Computer-simulated bone architecture in a simple bone-remodeling model based on a reaction-diffusion system

Abstract

Bone is a complex system with functions including those of adaptation and repair. To understand how bone cells can create a structure adapted to the mechanical environment, we propose a simple bone remodeling model based on a reaction-diffusion system influenced by mechanical stress. Two-dimensional bone models were created and subjected to mechanical loads. The conventional finite element method (FEM) was used to calculate stress distribution. A stress-reactive reaction-diffusion model was constructed and used to simulate bone remodeling under mechanical loads. When an external mechanical stress was applied, stimulated bone formation and subsequent activation of bone resorption produced an efficient adaptation of the internal shape of the model bone to a given stress, and demonstrated major structures of trabecular bone seen in the human femoral neck. The degree of adaptation could be controlled by modulating the diffusion constants of hypothetical local factors. We also tried to demonstrate the deformation of bone structure during osteoporosis by the modulation of a parameter affecting the balance between formation and resorption. This simple model gives us an insight into how bone cells can create an architecture adapted to environmental stress, and will serve as a useful tool to understand both physiological and pathological states of bone based on structural information.