**4.2. Effects of overweight on the spinal biomechanics**

The WHO called being overweight and obesity the leading chronic health problems [35]. In the world more than 1.9 billion adults, 18 years and older, were overweight in 2014 and of these over 600 million were obese [36]. Overweight and obesity are contributing factors for many ailments and can lead to the development of chronic diseases, like diabetes, cardiovas‐ cular disease, coronary heart disease, or osteoarthritis [37–39]. While there are a large number of studies on the effects of these factors on the cardiovascular system and the psyche of the concerned person [40, 41], the potential consequences of orthopedic damage, particularly of the spine, associated with obesity are hardly known yet. In [3–5], a direct correlation between back pain and obesity is described. The exact load changes within the various spinal structures have not been sufficiently explored yet. With the help of computer modeling, the effects of obesity on the kinematics and kinetics of various spine structures can be analyzed. In the following the potential effects of obesity of an adult and an adolescent human are illustrated by specific MBS models exemplary.

Example 1: Simulation of the effects on the spinal structures of body weight of a normal-weight and an overweight adult male

The modeling was carried out in three steps: step 1 is the creation of an MBS model of the lumbar spine, step 2 the creation of a suitable surface models of the two weight classes, including the determination of their anthropometric characteristics, and step 3 the fusion of the MBS lumbar spine model with the surface model [42]. In this example, the force application point is also located in the center of gravity. Taking into account the body weight, body height (1.85 m), sex (male), age (37), and the original two surface models, a normal-weight man (75 kg) and an obese man (127 kg, grade II) are created with the help of an open-source software for the creation of human 3D surfaces. By means of the mass-distribution model of Zatsiorskj [43], the mass distribution of the individual body segments is determined. All other model parameters are identical in both models. By fusing the surface models with the detailed biomechanical model of the lumbar spine, two new simulation models are built up, so that the effects of a normal-weight and obese man on the spinal structures can be analyzed.

Due to the body weight, the intervertebral discs are deformed. In the case of the normal-weight person, in general the intervertebral deformations in all FSUs are very small (**Figure 6**). The cranial located intervertebral discs are more deformed than the caudal intervertebral discs. Comparing the deformation values of the obese with those of normal weight, it can be seen that they are about 1.7 times greater. The validation of the deformation values is difficult, because we are not aware of studies, whose study design corresponds exactly to ours. Brinkmann investigated the fatigue fracture of human lumbar vertebra under cyclic axial compression and presented an example of force versus deformation curve of a specimen with material properties characterized as "tough" [44]. The force versus deformation curve indicates that a force of 500 N causes a deformation of about 0.025 cm and a force of 750 N a deformation of 0.044 cm. Because the simulated acting weight force of the upper body segments is in the case of normal body weight approximately 460 N, and in the case of overweight approximately 780 N and the deformations are in the range of 0.025 cm–0.04 cm (normal weight) and between 0.042 cm and 0.068 cm (obese), it is seen that the magnitude of this values corresponds to those of Brinkmann.

**Figure 6.** Deformations of the intervertebral discs.

assumption is not immediately evident from **Figure 5**. However, the percentage difference of the maximum and minimum intradiscal pressure value of an FSU is determined, and the percentage difference of the FSUs L5-Sac and L4-L5 is 8% and of the FSU L2-L3 even 13%. For the intervertebral discs, the resulting percentages of L3-L4 and L1-L2 are 3% and 5% respec‐

To sum up, it can be stated that the individual spinal alignment has an impact on the load

The WHO called being overweight and obesity the leading chronic health problems [35]. In the world more than 1.9 billion adults, 18 years and older, were overweight in 2014 and of these over 600 million were obese [36]. Overweight and obesity are contributing factors for many ailments and can lead to the development of chronic diseases, like diabetes, cardiovas‐ cular disease, coronary heart disease, or osteoarthritis [37–39]. While there are a large number of studies on the effects of these factors on the cardiovascular system and the psyche of the concerned person [40, 41], the potential consequences of orthopedic damage, particularly of the spine, associated with obesity are hardly known yet. In [3–5], a direct correlation between back pain and obesity is described. The exact load changes within the various spinal structures have not been sufficiently explored yet. With the help of computer modeling, the effects of obesity on the kinematics and kinetics of various spine structures can be analyzed. In the following the potential effects of obesity of an adult and an adolescent human are illustrated

Example 1: Simulation of the effects on the spinal structures of body weight of a normal-weight

The modeling was carried out in three steps: step 1 is the creation of an MBS model of the lumbar spine, step 2 the creation of a suitable surface models of the two weight classes, including the determination of their anthropometric characteristics, and step 3 the fusion of the MBS lumbar spine model with the surface model [42]. In this example, the force application point is also located in the center of gravity. Taking into account the body weight, body height (1.85 m), sex (male), age (37), and the original two surface models, a normal-weight man (75 kg) and an obese man (127 kg, grade II) are created with the help of an open-source software for the creation of human 3D surfaces. By means of the mass-distribution model of Zatsiorskj [43], the mass distribution of the individual body segments is determined. All other model parameters are identical in both models. By fusing the surface models with the detailed biomechanical model of the lumbar spine, two new simulation models are built up, so that the

effects of a normal-weight and obese man on the spinal structures can be analyzed.

Due to the body weight, the intervertebral discs are deformed. In the case of the normal-weight person, in general the intervertebral deformations in all FSUs are very small (**Figure 6**). The cranial located intervertebral discs are more deformed than the caudal intervertebral discs. Comparing the deformation values of the obese with those of normal weight, it can be seen that they are about 1.7 times greater. The validation of the deformation values is difficult,

tively.

distribution of the intervertebral disc.

36 Numerical Simulation - From Brain Imaging to Turbulent Flows

by specific MBS models exemplary.

and an overweight adult male

**4.2. Effects of overweight on the spinal biomechanics**

Each intervertebral disc develops a disc force, which depends on the deformation and deformation velocity of the corresponding FSU. **Figure 7** shows the force component acting

**Figure 7.** Intervertebral disc force of the different FSUs.

perpendicular to the disc. It can be clearly seen that the intervertebral discs of the obese are much more stressed than those of normal weight. The intervertebral disc force of the obese is, as well as in the above-discussed case of deformation, 1.7 times higher than the intervertebral disc force of the normal weighted. It could therefore be concluded that the deformation value, as opposed to the deformation velocity (see Section 3.3), has a great impact on the intervertebral disc force.

**Figure 8** shows the intersegmental rotations of the intervertebral discs. Whereas all interver‐ tebral discs of the obese person perform flexions, the intervertebral discs of the normal-weight person are deflected in different directions. The lowest two intervertebral discs of normalweight person perform flexion. The FSU L4-L3 and L2-L1 rotate backwards and the uppermost FSU L2-L1 rotates forward. Particularly evident is the high rotation values of the obese person. The FSU L1-L2 performs with about 17°, the largest rotational movement. In the literature [45, 46], the maximum range of motion (RoM) of FSU L1-L2 is specified by values between 2 and 13°. Consequently, our simulation values differ from these values. But the difference is relativized by the therein given standard deviations of about 2.5°. Further, it has to be analyzed whether the model of the obese person sufficiently reflects the reality, because identical biomechanical parameters are used in both simulation models. It is necessary to investigate in further work whether the biomechanical properties of the spinal structures are adapted in reality to the body weight, in order to avoid such rotations and prevent overloading or degenerative damage. Moreover, in this model, the stabilizing muscles are not considered, which could prevent such rotation.

**Figure 8.** Intervertebral rotations of the different FSUs: Positive rotation angles represent flexion and negative rotation angles extension movements.

The movements of the FSUs can affect the biomechanical behavior of posterior located facet joints (**Figure 9**). It is striking that the loads of the FSU L1-L2 respectively L2-L3 are not loaded. Further it can be seen, that in the case of obesity the loads decrease to cranial. A possible reason may be, in this section, the pure ventral directed rotations. The two corresponding joint surfaces of the facets are distracted, and thus no contact force is build. To achieve a complete clarification of this, a model specification in the form of a sophisticated 3D facet joints modeling is required (see Section 5).

**Figure 9.** Contact forces of the facet joints.

perpendicular to the disc. It can be clearly seen that the intervertebral discs of the obese are much more stressed than those of normal weight. The intervertebral disc force of the obese is, as well as in the above-discussed case of deformation, 1.7 times higher than the intervertebral disc force of the normal weighted. It could therefore be concluded that the deformation value, as opposed to the deformation velocity (see Section 3.3), has a great impact on the intervertebral

**Figure 8** shows the intersegmental rotations of the intervertebral discs. Whereas all interver‐ tebral discs of the obese person perform flexions, the intervertebral discs of the normal-weight person are deflected in different directions. The lowest two intervertebral discs of normalweight person perform flexion. The FSU L4-L3 and L2-L1 rotate backwards and the uppermost FSU L2-L1 rotates forward. Particularly evident is the high rotation values of the obese person. The FSU L1-L2 performs with about 17°, the largest rotational movement. In the literature [45, 46], the maximum range of motion (RoM) of FSU L1-L2 is specified by values between 2 and 13°. Consequently, our simulation values differ from these values. But the difference is relativized by the therein given standard deviations of about 2.5°. Further, it has to be analyzed whether the model of the obese person sufficiently reflects the reality, because identical biomechanical parameters are used in both simulation models. It is necessary to investigate in further work whether the biomechanical properties of the spinal structures are adapted in reality to the body weight, in order to avoid such rotations and prevent overloading or degenerative damage. Moreover, in this model, the stabilizing muscles are not considered,

**Figure 8.** Intervertebral rotations of the different FSUs: Positive rotation angles represent flexion and negative rotation

The movements of the FSUs can affect the biomechanical behavior of posterior located facet joints (**Figure 9**). It is striking that the loads of the FSU L1-L2 respectively L2-L3 are not loaded. Further it can be seen, that in the case of obesity the loads decrease to cranial. A possible reason may be, in this section, the pure ventral directed rotations. The two corresponding joint

disc force.

which could prevent such rotation.

38 Numerical Simulation - From Brain Imaging to Turbulent Flows

angles extension movements.

Example 2: Simulation of the effects on the spinal structures of body weight of a normal-weight, an overweight, and an obese child

More than 42 million children under the age of five were overweight in 2013 worldwide [35]. According to Deckelbaum [47], not only in the USA the number of overweight children and adolescents has doubled in the last two to three decades but also the similar doubling rates are being observed worldwide. Therefore, the WHO called overweight and obesity as the leading chronic health problem [35].

Three MBS models of the child's lumbar spine were created to quantify the effects of normalweight, overweight, and obese children to the kinematics and transmitted forces and torques of the different spinal structures. With the help of these 3D models, dynamic movements and static situations can be simulated. For simulation and load calculation of the effects of different weight classes, the masses of the body segments are adapted to these weight classes [48]. Therefore, the first lumbar vertebra L1 is loaded with the weight of the upper body segments of a normal weight, an overweight, and an obese child in different simulations. The total mass fractions of the segment parts is *m*normal = 22.91 kg for normal-weight child, *m*overweight = 27.73 kg for overweight child, and *m*obese = 32.56 kg for obese child. In the case of overweight and obesity, the intervertebral discs are more heavily loaded in comparison to the normal-weight child. In both cases, the intervertebral discs of the FSU L4-L5 are most loaded (**Figure 10**). The slightest load undergoes the FSU L1-L2. The increase in body weight has a direct influence on the loading structure of the intervertebral discs. If the normal-weight child would become overweight, the loads of the intervertebral discs would rise by an average of 1.5 times. In the case of obesity, the intervertebral discs are more than 2.3 times higher loaded.

**Figure 10.** Percentage load of the intervertebral disc.

Through the increased body weight, the intervertebral discs perform pure flexion (**Figure 11**). Here, the amount of flexion of the obese child is mostly more than doubled compared with the movement of the normal-weight child. Particularly obvious is the difference in the FSU L3-L4. In the case of obesity, this FSU is deflected more than 3.5 times larger from its initial position (normal weight).

**Figure 11.** Percentage intersegmental rotation.

Through the forward rotations of the intervertebral discs, the approach and origin points of the posterior ligaments move away from each other. As a result, the corresponding ligaments are stretched and develop in an opposite direction acting as reaction force (**Figure 12**). In the

case of an obese child, the posterior ligaments are 2 to 2.5 times more loaded than under normal body weight. Under obesity, a particularly extreme ligament load occurs in the FSU L3-L4. This more than 4 times larger load may result from the above-described extensive interseg‐ mental rotations in these FSU.

**Figure 12.** Percentage load of the posterior ligaments.

**Figure 10.** Percentage load of the intervertebral disc.

40 Numerical Simulation - From Brain Imaging to Turbulent Flows

**Figure 11.** Percentage intersegmental rotation.

(normal weight).

Through the increased body weight, the intervertebral discs perform pure flexion (**Figure 11**). Here, the amount of flexion of the obese child is mostly more than doubled compared with the movement of the normal-weight child. Particularly obvious is the difference in the FSU L3-L4. In the case of obesity, this FSU is deflected more than 3.5 times larger from its initial position

Through the forward rotations of the intervertebral discs, the approach and origin points of the posterior ligaments move away from each other. As a result, the corresponding ligaments are stretched and develop in an opposite direction acting as reaction force (**Figure 12**). In the It seems to be evident that by the increase of body weight, the loads of the internal structures rise to the same extent. This correlation, which can be predicted even before the simulation, was confirmed by the simplest load case, the upright standing. Further investigations, such as the analysis of load distribution in different structures of an overweight or obese child during everyday activities or during highly dynamic movements, like they occur in sports, can give additional insights into the effects of obesity on the musculoskeletal system.

## **4.3. Application possibilities of biomechanical computer models in medicine**

Because the MBS features very short computation times and surgical planning is increasingly computer-based, preoperative simulations can be used to predict the effects of different surgical methods and to identify the best possible surgical option. Furthermore, in future a transfer of topographic and kinematic simulation data of implants in 3D planning and navigation procedures is conceivable. In this process, coordinates of the implants from the computer model and the 3D model data of the spine may be transferred to the navigation system in the appropriate data format. It should be noted that the MBS modeling of the biomechanical properties of the intervertebral disc represents an initial approach. Therefore, the implementation of FE parts is indispensable to simulate patient-specific biomechanical properties.

To demonstrate the medical application possibilities of the simulation, the effect of a spinal fusion under different load cases is exemplified by an appropriate computer model (**Figure 13**). For that the mechanical properties of the MBS model were adjusted, so that no residual movement in FSU L4-L5 is possible. Thus, two models of the lumbar spine were created [49]. As in previous models, the upright position is used as the load case in this simulation, and also an external load of 600 N and 700 N is applied at the center of the vertebral endplate of L1.

**Figure 13.** Detailed MBS lumbar spine model with fused FSU L4-L5.

Considering only the disc force of the model without fused FSU L5-L4, it can be seen that the pressures in all FSUs increase with higher external force (**Figure 14**). Comparing the pressure of the intervertebral discs of both models, the disc loads of the FSU L1-L2 are almost the same. A deviation results for the other functional units. The pressure in the FSU's L5-Sac to L2-L3, of the model with fused FSU L4-L5, is lower than without fusion.

**Figure 14.** Effect of a spinal fusion under different load cases: intradiscal pressure.

In this case, a spinal fusion affects especially the loads of the facet joints. **Figure 15** clearly shows that after fusion, the forces in the facet joints are particularly higher in the upper FSU. Through such an increased load situation degenerative changes can be caused in the facet joints in long term.

**Figure 15.** Effect of a spinal fusion on the facet loads.

the implementation of FE parts is indispensable to simulate patient-specific biomechanical

To demonstrate the medical application possibilities of the simulation, the effect of a spinal fusion under different load cases is exemplified by an appropriate computer model (**Figure 13**). For that the mechanical properties of the MBS model were adjusted, so that no residual movement in FSU L4-L5 is possible. Thus, two models of the lumbar spine were created [49]. As in previous models, the upright position is used as the load case in this simulation, and also an external load of 600 N and 700 N is applied at the center of the vertebral endplate of L1.

Considering only the disc force of the model without fused FSU L5-L4, it can be seen that the pressures in all FSUs increase with higher external force (**Figure 14**). Comparing the pressure of the intervertebral discs of both models, the disc loads of the FSU L1-L2 are almost the same. A deviation results for the other functional units. The pressure in the FSU's L5-Sac to L2-L3,

**Figure 13.** Detailed MBS lumbar spine model with fused FSU L4-L5.

42 Numerical Simulation - From Brain Imaging to Turbulent Flows

of the model with fused FSU L4-L5, is lower than without fusion.

**Figure 14.** Effect of a spinal fusion under different load cases: intradiscal pressure.

properties.

Comparing the intersegmental rotation of the discs (**Figure 16**) with and without fused L4-L5 disc, it can be seen that the discs of the fused model perform less deflection in the FSUs L5-Sac to L2-L3. The lower lumbar spine thus has lower mobility than in the non-fused state. This means that after an intervertebral disc stiffening, the lower lumbar spine would have a lower mobility than in a non-fused state.

**Figure 16.** Effect of a spinal fusion on the intersegmental rotation.

In summary, it can be stated that a fusion can lead to load redistribution. In this simulation case, especially the posterior structures that are located above the fused FSUs are stressed more than the ventrally located structures. A further example in the field of medicine is studying the effects of different body weights on selected surgical procedures.
