Finite Element Analysis of Osteosynthesis Screw Fixation in the Bone Stock: An Appropriate Method for Automatic Screw Modelling

The use of finite element analysis (FEA) has grown to a more and more important method in the field of biomedical engineering and biomechanics. Although increased computational performance allows new ways to generate more complex biomechanical models, in the area of orthopaedic surgery, solid modelling of screws and drill holes represent a limitation of their use for individual cases and an increase of computational costs. To cope with these requirements, different methods for numerical screw modelling have therefore been investigated to improve its application diversity. Exemplarily, fixation was performed for stabilization of a large segmental femoral bone defect by an osteosynthesis plate. Three different numerical modelling techniques for implant fixation were used in this study, i.e. without screw modelling, screws as solid elements as well as screws as structural elements. The latter one offers the possibility to implement automatically generated screws with variable geometry on arbitrary FE models. Structural screws were parametrically generated by a Python script for the automatic generation in the FE-software Abaqus/CAE on both a tetrahedral and a hexahedral meshed femur. Accuracy of the FE models was confirmed by experimental testing using a composite femur with a segmental defect and an identical osteosynthesis plate for primary stabilisation with titanium screws. Both deflection of the femoral head and the gap alteration were measured with an optical measuring system with an accuracy of approximately 3 µm. For both screw modelling techniques a sufficient correlation of approximately 95% between numerical and experimental analysis was found. Furthermore, using structural elements for screw modelling the computational time could be reduced by 85% using hexahedral elements instead of tetrahedral elements for femur meshing. The automatically generated screw modelling offers a realistic simulation of the osteosynthesis fixation with screws in the adjacent bone stock and can be used for further investigations

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Overview of the investigated fixation cases.

<p>Five different cases for the three fixation methods are investigated, based on the three different femur models. Furthermore, information of the implemented screws is also provided.</p

Distribution of the material properties along the femur.

<p>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.</p

Alignment of the marker points to the FE model.

<p>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).</p

Results for the gap decrease.

<p>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.</p

Summary of the investigated models.

<p>For each investigated femoral model element types and number of elements are listed. The osteosynthesis plate (NCB®) was the same for each model.</p

Results of the optical measurements.

<p>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.</p

Elapsed total CPU time for one equilibrium iteration.

<p>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.</p