Towards Patient-Specific Hierarchical Simulation of Proximal Femur

INTRODUCTION: Clinical researchers lack convenient software tools to investigate mechanisms of bone fracture on a patient-specific basis. Such a tool must be user-friendly and, as bone mineral density alone fails to predict fracture, incorporate both macroand micro-structural information. Micro-parameters relevant to initiation, propagation and arrest of microcracks that cumulatively lead to fracture include local collagen-apatite orientation, degree of calcification and presence of osteocyte lacunae. METHODS: First, a macro-structural finite element (FE) model is created from the patient CT scan images at the proximal femur (Lian et al., 2005; Keyak et al., 2009; Fig. 1a). Second, FE analysis determines the macrostructural strain state at a region of interest. Third, at such region, a micro-structural FE submodel is based on the macro-structural patientspecific FE analysis and the micro-structural model of donor-matched information (Fig. 1b, 1c). The micro-structural FE model represents groups of secondary osteons and includes location-specific collagenapatite orientation, degree of calcification, and osteocyte lacunae (Ascenzi et al., 2008; Fig. 1d). A meso-scale model (Fig. 2) provides the transition between the 3mm homogeneous elements of the macro-model and the 0.5mm nonhomogeneous elements of the micro-model cubes. The FE analysis of the macro-model is conducted with Abaqus 6.3 on an SGI computer. The mesoand micromodels are prepared with Maple software programmed to yield the input files for Abaqus. UCLA’s Bewoulf2 supercomputer allows further preparation of FE models and visualization of results through Abaqus cae. TeraGrid’s capabilities allow the FE analysis of the mesoand micro-scale models. RESULTS: Transition between macroand mesomodels. The FE analysis of the CT scan-based macro-scale model yields the displacements at the eight nodes of the macro-scale element of interest. Such displacements are transferred to the many nodes on the surface of the meso-scale model (which has a much finer mesh) through use of the macro-element’s interpolation equations. Meso-model. The distribution of 433,703 elements within a 3mm cube forms models of osteons with cement lines distributed in rows within the interstitial bone model (Fig. 2a). The osteons and cement lines are modeled with 20-node quadratic elements, and the interstitial bone is modeled with wedge elements. Each of osteons, cement lines and interstitial bone are modeled as homogeneous orthotropic material. The material properties of osteons follow the experimental results of mechanical testing of single osteons of specific collagen-apatite orientation and degree of calcification (Ascenzi et al., 2000). So as to adapt the model to experimental data to simulate normal and pathological bone tissue specifications, the programming of the meso FE models allows material properties to be varied in terms of collagenorientation and degree of calcification of osteons and interstitial bone, plus to vary cement line material properties and dimensions of entities. Micro-model. Each 0.5mm cube comprises single osteon models previously developed plus the models of 3μm thick cement lines and of interstitial bone. The FE mesh consists of 20-node and 8-node elements of 3μm average side for a total on the order of 2,000,000 elements. DISCUSSION: Bone fracture depends on the microand macrostructural parameters that define the tissue’s ability to perform its function. The ultimate goal of this multi-scale modeling is patient-specific assessment of the microstructural specifications that can lead to fracture. The fully developed methodology is intended to discern fracture risk by location on a patientspecific basis in relation to age, sex, height, weight, alcohol use, smocking, use of medications that alter bone metabolism and presence of pathologies that affect bone. The results here presented are three elements of the broader project to include compact bone microstructure in the hierarchical model of the proximal femur. The achievement of the transition between macroand mesomodels and of the mesoand micromodels is significant given the challenges of complexity, size and consequent necessity of optimization of the model. The confinement in the meso-model of distribution of osteon groups to a 2D grid will be easily relaxed, as the programs allow osteon distribution in accord with biological variation. The model of each hierarchical level will be validated with mechanical testing of bone. The models presented here can be easily adjusted, if needed, to better adhere to biomechanical reality. In future hierarchical models, trabecular bone will also be modeled in terms of the micro-structure. REFERENCES: Ascenzi at al., J. Biomech. 41, 3428, 2008. Ascenzi et al., In: Mechanical Testing of Bone (An and Draughn Eds.), 271, CRC Press. Keyak et al. (2009) Bone 44, 449. Lian K et al., Osteoporosis Int 16: 642, 2005.