Formulation of a mathematical model of bone remodeling taking accont of bone resorption by overload and its application to clinical problems

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The phenomenon where bone changes its structure and mechanical property to adapt to mechanical circumstances is called mechanical bone remodeling. In the present study, we formulate a mathematical model of mechanical bone remodeling to describe phenomenological process of bone remodeling with time, and the validity and the accuracy of the proposed model are examined. The incorporation of the model into the finite element code ABAQUS is also discussed. The results obtained from the present study are summarized in the following :1. A mathematical model for uniaxial loading is formulated by representing physiological signal transmission processes of remodeling from the mechanical stimulus to change of bone density by n+1 sequential evolution equations with n+1 macroscopic internal state variables.2. This model can quantitatively describe a time dependent process of bone remodeling. The model also shows the independence of loading histories.3. The model was extended to the multiaxial loading case, and is improved to take into account bone resorption by overload.4. The proposed model showed clinically adequate history dependence of bone remodeling : the model may be applicable to problems of rehabilitation and training.5. The model was incorporated into the finite element code ABAQUS to examine the applicability of the model. A single element model is constructed, and the results are compared with the simulation results using only the model. The two results coincide with each other qualitatively.6. The model was also applied to a finite element model of femur. The results showed the optimum structural design of bone trabecula.