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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.

It is well known that bone tissue can change its outer shape and internal structure by remodeling according to a changing mechanical environment. However, the mechanism of bone functional adaptation induced by the collaborative metabolic activities of bone cells in response to mechanical stimuli remains elusive. In this article, we focus on the hierarchy of bone structure and function from the microscopic cellular level to the macroscopic tissue level. We provide an overview of a mathematical approach to understand the adaptive changes in trabecular morphology under the application of mechanical stress.

Osteocytes embedded in bone matrix, making a three-dimensional network system connected each other via cell processes, are considered as the mechanosensor cells that play important roles in the regulatory mechanism of adaptive bone remodeling. Three-dimensional network structure of the lacuna-canalicular system in a trabecula was fluorescently visualized by confocal laser-scanning microscopy, and the morphological characteristics of the network were quantitatively evaluated. The canalicular network orientation was determined by fitting the fabric ellipse, and the normal vector field was derived from the gradient of a distance function from trabecular surface. As a result, the network orientation was found to approximately coincide with the normal direction to the trabecular surface.

In cancellous bone mechanics, it is important to consider that the macroscopic mechanical properties depend on microscopic trabecular structure as well as density. By using image data obtained by X-ray micro CT, three-dimensional digital model of trabecular structure with complicated architecture can be constructed and its macroscopic mechanical properties can be analyzed using a voxel finite element method.