MATHEMATICAL APPROACHS TO BONE TISSUE MODELLING

Abstract

This paper is dedicated to an overview of the existing approaches and their assumptions in the mathematical modeling of bone tissue and will thus necessarily emphasize future paths of understanding and communicating in this field of science. The understanding of the bone tissue processes, and the possibility of their mathematical modeling is important for several different directions of practical demands, all encompassed in the development of medicine and technology. One aspect of bone tissue modeling is directed towards the bone medicine field that solves acute and chronic problems as computer-assisted orthopedic surgery which requires real-time simulation, disease treatment and improvement of the quality of life. The other aspect is directed towards material science and tissue engineering. On the one hand, we have mathematics and mechanics with their approximations and assumptions and, on the other, we have very complex practical requirements for real-time simulations and in-silico experiments. To meet these two complex fields with efficiency, it is necessary to further explore and better understand all the conditions that influence the feasibility and accuracy of the mathematical models for bone tissue. The first step in this enticing field is to make an overview by categorizing the models into distinct categories from the mathematical attitude to the practical demands. Different practical demands cause different mathematical approaches to modeling. This paper presents, as clearly as possible, the collection of models and approaches according to these practical requirements. Since mathematical methods have their own constraints, we first present the description of mathematical modeling and its challenges and obstacles in biology. As a practical example, the bone cell population model for mechanotransduction of external periodic signals is presented.