Simulation on bone remodeling with stochastic nature of adult and elderly using topology optimization algorithm

Reliable and accurate predictions of bone remodeling provide essential assistance for personalized implant design and orthopedic diagnosis. However, the bone remodeling simulations fail to accurately mimic the sophisticated architecture of trabecular bone so far, due to the neglection of the stochastic behaviors of bone remodeling. In this study, we coupled the Physiological Stochasticity in Bone Remodeling into the conventional Topology Optimization algorithm (named PSBR-TO method) to predict the cancellous structure of human femur. The sensitivity function of topology optimization was amended according to the bone remodeling rules from in vivo study (Razi et al., 2015) to reflect the stochastic process of bone remodeling in various physiological conditions. To demonstrate the algorithm, the bone structures of adults and the elderly were simulated by adopting the corresponding remodeling rules. The results showed that PSBR-TO gives rise to highly similar morphological features with the natural femur bone, in terms of the trabecular orientations and bone content distribution. The predicted femurs for adults and the elderly showed that the region-dependent variations in trabecular structural parameters during aging, including BV/TV, Tb.Th, and Tb.Sp, were consistent with the natural bone. Additionally, a loading collection of thirteen activities was employed in the algorithm and succeeded in driving the femur model to reproduce cancellous structure without extra constraint of structure perimeter or local density. By means of PSBR-TO, the trabecular structure in diverse physiological conditions can be accurately predicted, showing the valuable contribution on the clinical diagnosis and patient-specific design of bone implants.