A mathematical model for the growth of elongated bones

Abstract

A mathematical model to describe the process of formation of bone tissue by replacement of cartilage tissue is presented and discussed. This model is based on an absorption-diffusion system which describes the interaction of two key signalling molecules. These molecules characterize the dynamics of the transition zone between the cartilage and the bone tissue. Some experimental data are needed to estimate some model parameters. We discuss how our results are essentially unaffected by small variations, and in a particular case, not necessarily small variations in the experimental values.