Force-induced bone growth and adaptation: A system theoretical approach to understanding bone mechanotransduction

Abstract

The modeling, analysis, and design of treatment therapies for bone disorders based on the paradigm of force-induced bone growth and adaptation is a challenging task. Mathematical models provide, in comparison to clinical, medical and biological approaches an structured alternative framework to understand the concurrent effects of the multiple factors involved in bone remodeling. By now, there are few mathematical models describing the appearing complex interactions. However, the resulting models are complex and difficult to analyze, due to the strong nonlinearities appearing in the equations, the wide range of variability of the states, and the uncertainties in parameters. In this work, we focus on analyzing the effects of changes in model structure and parameters/inputs variations on the overall steady state behavior using systems theoretical methods. Based on an briefly reviewed existing model that describes force-induced bone adaptation, the main objective of this work is to analyze the stationary behavior and to identify plausible treatment targets for remodeling related bone disorders. Identifying plausible targets can help in the development of optimal treatments combining both physical activity and drug-medication. Such treatments help to improve/maintain/restore bone strength, which deteriorates under bone disorder conditions, such as estrogen deficiency.