Mathematical modeling of growing biological tissues: from discrete to continual models

A brief review of mathematical models of growing biological materials is given. Surface and volumetric growth and remodeling at different external conditions are considered. The main experimental results on influence of expansion/compression load on the growing biological bodies are presented. The ‘from single-cell to tissues’ approach, discrete models and their finite element implementations are discussed. The model of the growing body as open thermodynamic system with distributed sources of mass and energy is presented. Applications to the tissue engineering problems at passive and active load conditions are discussed.