Plate-Rod Microstructural Modeling for Accurate and Fast Assessment of Bone Strength

Progressive bone loss and weakening bone strength associated with aging predispose the elderly population to osteoporosis and millions of costly fragility fractures. Micro finite element (µFE) analysis based on clinical high-resolution skeletal imaging provides an accurate computational solution to assessing the mechanical properties of bone, which can be used as the dominant factors for fracture risk. However, the current µFE analysis technique is impractical for clinical use due to its prohibitive computational costs, which result from the “voxel-to-element” approach of modeling human bone regardless of its microstructural pattern. I developed a novel plate-rod microstructural modeling technique for highly efficient patient-specific µFE analysis and translated it to clinical research for the assessment of bone strength in osteoporosis and fragility fractures. Trabecular microstructure is composed of interconnected plate-like and rod-like trabeculae. Instead of converting every image voxel directly into an element, the plate-rod modeling approach created mechanical characterization for every individual trabecular plate and rod. The validation studies demonstrated that the PR model was able to reproduce the morphology and mechanical behavior of the original trabecular microstructure, while reducing the size of the µFE model and improving the efficiency of µFE simulations. First, the PR models of trabecular bone were developed based on high-resolution micro computed tomography (µCT), and evaluated in comparison with computational gold standard-voxel µFE models and experimental gold standard-mechanical testing for estimating Young’s modulus and yield strength of human trabecular bone. Results suggested that PR model predictions of the trabecular bone mechanical properties were strongly correlated with voxel models and mechanical testing results. Moreover, the PR models were indistinguishable from the corresponding voxel models constructed from the same images in the prediction of trabecular bone Young’s modulus and yield strength. In addition, PR model nonlinear µFE analyses resulted in over 200-fold reduction in computation time compared with voxel model µFE analyses. In the effort of studying the heterogeneous bone mineralization in trabecular plates and rods, I developed an individual trabecula mineralization (ITM) analysis technique that allows quantification of the tissue mineral density of each individual trabecular plate and rod. By examining the variation of mineral density with trabecular types and orientations, it was found that trabecular plates were higher mineralized than trabecular rods. Furthermore, trabecular plate mineral density varied with trabecular orientation, increasing from the longitudinal direction to the transverse direction. ITM provided measurement of mineral density of each trabecular plate and rod, which was converted to trabecula-specific tissue modulus and used in the PR models to incorporate mineral heterogeneity in µFE simulations. Results suggested that heterogeneous PR models did not differ from the homogeneous PR models or specimen-specific PR models in their predictions of apparent Young’s modulus and yield strength of the human trabecular bone specimens from non-diseased donors. Based on the trabecular bone PR model, a whole bone PR model was developed for assessing whole bone mechanical strength at the distal radius and the distal tibia from high-resolution peripheral quantitative computed tomography (HR-pQCT). The accuracy of the whole bone PR model was evaluated on human cadaver radius and tibia specimens which were imaged using HR-pQCT and µCT, respectively, and tested to failure. The whole bone stiffness and yield load of the radius and tibia segments predicted by HR-pQCT PR models were strongly correlated with those predicted by corresponding HR-pQCT voxel models, µCT voxel models, and mechanical testing measurements. The PR models µFE results were indistinguishable from the voxel models constructed from the same HR-pQCT images. Moreover, the PR models significantly reduced the computational time for nonlinear µFE assessment of whole bone strength. After evaluating the accuracy and efficiency of the newly developed whole bone PR model, it was employed in a clinical study aimed at characterizing the abnormalities of trabecular plate and rod microstructure, cortical bone, and whole bone mechanical properties in postmenopausal women with vertebral fractures. Women with vertebral fractures had thinner cortical bone, and larger trabecular area compared to their non-fractured peers. ITS analyses suggested vertebral fracture subjects had deteriorated trabecular microstructure, evidenced by fewer trabecular plates, less axially aligned trabeculae and less trabecular connectivity at both radius and tibia. These microstructural deficits translated into reduced whole bone stiffness and yield load at radius and tibia as predicted by PR model nonlinear µFE simulation. More importantly, logistic regression indicated that whole bone yield load was effective in discriminating the vertebral fracture subjects from the non-fractured controls

Contributions of anisotropic and heterogeneous tissue modulus to apparent trabecular bone mechanical properties

The highly optimized hierarchical structure of trabecular bone is a major contributor to its remarkable mechanical properties. At the micro-scale level, individual plate-like and rod-like trabeculae are interconnected, forming a complex trabecular architecture. It is widely believed that bone strength, an important mechanical characteristic that describes the capability of bone to resist fracture, is largely determined by the tissue-level material properties of these microscopic trabecular elements. However, due to the complicated microstructure and irregular morphology of trabecular bone, a link between the tissue-level and the apparent level mechanics in trabecular bone has never been established. Thus, the goal of this thesis is to examine the tissue-level material properties of trabecular bone and their contribution to apparent-level bone mechanics, and ultimately to improve our fundamental understanding and assessment of bone strength in diseased and healthy patients. At the micro-scale level, plate-like and rod-like trabeculae are distinctly aligned along different orientations on the anatomical axis of the skeleton. Also, the highly organized underlying ultrastructure of bone tissue suggests trabecular bone might possess an anisotropic tissue modulus, i.e. different modulus in the axial and lateral cross-section of a trabecula. In this thesis, we studied this tissue-level anisotropy by examining mechanical properties of individual trabecular plates and rods aligned longitudinally, obliquely, and transversely on the anatomical axis using micro-indentation. We discovered that, despite the different orientations of trabeculae, tissue moduli are higher in the axial direction than in the lateral direction for both plates and rods. We also discovered that plates have a higher tissue modulus than rods, suggesting different degrees of mineralization. Furthermore, the tissue mineral density correlated strongly but distinctly with tissue modulus in the axial and lateral directions, providing descriptions on how spatially heterogeneous mineralization at the tissue level affects the tissue modulus. After characterization of the anisotropic and heterogeneous modulus of trabecular bone at the tissue level, we then sought to investigate its contribution to apparent-level mechanical properties, including apparent Young’s modulus and yield strength. Non-linear FE voxel models incorporating experimentally determined anisotropy and heterogeneity were created from micro-computed tomography (µCT) images of healthy trabecular bone samples. Apparent Young's modulus and yield strength predicted by the models were compared to and correlated with gold standard mechanical testing measurements, as well as to the same FE models without incorporation of anisotropy and/or heterogeneity. We discovered that the anisotropic model prediction was highly correlated and indistinguishable from mechanical testing measurements. However, the prediction power of the model was not enhanced by incorporating anisotropy and heterogeneity (compared to a homogeneous and isotropic model), suggesting that variances in tissue-level material properties contribute minimally to the apparent level bone behaviors in healthy bone. However, the possibility remained that a more substantial contribution could arise in diseased bone, particularly diseases in which tissue-level properties are compromised. Therefore, we studied trabecular bone in two diseased conditions – subchondral bone in human knees affected by osteoarthritis and pelvic bone affected by adolescent idiopathic sclerosis – to see how disease can alter the tissue-level and, consequently, apparent-level bone mechanics. In OA bone, we found a significant decrease in tissue modulus in the subchondral bone under severely damaged cartilage compared to control, which provides an explanation for a minimal increase in apparent stiffness with an almost doubled bone volume fraction. In AIS bone, no differences were found in tissue-level or apparent level Young’s modulus compared to control. However, the mineral density was found to play a distinct role in the modulus of growing bone tissue compared to mature bone