Modeling and simulation of trabecular pattern formation in a cancellous bone defect under mechanical forces.

Abstract

Understanding regeneration of the trabecular structure in cancellous bone defects is an important issue in bone tissue engineering and regenerative medicine. Biochemical and biomechanical viewpoints are indispensable for understanding the fundamental mechanism that underlies the regeneration of the trabecular structure. In vitro observations of the Turing pattern-like bone differentiation into osteoblasts from human mesenchymal stem cells suggest that mathematical modeling and simulation based on a reaction-diffusion system model would help us to understand the mechanism of trabecular pattern formation during cancellous bone regeneration. In this article, we propose a mathematical model of trabecular morphogenesis based on the reaction-diffusion system in 3D, which comprises activators and inhibitors of bone formation by combining with mechanical factors. Based on the proposed model, we conduct computational simulation of trabecular regeneration in a cancellous bone defect using a voxel-based finite element method for stress analysis and a finite difference method for reaction-diffusion analysis. The proposed model could express the regeneration of the three-dimensional trabecular structure with mechanically adapted functions as a load-bearing structure. Based on these results, the proposed model and simulation framework are expected to facilitate the analysis of regeneration of the cancellous bone;this will help us to examine bone regeneration that involve complex biological factors.