A constitutive model for tissue adaptation: Necrosis and stress driven growth

Abstract

This paper presents a general constitutive model for tissue stress driven growth and necrotic remodeling. The general theoretical framework is given by a kinematics formulation in large strain. The model allows the analysis of tissue behaviour considering the coupling of biological and mechanical fields, through the implementation of an internal variable that represents the bioavailability, together with the growth induced by mechanical stimuli. To take into account the tissue necrosis phenomenon a reinterpretation of the classical theory of mixtures is proposed. The proposed formulation is based on the consideration of two components, normal tissue and necrotic tissue, each one with its own volumetric participation, which is treated in an evolutive way, allowing simulating the phenomena of ischemia. This article also presents a brief description of the numerical implementation of the model as well as the obtained results, which shows the process of necrosis of part of the tissue, its influence on the surrounding healthy tissue, and the interaction between the nutrients availability and the stress driven growth and necrotic remodeling process.

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