Macroscale Bone Remodeling using Topology Optimization with Stress and Mass Constraints and Verification of the Model

Abstract

Bone remodeling using topology optimization has been proven to be a powerful tool in predicting the structural adaptation of bone and providing insights into the formation of trabecular architecture under physiological constraints. Recent studies have focused on microscale predictions of trabecular bone using constraints that are not akin to previous theories of bone remodeling when considering only mechanical stimuli. The primary objective of this research was to create a macroscale method of predicting cortical and trabecular bone in the human femur simultaneously using constraints based on well established mechanisms of bone remodeling, analyze the results against an improved verification model, and verify the bone remodeling theories proposed by authors like Wolff and Frost. The simulation used a voxel mesh with a resolution of 0.6mm, isotropic material properties, and incorporated two common loading scenarios: walking and stair climbing. The resulting simulated femur structure was almost equivalent to the verification model, having a comparable distribution of elemental densities, bone volume in key regions of interest, and magnitudes of stress and strain. The qualitative analysis revealed the predicted cortical and trabecular structure closely mirrored Wolff’s trajectory theory, with stress vectors aligning with the major trabecular loading groups. Quantitatively, the bone volume fractions in the simulated model were akin to earlier computed tomography (CT) analyses of the human femur. The correlation of the simulated model to the verification and literature models demonstrates the potential of the proposed method to accurately predict bone adaptation in cortical and trabecular bone considering only biomechanical stimuli.