D. I. Wimpenny

Bone Turnover Cycle Model with a Torus-Like Steady State

A quantitative understanding of the bone remodeling process is of considerable biomedical and practical biotechnological interest to support the application of layer manufacturing techniques to produce scaffolds for surgical applications. Osteoclasts and osteoblasts play a principal role in different models of the bone multicellular unit operating in bone and display a rich spectrum of behaviour. The goal of this work is to show that it is possible to capture the cyclic dynamics of operating cells. The central idea of the mathematical model is that the regulatory nature of osteocytes is the basis of the cyclic-like behaviour associated with the system (remodeling process)as a whole. We developed this model taking due account of the apoptosis of osteocytes as a possible regulation loop in bone remodeling control. By applying the ordinary differential equations technique to the model, we show cyclic modes over a wide range of constants that have clear biological relevance. Simulations show that for a particular range of constants the model exhibits a torus-like quasi-steady state. Further investigation into these simulations indicates the existence of a surface in the osteoclasts-osteoblasts-osteocytes-bone space, that could be interpreted as a conservative value confirming the substrate-energy regenerative capability of the bone remodeling system. It is suggested that the nature of this recovering potential is directed against both mechanical and biochemical damage to the bone.