*4.3.1. Mechanical experiment with PU-foam based synthetic pelvis*

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2001) which used the DE theory of fracture as well as material non-linearity. However, our approach differs from their work in that we simulated acetabular fractures not fractures of the proximal femur which are generally more complicated than fractures of the proximal femur. Moreover, rather than applying force directly to the bone of interest as done in majority of the FE fracture studies, we employed a contact mechanics approach where the force was applied to the acetabulum via the femoral head. Another novel approach of our study is that we incorporated geometric non-linearity to the model by using full finite elasticity governing equations, which has been found to enhance the fracture prediction

However the most notable feature of our approach is the use of PU-based synthetic bone in validating FE fracture predictions. At present, it is not known whether our model can predict human bone fractures with the same degree of accuracy as the synthetic bones. Therefore caution is required when interpreting the data. However we are confident that our result will translate into human bones due to the following reasons. Firstly our experimental results with PU-foam pelves showed similar results as other human cadaver results as the fracture patterns generated in seating and standing cases correspond well with clinical results. Moreover the sensitivity analysis revealed that our model behaves in a similar manner as the cadaver bones despite the apparent difference in absolute magnitudes

In fact, PU-foam based synthetic bone served our purpose of model validation very well due to their uniformity and consistency (Nabavi et al., 2009). As such, the ASTM standard states that it is "an ideal material for comparative testing" of various orthopaedic devices (American Society for Testing and Materials, 2008b). Although the fracture load is expected to be different from the fracture load of human pelvis, the material behaviour is expected to be comparable to human bones, both of which exhibit brittle fracture (Schileo et al., 2008, Thompson et al., 2003). Therefore the model's ability to predict fracture load and location of the synthetic bone can be regarded as a positive indication that it will also be applicable to human cases. Therefore we continued to use this approach in developing and validating FE model predictions for fracture stability with PU-foam based synthetic bones, which will be

**4.3. Development and validation of finite element predictions of the stability of** 

The posterior wall fracture is the most common fracture type of the acetabulum(Baumgaertner, 1999). Depending on the fragment size, open reduction and internal fixation (ORIF) is performed especially when the fracture involves more than 50% of the posterior wall. But ORIF requires considerable exposure that often leads to major blood loss and significant complications(Shuler et al., 1995). Percutaneous screw fixations, on the other hand, have become an attractive treatment option as they minimize exposure, blood loss and risk of infection. As such, they have been advocated by some authors

capabilities of FE models (Stˆlken and Kinney, 2003).

in modulus values between PU-foams and bones.

described in the next section(Shim et al., 2011).

**fracture fixation with PU-foam based synthetic bones** 

Seven synthetic pelves (Full Male Pelvis 1301-1, Pacific Research Laboratories Inc) were loaded until failure with the loading condition that resembled seating fracture[10], creating posterior wall fractures[11]. The fractures were then reduced and fixed with two fixation methods –with two screws (3.5mm Titan Screws, Synthes) and then with a 10-12 hole plates (3.5mm Titan Reconstruction- or LCDC-Plates, Synthes) by an experienced surgeon (JB) (Figure 13 A and B). The maximum remaining crack was 0.7 mm.

(a) Screw fixation (b) Plate fixation

The pelves were then loaded in the Instron Machine (Instron 5800 series) with a cyclic load that oscillated between 0N to 900N at 40N/s. The force was applied using a synthetic femoral head (Large Left Femur, 1129, Pacific Research Laboratories Inc) attached to the crosshead of the Instron Machine (Figure 14). At the multiple of 300N the loading was paused for 3 seconds to measure the displacement between the fragment and the bone by taking photographs of the crack opening (Figure 14 (a)). A digital SLR camera (Nikon D70) with a 50mm macro lens (NIKKOR dental lens) was used to accurately measure the amount of crack openings (resolution of 10 μm (Figure 14 (b))). A resolution of 10μm was achieved (Figure 15).

(a) Measurement set-up (b) Optical set-up with macro

Use of Polyurethane Foam in Orthopaedic Biomechanical Experimentation and Simulation 191

The displacement was measured in two different positions – front and side - to obtain the fragment movement in three directions – frontal, vertical and lateral directions (Figure 16).

**Figure 16.** Getting fragment movements in three directions – horizontal, vertical and lateral – using photos taken at two different views. The actual movement of the fragment is from P1 to P2 from no load

The stability of screw fixation was analyzed with finite element models. We developed the models of the fractured pelvis, fragment and femoral head in order to perform the mechanical testing that we did in silico. Firstly, one of the PU-foam based synthetic fractured pelves that had been fixed with two screws was dismantled. The resulting fractured pelvis and its fragment were scanned separately with a Faro Arm (Siler Series Faro Arm) and a laser scanner (Model Maker H40 Laser Scanner). Two sets of data point

to full load conditions. The front view photo gives the triangle P1P4P3, allowing us to calculate horizontal and vertical movement. The side view photo gives the triangle P4P2P3 which allows us to

calculate the lateral movement.

*4.3.2. Finite element simulation* 

10 photographs were taken at each angle and load and the mean value was taken.

**Figure 14.** Interfragmentary movement measuring set-up with a digital single-lens reflex camera and an Instron machine

**Figure 15.** A photo taken with the macro lens. The magnified view shown in the box left has the resolution of 10μm

The displacement was measured in two different positions – front and side - to obtain the fragment movement in three directions – frontal, vertical and lateral directions (Figure 16). 10 photographs were taken at each angle and load and the mean value was taken.

**Figure 16.** Getting fragment movements in three directions – horizontal, vertical and lateral – using photos taken at two different views. The actual movement of the fragment is from P1 to P2 from no load to full load conditions. The front view photo gives the triangle P1P4P3, allowing us to calculate horizontal and vertical movement. The side view photo gives the triangle P4P2P3 which allows us to calculate the lateral movement.

#### *4.3.2. Finite element simulation*

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(Figure 15).

an Instron machine

resolution of 10μm

The pelves were then loaded in the Instron Machine (Instron 5800 series) with a cyclic load that oscillated between 0N to 900N at 40N/s. The force was applied using a synthetic femoral head (Large Left Femur, 1129, Pacific Research Laboratories Inc) attached to the crosshead of the Instron Machine (Figure 14). At the multiple of 300N the loading was paused for 3 seconds to measure the displacement between the fragment and the bone by taking photographs of the crack opening (Figure 14 (a)). A digital SLR camera (Nikon D70) with a 50mm macro lens (NIKKOR dental lens) was used to accurately measure the amount of crack openings (resolution of 10 μm (Figure 14 (b))). A resolution of 10μm was achieved

**Figure 14.** Interfragmentary movement measuring set-up with a digital single-lens reflex camera and

(a) Measurement set-up (b) Optical set-up with macro

**Figure 15.** A photo taken with the macro lens. The magnified view shown in the box left has the

The stability of screw fixation was analyzed with finite element models. We developed the models of the fractured pelvis, fragment and femoral head in order to perform the mechanical testing that we did in silico. Firstly, one of the PU-foam based synthetic fractured pelves that had been fixed with two screws was dismantled. The resulting fractured pelvis and its fragment were scanned separately with a Faro Arm (Siler Series Faro Arm) and a laser scanner (Model Maker H40 Laser Scanner). Two sets of data point clouds, which accurately described the shapes of the fragment and the fractured pelvis, were obtained (Figure 17). The fractured pelvis model was developed from our previous FE model of the pelvis, which was generated from CT scans of the synthetic pelvis used in the experiment (Shim et al., 2010) . Our elements had inhomogeneous location dependent material properties despite large element size and different material properties were assigned to solid and cellular polyurethane foams which mimic cortical and cancellous bone properties separately. The loading and boundary condition that mimics the mechanical experiment setup were employed. The FE models of the screws were not generated explicitly. Instead tied contact was used to model the bond between the fractured pelvis and the fragment from the screws. The locations of the screws on the fragment FE model were identified first from the laser scanned data. Then, the tied contact condition that ensures a perfect bond between slave and master faces was imposed on the identified faces to simulate the bond that screws provide when connecting the fragment with the bone. The rest of fragment faces were modeled with frictional contact (μ=0.4)(Gordon et al., 1989). The predicted interfragmentary movements from the FE model under the same loading and boundary conditions as the experiment were then compared with the experimental value to test our hypothesis. Once tested, then, the screw positions were varied by changing tied contact faces to simulate all possible screw positions in order to identify the positions that achieved the most stable fixation.

Data clouds obtained from laser scanning PUfoam pelvis

Model generated from data points by geometric fitting

Model for fracture reduced pelvis

Use of Polyurethane Foam in Orthopaedic Biomechanical Experimentation and Simulation 193

*4.3.3. Interfragmentary movement in acetabular fracture osteosynthesis measured with* 

the stability of screw fixation was sufficient for the cyclic loading condition used.

**Figure 18.** Comparison of interfragmentary movement between plate and screw fixation

measurement (mean + 1 SD) but still very close to it as the difference was 0.05 mm.

*4.3.4. Accuracy of FE model interfragmentary movement predictions validated with PU-*

The FE model predicted the movement of the fragment in screw fixations with a good accuracy. The values predicted by the FE simulation were within one standard deviation of the experimental measurements (Figure 19) in the horizontal and lateral directions. The predicted vertical direction movement was a little bit greater than the upper limit of the experimental

horizontal vertical lateral

Plate fixation Screw fixation

The optimized screw positions were found to be on the two diagonal corners of the fragment. When the virtual screws were placed in this manner, the stability of screw fixations improved dramatically to the level that is comparable to plate fixation (Figure 20). The fragment movements in the horizontal and lateral directions were smaller than the average movements in the plate fixation in these directions. Although the movement in the vertical direction was bigger than the upper limit of the experimental measurement, the

The overall amount of displacement between the pelvis and the fragment was relatively small and the main direction of the fragment movement was in the lateral posterior direction (in body directions). The average displacement was around 0.4 – 0.9 mm for both screw and plate fixations. The plates gave higher stability especially in the horizontal and lateral directions (Figure 18). However, screw fixations also gave good stability of less than 1mm on average in all directions. Therefore, considering the fact that the maximum load of our experiment was higher than normally allowed weight bearing (around 20kg after the surgery for 3 months),

*PU- foam based synthetic bones* 

*foam based synthetic bones* 

0 0.2 0.4 0.6 0.8 1 1.2 1.4

difference was small 0.1mm.

**Figure 17.** The far left column shows clouds of data points obtained from laser scanning. The center column shows the meshes for the fragment and fractured pelvis that were generated by geometric fitting to laser scanned data points. The red faces on the fragment mesh indicate where tied contact conditions were imposed in order to simulate the support provided by the screws. The final mesh is shown on the far right column.
