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Modelling and remodelling of biological tissue in the framework of continuum biomechanics
Author(s) -
Ehlers Wolfgang,
Krause Robert,
Markert Bernd
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110010
Subject(s) - extracellular matrix , context (archaeology) , interstitial fluid , finite element method , mixture theory , porous medium , chemistry , mechanics , biophysics , biological system , materials science , porosity , thermodynamics , physics , computer science , biology , composite material , biochemistry , paleontology , mixture model , artificial intelligence , endocrinology
A biological tissue in general is formed by cells, extracellular matrix (ECM) and fluids. Consequently, its overall material behaviour results from its components and their interaction among each other. Furthermore, in case of living tissues, the material properties do not remain constant but naturally change due to adaptation processes or diseases. In the context of the Theory of Porous Media (TPM), a continuum‐mechanical model is introduced to describe the complex fluid‐structure interaction in biological tissue on a macroscopic scale. The tissue is treated as an aggregate of two immiscible constituents, where the cells and the ECM are summarised to a solid phase, whereas the fluid phase represents the extracellular and interstitial liquids as well as necrotic debris and cell or matrix precursors in solution. The growth and remodelling processes are described by a distinct mass exchange between the fluid and solid phase, which also results in a change of the constituent material behaviour. To furthermore guarantee the compliance with the entropy principle, the growth energy is introduced as an additional quantity. It measures the average of chemical energy available for cell metabolism, and thus, controls the growth and remodelling processes. To set an example, the presented model is applied for the simulation of the early stages of avascular tumour growth in the framework of the finite element method (FEM). (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)