Figure 1.
Magnification of the mesh for the three different femoral models.
Magnifications are given for the area around the femoral head (red box), the area around the screw (blue box) and the area of the medial condylus (green box). Thereby, Model A and B consisted of tetrahedral elements, whereat Model A did not consider any screw holes. Model C was discretised with hexahedral elements and did not consider any screw holes, either.
Table 1.
Summary of the investigated models.
Figure 2.
Distribution of the material properties along the femur.
Femur with its segmental defect at the lower third is shown. An additional view cut in the frontal plane was created at the proximal end to show the cortical structure along the femoral axis. Dark colour represents areas with low HU values, e.g. air and cancellous bone, light colour represents areas with high HU values, i.e. cortical bone.
Table 2.
Overview of the investigated fixation cases.
Figure 3.
Osteosynthesis plate and structural screws.
FE model of the osteosynthesis plate and the seven generated screws (a) (view from anterior, see (b) and (c) for detailed illustration). Angular stable fixation of the screw heads to the nodes of the osteosynthesis plate (b) (view from lateral). Screw with the rigid connector elements C between the base points on the wire W and the FE elements of the bone (c).
Figure 4.
CAD model of the plate as a schematic figure for the screw position.
Arrows marking the position at which screws are placed for the fixation to the bone.
Figure 5.
Posterior view of the test arrangement with a composite left femur mounted in the universal testing machine (Zwick/Roell). Segmental defect is bridged with an osteosynthesis system on the lateral (outer) side and fixed with seven titanium screws. Distal end of the femur is embedded in a metallic socket, filled with casting resin. 57 optical markers were attached onto the femur, socket and the testing machine to calculate their displacement during loading.
Figure 6.
Results of the optical measurements.
Displacement vectors calculated for each marker along the femur at a maximum applied load of 227 N. Direction and magnitude are plotted in the picture taken from the optical measuring system at the last loading step. Calculation of the gap alteration was calculated with displacement vectors between two marker points (indicated with red double-sided arrow). The colour legend represents the displacement magnitude.
Figure 7.
Displacement magnitude |U| of the numerical analysis.
Displacement field of the femoral bone and displacement vectors for individual nodes (not equal to those of the experimental test setup) are shown.
Figure 8.
Alignment of the marker points to the FE model.
Overlay plot of the test setup picture with the marker points and the FE model within the FE software package. By using the translucency for the FE model the position of the marker points could be adapted to the FE model. Red marks show position of the nodes, used for the calculation of the femoral head deflection (1) and for the gap alteration (2 and 3).
Figure 9.
Results for the femoral head displacement.
Results were obtained from the experimental testing (Pontos) and the five numerical analyses. Mean value and standard deviations are shown for the experimental data, while magnitudes of femoral head displacement are shown for the data of all numerical models. All results were achieved at a load of 227 N.
Figure 10.
Results were obtained from the experimental testing (Pontos) and different numerical analyses. Mean value and standard deviations are shown for the experimental data, while magnitudes of gap width are shown for the numerical data of all five numerical models. All results were achieved at a load of 227 N.
Figure 11.
Elapsed total CPU time for one equilibrium iteration.
For all five numerical models the calculations were performed on an Intel® Xeon® processor E 5504 2.0 GHz. Elapsed time for one equilibrium iteration and the DOF for each model are shown. Least DOF and subsequently least computational time was determined for the hexahedral model.
Figure 12.
Stress distribution within the area between the bone and the osteosynthesis plate.
Results are shown on the surface of the bone (marked with red rectangle on the right). An upper limit of 60 MPa was set for comparison of all cases. Stresses are shown on the lateral site of the femur without the osteosynthesis plate for both tied contact models (Case A1 and A2), the model concerning the screw holes (Case B) and both models with the implemented structural screws (Case C and D).