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| Biomechanical Simulation of Regeneration and Remodeling of Bones and its Application to Medical Engineering |
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It is known that during the processes of generation, development, reconstruction, and regeneration, bones adaptively alter their conformation and properties under the influence of the surrounding mechanical environment. For example, as illustrated by Wolff's hypothesis, it is known that the trabecular structure of cancellous bones exhibits a conformation that is adapted to the surrounding mechanical environment.
In order to design implants with a view to the adaptive alteration of bones, or to design a scaffold for the regeneration of bone that consists of bioabsorbable materials, it is essential to employ the modeling of bone and biomechanical simulations that consider bone’s complex conformational structure. |
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| Fig. 1: Cross section of newly formed bone in the rat cancellous bone defect model |
Fig. 2: Trabecular pattern formation using a reaction-diffusion system model |
In this study, several investigations regarding the mathematical modeling of the regeneration and remodeling of bones and their biomechanical simulation were conducted.
Firstly, we conducted an experimental investigation of the trabecular patterns during the process of cancellous bone regeneration in a rat model in which the cancellous bones had an artificial defect (Fig. 1). The bone structure that was newly formed in the defect region was observed by X-ray micro-computed tomography (CT) and the relationship between the mechanical properties of the formed bone and the CT values was quantitatively evaluated. Next, by taking the activation effect of bone formation caused by mechanical factors into account on the reaction-diffusion system model, which is used as a pattern formation model for a living organism, a trabecular pattern formation model for cancellous bone was proposed and its mechanism was investigated by computational mechanical simulation from the viewpoint of mechanics (Fig. 2). |
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| Fig. 3: Bone regeneration simulation using a porous scaffold |
Fig. 4: Optimum shape of cantilever determined by a traction method using voxel FEM |
Furthermore, a 3D bone regeneration model that represents the bone regeneration process was constructed using a porous scaffold, and the alteration of the mechanical properties of bone-scaffold system on the process of bone regeneration was evaluated (Fig. 3). Based on this model, a framework for an optimum scaffold structure design method was newly proposed. Furthermore, the establishment of a practical method for conformational determination that integrates the modeling of the material’s conformation, its mechanical analysis, and the conformational correction based on the results was targeted; a novel method of conformational optimization was accordingly proposed (Fig. 4). |
In this manner, the adaptation phenomena inherent in the regeneration or the remodeling of bones are significantly influenced by mechanical factors. Therefore, when designing implants that are to be used inside the living body, it is crucial that the mechanical interactions between the living body and artificial materials are taken into consideration.
Additionally, for the modeling and simulation of biological tissues that exhibit complex conformations and hierarchical structures, the modeling technology based on the digital images used in this study and its application to the voxel FEM was demonstrated to be an effective method. Furthermore, if the objective is to apply these methods to medical engineering, the integration of the living body and artificial materials in the computer as digital information, and the simulation of biological phenomena through mechanical analysis, is considered to be a potentially important technique for the acquisition of further valuable information and guidelines. |
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