Analyses of trabecular bone failure

Osteoporosis is a common condition among the elderly. It is characterized by decreased bone mass and increased fracture risk. Trabecular bone, the porous type of bone that consists of micro-scale rods and plates, the so-called trabeculae, is primarily affected by this condition. Trabecular bone strength decreases as a result of decreasing bone density. This can lead to fractures at sites with relatively large amounts of trabecular bone, for example in vertebral bodies and at the end of long bones. The combination of decreased bone strength and increased fall risk for the elderly mainly results in fractures of the vertebrae, distal radius and femur. These fractures, with hip fractures in particular, are associated with high medical costs and personal trauma. Therefore, it is important to understand the mechanical properties of trabecular bone, not only to identify those at risk, but also to prevent such osteoporotic fractures. The objective of this research project was to improve our knowledge about the failure behavior of trabecular bone, in order to enable accurate predictions of trabecular and whole-bone strength. Failure of trabecular bone was analyzed with numerical and experimental techniques to investigate its function as part of the whole organ and to determine the mechanical properties of trabecular bone tissue itself. Bone mass decreases due to osteoporosis. The effect on bone strength could be reduced with selective resorption of bone tissue that is not highly loaded in normal situations. As a result, the bones can resist normal-day loading, but are vulnerable for nonhabitual loads, such as a fall. This phenomenon has been demonstrated for vertebral bodies. In a recent study, micro-finite element models of a healthy and an osteoporotic human proximal femur were analyzed for the stance phase of walking. In the first study described in this thesis, the same models were analyzed for a simulated fall to the side, to determine the contribution of the trabecular bone to bone strength in the proximal femurs and to estimate the yield and ultimate loads for the femurs. The results suggested that the contributions to bone strength of trabecular and cortical bone are similar. However, a thick cortical shell is preferred in the femoral neck over a dense trabecular structure. The osteoporotic femur did not seem to be more vulnerable to non-habitual loads. Micro-finite element models incorporate the trabecular structure in detail. Although this enables accurate analyses, a lot of computer time and memory is required to solve those models. Increasing the element size reduces the demands on computer hardware, but the anisotropic trabecular structure is lost. The aforementioned micro-finite element models of the proximal femurs were coarsened to create continuum-level models. Such models are usually created from low-resolution computed-tomography scans and became a standard for the study of human bones in vivo. Instead of the full anisotropic trabecular structure, the reduced resolution results in isotropic bone-density values that cannot be uniquely related to mechanical properties. Therefore, different models were created to study the influence of element size and the chosen relation for the conversion of bone density to an isotropic stiffness. By comparing the results of the continuum-level and micro-finite element models, we determined the effects of the reduced resolution. It was found that very similar results could be obtained for both the healthy and the osteoporotic femur. Linear finite element models were used to estimate femoral strength in the aforementioned studies. Accurate predictions of bone strength, however, require models that incorporate geometric and material nonlinearities, due to the nonlinear nature of bone failure. This means that the failure behavior of the tissue must be included in the models. Due to the small sizes and irregular shapes of trabeculae, experimental data on the failure properties of trabecular tissue does not exist. Existing nonlinear models are, therefore, based on the assumption that trabecular bone tissue is similar to cortical bone tissue. To test this hypothesis, different meshes were combined with different material models based on cortical bone. A bovine trabecular bone specimen was compressed beyond its apparent ultimate point and the results were compared with those from the simulated compression experiment. The material model chosen, element type and size had an effect on the apparent simulated behavior, but none of the finite element models were able to produce the typical descent in the loaddisplacement curve seen during compression of trabecular bone. Based on these findings, we tried to determine the failure properties of trabecularbone tissue indirectly, by iterative adjustment of the assumed properties. Seven specimens were compressed using similar compression experiments. The tissue properties of the specimens were fitted to minimize the error between measured and simulated apparent load-displacement curves. The tissue properties determined were subsequently averaged and used to study their predictive value. The results showed that the correct apparent behavior could be obtained for the selected specimens when compression softening was introduced. When the averaged tissue properties were incorporated in the same finite element models of the seven trabecular bone specimens, larger differences were found between predicted and measured apparent loaddisplacement curves, suggesting specimen-specific tissue properties. Further research is necessary to investigate whether the variation in the tissue properties determined can be reduced by adjustment of the material model. Presently, it is not possible to measure strains at the level of trabeculae, due to experimental difficulties. This prevents the determination of mechanical trabecular bone properties and the validation of nonlinear finite element models for bone strength predictions. Therefore, a three-dimensional digital image correlation technique was developed for strain measurements in open-cell structures, such as trabecular bone. The technique uses high-resolution computed-tomography images for displacement measurements at selected positions in the solid structure. The displacement data was subsequently converted to local deformation and strain tensors. A precision analysis with computed-tomography images of aluminum foam specimens showed that the method is currently limited to strain measurements beyond the expected yield strain of trabecular bone tissue. The method is applicable to all sorts of porous structures and may be used to validate nonlinear micro-finite element simulations of trabecular bone failure. Accurate diagnoses of bone strength require detailed analyses of the trabecular structure. With the methods presented, this resulted in considerable hardware requirements. To reduce processing time, small amounts of specimens were analyzed in the various studies presented in this thesis. With the expected increase in computer power, however, our techniques can be used for analyses of larger pieces of trabecular bone and, perhaps, whole bones in the near future.