THE COUPLING OF DIFFUSION, REACTION AND MECHANICS IN BIOLOGICAL GROWTH: THEORY AND NUMERICAL MODELS

Growth in biological tissue depends upon cascades of complex biochemical reactions in-volving several species, as well as their transport through the extra cellular matrix and diusion across cell membranes. In this work, a theoretical and numerical framework for the macroscopic treatment of growth is formulated within the context of open system continuum thermodynamics. Assumptions central to classical mechanics being too restrictive to cap-ture such detail, this treatment involves the introduction of additional quantities (including mass sources/sinks, mass uxes, terms for energy and momentum transfer between species) and deduces implications for balance laws. The framework, consistent with classical mixture theory, accounts for the multiple inter-converting and interacting species present in the tis-sue. Systematic adherence to fundamental physical principles, such as frame indierence of the response in the reference conguration and non-violation of the dissipation inequality, result in constitutive laws whose forms are clearly motivated and arise naturally from the treatment. Notably, the transport of the extra cellular uid relative to the matrix is shown to be driven by the gradients of stress, concentration and chemical potential|a coupling o