injurious loads and movements, this protection works only if the neural system has time enough to activate the muscles.

#### **3.2 Internal forces arising in the lumbar spine**

The main internal force acting on the lumbar spine is the *compressive normal force* acting perpendicularly to the middle plane of the discs, causing the compression of the discs. It is accompanied by mainly sagittal and less lateral *shear forces* acting in the middle plane of the discs, causing the slope of the discs to each other. The moment components causing the forwards/backwards bending (flexion/extension) and the lateral bending of the spine are the sagittal and lateral *bending moments*, respectively; and the component that causes the spine to rotate about its long axis is the *torque or torsional moment*. The *tensile force* is also a normal force acting perpendicularly to the middle plane of the discs and causing the elongation of it. Although from physiologic loads there is no pure tensile force acting on the spine, since it acts generally to a part of the discs only as a side effect of other internal forces, however, the aim of traction therapies is even to apply pure tensional force to the lumbar spine.

#### **3.3 Mobility of the lumbar spine**

196 Finite Element Analysis – From Biomedical Applications to Industrial Developments

The lumbar spine is the most critical part of the spine in aspect of instability and injury since this part is the maximally loaded part of spine and this part has the maximal mobility at the same time, moreover, this part has the minimal stiffening support from the surrounding

The spinal loads based on biomechanical studies are summarized by Dolan and Adams (2001). The loads acting on the spine can be physiologic and traumatic loads. The *physiologic loads* due to the common, normal activity of the spine have further classes: short-term loads (in flexion, extension), long-term loads (in sitting, standing), repeated or cyclic loads (in gait, walk), dynamic loads (in running, jumping). The *traumatic loads* generally occur suddenly,

Each part of the body is subjected to *gravity load*, proportionally to its mass. The compressive gravity load increases towards the support of the body. This load can be multiplied in

*Muscle loads* depend on the muscle activity. The muscles are active tissues, they can contract, and their ability of contraction is governed by the nervous system. The back and abdomen muscles stabilize the spine in upright standing; moreover, they prevent the spine from extreme movements. At the same time, the muscle contraction causes high compressive forces to the lumbar spine. Nachemson (1981) and Sato et al. (1999) classified the muscle

The *intra-abdominal pressure* decreases generally the spinal compression due to the abdominal

*Ergonomic loads* afflict mostly the lumbar spine. By lifting and holding weights the lumbar spine is subjected to high compressive load, depending on the horizontal distance of the load from the lumbar spine. Long-term vibration and cyclical effects may increase the compression in the lumbar spine leading to structural changes and fatigue effects in the

*Traumatic overload* of the spine may cause damage in the discs and facet joints. Although muscles can save the spine from excessive injurious loads and movements, this protection

The main internal force acting on the lumbar spine is the *compressive normal force* acting perpendicularly to the middle plane of the discs, causing the compression of the discs. It is accompanied by mainly sagittal and less lateral *shear forces* acting in the middle plane of the discs, causing the slope of the discs to each other. The moment components causing the forwards/backwards bending (flexion/extension) and the lateral bending of the spine are the sagittal and lateral *bending moments*, respectively; and the component that causes the spine to rotate about its long axis is the *torque or torsional moment*. The *tensile force* is also a normal force acting perpendicularly to the middle plane of the discs and causing the elongation of it. Although from physiologic loads there is no pure tensile force acting on the spine, since it acts

muscle activity. Wide abdominal belts help to reduce the spinal compressive forces.

works only if the neural system has time enough to activate the muscles.

**3.2 Internal forces arising in the lumbar spine** 

acceleration, during a fall, or other effects with acceleration or deceleration.

organs.

**3.1 Loads acting on the lumbar spine** 

forces in different body postures.

tissue of discs and vertebrae.

unexpectedly with great amplitude (impact, whiplash).

The range of *spinal movements* can be measured both in vivo and in vitro. The spinal movement has six components: three deflections and three rotations. The physiologic movements are the flexion and extension in the sagittal plane, the lateral bending in the frontal plane and the rotation around the long axis of the spine. The spinal motions are generally characterized by three parameters: the *neutral zone* in which the spine shows no resistance, the *elastic zone* in which the spinal resistance works, and the *range of motion,* the sum of the two latter zones.

The mobility of the spine depends on several factors. It depends first of all on the state of the intervertebral discs: the geometry, the stiffness, the fluid content, the degeneration and aging of it. The lumbar region of the spine has greater mobility than the thoracic spine. The range of motion is influenced also by the state of ligaments, the articular facet joints and the posterior bony elements. Viscoelastic properties of discs and ligaments also have an effect on the mobility.

#### **3.4 Biomechanics of the lumbar functional spinal units**

The three-dimensional FSU has six force and six motion components that depend highly on the mechanical properties, stiffness or flexibility, load bearing capacity of each structural component of the motion segment, that all depend on the age and degeneration state of them.

Lumbar *vertebral bodies* resist most of the compressive force acting along the long axis of the spine. Most of this load must resisted by the dense network of trabeculae, and less by the cortical shell. The state of the cancellous bone is the main factor of compressive failure tolerance of vertebrae (McGill, 2000). Moreover, the cancellous bone of vertebrae acts as shock absorber of the spine in accidental injurious effects. The load bearing capacity of vertebrae depends on the geometry, mass, bone mineral density (BMD) and the bone architecture of the vertebra, which all are in correlation with aging sex and degeneration. Mosekilde (2000) demonstrated that age is the major determinant of vertebral bone strength, mass, and micro-architecture. The posterior elements of vertebrae have also important role in the load bearing capacity and mobility of segments. Facet joints work as typical contact structures, by limiting the spinal movements. They stabilize the lumbar spine in compression, and prevent excessive bending and translation between adjacent vertebrae, to protect the disc and the spinal cord.

The *intervertebral discs* provide the compressive force transfer between the two adjacent vertebrae, and at the same time they allow the intervertebral mobility and flexibility. The arrangement of the collagen fibers in the annulus fibrosus is optimal for absorbing the stresses generated by the hydrostatic compression state nucleus pulposus in axial loading of the disc, and they play an important role in restricting axial rotation of the spine. Axial compressive stiffness is higher in the outer and posterior regions than in the inner and anterior regions. Tensile stiffness is higher in the anterior and posterior part than in the

Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 199

Degeneration of FSU starts generally in the intervertebral discs. The first age-related changes of disc occur within the nucleus. Changes to any tissue property of the disc markedly alter the mechanics of load transfer and stability of the whole segment (Ferguson and Steffen, 2003). The mechanical properties of the segment depend also on the state of the bony structures, first of all on the trabecular structure of the internal spongy bone of vertebrae. The osteoporotic changes may also decrease the load bearing capacity of FSU.

*Long-term age-related degeneration* of the discs is manifested in the loss of hydration, a drying and stiffening procedure in the texture of mainly the nucleus (McNally and Adams 1992; Adams et al., 2002; Cassinelli and Kang, 2000). The functional consequences of aging are that the nucleus becomes dry, fibrous and stiff. The volume of nucleus and the region of hydrostatic pressure of it decrease, consequently, the compressive load-bearing of the disc passes to the annulus. The age-related changes of disc can be accompanied by the appearance of buckling, lesions, tears, fiber break in the annulus or disruption in the endplates, collapse of osteoporotic vertebral cancellous bone. Since the annulus becomes weaker with aging, so the overloading of it can lead to the inward buckling of the internal annulus, or to circumferential or radial tears, fiber break in the annulus, disc prolapse or herniation, or to large radial bulging of the external annulus, reduction of the disc height, or moreover, to endplate damages (Natarajan et al., 2004). The main cause of all these problems is that while the healthy disc has a hydrostatic nucleus, during aging, it becomes fibrous being no longer as a pressurized fluid. Several recent studies concluded that light degeneration of young discs leaded to instability of lumbar spine, while the stability

*Sudden accidental, often unexpected traumatic degeneration or damage* of overload may yield the sudden loss of hydrostatic compression in nucleus, accompanied or due to some other failures mentioned above. In these cases the material of nucleus remains changeless, depending on the actual aging state in which the accidental effect happened. For this reason,

Experimental analyses of spinal degenerations are very difficult, sometimes impossible. However, by means of numerical simulation, the effect of the main mechanical factors of

Finite element modeling of any structure consists of five main steps: geometrical, material,

Geometrical modeling of the FSU must follow the anatomy of the segment. Beside the topology, additional data such as volume density, surface texture, etc. are needed. Different methods of medical image analyses can be used, like scanners, computer tomography, or

In geometrical modeling the *vertebral body*, its cortical shell, cancellous core, posterior bony elements and the bony endplates are generally distinguished. For the width of the

sudden traumatic degenerations may be also dangerous in younger age.

element type and load modeling, and finally, validating the complete model.

restored with further aging (Adams et al., 2002).

**5. Finite element modeling of the lumbar spine** 

**5.1 Geometrical modeling of the lumbar spine segments** 

degenerations can be analyzed.

magnetic resonance imaging methods.

lateral and inner regions. Thus, the inner annulus near the nucleus seems to be the weakest area of annulus, and the outer posterior part the strongest region. In sustained loading the spine shows viscoelastic features. In quasi-static compression the disc creep is 5-7 times higher than the creep in the bony structures of the segment. Thus, the main factor of segment viscosity is the disc, mainly the disc annulus. The creep of the disc depends on the fluid content of it, mainly on the diurnal variation of it, namely on the fluid loss of daily activity and the overnight bed rest with fluid recovery.

The *ligaments* are *passive tissues* working against tension only. The primary action of the spinal ligaments lying posterior to the centre of sagittal plane rotation is to protect the spine by preventing excessive lumbar flexion. However, during this protection the ligaments may compress the discs by 100% or more. Indeed, the effectiveness of a ligament depends mainly on the moment arm through which it acts. The most elastic ligament, the ligamentum flavum being under pretension throughout all levels of flexion prevents any forms of buckling of spine. The interspinous and supraspinous ligaments may protect against excessive flexion. The capsular ligaments of facet joints restrict joint flexion and distraction of the facet surfaces of axial torsion.

The *muscles* being *active tissues* governed by the *neuromuscular control* are required to provide dynamic stability of the spine in the given activity and posture, and to provide mobility during physiologic activity, moreover to protect the spine during trauma in the post-injury phase. Two mechanical characteristics are necessary to provide these physiologic functions: the muscles must generate forces isometrically and by length change (contraction and elongation), and they must increase the stiffness of the spinal system.

The mechanical behaviour of the whole *functional spinal units* (FSU) depends on the physical properties of its components, mainly on the behaviour of the intervertebral disc, ligaments and articular facet joints. The average *load tolerance* of lumbar segments under quasi-static loading is about 5000 N for compression, 2800 N for tension, 150 N for shear and 20 Nm for axial rotation (Bader and Bouten, 2000). *Flexibility* of the FSU is the ability of the structure to deform under the applied load. Inversely, the *stiffness* is the ability to resist by force to a deformation. The stiffness of the spinal segments increases from cervical to lumbar regions for all loading cases. In lumbar region the stiffness is about 2000-2500 N/mm for compression, 800-1000N/mm for tension, 200-400 N/mm for lateral and 120-200 N/mm for anterior/posterior shear. The rotational stiffness is about 1.4-2.2 Nm/degree for flexion, 2.0- 2.8 Nm/degree for extension, 1.8-2.0 Nm/degree for lateral bending and 5 Nm/degree for axial torsion (White and Panjabi, 1990; Bader and Bouten, 2000). The stiffness of the lumbar spine depends on the age and degeneration. In advanced degeneration the stiffness is higher. The stiffness is influenced by the viscous properties of the segments and the load history as well.

#### **4. Degeneration of the lumbar spine and spine segments**

The lumbar part is the most vulnerable section of the spine since both the compressive loads and the spinal mobility are maximal in this area. Consequently, the lumbar discs are mostly endangered by degenerations that influence the load bearing capacity of the segments. *Degeneration* means an injurious change in the function and structure of the disc, caused by *aging* or by *environmental effects*, like mechanical overloading (Adams et al., 2000).

lateral and inner regions. Thus, the inner annulus near the nucleus seems to be the weakest area of annulus, and the outer posterior part the strongest region. In sustained loading the spine shows viscoelastic features. In quasi-static compression the disc creep is 5-7 times higher than the creep in the bony structures of the segment. Thus, the main factor of segment viscosity is the disc, mainly the disc annulus. The creep of the disc depends on the fluid content of it, mainly on the diurnal variation of it, namely on the fluid loss of daily

The *ligaments* are *passive tissues* working against tension only. The primary action of the spinal ligaments lying posterior to the centre of sagittal plane rotation is to protect the spine by preventing excessive lumbar flexion. However, during this protection the ligaments may compress the discs by 100% or more. Indeed, the effectiveness of a ligament depends mainly on the moment arm through which it acts. The most elastic ligament, the ligamentum flavum being under pretension throughout all levels of flexion prevents any forms of buckling of spine. The interspinous and supraspinous ligaments may protect against excessive flexion. The capsular ligaments of facet joints restrict joint flexion and distraction

The *muscles* being *active tissues* governed by the *neuromuscular control* are required to provide dynamic stability of the spine in the given activity and posture, and to provide mobility during physiologic activity, moreover to protect the spine during trauma in the post-injury phase. Two mechanical characteristics are necessary to provide these physiologic functions: the muscles must generate forces isometrically and by length change (contraction and

The mechanical behaviour of the whole *functional spinal units* (FSU) depends on the physical properties of its components, mainly on the behaviour of the intervertebral disc, ligaments and articular facet joints. The average *load tolerance* of lumbar segments under quasi-static loading is about 5000 N for compression, 2800 N for tension, 150 N for shear and 20 Nm for axial rotation (Bader and Bouten, 2000). *Flexibility* of the FSU is the ability of the structure to deform under the applied load. Inversely, the *stiffness* is the ability to resist by force to a deformation. The stiffness of the spinal segments increases from cervical to lumbar regions for all loading cases. In lumbar region the stiffness is about 2000-2500 N/mm for compression, 800-1000N/mm for tension, 200-400 N/mm for lateral and 120-200 N/mm for anterior/posterior shear. The rotational stiffness is about 1.4-2.2 Nm/degree for flexion, 2.0- 2.8 Nm/degree for extension, 1.8-2.0 Nm/degree for lateral bending and 5 Nm/degree for axial torsion (White and Panjabi, 1990; Bader and Bouten, 2000). The stiffness of the lumbar spine depends on the age and degeneration. In advanced degeneration the stiffness is higher. The stiffness is influenced by the viscous properties of the segments and the load

The lumbar part is the most vulnerable section of the spine since both the compressive loads and the spinal mobility are maximal in this area. Consequently, the lumbar discs are mostly endangered by degenerations that influence the load bearing capacity of the segments. *Degeneration* means an injurious change in the function and structure of the disc, caused by *aging* or by *environmental effects*, like mechanical overloading (Adams et al., 2000).

elongation), and they must increase the stiffness of the spinal system.

**4. Degeneration of the lumbar spine and spine segments** 

activity and the overnight bed rest with fluid recovery.

of the facet surfaces of axial torsion.

history as well.

Degeneration of FSU starts generally in the intervertebral discs. The first age-related changes of disc occur within the nucleus. Changes to any tissue property of the disc markedly alter the mechanics of load transfer and stability of the whole segment (Ferguson and Steffen, 2003). The mechanical properties of the segment depend also on the state of the bony structures, first of all on the trabecular structure of the internal spongy bone of vertebrae. The osteoporotic changes may also decrease the load bearing capacity of FSU.

*Long-term age-related degeneration* of the discs is manifested in the loss of hydration, a drying and stiffening procedure in the texture of mainly the nucleus (McNally and Adams 1992; Adams et al., 2002; Cassinelli and Kang, 2000). The functional consequences of aging are that the nucleus becomes dry, fibrous and stiff. The volume of nucleus and the region of hydrostatic pressure of it decrease, consequently, the compressive load-bearing of the disc passes to the annulus. The age-related changes of disc can be accompanied by the appearance of buckling, lesions, tears, fiber break in the annulus or disruption in the endplates, collapse of osteoporotic vertebral cancellous bone. Since the annulus becomes weaker with aging, so the overloading of it can lead to the inward buckling of the internal annulus, or to circumferential or radial tears, fiber break in the annulus, disc prolapse or herniation, or to large radial bulging of the external annulus, reduction of the disc height, or moreover, to endplate damages (Natarajan et al., 2004). The main cause of all these problems is that while the healthy disc has a hydrostatic nucleus, during aging, it becomes fibrous being no longer as a pressurized fluid. Several recent studies concluded that light degeneration of young discs leaded to instability of lumbar spine, while the stability restored with further aging (Adams et al., 2002).

*Sudden accidental, often unexpected traumatic degeneration or damage* of overload may yield the sudden loss of hydrostatic compression in nucleus, accompanied or due to some other failures mentioned above. In these cases the material of nucleus remains changeless, depending on the actual aging state in which the accidental effect happened. For this reason, sudden traumatic degenerations may be also dangerous in younger age.

Experimental analyses of spinal degenerations are very difficult, sometimes impossible. However, by means of numerical simulation, the effect of the main mechanical factors of degenerations can be analyzed.

#### **5. Finite element modeling of the lumbar spine**

Finite element modeling of any structure consists of five main steps: geometrical, material, element type and load modeling, and finally, validating the complete model.

#### **5.1 Geometrical modeling of the lumbar spine segments**

Geometrical modeling of the FSU must follow the anatomy of the segment. Beside the topology, additional data such as volume density, surface texture, etc. are needed. Different methods of medical image analyses can be used, like scanners, computer tomography, or magnetic resonance imaging methods.

In geometrical modeling the *vertebral body*, its cortical shell, cancellous core, posterior bony elements and the bony endplates are generally distinguished. For the width of the

Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 201

The high strength *bony endplate* of vertebrae and the lower strenght *cartiliginous endplate* of disc can hardly be distinguished when specifying material properties. Both bony and cartilaginous endplates are considered generally linear elastic isotropic material, with

The *posterior bony elements* are considered linear elastic isotropic material, generally by the

The *articular facet joints* are considered as unilateral friction or frictionless connections with

*Disc nucleus pulposus* is the most important element in the compressive stiffness of the disc: the hydrostatic compression in it guarantees the stability of the whole disc and segment. The healthy young nucleus is generally modeled as an incompressible fluid-like material. In the case of fluid like linear elastic isotropic solid generally the material moduli E=1-4 MPa with nu=0.49-0.499 are considered. Several authors model the nucleus as incompressible fluid, quasi incompressible fluid, hyperelastic neo-Hookean, or Mooney-Rivlin type material, moreover, poroelastic or viscoelastic or osmoviscoelastic solid with the concerning material

*Disc annulus fibrosus* is a typical composite-like material with a ground substance of many layers and fiber reinforcements. Material moduli of the ground substance are considered as E=2-10 MPa with nu=0.4-0.45, and of the fibers E=300-500 MPa depending of the radial

Numerical modeling of *ligaments*, as typical exponentially stiffening soft tissues is not a simple task. Generally, the seven ligaments are incorporated to the FE models as tension only elements. In contrast to its strong nonlinear behaviour (White and Panjabi, 1990), most

*Aging type degeneration* starts generally in the nucleus. A healthy young fluid-like nucleus is in a hydrostatic compression state. During aging, the nucleus loses its incompressibility and becomes even stiffer and stiffer, changing from fluid to solid material. This kind of nucleus degeneration can be modeled by decreasing Poisson's ratio with increasing Young's modulus. This behavior is generally accompanied by the stiffening process of the disc as a whole and by the volume reduction of the nucleus and volume extension of the annulus, furthermore, height reduction of the disc. Moreover, at the same time, annulus tears or internal annulus buckling, or break of the annular fibers, damage and crack or rupture of endplates, osteoporotic defects of vertebral cancellous bone can happen. Consequently, modeling age-related degeneration of FSU is a compound task; it must be done in progress,

In contrast to the age-related degeneration, in *sudden, often unexpected injurious degeneration* the nucleus may lose its incompressibility without any stiffening and volume change process. In this case the nucleus may quasi burst out and the hydrostatic compression may suddenly stop in it. This kind of nucleus degeneration can be modeled by suddenly decreasing Poisson's ratio with unchanged Young's modulus of nucleus (Kurutz and

of the reported FEM studies have adopted linear or bilinear elastic models.

**5.2.2 Material models of the degenerated lumbar segments** 

E=100-12000 MPa and nu=0.3-0.4, and E=20-25 MPa with nu=0.4, respectively.

same Young's modulus E=2500-3000 MPa and Poisson's coefficient nu=0.2-0.25.

an initial gap of generally 0.5-1 mm.

data (Kurutz, 2010).

position, with nu=0.3.

relating to a lifelong process.

cylindrical vertebral body, 40-45 mm, for the depth 30-35 mm, and for the height 25-29 mm is generally used. For the thickness of the vertebral cortical wall about 1-1.5 mm, and for the thickness of the cartilaginous endplates 0.5-1 mm, and for the thickness of the cartilage layer of facet joint 0.2 mm, for the area about 1.6 cm2 are generally used.

In geometrical modeling the *intervertebral disc*, for the height of it about 8-12 mm are generally used, depending on the sex and body height of the subject. In the disc model, the nucleus, the annulus ground substance, the annulus fibers and the cartilaginous endplates are generally distinguished. For the volumetric relation between annulus and nucleus, ratio 3:7 is generally used for the lumbar part L1-S1, and for the area ratio of nucleus 30-50% of the total disc area in cross section is generally used. The sagittal diameter length of the lumbar disc is about 36 mm, the lateral length is about 44 mm. For the orientation of annulus fibers to the mid cross-sectional area of the disc about 30° is used.

As for the cross sectional area of the *ligaments*, for the anterior longitudinal ligaments about 30-70 mm2, for the posterior longitudinal ligaments about 10-20 mm2, for the ligamentum flavum 40-100 mm2, for the capsular ligaments about 30-60 mm2, for the intertransverse ligaments 2-10 mm2, for the interspinous ligaments 30-40 mm2, for the supraspinous ligaments 25-40 mm2 are generally used.

In modeling the *degenerated segments*, the height of both the vertebrae and the disc is reduced. Volume reduction of the nucleus during aging is also considered.

#### **5.2 Material modeling of the lumbar spine segments**

Since FSU is a highly heterogeneous compound structure, the material modeling must be related to the components of it. First the material models of the healthy components are considered.

The detailed data of the material modeling based on the international literature can be studied in Kurutz (2010).

#### **5.2.1 Material models of the healthy lumbar segments**

The material models and constants of the components of FSU were generally obtained by experimental mechanical tests of certain specimens obtained from the given component.

The high strength *vertebral cortical shell* is generally considered linear elastic isotropic or transversely isotropic, orthotropic material. In linear elastic isotropic case its Young modulus is considered about 5000-12000 MPa with the Poisson ratio about nu=0.2-0.3. In linear elastic, transversely isotropic case these data are E=12000-22000 MPa and G=3000- 5000 MPa with nu=0.2-0.4 in the compressive direction, and E=8000-12000 MPa and G=3000- 5000 MPa with nu=0.4-0.5 perpendicularly.

The vertebral *cancellous bone* is modeled generally also as linear elastic isotropic or transversely isotropic, or orthotropic material. In linear elastic isotropic case its Young modulus is considered about 10-500 MPa with the Poisson ratio about nu=0.2-0.3. In linear elastic, transversely isotropic case these data are E=200-250 MPa and G=50-80 MPa with nu=0.3-0.35 in the compressive direction, and E=100-150 MPa and G=50-80 MPa with nu=0.3-0.45 perpendicularly.

cylindrical vertebral body, 40-45 mm, for the depth 30-35 mm, and for the height 25-29 mm is generally used. For the thickness of the vertebral cortical wall about 1-1.5 mm, and for the thickness of the cartilaginous endplates 0.5-1 mm, and for the thickness of the cartilage layer

In geometrical modeling the *intervertebral disc*, for the height of it about 8-12 mm are generally used, depending on the sex and body height of the subject. In the disc model, the nucleus, the annulus ground substance, the annulus fibers and the cartilaginous endplates are generally distinguished. For the volumetric relation between annulus and nucleus, ratio 3:7 is generally used for the lumbar part L1-S1, and for the area ratio of nucleus 30-50% of the total disc area in cross section is generally used. The sagittal diameter length of the lumbar disc is about 36 mm, the lateral length is about 44 mm. For the orientation of

As for the cross sectional area of the *ligaments*, for the anterior longitudinal ligaments about 30-70 mm2, for the posterior longitudinal ligaments about 10-20 mm2, for the ligamentum flavum 40-100 mm2, for the capsular ligaments about 30-60 mm2, for the intertransverse ligaments 2-10 mm2, for the interspinous ligaments 30-40 mm2, for the supraspinous

In modeling the *degenerated segments*, the height of both the vertebrae and the disc is

Since FSU is a highly heterogeneous compound structure, the material modeling must be related to the components of it. First the material models of the healthy components are

The detailed data of the material modeling based on the international literature can be

The material models and constants of the components of FSU were generally obtained by experimental mechanical tests of certain specimens obtained from the given component.

The high strength *vertebral cortical shell* is generally considered linear elastic isotropic or transversely isotropic, orthotropic material. In linear elastic isotropic case its Young modulus is considered about 5000-12000 MPa with the Poisson ratio about nu=0.2-0.3. In linear elastic, transversely isotropic case these data are E=12000-22000 MPa and G=3000- 5000 MPa with nu=0.2-0.4 in the compressive direction, and E=8000-12000 MPa and G=3000-

The vertebral *cancellous bone* is modeled generally also as linear elastic isotropic or transversely isotropic, or orthotropic material. In linear elastic isotropic case its Young modulus is considered about 10-500 MPa with the Poisson ratio about nu=0.2-0.3. In linear elastic, transversely isotropic case these data are E=200-250 MPa and G=50-80 MPa with nu=0.3-0.35 in the compressive direction, and E=100-150 MPa and G=50-80 MPa with

of facet joint 0.2 mm, for the area about 1.6 cm2 are generally used.

annulus fibers to the mid cross-sectional area of the disc about 30° is used.

reduced. Volume reduction of the nucleus during aging is also considered.

ligaments 25-40 mm2 are generally used.

considered.

studied in Kurutz (2010).

**5.2 Material modeling of the lumbar spine segments** 

**5.2.1 Material models of the healthy lumbar segments** 

5000 MPa with nu=0.4-0.5 perpendicularly.

nu=0.3-0.45 perpendicularly.

The high strength *bony endplate* of vertebrae and the lower strenght *cartiliginous endplate* of disc can hardly be distinguished when specifying material properties. Both bony and cartilaginous endplates are considered generally linear elastic isotropic material, with E=100-12000 MPa and nu=0.3-0.4, and E=20-25 MPa with nu=0.4, respectively.

The *posterior bony elements* are considered linear elastic isotropic material, generally by the same Young's modulus E=2500-3000 MPa and Poisson's coefficient nu=0.2-0.25.

The *articular facet joints* are considered as unilateral friction or frictionless connections with an initial gap of generally 0.5-1 mm.

*Disc nucleus pulposus* is the most important element in the compressive stiffness of the disc: the hydrostatic compression in it guarantees the stability of the whole disc and segment. The healthy young nucleus is generally modeled as an incompressible fluid-like material. In the case of fluid like linear elastic isotropic solid generally the material moduli E=1-4 MPa with nu=0.49-0.499 are considered. Several authors model the nucleus as incompressible fluid, quasi incompressible fluid, hyperelastic neo-Hookean, or Mooney-Rivlin type material, moreover, poroelastic or viscoelastic or osmoviscoelastic solid with the concerning material data (Kurutz, 2010).

*Disc annulus fibrosus* is a typical composite-like material with a ground substance of many layers and fiber reinforcements. Material moduli of the ground substance are considered as E=2-10 MPa with nu=0.4-0.45, and of the fibers E=300-500 MPa depending of the radial position, with nu=0.3.

Numerical modeling of *ligaments*, as typical exponentially stiffening soft tissues is not a simple task. Generally, the seven ligaments are incorporated to the FE models as tension only elements. In contrast to its strong nonlinear behaviour (White and Panjabi, 1990), most of the reported FEM studies have adopted linear or bilinear elastic models.

#### **5.2.2 Material models of the degenerated lumbar segments**

*Aging type degeneration* starts generally in the nucleus. A healthy young fluid-like nucleus is in a hydrostatic compression state. During aging, the nucleus loses its incompressibility and becomes even stiffer and stiffer, changing from fluid to solid material. This kind of nucleus degeneration can be modeled by decreasing Poisson's ratio with increasing Young's modulus. This behavior is generally accompanied by the stiffening process of the disc as a whole and by the volume reduction of the nucleus and volume extension of the annulus, furthermore, height reduction of the disc. Moreover, at the same time, annulus tears or internal annulus buckling, or break of the annular fibers, damage and crack or rupture of endplates, osteoporotic defects of vertebral cancellous bone can happen. Consequently, modeling age-related degeneration of FSU is a compound task; it must be done in progress, relating to a lifelong process.

In contrast to the age-related degeneration, in *sudden, often unexpected injurious degeneration* the nucleus may lose its incompressibility without any stiffening and volume change process. In this case the nucleus may quasi burst out and the hydrostatic compression may suddenly stop in it. This kind of nucleus degeneration can be modeled by suddenly decreasing Poisson's ratio with unchanged Young's modulus of nucleus (Kurutz and

Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 203

The loading system of numerical simulation applied by several authors can be studied in

The compressive strength of the lumbar spine varies between 2 kN and 14 kN, depending on the sex, age and bodymass (Adams et al, 2002). For injurious accidental degeneration load for compression about 5 kN can be considered for young, and about 3 kN for old subjects. The lumbar facet joints can resist about 2 kN for shear before fracture occurs. For torsion, damage is initiated when the applied torque rises to about 10-30 Nm. A combination of full backwards bending and 1 kN of compressive load can cause damage in the relating facet joint. In forward bending, injury can occur when the bending moment rises

By using FE models in a numerical simulation, the results should be trustworthy. For this reason, the models to be applied must be checked. Correlation between FE and experimental

In numerical simulations of biomechanics, for FE prediction accuracy assessment, a gold standard can be the experimental validation of numerical results. This enables the analyst to improve the quality and reliability of the FE model and the modeling methodology. If there is very poor agreement between the analytical and experimental data, by using certain numerical techniques for model updating allow the user to create improved models which

Kurutz and Oroszváry (2010) validated the lumbar segment model for both compression and tension and for both healthy and degenerated disc. Distribution of vertical compressive stresses of healthy and degenerated discs in the mid-sagittal horizontal section of the disc was compared with the experimental results of Adams et al. (1996, 2002), obtained by stress profilometry. In axial tension, the calculated disc elongations were compared with the in vivo measured elongations of Kurutz et al. (2003) and Kurutz (2006a) for healthy and degenerated segments in weightbath hydrotraction treatment (Kurutz and Bender, 2010).

**6. Finite element simulation of the behaviour of healthy and degenerated** 

Finite element analyses are able to simulate processes in progress that are impossible to measure experimentally, like spinal degeneration processes. 3D FE simulations of long-term age-related and sudden accidental degeneration processes of human lumbar spinal segments are presented to analyze the compression-related degeneration processes, moreover, to analyze the efficiency of the so-called weightbath hydrotraction treatment.

A 3D geometrical model of a typical lumbar segment L4-5 was created (Fig. 1a). The geometrical data of the segment were obtained by the anatomical measures of a typical lumbar segment (Denoziere, 2004). Cortical and cancellous bones of vertebrae were separately modeled, including posterior bony elements. The thickness of vertebral cortical walls and endplates were 0.35 and 0.5 mm, respectively. For this simple model, we kept the disc height constant by applying 10 mm height. Annulus fibrous consisted of ground substance and elastic fibers (Fig. 1b). Annulus matrix was divided to internal and external

Kurutz (2010).

to 50-80 Nm.

**5.5 Validation of the finite element models** 

represent reality much better than the original ones.

results can lead to use the FE model predictions with confidence.

**lumbar spine and underwater spinal traction therapy** 

Oroszváry, 2010). This behaviour is generally caused or accompanied by the tear or buckling of the internal annulus, break of the annular fibers, fracture of endplates, or collapse of vertebral cancellous bone, depending on the age in which the sudden accidental event happens. Namely, accidental failures can happen in a young disc, as well, or in any age and aging degeneration phases. These effects can be modeled by sudden damage of tissues of the concerning components of the segment. In contrast to the long term aging degeneration, these kinds of damage instability occurs suddenly, generally due to a mechanical overloading (Acaraglou et al., 1995).

The material modeling of segment degeneration can be studied in Kurutz (2010).

#### **5.3 Element type modeling of the lumbar segments**

The cancellous core and the posterior bony elements of *vertebrae* can be modeled as 3D solid continuum elements, as isoparametric 8-node hexahedral elements, or as 20- or 27-noded brick elements, moreover, as 10-noded tetrahedral elements. The cortical shell and the endplates can be modeled as thin shell elements, like 4-node shell elements. Quasi-rigid beam elements can connect the posterior vertebra with the medial transverse processes (pedicles) and from the medial transverse processes to the medial spinous process (lamina). Beam elements can also be used to represent the transverse and spinous processes. The bony surface of the facet joints can be represented by shell elements where beam elements link these facets to the lamina, simulating the inferior and superior articular processes. The facet joints can be modeled as 3D 8-noded surface-to-surface contact elements.

The *disc* annulus ground substance is generally modeled as 3D continuum elements. The collagen fibers can be modeled as truss elements or as reinforced bar (rebar) type elements embedded in 3D solid elements. The nucleus pulposus can be modeled as hydrostatic fluid volume elements.

The anterior and posterior longitudinal *ligament*s can be modeled as thin shell elements, or, the ligaments can be modeled as 2-noded axial elements, that is, tension only linear or nonlinear truss or cable or spring elements.

#### **5.4 Load models of the lumbar spine**

Loads on lumbar spinal motion segments depend on the aims of the analysis. The segment is generally supported rigidly along the inferior endplate of the lower vertebra, thus, the loads are generally applied on the superior endplate of the upper vertebra.

The loads can be applied as static or dynamic or cyclic loads. Constant static loads or incrementally changing quasi-static loads are generally applied in lumbar spine analyses. In load history analyses the basic loading types are the force or displacement loads, in a load or displacement controlled device.

For different loading, pre-compression is also applied for modeling the upper body weight as 700-1000 N, simulating the intervertebral pressure of standing position and additional compressive forces can be applied to the suitable areas of the endplates to simulate severe motions: 2000 N for lifting a load with straight legs in full flexion; 1000 N for full extension; 1300 N for full lateral bending. For flexion and extension and for axial torsion generally 10- 15 Nm is applied.

The loading system of numerical simulation applied by several authors can be studied in Kurutz (2010).

The compressive strength of the lumbar spine varies between 2 kN and 14 kN, depending on the sex, age and bodymass (Adams et al, 2002). For injurious accidental degeneration load for compression about 5 kN can be considered for young, and about 3 kN for old subjects. The lumbar facet joints can resist about 2 kN for shear before fracture occurs. For torsion, damage is initiated when the applied torque rises to about 10-30 Nm. A combination of full backwards bending and 1 kN of compressive load can cause damage in the relating facet joint. In forward bending, injury can occur when the bending moment rises to 50-80 Nm.

#### **5.5 Validation of the finite element models**

202 Finite Element Analysis – From Biomedical Applications to Industrial Developments

Oroszváry, 2010). This behaviour is generally caused or accompanied by the tear or buckling of the internal annulus, break of the annular fibers, fracture of endplates, or collapse of vertebral cancellous bone, depending on the age in which the sudden accidental event happens. Namely, accidental failures can happen in a young disc, as well, or in any age and aging degeneration phases. These effects can be modeled by sudden damage of tissues of the concerning components of the segment. In contrast to the long term aging degeneration, these kinds of damage instability occurs suddenly, generally due to a mechanical

The cancellous core and the posterior bony elements of *vertebrae* can be modeled as 3D solid continuum elements, as isoparametric 8-node hexahedral elements, or as 20- or 27-noded brick elements, moreover, as 10-noded tetrahedral elements. The cortical shell and the endplates can be modeled as thin shell elements, like 4-node shell elements. Quasi-rigid beam elements can connect the posterior vertebra with the medial transverse processes (pedicles) and from the medial transverse processes to the medial spinous process (lamina). Beam elements can also be used to represent the transverse and spinous processes. The bony surface of the facet joints can be represented by shell elements where beam elements link these facets to the lamina, simulating the inferior and superior articular processes. The facet

The *disc* annulus ground substance is generally modeled as 3D continuum elements. The collagen fibers can be modeled as truss elements or as reinforced bar (rebar) type elements embedded in 3D solid elements. The nucleus pulposus can be modeled as hydrostatic fluid

The anterior and posterior longitudinal *ligament*s can be modeled as thin shell elements, or, the ligaments can be modeled as 2-noded axial elements, that is, tension only linear or

Loads on lumbar spinal motion segments depend on the aims of the analysis. The segment is generally supported rigidly along the inferior endplate of the lower vertebra, thus, the

The loads can be applied as static or dynamic or cyclic loads. Constant static loads or incrementally changing quasi-static loads are generally applied in lumbar spine analyses. In load history analyses the basic loading types are the force or displacement loads, in a load or

For different loading, pre-compression is also applied for modeling the upper body weight as 700-1000 N, simulating the intervertebral pressure of standing position and additional compressive forces can be applied to the suitable areas of the endplates to simulate severe motions: 2000 N for lifting a load with straight legs in full flexion; 1000 N for full extension; 1300 N for full lateral bending. For flexion and extension and for axial torsion generally 10-

The material modeling of segment degeneration can be studied in Kurutz (2010).

joints can be modeled as 3D 8-noded surface-to-surface contact elements.

loads are generally applied on the superior endplate of the upper vertebra.

overloading (Acaraglou et al., 1995).

volume elements.

nonlinear truss or cable or spring elements.

**5.4 Load models of the lumbar spine** 

displacement controlled device.

15 Nm is applied.

**5.3 Element type modeling of the lumbar segments** 

By using FE models in a numerical simulation, the results should be trustworthy. For this reason, the models to be applied must be checked. Correlation between FE and experimental results can lead to use the FE model predictions with confidence.

In numerical simulations of biomechanics, for FE prediction accuracy assessment, a gold standard can be the experimental validation of numerical results. This enables the analyst to improve the quality and reliability of the FE model and the modeling methodology. If there is very poor agreement between the analytical and experimental data, by using certain numerical techniques for model updating allow the user to create improved models which represent reality much better than the original ones.

Kurutz and Oroszváry (2010) validated the lumbar segment model for both compression and tension and for both healthy and degenerated disc. Distribution of vertical compressive stresses of healthy and degenerated discs in the mid-sagittal horizontal section of the disc was compared with the experimental results of Adams et al. (1996, 2002), obtained by stress profilometry. In axial tension, the calculated disc elongations were compared with the in vivo measured elongations of Kurutz et al. (2003) and Kurutz (2006a) for healthy and degenerated segments in weightbath hydrotraction treatment (Kurutz and Bender, 2010).

#### **6. Finite element simulation of the behaviour of healthy and degenerated lumbar spine and underwater spinal traction therapy**

Finite element analyses are able to simulate processes in progress that are impossible to measure experimentally, like spinal degeneration processes. 3D FE simulations of long-term age-related and sudden accidental degeneration processes of human lumbar spinal segments are presented to analyze the compression-related degeneration processes, moreover, to analyze the efficiency of the so-called weightbath hydrotraction treatment.

A 3D geometrical model of a typical lumbar segment L4-5 was created (Fig. 1a). The geometrical data of the segment were obtained by the anatomical measures of a typical lumbar segment (Denoziere, 2004). Cortical and cancellous bones of vertebrae were separately modeled, including posterior bony elements. The thickness of vertebral cortical walls and endplates were 0.35 and 0.5 mm, respectively. For this simple model, we kept the disc height constant by applying 10 mm height. Annulus fibrous consisted of ground substance and elastic fibers (Fig. 1b). Annulus matrix was divided to internal and external

Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 205

Collagen fibers of the annulus were considered as bilinear elastic isotropic tension-only material. To simulate the radial variation of collagen in the fibers, the stiffness of them was increased outwards. All seven ligaments were integrated in the model with bilinear elastic

**6.1 Finite element simulation of age-related degeneration processes of lumbar spine**  Age-related degeneration starts generally in the nucleus. A healthy young nucleus is in hydrostatic compression state. During aging, the nucleus loses its incompressibility by changing gradually from fluid-like to solid material. This kind of nucleus degeneration was modeled by decreasing Poisson's ratio with increasing Young's modulus. This behavior is generally accompanied by the hardening process of the disc as a whole and by tears, buckling or fiber break of the annulus, and damage of endplates or vertebral cancellous bone. The data of five grades of normal aging degeneration process from healthy to fully degenerated case are seen in Table 2, by gradually decreasing Poisson's ratio with gradually increasing Young's modulus of nucleus, accompanied by aging of other tissues of FSU.

For our numerical experiments, the basic data of Table 1 were modified.

**grade 1** 

nucleus 1/0.499 3/0.45 9/0.4 27/0.35 81/0.3 annulus ground substance 4/0.45 4.5/0.45 5/0.45 5.5/0.45 6/0.45 cancellous bone 150/0.3 125/0.3 100/0.3 75/0.3 50/0.3 endplate 100/0.4 80/0.4 60/0.4 40/0.4 20/0.4

Table 2. Modeling of age-related degeneration process: material moduli of components of

and lower vertebra of FSU, by applying rigid load distributor plates at both surfaces.

Simulating aging degeneration processes, 1000 N axial compression load was applied, by considering that the lumbar compression load is about 60% of the total body weight, completed by the muscle forces being nearly the same (Nachemson, 1981; Sato et al., 1999). The compression load was distributed along the superior and inferior surface of the upper

Figure 2 illustrates the maximum stress rearrange in the mid-sagittal section of the disc during the degeneration process. While in a healthy disc in Fig. 2a, due to the hydrostatic compression stress state, the maximum compressive stresses occur in the middle of nucleus, in a fully degenerated disc in Fig. 2b, due to the lost hydrostatic compression, the maximum compressive stresses move outwards to the edge of nucleus, towards the annulus ring.

Figure 3a shows the change of mid-sagittal vertical compressive stresses for aging degeneration models of Table 2, in the middle and border of nucleus and in the internal and external nucleus, for 1000 N axial compressive load. The vertical stresses in the center and border of nucleus first decreased and later increased with aging, yielding stress minimum in the nucleus in mildly degenerated state. In the internal annulus monotonous stress decrease

**(healthy) grade 2 grade 3 grade 4 grade 5** 

**(fully deg.)** 

tension-only material.

**Grades of age-related degeneration\* (Young's mod/Poisson's ratio)**

\* Bony elements and annulus fibers are seen in Table 1

segments from healthy (1) to fully degenerated (5) phases

ring; with three layers of annulus fibers of 0.1 mm2 cross section. The geometry and orientation of facet joints were chosen according to Panjabi et al. (1993).

FE mesh was created in three steps (Fig. 1c). First the geometrical model of FSU was created by using Pro/Engineer code; then the FE mesh was generated by ANSYS Workbench; finally, the several components were integrated to the FE model by ANSYS Classic.

Fig. 1. The geometrical model of a) the segment and b) the intervertebral disc and c) the finite element mesh of the segment

The material moduli of the healthy segment (Table 1) were obtained from the literature (Rohlmann et al., 2006; Goel et al., 1995; Denoziere, 2004; Denoziere and Ku, 2006; Cheung et al., 2003; Antosik and Awrejcewicz, 1999; Noailly et al., 2007; Williams et al., 2007; Shirazi-Adl et al, 1984, 1986; Shirazi-Adl, 1989; Lavaste et al., 1992; Zander et al., 2004). For the bony elements and endplates we considered linear elastic isotropic materials for both tension and compression. Annulus ground substance and nucleus were considered linear elastic for both compression and tension. For the fluid-like healthy nucleus and for the annulus matrix also linear elastic material was considered.


\*external/middle/internal fibers, tension \*\*tension only

Table 1. Material moduli of the components of healthy segment

Collagen fibers of the annulus were considered as bilinear elastic isotropic tension-only material. To simulate the radial variation of collagen in the fibers, the stiffness of them was increased outwards. All seven ligaments were integrated in the model with bilinear elastic tension-only material.

For our numerical experiments, the basic data of Table 1 were modified.

204 Finite Element Analysis – From Biomedical Applications to Industrial Developments

ring; with three layers of annulus fibers of 0.1 mm2 cross section. The geometry and

FE mesh was created in three steps (Fig. 1c). First the geometrical model of FSU was created by using Pro/Engineer code; then the FE mesh was generated by ANSYS Workbench;

**Annulus fibers**

**Nucleus**

**Young's mod [MPa]** 

**Poisson's ratio** 

finally, the several components were integrated to the FE model by ANSYS Classic.

orientation of facet joints were chosen according to Panjabi et al. (1993).

**Annulus matrix**

a) b) c)

finite element mesh of the segment

linear elastic material was considered.

\*external/middle/internal fibers, tension \*\*tension only

Table 1. Material moduli of the components of healthy segment

**Components of FSU** 

Fig. 1. The geometrical model of a) the segment and b) the intervertebral disc and c) the

Vertebral cortical bone 12000 0,3 Vertebral cancellous bone 150 0,3 Posterior elements, facet 3500 0,3 Endplate 100 0,4 Annulus ground substance 4 0,45 Annulus fibers 500/400/300\* - Nucleus 1 0,499 Anterior longitud. ligament 8\*\* 0,35 Posterior longitud. ligament 10\*\* 0,35 Other ligaments 5\*\* 0,35

The material moduli of the healthy segment (Table 1) were obtained from the literature (Rohlmann et al., 2006; Goel et al., 1995; Denoziere, 2004; Denoziere and Ku, 2006; Cheung et al., 2003; Antosik and Awrejcewicz, 1999; Noailly et al., 2007; Williams et al., 2007; Shirazi-Adl et al, 1984, 1986; Shirazi-Adl, 1989; Lavaste et al., 1992; Zander et al., 2004). For the bony elements and endplates we considered linear elastic isotropic materials for both tension and compression. Annulus ground substance and nucleus were considered linear elastic for both compression and tension. For the fluid-like healthy nucleus and for the annulus matrix also

#### **6.1 Finite element simulation of age-related degeneration processes of lumbar spine**

Age-related degeneration starts generally in the nucleus. A healthy young nucleus is in hydrostatic compression state. During aging, the nucleus loses its incompressibility by changing gradually from fluid-like to solid material. This kind of nucleus degeneration was modeled by decreasing Poisson's ratio with increasing Young's modulus. This behavior is generally accompanied by the hardening process of the disc as a whole and by tears, buckling or fiber break of the annulus, and damage of endplates or vertebral cancellous bone. The data of five grades of normal aging degeneration process from healthy to fully degenerated case are seen in Table 2, by gradually decreasing Poisson's ratio with gradually increasing Young's modulus of nucleus, accompanied by aging of other tissues of FSU.


\* Bony elements and annulus fibers are seen in Table 1

Table 2. Modeling of age-related degeneration process: material moduli of components of segments from healthy (1) to fully degenerated (5) phases

Simulating aging degeneration processes, 1000 N axial compression load was applied, by considering that the lumbar compression load is about 60% of the total body weight, completed by the muscle forces being nearly the same (Nachemson, 1981; Sato et al., 1999).

The compression load was distributed along the superior and inferior surface of the upper and lower vertebra of FSU, by applying rigid load distributor plates at both surfaces.

Figure 2 illustrates the maximum stress rearrange in the mid-sagittal section of the disc during the degeneration process. While in a healthy disc in Fig. 2a, due to the hydrostatic compression stress state, the maximum compressive stresses occur in the middle of nucleus, in a fully degenerated disc in Fig. 2b, due to the lost hydrostatic compression, the maximum compressive stresses move outwards to the edge of nucleus, towards the annulus ring.

Figure 3a shows the change of mid-sagittal vertical compressive stresses for aging degeneration models of Table 2, in the middle and border of nucleus and in the internal and external nucleus, for 1000 N axial compressive load. The vertical stresses in the center and border of nucleus first decreased and later increased with aging, yielding stress minimum in the nucleus in mildly degenerated state. In the internal annulus monotonous stress decrease was observed, demonstrating the possible internal annulus buckling. In the external annulus the stresses slightly changed.

Fig. 2. Mid-sagittal vertical compressive stresses for a) healthy and b) fully degenerated disc

Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 207

maximum tensile forces in the outermost posterolateral annulus fibers in Fig 4b, that is, the maximum fiber forces belonged also to the mildly degenerated state. Fig. 5a and 5b illustrate

the tensile forces in healthy and fully degenerated annulus fibers, respectively.

a) b)

 a) b) Fig. 5. Annulus fiber forces for a) healthy and b) fully degenerated case

(Kurutz and Oroszváry, 2010)

Fig. 4. a) Height loss of disc and b) maximum fiber forces during aging degeneration

Fig. 6a illustrate the change of posterior, anterior and lateral disc bulging during aging degeneration process, demonstrating that the bulging deformability is maximum in young age or mild degeneration, and it decreases with aging. Fig. 6b shows the change of the mean vertical compressive stiffness of disc components during the aging degeneration process.

The stiffness of the whole disc depends mainly on the stiffness of the nucleus. In the first period of aging, the dominant effect is the loss of incompressibility of nucleus when the other disc components are considerable soft. This yields that the stresses and the vertical load transfer through the nucleus is minimum (Fig. 3a) and the deformability of disc is maximum in young age (Fig. 4a) leading to the minimum vertical compressive stiffness of

The minimum of each stiffness function belonged to the mildly degenerated state.

Fig. 3. a) Mid-sagittal vertical compressive stresses in disc components during aging degeneration and b) stress divergence in nucleus center during the loss of hydrostatic compression state in nucleus (Kurutz and Oroszváry, 2010).

In degenerated disc the pressure in the nucleus is not hydrostatic any more, being nonuniform and direction-dependent. In Fig. 3b the stress divergence is seen in the nucleus center between vertical and horizontal stresses, increasing rapidly and quasi linearly with the loss of hydrostatic compression in the nucleus. The initial stress divergence between vertical and horizontal stresses in hydrostatic state at nu=0.499 for the fluid-like nucleus of E=1 MPa was 8-10%, and naturally, for harder nucleus it was higher. By applying more fluid-like material for nucleus (E=0.1 MPa), the initial hydrostatic stress divergence could be decreased to 1-2%.

Fig. 4a illustrates the disc shortening with aging, demonstrating that the maximum disc deformability occurred in mild degeneration. Similar behaviour was observed for the

was observed, demonstrating the possible internal annulus buckling. In the external annulus

Fig. 2. Mid-sagittal vertical compressive stresses for a) healthy and b) fully degenerated disc

a) b)

a) b)

compression state in nucleus (Kurutz and Oroszváry, 2010).

decreased to 1-2%.

Fig. 3. a) Mid-sagittal vertical compressive stresses in disc components during aging degeneration and b) stress divergence in nucleus center during the loss of hydrostatic

In degenerated disc the pressure in the nucleus is not hydrostatic any more, being nonuniform and direction-dependent. In Fig. 3b the stress divergence is seen in the nucleus center between vertical and horizontal stresses, increasing rapidly and quasi linearly with the loss of hydrostatic compression in the nucleus. The initial stress divergence between vertical and horizontal stresses in hydrostatic state at nu=0.499 for the fluid-like nucleus of E=1 MPa was 8-10%, and naturally, for harder nucleus it was higher. By applying more fluid-like material for nucleus (E=0.1 MPa), the initial hydrostatic stress divergence could be

Fig. 4a illustrates the disc shortening with aging, demonstrating that the maximum disc deformability occurred in mild degeneration. Similar behaviour was observed for the

the stresses slightly changed.

maximum tensile forces in the outermost posterolateral annulus fibers in Fig 4b, that is, the maximum fiber forces belonged also to the mildly degenerated state. Fig. 5a and 5b illustrate the tensile forces in healthy and fully degenerated annulus fibers, respectively.

Fig. 4. a) Height loss of disc and b) maximum fiber forces during aging degeneration (Kurutz and Oroszváry, 2010)

Fig. 5. Annulus fiber forces for a) healthy and b) fully degenerated case

Fig. 6a illustrate the change of posterior, anterior and lateral disc bulging during aging degeneration process, demonstrating that the bulging deformability is maximum in young age or mild degeneration, and it decreases with aging. Fig. 6b shows the change of the mean vertical compressive stiffness of disc components during the aging degeneration process. The minimum of each stiffness function belonged to the mildly degenerated state.

The stiffness of the whole disc depends mainly on the stiffness of the nucleus. In the first period of aging, the dominant effect is the loss of incompressibility of nucleus when the other disc components are considerable soft. This yields that the stresses and the vertical load transfer through the nucleus is minimum (Fig. 3a) and the deformability of disc is maximum in young age (Fig. 4a) leading to the minimum vertical compressive stiffness of

Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 209

Simulating sudden accidental degeneration processes, the 1000 N axial compression load was completed by an unexpected sudden overload of 1000 N, thus, 2000 N axial

Fig. 7a shows the sudden change of the mid-sagittal vertical compressive stresses in disc components, Fig. 7b illustrates the mid-sagittal central, posterior and anterior disc shortening during the sudden degeneration process in young age with annulus tears and fiber break (Table 3). The mean stress decreased strongly in the nucleus (by 70%), and moderately in the internal annulus (by 25%), while slightly increased in the external annulus (by 8-10%). Disc shortening radically increased during the process, finally by about 200-

a) b)

a) b)

disc components during sudden degeneration process

Fig. 8. a) Posterior, anterior and lateral disc bulging and b) mean compressive stiffness of

Fig. 8a shows the sudden mid-sagittal anterior, posterior and lateral disc bulging. In Fig. 8b the mean compressive stiffness of disc components during the sudden degeneration process

shortening during sudden degeneration process

Fig. 7. a) Mid-sagittal vertical compressive stresses in disc components and b) disc

compression load was applied.

230%.

discs and the risk of instability of FSUs in mildly degenerated state (Fig. 6b.) Consequently, the lumbar segments are most vulnerable in young age, and the segmental stability increases with further aging and degeneration.

Fig. 6. a) Posterior, anterior and lateral disc bulging and b) mean compressive stiffness of disc components during aging degeneration (Kurutz and Oroszváry, 2010).

#### **6.2 Finite element simulation of sudden degeneration processes of lumbar spine**

In contrast to the age-related degeneration process that lasts during a lifelong time, the sudden degeneration has very short, sometimes unexpected, instant processes. For modeling sudden degeneration accompanied by other damaging phenomena, the data of the concerning tissues were modified in Table 1 and Table 2, depending on the actual aging degeneration phase in which the sudden accidental degeneration happened, considering also five phases of accidental degeneration process.

For example, data in Table 3 show the model of sudden degeneration in young age with annulus fiber breaks and tears. In this case the sudden degeneration happened in the first aging degeneration phase of Table 2, when the sudden loss of hydrostatic compression was modeled by rapid immediate decrease of Poisson ratio of nucleus with changeless Young's modulus of it. Annulus tears and fiber breaks were modeled by weakened annulus matrix and fibers, respectively, seen also in Table 3.


\* Bony elements are seen in Table 1

Table 3. Modeling of sudden degeneration process with annulus tears and fiber break in young age: modified material moduli of components of segments

discs and the risk of instability of FSUs in mildly degenerated state (Fig. 6b.) Consequently, the lumbar segments are most vulnerable in young age, and the segmental stability

a) b)

disc components during aging degeneration (Kurutz and Oroszváry, 2010).

Fig. 6. a) Posterior, anterior and lateral disc bulging and b) mean compressive stiffness of

**6.2 Finite element simulation of sudden degeneration processes of lumbar spine** 

In contrast to the age-related degeneration process that lasts during a lifelong time, the sudden degeneration has very short, sometimes unexpected, instant processes. For modeling sudden degeneration accompanied by other damaging phenomena, the data of the concerning tissues were modified in Table 1 and Table 2, depending on the actual aging degeneration phase in which the sudden accidental degeneration happened, considering

For example, data in Table 3 show the model of sudden degeneration in young age with annulus fiber breaks and tears. In this case the sudden degeneration happened in the first aging degeneration phase of Table 2, when the sudden loss of hydrostatic compression was modeled by rapid immediate decrease of Poisson ratio of nucleus with changeless Young's modulus of it. Annulus tears and fiber breaks were modeled by weakened annulus matrix

nucleus 1/0.499 1/0.45 1/0.40 1/0.35 1/0.3

substance 4/0.45 3.5/0.45 3/0.45 2.5/0.45 2/0.45 annulus fibers 500/400/300 375/300/225 250/200/150 125/100/75 5/4/3

Table 3. Modeling of sudden degeneration process with annulus tears and fiber break in

young age: modified material moduli of components of segments

**grade 1 grade 2 grade 3 grade 4 grade 5** 

increases with further aging and degeneration.

also five phases of accidental degeneration process.

and fibers, respectively, seen also in Table 3.

**Phases of sudden degeneration\* (Young's mod/Poisson's ratio)**

\* Bony elements are seen in Table 1

annulus ground

Simulating sudden accidental degeneration processes, the 1000 N axial compression load was completed by an unexpected sudden overload of 1000 N, thus, 2000 N axial compression load was applied.

Fig. 7a shows the sudden change of the mid-sagittal vertical compressive stresses in disc components, Fig. 7b illustrates the mid-sagittal central, posterior and anterior disc shortening during the sudden degeneration process in young age with annulus tears and fiber break (Table 3). The mean stress decreased strongly in the nucleus (by 70%), and moderately in the internal annulus (by 25%), while slightly increased in the external annulus (by 8-10%). Disc shortening radically increased during the process, finally by about 200- 230%.

Fig. 7. a) Mid-sagittal vertical compressive stresses in disc components and b) disc shortening during sudden degeneration process

Fig. 8. a) Posterior, anterior and lateral disc bulging and b) mean compressive stiffness of disc components during sudden degeneration process

Fig. 8a shows the sudden mid-sagittal anterior, posterior and lateral disc bulging. In Fig. 8b the mean compressive stiffness of disc components during the sudden degeneration process

Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 211

related degeneration process, in the indirect phase of traction, the compressive material moduli were used, seen in Table 2; while for the direct phase of traction, special tensile Young's moduli were applied, obtained by parameter identification (Kurutz and Tornyos, 2004), seen in Table 4. For healthy nucleus we applied fluid-like incompressible material

nucleus 0.4/0.499 1.0/0.45 1.6/0.4 2.2/0.35 2.8/0.3 annulus ground substance 0.4/0.45 1.0/0.45 1.6/0.45 2.2/0.45 2.8/0.45 cancellous bone 150/0.3 125/0.3 100/0.3 75/0.3 50/0.3 endplate 100/0.4 80/0.4 60/0.4 40/0.4 20/0.4

Table 4. Modeling of age-related degeneration process for direct traction in WHT: material moduli of components of segments from healthy (1) to fully degenerated (5) phases

The unloading effect of WHT in its instant elastic phase is illustrated in Fig. 9 and 10 in terms of aging degeneration. The term 'unloading' is relative: it is related to the compressed state of segments just before the treatment. Due to the bilinear behaviour of the disc during hydrotraction, the results of deformation and stress unloading are distinguished: caused by

a) b)

Fig. 9. Unloading effect of WHT on a) disc compression and b) posterior disc bulging

In Fig. 9a the relative elongations of discs are seen compared with their compressed state before the treatment. These initial elastic elongations will be quasi doubled in the creeping phase of WHT (Kurutz, 2006b). The ratio of direct traction extensions versus total extensions is 32%, 19%, 20%, 28% and 47% for degeneration grades 1 to 5, respectively. The ratios of direct/indirect extensions are: 47%, 24%, 25%, 39% and 89%. The minimum ratio belongs to

**grade 2 grade 3 grade 4 grade 5** 

**(fully deg.)** 

**grade 1 (healthy)** 

both for tension and compression.

**Grades of age-related degeneration for direct traction\* (Young's mod/Poisson's ratio)**

indirect and direct traction loads.

(Kurutz and Oroszváry, 2010).

\* Bony elements and annulus fibers are seen in Table 1

are illustrated. Disc bulging radically increased in all directions (by 80-200%) due to the fiber breaks with radically decreasing maximum fiber forces from 1.38 N to 0.06 N. Significant stiffness loss was observed for the disc components (nucleus 91%, internal annulus 70%, external annulus 62%). The stiffness loss of the whole disc was 76%.

During sudden degeneration process the vertical compressive load transfer moves from inside to outside, from the nucleus to the external annulus during the progress of degeneration. In the case of internal annulus buckling, the sudden overload of the external annulus may lead to annulus tears and injury. In the case of fiber break and annulus tears, the internal annulus is overloaded.

In contrast to age-related degeneration processes where the disc deformability (shortening, bulging) decreases during aging, in sudden degeneration processes the deformability increases strongly that may lead to injury and pain mainly in younger age. Also in contrast to age-related degeneration processes where the vertical compressive stiffness of discs increases during aging, in sudden degeneration processes it decreases significantly leading to segmental instability and injury. In agreement with the literature we have found by numerical simulation of age-related degeneration that the young and mildly degenerated segments had the smallest stiffness and later the stiffness increased rapidly (Adams et al., 2002; Rohlmann et al., 2006; Schmidt et al., 2006, 2007). Similarly to the age-related degeneration, accidental degeneration may be the most dangerous in young age, due to the sudden stiffness loss starting at the smallest stiffness level, consequently, accidental disc shortening and bulging may cause sudden injury and low back pain in young age again.

#### **6.3 Finite element simulation of weightbath hydrotraction treatment of lumbar spine**

Kurutz and Oroszváry (2010) analyzed by FE simulation the stretching effect of a special underwater traction treatment applied for treating degenerative diseases of the lumbar spine, when the patients are suspended cervically in vertical position in the water, supported on a cervical collar alone, loaded by extra lead weights on the ankles.

The biomechanics of WHT has been reported first by Bene and Kurutz (1993). Elongations of lumbar segments during WHT have been measured in vivo by Kurutz et al. (2003). The clinical impacts of WHT have been analyzed by Oláh et al. (2008). The complex description of WHT has been given by Kurutz and Bender (2010) with its application, biomechanics and clinical effects. This numerical study aims to determine the disc elongation, bulging contraction, stress and fiber relaxation effects of WHT during age-related degeneration.

In this underwater cervical suspension, the traction load consists of two parts: (1) the removal of the compressive preload of body weight and muscle forces in water, named *indirect traction load*; and (2) the tensile force of buoyancy with the applied extra lead loads, named *direct traction load*. Based on mechanical calculations, for the standard body weight of 700 N, and the applied extra lead weights 40 N, the indirect and direct traction loads yields 840 N and 50 N, respectively. Thus, for the numerical analysis of WHT we applied 840 *N* indirect and 50 N direct traction loads.

In the finite element analysis of WHT the above detailed material, geometric and finite element model has been used. Annulus ground substance and nucleus were considered linear elastic in compression, and bilinear elastic in traction. Thus, for the five grades of agerelated degeneration process, in the indirect phase of traction, the compressive material moduli were used, seen in Table 2; while for the direct phase of traction, special tensile Young's moduli were applied, obtained by parameter identification (Kurutz and Tornyos, 2004), seen in Table 4. For healthy nucleus we applied fluid-like incompressible material both for tension and compression.


\* Bony elements and annulus fibers are seen in Table 1

210 Finite Element Analysis – From Biomedical Applications to Industrial Developments

are illustrated. Disc bulging radically increased in all directions (by 80-200%) due to the fiber breaks with radically decreasing maximum fiber forces from 1.38 N to 0.06 N. Significant stiffness loss was observed for the disc components (nucleus 91%, internal annulus 70%,

During sudden degeneration process the vertical compressive load transfer moves from inside to outside, from the nucleus to the external annulus during the progress of degeneration. In the case of internal annulus buckling, the sudden overload of the external annulus may lead to annulus tears and injury. In the case of fiber break and annulus tears,

In contrast to age-related degeneration processes where the disc deformability (shortening, bulging) decreases during aging, in sudden degeneration processes the deformability increases strongly that may lead to injury and pain mainly in younger age. Also in contrast to age-related degeneration processes where the vertical compressive stiffness of discs increases during aging, in sudden degeneration processes it decreases significantly leading to segmental instability and injury. In agreement with the literature we have found by numerical simulation of age-related degeneration that the young and mildly degenerated segments had the smallest stiffness and later the stiffness increased rapidly (Adams et al., 2002; Rohlmann et al., 2006; Schmidt et al., 2006, 2007). Similarly to the age-related degeneration, accidental degeneration may be the most dangerous in young age, due to the sudden stiffness loss starting at the smallest stiffness level, consequently, accidental disc shortening and bulging may cause sudden injury and low back pain in young age again.

**6.3 Finite element simulation of weightbath hydrotraction treatment of lumbar spine**  Kurutz and Oroszváry (2010) analyzed by FE simulation the stretching effect of a special underwater traction treatment applied for treating degenerative diseases of the lumbar spine, when the patients are suspended cervically in vertical position in the water,

The biomechanics of WHT has been reported first by Bene and Kurutz (1993). Elongations of lumbar segments during WHT have been measured in vivo by Kurutz et al. (2003). The clinical impacts of WHT have been analyzed by Oláh et al. (2008). The complex description of WHT has been given by Kurutz and Bender (2010) with its application, biomechanics and clinical effects. This numerical study aims to determine the disc elongation, bulging contraction, stress and fiber relaxation effects of WHT during age-related degeneration.

In this underwater cervical suspension, the traction load consists of two parts: (1) the removal of the compressive preload of body weight and muscle forces in water, named *indirect traction load*; and (2) the tensile force of buoyancy with the applied extra lead loads, named *direct traction load*. Based on mechanical calculations, for the standard body weight of 700 N, and the applied extra lead weights 40 N, the indirect and direct traction loads yields 840 N and 50 N, respectively. Thus, for the numerical analysis of WHT we applied 840 *N*

In the finite element analysis of WHT the above detailed material, geometric and finite element model has been used. Annulus ground substance and nucleus were considered linear elastic in compression, and bilinear elastic in traction. Thus, for the five grades of age-

supported on a cervical collar alone, loaded by extra lead weights on the ankles.

external annulus 62%). The stiffness loss of the whole disc was 76%.

the internal annulus is overloaded.

indirect and 50 N direct traction loads.

Table 4. Modeling of age-related degeneration process for direct traction in WHT: material moduli of components of segments from healthy (1) to fully degenerated (5) phases

The unloading effect of WHT in its instant elastic phase is illustrated in Fig. 9 and 10 in terms of aging degeneration. The term 'unloading' is relative: it is related to the compressed state of segments just before the treatment. Due to the bilinear behaviour of the disc during hydrotraction, the results of deformation and stress unloading are distinguished: caused by indirect and direct traction loads.

Fig. 9. Unloading effect of WHT on a) disc compression and b) posterior disc bulging (Kurutz and Oroszváry, 2010).

In Fig. 9a the relative elongations of discs are seen compared with their compressed state before the treatment. These initial elastic elongations will be quasi doubled in the creeping phase of WHT (Kurutz, 2006b). The ratio of direct traction extensions versus total extensions is 32%, 19%, 20%, 28% and 47% for degeneration grades 1 to 5, respectively. The ratios of direct/indirect extensions are: 47%, 24%, 25%, 39% and 89%. The minimum ratio belongs to

Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 213

stiffness of disc at mildly degenerated state. In sudden degeneration processes the smallest stiffness happened also in mildly degenerated state. The 2100 N/mm stiffness suddenly decreased by 75-80% to 400-500 N/mm for mild, and the 3600 N/mm stiffness decreased by 60-65% to 1300 N/mm for severely degenerated case. Vertical intradiscal stresses showed significant change during aging degeneration, between 0.6-1.6 MPa. Disc deformability and bulging was maximum in mildly degenerated state and decreased during aging by 30-85%,

As for conclusion, FE simulations of degeneration processes of lumbar segments and discs may help clinicians to understand the initiation and progression of disc degeneration and will help to improve prevention methods and treating tools for regeneration of disc tissues. In WHT, discs show a bilinear material behaviour with higher resistance in indirect and smaller in direct traction phase. Consequently, although the direct traction load is only 6% of the indirect one, direct traction deformations are 15-90% of the indirect ones, depending on the grade of degeneration. Moreover, the ratio of direct stress relaxation remains equally about 6-8% only. Consequently, direct traction controlled by extra lead weights influences mostly the deformations being responsible for the nerve release; while the stress relaxation is influenced mainly by the indirect traction load coming from the removal of the compressive body weight and muscle forces in the water. A mildly degenerated disc in WHT shows 0.15 mm direct, 0.45 mm indirect and 0.6 mm total extension; and 0.2 mm direct, 0.6 mm indirect and 0.8 mm total posterior contraction. A severely degenerated disc exhibits 0.05 mm direct, 0.05 mm indirect and 0.1 mm total extension; 0.05 mm direct, 0.25 mm indirect and 0.3 mm total posterior contraction. These deformations are related to the instant elastic phase of WHT that are doubled during the creep period of the treatment.

As for conclusion, WHT unloads the compressed disc: extends disc height, decreases bulging, stresses and fiber forces, increases joint flexibility, relaxes muscles, unloads nerve roots, relieves pain and may prevent graver problems. WHT is an effective non-invasive method to treat lumbar discopathy. By the presented numerical analysis its beneficial clinical impacts can be supported, moreover, the treatment could be planned, the magnitudes of extra loads could be determined by considering the patient's clinical status.

The present study was supported by the Hungarian National Science Foundation projects OTKA T-022622, T-033020, T-046755 and K-075018. The authors are grateful to Knorr Bremse

Acaroglu, E.R., Iatridis, J.C., Setton, L.A., Foster, R.J., Mow, V.C., Weidenbaum, M. (1995).

Adams, M.A., Bogduk, N., Burton, K., Dolan, P. (2002). *The Biomechanics of Back Pain*,

Adams, M.A., Freeman, B.J., Morrison, H.P., Nelson, I.W., Dolan, P. (2000), Mechanical initiation of intervertebral disc degeneration, *Spine,* 25(13), 1625-1636.

Degeneration and aging affect the tensile behaviour of human lumbar anulus

while in sudden degeneration increased suddenly by 200-300%.

**8. Acknowledgment** 

**9. References** 

Hungaria for the help in FE modeling of FSU.

fibrosus, *Spine*, 20(24), 2690-2701.

Churchill Livingstone, London.

the mild degeneration and increases rapidly with advanced degeneration and aging. The maximum ratio belongs to the fully degenerated cases.

The unloading of posterior bulging, namely, the relative disc contractions can be seen in Fig. 9b. The ratio of direct/total traction contractions decreases monotonously from 27% to 15% for posterior bulging for degeneration grades 1 to 5. The ratio of direct/indirect contractions changes from 37% to 18% in posterior bulging. The minimum ratio belongs to the fully degenerated case.

Fig. 10a and 10b show the vertical stress relaxation in the centre of nucleus and in the annulus external ring. The ratio of direct/total and direct/indirect stress unloading is equally small, 7-8% in healthy and 2-4% in fully degenerated cases. Thus, in stress relaxation the dominant effect is the indirect traction load.

Fig. 10. Stress unloading effect of WHT a) in nucleus centre and b) in the external annulus (Kurutz and Oroszváry, 2010).

It can be concluded that direct traction load with extra lead weights influences mainly the deformations that are responsible for nerve release, while stress relaxation is influenced mainly by the indirect traction load. The traction effect can be increased by applying larger extra lead weights.

#### **7. Conclusion**

After a short survey of the structural anatomy and biomechanics of healthy and degenerated lumbar spine, FE modeling and a systematic numerical analysis of the main mechanical features of lumbar spine degenerations was investigated to study the agerelated and sudden degeneration processes of it. The fact that mildly degenerated segments have the smallest stiffness both in aging and sudden degeneration processes was numerically proved by answering the question why the LBP problems insult so frequently the young adults.

At the beginning of aging degeneration process, the effect of loss of incompressibility of nucleus, later the hardening of nucleus dominated, yielding the smallest compressive stiffness of disc at mildly degenerated state. In sudden degeneration processes the smallest stiffness happened also in mildly degenerated state. The 2100 N/mm stiffness suddenly decreased by 75-80% to 400-500 N/mm for mild, and the 3600 N/mm stiffness decreased by 60-65% to 1300 N/mm for severely degenerated case. Vertical intradiscal stresses showed significant change during aging degeneration, between 0.6-1.6 MPa. Disc deformability and bulging was maximum in mildly degenerated state and decreased during aging by 30-85%, while in sudden degeneration increased suddenly by 200-300%.

As for conclusion, FE simulations of degeneration processes of lumbar segments and discs may help clinicians to understand the initiation and progression of disc degeneration and will help to improve prevention methods and treating tools for regeneration of disc tissues.

In WHT, discs show a bilinear material behaviour with higher resistance in indirect and smaller in direct traction phase. Consequently, although the direct traction load is only 6% of the indirect one, direct traction deformations are 15-90% of the indirect ones, depending on the grade of degeneration. Moreover, the ratio of direct stress relaxation remains equally about 6-8% only. Consequently, direct traction controlled by extra lead weights influences mostly the deformations being responsible for the nerve release; while the stress relaxation is influenced mainly by the indirect traction load coming from the removal of the compressive body weight and muscle forces in the water. A mildly degenerated disc in WHT shows 0.15 mm direct, 0.45 mm indirect and 0.6 mm total extension; and 0.2 mm direct, 0.6 mm indirect and 0.8 mm total posterior contraction. A severely degenerated disc exhibits 0.05 mm direct, 0.05 mm indirect and 0.1 mm total extension; 0.05 mm direct, 0.25 mm indirect and 0.3 mm total posterior contraction. These deformations are related to the instant elastic phase of WHT that are doubled during the creep period of the treatment.

As for conclusion, WHT unloads the compressed disc: extends disc height, decreases bulging, stresses and fiber forces, increases joint flexibility, relaxes muscles, unloads nerve roots, relieves pain and may prevent graver problems. WHT is an effective non-invasive method to treat lumbar discopathy. By the presented numerical analysis its beneficial clinical impacts can be supported, moreover, the treatment could be planned, the magnitudes of extra loads could be determined by considering the patient's clinical status.

### **8. Acknowledgment**

The present study was supported by the Hungarian National Science Foundation projects OTKA T-022622, T-033020, T-046755 and K-075018. The authors are grateful to Knorr Bremse Hungaria for the help in FE modeling of FSU.

#### **9. References**

212 Finite Element Analysis – From Biomedical Applications to Industrial Developments

the mild degeneration and increases rapidly with advanced degeneration and aging. The

The unloading of posterior bulging, namely, the relative disc contractions can be seen in Fig. 9b. The ratio of direct/total traction contractions decreases monotonously from 27% to 15% for posterior bulging for degeneration grades 1 to 5. The ratio of direct/indirect contractions changes from 37% to 18% in posterior bulging. The minimum ratio belongs to the fully

Fig. 10a and 10b show the vertical stress relaxation in the centre of nucleus and in the annulus external ring. The ratio of direct/total and direct/indirect stress unloading is equally small, 7-8% in healthy and 2-4% in fully degenerated cases. Thus, in stress relaxation

maximum ratio belongs to the fully degenerated cases.

the dominant effect is the indirect traction load.

(Kurutz and Oroszváry, 2010).

frequently the young adults.

extra lead weights.

**7. Conclusion** 

a) b)

Fig. 10. Stress unloading effect of WHT a) in nucleus centre and b) in the external annulus

It can be concluded that direct traction load with extra lead weights influences mainly the deformations that are responsible for nerve release, while stress relaxation is influenced mainly by the indirect traction load. The traction effect can be increased by applying larger

After a short survey of the structural anatomy and biomechanics of healthy and degenerated lumbar spine, FE modeling and a systematic numerical analysis of the main mechanical features of lumbar spine degenerations was investigated to study the agerelated and sudden degeneration processes of it. The fact that mildly degenerated segments have the smallest stiffness both in aging and sudden degeneration processes was numerically proved by answering the question why the LBP problems insult so

At the beginning of aging degeneration process, the effect of loss of incompressibility of nucleus, later the hardening of nucleus dominated, yielding the smallest compressive

degenerated case.


Finite Element Modeling and Simulation of Healthy and Degenerated Human Lumbar Spine 215

Kurutz, M, Bender, T. (2010). Weightbath hydrotraction treatment: application,

Kurutz, M., Oroszváry, L. (2010). Finite element analysis of weightbath hydrotraction

Kurutz, M., Tornyos, Á., (2004). Numerical simulation and parameter identification of

Kurutz, M., Bene É., Lovas, A., (2003). In vivo deformability of human lumbar spine

Lavaste, F., Skalli, W., Robin, S., Roy-Camille, R., Mazel, C., (1992). Three-dimensional

McGill, S.M. (2000). Biomechanics of the thoracolumbar spine, In: Dvir, Z. (Ed.), *Clinical* 

McNally, D.S., Adams, M.A. (1992). Internal intervertebral disc mechanics as revealed by

Moll, K., (1956). Die Behandlung der Discushernien mit den sogenannten

Moll, K., (1963). The role of traction therapy in the rehabilitation of discopathy, *Rheum.* 

Mosekilde, L. (2000). Age-related changes in bone mass, structure, and strength effects of

Natarajan, R.N., Williams, J.R., Andersson, G.B., (2004). Recent advances in analytical

Noailly, J., Wilke, H.J., Planell, J.A., Lacroix, D., (2007). How Does the Geometry Affect the

Panjabi, M.M., Oxland, T., Takata, K., Goel, V., Duranceau, J., Krag, M., (1993). Articular

Ramos, G., Martin, W., (1994). Effects of vertebral axial decompression on intradiscal

Rohlmann, A., Zander, T., Schmidt, H., Wilke, H.J., Bergmann, G., (2006). Analysis of the

Internal Biomechanics of a Lumbar Spine Bi-segment Finite Element Model? Consequences on the Validation Process, *Journal of Biomechanics*, 40(11), 2414-2425. Oláh, M., Molnár, L., Dobai, J., Oláh, C., Fehér, J., Bender, T., (2008). The effects of

weightbath traction hydrotherapy as a component of complex physical therapy in disorders of the cervical and lumbar spine: a controlled pilot study with follow-up,

Facets of the Human Spine, Quantitative Three-dimensional Anatomy, *Spine*,

influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method, *Journal of Biomechanics*, 39(13), 2484-2490.

modelling of lumbar disc degeneration. *Spine*, 29(23), 2733-2741.

27.

*Biomechanics,* 43(3), 433-441.

*Bioengineering and Biomechanics, 5*(1), 67-92.

sress profilometry, *Spine*, 17(1), 66-73.

*Rheumatology International*, 28(8), 749-756.

pressure, *Journal of Neurosurgery*. 81(3), 350-353.

*Balneol. Allerg., 3,* 174-177.

18(10), 1298-1310.

"Gewichtsbadern", *Contempl. Rheum., 97*, 326-329.

loading, *Zeitschrift für Rheumatologie*, 59(Suppl.1), 1-9. Nachemson, A.L. (1981). Disc pressure measurements, *Spine,* 6(1), 93-97.

963 420 799 5, 254-263.

25(10), 1153-1164.

103-139.

biomechanics and clinical effects, *Journal of Multidisciplinary Healthcare*, 2010(3), 19-

treatment of degenerated lumbar spine segments in elastic phase, *Journal of* 

human lumbar spine segments in traction, In: Bojtár I. (ed.): *Proc. of the First Hungarian Conference on Biomechanics*, Budapest, Hungary, June 10-11, 2004, ISBN

segments in pure centric tension, measured during traction bath therapy, *Acta of* 

Geometrical and Mechanical Modelling of Lumbar Spine, *Journal of Biomechanics*,

*Biomechanics*, Churchill Livingstone, New York, Edinburgh, London, Philadelphia,


Adams, M.A., McNally, D.S., Dolan, P. (1996). Stress distributions inside intervertebral discs. The effects of age and degeneration. *J. Bone Joint Surg. Br.* 78(6), 965-972. Andersson, G.B., Schultz, A.B., Nachemson, A.L., (1983). Intervertebral disc pressures

Antosik, T., Awrejcewicz, J., (1999). Numerical and Experimental Analysis of Biomechanics

Bader, D.L., Bouten, C. (2000). Biomechanics of soft tissues. In: Dvir, Z. (Ed.), *Clinical* 

Bene, É., (1988). Das Gewichtbad, Zeitschrift für Physikalische Medizin, Balneologie,

Bene É., Kurutz, M., (1993). Weightbath and its biomechanics, (in Hungarian), *Orvosi Hetilap*,

Benzel, E.C.: *Biomechanics of Spine Stabilization,* (2001). American Association of Neurological

Bogduk, N., Twomey, L.T. (1987). *Clinical Anatomy of the Lumbar Spine,* Churchill

Cassinelli, E., Kang, J.D. (2000). Current understanding of lumbar disc degeneration,

Cheung, J.T.M., Zhang, M., Chow, D.H.K., (2003). Biomechanical Responses of the

Denoziere, G., (2004). *Numerical Modeling of Ligamentous Lumbar Motion Segment*, Master

Denoziere, G., Ku, D.N., (2006). Biomechanical Comparison Between Fusion of Two

Dolan, P., Adams, M.A. (2001). Recent advances in lumbar spinal mechanics and their

Dvir, Z. (2000). *Clinical Biomechanics,* Churchill Livingstone, New York, Edinburgh, London,

Ferguson, S.J., Steffen, T. (2003). Biomechanics of the aging spine, *European Spine Journal*,

Goel, V.K., Monroe, B.T., Gilbertson, L.G., Brinckmann, P. (1995). Interlaminar shear stresses

Kurutz, M. (2006a). Age-sensitivity of time-related in vivo deformability of human lumbar

Kurutz, M., (2006b). In vivo age- and sex-related creep of human lumbar motion segments and discs in pure centric tension, *Journal of Biomechanics, 39*(7), 1180-9*.* Kurutz, M. (2010). Finite element modeling of the human lumbar spine, In: Moratal, D. (ed.):

and laminae separation in the disc. Finite element analysis of the L3-L4 motion

motion segments and discs in pure centric tension, *Journal of Biomechanics, 39*(1),

significance for modelling, *Clinical Biomechanics, 16(Suppl.),* S8-S16*.* 

segment subjected to axial compressive loads. *Spine*, 20(6), 689-698.

*Finite Element Analysis*, SCIYO, Rijeka, 690 p., 209-236.

Intervertebral Joints to Static and Vibrational Loading: a Finite Element Study,

Vertebrae and Implantation of an Artificial Intervertebral Disc, *Journal of* 

of Three Lumbar Vertebrae, *Journal of Theoretical and Applied Mechanics*, 37(3). 413-

*Biomechanics*, Churchill Livingstone, New York, Edinburgh, London, Philadelphia,

during traction, *Scand. J. Rehabil. Med.* Suppl. 9, 88-91.

*Medizinische Klimatologie*. 17, 67-71.

Surgeons, Rolling Meadows, Illinois.

*Clinical Biomechnaics*, 18(9), 790-799.

*Biomechanics,* 39(4), 766-775.

Philadelphia.

147-157*.* 

Suppl 2, S97-S103.

*Operative Techniques in Orthopaedics*, 10(4), 254-262.

thesis, Georgia Institute of Technology, 148 p.

434.

35-64.

134. 21. 1123-1129.

Livingstone, New York.


**9**

*Spain* 

Luis Gracia et al.\*

**Simulation by Finite Elements**

**Implantation of Femoral Stems**

*Engineering and Architecture Faculty, University of Zaragoza,* 

Degenerative osteoarthritis and rheumatoid diseases lead to a severe destruction of the hip joint and to an important functional disability of the patient. Several attempts by many surgeons were documented, in the history of Orthopedic Surgery, to restore an adequate function of the pathologic joint. All these attempts failed due to the use of inadequate

In the past 20th century, during the sixties, a successful replacement of a pathologic hip joint was finally achieved. It was the first arthroplasty of the hip providing a good functional outcome. This new technique was described by Charnley in 1961 (Charnley, 1961). Two materials were then introduced in the orthopedic surgery, the polyethylene and the polymethyl methacrylate. This later is known as bone cement, and allowed a good fixation of the prosthetic implants into the femoral canal and the pelvic acetabulum. This technique represented one of the most important advances in the Orthopedic Surgery during the 20th

Based on the original model developed by Charnley, total cemented hip implants have been improved with new materials and prosthetic designs. The most important advances have been described in the cements and cementation techniques (Mulroy & Harris, 1990; Noble et al., 1998; Reading et al., 2000), and in the sterilization and manufacture of the prosthetic polyethylene (Medel et al., 2004; Urries et al., 2004; D'Antonio et al, 2005; Oral et al., 2006; Faris et al., 2006; Gordon et al., 2006; Wolf et al., 2006). Nevertheless, the original stem

First generation cemented prosthesis, inserted by manual techniques (first generation cement fixation), were associated with high rates of aseptic loosening and mechanical failures (Olsson et al., 1981; Stauffer, 1982; Harris et al., 1982; Halley & Wroblewski, 1986;

Elena Ibarz1, José Cegoñino1, Antonio Lobo-Escolar2,3, Sergio Gabarre1, Sergio Puértolas1,

design of Charnley remains unaltered and fully operational.

*1Engineering and Architecture Faculty, University of Zaragoza, Spain* 

Enrique López1, Jesús Mateo2,3, Antonio Herrera2,3

*2Medicine School, University of Zaragoza, Spain 3Miguel Servet University Hospital, Zaragoza, Spain* 

**1. Introduction** 

century.

\*

materials or due to technical problems.

**of Bone Remodelling After** 


### **Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems**

Luis Gracia et al.\* *Engineering and Architecture Faculty, University of Zaragoza, Spain* 

#### **1. Introduction**

216 Finite Element Analysis – From Biomedical Applications to Industrial Developments

Sato, K., Kikuchi, S., Yonezawa, T. (1999). In vivo intradiscal pressure measurement in

Schmidt, H., Heuer, F., Simon, U., Kettler, A., Rohlmann, A., Claes, L., Wilke, H.J., (2006).

Schmidt, H., Kettler, A., Rohlmann, A., Claes, L., Wilke, H,J.. (2007). The Risk of Disc

Shirazi-Adl, A., (1989). On the Fibre Composite Material Models of the Annulus – Comparison of Predicted Stresses. *Journal of Biomechanics*, 22(4), 357-365. Shirazi-Adl, S.A., Shrivastava, S.C., Ahmed, A.M., (1984). Stress Analysis of the Lumbar

Shirazi-Adl, A., Ahmed, A.M., Shrivastava, S.C., (1986). A Finite Element Study of a Lumbar

White, A. A., Panjabi, M. M. (1990). *Clinical Biomechanics of the Spine*, Lippincott Williams

Williams, J.R., Natarajan, R.N., Andersson, G.B.J., (2007). Inclusion of Regional Poroelastic

Subjected to Dynamic Loading, *Journal of Biomechanics*, 40(9), 1981-1987. Zander, T., Rohlmann, A., Bergmann, G., (2004). Influence of Ligament Stiffness on the

Finite Element Analysis, *Clinical Biomechanics*, 22(9), 988-998.

2468-2474.

Study, *Spine*, 9(2), 120-34.

and Wilkins, Philadelphia, etc.

19(4), 331-350.

1107-1111.

healthy individuals and in patients with ongoing back problems, *Spine,* 24(23),

Application of a New Calibration Method for a Three-dimensional Finite Element Model of a Human Lumbar Annulus Fibrosus, *Clinical Biomechanics*, 21(4), 337-344.

Prolapses With Complex Loading in Different Degrees of Disc Degeneration - a

Disc-body unit in Compression. A Three-dimensional Nonlinear Finite Element

Motion Segment Subjected to Pure Sagittal Plane Moments, *Journal of Biomechanics*,

Material Properties Better Predicts Biomechanical Behaviour of Lumbar Discs

Mechanical Behaviour of a Functional Spinal Unit, *Journal of Biomechanics,* 37(7),

Degenerative osteoarthritis and rheumatoid diseases lead to a severe destruction of the hip joint and to an important functional disability of the patient. Several attempts by many surgeons were documented, in the history of Orthopedic Surgery, to restore an adequate function of the pathologic joint. All these attempts failed due to the use of inadequate materials or due to technical problems.

In the past 20th century, during the sixties, a successful replacement of a pathologic hip joint was finally achieved. It was the first arthroplasty of the hip providing a good functional outcome. This new technique was described by Charnley in 1961 (Charnley, 1961). Two materials were then introduced in the orthopedic surgery, the polyethylene and the polymethyl methacrylate. This later is known as bone cement, and allowed a good fixation of the prosthetic implants into the femoral canal and the pelvic acetabulum. This technique represented one of the most important advances in the Orthopedic Surgery during the 20th century.

Based on the original model developed by Charnley, total cemented hip implants have been improved with new materials and prosthetic designs. The most important advances have been described in the cements and cementation techniques (Mulroy & Harris, 1990; Noble et al., 1998; Reading et al., 2000), and in the sterilization and manufacture of the prosthetic polyethylene (Medel et al., 2004; Urries et al., 2004; D'Antonio et al, 2005; Oral et al., 2006; Faris et al., 2006; Gordon et al., 2006; Wolf et al., 2006). Nevertheless, the original stem design of Charnley remains unaltered and fully operational.

First generation cemented prosthesis, inserted by manual techniques (first generation cement fixation), were associated with high rates of aseptic loosening and mechanical failures (Olsson et al., 1981; Stauffer, 1982; Harris et al., 1982; Halley & Wroblewski, 1986;

Enrique López1, Jesús Mateo2,3, Antonio Herrera2,3

<sup>\*</sup> Elena Ibarz1, José Cegoñino1, Antonio Lobo-Escolar2,3, Sergio Gabarre1, Sergio Puértolas1,

*<sup>1</sup>Engineering and Architecture Faculty, University of Zaragoza, Spain* 

*<sup>2</sup>Medicine School, University of Zaragoza, Spain* 

*<sup>3</sup>Miguel Servet University Hospital, Zaragoza, Spain* 

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 219

loads caused by implantation of the prosthesis in the femur, the physical characteristics of the implant (size, implant design and alloy), and the type of anchoring in the femur: metaphyseal, diaphyseal, hybrid, etc. (Summer & Galante, 1992; Sychter & Engh, 1996; Rubash et al., 1998; McAuley et al., 2000; Gibson et al., 2001; Glassman et al., 2001). Biologics are related to age and weight of the individual, initial bone mass, quality of primary fixation and loads applied to the implant. Of these biological factors, the most important is initial

Orthopedic surgeons have taken many years to learn the biomechanics and biology of bone tissue. We began to focus on these sciences when long-term revisions of cemented and cementless femoral stems proved extensive atrophy of the femoral cortical bone, a pathological phenomenon caused by *stress-shielding*. Different models of cementless stems have tried to achieve perfect load transfer to the femur, mimicking the physiological transmission from the femoral calcar to the femoral shaft. The main objective was to avoid stress-shielding, since in absence of physiological transmission of loads, and lack of

Cemented stem fixation is achieved by the introduction of cement into bone, forming a bone-cement interface. Inside the cement mantle a new interface is made up between cement and stem. It might seem that the cement mantle enables better load distribution in the femur; however the design, material and surface of prostheses, play an important role in transmission and distribution of charges, influencing bone remodeling (Ramaniraka et al.,

Long-term follow-up of different models of cementless stems have shown that this is not achieved, and to a greater or lesser extent the phenomenon of stress-shielding is present in all the models, and therefore the proximal bone atrophy. It is interesting to know, in cemented stems, not only the stress-shielding and subsequent proximal bone atrophy, but also the long-term behavior of cement-bone and stem-cement interfaces. This requires long-

Research in different fields concerning Orthopaedic Surgery and Traumatology requires a methodology that allows, at the same time, a more economic approach and the possibility of reproducing in an easy way different situations. Such a method could be used as a guide for research on biomechanics of the locomotor system, both in healthy and pathologic conditions, along with the study of performance of different prostheses and implants. To that effect, the use of simulation models, introduced in the field of Bioengineering in recent years, can undoubtedly mean an essential tool to assess the best clinical option, provided that it will be accurate enough in the analysis of specific physiological conditions concerning

Finite element (FE) simulation has proved to be specially suitable in the study of the behaviour of any physiological unit, despite its complexity. Nowadays, it has become a powerful tool in the field of Orthopaedic Surgery and Traumatology, helping the surgeons to have a better understanding of the biomechanics, both in healthy and pathological conditions. FE simulation let us know the biomechanical changes that occur after prosthesis or osteosynthesis implantation, and biological responses of bone to biomechanical changes. It also has an additional advantage in predicting the changes in the stress distribution around the implanted zones, allowing preventing future pathologies derived from an

mechanical stimulus in this area, causes proximal bone atrophy.

term studies monitoring the different models of stems.

bone mass (Sychter & Engh, 1996).

2000; Li et al., 2007)

certain pathology.

unsuitable positioning of the prostheses.

Mohler et al., 1995). Cementless implants were developed as an alternative for young and active patients. In the cementless hip replacement, there exists a direct contact between the prosthesis and the bone, and a primary rigid fixation of the implant is required for a proper outcome. This is obtained with a press-fit fixation technique, where for a perfect adjustment the implant is slightly larger than the surrounding bone.

In the postoperative first months, a secondary fixation is achieved when the surrounding bone ingrowths into the implant (bone ingrowth fixation) (Herrera et al., 2001). The designs and materials of cementless femoral stems have evolved from the original, in order to obtain more physiologic load transmissions and a better fixation. In the earlier femoral stem models, the goal was to achieve a great fixation into the femoral diaphysis. Examples of these models were AML and Lord femoral implants, with large porous coating surfaces along their diaphyseal areas. Over the years, the osteointegration rates of these large porous coating stems were found to be only around 35% (Hennessy et al., 2009). A strong devitalization of the proximal femoral metaphysis, and the proximal diaphysis in the case of Lord stems, was also demonstrated with the use of these implants (Grant & Nordsletten, 2004).

These prostheses were found to be stable in the long term, but their distal diaphyseal fixation produced a removal of normal stress on the proximal bone, being the main cause of the proximal devitalization. This situation is known as *stress shielding*. New models were then designed taking into account not only mechanical concepts but also bone biology. In order to preserve proximal bone stock, modern femoral stems have a lesser diameter, and are coated only proximally with hydroxyapatite. Despite these improvements, the stress shielding is still found in the long term in all total hip replacements.

Bone is living tissue undergoes a constant process of replacement of its structure, characterized by bone resorption and new bone formation, without changing their morphology. This process is called bone remodeling. On the other hand, bone adapts its structure, according to Wolff's Law, to the forces and biomechanical loads that receives (Buckwalter et al., 1995). In a normal hip joint, loads from the body are transmitted to the femoral head, then to the medial cortical bone of femoral neck towards the lesser trochanter, where they are distributed by the diaphyseal bone (Radin, 1980).

Body weight is transmitted to the femoral head in a normal hip joint. This load goes through the cortical bone of the medial femoral neck down to the lesser trochanter, where it is distributed to the diaphyseal bone. The implantation of a cemented or cementless femoral stem involves a clear alteration of the physiological load transmission. Loads are now passed through the prosthetic stem in a centripetal way, from the central marrow cavity to cortical bone (Herrera & Panisello 2006). This alteration of the normal biomechanics of the hip results in a phenomenon called *adaptive bone remodeling* (Huiskes et al, 1989), which means that physiological remodeling takes place in a new biomechanical environment.

The implantation of a cemented or cementless femoral stem produced a clear alteration of the physiological transmission of loads, as these are now passed through the prosthetic stem, in a centripetal way, from the central marrow cavity to the cortical bone (Marklof et al., 1980). These changes of the normal biomechanics of the hip bone leads to a phenomenon called adaptive remodeling (Huiskes et al., 1989), since bone has to adapt to the new biomechanical situation. Remodeling is a multifactorial process dependent on both mechanical and biological factors. Mechanical factors are related to the new distribution of

Mohler et al., 1995). Cementless implants were developed as an alternative for young and active patients. In the cementless hip replacement, there exists a direct contact between the prosthesis and the bone, and a primary rigid fixation of the implant is required for a proper outcome. This is obtained with a press-fit fixation technique, where for a perfect adjustment

In the postoperative first months, a secondary fixation is achieved when the surrounding bone ingrowths into the implant (bone ingrowth fixation) (Herrera et al., 2001). The designs and materials of cementless femoral stems have evolved from the original, in order to obtain more physiologic load transmissions and a better fixation. In the earlier femoral stem models, the goal was to achieve a great fixation into the femoral diaphysis. Examples of these models were AML and Lord femoral implants, with large porous coating surfaces along their diaphyseal areas. Over the years, the osteointegration rates of these large porous coating stems were found to be only around 35% (Hennessy et al., 2009). A strong devitalization of the proximal femoral metaphysis, and the proximal diaphysis in the case of Lord stems, was also demonstrated with the use of these implants (Grant & Nordsletten,

These prostheses were found to be stable in the long term, but their distal diaphyseal fixation produced a removal of normal stress on the proximal bone, being the main cause of the proximal devitalization. This situation is known as *stress shielding*. New models were then designed taking into account not only mechanical concepts but also bone biology. In order to preserve proximal bone stock, modern femoral stems have a lesser diameter, and are coated only proximally with hydroxyapatite. Despite these improvements, the stress

Bone is living tissue undergoes a constant process of replacement of its structure, characterized by bone resorption and new bone formation, without changing their morphology. This process is called bone remodeling. On the other hand, bone adapts its structure, according to Wolff's Law, to the forces and biomechanical loads that receives (Buckwalter et al., 1995). In a normal hip joint, loads from the body are transmitted to the femoral head, then to the medial cortical bone of femoral neck towards the lesser trochanter,

Body weight is transmitted to the femoral head in a normal hip joint. This load goes through the cortical bone of the medial femoral neck down to the lesser trochanter, where it is distributed to the diaphyseal bone. The implantation of a cemented or cementless femoral stem involves a clear alteration of the physiological load transmission. Loads are now passed through the prosthetic stem in a centripetal way, from the central marrow cavity to cortical bone (Herrera & Panisello 2006). This alteration of the normal biomechanics of the hip results in a phenomenon called *adaptive bone remodeling* (Huiskes et al, 1989), which means that physiological remodeling takes place in a new biomechanical environment.

The implantation of a cemented or cementless femoral stem produced a clear alteration of the physiological transmission of loads, as these are now passed through the prosthetic stem, in a centripetal way, from the central marrow cavity to the cortical bone (Marklof et al., 1980). These changes of the normal biomechanics of the hip bone leads to a phenomenon called adaptive remodeling (Huiskes et al., 1989), since bone has to adapt to the new biomechanical situation. Remodeling is a multifactorial process dependent on both mechanical and biological factors. Mechanical factors are related to the new distribution of

shielding is still found in the long term in all total hip replacements.

where they are distributed by the diaphyseal bone (Radin, 1980).

the implant is slightly larger than the surrounding bone.

2004).

loads caused by implantation of the prosthesis in the femur, the physical characteristics of the implant (size, implant design and alloy), and the type of anchoring in the femur: metaphyseal, diaphyseal, hybrid, etc. (Summer & Galante, 1992; Sychter & Engh, 1996; Rubash et al., 1998; McAuley et al., 2000; Gibson et al., 2001; Glassman et al., 2001). Biologics are related to age and weight of the individual, initial bone mass, quality of primary fixation and loads applied to the implant. Of these biological factors, the most important is initial bone mass (Sychter & Engh, 1996).

Orthopedic surgeons have taken many years to learn the biomechanics and biology of bone tissue. We began to focus on these sciences when long-term revisions of cemented and cementless femoral stems proved extensive atrophy of the femoral cortical bone, a pathological phenomenon caused by *stress-shielding*. Different models of cementless stems have tried to achieve perfect load transfer to the femur, mimicking the physiological transmission from the femoral calcar to the femoral shaft. The main objective was to avoid stress-shielding, since in absence of physiological transmission of loads, and lack of mechanical stimulus in this area, causes proximal bone atrophy.

Cemented stem fixation is achieved by the introduction of cement into bone, forming a bone-cement interface. Inside the cement mantle a new interface is made up between cement and stem. It might seem that the cement mantle enables better load distribution in the femur; however the design, material and surface of prostheses, play an important role in transmission and distribution of charges, influencing bone remodeling (Ramaniraka et al., 2000; Li et al., 2007)

Long-term follow-up of different models of cementless stems have shown that this is not achieved, and to a greater or lesser extent the phenomenon of stress-shielding is present in all the models, and therefore the proximal bone atrophy. It is interesting to know, in cemented stems, not only the stress-shielding and subsequent proximal bone atrophy, but also the long-term behavior of cement-bone and stem-cement interfaces. This requires longterm studies monitoring the different models of stems.

Research in different fields concerning Orthopaedic Surgery and Traumatology requires a methodology that allows, at the same time, a more economic approach and the possibility of reproducing in an easy way different situations. Such a method could be used as a guide for research on biomechanics of the locomotor system, both in healthy and pathologic conditions, along with the study of performance of different prostheses and implants. To that effect, the use of simulation models, introduced in the field of Bioengineering in recent years, can undoubtedly mean an essential tool to assess the best clinical option, provided that it will be accurate enough in the analysis of specific physiological conditions concerning certain pathology.

Finite element (FE) simulation has proved to be specially suitable in the study of the behaviour of any physiological unit, despite its complexity. Nowadays, it has become a powerful tool in the field of Orthopaedic Surgery and Traumatology, helping the surgeons to have a better understanding of the biomechanics, both in healthy and pathological conditions. FE simulation let us know the biomechanical changes that occur after prosthesis or osteosynthesis implantation, and biological responses of bone to biomechanical changes. It also has an additional advantage in predicting the changes in the stress distribution around the implanted zones, allowing preventing future pathologies derived from an unsuitable positioning of the prostheses.

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 221

Currently, there are methodologies developed over recent years that avoid such problems, allowing the generation of models with the desired precision in a reasonable time and cost is not excessive. Thus, the use of 3D laser scanners (Fig. 1) together with three-dimensional images obtained by CT allow making geometric models that combine high accuracy in the external form with an excellent definition of internal interfaces. The method requires not only appropriate software tools, capable of processing images, but also its compatibility with the programs used later to generate the finite element model. For example, in Fig. 1 (left) is shown the real model of an implanted femur and in Fig. 2 the result obtained by a three-dimensional laser scanner Roland Picza (after processing by Dr. Picza 3 and 3D Editor

Fig. 2. 3D scanning of the implanted femur shown in Fig. 1

finite elements mesh.

In these models, the characterization of the internal structure is made by 3D CT, from images like that shown in Figs. 3 and 4. An alternative to the above procedure is the use of 3D geometrical reconstruction programs, for example, MIMICS (Mimics, 2010). In any case, the final result is a precise geometrical model which serves as a basis for the generation of a

programs).

In this sense, finite element simulation has made easier to understand how the load is transmitted after the implantation of a femoral stem, and to predict how the stem impacts on the biomechanics in the long-term. Finite Element method can find out the long-term behavior and the impact on biomechanics of any prosthetic models. Up to now, long clinical trials, with a follow-up of at least 10 years, were needed to achieve this knowledge. Design of new femoral stem models is another important application of the Finite Element simulation. New models can be pre-tested by simulation in order to improve the design and minimize the stress-shielding phenomenon.

The Finite Element Method (FEM) was originally developed for solving structural analysis problems relating to Mechanics, Civil and Aeronautical Engineering. The paternity of this method is attributed to Turner, who published his first, historic, job in 1956 (Turner et al., 1956). In 1967, Zienkiewicz OC published the book "The finite element method in structural and continuum mechanics" (Zienkiewicz, 1967) which laid down mathematical basis of the method. Other fundamental contributions to the development of Finite Element Method (FEM) took place on dates nearest (Imbert, 1979; Bathe, 1982; Zienkiewicz & Morgan, 1983; Hughes, 1987).

#### **2. Methodology for the finite element analysis of biomechanical systems**

One of the most significant aspects of biomechanical systems is its geometric complexity, which greatly complicates the generation of accurate simulation models. Classic models just suffered from this lack of geometrical precision, present even in recent models, which challenged, in most studies, the validity of the results and their extrapolation to clinical settings.

Fig. 1. Real model of an implanted femur, 3D laser scanner and femoral stem

In this sense, finite element simulation has made easier to understand how the load is transmitted after the implantation of a femoral stem, and to predict how the stem impacts on the biomechanics in the long-term. Finite Element method can find out the long-term behavior and the impact on biomechanics of any prosthetic models. Up to now, long clinical trials, with a follow-up of at least 10 years, were needed to achieve this knowledge. Design of new femoral stem models is another important application of the Finite Element simulation. New models can be pre-tested by simulation in order to improve the design and

The Finite Element Method (FEM) was originally developed for solving structural analysis problems relating to Mechanics, Civil and Aeronautical Engineering. The paternity of this method is attributed to Turner, who published his first, historic, job in 1956 (Turner et al., 1956). In 1967, Zienkiewicz OC published the book "The finite element method in structural and continuum mechanics" (Zienkiewicz, 1967) which laid down mathematical basis of the method. Other fundamental contributions to the development of Finite Element Method (FEM) took place on dates nearest (Imbert, 1979; Bathe, 1982; Zienkiewicz & Morgan, 1983;

**2. Methodology for the finite element analysis of biomechanical systems** 

Fig. 1. Real model of an implanted femur, 3D laser scanner and femoral stem

One of the most significant aspects of biomechanical systems is its geometric complexity, which greatly complicates the generation of accurate simulation models. Classic models just suffered from this lack of geometrical precision, present even in recent models, which challenged, in most studies, the validity of the results and their extrapolation to clinical

minimize the stress-shielding phenomenon.

Hughes, 1987).

settings.

Currently, there are methodologies developed over recent years that avoid such problems, allowing the generation of models with the desired precision in a reasonable time and cost is not excessive. Thus, the use of 3D laser scanners (Fig. 1) together with three-dimensional images obtained by CT allow making geometric models that combine high accuracy in the external form with an excellent definition of internal interfaces. The method requires not only appropriate software tools, capable of processing images, but also its compatibility with the programs used later to generate the finite element model. For example, in Fig. 1 (left) is shown the real model of an implanted femur and in Fig. 2 the result obtained by a three-dimensional laser scanner Roland Picza (after processing by Dr. Picza 3 and 3D Editor programs).

Fig. 2. 3D scanning of the implanted femur shown in Fig. 1

In these models, the characterization of the internal structure is made by 3D CT, from images like that shown in Figs. 3 and 4. An alternative to the above procedure is the use of 3D geometrical reconstruction programs, for example, MIMICS (Mimics, 2010). In any case, the final result is a precise geometrical model which serves as a basis for the generation of a finite elements mesh.

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 223

However, work continues on the achievement of increasingly realistic models that allow putting the generated results and predictions into a clinical setting. To that purpose it is mainly necessary the use of meshes suitable for the particular problem, as regards both the type of elements and its size. It is always recommended to perform a sensitivity analysis of the mesh to determine the optimal features or, alternatively, the minimum necessary to achieve the required accuracy. In Fig. 5 is shown a FE mesh of healthy and implanted femurs, using tetrahedron type elements. It can be seen that the element size allows depicting, with little error, the geometry of the implanted femur, compared with Fig. 2.

Fig. 4. CT images of an implanted femur

In view of the difficulties experienced in living subjects, FE simulation models have been developed to carry out researches on biomechanical systems with high reproducibility and versatility. These models allow repeating the study as many times as desired, being a nonaggressive investigation of modified starting conditions

Fig. 3. CT images of a healthy femur

In view of the difficulties experienced in living subjects, FE simulation models have been developed to carry out researches on biomechanical systems with high reproducibility and versatility. These models allow repeating the study as many times as desired, being a non-

aggressive investigation of modified starting conditions

Fig. 3. CT images of a healthy femur

Fig. 4. CT images of an implanted femur

However, work continues on the achievement of increasingly realistic models that allow putting the generated results and predictions into a clinical setting. To that purpose it is mainly necessary the use of meshes suitable for the particular problem, as regards both the type of elements and its size. It is always recommended to perform a sensitivity analysis of the mesh to determine the optimal features or, alternatively, the minimum necessary to achieve the required accuracy. In Fig. 5 is shown a FE mesh of healthy and implanted femurs, using tetrahedron type elements. It can be seen that the element size allows depicting, with little error, the geometry of the implanted femur, compared with Fig. 2.

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 225

Fig. 6. Contact interface femur-stem

Fig. 7. Strain-stress curves for cortical bone

Fig. 5. Meshing of proximal femur: a) Healthy femur; b) Implanted femur

A key issue in FE models is the interaction between the different constitutive elements of the biomechanical system, especially when it comes to conditions which are essential in the behaviour to be analyzed. The biomechanical behaviour of a cementless stem depends basically on the conditions of contact between the stem and bone, so that the correct simulation of the latter determines the validity of the model. In Fig 6 can be seen the stemfemur contact interface, defined by the respective surfaces and the frictional conditions needed to produce the press-fit which is achieved at surgery.

Finally, in FE simulation models is essential the appropriate characterization of the mechanical behaviour of the different materials, usually very complex. So, the bone exhibits an anisotropic behaviour with different responses in tension and compression (Fig. 7). Moreover, it varies depending on the bone type (cortical or cancellous) and even along different zones in the same specimen. This kind of behaviour is reproducible in a reliable way in the simulation, but it leads to an excessive computational cost in global models. For this reason, in most cases, and specially in long bones, a linear elastic behaviour in the operation range concerning strains and stresses is considered.

Fig. 6. Contact interface femur-stem

(a) (b)

Fig. 5. Meshing of proximal femur: a) Healthy femur; b) Implanted femur

needed to produce the press-fit which is achieved at surgery.

operation range concerning strains and stresses is considered.

A key issue in FE models is the interaction between the different constitutive elements of the biomechanical system, especially when it comes to conditions which are essential in the behaviour to be analyzed. The biomechanical behaviour of a cementless stem depends basically on the conditions of contact between the stem and bone, so that the correct simulation of the latter determines the validity of the model. In Fig 6 can be seen the stemfemur contact interface, defined by the respective surfaces and the frictional conditions

Finally, in FE simulation models is essential the appropriate characterization of the mechanical behaviour of the different materials, usually very complex. So, the bone exhibits an anisotropic behaviour with different responses in tension and compression (Fig. 7). Moreover, it varies depending on the bone type (cortical or cancellous) and even along different zones in the same specimen. This kind of behaviour is reproducible in a reliable way in the simulation, but it leads to an excessive computational cost in global models. For this reason, in most cases, and specially in long bones, a linear elastic behaviour in the

Fig. 7. Strain-stress curves for cortical bone

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 227

studies and statistical analysis were identical (Panisello et al., 2009b). The study confirmed less proximal atrophy, therefore one could ask if the new design has effectively improved the load transfer conditions in the proximal femur, producing less stress-shielding. The simulation with Finite Elements (FE) allows us to verify the correlation between the mechanical stimulus and the changes detected in the bone density. In order to do this, the evolution of the mechanical stimulus over a period of 5 years has been analysed, correlating the findings with the quantified Bone Mineral Density (BMD) evolution in the studies using

Several objectives can be covered by the FE simulation: firstly, to determine the long-term changes of BMD in the femur after the implantation of ABG-I and ABG-II stems throughout the first five postoperative years, analysing the correlation between evolution of BMD and stress level, focussed on the average stresses (tension and compression) in cortical and cancellous bone for each one of the Gruen zones (Gruen et al., 1979) (Fig 8); secondly, to analyse the appropriate transfer of loads through contact between the bone and prosthesis. And finally, to analyse the long term differences between the implantation of an ABG-I and ABG-II prostheses to test if the changes in the design and alloy of the prosthesis produce a

The development of the model of a healthy femur is crucial to make accurate the whole process of simulation, and to obtain reliable results. The development of the FE models was made following the same methodology as explained before. A cadaverous femur was used with two hip prostheses type ABG-I ad ABG-II, manufactured by Stryker (Fig. 9). This cadaverous femur had originally belonged to a healthy 60 year old man and was only used in order to define the geometry of the model, without any relation with BMD measures. Firstly, each of the parts necessary to set the final model were scanned using a three dimensional scanner Roland Picza brand. As a result, a cloud of points which approximates

DXA.

Fig. 8. Gruen zones

better transfer of loads in the proximal zone.

In soft tissues, the behaviour is even more complex, usually as a hyperelastic material. This is the case of ligaments, cartilages and muscles, also including a reologic effect with deferred strains when the load conditions are maintained (viscoelastic behaviour).

This inherent complexity to the different biological tissues, reproducible in reduced or local models, is very difficult to be considered in global models as the used to analyse prostheses and implants, because the great amount of non-linearities do the convergence practically unfeasible. On the other hand, it leads to a prohibitive computational cost, only possible to undertake by supercomputers.

#### **3. Application to the behaviour of hip prostheses. Cementless stems**

In the last three decades, different designs of cementless stem have sought to obtain a physiological load transfer to the proximal femur so as to avoid stress-shielding and bone loss due to proximal atrophy. Nevertheless, most of the reports about this class of stems have proved that they do not completely prevent proximal bone atrophy (Tanzer et al., 1992; Bugbee et al., 1997; Hellmann et al., 1999; Engh et al., 2003; Sinha et al., 2004; Braun et al., 2003; Herrera et al., 2004; Canales et al., 2006). More recently, several stems incorporated a hydroxyapatite coating (HA) in their metaphyseal zone, seeking to obtain a better proximal osteointegration (Tonino et al., 1999) as a way to achieve a better load transfer and avoid stress shielding (Nourissat et al., 1995). However, the reports on this improvement showed a moderate increase in the amount of the implant surface with bone on-growth, which ranged between 35-50% in porous coated implants and between 45-60% in HA coated implants.

Considering that a loss of 30-40% in bone mass is required for it to be observed in a serial X-Ray (Engh et al., 2000), prospective studies using densitometry (DXA) are considered the ideal method for quantifying the changes of bone mass produced by different stems over the years (Kroger et al., 1996; Rosenthall et al., 1999; Schmidt et al., 2004).

Long term studies of different cementless stems show a high incidence of stress-shielding, caused by the change in the distribution of loads on the femur (Engh et al., 2003; Glassman et al., 2006; Wick & Lester, 2004). The monitoring of an anatomic femoral stem with metaphyseal load-bearing and HA coating (ABG-I), that was carried out through a prospective, controlled study that included 67 patients (Group I) in the period 1994-99, has confirmed that even though the clinical results are very favourable, a high percentage of cases with stress-shielding are detected (Herrera et al., 2004). This results in a proximal atrophy which has been quantified with DXA (Panisello et al., 2009a). For that reason the stem has been redesigned (ABG-II) in an attempt to improve the proximal transfer of loads and reduce the phenomenon of stress-shielding. The main differences between both stems concern geometrical design and material. The overall length has been reduced by 8% and the proximal and distal diameters by 10%. The prosthesis shoulder has been modified. The material has changed from Wrought Titanium (Ti 6Al-4V) alloy to TMZF (Titanium, Molybdenum, Zirconium and Ferrous) alloy.

A similar design study was done with the ABG-II stem in the period 2000-05, with 69 patients of comparable demographic characteristics than the previous one (Group II). In both studies the surgical technique, post-operative rehabilitation program, densitometry studies and statistical analysis were identical (Panisello et al., 2009b). The study confirmed less proximal atrophy, therefore one could ask if the new design has effectively improved the load transfer conditions in the proximal femur, producing less stress-shielding. The simulation with Finite Elements (FE) allows us to verify the correlation between the mechanical stimulus and the changes detected in the bone density. In order to do this, the evolution of the mechanical stimulus over a period of 5 years has been analysed, correlating the findings with the quantified Bone Mineral Density (BMD) evolution in the studies using DXA.

Several objectives can be covered by the FE simulation: firstly, to determine the long-term changes of BMD in the femur after the implantation of ABG-I and ABG-II stems throughout the first five postoperative years, analysing the correlation between evolution of BMD and stress level, focussed on the average stresses (tension and compression) in cortical and cancellous bone for each one of the Gruen zones (Gruen et al., 1979) (Fig 8); secondly, to analyse the appropriate transfer of loads through contact between the bone and prosthesis. And finally, to analyse the long term differences between the implantation of an ABG-I and ABG-II prostheses to test if the changes in the design and alloy of the prosthesis produce a better transfer of loads in the proximal zone.

#### Fig. 8. Gruen zones

226 Finite Element Analysis – From Biomedical Applications to Industrial Developments

In soft tissues, the behaviour is even more complex, usually as a hyperelastic material. This is the case of ligaments, cartilages and muscles, also including a reologic effect with deferred

This inherent complexity to the different biological tissues, reproducible in reduced or local models, is very difficult to be considered in global models as the used to analyse prostheses and implants, because the great amount of non-linearities do the convergence practically unfeasible. On the other hand, it leads to a prohibitive computational cost, only possible to

In the last three decades, different designs of cementless stem have sought to obtain a physiological load transfer to the proximal femur so as to avoid stress-shielding and bone loss due to proximal atrophy. Nevertheless, most of the reports about this class of stems have proved that they do not completely prevent proximal bone atrophy (Tanzer et al., 1992; Bugbee et al., 1997; Hellmann et al., 1999; Engh et al., 2003; Sinha et al., 2004; Braun et al., 2003; Herrera et al., 2004; Canales et al., 2006). More recently, several stems incorporated a hydroxyapatite coating (HA) in their metaphyseal zone, seeking to obtain a better proximal osteointegration (Tonino et al., 1999) as a way to achieve a better load transfer and avoid stress shielding (Nourissat et al., 1995). However, the reports on this improvement showed a moderate increase in the amount of the implant surface with bone on-growth, which ranged between 35-50% in porous coated implants and between 45-60% in HA coated

Considering that a loss of 30-40% in bone mass is required for it to be observed in a serial X-Ray (Engh et al., 2000), prospective studies using densitometry (DXA) are considered the ideal method for quantifying the changes of bone mass produced by different stems over the

Long term studies of different cementless stems show a high incidence of stress-shielding, caused by the change in the distribution of loads on the femur (Engh et al., 2003; Glassman et al., 2006; Wick & Lester, 2004). The monitoring of an anatomic femoral stem with metaphyseal load-bearing and HA coating (ABG-I), that was carried out through a prospective, controlled study that included 67 patients (Group I) in the period 1994-99, has confirmed that even though the clinical results are very favourable, a high percentage of cases with stress-shielding are detected (Herrera et al., 2004). This results in a proximal atrophy which has been quantified with DXA (Panisello et al., 2009a). For that reason the stem has been redesigned (ABG-II) in an attempt to improve the proximal transfer of loads and reduce the phenomenon of stress-shielding. The main differences between both stems concern geometrical design and material. The overall length has been reduced by 8% and the proximal and distal diameters by 10%. The prosthesis shoulder has been modified. The material has changed from Wrought Titanium (Ti 6Al-4V) alloy to TMZF (Titanium,

A similar design study was done with the ABG-II stem in the period 2000-05, with 69 patients of comparable demographic characteristics than the previous one (Group II). In both studies the surgical technique, post-operative rehabilitation program, densitometry

years (Kroger et al., 1996; Rosenthall et al., 1999; Schmidt et al., 2004).

Molybdenum, Zirconium and Ferrous) alloy.

**3. Application to the behaviour of hip prostheses. Cementless stems** 

strains when the load conditions are maintained (viscoelastic behaviour).

undertake by supercomputers.

implants.

The development of the model of a healthy femur is crucial to make accurate the whole process of simulation, and to obtain reliable results. The development of the FE models was made following the same methodology as explained before. A cadaverous femur was used with two hip prostheses type ABG-I ad ABG-II, manufactured by Stryker (Fig. 9). This cadaverous femur had originally belonged to a healthy 60 year old man and was only used in order to define the geometry of the model, without any relation with BMD measures. Firstly, each of the parts necessary to set the final model were scanned using a three dimensional scanner Roland Picza brand. As a result, a cloud of points which approximates

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 229

The program *Abaqus 6.7* (Abaqus, 2009) was used for the calculation, with the *Abaqus Viewer* being used for the results post processing. It was necessary to undertake a contact simulation between the prosthesis and the cancellous bone for which a friction coefficient of 0.5 was considered simulating the press-fit setting according with (Shirazi et al., 1993). In light of the former results a sensitivity analysis was carried out in order to determine the appropriate interface conditions, considering several friction coefficient values from 0.2 to 0.5 in steps of 0.05, obtaining significant differences in the analyzed range, but with similar results from 0.4 to 0.5. An analysis with bonded interface was also realized. It was observed that the value of 0.5 for the friction coefficient corresponds practically to a bonded interface concerning the stem mobility, but with the advantage that allows moving apart the stem from the bone in higher tension zones, providing a more realistic stress distribution inside

The final model for the healthy femur contains a total of 68086 elements (38392 for cortical bone, 27703 for cancellous bone and 1990 for bone marrow) (Fig. 10). The final model with ABG-I stem comprises a total of 60401 elements (33504 for cortical bone, 22088 for cancellous bone and 4809 for ABG-I stem) (Fig. 5b). The final model with the ABG-II stem is made up of 63784 elements (33504 for cortical bone, 22730 for cancellous bone and 7550 for ABG-II

the bone.

stem) (Fig. 11).

Fig. 10. FE model of healthy femur. Coronal section

the scanned geometry was obtained. These surfaces must be processed through the programs Dr.Picza-3 and 3D-Editor. This will eliminate the noise and performs smooth surfaces, resulting in a geometry that reliably approximates to the actual geometry.

From the scanned femur a geometric model of the outer geometry of the femur was obtained with no distinction between cortical bone, cancellous bone and bone marrow. To determine the geometry of the cancellous bone and medullar cavity 30 transverse direction (5 mm gap) tomographic cross-sections and eight longitudinal direction cross-sections were taken using CT scan (General Electric Brightspeed Elite). A three-dimensional mesh of healthy femur, based on linear tetrahedral elements (Fig. 5, healthy model), was made in Ideas software (I-deas, 2009). So as to develop the pattern with prosthesis, an ABG-I prosthesis was scanned to obtain its geometry. Afterwards we proceeded with the operation on a cadaver femur with a prosthesis being implanted in the same way as a real hip replacement operation would be carried out.

Fig. 9. Material for the development of finite element model: a) Healthy femur; b) ABG-I stem; c) ABG-II stem

Once the three meshes had been generated in I-deas (healthy femur, prosthesis ABG-I and operated femur), the prosthesis was positioned in the femur always taking the mesh of the operated femur as the base. From the previous process of modelling on the cadaveric femur, only the cortical bone was used, from which the cancellous bone was modelled again, in such a way that it fit perfectly to the contact with the prosthesis. Work with the ABG-II prosthesis was undertaken in the same way.

the scanned geometry was obtained. These surfaces must be processed through the programs Dr.Picza-3 and 3D-Editor. This will eliminate the noise and performs smooth

From the scanned femur a geometric model of the outer geometry of the femur was obtained with no distinction between cortical bone, cancellous bone and bone marrow. To determine the geometry of the cancellous bone and medullar cavity 30 transverse direction (5 mm gap) tomographic cross-sections and eight longitudinal direction cross-sections were taken using CT scan (General Electric Brightspeed Elite). A three-dimensional mesh of healthy femur, based on linear tetrahedral elements (Fig. 5, healthy model), was made in Ideas software (I-deas, 2009). So as to develop the pattern with prosthesis, an ABG-I prosthesis was scanned to obtain its geometry. Afterwards we proceeded with the operation on a cadaver femur with a prosthesis being implanted in the same way as a real hip

surfaces, resulting in a geometry that reliably approximates to the actual geometry.

 (a) (b) (c) Fig. 9. Material for the development of finite element model: a) Healthy femur;

Once the three meshes had been generated in I-deas (healthy femur, prosthesis ABG-I and operated femur), the prosthesis was positioned in the femur always taking the mesh of the operated femur as the base. From the previous process of modelling on the cadaveric femur, only the cortical bone was used, from which the cancellous bone was modelled again, in such a way that it fit perfectly to the contact with the prosthesis. Work with the ABG-II

replacement operation would be carried out.

b) ABG-I stem; c) ABG-II stem

prosthesis was undertaken in the same way.

The program *Abaqus 6.7* (Abaqus, 2009) was used for the calculation, with the *Abaqus Viewer* being used for the results post processing. It was necessary to undertake a contact simulation between the prosthesis and the cancellous bone for which a friction coefficient of 0.5 was considered simulating the press-fit setting according with (Shirazi et al., 1993). In light of the former results a sensitivity analysis was carried out in order to determine the appropriate interface conditions, considering several friction coefficient values from 0.2 to 0.5 in steps of 0.05, obtaining significant differences in the analyzed range, but with similar results from 0.4 to 0.5. An analysis with bonded interface was also realized. It was observed that the value of 0.5 for the friction coefficient corresponds practically to a bonded interface concerning the stem mobility, but with the advantage that allows moving apart the stem from the bone in higher tension zones, providing a more realistic stress distribution inside the bone.

The final model for the healthy femur contains a total of 68086 elements (38392 for cortical bone, 27703 for cancellous bone and 1990 for bone marrow) (Fig. 10). The final model with ABG-I stem comprises a total of 60401 elements (33504 for cortical bone, 22088 for cancellous bone and 4809 for ABG-I stem) (Fig. 5b). The final model with the ABG-II stem is made up of 63784 elements (33504 for cortical bone, 22730 for cancellous bone and 7550 for ABG-II stem) (Fig. 11).

Fig. 10. FE model of healthy femur. Coronal section

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 231

 **ELASTIC POISSON MAXIMUM MAXIMUM MODULUS RATIO COMPRESSION TENSION (MPa) (MPa) (MPa)** 

Taking various studies as reference (Kerner et al., 1999; Turner et al., 2005), a linear relationship between the bone mass values, which come from the medical study collected in Panisello (Panisello, 2009a), and the apparent density was established in addition to a cubic relationship between the latter and the elastic modulus, using a maximal Young's modulus of 20 GPa, thereby obtaining the cortical bone modulus of elasticity values for each one of the 7 Gruen zones. To carry out the analysis of the results, the cortical bone of each model is divided into seven zones which coincide with the Gruen zones. The elastic modulus obtained from the values in Panisello (Panisello, 2009a) was used as an input in the cortical bone. These values are being successively adjusted for each one of the models (femur with ABG-I stem and femur with ABG-II stem) in different moments of time: post-operative, 6 months, 1, 3 and 5 years. In addition, the initial data corresponding to the pre-operative moment are used as an input in the healthy model. The mechanical properties of the cortical bone have been calculated from the bone mass data from groups I and II respectively.

For the complete comparative analysis of both stems, all of the possible combinations of bone mass (group I, ABG-I, 67 patients in the period 1994-99 and group II, ABG-II, 69 patients in the period 2000-05) prosthetic geometry (ABG-I and ABG-II) and stem material (Wrought Titanium or TMZF) were simulated. This way it was possible to compare the mechanical performance of both prostheses in what refers to the transmission of loads and the interaction in the bone-prosthesis contact zone. It also makes possible to distinguish the most influential parameter (geometry or material) for the design of future prosthetic stems. The average von Mises stress is used, given that despite not distinguishing between tension and compression values, it is sufficiently indicative of the tendency of the mechanical

The middle zone has been clamped instead of distal zone because middle zone is considered enough away from proximal bone (Fig. 12). This model can be compared with other that have been clamped at a distal point, since the loads applied practically coincided with the

**BONE** 20000 15, 20, 21 0.30 16, 18 150 16, 18 90 16, 18

**BONE** 959 14 0.12 17 23 16, 18

**MARROW** 1 16, 18 0.30 16, 18 **ABG-I STEM** 110000 22 0.33 19 **ABG-II STEM** 74000 - 85000 22 0.33 19

Table 1. Mechanical properties of materials

stimulus and it is standard in FE software.

1. Clamped in the middle of the femoral shaft

The main features of each of the boundary conditions are:

femoral axis direction thus reducing the differences in final values.

**CORTICAL** 

**BONE** 

**CANCELLOUS** 

Fig. 11. FE model after removal of the femoral head and positioning of the cementless stems ABG-II.

Three boundary conditions were defined: clamped in the medial diaphyseal part of the femur, force on the prosthetic head due to the reaction of the hip caused by the weight of the person (400% body weight) and force on the greater trochanter (200% body weight) generated by the abductor muscles (Herrera et al., 2007).

The values of the mechanical properties used in the prostheses as well as the biological materials are shown in Table 1. These values have been obtained from the bibliography specializing in the subject (Ashman and Rho, 1988; Ashman et al., 1984; Evans, 1973; Ionescu et al., 2003; Jacobs, 1994; Mat Web, 2009; Meunier et al., 1989; Turner et al., 1999; Van der Val et al., 2006) and they have been simplified considering an isotropic behaviour. In the design of the ABG-II second generation prosthesis a different titanium alloy was used to that of the ABG-I. The prosthetic ABG-I stem is made with a Wrought Titanium (Ti 6Al-4V) alloy, the elasticity modulus of which is 110 GPa. On the other hand the TMZF alloy which is used on the ABG-II stem has a Young's modulus of 74-85 GPa, according to the manufacturer information, using a mean value of 79.5 GPa in the different analyses.


Table 1. Mechanical properties of materials

230 Finite Element Analysis – From Biomedical Applications to Industrial Developments

Fig. 11. FE model after removal of the femoral head and positioning of the cementless stems

Three boundary conditions were defined: clamped in the medial diaphyseal part of the femur, force on the prosthetic head due to the reaction of the hip caused by the weight of the person (400% body weight) and force on the greater trochanter (200% body weight)

The values of the mechanical properties used in the prostheses as well as the biological materials are shown in Table 1. These values have been obtained from the bibliography specializing in the subject (Ashman and Rho, 1988; Ashman et al., 1984; Evans, 1973; Ionescu et al., 2003; Jacobs, 1994; Mat Web, 2009; Meunier et al., 1989; Turner et al., 1999; Van der Val et al., 2006) and they have been simplified considering an isotropic behaviour. In the design of the ABG-II second generation prosthesis a different titanium alloy was used to that of the ABG-I. The prosthetic ABG-I stem is made with a Wrought Titanium (Ti 6Al-4V) alloy, the elasticity modulus of which is 110 GPa. On the other hand the TMZF alloy which is used on the ABG-II stem has a Young's modulus of 74-85 GPa, according to the manufacturer

generated by the abductor muscles (Herrera et al., 2007).

information, using a mean value of 79.5 GPa in the different analyses.

ABG-II.

Taking various studies as reference (Kerner et al., 1999; Turner et al., 2005), a linear relationship between the bone mass values, which come from the medical study collected in Panisello (Panisello, 2009a), and the apparent density was established in addition to a cubic relationship between the latter and the elastic modulus, using a maximal Young's modulus of 20 GPa, thereby obtaining the cortical bone modulus of elasticity values for each one of the 7 Gruen zones. To carry out the analysis of the results, the cortical bone of each model is divided into seven zones which coincide with the Gruen zones. The elastic modulus obtained from the values in Panisello (Panisello, 2009a) was used as an input in the cortical bone. These values are being successively adjusted for each one of the models (femur with ABG-I stem and femur with ABG-II stem) in different moments of time: post-operative, 6 months, 1, 3 and 5 years. In addition, the initial data corresponding to the pre-operative moment are used as an input in the healthy model. The mechanical properties of the cortical bone have been calculated from the bone mass data from groups I and II respectively.

For the complete comparative analysis of both stems, all of the possible combinations of bone mass (group I, ABG-I, 67 patients in the period 1994-99 and group II, ABG-II, 69 patients in the period 2000-05) prosthetic geometry (ABG-I and ABG-II) and stem material (Wrought Titanium or TMZF) were simulated. This way it was possible to compare the mechanical performance of both prostheses in what refers to the transmission of loads and the interaction in the bone-prosthesis contact zone. It also makes possible to distinguish the most influential parameter (geometry or material) for the design of future prosthetic stems.

The average von Mises stress is used, given that despite not distinguishing between tension and compression values, it is sufficiently indicative of the tendency of the mechanical stimulus and it is standard in FE software.

The main features of each of the boundary conditions are:

1. Clamped in the middle of the femoral shaft

The middle zone has been clamped instead of distal zone because middle zone is considered enough away from proximal bone (Fig. 12). This model can be compared with other that have been clamped at a distal point, since the loads applied practically coincided with the femoral axis direction thus reducing the differences in final values.

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 233

Both models with prostheses ABG-I and II have been simulated in five different moments of time coincident with the DXA measurements: postoperative, 6 months, 1, 3 and 5 years, in addition to the healthy femur as the initial reference. In both groups of bone mass an increase of stress in the area of the cancellous bone is produced, which coincides with the end of the HA coating, as a consequence of the bottleneck effect which is produced in the transmission of loads, and corresponds to Gruen zones 2 and 6, where no osteopenia can be

BMD evolution in the operated and healthy hip is shown in Fig. 13 for both prostheses. For ABG-I, the preoperative measurements performed in both hips showed slightly higher BMD rates in the healthy hip, although these were not statistically significant. Postoperative values were taken as a reference for the operated hip. A decrease in BMD was detected in all zones except zone 4, six months after surgery. Between 6 and 12 postoperative months there was a slight additional loss of BMD in zones 1 and 7, but some bone recovery in the middle and distal areas around the implant. No significant changes in BMD were observed in zones

For ABG-II, the preoperative measurements performed in both hips showed again slightly higher bone density rates in the healthy hip, although these were not statistically significant. No changes or a minimal decrease in bone density was detected in zones 1 to 6, six months after surgery, attributed to rest period, partial weight bearing and the later effects of surgery. The bone loss was statistically significant only in zone 7. A slight additional loss of bone density was observed in zone 7, as well as some bone recovery in the middle and distal areas around the implant. Minor changes in bone density were observed in zones 1 to 6 from the end of the first year to the end of the fifth year. The bone mass remains stable in this period, with a little bone recovery in zones 2 and 6. Nevertheless, there was some decrease in zone 7 in the period between the first and fifth year, when a loss of 23.88% can be reached. The bone density in the contra-lateral healthy hip (bone mass group II) showed some slight differences during the follow-up, with decreases between 1.4 and 2.7%, more evident in the proximal part of the femur, richer in cancellous bone. The values obtained for zones 3 to 5 were similar to those of the operated femurs; in zones 2 and 6 they were slightly

Fig. 14 shows the results of the average von Mises stress (MPa), corresponding to the combinations of geometry (ABG-I, ABG-II) and prosthesis material for group I of bone mass at five years, and Fig. 15 shows the equivalent results for group II of bone mass. It can be confirmed that the global behaviour of the prostheses is the same in both models; however, in the case of the ABG-II stem higher stress values are reached on both the cancellous and

A tensional increase is noticeable in the whole area close to the lesser trochanter with the use of the ABG-II stem, as well as the tensional increase that the insertion of the ABG-II prosthesis involves with respect to the ABG-I. These differences can be observed in a more clear way in Figs. 14 and 15. In both figures it is clearly noticeable that the result corresponding to the two material for every stem are practically the same (superimposed lines); however, the results corresponding to both geometrical designs (ABG I, ABG II) are

seen in contrast to zones 1 and 7.

1 to 6 from the end of the first year to the end of the fifth year.

superior; only zones 1 and 7 showed significant differences.

cortical bones, fundamentally in the proximal zones.

different, with a higher tensional level for the ABG II stem.

#### 2. Hip muscles Loads

Forces generated by the abductor muscles are applied on the greater trochanter, in agreement with most authors' opinion (Weinans et al., 1994; Kerner et al., 1999). Generally, muscle strength generated in the hip joint is 2 times the body weight, and this produces a reaction in the femoral head that accounts for 2.75 times the body weight. However, when the heel impacts to the ground, and in double support stage of the gait, the load increases up to 4 times the body weight. The latter case, being the worst one, has been considered to impose the boundary conditions. It has also been considered a body weight of 79.3 kg for cementless stems, and 73 kg for cemented stems. Those were the average values obtained from the clinical sample to be contrasted with the simulation results. The load due to the abductor muscles, accounting for 2 times the corporal weight, is applied to the proximal area of the greater trochanter, at an angle of 21 degrees, as shown in Fig. 12.

#### 3. Reaction strength on the femoral head due to the body weight.

As already mentioned, we have studied the case of a person to 79.3 kg in cementless stems, and 73 kg in cemented stems, in the worst case of double support or heel impact stages of the gait. The resultant force on the femoral head would be worth 4 times the body weight (Fig. 12).

Fig. 12. Boundary conditions applied in the healthy femur model. Similar conditions are used in the implanted models

Forces generated by the abductor muscles are applied on the greater trochanter, in agreement with most authors' opinion (Weinans et al., 1994; Kerner et al., 1999). Generally, muscle strength generated in the hip joint is 2 times the body weight, and this produces a reaction in the femoral head that accounts for 2.75 times the body weight. However, when the heel impacts to the ground, and in double support stage of the gait, the load increases up to 4 times the body weight. The latter case, being the worst one, has been considered to impose the boundary conditions. It has also been considered a body weight of 79.3 kg for cementless stems, and 73 kg for cemented stems. Those were the average values obtained from the clinical sample to be contrasted with the simulation results. The load due to the abductor muscles, accounting for 2 times the corporal weight, is applied to the proximal

As already mentioned, we have studied the case of a person to 79.3 kg in cementless stems, and 73 kg in cemented stems, in the worst case of double support or heel impact stages of the gait. The resultant force on the femoral head would be worth 4 times the body weight

Fig. 12. Boundary conditions applied in the healthy femur model. Similar conditions are

area of the greater trochanter, at an angle of 21 degrees, as shown in Fig. 12.

3. Reaction strength on the femoral head due to the body weight.

2. Hip muscles Loads

(Fig. 12).

used in the implanted models

Both models with prostheses ABG-I and II have been simulated in five different moments of time coincident with the DXA measurements: postoperative, 6 months, 1, 3 and 5 years, in addition to the healthy femur as the initial reference. In both groups of bone mass an increase of stress in the area of the cancellous bone is produced, which coincides with the end of the HA coating, as a consequence of the bottleneck effect which is produced in the transmission of loads, and corresponds to Gruen zones 2 and 6, where no osteopenia can be seen in contrast to zones 1 and 7.

BMD evolution in the operated and healthy hip is shown in Fig. 13 for both prostheses. For ABG-I, the preoperative measurements performed in both hips showed slightly higher BMD rates in the healthy hip, although these were not statistically significant. Postoperative values were taken as a reference for the operated hip. A decrease in BMD was detected in all zones except zone 4, six months after surgery. Between 6 and 12 postoperative months there was a slight additional loss of BMD in zones 1 and 7, but some bone recovery in the middle and distal areas around the implant. No significant changes in BMD were observed in zones 1 to 6 from the end of the first year to the end of the fifth year.

For ABG-II, the preoperative measurements performed in both hips showed again slightly higher bone density rates in the healthy hip, although these were not statistically significant. No changes or a minimal decrease in bone density was detected in zones 1 to 6, six months after surgery, attributed to rest period, partial weight bearing and the later effects of surgery. The bone loss was statistically significant only in zone 7. A slight additional loss of bone density was observed in zone 7, as well as some bone recovery in the middle and distal areas around the implant. Minor changes in bone density were observed in zones 1 to 6 from the end of the first year to the end of the fifth year. The bone mass remains stable in this period, with a little bone recovery in zones 2 and 6. Nevertheless, there was some decrease in zone 7 in the period between the first and fifth year, when a loss of 23.88% can be reached. The bone density in the contra-lateral healthy hip (bone mass group II) showed some slight differences during the follow-up, with decreases between 1.4 and 2.7%, more evident in the proximal part of the femur, richer in cancellous bone. The values obtained for zones 3 to 5 were similar to those of the operated femurs; in zones 2 and 6 they were slightly superior; only zones 1 and 7 showed significant differences.

Fig. 14 shows the results of the average von Mises stress (MPa), corresponding to the combinations of geometry (ABG-I, ABG-II) and prosthesis material for group I of bone mass at five years, and Fig. 15 shows the equivalent results for group II of bone mass. It can be confirmed that the global behaviour of the prostheses is the same in both models; however, in the case of the ABG-II stem higher stress values are reached on both the cancellous and cortical bones, fundamentally in the proximal zones.

A tensional increase is noticeable in the whole area close to the lesser trochanter with the use of the ABG-II stem, as well as the tensional increase that the insertion of the ABG-II prosthesis involves with respect to the ABG-I. These differences can be observed in a more clear way in Figs. 14 and 15. In both figures it is clearly noticeable that the result corresponding to the two material for every stem are practically the same (superimposed lines); however, the results corresponding to both geometrical designs (ABG I, ABG II) are different, with a higher tensional level for the ABG II stem.

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 235

It could be checked that in every case the stress corresponding to the ABG-II stem is greater than the one resulting from the insertion of the ABG-I stem (Figs. 14 and 15). In the figures it can be seen that in every zone and for any time the stress achieve higher values in ABG-II than in ABG-I stem. This way it is possible to confirm that with the second generation of stem (ABG-II) the stress increases in practically every zone with this increase being most

Fig. 14. Comparison of the average von Mises stress as a function of design and material for

evident in zone 7.

bone mass group I

Fig. 13. Evolution of bone mass density for ABG I (bone mass group I) and ABG II (bone mass group II), corresponding to five years, in the Gruen zones.

Fig. 13. Evolution of bone mass density for ABG I (bone mass group I) and ABG II

(bone mass group II), corresponding to five years, in the Gruen zones.

It could be checked that in every case the stress corresponding to the ABG-II stem is greater than the one resulting from the insertion of the ABG-I stem (Figs. 14 and 15). In the figures it can be seen that in every zone and for any time the stress achieve higher values in ABG-II than in ABG-I stem. This way it is possible to confirm that with the second generation of stem (ABG-II) the stress increases in practically every zone with this increase being most evident in zone 7.

Fig. 14. Comparison of the average von Mises stress as a function of design and material for bone mass group I

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 237

Fig. 16. Bone mass (%) variation versus time and variation in average von Mises (%) stress

versus time for the femur with prosthesis ABG-I and ABG-II in the Gruen zones

Fig. 15. Comparison of the average von Mises stress as a function of design and material for bone mass group II

Figure 16 shows the evolution of the bone mass (%) and the average von Mises stress (%) for each one of the 7 Gruen zones in both models, considering the corresponding group and material for each stem.

Fig. 15. Comparison of the average von Mises stress as a function of design and material for

Figure 16 shows the evolution of the bone mass (%) and the average von Mises stress (%) for each one of the 7 Gruen zones in both models, considering the corresponding group and

bone mass group II

material for each stem.

Fig. 16. Bone mass (%) variation versus time and variation in average von Mises (%) stress versus time for the femur with prosthesis ABG-I and ABG-II in the Gruen zones

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 239

Fig. 18. Longitudinal section of the FE models with cemented femoral prostheses: (a) ABG-

(a) (b)

(a) (b)

Fig. 19. FE model with cemented femoral prostheses: (a) ABG-cemented and (b) Versys.

cemented and (b) Versys.

#### **4. Application to the behaviour of hip prostheses. Cemented stems**

In the case of cemented stems the process of modelling was similar, varying the surgical cut in the femoral neck of the healthy femur. Each stem was positioned into the femur, always taking the superimposed mesh of the operated femur as a base (Fig. 17). In the previous process of modelling, on the cadaveric femur, only the cortical bone was used. The cancellous bone was modelled again taking into account the cement mantle surrounding the prosthesis and the model of stem (ABG or Versys), so as to obtain a perfect union between cement and cancellous bone. The cement mantle was given a similar thickness, in mm, which corresponds to that usually achieved in patients operated on, different for each of the stem models studied and each of the areas of the prosthesis, so that the model simulation be as accurate as possible. Cemented anatomical stem ABG, and the Versys straight, polished stem, were used in the study.

Fig. 17. Removal of the femoral head and cemented prosthesis positioning: (a) ABG-cemented and (b) Versys

In the models of cemented prostheses it is not necessary to define contact conditions between the cancellous bone and the stem. In this type of prosthesis the junction between these two elements is achieved by cement, which in the EF model should simulate conditions of perfect union between cancellous bone-cement and cement-stem. It has also been necessary to model the diaphyseal plug that is placed in actual operations to prevent the spread of the cement down to femoral medullary canal. Fig. 18 shows the coronal sections of the final models.

In the case of cemented stems the process of modelling was similar, varying the surgical cut in the femoral neck of the healthy femur. Each stem was positioned into the femur, always taking the superimposed mesh of the operated femur as a base (Fig. 17). In the previous process of modelling, on the cadaveric femur, only the cortical bone was used. The cancellous bone was modelled again taking into account the cement mantle surrounding the prosthesis and the model of stem (ABG or Versys), so as to obtain a perfect union between cement and cancellous bone. The cement mantle was given a similar thickness, in mm, which corresponds to that usually achieved in patients operated on, different for each of the stem models studied and each of the areas of the prosthesis, so that the model simulation be as accurate as possible. Cemented anatomical stem ABG, and the Versys straight, polished

**4. Application to the behaviour of hip prostheses. Cemented stems** 

 (a) (b) Fig. 17. Removal of the femoral head and cemented prosthesis positioning:

In the models of cemented prostheses it is not necessary to define contact conditions between the cancellous bone and the stem. In this type of prosthesis the junction between these two elements is achieved by cement, which in the EF model should simulate conditions of perfect union between cancellous bone-cement and cement-stem. It has also been necessary to model the diaphyseal plug that is placed in actual operations to prevent the spread of the cement down to femoral medullary canal. Fig. 18 shows the coronal

stem, were used in the study.

(a) ABG-cemented and (b) Versys

sections of the final models.

Fig. 18. Longitudinal section of the FE models with cemented femoral prostheses: (a) ABGcemented and (b) Versys.

Fig. 19. FE model with cemented femoral prostheses: (a) ABG-cemented and (b) Versys.

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 241

Fig. 21. BMD and average von Mises stress evolution for ABG cemented stem

Both models were meshed with tetrahedral solid elements linear type, with a total of 74192 elements in the model for ABG-cemented prosthesis (33504 items cortical bone, cancellous bone 17859, 6111 for the ABG stem-cement, cement 13788 and 2930 for diaphyseal plug), and 274651 in the model for prosthetic Versys (119151 items of cortical bone, cancellous bone 84836, 22665 for the Versys stem, 44661 for the cement and 3338 in diaphyseal plug). In Fig. 19 are shown both models for cemented stems. Boundary conditions were imposed in the same way as in the cementless stems (Fig. 20).

Fig. 20. Boundary conditions

Calculation was performed using again the program Abaqus 6.7. Both prostheses have been simulated with the same mechanical properties, thus, the result shows the influence of stem geometry on the biomechanical behavior. Figs. 21 and 22 show the variation (%) of bone mass and average von Mises stress (%) in each of the Gruen zones for each of the models of cemented prostheses, with reference to the preoperative time. It can be seen that for both stems, the maximum decrease in bone mass occurred in Zone 7. This decrease in bone mass is greater in the Versys model than in the ABG stem

Both models were meshed with tetrahedral solid elements linear type, with a total of 74192 elements in the model for ABG-cemented prosthesis (33504 items cortical bone, cancellous bone 17859, 6111 for the ABG stem-cement, cement 13788 and 2930 for diaphyseal plug), and 274651 in the model for prosthetic Versys (119151 items of cortical bone, cancellous bone 84836, 22665 for the Versys stem, 44661 for the cement and 3338 in diaphyseal plug). In Fig. 19 are shown both models for cemented stems. Boundary conditions were imposed in the

Calculation was performed using again the program Abaqus 6.7. Both prostheses have been simulated with the same mechanical properties, thus, the result shows the influence of stem geometry on the biomechanical behavior. Figs. 21 and 22 show the variation (%) of bone mass and average von Mises stress (%) in each of the Gruen zones for each of the models of cemented prostheses, with reference to the preoperative time. It can be seen that for both stems, the maximum decrease in bone mass occurred in Zone 7. This decrease in bone mass

same way as in the cementless stems (Fig. 20).

Fig. 20. Boundary conditions

is greater in the Versys model than in the ABG stem

Fig. 21. BMD and average von Mises stress evolution for ABG cemented stem

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 243

Prior to the development of our FE models several long-term studies of bone remodeling after the implantation of two different cementless stems, ABG I and ABG II, were performed (Panisello et al., 2006; Panisello et al., 2009a; Panisello et al., 2009b). These studies were performed using DXA, a technique that allows an accurate assessment of bone density losses in the different Gruen zones. We take as a reference to explore this evolution the postoperative value obtained in control measurements and those obtained from contralateral healthy hip. New measurements were made at 6 months, one year and 5 years after surgery. The ABG II stem is an evolution of the ABG I, which has been modified both in its alloy and design. The second generation prosthesis ABG-II is manufactured with a different titanium alloy from that used in the ABG-I. The prosthetic ABG-I stem is made with a Wrought Titanium alloy (Ti 6Al-4V) of which elasticity modulus is 110 GPa. Meanwhile, the TMZF alloy, which is used on the ABG-II stem, has a Young's modulus of 74-85 GPa, according to the manufacturer information, using a mean value of 79.5 GPa in the different analyses. On the other hand, the ABG II stem has a new design with less proximal and distal diameter, less length and the shoulder of stem has been redesign to

In our DXA studies, directed to know the loss of bone mass in the different zones of Gruen caused by the stress-shielding, we found that ABG II model produces less proximal bone atrophy in post-operative measurements, for similar follow-up periods. In the model ABG II, we keep finding in studies with DXA a proximal bone atrophy, mainly in zones 1 and 7 of Gruen, but with an improvement of 8.7% in the values obtained in ABG I series. We can infer that improvements in the design of the stem, with a narrower diameter in the metaphyseal area, improve the load transfer to the femur and therefore minimizes the stress-shielding phenomenon, resulting in a lower proximal bone atrophy, because this area receive higher mechanical stimuli. These studies for determination of bone mass in Gruen zones, and the comparative study of their postoperative evolution during 5 years have allowed us to draw a number of conclusions: a) bone remodelling, after implantation of a femoral stem, is finished one year after surgery; b) variations in bone mass, after the first

The importance of these studies is that objective data from a study with a series of patients allow us to confirm the existence of stress-shielding phenomenon, and quantify exactly the proximal bone atrophy that occurs. At the same time they have allowed us to confirm that the improvements in the ABG stem design, mean in practice better load transfer and less

DXA studies have been basic to validate our FE models, because we have handled real values of patients' bone density, which allowed us to measure mechanical properties of real bone in different stages. Through computer simulation with our model, we have confirmed the decrease of mechanical stimulus in femoral metaphyseal areas, having a higher stimulus in ABG II type stem, which corresponds exactly with the data obtained in studies with DXA

In the case of cemented stems, densitometric studies were performed with two different types of stem: one straight (Versys, manufactured in a cobalt-chromium alloy) and other anatomical (ABG, manufactured in forged Vitallium patented by Stryker Howmedica). It

**5. Conclusion** 

improve osteointegration in the metaphyseal area.

stres-shielding phenomenon when using the ABG II stem.

achieved in patients operated with both models stems.

year, are not significant.

Fig. 22. BMD and average von Mises stress evolution for Versys cemented stem

#### **5. Conclusion**

242 Finite Element Analysis – From Biomedical Applications to Industrial Developments

Fig. 22. BMD and average von Mises stress evolution for Versys cemented stem

Prior to the development of our FE models several long-term studies of bone remodeling after the implantation of two different cementless stems, ABG I and ABG II, were performed (Panisello et al., 2006; Panisello et al., 2009a; Panisello et al., 2009b). These studies were performed using DXA, a technique that allows an accurate assessment of bone density losses in the different Gruen zones. We take as a reference to explore this evolution the postoperative value obtained in control measurements and those obtained from contralateral healthy hip. New measurements were made at 6 months, one year and 5 years after surgery. The ABG II stem is an evolution of the ABG I, which has been modified both in its alloy and design. The second generation prosthesis ABG-II is manufactured with a different titanium alloy from that used in the ABG-I. The prosthetic ABG-I stem is made with a Wrought Titanium alloy (Ti 6Al-4V) of which elasticity modulus is 110 GPa. Meanwhile, the TMZF alloy, which is used on the ABG-II stem, has a Young's modulus of 74-85 GPa, according to the manufacturer information, using a mean value of 79.5 GPa in the different analyses. On the other hand, the ABG II stem has a new design with less proximal and distal diameter, less length and the shoulder of stem has been redesign to improve osteointegration in the metaphyseal area.

In our DXA studies, directed to know the loss of bone mass in the different zones of Gruen caused by the stress-shielding, we found that ABG II model produces less proximal bone atrophy in post-operative measurements, for similar follow-up periods. In the model ABG II, we keep finding in studies with DXA a proximal bone atrophy, mainly in zones 1 and 7 of Gruen, but with an improvement of 8.7% in the values obtained in ABG I series. We can infer that improvements in the design of the stem, with a narrower diameter in the metaphyseal area, improve the load transfer to the femur and therefore minimizes the stress-shielding phenomenon, resulting in a lower proximal bone atrophy, because this area receive higher mechanical stimuli. These studies for determination of bone mass in Gruen zones, and the comparative study of their postoperative evolution during 5 years have allowed us to draw a number of conclusions: a) bone remodelling, after implantation of a femoral stem, is finished one year after surgery; b) variations in bone mass, after the first year, are not significant.

The importance of these studies is that objective data from a study with a series of patients allow us to confirm the existence of stress-shielding phenomenon, and quantify exactly the proximal bone atrophy that occurs. At the same time they have allowed us to confirm that the improvements in the ABG stem design, mean in practice better load transfer and less stres-shielding phenomenon when using the ABG II stem.

DXA studies have been basic to validate our FE models, because we have handled real values of patients' bone density, which allowed us to measure mechanical properties of real bone in different stages. Through computer simulation with our model, we have confirmed the decrease of mechanical stimulus in femoral metaphyseal areas, having a higher stimulus in ABG II type stem, which corresponds exactly with the data obtained in studies with DXA achieved in patients operated with both models stems.

In the case of cemented stems, densitometric studies were performed with two different types of stem: one straight (Versys, manufactured in a cobalt-chromium alloy) and other anatomical (ABG, manufactured in forged Vitallium patented by Stryker Howmedica). It

Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 245

was carried on the same methodology used in the cemented stems series. Densitometric studies previously made with cementless stems allow us to affirm that bone remodeling is done in the first postoperative year, a view shared by most of the authors. So, we accept that bone mineral density values obtained one year after surgery can be considered as definitive. As in cementless models, densitometric values have been used for comparison with those obtained in the FE simulation models. Our studies confirmed that the greatest loss of bone density affects the zone 7 of Gruen (Joven, 2007), which means that stress-shielding and atrophy of metaphyseal bone also occurs in cemented prostheses. This phenomenon is less severe than in non-cemented stems, therefore we can conclude that the load transfer is better with cemented stems than with cementless stems. The findings of proximal bone atrophy, mainly in the area 7, agree with those published by other authors (Arabmotlagh et al., 2006; Dan et al., 2006). We have also found differences in the rates of decrease in bone density in the area 7 of Gruen, wich were slightly lower in the anatomical ABG stem than in the Versys straight stem. This also indicates that the prosthesis design has influence in the remodeling

From a mechanical point of view, in the case of cementless stems, the improvements in the design are limited for the intrinsic behaviour of the mechanical system stem-bone. So if the compression and tension distributions are depicted (Fig. 23), one can see that, at initial steps without osteointegration, compression stresses can be transmitted in the contact interface but not tension stresses. Therefore the bending moment due to the load eccentricity only can be equilibrated by means of a couple of forces acting at points A and B, respectively, as shown in Fig. 23b. This behaviour explain the proximal bone atrophy in zone 7 of Gruen, and depending on the actual position of point A the same effect in zone 1 of Gruen. A similar effect occurs in cemented stems when the debonding appears at the bone-cement

Arabmotlagh, M.; Sabljic, R. & Rittmeister, M. (2006). Changes of the biochemical markers of

Ashman, R. B., Cowin, S. C.; Van Buskirk, W. C. et al. (1984). A continuous wave technique

Ashman, R. B. & Rho, J. Y. (1988). Elastic modulus of trabecular bone material. *J Biomech*, 21,

Bathe, K. J. (1982). *Finite element procedures in engineering analysis*, Prentice-Hall, New Jersey.

Braun, A.; Papp, J. & Reiter, A. (2003). The periprosthetic bone remodelling process signs of

Buckwalter, J. A.; Glimcher, M. J.; Cooper, R. R. et al. (1995). Bone biology, *J Bone Joint Surg* 

Bugbee, W.; Culpepper, W.; Engh, A. et al. (1997). Long-term clinical consequences of stress-

shielding after total hip arthroplasty without cement. *J Bone Joint Surg Am*, 79, 1007-

vital bone reaction. *Int Orthop*, 27, S1, 7-10. ISSN: 0341-2695

bone turnover and periprosthetic bone remodelling after cemented arthroplasty. *J* 

for the measurement of the elastic properties of cortical bone. *J Biomech*, 17, 349–61.

process, and that mechanical stimuli are different and related to the design.

interface in the tensioned zones.

ISSN: 0021-9290

177-81. ISSN: 0021-9290

ISBN-10: 0133173054

12. ISSN: 0021-9355

ABAQUS (2009). Web site, http://www.simulia.com/

*Am,* 77, 1276-1289. ISSN: 0021-9355

*Arthroplasty*, 21, 1, 129-34. ISSN: 0883-5403

**6. References** 

Fig. 23. Stress distributions in coronal plane: a) minimum principal (compression); b) maximum principal (tension)

was carried on the same methodology used in the cemented stems series. Densitometric studies previously made with cementless stems allow us to affirm that bone remodeling is done in the first postoperative year, a view shared by most of the authors. So, we accept that bone mineral density values obtained one year after surgery can be considered as definitive. As in cementless models, densitometric values have been used for comparison with those obtained in the FE simulation models. Our studies confirmed that the greatest loss of bone density affects the zone 7 of Gruen (Joven, 2007), which means that stress-shielding and atrophy of metaphyseal bone also occurs in cemented prostheses. This phenomenon is less severe than in non-cemented stems, therefore we can conclude that the load transfer is better with cemented stems than with cementless stems. The findings of proximal bone atrophy, mainly in the area 7, agree with those published by other authors (Arabmotlagh et al., 2006; Dan et al., 2006). We have also found differences in the rates of decrease in bone density in the area 7 of Gruen, wich were slightly lower in the anatomical ABG stem than in the Versys straight stem. This also indicates that the prosthesis design has influence in the remodeling process, and that mechanical stimuli are different and related to the design.

From a mechanical point of view, in the case of cementless stems, the improvements in the design are limited for the intrinsic behaviour of the mechanical system stem-bone. So if the compression and tension distributions are depicted (Fig. 23), one can see that, at initial steps without osteointegration, compression stresses can be transmitted in the contact interface but not tension stresses. Therefore the bending moment due to the load eccentricity only can be equilibrated by means of a couple of forces acting at points A and B, respectively, as shown in Fig. 23b. This behaviour explain the proximal bone atrophy in zone 7 of Gruen, and depending on the actual position of point A the same effect in zone 1 of Gruen. A similar effect occurs in cemented stems when the debonding appears at the bone-cement interface in the tensioned zones.

#### **6. References**

244 Finite Element Analysis – From Biomedical Applications to Industrial Developments

Fig. 23. Stress distributions in coronal plane: a) minimum principal (compression);

b) maximum principal (tension)

ABAQUS (2009). Web site, http://www.simulia.com/


Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 247

Hennessy, D. W.; Callaghan, J. J. & Liu, S. S. (2009). Second-generation extensively porous-

Herrera, A.; Domingo, J. J. & Panisello, J. J. (2001). Controversias en la artroplastia total de

Herrera, A.; Canales, V.; Anderson, J. et al. (2004). Seven to ten years follow up of an anatomic hip protesis. *Clin Orthop Relat R*, 423, 129-37. ISSN: 0009-921X Herrera, A. & Panisello, J. J. (2006). Fisiología del hueso y remodelado óseo. In: *Biomecánica y* 

Herrera, A.; Panisello, J. J., Ibarz, E. et al (2007). Long-term study of bone remodelling after

Herrera, A.; Panisello, J. J.; Ibarz, E. et al. (2009). Comparison between DEXA and Finite

Hughes, T. J. R. (1987). *The finite element method*, Prentice-Hall, New Jersey. ISBN-10

Huiskes, R.; Weinans, H. & Dalstra, M. (1989). Adaptative bone remodeling and

Imbert, F. J. (1979). *Analyse des structures par élément finis*, Cepadues Edit, Toulouse. ISBN:

Ionescu, I.; Conway, T.; Schonning, A. et al. (2003). Solid modeling and static finite element analysis of the human tibia. *Summer Bioengineering Conference*, 889-90, Florida. Jacobs, C. R. (1994). *Numerical simulation of bone adaptation to mechanical loading*. Dissertation

Joven, E. (2007). *Densitometry study of bone remodeling in cemented hip arthroplasty with stem straight and anatomical*. Doctoral Degree Disertation, University of Zaragoza. Kerner, J.; Huiskes, R. ; van Lenthe, G. H. et al. (1999). Correlation between pre-operative

strain-adaptative remodelling. *J Biomech*, 32, 695-703. ISSN: 0021-9290 Kroger, H.; Miettinen, H.; Arnala, I. et al. (1996). Evaluation of periprosthetic bone using

on bone mineral density. *J Bone Miner Res*, 11, 1526-30. ISSN: 0884-0431 Li, M. G.; Rohrl, S. M.; Wood, D. J. et al. (2007). Periprosthetic Changes in Bone Mineral

Relation to Stem Migration. *J Arthroplasty*, 22, 5, 698-91. ISSN: 0883-5403 Marklof, K. L.; Amstutz, H. C. & Hirschowitz, D. L. (1980). The effect of calcar contact on

McAuley, J., Sychterz, Ch. & Ench, C. A. (2000). Influence of porous coating level on proximal femoral remodeling. *Clin Orthop Relat R*, 371, 146-153. ISSN: 0009-921X

Mat Web (Material Property Data) (2009). Web site, http://www.matweb.com/

periprosthetic BMD and post-operative bone loss in THA can be explained by

dual energy X-ray absorptiometry: precision of the method and effect of operation

Density in 5 Stem Designs 5 Years After Cemented Total Hip Arthroplasty. No

femoral component micromovement.A mechanical study. *J Bone Joint Surg Am*, 62,

for the degree of Doctor of Philosophy, Stanford University.

*Traumatología II*, 141-62, Edit. Masson, Barcelona. ISBN: 8445810944

*resistencia ósea*, 27-42, Edit MMC, Madrid. ISBN: 8468977116

6. ISSN: 0009-921X

013317025X

2854280512

40, 16: 3615-25. ISSN: 0021-9290

I-DEAS (2009). Web site, http://www.ugs.com/

1315-1323. ISSN: 0021-9355

*Biomech Eng*, 31, 4, 1004-13. ISSN: 0148-0731

*Orthopedics*, 12, 1255-1267. ISSN: 0147-7447

coated THA stems at minimum 10-year followup. *Clin Orthop Relat R*, 467, 9, 2290-

cadera. Elección del implante. In: *Actualizaciones en Cirugía Ortopedica y* 

femoral stem: A comparison between dexa and finite element simulation. *J Biomech*,

Element studies in the long term bone remodelling o an anatomical femoral stem. *J* 

biomechanical design considerations for noncemented total hip arthroplasty.


Canales, V.; Panisello, J. J.; Herrera, A. et al. (2006). Ten year follow-up of an anatomical hydroxyapatite-coated total hip prosthesis. *Int Orthop*, 30, 84-90. ISSN: 0341-2695 Charnley, J. (1961). Arthroplasty of the hip: a new operation. *Lancet*, 1129-32. ISSN: 0140-

D'Antonio, J. A.; Manley, M. T.; Capello, W. N. et al. (2005). Five year experience with

Dan, D.; Germann, D.; Burki, H. et al. (2006). Bone loss alter total hip arthroplasty. *Rheumatol* 

Engh, C. A. Jr.; Mc Auley, J.P.; Sychter, C.J. et al. (2000). The accuracy and reproducibility of

Engh, C. A. Jr; Young, A. M.; Engh, C. A. Sr. et al. (2003). Clinical consequences of stress

Evans, F. G. (1973). *The Mechanical Properties of Bone*. American Lecture Series, n. 881,

Faris, P. M.; Ritter, M. A.; Pierce A. L. et al. (2006). Polyethylene sterilization and production

Gibbons, C. E. R.; Davies, A. J.; Amis, A. A. et al. (2001). Periprosthetic bone mineral density

Glassman, A. H.; Crowninshield, R. D.; Schenck, R. et al. (2001). A low stiffness composite biologically fixed prostheses. *Clin Orthop Relat R*,, 393, 128-136. ISSN: 0009-921X Glassman, A. H.; Bobyn, J. D. & Tanzer, M. (2006). New femoral designs: do they influence

Gordon, A. C.; D'Lima, D. D. & Colwell, C. W. (2006). Highly cross-linked polyethylene in total hip arthroplasty. *J Am Acad Orthop Surg*, 14, 9, 511-23. ISSN: 1067-151X Grant, P. & Nordsletten, L. (2004). Influence of porous coating level on proximal femoral remodelling. *J Bone Joint Surg Am*, 86-A, 12, 2636-41. ISSN: 0021-9355 Gruen, T. A.; McNeice, G. M. & Amstutz H. C. (1979). Modes of failure of cemented stem-

Halley, D. K. & Wroblewski, B. M. (1986). Long-term results of low-friction arthroplasty in

Harris, W. H.; McCarthy, J. & O'Neill, D. A. (1982). Femoral component loosening using

Hellman, E. J.; Capello, W. N. & Feinberg, J. R. (1999). Omnifit cementless total hip

stress-shielding? *Clin Orthop Relat R*, 453, 64-74. ISSN: 0009-921X

Crossfire highly cross-linked polyethylene. *Clin Orthop Relat R*, 441, 143-50. ISSN:

radiographic assessment of stress-shielding. *J Bone Joint Surg Am*, 82, 1414-20. ISSN:

shielding after porous-coated total hip arthroplasty. *Clin Orthop Relat R*, 417, 157-63.

affects wear in total hip arthroplasties. *Clin Orthop Relat R*, 453, 305-8. ISSN: 0009-

changes with femoral components of different design philosophy. *In Orthop*, 25, 89-

type femoral components: a radiographic analysis of loosening. *Clin Orthop Relat R*,

patients 30 years of age or younger. *Clin Orthop Relat R*, 211, 43-50. ISSN: 0009-

contemporary techniques of femoral cement fixation. *J Bone Joint Surg Am*, 64, 7,

arthroplasty: A 10-years average follow up. *Clin Orthop Relat R*, 364, 164-174. ISSN:

6736

0009-921X

0021-9355

921X

921X

0009-921X

ISSN: 0009-921X

92. ISSN: 0341-2695

141, 17-27. ISSN: 0009-921X

1063-67. ISSN: 0021-9355

*Int*, 26, 9, 792-8. ISSN: 0172-8172

Springfield, IL. ISBN: 0398027757


Simulation by Finite Elements of Bone Remodelling After Implantation of Femoral Stems 249

Rosenthall, L.; Bobyn, J.D. & Tanzer, M. (1999). Bone densitometry: influence of prosthetic

Rubash, H. E.; Sinha, R. K.; Shanbhag, A. S. et al. (1998). Pathogenesis of bone loss after total

Schmidt, R.; Nowak, T.; Mueller, L. et al. (2004). Osteodensitometry after total hip

Shirazi-Adl, A., Dammak, M. & Paiement, G. (1993). Experimental determination of friction

Sinha, R. K.; Dungy, D. S. & Yeon, H. B. (2004). Primary total hip arthroplasty with a

Stauffer, R. N. (1982). Ten-year follow-up study of total hip replacement. *J Bone Joint Surg* 

Sumner, D.R. & Galante, J. O. (1992). Determinants of stress shielding: design versus materials versus interface. *Clin Orthop Relat R*, 274, 202-12. ISSN: 0009-921X Sychter, C. J. & Engh, C. A. (1992). The influence of clinical factor on periprosthetic bone

Tanzer, M.; Maloney, W. J.; Jasty, M. et al. (1992). The progression of femoral cortical

Tonino, A. J.; Therin, M. & Doyle, C. (1999). Hydroxyapatite coated femoral stems:

Turner, M. J.; Clough, R. W.; Martin, M. C. & Topp, L. J. (1956). Stiffness and deflection

Turner, C. H.; Rho, J. ; Takano, Y. et al. (1999). The elastic properties of trabecular and

Turner, A. W. L.; Gillies, R.M.; Sekel, R. et al. (2005). Computational bone remodelling

Urriés, I; Medel, F. J.; Ríos F. et al. (2004). Comparative cyclic stress-strain and fatigue

van der Val, B. C. H.; Rahmy, A. ; Grimm, B. et al. (2006). Preoperative bone quality as a

Weinans, H.; Huiskes, R. & Grootenboer, H. J. (1994). Effects of fit and bonding

between two implant types. *Int Orthop*, On line. ISSN: 0341-2695

osteolysis in association with total hip arthroplasty without cement. *J Bone Joint* 

Histology and histomorphometry around five components retrieved at post-

analysis of complex structures. *J Aeronautical Sciences*, 23, 9, 805-823. ISSN: 0095-

cortical bone tissues are similar: results from two microscopic measurement

simulations and comparisons with DEXA results. *J Orthop Res*, 23, 705-12. ISSN:

resistance behaviour of electron-beam and gamma irradiated UHMWPE. *J Biomed* 

factor in dual-energy X-ray absorptiometry analysis comparing bone remodelling

characteristics of femoral stems on adaptative bone remodelling. *J Biomech Eng,* 116,

remodeling. *Clin Orthop Relat R*, 322, 285-92. ISSN: 0009-921X

mortem. *J Bone Joint Surg Br*, 81, 148-54. ISSN: 0301-620X

techniques. *J Biomech*, 32, 437-41. ISSN: 0021-9290

*Mater Res B*, 70, 1, 152-60. ISSN: 1552-4973

4, 393-400. ISSN: 0148-0731

hip arthroplasty. *Orthop Clin N Am*, 29(2), 173-186. ISSN: 0030-5898.

implants. *J Bio Mat Res A*, 27, 167-75. ISSN: 1549-3296

*Orthop*, 23, 325-29. ISSN: 0341-2695

*Am*, 64, 7, 983-90. ISSN: 0021-9355

*Surg Am*, 74, 404-10. ISSN: 0021-9355

2695

0021-9355

9812

0736-0266

design and hydroxyapatite coating on regional adaptative bone remodelling. *Int* 

replacement with uncemented taper-design stem. *Int Orthop*, 28, 74-7. ISSN: 0341-

characteristics at the trabecular bone/porous-coated metal interface in cementless

proximally porous-coated femoral stem. *J Bone Joint Surg Am* 86, 6, 1254-61. ISSN:


Medel, F. J.; Gómez-Barrena, E.; García-Álvarez, F. et al. (2004). Fractography evolution in

Meunier, A.; Riot, O. ; Christel, P. et al. (1989). Inhomogeneities in anisotropic elastic

Mohler, C. G.; Callaghan, J. J.; Collis, D. K. et al. (1995). Early loosening of the femoral

Mulroy, R. D.; Harris, W. H. (1990). The effect of improved cementing techniques on

Noble, P. C.; Collier, M. B.; Maltry, J. A. et al. (1998). Pressurization and centralization

Nourissat, C.; Adrey, J.; Berteaux, D. et al. (1995). The ABG Standar hip prosthesis: Five year

Oral, E.; Christensen, S. D.; Malhi, A. S. et al. (2005). Wear resistance and mechanical

Panisello, J. J.; Herrero, L.; Herrera, A. et al. (2006). Bone remodelling after total hip

study using bone densitometry. *J Orthop Surg*, 14, 122-25. ISSN: 1022-5536 Panisello, J. J.; Herrero, L.; Canales, V. et al. (2009a). Long-term remodelling in proximal

Panisello, J. J.; Canales, V.; Herrero, L. et al. (2009b). Changes in periprosthetic bone

Radin, E. L. (1980). Bimechanics of the Human hip. *Clin Orthop Relat R,* 152, 28-34. ISSN:

Ramaniraka, N. A.; Rakotomanana, L. R. & Leyvraz, P. F. (2000). The fixation of the

Reading, A. D.; McCaskie, A. W.; Barnes, M. R. et al. (2000). A comparison of 2 modern

with vitamin E. *J Arthroplasty*, 21, 4, 580-91. ISSN: 0883-5403

follow-up. *J Arthroplasty*, 24, 1, 56-64. ISSN: 0883-5403

*Arthroplasty*, 15, 4, 479-87. ISSN: 0883-5403

constants of cortical bone. *Ultrasonics Symposium*, 1015-1018.

MIMICS. (2010). Web site, http://www.materialise.com/

*Joint Surg Am*, 77, 9, 1315-22. ISSN: 0021-9355

*Bone Joint Surg Br*, 72, 5, 757-60. ISSN: 0301-620X

21. ISSN: 0142-9612

89. ISSN: 0009-921X

80. ISSN: 0341-2695

0009-921X

620X

6470

accelerated aging of UHMWPE after gamma irradiation in air. *Biomaterials*, 25, 1, 9-

component at the cement-prosthesis interface after total hip replacement. *J Bone* 

component loosening in total hip replacement. An 11 year radiographic review. *J* 

enhance the quality and reproductibility of cementless. *Clin Orthop Relat R*, 355, 77-

results. In: *Hydroxyapatite coated hip and knee arthroplasty*, 227-38, Epinette JA, Geesink RGT, Eds. Edit Expansion Cientifique Francaise, Paris. ISBN: 2704614709 Olsson, S. S.; Jenberger, A. & Tryggo, D. (1981). Clinical and radiological long-term results

after Charnley-Muller total hip replacement. A 5 to 10 year follow-up study with special reference to aseptic loosening. *Acta Orthop Scand*, 52, 5, 531-42. ISSN: 0001-

properties of highly cross-linked, ultrahigh-molecular weight polyethylene doped

arthroplasty using an uncemented anatomic femoral stem: a three-year prospective

femur around a hydroxyapatite-coated anatomic stem. Ten years densitometric

remodelling alter redesigning an anatomic cementless stem. *Inter Orthop*, 33, 2, 373-

cemented femoral component .Effects of stem stiffness, cement thickness and roughness of the cement-bone surface . *J Bone Joint Surg Br*, 82, 297-303. ISSN: 0301-

femoral cementing techniques: analysis by cement-bone interface pressure measurement, computerized image analysis and static mechanical testing. *J* 


**10**

*China* 

, Li Wang, Ruonan Wang, Yunbo Wang and Feng Zhou *Mechanical Engineering School,* 

**Tissue Modeling and Analyzing for**

*University of Science and Technology Beijing, Beijing,* 

**Cranium Brain with Finite Element Method** 

Xianfang Yue

Numerous methods for measuring intracranial pressure (ICP) have been described, and many of them are suitable for different clinical disorders [1-5]. One method for ICP monitoring is through the ventricular system [6,7], which requires stereotaxic techniques and may not be practical for surgical experiments in the brain regions. Ventricular monitoring of ICP is also associated with intracerebral hemorrhage and infection [6]. Another method to monitor ICP is through the subarachnoid space at the cisterna magna, in which catheter placement may be difficult and dangerous due to the anatomy [8,9]. Some studies monitored ICP via epidural [10,12], which has limitations in measuring acute changes in ICP and is inaccurate in some cases when compared with ventricular monitoring [8]. These methods have many disadvantages of invasion, low-accuracy, cross-infection, etc [13,14]. Although many efforts have recently been made to improve the minitraumatic or non-invasive methods [15-19], noninvasive means of measuring ICP do not exist unfortunately in clinic [20,21]. With the significance of raised ICP in the studies of intracranial pathophysiology, espacially in neurosurgical disorders, it would be valuable to have a simple and reliable method to monitor intracranial pressure (ICP) in clinic. Therefore, the minitraumatic or non-invasive, accurate and simple method to measure ICP is an important question of research in neurosurgery. In this study, we propose a new, minitraumatic, simple, and reliable measurable system that can be used to monitor ICP from

The 'Monro [22] – Kellie [23] doctrine' states that an adult cranial compartment is incompressible, and the volume inside the cranium is a fixed volume thus creates a state of volume equilibrium, such that any increase of the volumes of one component (i.e. blood, CSF, or brain tissue) must be compensated by a decrease in the volume of another. If this cannot be achieved then pressure will rise and once the compliance of the intracranial space is exhausted then small changes in volume can lead to potentially lethal increases in ICP. The compensatory mechanism for intracranial space occupation obviously has limits. When the amount of CSF and venous blood that can be extruded from the skull has been

**1. Introduction** 

the exterior surface of skull bone.

Corresponding Author


### **Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method**

Xianfang Yue , Li Wang, Ruonan Wang, Yunbo Wang and Feng Zhou *Mechanical Engineering School, University of Science and Technology Beijing, Beijing, China* 

#### **1. Introduction**

250 Finite Element Analysis – From Biomedical Applications to Industrial Developments

Wick, M. & Lester D.K. (2004). Radiological changes in second and third generation Zweymuller stems. *J Bone Joint Sur Br*, 86, 8, 1108-14. ISSN: 0301-620X Wolf, C.; Maninger, J.; Lederer, K. et al. (2006). Stabilisation of crosslinked ultra-high

Zienkiewicz, O. C. (1967). *The finite element method in structural and continuum mechanics*,

Zienkiewicz, O. C. & Morgan, K. (1983). *Finite element and approximation*, John Wiley & Sons,

tocopherol. *J Mater Sci Mater Med*, 17, 12, 1323-31. ISSN: 0957-4530

Prentice-Hall, New Jersey. ASIN: B000HF38VG

New York. ISBN 10: 0471982407

molecular weight polyethylene (UHMWPE)-acetabular components with alpha-

Numerous methods for measuring intracranial pressure (ICP) have been described, and many of them are suitable for different clinical disorders [1-5]. One method for ICP monitoring is through the ventricular system [6,7], which requires stereotaxic techniques and may not be practical for surgical experiments in the brain regions. Ventricular monitoring of ICP is also associated with intracerebral hemorrhage and infection [6]. Another method to monitor ICP is through the subarachnoid space at the cisterna magna, in which catheter placement may be difficult and dangerous due to the anatomy [8,9]. Some studies monitored ICP via epidural [10,12], which has limitations in measuring acute changes in ICP and is inaccurate in some cases when compared with ventricular monitoring [8]. These methods have many disadvantages of invasion, low-accuracy, cross-infection, etc [13,14]. Although many efforts have recently been made to improve the minitraumatic or non-invasive methods [15-19], noninvasive means of measuring ICP do not exist unfortunately in clinic [20,21]. With the significance of raised ICP in the studies of intracranial pathophysiology, espacially in neurosurgical disorders, it would be valuable to have a simple and reliable method to monitor intracranial pressure (ICP) in clinic. Therefore, the minitraumatic or non-invasive, accurate and simple method to measure ICP is an important question of research in neurosurgery. In this study, we propose a new, minitraumatic, simple, and reliable measurable system that can be used to monitor ICP from the exterior surface of skull bone.

The 'Monro [22] – Kellie [23] doctrine' states that an adult cranial compartment is incompressible, and the volume inside the cranium is a fixed volume thus creates a state of volume equilibrium, such that any increase of the volumes of one component (i.e. blood, CSF, or brain tissue) must be compensated by a decrease in the volume of another. If this cannot be achieved then pressure will rise and once the compliance of the intracranial space is exhausted then small changes in volume can lead to potentially lethal increases in ICP. The compensatory mechanism for intracranial space occupation obviously has limits. When the amount of CSF and venous blood that can be extruded from the skull has been

Corresponding Author

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 253

and quasi-isotropic. In addition, the sutures of cranial cavity are also the continuous

When the objects are under tension, not only the length is drawn out from *l* to 1*l* , but also the width is reduced from *b* to 1*b* . This shows that there are the horizontal compressive stresses in the objects. Similarly, while the object is compressed, not only its length shortens but its width increases. It indicates that the horizontal tensile stress distributes in the objects. The horizontal absolute deformation is noted as 1 *bbb* , and the transverse strain is

of the same material within the scope of the Hooke theorems' application. The ratio of its

While vertically compressed, the objects simultaneously have a horizontal tension. Therefore, when the head attacked in opposite directions force, the entire human skull will take place the longitudinal compression and transverse tension with the same direction of force. Then the longitudinal compressive stress and the horizontal tensile stress will be generated in the scelrotin. Thus, the stress of arbitrary section along radial direction in shell is just equal to the tangential pulling force along direction perpendicular to the normal

**2.1.1 The finite-element analysis of strains by ignoring the viscoelasticity of cranial** 

The geometric shape of human skull is irregular and variable with the position, age, gender and individual. So the cranial cavity system is very complex. Moreover, the cranial cavity is a kind of viscoelactic solid with large elastic modulus, and the brain tissue is also a viscoelastic fluid with great bulk modulus. It is now almost impossible to accurately analyze the brain system. Only by some simplification and assumptions, the complex issues can be made. Considering the special structure of cranial cavity composed of skull, duramater, encephalic substance, etc, here we simplify the model of cranial cavity as a regular geometry spheroid of about 200mm external diameter, which is an hollow equal-thickness thin-wall

The craniospinal cavity may be considered as a balloon. For the purpose of our analysis, we adopted the model of hollow sphere. We presented the development and validation of a 3D finite-element model intended to better understand the deformation mechanisms of human skull corresponding to the ICP change. The skull is a layered sphere constructed in a

or Poisson ratio. The Poisson ratio of any objects can be detected by the experiment.

is proportional to the longitudinal strain

is known as the coefficient of lateral deformation,

Stress is the internal force per unit area. The calculation unit is <sup>2</sup> kg/cm or <sup>2</sup> kg/mm **.** 

integration with ages.

)

2. Transverse deformation coefficient

In mechanics of materials, the transverse strain 0

is a constant.

**(2) Two concepts** 

1. stress (

0 *b b* .

**cavity** 

shell.

absolute value

 <sup>0</sup> 

vertical when ICP is raised.

exhausted, the ICP becomes unstable and waves of pressure develop. As the process of space occupation continues, the ICP can rise to very high levels and the brain can become displaced from its normal position. Dr. Sutherland firstly perceived a subtle palpable movement within the bones of cranium. Dr. Upledger [24] discovered that the inherent rhythmic motion of cranial bones was caused by the fluctuation of CSF. Accordingly, the cranium can move and be deformed as the ICP fluctuates. By pasting strain foils on the exterior surface of skull bone, the skull strains can be measured with the strain gauge. ICP variation can be obtained through the corresponding processing based on the strains. So the ICP can be monitored by measuring the strains of skull bone [25].

#### **2. Mechanical analysis of cranial cavity deformation**

#### **2.1 Mechanical analysis of deformation of the skull as a whole**

There are two aspects of effects on forces on the objects. One can make objects produce the acceleration, another is make objects deform. In discussing the external force effect, the objects are assumed to be a rigid body not compressed. But in fact, all objects will deform under loading, but different with the degrees. Here, we will mechanically analyze the overall deformation of cranial cavity under the external force.

#### **(1) Two basic assumptions**

To simplify the analysis of deformation of human skull, we assume:

1. Uniformly-continuous materials

The human skull is presumed to be everywhere uniform, and the sclerotin is no gap in bone of cranial cavity.

2. The isotropy

The human skull is supposed to have the same mechanical properties in all directions. The thickness and curvature of human skull vary here and there. The external and internal boards are all compact bones, in which external board is thicker than internal board but the radian of external board is smaller than that of the internal board. The diploe is the cancellous bone between the external board and the internal board, which consists of the marrow and diploe vein. The parietal bone is the transversely isotropic material [26], namely, it has the mechanical property of rotational symmetry in any axially vertical planes of skull [27]. The tensile and compressive abilities of compact bone are strong. The important mechanical characteristics of cancellous bone are viscoelasticity [28], which is generally considered as the construction of semi-closed honeycomb composed of bone trabecula reticulation. The main composition of cerebral duramater, a thick and tough bilayer membrane, is collagenous fiber11, which is viscoelastic material [29]. And the thickness of duramater is obviously variable with the changing ICP [30]. The mechanical performance of skull is isotropic along tangential direction on the skull surface [31], in which the performance of compact bone in the external board is basically the same as that in the internal board [32], thus both cancellous bone and duramater can be regarded as isotropic materials [33]. And the elastic modulus of fresh duramater is variable with delay time [34]. And there are a number of sutures in the cranial cavity. But while a partial skull is studied on the local deformation, we can regard each partial skull as quasi-homogeneous and quasi-isotropic. In addition, the sutures of cranial cavity are also the continuous integration with ages.

#### **(2) Two concepts**

1. stress ()

252 Finite Element Analysis – From Biomedical Applications to Industrial Developments

exhausted, the ICP becomes unstable and waves of pressure develop. As the process of space occupation continues, the ICP can rise to very high levels and the brain can become displaced from its normal position. Dr. Sutherland firstly perceived a subtle palpable movement within the bones of cranium. Dr. Upledger [24] discovered that the inherent rhythmic motion of cranial bones was caused by the fluctuation of CSF. Accordingly, the cranium can move and be deformed as the ICP fluctuates. By pasting strain foils on the exterior surface of skull bone, the skull strains can be measured with the strain gauge. ICP variation can be obtained through the corresponding processing based on the strains. So the

There are two aspects of effects on forces on the objects. One can make objects produce the acceleration, another is make objects deform. In discussing the external force effect, the objects are assumed to be a rigid body not compressed. But in fact, all objects will deform under loading, but different with the degrees. Here, we will mechanically analyze the

The human skull is presumed to be everywhere uniform, and the sclerotin is no gap in bone

The human skull is supposed to have the same mechanical properties in all directions. The thickness and curvature of human skull vary here and there. The external and internal boards are all compact bones, in which external board is thicker than internal board but the radian of external board is smaller than that of the internal board. The diploe is the cancellous bone between the external board and the internal board, which consists of the marrow and diploe vein. The parietal bone is the transversely isotropic material [26], namely, it has the mechanical property of rotational symmetry in any axially vertical planes of skull [27]. The tensile and compressive abilities of compact bone are strong. The important mechanical characteristics of cancellous bone are viscoelasticity [28], which is generally considered as the construction of semi-closed honeycomb composed of bone trabecula reticulation. The main composition of cerebral duramater, a thick and tough bilayer membrane, is collagenous fiber11, which is viscoelastic material [29]. And the thickness of duramater is obviously variable with the changing ICP [30]. The mechanical performance of skull is isotropic along tangential direction on the skull surface [31], in which the performance of compact bone in the external board is basically the same as that in the internal board [32], thus both cancellous bone and duramater can be regarded as isotropic materials [33]. And the elastic modulus of fresh duramater is variable with delay time [34]. And there are a number of sutures in the cranial cavity. But while a partial skull is studied on the local deformation, we can regard each partial skull as quasi-homogeneous

ICP can be monitored by measuring the strains of skull bone [25].

**2.1 Mechanical analysis of deformation of the skull as a whole** 

**2. Mechanical analysis of cranial cavity deformation** 

overall deformation of cranial cavity under the external force.

To simplify the analysis of deformation of human skull, we assume:

**(1) Two basic assumptions** 

of cranial cavity. 2. The isotropy

1. Uniformly-continuous materials

Stress is the internal force per unit area. The calculation unit is <sup>2</sup> kg/cm or <sup>2</sup> kg/mm **.** 

2. Transverse deformation coefficient

When the objects are under tension, not only the length is drawn out from *l* to 1*l* , but also the width is reduced from *b* to 1*b* . This shows that there are the horizontal compressive stresses in the objects. Similarly, while the object is compressed, not only its length shortens but its width increases. It indicates that the horizontal tensile stress distributes in the objects.

The horizontal absolute deformation is noted as 1 *bbb* , and the transverse strain is 0 *b b* .

In mechanics of materials, the transverse strain 0 is proportional to the longitudinal strain of the same material within the scope of the Hooke theorems' application. The ratio of its absolute value <sup>0</sup> is a constant. is known as the coefficient of lateral deformation, or Poisson ratio. The Poisson ratio of any objects can be detected by the experiment.

While vertically compressed, the objects simultaneously have a horizontal tension. Therefore, when the head attacked in opposite directions force, the entire human skull will take place the longitudinal compression and transverse tension with the same direction of force. Then the longitudinal compressive stress and the horizontal tensile stress will be generated in the scelrotin. Thus, the stress of arbitrary section along radial direction in shell is just equal to the tangential pulling force along direction perpendicular to the normal vertical when ICP is raised.

#### **2.1.1 The finite-element analysis of strains by ignoring the viscoelasticity of cranial cavity**

The geometric shape of human skull is irregular and variable with the position, age, gender and individual. So the cranial cavity system is very complex. Moreover, the cranial cavity is a kind of viscoelactic solid with large elastic modulus, and the brain tissue is also a viscoelastic fluid with great bulk modulus. It is now almost impossible to accurately analyze the brain system. Only by some simplification and assumptions, the complex issues can be made. Considering the special structure of cranial cavity composed of skull, duramater, encephalic substance, etc, here we simplify the model of cranial cavity as a regular geometry spheroid of about 200mm external diameter, which is an hollow equal-thickness thin-wall shell.

The craniospinal cavity may be considered as a balloon. For the purpose of our analysis, we adopted the model of hollow sphere. We presented the development and validation of a 3D finite-element model intended to better understand the deformation mechanisms of human skull corresponding to the ICP change. The skull is a layered sphere constructed in a

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 255

Fig. 2.2. Block diagram of **numerical solution** steps of cranial cavity with the finite-element

To make the nodal displacement express the displacement, strain and stress of element body, the displacement distribution in the elements are assumed to be the polynomial interpolation function of coordinates. The items of polynomial number are equal to the freedom degrees number of elements, that is, the number of independent displacement of

According to the selected displacement mode, the nodal displacement is derived to express

 *<sup>e</sup> f N* 

Where: *f* - The displacement array of any point within the element; *N*- The shape

The block approximation is adopted to solve the displacement of cranial cavity in the entire solving region, and an approximate displacement function is selected in an element, where

(2.1)


element node. The orders of polynomial contain the constant term and linear terms.

the displacement relationship of any point in the elements. Its matrix form is:

function matrix, its elements is a function of location coordinates; *<sup>e</sup>*

method

2. The selection of displacement mode

displacement array of element.

specially designed form with a Tabula externa, Tabula interna, and a porous Diploe sandwiched in between. Based on the established knowledge of cranial cavity importantly composed of skull and dura mater (Fig2.1), a thin-walled structure was simulated by the composite shell elements of the finite-element software [35]. The thickness of skull is 6mm, that of duramater is 0.4mm, that of external compact bone is 2.0mm, that of cancellous bone is 2.8mm, and that of internal compact bone is 1.2mm.

Fig. 2.1. Sketch of layered sphere. The thin-walled structure of cranial cavity is mainly composed of Tabula externa, Diploe, Tabula interna and dura mater.

Above all, we should prove the theoretical feasibility of the strain-electrometric method to monitor ICP. We simplify the theoretical calculation by ignoring the viscoelasticity of cancellous bone and dura mater. And then we make the analysis of the actual deformation of cranial cavity by considering the viscoelasticity of human skull-dura mater system with the finite-element software. At the same time, we can determine how the viscoelasticity of human skull and dura mater influences the strains of human skull respectively by ignoring and considering the viscoelasticity of human skull and dura mater.

#### **2.1.2 The stress and strain analysis of discretized elements of cranial cavity**

In order to obtain the numerical solution of the skull strain, the continuous solution region of cranial cavity divided into a finite number of elements, and a group element collection glued on the adjacent node points. Then the large number of cohesive collection can be simulated the overall cranial cavity to carry out the strain analysis in the solving region. Based on the block approximation ideas, a simple interpolation function can approximately express the distribution law of displacement in each element. The node data of the selected field function, the relationship between the nodal force and displacement is established, and the algebraic equations of regarding the nodal displacements as unknowns can be formed, thus the nodal displacement components can be solved. Then the field function in the element collection can be determined by using the interpolation function. If the elements meet the convergence requirements, with the element numbers increase in the solving region with the shrinking element size, and the approximate solution will converge to exact solutions [36].

The solving steps for the strains of cranial cavity with the ICP changes are shown in Fig2.2. The specific numerical solution process is:

1. The discretized cranial cavity

The three-dimensional hollow sphere of cranial cavity is divided into a finite number of elements. By setting the nodes in the element body, an element collection can replace the structure of cranial cavity after the parameters of adjacent elements has a certain continuity.

specially designed form with a Tabula externa, Tabula interna, and a porous Diploe sandwiched in between. Based on the established knowledge of cranial cavity importantly composed of skull and dura mater (Fig2.1), a thin-walled structure was simulated by the composite shell elements of the finite-element software [35]. The thickness of skull is 6mm, that of duramater is 0.4mm, that of external compact bone is 2.0mm, that of cancellous bone

Fig. 2.1. Sketch of layered sphere. The thin-walled structure of cranial cavity is mainly

**2.1.2 The stress and strain analysis of discretized elements of cranial cavity** 

Above all, we should prove the theoretical feasibility of the strain-electrometric method to monitor ICP. We simplify the theoretical calculation by ignoring the viscoelasticity of cancellous bone and dura mater. And then we make the analysis of the actual deformation of cranial cavity by considering the viscoelasticity of human skull-dura mater system with the finite-element software. At the same time, we can determine how the viscoelasticity of human skull and dura mater influences the strains of human skull respectively by ignoring

In order to obtain the numerical solution of the skull strain, the continuous solution region of cranial cavity divided into a finite number of elements, and a group element collection glued on the adjacent node points. Then the large number of cohesive collection can be simulated the overall cranial cavity to carry out the strain analysis in the solving region. Based on the block approximation ideas, a simple interpolation function can approximately express the distribution law of displacement in each element. The node data of the selected field function, the relationship between the nodal force and displacement is established, and the algebraic equations of regarding the nodal displacements as unknowns can be formed, thus the nodal displacement components can be solved. Then the field function in the element collection can be determined by using the interpolation function. If the elements meet the convergence requirements, with the element numbers increase in the solving region with the shrinking element size, and the approximate solution will converge to exact

The solving steps for the strains of cranial cavity with the ICP changes are shown in Fig2.2.

The three-dimensional hollow sphere of cranial cavity is divided into a finite number of elements. By setting the nodes in the element body, an element collection can replace the structure of cranial cavity after the parameters of adjacent elements has a certain continuity.

composed of Tabula externa, Diploe, Tabula interna and dura mater.

and considering the viscoelasticity of human skull and dura mater.

solutions [36].

The specific numerical solution process is:

1. The discretized cranial cavity

is 2.8mm, and that of internal compact bone is 1.2mm.

Fig. 2.2. Block diagram of **numerical solution** steps of cranial cavity with the finite-element method

#### 2. The selection of displacement mode

To make the nodal displacement express the displacement, strain and stress of element body, the displacement distribution in the elements are assumed to be the polynomial interpolation function of coordinates. The items of polynomial number are equal to the freedom degrees number of elements, that is, the number of independent displacement of element node. The orders of polynomial contain the constant term and linear terms.

According to the selected displacement mode, the nodal displacement is derived to express the displacement relationship of any point in the elements. Its matrix form is:

$$\{f\} = \begin{bmatrix} \mathcal{N} \end{bmatrix} \{\mathcal{S}\}^{\varepsilon} \tag{2.1}$$

Where: *f* - The displacement array of any point within the element; *N*- The shape function matrix, its elements is a function of location coordinates; *<sup>e</sup>* - The nodal displacement array of element.

The block approximation is adopted to solve the displacement of cranial cavity in the entire solving region, and an approximate displacement function is selected in an element, where

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 257

According to the displacement equal principle of the public nodes in all adjacent elements, the relationship between force and displacement of overall cranial cavity collected from the

*F K*

After the formula (2.1) ~ (2.5) eliminating the stiffness displacement of geometric boundary conditions, the nodal displacement can be solved from the gathered relationship groups

6. By classifying the nodal displacement solved from the formula (2.2) and (2.3), the strain

In this paper, the studied cranial cavity is a hollow three-dimensional sphere, its external radius 100 mm *R* , the curvature of hollow shell is 0 01 rad/mm *.* , the thickness of shell wall is 6mm, so the element body of hollow spherical can be treated as the regular hexahedron. The following is the stress and strain analyses in the three-dimensional elements in the cranial space. The 8-node hexahedral element (Fig2.3) is used to be the

Trough the transformation between rectangular coordinates and local coordinates, the space 8-node isoparametric centroid element can be obtained. The relationship of coordinate

Where: *F* - Load array; *K* - The overall stiffness matrix;

and stress in each element can be calculated.

master element. The origin is set up as the local coordinate system (

Fig. 2.3. The space 8-node isoparametric centroid element

(2.5)

 *, ,* 

) in the element.


element stiffness matrix:

array of the entire cranial cavity. 5. Solve the nodal displacement

between force and displacement.

transformation is:

need only consider the continuity of displacement between elements, not the boundary conditions of displacement. Considering the special material properties of the middle cancellous and duramater, the approximate displacement function can adopt the piecewise function.


$$\text{Strain equations} \begin{cases} \varepsilon\_x = \frac{\partial u}{\partial x}, \gamma\_{xy} = \frac{\partial u}{\partial y} + \frac{\partial v}{\partial x} \\ \varepsilon\_y = \frac{\partial u}{\partial y}, \gamma\_{yz} = \frac{\partial u}{\partial z} + \frac{\partial w}{\partial y} \\ \varepsilon\_z = \frac{\partial u}{\partial z}, \gamma\_{zx} = \frac{\partial u}{\partial x} + \frac{\partial v}{\partial z} \end{cases}$$
 
$$\{\varepsilon\} = \left[B\right] \{\mathcal{S}\}^\varepsilon \tag{2.2}$$

Where:[B]—The strain matrix of elements; —The strain array at any points within the elements.

b. The constitutive equation reflecting the physical characteristics of material is *D* , so the stress relationship of stress can be expressed with the nodal displacements derived from the strain formula (2.2):

$$\mathbb{E}\{\sigma\} = \left[D\right] \left[B\right] \left\{\delta\right\}^{\varepsilon} \tag{2.3}$$

Where: - The stress array of any points in the elements; *D*- The elastic matrix related to the element material.

c. Using the variational principle, the relationship between force and displacement of the element nodes is established:

$$\left\{F\right\}^{\varepsilon} = \left\lbrack k\right\rbrack^{\varepsilon}\left\{\delta\right\}^{\varepsilon} \tag{2.4}$$

Where: *<sup>e</sup> <sup>k</sup>* - Element stiffness matrix, *e T k B D B dxd ydz* ; *<sup>e</sup> <sup>F</sup>* - Equivalent nodal force array, *<sup>e</sup> ee e FF F F VSC* ; *<sup>e</sup> FV* - Equivalent nodal force on the nodes transplanted from the element volume force *PV* , *<sup>e</sup> <sup>T</sup> V V V F N P dV* ; *<sup>e</sup> FS* - Equivalent nodal force on the nodes transplanted from the element surface force, *<sup>e</sup> <sup>T</sup> A S A F N P dA* ; *<sup>e</sup> FC* - Concentration force of nodes.

4. Collecting all relationship between force and displacement, and establish the relationship between force and displacement of cranial cavity

According to the displacement equal principle of the public nodes in all adjacent elements, the relationship between force and displacement of overall cranial cavity collected from the element stiffness matrix:

$$\{F\} = [K]\{\delta\} \tag{2.5}$$

Where: *F* - Load array; *K* - The overall stiffness matrix; - The nodal displacement array of the entire cranial cavity.

5. Solve the nodal displacement

256 Finite Element Analysis – From Biomedical Applications to Industrial Developments

need only consider the continuity of displacement between elements, not the boundary conditions of displacement. Considering the special material properties of the middle cancellous and duramater, the approximate displacement function can adopt the piecewise

3. Analyze the mechanical properties of elements, and derive the element stiffness matrix a. Using the following strain equations, the relationship of element strain (2.2) is expressed by the nodal displacements derived from the displacement equation (2.1):

> *<sup>e</sup> B*

b. The constitutive equation reflecting the physical characteristics of material is

*<sup>e</sup>*

c. Using the variational principle, the relationship between force and displacement of the

*e e <sup>e</sup> F k*

Where: *<sup>e</sup> <sup>k</sup>* - Element stiffness matrix, *e T k B D B dxd ydz* ; *<sup>e</sup> <sup>F</sup>* - Equivalent nodal force array, *<sup>e</sup> ee e FF F F VSC* ; *<sup>e</sup> FV* - Equivalent nodal force on the nodes

nodal force on the nodes transplanted from the element surface force,

4. Collecting all relationship between force and displacement, and establish the

*D B*

transplanted from the element volume force *PV* , *<sup>e</sup> <sup>T</sup>*

relationship between force and displacement of cranial cavity

*F N P dA* ; *<sup>e</sup> FC* - Concentration force of nodes.

, so the stress relationship of stress can be expressed with the nodal


*V V V*

(2.2)

(2.3)

(2.4)

*F N P dV* ; *<sup>e</sup> FS* - Equivalent

—The strain array at any points within the

function.

Strain equations

elements.

 *D*

Where:

 *<sup>e</sup> <sup>T</sup> A S A*

to the element material.

element nodes is established:

*x xy*

 

 

 

 

*u uv , x yx u uw , y z y u uv , z xz*

displacements derived from the strain formula (2.2):

*y yz*

*z zx*

Where:[B]—The strain matrix of elements;

After the formula (2.1) ~ (2.5) eliminating the stiffness displacement of geometric boundary conditions, the nodal displacement can be solved from the gathered relationship groups between force and displacement.

6. By classifying the nodal displacement solved from the formula (2.2) and (2.3), the strain and stress in each element can be calculated.

In this paper, the studied cranial cavity is a hollow three-dimensional sphere, its external radius 100 mm *R* , the curvature of hollow shell is 0 01 rad/mm *.* , the thickness of shell wall is 6mm, so the element body of hollow spherical can be treated as the regular hexahedron. The following is the stress and strain analyses in the three-dimensional elements in the cranial space. The 8-node hexahedral element (Fig2.3) is used to be the master element. The origin is set up as the local coordinate system ( *, ,* ) in the element. Trough the transformation between rectangular coordinates and local coordinates, the space 8-node isoparametric centroid element can be obtained. The relationship of coordinate transformation is:

Fig. 2.3. The space 8-node isoparametric centroid element

$$\begin{cases} \mathbf{x} = \sum\_{i=1}^{8} N\_i \left( \boldsymbol{\xi}, \boldsymbol{\eta}, \boldsymbol{\zeta}^\* \right) \mathbf{x}\_i \\ \mathbf{y} = \sum\_{i=1}^{8} N\_i \left( \boldsymbol{\xi}, \boldsymbol{\eta}, \boldsymbol{\zeta}^\* \right) \mathbf{y}\_i \\ \mathbf{z} = \sum\_{i=1}^{8} N\_i \left( \boldsymbol{\xi}, \boldsymbol{\eta}, \boldsymbol{\zeta}^\* \right) \mathbf{z}\_i \end{cases} \tag{2.6}$$

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 259

 8

*e*

 *B B* 

*i*

*N x*

*i*

1

0 0

0

*i i*

888

111 888

*iii*

*iii*

*iii*

*iii iii*

*xyz*

 

(2.15)

*iii iii*

 

*iii iii*

*xyz*

111 888

111

 

*N N z y*

*i*

*N*

*i*

0 0

*N y*

*i*

0

<sup>1</sup>

*N N <sup>J</sup>*

*N N*

The matrix *J* is the three-dimensional Yake ratio matrix of coordinate transformation:

*i i*

*i i*

*x z y NNN*

*x z y NNN*

*x zN N N <sup>y</sup> <sup>J</sup> xyz*

 

*<sup>e</sup>*

 *D DB* 

*i i*

*N N*

 

*x*

*y*

*z*

The stress-strain relationship of space elements is:

*N N z x*

*i i*

0 0

*<sup>z</sup> <sup>B</sup> N N*

*i i*

*y x*

0

*i i*

 

(2.11)

(2.12)

(2.13)

(2.14)

The strain relationship of space elements is:

The strain matrix *B* of space element:

The shape function was derivative to be:

The elasticity matrix *D* is:

Then the displacement function of element is:

$$\begin{cases} u = \sum\_{i=1}^{8} N\_i \left( \boldsymbol{\xi}, \boldsymbol{\eta}, \boldsymbol{\zeta} \right) u\_i \\ v = \sum\_{i=1}^{8} N\_i \left( \boldsymbol{\xi}, \boldsymbol{\eta}, \boldsymbol{\zeta} \right) v\_i \\ w = \sum\_{i=1}^{8} N\_i \left( \boldsymbol{\xi}, \boldsymbol{\eta}, \boldsymbol{\zeta} \right) w\_i \end{cases} \tag{2.7}$$

Where: *xi* , *yi* , *<sup>i</sup> z* and *ui* , *vi* , *wi* are respectively the coordinate values and actual displacement of nodes.

The element displacement function with matrix is expressed as:

$$\{\mathcal{S}\} = \begin{Bmatrix} \boldsymbol{\mu} \\ \boldsymbol{\upsilon} \\ \boldsymbol{w} \end{Bmatrix} = \sum\_{i=1}^{8} \begin{bmatrix} N\_i & 0 & 0 \\ 0 & N\_i & 0 \\ 0 & 0 & N\_i \end{bmatrix} \begin{bmatrix} \boldsymbol{\mu}\_i \\ \boldsymbol{\upsilon}\_i \\ \boldsymbol{w}\_i \end{bmatrix} = \sum\_{i=1}^{8} \begin{bmatrix} N\_i \end{bmatrix} \{\mathcal{S}\_i\} = \begin{bmatrix} \boldsymbol{N} \end{bmatrix} \{\mathcal{S}\}^{\boldsymbol{\varepsilon}} \tag{2.8}$$

Where: *<sup>i</sup>* - Nodal displacement array, *<sup>T</sup> i ii i uvw i ,, ,* 12 8 ; *<sup>e</sup>* - The nodal displacement array of entire element, 12 8 *<sup>e</sup> <sup>T</sup>* ; *Ni* - The uniform shape function of 8 nodes, which can be expressed as:

$$N\_i = \frac{1}{8} (1 + \xi\_i \xi') (1 + \eta\_i \eta) (1 + \zeta\_i \zeta') \quad (i = 1, 2, \dots, 8) \tag{2.9}$$

Where: *i* , *i* , *<sup>i</sup>* is the coordinates of node *i* in the local coordinate system *, ,* . The derivative of composite function to local coordinates is:

$$\begin{cases} \frac{\partial N\_i}{\partial \boldsymbol{\xi}} = \frac{1}{8} \boldsymbol{\xi}\_1 (1 + \eta\_1 \eta) (1 + \boldsymbol{\zeta}\_1 \boldsymbol{\zeta}) \\ \frac{\partial N\_i}{\partial \boldsymbol{\eta}} = \frac{1}{8} \eta\_1 (1 + \boldsymbol{\xi}\_1 \boldsymbol{\xi}) (1 + \boldsymbol{\zeta}\_1 \boldsymbol{\zeta}) \\ \frac{\partial N\_i}{\partial \boldsymbol{\zeta}} = \frac{1}{8} \boldsymbol{\zeta}\_1 (1 + \boldsymbol{\xi}\_1 \boldsymbol{\xi}) (1 + \eta\_1 \eta) \end{cases} \tag{2.10}$$

The strain relationship of space elements is:

258 Finite Element Analysis – From Biomedical Applications to Industrial Developments

*x N ,, x*

*y N ,, y*

*z N ,, z*

*u N ,, u*

*v N ,, v*

*w N ,, w*

Where: *xi* , *yi* , *<sup>i</sup> z* and *ui* , *vi* , *wi* are respectively the coordinate values and actual

 8 8

*v NvN N*

*i i*

 

 

 

 

11 1

11 1

11 1

*<sup>i</sup>* is the coordinates of node *i* in the local coordinate system

<sup>1</sup> 1 1

<sup>1</sup> 1 1

<sup>1</sup> 1 1

1 1

0 0 0 0 0 0

*uN u*

*w N w*

*<sup>i</sup>* - Nodal displacement array, *<sup>T</sup>*

*Ni iii* 

*i*

*N*

 

*N*

*N*

*i*

*i*

*i i*

nodal displacement array of entire element, 12 8 *<sup>e</sup> <sup>T</sup>*

<sup>1</sup> <sup>111</sup>

8

8

8

 

 

8

1 8

*i*

 

Then the displacement function of element is:

displacement of nodes.

Where:

Where:

*i* , *i* , 

 *i*

*i*

8

1 8

*i*

 

The element displacement function with matrix is expressed as:

uniform shape function of 8 nodes, which can be expressed as:

8

The derivative of composite function to local coordinates is:

*i*

1 8

1

*i*

1 8

1

*i i*

*i i*

(2.6)

(2.7)

*i i*

*i i*

*i i*

*i i <sup>e</sup> i i ii*

> 

*i ii i uvw i ,, ,* 12 8 ; *<sup>e</sup>*

(2.8)

 

 ; *Ni* - The

> *, ,* .

(2.10)

*i ,, ,* 12 8 (2.9)


*i i*

$$\left\{ \mathcal{E} \right\} = \left[ \mathcal{B} \right] \left\{ \mathcal{S} \right\}^{\varepsilon} = \sum\_{i=1}^{8} \left[ B\_{i} \right] \left\{ \mathcal{S}\_{i} \right\} \tag{2.11}$$

The strain matrix *B* of space element:

$$\begin{bmatrix} \begin{bmatrix} B\_i \\ \end{bmatrix} = \begin{bmatrix} \frac{\partial N\_i}{\partial \mathbf{x}} & 0 & 0 \\ 0 & \frac{\partial N\_i}{\partial y} & 0 \\\\ 0 & 0 & \frac{\partial N\_i}{\partial z} \\ \frac{\partial N\_i}{\partial y} & \frac{\partial N\_i}{\partial x} & 0 \\\\ 0 & \frac{\partial N\_i}{\partial z} & \frac{\partial N\_i}{\partial y} \\\\ \frac{\partial N\_i}{\partial z} & 0 & \frac{\partial N\_i}{\partial x} \end{bmatrix} \tag{2.12}$$

The shape function was derivative to be:

$$\begin{Bmatrix} \frac{\partial N\_i}{\partial \mathbf{x}}\\ \frac{\partial N\_i}{\partial y} \\ \frac{\partial N\_i}{\partial z} \\ \frac{\partial N\_i}{\partial z} \end{Bmatrix} = \left[J\right]^{-1} \begin{Bmatrix} \frac{\partial N\_i}{\partial \xi'}\\ \frac{\partial N\_i}{\partial \eta} \\ \frac{\partial N\_i}{\partial \zeta'}\\ \frac{\partial N\_i}{\partial \zeta'} \end{Bmatrix} \tag{2.13}$$

The matrix *J* is the three-dimensional Yake ratio matrix of coordinate transformation:

$$\begin{bmatrix} \begin{matrix} \overleftarrow{\partial x} & \overleftarrow{\partial y} & \overleftarrow{\partial z} \\ \overleftarrow{\partial \xi} & \overleftarrow{\partial \xi} & \overleftarrow{\partial \xi} \end{matrix} \end{bmatrix} = \begin{bmatrix} \begin{matrix} \frac{8}{\sqrt{2}} & \overleftarrow{\partial N\_{i}} \\ \overleftarrow{\partial \xi} & \overleftarrow{\partial \xi} \end{matrix} x\_{i} & \sum\_{i=1}^{8} \frac{\partial N\_{i}}{\partial \xi} y\_{i} & \sum\_{i=1}^{8} \frac{\partial N\_{i}}{\partial \xi} z\_{i} \\ \sum\_{i=1}^{8} \frac{\partial N\_{i}}{\partial \eta} x\_{i} & \sum\_{i=1}^{8} \frac{\partial N\_{i}}{\partial \eta} y\_{i} & \sum\_{i=1}^{8} \frac{\partial N\_{i}}{\partial \eta} z\_{i} \\ \sum\_{i=1}^{8} \frac{\partial N\_{i}}{\partial \zeta} x\_{i} & \sum\_{i=1}^{8} \frac{\partial N\_{i}}{\partial \zeta} y\_{i} & \sum\_{i=1}^{8} \frac{\partial N\_{i}}{\partial \zeta} z\_{i} \end{matrix} \tag{2.14}$$

The stress-strain relationship of space elements is:

$$\{\sigma\} = [D]\{\varepsilon\} = [D][B] \{\delta\}^{\varepsilon} \tag{2.15}$$

The elasticity matrix *D* is:

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 261

cancellous bone, inner compact bone and duramater, which is consistent with the characteristics of composite materials [37]. Four layered composite structure of cranial cavity is almost lamelleted distribution. Therefore, the lamelleted structure is adopted to establish and analyze the finite-element model of cranial cavity, and the laminated shell element is used to describe the thin cranial cavity made up of skull and duramater. Here the cranial

Each layers of cranial cavity are all thin flat film. The skulls are transversely isotropic material. The thickness of Tabula externa, diploe, Tabula interna, duramater is all very small. So compared with the components in the surface, the stress components are very small along the normal direction, and can be neglected. So the deformation analysis to single-layer cranial cavity can be simplified to be the stress problems of two-dimensional

> 1 11 12 1 2 21 22 2 12 66 12

Where, 1,2 - The main direction of elasticity in the plane; *Q*- Stiffness matrix,

Poisson's ratio of transverse strain along the 2 direction that the stress acts on the 1 direction.

The cranial cavity is as a whole formed by the four-layer structures. So the material, thickness and elastic main direction are all different. The overall performance of cranial cavity is anisotropic, macroscopic non-uniformity along the thickness direction and noncontinuity of mechanical properties. Thus, the assumptions need to be made before

Each single layer is strong glued. There are the same deformation, and no relative

The straight line vertical to the middle surface in each layer before the deformation remains still the same after the deformation, and the length of this line remains unchanged whether

0 0

modulus of four independent surfaces in each layer structure; *G*<sup>12</sup> - Shear modulus;

**(2) The stress and strain analysis for the laminated deformation of cranial cavity** 

*Q Q Q Q* 0 0

 

 

 

<sup>1</sup> <sup>2</sup> 12 2 1 <sup>1</sup> *<sup>E</sup>*

*E* 

*Q*

*m*

(2.22)

(2.23)

; *E*<sup>1</sup> , *E*<sup>2</sup> - The elastic

<sup>12</sup> -

cavity deformation of laminated structure is analyzed as follows:

, *Q mE* 22 2 , *Q G* 66 12 ;

analyzing the overall deformation of cranial cavity [38]:

generalized plane.

*Q mE* 11 1 , *Q mE* 12 12 2

displacement;

1. The same deformation in each layer

2. No change of direct normal

before or after deformation;

Namely:

**(1) The stress and strain analysis for the single layer of cranial deformation** 

The stress-strain relationship of each single-layer structure in the cranial cavity:

 *Q*

$$[D] = \frac{E(1-\mu)}{(1+\mu)(1-2\mu)} \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0\\ \frac{\mu}{1-\mu} & 1 & 0 & 0 & 0 & 0\\ \frac{\mu}{1-\mu} & \frac{\mu}{1-\mu} & 1 & 0 & 0 & 0\\ 0 & 0 & 0 & \frac{1-2\mu}{2(1-\mu)} & \frac{\mu}{1-\mu} & \frac{\mu}{1-\mu}\\ 0 & 0 & 0 & 0 & \frac{1-2\mu}{2(1-\mu)} & \frac{\mu}{1-\mu}\\ 0 & 0 & 0 & 0 & 0 & \frac{1-2\mu}{2(1-\mu)} \end{bmatrix} \tag{2.16}$$

The element stiffness matrix from the principle of virtual work is:

$$\begin{bmatrix} \mathbf{k} \end{bmatrix}^{\varepsilon} = \iiint \begin{bmatrix} \mathbf{B} \end{bmatrix}^{T} \begin{bmatrix} D \end{bmatrix} \begin{bmatrix} B \end{bmatrix} \mathbf{dx} \,\mathbf{d}\mathbf{y} \,\mathbf{d}z = \begin{bmatrix} k\_{11} & k\_{12} & \cdots & k\_{18} \\ k\_{21} & k\_{22} & \cdots & k\_{28} \\ & \cdots & \cdots \\ k\_{81} & k\_{82} & \cdots & k\_{88} \end{bmatrix} \tag{2.17}$$

Where:

$$
\begin{bmatrix} k\_{\bar{\eta}} \end{bmatrix} = \iiint\limits\_{V} [B]^T [D] [B] \,\mathrm{d}\mathrm{d}\eta \,\mathrm{d}z = \int\_{-1}^{1} \int\_{-1}^{1} \int\_{-1}^{1} [B] \, \left[D\right] [B] \,\mathrm{d}\xi \,\mathrm{d}\eta \,\mathrm{d}\zeta \tag{2.18}
$$

The equivalent nodal forces acting on the space element nodes are:

$$\left\{F\right\}^{\mathscr{e}} = \left[k\right]^{\mathscr{e}} \left\{\mathscr{S}\right\}^{\mathscr{e}} \tag{2.19}$$

Because the internal pressure in the cranial cavity is surface force, the equivalent load for the pressure acting on the element nodes is:

$$\left\{F\_{\mathcal{S}}\right\}^{\mathcal{e}} = \iint \left[\boldsymbol{N}\right]^{T} \left\{\boldsymbol{P}\_{\mathcal{S}}\right\} \,\mathrm{d}\mathcal{S} \tag{2.20}$$

The relationship between force and displacement in the entire cranial cavity is:

$$\{F\} = \begin{bmatrix} K \end{bmatrix} \{\delta\} \tag{2.21}$$

Then after obtaining the nodal displacement, the stress and strain in each element can be calculated by combining the formula (2.11) and (2.15).

#### **2.2 The stress and strain analysis for complex structure of cranial cavity deformation**

Cranial cavity is the hollow sphere formed by the skull and the duramater. From the Fig2.2, there are obvious interfaces among the various parts of outer compact bone, middle cancellous bone, inner compact bone and duramater, which is consistent with the characteristics of composite materials [37]. Four layered composite structure of cranial cavity is almost lamelleted distribution. Therefore, the lamelleted structure is adopted to establish and analyze the finite-element model of cranial cavity, and the laminated shell element is used to describe the thin cranial cavity made up of skull and duramater. Here the cranial cavity deformation of laminated structure is analyzed as follows:

#### **(1) The stress and strain analysis for the single layer of cranial deformation**

Each layers of cranial cavity are all thin flat film. The skulls are transversely isotropic material. The thickness of Tabula externa, diploe, Tabula interna, duramater is all very small. So compared with the components in the surface, the stress components are very small along the normal direction, and can be neglected. So the deformation analysis to single-layer cranial cavity can be simplified to be the stress problems of two-dimensional generalized plane.

The stress-strain relationship of each single-layer structure in the cranial cavity:

$$\{\sigma\} = [Q]\{\varepsilon\} \tag{2.22}$$

Namely:

260 Finite Element Analysis – From Biomedical Applications to Industrial Developments

<sup>1</sup> 1 2 0 00 1 12 21 1 1

<sup>111</sup>

*e e <sup>e</sup> F k*

Because the internal pressure in the cranial cavity is surface force, the equivalent load for the

 <sup>d</sup> *<sup>e</sup> <sup>T</sup> S S S*

*F K*

Then after obtaining the nodal displacement, the stress and strain in each element can be

**2.2 The stress and strain analysis for complex structure of cranial cavity deformation**  Cranial cavity is the hollow sphere formed by the skull and the duramater. From the Fig2.2, there are obvious interfaces among the various parts of outer compact bone, middle

The relationship between force and displacement in the entire cranial cavity is:

*T T*

*k B D B x y z B D BJ*

111 ddd ddd

(2.18)

1 2 0 00 0

1 2 0 00 0 0

1 00 0 0 0

10 0 0 0

10 0 0

11 12 18 21 22 28

*kk k kk k*

81 82 88

*kk k*

(2.17)

21 1

 

*F NPS* (2.20)

(2.19)

(2.21)

 

 

  (2.16)

 

2 1

1 1

 

> 

1

*ij*

pressure acting on the element nodes is:

*V*

calculated by combining the formula (2.11) and (2.15).

> 

The element stiffness matrix from the principle of virtual work is:

The equivalent nodal forces acting on the space element nodes are:

*V*

ddd *<sup>e</sup> <sup>T</sup>*

*k B DB xyz*

*<sup>E</sup> <sup>D</sup>*

Where:

$$
\begin{Bmatrix} \sigma\_1\\ \sigma\_2\\ \tau\_{12} \end{Bmatrix} = \begin{bmatrix} Q\_{11} & Q\_{12} & 0\\ Q\_{21} & Q\_{22} & 0\\ 0 & 0 & Q\_{66} \end{bmatrix} \begin{Bmatrix} \varepsilon\_1\\ \varepsilon\_2\\ \mu\_{12} \end{Bmatrix} \tag{2.23}
$$

Where, 1,2 - The main direction of elasticity in the plane; *Q*- Stiffness matrix,

*Q mE* 11 1 , *Q mE* 12 12 2 , *Q mE* 22 2 , *Q G* 66 12 ; <sup>1</sup> <sup>2</sup> 12 2 1 <sup>1</sup> *<sup>E</sup> m E* ; *E*<sup>1</sup> , *E*<sup>2</sup> - The elastic

modulus of four independent surfaces in each layer structure; *G*<sup>12</sup> - Shear modulus; <sup>12</sup> - Poisson's ratio of transverse strain along the 2 direction that the stress acts on the 1 direction.

#### **(2) The stress and strain analysis for the laminated deformation of cranial cavity**

The cranial cavity is as a whole formed by the four-layer structures. So the material, thickness and elastic main direction are all different. The overall performance of cranial cavity is anisotropic, macroscopic non-uniformity along the thickness direction and noncontinuity of mechanical properties. Thus, the assumptions need to be made before analyzing the overall deformation of cranial cavity [38]:

1. The same deformation in each layer

Each single layer is strong glued. There are the same deformation, and no relative displacement;

2. No change of direct normal

The straight line vertical to the middle surface in each layer before the deformation remains still the same after the deformation, and the length of this line remains unchanged whether before or after deformation;

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 263

4

1 *k k h t* 

The displacement components at any point within the laminated structure of cranial cavity:

*u u(x,y,z) v v(x,y,z) w w(x,y,x)*

0

 

> 

 - Strain array in the plane, 0 00 0

> 22 2 2 2 2

*x y x y* 

*h / i i h / h / i i h /*

*N z*

 

*M z z*

The mean internal force and torque acting on the laminated structure of cranial cavity in the

d

d

*ww w k ,,*

*uu w z x x x vv w z y y y*

*x*

*y*

*xy*

Fomular (2.26) can be expressed to be in matrix form:

0

Where: *u u(x,y,z)* , *v v(x,y,z)* , *w w(x,y,z)* - The displacement components at any point within the cranial cavity; *u (x,y)* <sup>0</sup> , *v (x,y)* <sup>0</sup> - The displacement components in the middle surface; *w(x,y)* - Deflection function, the deflection function of each layer is the

 

2

2 2

2

*uvu v w y x y x xy*

0 0 2

2

*uv u v <sup>o</sup> , , xy y x*

*T*

.

<sup>0</sup> *z k* (2.27)

( *i x,y,xy* ) (2.28)

*T*

; *<sup>k</sup>* - Strain array of

The *z* coordinates is respectively *<sup>k</sup>* <sup>1</sup> *z* and *<sup>k</sup> z* ,then *z h* <sup>0</sup> 2 and *z h* <sup>4</sup> 2 .

(2.24)

(2.25)

(2.26)

Then

The strain is:

same.

Where: 0 

unit width is:

bending in the surface,

#### 3. *<sup>z</sup>* 0

The positive stress along the direction of thickness is small compared to other stress, and can be ignored;

4. The plane stress state in each single layer

Each single-layer structure is similar to be assumed in plane stress state.

From the four-layer laminated structure composed of Tabula externa, diploe, Tabula interna, duramater, the force of each single-layer structure is indicated in Fig2.4. The middle surface in the laminated structure of cranial cavity is the *xy* coordinate plane. z axis is perpendicular to the middle surface in the plate. Along the z axis, each layer in turn will be compiled as layer 1, 2, 3, and 4. The corresponding thickness is respectively 1*t* , <sup>2</sup>*t* , <sup>3</sup>*t* , <sup>4</sup>*t* . As a overall laminated structure, the thickness of cranial cavity is *h* , shown in Fig2.5.

Fig. 2.4. The orientation relationship in each single-layer structure of cranial cavity

Fig. 2.5. The sketch of four-layered laminated structure of cranial cavity

Then

262 Finite Element Analysis – From Biomedical Applications to Industrial Developments

The positive stress along the direction of thickness is small compared to other stress, and can

From the four-layer laminated structure composed of Tabula externa, diploe, Tabula interna, duramater, the force of each single-layer structure is indicated in Fig2.4. The middle surface in the laminated structure of cranial cavity is the *xy* coordinate plane. z axis is perpendicular to the middle surface in the plate. Along the z axis, each layer in turn will be compiled as layer 1, 2, 3, and 4. The corresponding thickness is respectively 1*t* , <sup>2</sup>*t* , <sup>3</sup>*t* , <sup>4</sup>*t* . As

a overall laminated structure, the thickness of cranial cavity is *h* , shown in Fig2.5.

Fig. 2.4. The orientation relationship in each single-layer structure of cranial cavity

Fig. 2.5. The sketch of four-layered laminated structure of cranial cavity

Each single-layer structure is similar to be assumed in plane stress state.

3.

*<sup>z</sup>* 0

be ignored;

4. The plane stress state in each single layer

$$h = \sum\_{k=1}^{4} t\_k \tag{2.24}$$

The *z* coordinates is respectively *<sup>k</sup>* <sup>1</sup> *z* and *<sup>k</sup> z* ,then *z h* <sup>0</sup> 2 and *z h* <sup>4</sup> 2 .

The displacement components at any point within the laminated structure of cranial cavity:

$$\begin{cases} u = u(x, y, z) \\ v = v(x, y, z) \\ w = w(x, y, x) \end{cases} \tag{2.25}$$

The strain is:

$$\begin{cases} \mathcal{L}\_{\chi} = \frac{\partial u}{\partial \mathbf{x}} = \frac{\partial u\_{0}}{\partial \mathbf{x}} - z \frac{\partial^{2} w}{\partial \mathbf{x}^{2}} \\\\ \mathcal{L}\_{y} = \frac{\partial v}{\partial y} = \frac{\partial v\_{0}}{\partial y} - z \frac{\partial^{2} w}{\partial y^{2}} \\\\ \mathcal{V}\_{xy} = \frac{\partial u}{\partial y} + \frac{\partial v}{\partial \mathbf{x}} = \frac{\partial u\_{0}}{\partial y} + \frac{\partial v\_{0}}{\partial \mathbf{x}} - 2 \frac{\partial^{2} w}{\partial \mathbf{x} \partial y} \end{cases} \tag{2.26}$$

Where: *u u(x,y,z)* , *v v(x,y,z)* , *w w(x,y,z)* - The displacement components at any point within the cranial cavity; *u (x,y)* <sup>0</sup> , *v (x,y)* <sup>0</sup> - The displacement components in the middle surface; *w(x,y)* - Deflection function, the deflection function of each layer is the same.

Fomular (2.26) can be expressed to be in matrix form:

$$z\{\boldsymbol{\varepsilon}\} = \{\boldsymbol{\varepsilon}\_0\} + z\{\boldsymbol{k}\} \tag{2.27}$$

Where: 0 - Strain array in the plane, 0 00 0 *T uv u v <sup>o</sup> , , xy y x* ; *<sup>k</sup>* - Strain array of

bending in the surface, 22 2 2 2 2 *T ww w k ,, x y x y* .

The mean internal force and torque acting on the laminated structure of cranial cavity in the unit width is:

$$\begin{cases} \mathbf{N}\_i = \int\_{-h/2}^{h/2} \sigma\_i \mathbf{d}z \\ \mathbf{M}\_i = \int\_{-h/2}^{h/2} \sigma\_i z \mathbf{d}z \end{cases} \text{ ( $i = \mathbf{x}$ ,  $y$ ,  $\mathbf{x}$ )}\tag{2.28}$$

Taking into account the discontinuous stress caused by the discontinuity along the direction of laminated structure in the cranial cavity, the formula (2.28) can be rewritten in matrix form:

$$\begin{cases} \{N\} = \sum\_{k=1}^{n} \int\_{z\_{k-1}}^{z\_{k}} \{\sigma\} \, \mathrm{d}z \\\\ \{M\} = \sum\_{k=1}^{n} \int\_{z\_{k-1}}^{z\_{k}} \{\sigma\} \, \mathrm{z} \, \mathrm{d}z \end{cases} \tag{2.29}$$

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 265

system with the finite-element software MSC\_PATRAN/NASTRAN and ANSYS. Considering the complexity to calculate the viscoelasticity of human skull and duramater, we can simplify the calculation while on-line analysis only considering the elasticity but ignoring the viscoelasticity of human skull and duramater after obtaining the regularity

**2.2.1 The finite-element analysis of strains by ignoring the viscoelasticity of human** 

The craniospinal cavity may be considered as a balloon. For the purpose of our analysis, we adopted the model of hollow sphere (Fig2.6). We presented the development and validation of a 3D finite-element model intended to better understand the deformation mechanisms of human skull corresponding to the ICP change. The skull is a layered sphere constructed in a specially designed form with a Tabula externa, Tabula interna, and a porous Diploe sandwiched in between. Based on the established knowledge of cranial cavity importantly composed of skull and duramater, a thin-walled structure was simulated by the composite

Of course, the structure, dimension and characteristic parameter of human skull must be given before the calculation. The thickness of calvaria [40] varies with the position, age, gender and individual, so does dura mater [41]. Tabula externa and interna are all compact bones and the thickness of Tabula externa is more than that of Tabula interna. Diploe is the cancellous bone between Tabula externa and Tabula interna [42]. The parietal bone is the transversely isotropic material, namely it has the mechanical property of rotational symmetry in the axially vertical planes of skull [43]. The important mechanical characteristic of cancellous bone is viscoelasticity, which is generally considered as the semi-closed honeycomb structure composed of bone trabecula reticulation. The main composition of cerebral dura mater, a thick and tough bilayer membrane, is the collagenous fiber which has the characteristic of linear viscoelasticity [44]. And the thickness of dura mater obviously varies with the changing ICP [45]. The mechanical performance of skull is isotropic along the tangential direction on the surface of skull bone [46], in which the performance of compact bone in the Tabula externa is basically the same as that in the Tabula interna [47]. Thus both cancellous bone and dura mater can be regarded as isotropic materials. And the

how the viscoelasticity influences the deformation of cranial cavity.

shell elements of the finite-element software [39].

Fig. 2.6. The sketch of 3D cranial cavity and grid division

elastic modulus of fresh dura mater varies with the delay time [48].

**skull and duramater** 

After substituting the formula (2.22) and (2.27) into equation (2.29), the average internal force and internal moment of the laminated structure in the cranial cavity is:

$$
\begin{bmatrix} N \\ M \end{bmatrix} = \begin{bmatrix} \sum \int [Q] \, \mathrm{d}z & \sum \int [Q] z \, \mathrm{d}z \\ \sum \int [Q] z \, \mathrm{d}z & \sum \int [Q] z^2 \, \mathrm{d}z \end{bmatrix} \begin{Bmatrix} \varepsilon\_0 \\ k \end{Bmatrix} = \begin{bmatrix} A & B \\ B & D \end{bmatrix} \begin{Bmatrix} \varepsilon\_0 \\ k \end{Bmatrix} \tag{2.30}
$$

Where: *A* - The stiffness matrix in the plane, 1 1 *<sup>n</sup> (k) ij ij k k k A Q (z z )* ; *B* - Coupling

stiffness matrix, 2 2 1 1 1 2 *<sup>n</sup> (k) ij ij k k k B Q (z z )* ; *D*- Bending stiffness matrix, 3 3 1 1 1 3 *<sup>n</sup> (k) ij ij k k k D Q (z z )* , ( *i,j* 1, 2, 6).

Then the flexibility matrix of laminated structure in the cranial cavity is:

$$
\begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} A & B \\ B & D \end{bmatrix}^{-1} \tag{2.31}
$$

$$\begin{aligned} \text{Where: } [a] &= [A]^{-1} + [A]^{-1}[B] \left( [D] - [B][A]^{-1}[B] \right)^{-1} [B] [A]^{-1}; \\ [b] &= -[A]^{-1}[B] \left( [D] - [B][A]^{-1}[B] \right)^{-1}; \ [c] = -\left( [D] - [B][A]^{-1}[B] \right)^{-1} [B] [A]^{-1} = [b]^{T}; \\ [d] &= \left( [D] - [B][A]^{-1}[B] \right)^{-1} \end{aligned}$$

Thus, the stress-strain relationship of laminated structure in the cranial cavity is:

$$
\begin{Bmatrix} \mathcal{E}\_0 \\ \mathcal{k} \end{Bmatrix} = \begin{bmatrix} a & b \\ b^T & d \end{bmatrix} \begin{Bmatrix} N \\ M \end{Bmatrix} \tag{2.32}
$$

With the changing ICP, to determine how the viscoelasticity of human skull and duramater influences the strains of human skull respectively by ignoring and considering the viscoelasticity of human skull and duramater, we make the analysis of the actual deformation of cranial cavity by considering the viscoelasticity of human skull-duramater

Taking into account the discontinuous stress caused by the discontinuity along the direction of laminated structure in the cranial cavity, the formula (2.28) can be rewritten in matrix

*<sup>n</sup> <sup>z</sup> <sup>z</sup> <sup>k</sup> <sup>n</sup> <sup>z</sup> <sup>z</sup> <sup>k</sup>*

*N z*

*M z z*

1

 

force and internal moment of the laminated structure in the cranial cavity is:

Where: *A* - The stiffness matrix in the plane, 1

1

*k*

*<sup>n</sup> (k) ij ij k k*

*B Q (z z )*

Then the flexibility matrix of laminated structure in the cranial cavity is:

<sup>1</sup> 1 1 1 1 *a A A B D BA B BA* ;

<sup>1</sup> 1 1 *b A B D BA B* ;

Thus, the stress-strain relationship of laminated structure in the cranial cavity is:

0

*T*

*k M b d*

With the changing ICP, to determine how the viscoelasticity of human skull and duramater influences the strains of human skull respectively by ignoring and considering the viscoelasticity of human skull and duramater, we make the analysis of the actual deformation of cranial cavity by considering the viscoelasticity of human skull-duramater

*a b N*

1 2

Where:

stiffness matrix, 2 2

3 3 1

, ( *i,j* 1, 2, 6).

1

*k*

*<sup>n</sup> (k) ij ij k k*

*D Q (z z )*

<sup>1</sup> <sup>1</sup> *d D BA B*

1 3

 

d d d d *N Q z Qz z A B M Qz z Qz z k BDk*

1

*k k k k*

d

d

0 0

(2.30)

*<sup>n</sup> (k) ij ij k k*

*A Q (z z )*

(2.31)

1

; *D*- Bending stiffness matrix,

<sup>1</sup> 1 1 *<sup>T</sup> c D BA B BA b* ;

*k*

; *B* - Coupling

(2.32)

(2.29)

1

2

1

After substituting the formula (2.22) and (2.27) into equation (2.29), the average internal

1

<sup>1</sup> *ab AB cd BD* 

form:

system with the finite-element software MSC\_PATRAN/NASTRAN and ANSYS. Considering the complexity to calculate the viscoelasticity of human skull and duramater, we can simplify the calculation while on-line analysis only considering the elasticity but ignoring the viscoelasticity of human skull and duramater after obtaining the regularity how the viscoelasticity influences the deformation of cranial cavity.

#### **2.2.1 The finite-element analysis of strains by ignoring the viscoelasticity of human skull and duramater**

The craniospinal cavity may be considered as a balloon. For the purpose of our analysis, we adopted the model of hollow sphere (Fig2.6). We presented the development and validation of a 3D finite-element model intended to better understand the deformation mechanisms of human skull corresponding to the ICP change. The skull is a layered sphere constructed in a specially designed form with a Tabula externa, Tabula interna, and a porous Diploe sandwiched in between. Based on the established knowledge of cranial cavity importantly composed of skull and duramater, a thin-walled structure was simulated by the composite shell elements of the finite-element software [39].

Fig. 2.6. The sketch of 3D cranial cavity and grid division

Of course, the structure, dimension and characteristic parameter of human skull must be given before the calculation. The thickness of calvaria [40] varies with the position, age, gender and individual, so does dura mater [41]. Tabula externa and interna are all compact bones and the thickness of Tabula externa is more than that of Tabula interna. Diploe is the cancellous bone between Tabula externa and Tabula interna [42]. The parietal bone is the transversely isotropic material, namely it has the mechanical property of rotational symmetry in the axially vertical planes of skull [43]. The important mechanical characteristic of cancellous bone is viscoelasticity, which is generally considered as the semi-closed honeycomb structure composed of bone trabecula reticulation. The main composition of cerebral dura mater, a thick and tough bilayer membrane, is the collagenous fiber which has the characteristic of linear viscoelasticity [44]. And the thickness of dura mater obviously varies with the changing ICP [45]. The mechanical performance of skull is isotropic along the tangential direction on the surface of skull bone [46], in which the performance of compact bone in the Tabula externa is basically the same as that in the Tabula interna [47]. Thus both cancellous bone and dura mater can be regarded as isotropic materials. And the elastic modulus of fresh dura mater varies with the delay time [48].

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 267

After ignoring the viscoelasticity of human skull and dura mater, the strains of cranial cavity are shown in Table 1 with the finite-element software MSC\_PATRAN/NASTRAN as ICP changing from 1.5 kPa to 5.0 kPa (Fig2.7). There is the measurable correspondence between skull strains and ICP variation. The strains of human skull can reflect the ICP change. When ICP variation is raised up to 2.5 kPa, the stress and strain graphs of skull bone are shown in

The scope of stress change on the outside surface is from 22.1 kPa to 25.3 kPa when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura

variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura

to 1.57 μ

when ICP

Fig2.8~Fig2.13.

Fig. 2.8. Stress distribution

Fig. 2.9. Strain distribution

The scope of strain change on the outside surface is from 1.52 μ

mater.

mater.

Next we need determine the fluctuant scope of human ICP. ICP is not a static state, but one that influenced by several factors. It can rise sharply with coughing and sneezing, up to 50 or 60mmHg to settle down to normal values in a short time. It also varies according to the activity the person is involved with. For these reasons single measurement of ICP is not a true representation. ICP needs to be measured over a period. Measured by means of a lumbar puncture, the normal ICP in adults is 8 mmHg to 18 mmHg. But so far there are almost no records of the actual human being's ICP in clinic. The geometry and structure of monkey's skull, mandible and cervical muscle are closer to those of human beings than other animals'. So the ICP of monkeys [49] can be taken as the reference to that of human beings'. The brain appears to be mild injury when ICP variation is about 2.5 kPa, moderate injury when ICP variation is about 3.5 kPa and severe injury when ICP variation is about or more than 5 kPa. Therefore, we carried out the following theoretical analysis with the ICP scope from 1.5 kPa to 5 kPa.

In this paper, the finite-element software MSC\_PATRAN/NASTRAN and ANSYS are applied to theoretically analyze the deformation of human skull with the changing ICP. The external diameter of cranial cavity is about 200 mm. The thickness of shell is the mean thickness of calvarias. The average thickness of adult's calvaria is 6.0 mm, that of Tabula externa is 2.0 mm, diploe is 2.8 mm, Tabula interna is 1.2 mm and, dura mater in the parietal position is 0.4 mm.

Considering the characteristic of compact bone, cancellous bone and dura mater, we adopt their elastic modulus and Poisson ratios as 1.5×104 MPa, 4.5×103 MPa [50], 1.3×102 MPa [51] and 0.21, 0.01, 0.23 respectively.

Fig. 2.7. The strain curves of finite-element simulation under the conditions of ignoring and considering the viscoelasticity of human skull and duramater with the changing ICP from 1.5 kPa to 5 kPa

After ignoring the viscoelasticity of human skull and dura mater, the strains of cranial cavity are shown in Table 1 with the finite-element software MSC\_PATRAN/NASTRAN as ICP changing from 1.5 kPa to 5.0 kPa (Fig2.7). There is the measurable correspondence between skull strains and ICP variation. The strains of human skull can reflect the ICP change. When ICP variation is raised up to 2.5 kPa, the stress and strain graphs of skull bone are shown in Fig2.8~Fig2.13.

#### Fig. 2.8. Stress distribution

266 Finite Element Analysis – From Biomedical Applications to Industrial Developments

Next we need determine the fluctuant scope of human ICP. ICP is not a static state, but one that influenced by several factors. It can rise sharply with coughing and sneezing, up to 50 or 60mmHg to settle down to normal values in a short time. It also varies according to the activity the person is involved with. For these reasons single measurement of ICP is not a true representation. ICP needs to be measured over a period. Measured by means of a lumbar puncture, the normal ICP in adults is 8 mmHg to 18 mmHg. But so far there are almost no records of the actual human being's ICP in clinic. The geometry and structure of monkey's skull, mandible and cervical muscle are closer to those of human beings than other animals'. So the ICP of monkeys [49] can be taken as the reference to that of human beings'. The brain appears to be mild injury when ICP variation is about 2.5 kPa, moderate injury when ICP variation is about 3.5 kPa and severe injury when ICP variation is about or more than 5 kPa. Therefore, we carried out the following theoretical analysis with the ICP

In this paper, the finite-element software MSC\_PATRAN/NASTRAN and ANSYS are applied to theoretically analyze the deformation of human skull with the changing ICP. The external diameter of cranial cavity is about 200 mm. The thickness of shell is the mean thickness of calvarias. The average thickness of adult's calvaria is 6.0 mm, that of Tabula externa is 2.0 mm, diploe is 2.8 mm, Tabula interna is 1.2 mm and, dura mater in the parietal

Considering the characteristic of compact bone, cancellous bone and dura mater, we adopt their elastic modulus and Poisson ratios as 1.5×104 MPa, 4.5×103 MPa [50], 1.3×102 MPa [51]

> Ignoring the viscoelasticity Considering the viscoelasticity

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

ICP variation (kPa)

Fig. 2.7. The strain curves of finite-element simulation under the conditions of ignoring and considering the viscoelasticity of human skull and duramater with the changing ICP from

scope from 1.5 kPa to 5 kPa.

and 0.21, 0.01, 0.23 respectively.

0.0

1.5 kPa to 5 kPa

0.5

1.0

1.5

2.0

Strains of human skull with FEA (με)

2.5

3.0

3.5

4.0

4.5

position is 0.4 mm.

The scope of stress change on the outside surface is from 22.1 kPa to 25.3 kPa when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

#### Fig. 2.9. Strain distribution

The scope of strain change on the outside surface is from 1.52 μ to 1.57 μ when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 269

**2.2.2 The finite-element analysis of strains by considering the viscoelasticity of** 

Human skull has the viscoelastic material [52]. Considering the viscoelasticity of human skull and dura mater, we use the viscoelastic option of the ANSYS finite-element program to analysis the strains on the exterior surface of human skull as ICP changing. According to the symmetry of 3D model of human skull, the preprocessor of the ANSYS finite-element program is used to construct a 1/8 finite-element model of human skull and dura mater consisting of 25224 nodes and 24150 three-dimensional 8-node isoparametric solid elements,

The three-dimensional stress-strain relationships for a linear isotropic viscoelastic material

 

> 

; ( *i,j , ,* <sup>123</sup> ) (2.33)

 

*e( ) ( ) G(t ) K(t ) d* 

 

ignoring the viscoelasticity of human skull and dura mater.

Fig. 2.14. Finite element model of 1/8 cranial cavity shell

0 2 *t ij ij ij*

 when ICP variation is raised up to 2.5 kPa by

Fig. 2.13. Strain vector distribution The main strain vector is about 2.14 μ

**human skull and dura mater** 

shown in Fig2.14.

are given by:

Fig. 2.10. The maximal stress vector distribution

The maximal main stress is about 22.4 kPa when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

Fig. 2.11. The maximal strain vector distribution

The maximal main strain is about 2.2 μ when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

The main stress vector is about 21.8 kPa when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

Fig. 2.13. Strain vector distribution

268 Finite Element Analysis – From Biomedical Applications to Industrial Developments

The maximal main stress is about 22.4 kPa when ICP variation is raised up to 2.5 kPa by

The main stress vector is about 21.8 kPa when ICP variation is raised up to 2.5 kPa by

when ICP variation is raised up to 2.5 kPa by

Fig. 2.10. The maximal stress vector distribution

Fig. 2.11. The maximal strain vector distribution

ignoring the viscoelasticity of human skull and dura mater.

ignoring the viscoelasticity of human skull and dura mater.

The maximal main strain is about 2.2 μ

Fig. 2.12. Stress vector distribution

ignoring the viscoelasticity of human skull and dura mater.

The main strain vector is about 2.14 μ when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

#### **2.2.2 The finite-element analysis of strains by considering the viscoelasticity of human skull and dura mater**

Human skull has the viscoelastic material [52]. Considering the viscoelasticity of human skull and dura mater, we use the viscoelastic option of the ANSYS finite-element program to analysis the strains on the exterior surface of human skull as ICP changing. According to the symmetry of 3D model of human skull, the preprocessor of the ANSYS finite-element program is used to construct a 1/8 finite-element model of human skull and dura mater consisting of 25224 nodes and 24150 three-dimensional 8-node isoparametric solid elements, shown in Fig2.14.

Fig. 2.14. Finite element model of 1/8 cranial cavity shell

The three-dimensional stress-strain relationships for a linear isotropic viscoelastic material are given by:

$$
\sigma\_{\vec{ij}} = \int\_0^t \left[ 2G(t-\tau) \frac{\partial e\_{\vec{ij}}(\tau)}{\partial \tau} + \delta\_{\vec{ij}} K(t-\tau) \frac{\partial \theta(\tau)}{\partial \tau} \right] d\tau \; ; \{ \text{i, j} = 1, 2, 3 \} \tag{2.33}
$$

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 271

mechanical properties of human skull in the tensile experiments. Thus the Kelvin model of three parameters is adopted to describe the viscoelasticity of human skull in this paper.

For the Kelvin model of three parameters, the stress and strain of human skull are shown in

0 1 11 1 0 0 *E E*

 

 

After the calculation based on the equation (1), the elastic modulus of human skull is the

01 0 01 01

The generalized Kelvin model is shown in Fig2.17 (c). Fig2.17 (a) is the creep experimental curves of human duramater. Fig2.17 (b) is the curves of creep compliance for the generalized Kelvin model. It shows that the tendency of creep curve in the experiment is coincident with that of creep compliance for the generalized Kelvin model. Creep is the change law of

theoretical creep curve is totally the same as that of experimental one for human duramater. So in this paper, the generalized Kelvin model composed of three Kelvin-unit chains and a

spring is adopted to simulate the viscoelasticity of human dura mater in this paper.

(a) (b) (c)

Fig. 2.17. Creep train-time curves under different loads for fresh human duramater (L0=23 mm, θ=37 Ԩ). Creep compliance curves of human duramatar Kelvin model. And the Kelvin

*EE E <sup>P</sup> <sup>E</sup> EE EE* 

—Direct stress acted on elastic spring or impact stress acted on viscopot;

strain of elastic spring; *E* —Elastic modulus of tensile compression;

*P*

generalized Kelvin model, the stress-strain relationship is

0 1

*E E* **.** 

material deformation with time under the invariable stress, so here

1

*(t) J(t)*

e *t*

2

 

(2.34)

(2.35)

is constant. For the

. Thus the tendency of

—Viscosity coefficient

—Direct

 

equation (2.34),

Fig2.16,

Here, 

of viscopot;

model of the duramater.

—strain ratio; 1

**(2) Viscoelastic Model of human duramater** 

Here, *ij* —the Cauchy stress tensor; *ij e* —the deviatoric strain tensor; *ij* —the Kronecker delta; *G(t)* —the shear relaxation function; *K(t)*—the bulk relaxation function; *(t)* —the volumetric strain; *t* —the present time; —the past time.

Before the theoretical analysis of the minitraumatic strain-electrometric method, we need to set up the viscoelastic models to describe the relevant mechanical properties of human skull and dura mater.

#### **(1) Viscoelastic Model of human skull**

Under the constant action of stress, the strain of ideal elastic solid is invariable and that of ideal viscous fluid keeps on growing at the equal ratio with time. However, the strain of actual material increases with time, namely so-called creep. Generally, Maxwell and Kelvin models are the basic models to describe the performance of viscoelastic materials. Maxwell model represents in essence the liquid. Despite the representative of solid, Kelvin model can't describe stress relaxation but only stress creep (Fig2.15). So the combined models made up of the primary elements are usually adopted to describe the viscoelastic performance of actual materials. The creep of linear viscoelastic solid can be simulated by the Kelvin model of three parameters or the generalized Kelvin model.

Fig. 2.15. Three parameters Kelvin model of human skull.

Fig. 2.16. The relaxation and creep train-time curves between experiment and three parameters Kelvin theoretical model of human skull.

Kelvin model of three parameters is shown in Fig2.15. Fig2.16 (a) is the relaxation curves of human skull and Kelvin model of three parameters in the compressive experiment. Fig2.16(b) is the creep curves of human skull and Kelvin model of three parameters. It shows that the theoretical Kelvin model of three parameters can well simulate the mechanical properties of human skull in the tensile experiments. Thus the Kelvin model of three parameters is adopted to describe the viscoelasticity of human skull in this paper.

For the Kelvin model of three parameters, the stress and strain of human skull are shown in equation (2.34),

$$\begin{cases} \varepsilon = \varepsilon\_0 + \varepsilon\_1\\ \sigma = E\_1 \varepsilon\_1 + \eta \dot{\varepsilon}\_1\\ \sigma = E\_0 \varepsilon\_0 \end{cases} \tag{2.34}$$

After the calculation based on the equation (1), the elastic modulus of human skull is the Fig2.16,

$$E = \left(\frac{E\_0 E\_1}{E\_0 + E\_1}\right) + \left(\frac{E\_0^2}{E\_0 + E\_1}\right) \mathbf{e}^{\frac{l}{P\_1}}\tag{2.35}$$

Here, —Direct stress acted on elastic spring or impact stress acted on viscopot; —Direct strain of elastic spring; *E* —Elastic modulus of tensile compression; —Viscosity coefficient

of viscopot; —strain ratio; 1 0 1 *P E E* **.** 

270 Finite Element Analysis – From Biomedical Applications to Industrial Developments

—the past time.

Before the theoretical analysis of the minitraumatic strain-electrometric method, we need to set up the viscoelastic models to describe the relevant mechanical properties of human skull

Under the constant action of stress, the strain of ideal elastic solid is invariable and that of ideal viscous fluid keeps on growing at the equal ratio with time. However, the strain of actual material increases with time, namely so-called creep. Generally, Maxwell and Kelvin models are the basic models to describe the performance of viscoelastic materials. Maxwell model represents in essence the liquid. Despite the representative of solid, Kelvin model can't describe stress relaxation but only stress creep (Fig2.15). So the combined models made up of the primary elements are usually adopted to describe the viscoelastic performance of actual materials. The creep of linear viscoelastic solid can be simulated by the Kelvin model

*ij* —the Kronecker

*(t)* —the

*ij* —the Cauchy stress tensor; *ij e* —the deviatoric strain tensor;

delta; *G(t)* —the shear relaxation function; *K(t)*—the bulk relaxation function;

Here,

and dura mater.

volumetric strain; *t* —the present time;

**(1) Viscoelastic Model of human skull** 

of three parameters or the generalized Kelvin model.

Fig. 2.15. Three parameters Kelvin model of human skull.

parameters Kelvin theoretical model of human skull.

Fig. 2.16. The relaxation and creep train-time curves between experiment and three

Kelvin model of three parameters is shown in Fig2.15. Fig2.16 (a) is the relaxation curves of human skull and Kelvin model of three parameters in the compressive experiment. Fig2.16(b) is the creep curves of human skull and Kelvin model of three parameters. It shows that the theoretical Kelvin model of three parameters can well simulate the

#### **(2) Viscoelastic Model of human duramater**

The generalized Kelvin model is shown in Fig2.17 (c). Fig2.17 (a) is the creep experimental curves of human duramater. Fig2.17 (b) is the curves of creep compliance for the generalized Kelvin model. It shows that the tendency of creep curve in the experiment is coincident with that of creep compliance for the generalized Kelvin model. Creep is the change law of material deformation with time under the invariable stress, so here is constant. For the generalized Kelvin model, the stress-strain relationship is *(t) J(t)* . Thus the tendency of theoretical creep curve is totally the same as that of experimental one for human duramater. So in this paper, the generalized Kelvin model composed of three Kelvin-unit chains and a spring is adopted to simulate the viscoelasticity of human dura mater in this paper.

Fig. 2.17. Creep train-time curves under different loads for fresh human duramater (L0=23 mm, θ=37 Ԩ). Creep compliance curves of human duramatar Kelvin model. And the Kelvin model of the duramater.

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 273

Fig2.18 (a) ~ (e) are the analytic graphs of stress and strain with finite-element software ANASYS when ICP variation is raised up to 2.5 kPa. After considering the viscoelasticity of human skull and duramater, the stresses and strains of cranial cavity are shown in Fig2.18 as the ICP changing from 1.5 kPa to 5kPa with the finite-element software ANSYS. It shows that the stress and strain distributions on the exterior surface of human skull are wellproportioned and that the stress and strain variation on the exterior surface of cranial cavity is relatively small corresponding to the ICP change. The strains of cranial cavity are coincident with ICP variation. The deformation scope of human skull is theoretically from 0.9 με to 3.4 με as the ICP changing from 1.5 kPa to 5.0 kPa. Corresponding to ICP of 2.5 kPa, 3.5 kPa and 5.0 kPa, the strain of skull deformation separately for mild, moderate and

Stress nephogram Strain nephogram XY shear stress nephogram

XZ shear stress nephogram YZ shear stress nephogram Interbedded strain change

Fig. 2.18. The stress and strain distribution considering viscoelasticity of human skull and

From the relationships about total, elastic and viscous strains of human skull and dura mater in Fig2.19, the viscous strains account for about 40% and the elastic strains are about

nephogram in the human duramater and skull

**(3) The stress and strain distribution by the finite-element analysis** 

severe head injury is 1.5 με , 2.4 με , and 3.4 με or so.

duramater

60% of total strains with the increasing ICP.

For the viscoelastic model of human dura mater composed of the three Kelvin-unit chains and a spring, the stress and strain of human dura mater are shown in equation (2.36),

$$\begin{cases} \varepsilon = \varepsilon\_0 + \varepsilon\_1 + \varepsilon\_2 + \varepsilon\_3 \\ \varepsilon\_0 = \frac{\sigma}{E\_0} \\ \sigma = E\_1 \varepsilon\_1 + \eta\_1 \dot{\varepsilon}\_1 = E\_2 \varepsilon\_2 + \eta\_2 \dot{\varepsilon}\_2 = E\_3 \varepsilon\_3 + \eta\_3 \dot{\varepsilon}\_3 \end{cases} \tag{2.36}$$

After the calculation based on the equation (2.36), the creep compliance of human dura mater is equation (2.37),

$$f(t) = E\_0^{-1} + E(1 - \mathbf{e}^{-\bigvee\_{\tau\_1}}) + E\_2^{-1}(1 - \mathbf{e}^{-\bigvee\_{\tau\_2}}) + E\_3^{-1}(1 - \mathbf{e}^{-\bigvee\_{\tau\_3}}) \tag{2.37}$$

Then the elastic modulus of human dura mater is equation (2.38),

$$E = \left[ E\_0^{-1} + E\_1^{-1} \left( 1 - \mathbf{e}^{-t/\tau\_1} \right) + E\_2^{-1} \left( 1 - \mathbf{e}^{-t/\tau\_2} \right) + E\_3^{-1} \left( 1 - \mathbf{e}^{-t/\tau\_3} \right) \right]^{-1} \tag{2.38}$$

Here, , , *E* , , ——Ditto mark; 1 , 2 , 3 ——Lag time, that is 111 */ E* , 222 */ E* , 333 */ E* .

In the finite-element software ANSYS, there are three kinds of models to describe the viscoelasticity of actual materials, in which the Maxwell model is the general designation for the combined Kelvin and Maxwell models. Considering the mechanical properties of human skull and dura mater, we adopt the finite-element Maxwell model to simulate the viscoelasticity of human skull-dura mater system. The viscoelastic parameters of human skull and dura mater are respectively listed in Table 2.1 and Table 2.2.


$$\prescript{\*}{}{\tau}\_r = \bigvee\_{\mathbb{E}\_1 + \mathbb{E}\_2 \ \prime} \tau\_d = \bigvee\_{\mathbb{E}\_2} \prescript{}{\tau}\_r$$

Table 2.1. Coefficients for the viscoelastic properties for human skull


Table 2.2. Creep coefficients for the viscoelastic properties for fresh human duramater

For the viscoelastic model of human dura mater composed of the three Kelvin-unit chains

11 11 22 22 33 33

1 11 1 2 <sup>3</sup> 0 23 1e 1e 1e

 1 2 <sup>3</sup> <sup>1</sup> 1 1 <sup>1</sup> <sup>1</sup>

Elastic Modulus (GPa) Viscosity (GPa/s) Delay time

Compression 5.69±0.26 42.24±2.09 26.9±1.5 2022±198 2292±246 Tension 13.64±0.59 51.45±2.54 57.25±4.27 3180±300 4026±372

E0 E1 E2 E3

Table 2.2. Creep coefficients for the viscoelastic properties for fresh human duramater

Duramater 16.67 125.0 150.0 93.75 40 104 106

Elastic modulus (MPa) Delay time

 

(2.38)

*t t t*

   

(2.37)

(2.36)

——Lag time, that is 111

 */ E* ,

(s)

> \*

\* *<sup>d</sup>*

(s)

> 3

2

 

1

and a spring, the stress and strain of human dura mater are shown in equation (2.36),

*EE E*

 

After the calculation based on the equation (2.36), the creep compliance of human dura

*J(t) E E( ) E ( ) E ( )*

0 1 <sup>2</sup> <sup>3</sup> 1e 1e 1e *t / t / t / EE E <sup>E</sup> <sup>E</sup>*

 , 2 , 3 

In the finite-element software ANSYS, there are three kinds of models to describe the viscoelasticity of actual materials, in which the Maxwell model is the general designation for the combined Kelvin and Maxwell models. Considering the mechanical properties of human skull and dura mater, we adopt the finite-element Maxwell model to simulate the viscoelasticity of human skull-dura mater system. The viscoelastic parameters of human

——Ditto mark; 1

skull and dura mater are respectively listed in Table 2.1 and Table 2.2.

Table 2.1. Coefficients for the viscoelastic properties for human skull

E0 E1

0123

0

 

mater is equation (2.37),

Here,

   , , *E* ,

222

\* 1 2 *<sup>r</sup> E E* 

, <sup>2</sup> *<sup>d</sup> <sup>E</sup>*

 

 , 

 */ E* , 333 */ E* . 0

 

Then the elastic modulus of human dura mater is equation (2.38),

 

*E*

#### **(3) The stress and strain distribution by the finite-element analysis**

Fig2.18 (a) ~ (e) are the analytic graphs of stress and strain with finite-element software ANASYS when ICP variation is raised up to 2.5 kPa. After considering the viscoelasticity of human skull and duramater, the stresses and strains of cranial cavity are shown in Fig2.18 as the ICP changing from 1.5 kPa to 5kPa with the finite-element software ANSYS. It shows that the stress and strain distributions on the exterior surface of human skull are wellproportioned and that the stress and strain variation on the exterior surface of cranial cavity is relatively small corresponding to the ICP change. The strains of cranial cavity are coincident with ICP variation. The deformation scope of human skull is theoretically from 0.9 με to 3.4 με as the ICP changing from 1.5 kPa to 5.0 kPa. Corresponding to ICP of 2.5 kPa, 3.5 kPa and 5.0 kPa, the strain of skull deformation separately for mild, moderate and severe head injury is 1.5 με , 2.4 με , and 3.4 με or so.

XZ shear stress nephogram YZ shear stress nephogram Interbedded strain change

nephogram in the human duramater and skull

Fig. 2.18. The stress and strain distribution considering viscoelasticity of human skull and duramater

From the relationships about total, elastic and viscous strains of human skull and dura mater in Fig2.19, the viscous strains account for about 40% and the elastic strains are about 60% of total strains with the increasing ICP.

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 275

A self-programmed image boundary automatic recorder was used to acquire cranial information along the superior border to inferior border of cranium brain. The spatial boundary was recorded layer by layer. Following point selection from interior and exterior border of images, two-dimensional space coordinates were automatically recorded and saved in the .CDB form. After conversion, this file can be directly input into Mimics or CAD

A coordinate system was determined. The CT scanning image starting from the lowest layer of cranium brain was set as the working background. CT scan was performed based on a fixed coordinate axis, with a know layer interval and magnification proportion. The spatial threedimensional coordinate of each point in the image could be determined through drawing the horizontal coordinate of each point and referencing scanning interval. When CT machines recorded each layer of images, all images were in the same scanning range, which equaled to cranial location of two-dimensional CT images from each layer in the scanning direction. Calibration of two-dimensional images could be performed if the scar bar of CT scan images

Fig. 3.1. CT scan image of cranial cavity

**Methods** 

software. *Location* 

*Image boundary tracking* 

**3.1.3 Flowchart of finite element method** 

Fig. 2.19. Curves among total, elastic and viscous strain when the ICP increment is 2.5 kPa. Here EPELX is elastic strain curve, EPPLX is viscous strain curve. The viscous strain is about 40% of total strain.

### **3. Finite-element model of human cranial cavity**

#### **3.1 Materials and methods**

#### **3.1.1 CT scan**

A healthy male volunteer, aged 40 years old, with body height 176 cm, weighing 75 kg, was included in this study. The volunteer explained no history of cranium brain. Common projections (posterior-anterior, lateral, dual oblique, hyperextension and hyperflexion) were made to exclude cranium brain degenerative disorders, cranial instability, and brain destruction.

Spiral CT scans (1 mm thickness) were output in the JPG image file format and saved in the computer. Prior to experiment, informed consent was obtained from this volunteer, shown in Fig3.1.

#### **3.1.2 Experimental equipment**

High performance computer (Lenovo, X200) and mobile storage equipment were used. Solid modeling software Mimics 13.0 (Materiaise's interactive medical image control system) was used in this study. As a top software in computer aided design, Mimics 13.0 provides many methods of precise modeling and has been widely used for precise processing. Its equipped Ansys, Partron finite element analysis module sequence were used for finite element analysis, and then the strain and deformation regularity of the real human cranial cavity were simulated with the changing ICP.

Fig. 3.1. CT scan image of cranial cavity

#### **3.1.3 Flowchart of finite element method**

#### **Methods**

274 Finite Element Analysis – From Biomedical Applications to Industrial Developments

Fig. 2.19. Curves among total, elastic and viscous strain when the ICP increment is 2.5 kPa. Here EPELX is elastic strain curve, EPPLX is viscous strain curve. The viscous strain is about

A healthy male volunteer, aged 40 years old, with body height 176 cm, weighing 75 kg, was included in this study. The volunteer explained no history of cranium brain. Common projections (posterior-anterior, lateral, dual oblique, hyperextension and hyperflexion) were made to exclude cranium brain degenerative disorders, cranial instability, and brain

Spiral CT scans (1 mm thickness) were output in the JPG image file format and saved in the computer. Prior to experiment, informed consent was obtained from this volunteer, shown

High performance computer (Lenovo, X200) and mobile storage equipment were used. Solid modeling software Mimics 13.0 (Materiaise's interactive medical image control system) was used in this study. As a top software in computer aided design, Mimics 13.0 provides many methods of precise modeling and has been widely used for precise processing. Its equipped Ansys, Partron finite element analysis module sequence were used for finite element analysis, and then the strain and deformation regularity of the real human cranial cavity

**3. Finite-element model of human cranial cavity** 

40% of total strain.

**3.1.1 CT scan** 

destruction.

in Fig3.1.

**3.1 Materials and methods** 

**3.1.2 Experimental equipment** 

were simulated with the changing ICP.

#### *Image boundary tracking*

A self-programmed image boundary automatic recorder was used to acquire cranial information along the superior border to inferior border of cranium brain. The spatial boundary was recorded layer by layer. Following point selection from interior and exterior border of images, two-dimensional space coordinates were automatically recorded and saved in the .CDB form. After conversion, this file can be directly input into Mimics or CAD software.

#### *Location*

A coordinate system was determined. The CT scanning image starting from the lowest layer of cranium brain was set as the working background. CT scan was performed based on a fixed coordinate axis, with a know layer interval and magnification proportion. The spatial threedimensional coordinate of each point in the image could be determined through drawing the horizontal coordinate of each point and referencing scanning interval. When CT machines recorded each layer of images, all images were in the same scanning range, which equaled to cranial location of two-dimensional CT images from each layer in the scanning direction. Calibration of two-dimensional images could be performed if the scar bar of CT scan images

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 277

between, dura mater, solid of each part was generated independently, and the union of all parts was collected. The 3d finite-element models in each direction of cranial cavity are

Fig. 3.3. Each view drawing on the 3d finite-element model in of cranial cavity

Fig. 3.4. 3d finite-element model of cranial cavity is meshed

Fig. 3.5. Finite element model of 1/2 cranial cavity

Following type selection, finite element mesh generation was performed in the abovementioned models which were given material characteristics. Then, through simulating practical situation, boundary condition was exerted and proper numerical process. And the three-dimensional analysis was performed. Based on previously published manuscripts, the elastic modulus and the Poisson's ratio of compact bone, cancellous bone and dura mater, we adopt their elastic modulus and Poisson ratios as 1.5×104 MPa, 4.5×103 MPa, 1.3×102 MPa and 0.21, 0.01, 0.23 respectively. 3d finite-element model of cranial cavity is meshed in Fig3.4. Simulation analysis of cranium brain three-dimensional finite element model is

shown in Fig3.3.

**3.2.2 Model validation** 

shown in Fig3.5.

were given. In addition, each layer of image was scanned with some interval in the longitudinal direction, which was equivalent to calibration in the third dimensional direction.

#### *Image reconstruction*

In accordance with the sequence of CT scans and according to the scale bar and scan interval of CT faulted image, geometry data of each layer were input into the pre-processing module of finite element software to establish a geometry model in the rectangular coordinate in the sequence of point, line, area, and solid. The transverse plane of CT scan was parallel to xy plane, and the longitudinal plane was along the z axis. Three-dimensional reconstruction process is shown in Fig3.2.

Fig. 3.2. 3d model of cranial cavity

#### **3.2 Results**

#### **3.2.1 Reconstruction results**

The fitted curves were assigned into different layers to construct the solid structure of bone (Tabula externa, Tabula interna, Diploe sandwiched in between), spongy durameter. During reconstruction of structure of Tabula externa, Tabula interna, Diploe sandwiched in between, dura mater, solid of each part was generated independently, and the union of all parts was collected. The 3d finite-element models in each direction of cranial cavity are shown in Fig3.3.

Fig. 3.3. Each view drawing on the 3d finite-element model in of cranial cavity

#### **3.2.2 Model validation**

276 Finite Element Analysis – From Biomedical Applications to Industrial Developments

were given. In addition, each layer of image was scanned with some interval in the longitudinal direction, which was equivalent to calibration in the third dimensional direction.

In accordance with the sequence of CT scans and according to the scale bar and scan interval of CT faulted image, geometry data of each layer were input into the pre-processing module of finite element software to establish a geometry model in the rectangular coordinate in the sequence of point, line, area, and solid. The transverse plane of CT scan was parallel to xy plane, and the longitudinal plane was along the z axis. Three-dimensional reconstruction

The fitted curves were assigned into different layers to construct the solid structure of bone (Tabula externa, Tabula interna, Diploe sandwiched in between), spongy durameter. During reconstruction of structure of Tabula externa, Tabula interna, Diploe sandwiched in

*Image reconstruction* 

process is shown in Fig3.2.

Fig. 3.2. 3d model of cranial cavity

**3.2.1 Reconstruction results** 

**3.2 Results** 

Following type selection, finite element mesh generation was performed in the abovementioned models which were given material characteristics. Then, through simulating practical situation, boundary condition was exerted and proper numerical process. And the three-dimensional analysis was performed. Based on previously published manuscripts, the elastic modulus and the Poisson's ratio of compact bone, cancellous bone and dura mater, we adopt their elastic modulus and Poisson ratios as 1.5×104 MPa, 4.5×103 MPa, 1.3×102 MPa and 0.21, 0.01, 0.23 respectively. 3d finite-element model of cranial cavity is meshed in Fig3.4. Simulation analysis of cranium brain three-dimensional finite element model is shown in Fig3.5.

Fig. 3.4. 3d finite-element model of cranial cavity is meshed

Fig. 3.5. Finite element model of 1/2 cranial cavity

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 279

graph, and isogram drawn by post-processor visualizing the distribution ranges of stress or strain loaded on each part of cranium brain with the changing ICP. When loads are vertically added, the stress on the posterior wall of cranium brain, as well as on the end

Finite element analysis is an important mean to simulate human structural mechanical function in the field of biomechanics. A human finite element model with physical material characteristics under proper simulated in vivo condition can be used to effectively analyze the physical characteristics of human structure, for example, stress/strain of structure, modal analysis, exterior impact response, and fatigue test. With further understanding of cranium brain diseases, some complex models have not been developed, for example, finite element models of head and cranial cavity used to study the physio-pathological influences cervical spine loading in some complex exercises on cranium brain and soft tissue. Finite element analysis exhibits unexampled advantages in the biomechanical study of a severe medical brain problem. Theoretically, finite element method can simulate nearly all biomechanical experiments. Moreover, this method can better describe the interior changes of living body than practical study. Finite element method, as an emerging technique, has a broad developing space. However, it is a theoretical simulation analyses, only in conjunction with clinical detection and observation can it truly reflect the occurrence and progression of cranium brain disease and provide evidence for predicting curative effects, thereby exhibiting a synergic effect with clinical outcomes. The present model is only a represent. It can not reflect the changes between individual interior parts and between individuals in terms of bone contour and material characteristics. The present model is only a cranium brain motion segment. Its simulation analysis results might differ from the results from multiple motion segments. Actually, when much difference and many uncertainties exist between individuals, model simplification and idealization is to strengthen some research aspect, which removes experimental inherent difference. Of course, establishment of a finite element mechanical model is to provide mechanical methods for clinical and experimental studies. The present model needs further improvements due to some limitations, i.e., unable

plate and the posterior part of intervertebral discs, relatively centralizes.

Fig. 3.9. Strains curve of cranial cavity with the ICP variation

**3.2.3 Strains on the external surface of cranial cavity** 

Biomechanical model has been shown to play a key role in study of cranium brain, because it can be used to investigate the pathogenesis through model observation, thereby to propose the strategy of diagnosis and treatment.

Owing to irregular geometry and non-uniform composition of cervical spine cranium bone as well as impossible human mechanical tests, increasing attention has been recently paid to finite element method included in the biological study of cranium brain injury because this method exhibits unique advantages in analysis of complex structure.

Fig. 3.6. Loads on the finite element model of 1/2 cranial cavity

Fig. 3.7. Strain graph when the ICP is 3.0 kPa

Fig. 3.8. Strain graph when the ICP is 5.0 kPa

Experimental results are the best method to verify model accuracy. When exerting persistent pressure to vertebral spine, non-linear computation is supplemented to the two-dimensional unit calculation of ligament structure, which more corresponds to human mechanical structure. Statics solver exhibits the self-testing function and can automatically analyze computation process, report errors, and control error range. The displacement graph, stress

Biomechanical model has been shown to play a key role in study of cranium brain, because it can be used to investigate the pathogenesis through model observation, thereby to

Owing to irregular geometry and non-uniform composition of cervical spine cranium bone as well as impossible human mechanical tests, increasing attention has been recently paid to finite element method included in the biological study of cranium brain injury because this

Experimental results are the best method to verify model accuracy. When exerting persistent pressure to vertebral spine, non-linear computation is supplemented to the two-dimensional unit calculation of ligament structure, which more corresponds to human mechanical structure. Statics solver exhibits the self-testing function and can automatically analyze computation process, report errors, and control error range. The displacement graph, stress

propose the strategy of diagnosis and treatment.

method exhibits unique advantages in analysis of complex structure.

Fig. 3.6. Loads on the finite element model of 1/2 cranial cavity

Fig. 3.7. Strain graph when the ICP is 3.0 kPa

Fig. 3.8. Strain graph when the ICP is 5.0 kPa

graph, and isogram drawn by post-processor visualizing the distribution ranges of stress or strain loaded on each part of cranium brain with the changing ICP. When loads are vertically added, the stress on the posterior wall of cranium brain, as well as on the end plate and the posterior part of intervertebral discs, relatively centralizes.

Fig. 3.9. Strains curve of cranial cavity with the ICP variation

#### **3.2.3 Strains on the external surface of cranial cavity**

Finite element analysis is an important mean to simulate human structural mechanical function in the field of biomechanics. A human finite element model with physical material characteristics under proper simulated in vivo condition can be used to effectively analyze the physical characteristics of human structure, for example, stress/strain of structure, modal analysis, exterior impact response, and fatigue test. With further understanding of cranium brain diseases, some complex models have not been developed, for example, finite element models of head and cranial cavity used to study the physio-pathological influences cervical spine loading in some complex exercises on cranium brain and soft tissue. Finite element analysis exhibits unexampled advantages in the biomechanical study of a severe medical brain problem. Theoretically, finite element method can simulate nearly all biomechanical experiments. Moreover, this method can better describe the interior changes of living body than practical study. Finite element method, as an emerging technique, has a broad developing space. However, it is a theoretical simulation analyses, only in conjunction with clinical detection and observation can it truly reflect the occurrence and progression of cranium brain disease and provide evidence for predicting curative effects, thereby exhibiting a synergic effect with clinical outcomes. The present model is only a represent. It can not reflect the changes between individual interior parts and between individuals in terms of bone contour and material characteristics. The present model is only a cranium brain motion segment. Its simulation analysis results might differ from the results from multiple motion segments. Actually, when much difference and many uncertainties exist between individuals, model simplification and idealization is to strengthen some research aspect, which removes experimental inherent difference. Of course, establishment of a finite element mechanical model is to provide mechanical methods for clinical and experimental studies. The present model needs further improvements due to some limitations, i.e., unable

Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 281

ICP changing from 2.0 kPa to 6.0 kPa under the normal situation, and from 1.50 μ

deformation for mild, moderate and severe head injuries are separately 1.87 μ

In neurosurgery, one of the principle axes of treatment for neurosurgical disease is to control ICP. Because the skull bone is outside of and close to the brain, the surgical procedure in the strain-ICP monitoring system is relatively invasive and may affect experimental results from brain tissue. The strain-ICP monitoring has several advantages. First, the strain foil is far from the brain, and will not affect the surgery or experiments in the brain. Second, the wound surface on the parietal bone is very small and just about 11 mm2. Third, the surgical procedure is not extremely invasive for patients compared to the conventional monitoring. Fourth, it is possible to keep the strain foil for a longer time, the fixation of strain foil to the periosteum is much easier than other methods. Fifth, the operation is performed in the cephalic skin, the risk, difficulty, infection and trauma to patients are relatively small. Sixth, no special posture of patients is demanded, skull bone can be hardly influenced by any diseases and will be deformed as long as ICP is fluctuant in brain. ICP can be synchronously and continuously monitored based on the dynamic measurement of skull strains. Thus, this system is relatively safe, and it is easier to keep the strain foils in the cranial cavity for a

In this paper, the finite-element simulation was carried out to analyze the deformation of cranial cavity. Many complex relationships and influencing factors lie in the actual deformation of cranial cavity with the changing ICP. Therefore, in order to obtain the accurate deformation tendency of cranial cavity, the precise simulation to the finite-element

[1] Gregson BA, Banister K, Chambers IR. Statistics and analysis of the Camino ICP

[2] Hilton G. Cerebral oxygenation in the traumatically brain-injured patient: are ICP and

[3] Richard KE, Block FR, Weiser RR. First clinical results with a telemetric shunt-integrated

[4] Rosner MJ, Becker DP. ICP monitoring: complications and associated factors. Clin

[5] Schmidt B, Klingelhofer J. Clinical applications of a non-invasive ICP monitoring

[6] North B, Reilly P. Comparison among three methods of intracranial pressure recording.

model and further experimental studies in vivo and clinic need to be carried on.

monitor. J Neurol Neurosurg Psychiatry 1995; 70: 138.

CPP enough? J Neurosci Nurs 2000; 32: 278-282.

ICP-sensor. Neurol Res 1999; 21: 117-120.

method. Eur J Ultrasound 2002; 16: 37-45.

Neurosurg 1976; 23: 494-519.

Neurosurgery 1986; 18: 730-732.

under the mild hypothermia environment. Accordingly, the strains of skull

or so corresponding to ICP of 2.5 kPa, 3.5 kPa and 5.0 kPa.

to 4.52 μ

as the

> , 2.62

to

6. The deformation scope of human skull is theoretically from 1.50 μ

4.49 μ

**4.2 Discussion** 

and 3.74 μ

longer period of time.

**5. References** 

μ

to reflect some complex condition, but it ensures the geometry data and material characteristic approximation for application of multiple toolsequipped by various softwares during the process of model establishment. In addition, finite element method, as one of tools used in the biomechanical field, can qualitatively analyze the stress change of cranium brain interior parts when bearing forces. Only by changing local structure or materials can the present model established by finite element method simulate the common clinical situation and the effects of intervention on ICP force. The present model should be further improved in the clinical and experimental processes.

#### **4. Conclusion and discussion**

#### **4.1 Conclusion**

We develop a new minitraumatic method for measuring ICP with strain-electrometric technology. The strains of skull bone can reflect the ICP change. The surgical procedures for this new method are easy, simple, safe and reliable.

This paper carries respectively on the stress and strain analysis on both conditions of ignoring and considering the viscoelasticity of human skull and duramater by finite-element software MSC\_PPATRAN/NASTRAN and ANSYS as ICP changing from 1.5 kPa to 5 kPa. The three-dimensional finite element model of cranial cavity and the viscoelastic models of human skull and duramater are constructed in this paper. At the same time, the ANSYS finite-element software is in this paper used to reconstruct the three-dimensional cranial cavity of human being with the mild hypothermia treatment. The conclusion is as follows:


6. The deformation scope of human skull is theoretically from 1.50 μ to 4.52 μ as the ICP changing from 2.0 kPa to 6.0 kPa under the normal situation, and from 1.50 μ to 4.49 μ under the mild hypothermia environment. Accordingly, the strains of skull deformation for mild, moderate and severe head injuries are separately 1.87 μ , 2.62 μ and 3.74 μor so corresponding to ICP of 2.5 kPa, 3.5 kPa and 5.0 kPa.

#### **4.2 Discussion**

280 Finite Element Analysis – From Biomedical Applications to Industrial Developments

to reflect some complex condition, but it ensures the geometry data and material characteristic approximation for application of multiple toolsequipped by various softwares during the process of model establishment. In addition, finite element method, as one of tools used in the biomechanical field, can qualitatively analyze the stress change of cranium brain interior parts when bearing forces. Only by changing local structure or materials can the present model established by finite element method simulate the common clinical situation and the effects of intervention on ICP force. The present model should be further

We develop a new minitraumatic method for measuring ICP with strain-electrometric technology. The strains of skull bone can reflect the ICP change. The surgical procedures for

This paper carries respectively on the stress and strain analysis on both conditions of ignoring and considering the viscoelasticity of human skull and duramater by finite-element software MSC\_PPATRAN/NASTRAN and ANSYS as ICP changing from 1.5 kPa to 5 kPa. The three-dimensional finite element model of cranial cavity and the viscoelastic models of human skull and duramater are constructed in this paper. At the same time, the ANSYS finite-element software is in this paper used to reconstruct the three-dimensional cranial cavity of human being with the mild hypothermia treatment. The conclusion is as follows: 1. The human skull and duramater are deformed as ICP changing, which is corresponding

2. When analyzing the strain of human skull and duramater as ICP changing by the finiteelement software ANSYS, the strain by considering the viscoelasticity is about 14% less than that by ignoring the viscoelasticity of human skull and duramater. Because the viscoelasticity analysis by finite-element software ANSYS is relatively complex and the operation needs the huge memory and floppy disk space of computer, it is totally feasible to ignore the viscoelasticity while calculating the FEA strain of human skull and

3. The viscosity plays an important role in the total deformation strain of human skull and duramater as ICP changing. In the strains analysis of human skull and duramater with the changing ICP by the finite-element software ANASYS, the viscous strain accounts

5. The strains decreased under the mild hypothermia environment about 0.56% than those under the normal temperature conditions during the same circumstance of ICP changes.

for about 40% of total strain, and the elastic strain is about 60% of total strain. 4. Because the strains of human skull are proportional to ICP variation and the caniocerebra characteristic symptoms completely correspond to different deformation strains of human skull, ICP can be completely obtained by measuring the deformation strains of human skull. That is to say, the minitraumatic method of ICP by strain electrometric technique is feasible. Furthermore, ICP variation is respectively about 2.5 kPa when the strain value of human skull is about 1.4 µε, about 3.5 kPa when the strain value of human skull is about 2.1 µε, and about 5 kPa when the strain value of human

improved in the clinical and experimental processes.

this new method are easy, simple, safe and reliable.

with mechanical deformation mechanism.

duramater as ICP changing.

skull is about 3.9 µε.

**4. Conclusion and discussion** 

**4.1 Conclusion** 

In neurosurgery, one of the principle axes of treatment for neurosurgical disease is to control ICP. Because the skull bone is outside of and close to the brain, the surgical procedure in the strain-ICP monitoring system is relatively invasive and may affect experimental results from brain tissue. The strain-ICP monitoring has several advantages. First, the strain foil is far from the brain, and will not affect the surgery or experiments in the brain. Second, the wound surface on the parietal bone is very small and just about 11 mm2. Third, the surgical procedure is not extremely invasive for patients compared to the conventional monitoring. Fourth, it is possible to keep the strain foil for a longer time, the fixation of strain foil to the periosteum is much easier than other methods. Fifth, the operation is performed in the cephalic skin, the risk, difficulty, infection and trauma to patients are relatively small. Sixth, no special posture of patients is demanded, skull bone can be hardly influenced by any diseases and will be deformed as long as ICP is fluctuant in brain. ICP can be synchronously and continuously monitored based on the dynamic measurement of skull strains. Thus, this system is relatively safe, and it is easier to keep the strain foils in the cranial cavity for a longer period of time.

In this paper, the finite-element simulation was carried out to analyze the deformation of cranial cavity. Many complex relationships and influencing factors lie in the actual deformation of cranial cavity with the changing ICP. Therefore, in order to obtain the accurate deformation tendency of cranial cavity, the precise simulation to the finite-element model and further experimental studies in vivo and clinic need to be carried on.

#### **5. References**


Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method 283

[28] Willinger, R., Kang, H.S., Diaw, B.M. Development and validation of a human head

[29] Pithioux M, Lasaygues P, Chabrand P. An alternative ultrasonic method for measuring the elastic properties of cortical bone. Journal of Biomechanics 2002; 35: 961-968. [30] Hakim S, Watkin KL, Elahi MM, Lessard L. A new predictive ultrasound modality of

[31] Hatanaka M. Epidural electrical stimulation of the motor cortex in patients with facial

[32] Odgaard A. Three-Dimensional methods for quantification of cancellous bone

[33] Kabel J., Rietbergenvan B., Dalstra M., Odgaard A., Huiskes R. The role of an elective

[34] Noort van R., Black M.M., Martin T.R. A study of the uniaxial mechanical properties of human dura mater preserved in glycerol. Biomaterials 1981; 2: 41-45. [35] Kuchiwaki H., Inao S., Ishii N., Ogura Y., Sakuma N. Changes in dural thickness reflect changes in intracranial pressure in dogs. Neuroscience Letters 1995; 198: 68-70. [36] Cattaneo P.M., Kofod T., Dalstra M., Melsen B. Using the finite element method to

[37] Amit G., Nurit G., Qiliang Z., Ramesh R., Margulies S.S. Age-dependent changes in

[38] Andrus C. Dynamic observation and nursing of ICP. Foreign Medical Sciences (Nursing

[39] Min W. Observation and nursing for fever caused by Acute Cerebrovascular Disease.

[40] Shiozaki T., Sugimoto H., Taneda M., et al. Selection of Severely Head Injured Patients for Mild Hypothermia Therapy. Journal of Neurosurgery 1998; 89: 206—211. [41] Lingjuan C. Current situation and development trend at home and abroad of

[42] Yue X.F., Wang L., Zhou F. Experimental Study on the strains of skull in rats with the changing Intracranial Pressure.Tianjin Medicine Journal, 2007, 35(2):140-141. [43] Yue X.F., Wang L., Zhou F. Strain Analysis on the Superficial Surface of Skull as

[44] Qiang X., Jianuo Z. Impact biomechanics researches and finite element simulation for

[45] Zong Z., Lee H., Lu C. A three-dimensional human head finite element model and

isotropic tissue modulus in the elastic properties of cancellous bone. Journal of

model the biomechanics of the asymmetric mandible before, during and after skeletal correction by distraction osteogenesis. Computer Methods in Biomechanics

material properties of the brain and braincase of the rat. Journal of Neurotrauma

Hypothermia Therapy Nursing. Chinese Medicine of Factory and Mine 2005; 18(3):

Intracranial Pressure Changing.Journal of University of Science and Technology

human head and neck.Journal of Clinical Rehabilitative Tissue Engineering

power in human head subject to impact.Journal of Biomechanics, 2006, 39(2):284-

cranial bone thickness. IEEE Ultrason Sympos 1997; 2: 1153-1156.

neuralgia. Clinical Neurology and Neurosurgery 1997; 99: 155.

Mechanics, 1999, 327: 125-131.

architecture. Bone 1997; 20: 315-328.

& Biomedical Engineering 2005; 8(3): 157-165.

Foreign Medical Science) 1992; 11(6): 247-249.

Contemporary Medicine 2008; 143: 100-101.

Biomechanics1999; 32: 673-680.

2003; 20(11): 1163-1177.

Beijing, 2006, 28(12):1143-1151.

Research, 2008, 12(48):9557-9560.

268-269.

292.

mechanical model. Comptes Rendus de l'Academie des Sciences Series IIB


[7] Powell MP, Crockare HA. Behavior of an extradural pressure monitor in clinical use.

[9] Melton JE, Nattie EE. Intracranial volume adjustments and cerebrospinal fluid pressure in the osmotically swollen rat brain. Am J Physilo 1984; 246: 533-541. [10] Andrews BT, Levy M, M cIntosh TK, Pitts LH. An epidural intracranial pressure monitor for experimental use in the rat. Neurol Res 1988; 10: 123-126. [11] Yamane K, Shima T, Okada Y, Takeda T, Uozumi T. Acute brain swelling in cerebral

[12] Shah JL. Positive lumbar extradural space pressure. Br J Anaesthesia 1994; 73: 309-314. Sutherland WG. The cranial bowl. Mankato, Minn: Free Press Company 1939. [13] Zhong J, Dujovny M, Park H, Perez E, et al. Neurological Research 2003; 25: 339-350. [14] Schmiedek P, Bauhuf C, Horn P, Vajkoczy P, Munch E. International Congress Series

[15] Allocca JA. Method and apparatus for noninvasive monitoring of intracranial pressure.

[16] Rosenfeld JG. Method and apparatus for intracranial pressure estimation. U.S. Patent

[17] Marchbanks RJ. Method and apparatus for measuring intracranial fluid pressure. U.S.

[18] Mick EC. Method and apparatus for the measurement of intracranial pressure. U.S.

[19] Mick EC. Method and apparatus for the measurement of intracranial pressure. U.S.

[21] Czosnyka M, Pickard JD. Monitoring and interpretation of intracranial pressure. J

[22] Monro A. Observations on the structure and function of the nervous system.

[23] Kellie G. An account of the appearances observed in the dissection of two of the three

[24] Retzlaff EW, Jones L, Mitchell Jr FL, Upledger J. Possible autonomic innervation of cranial sutures of primates and other animals. Brain Res 1973; 58: 470-477. [25] Lakin WD, Stevens SA, Trimmer BI, Penar PL. A whole-body mathematical model for

[26] R. M. Jones. Composite Material. 1st Eds. Shanghai Science and Technology Publisher,

[27] Zhimin Zhang. Structural Mechanics of Composite Material. 1st Eds. Beijing: Publish of

intracranial pressure dynamics. J Math Biol, 2003Apr;46 (4):347-38.

individuals presumed to have perished in the storm of the 3rd, and whose bodies were discovered in the vicinity of Leith on the morning of the 4th November 1821 with some reflections on the pathology of the brain. Edinburgh: Trans Med Chir Sci

chronically raised intracranial pressure. J Neurosurg 1985; 53: 745-749. [8] Hayes KC, Corey J. Measurement of cerebrospinal fluid pressure in the rat. J Appl

Physiol 1970; 28: 872-873.

41: 477-481.

2002; 1247: 605-610.

4564022, 1986.1.14.

U.S. Patent 4204547, 1980.3.27.

Patent 4841986, 1989.6.27.

Patent 5074310, 1991.11.24.

Patent 5117835, 1992.1.2.

1824; 1: 84-169.

1981. 6: 41-73.

BUAA, 1993. 9: 85-86.

[20] Shepard S. Heat trauma. eMedicine 2004; 8: 20.

Edinburgh, Creech & Johnson 1823; 5.

Neurol Neurosurg Psychiatry 2004; 75: 813-821.

Comparison of extradural with intraventricular pressure in patients with acute and

embolization model of rats. Part I. Epidural pressure monitoring. Surg Neurol 1994;


**Part 3** 

**Materials, Structures, Manufacturing Industry** 

**and Industrial Developments** 

