Mathematical models of growth deformation

Abstract


Currently biology and medicine become one of the most attractive areas of applied mathematics. To fix certain pathologies of children, growth modelling for living tissue and growth management are the issues of major importance. In the process of growth a growing body itself experiences deformation that proves a fundamental difference of mechanics of growing bodies from the classical mechanics of bodies of constant composition. This paper presents an analysis of publications related to various models of the mechanism of living tissues growth and a brief analysis of biological growth concept. The authors considered basic principles of growth modelling and specified major areas for developing certain models of body-growing tissue. The following classification of growth models for living tissue has been given: models based on the hypothesis about the influence of intracellular pressure on tissue growth as a stimulating factor; models of multiphase media, the so-called “mixture theory”; model based on the hypothesis about the influence of residual stresses on tissue growth as a stimulating factor; models connecting the rate of growth from the deformations known from observations and experiments. The analysis resulted in specifying factors influencing the growth of living tissue. These are the chemical composition, concentration, transport and stresses in the material body. Stress is a significant factor affecting growth. The practical importance of growth model for mechanical deformation is based on its wide application for describing normal and pathological growth of hard tissues in the human body. In this case, from mechanical point of view, it becomes possible to model and control growth.

About the authors

O Y Dolganova

Perm National Research Polytechnic University, Perm, Russian Federation

Email: aoy85@yandex.ru
29, Komsomolsky av., 614990, Perm, Russian Federation Doctoral Student of Department of Theoretical Mechanics, Perm National Research Polytechnic University

V A Lokhov

Perm National Research Polytechnic University, Perm, Russian Federation

Email: valeriy.lokhov@yandex.ru
29, Komsomolsky av., 614990, Perm, Russian Federation Ph.D. in Physics and Mathematics Sciences, Department of Theoretical Mechanics, Perm National Research Polytechnic University

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