A mathematical model of bone remodelling under overload and its application to evaluation of bone resorption around dental implants

This paper deals with the formulation of a mathematical mosel allowing us to describe mechanical bone remodelling process and rapid bone resorption under overload. For this purpose, physiological signal transmission processes of remodelling from mechanical stimuli to the change of bone density are described by n +1 sequential evolution equations with n+1 macroscopic internal state variables. In the normal physiological situation, the value of internal variable K-th step approaches the value of the variable in the (k-1)-th step, but under overload conditions the target value in the k-th step reduces to a value much smaller that in the normal situation, which represents the loss of physiological balance. The value of the internal variable in the last step specifies the balance level of bone density. The simulation results showed that this model could describe a timedependent process of bone remodelling inclusing bone resorption. Finally, the proposed model was applied to problems of bone resorption around artificial implants. The simulation results predicted the bone resorption qualitatively.