Abstract
Introduction
The influence of the bone mineral density (BMD) on the mechanical behavior of bones can be examined using computer tomography (CT) data and finite element (FE) simulations, because the BMD correlates with the Hounsfield scale (HU) of the CT data. Therefor the material mapping strategy, which is required to assign the HU values to the FE mesh, is of crucial importance. In this study a nodal mapping strategy was analyzed concerning its sensitivity towards FE mesh parameters and an averaging of HU values from the area around the respective nodes.
Method
The FE simulation is based on CT data of a human proximal femur. Once the bone shape was reconstructed, the resulting model was meshed with quadratic tetrahedral elements in ABAQUS/CAE and all nodes were assigned an HU value from the CT data by using the respective node coordinates. In this process, the mesh density, the threshold, which could be used to exclude connective tissue and fat from the material mapping process, the considered volume around the nodes and the method of averaging were varied. The material assignment was realized by an HU value dependent, linear elastic material definition. The femur model was clamped at the level of the isthmus and a displacement of 0.5 mm was applied at the femoral head. The evaluation was based on the resulting reaction forces.
Results
The sensitivity analysis demonstrated, that threshold and mesh density mainly influenced the reaction force [Fig. 1]. If a threshold was applied, the reaction force increased by about 20 % in average. A threefold increase of the mesh density led to an average gain of the results of about 24 %. For a specific mesh density the curve progressions of the respective results intersected, i.e. an alteration of the considered volume or the method of averaging barely affected the reaction force [Fig. 2, Fig. 3]. Apart from this intersection, the comparison of the small and the large average volume led to a deviation of up to 11 %. On the other hand, the examination of different methods of averaging revealed only a maximum deviation of 4 % between “mean” and “median”.
Discussion
The present study indicates, that the material mapping strategy is an influential part of the modeling process, which should be validated to avoid misjudgments of the load situation. Accordingly, the use of a threshold to exclude non-bone tissue could be a helpful tool. But with the exclusion of lower HU values, the load-bearing structure gains stiffness and the reaction force in the femur rises. A finer mesh leads to a higher resolution of the bone structure and, therefore, to a higher accuracy of the results. The “equilibrium” between the different models at the intersection is caused by a more homogeneous distribution of the material property which is increased by a larger considered volume and the method “mean”.
