A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics |
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Authors: | K Garikipati EM Arruda H Narayanan |
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Institution: | a Department of Mechanical Engineering, University of Michigan, 2278 Brown Building, Ann Arbor, MI 48109, USA b Department of Mechanical Engineering, and Program in Macromolecular Science and Engineering, University of Michigan, Ann Arbor, MI 48109, USA c Departments of Mechanical Engineering, and Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA d Program in Macromolecular Science and Engineering, University of Michigan, Ann Arbor, MI 48109, USA |
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Abstract: | Growth (and resorption) of biological tissue is formulated in the continuum setting. The treatment is macroscopic, rather than cellular or sub-cellular. Certain assumptions that are central to classical continuum mechanics are revisited, the theory is reformulated, and consequences for balance laws and constitutive relations are deduced. The treatment incorporates multiple species. Sources and fluxes of mass, and terms for momentum and energy transfer between species are introduced to enhance the classical balance laws. The transported species include: (i) a fluid phase, and (ii) the precursors and byproducts of the reactions that create and break down tissue. A notable feature is that the full extent of coupling between mass transport and mechanics emerges from the thermodynamics. Contributions to fluxes from the concentration gradient, chemical potential gradient, stress gradient, body force and inertia have not emerged in a unified fashion from previous formulations of the problem. The present work demonstrates these effects via a physically consistent treatment. The presence of multiple, interacting species requires that the formulation be consistent with mixture theory. This requirement has far-reaching consequences. A preliminary numerical example is included to demonstrate some aspects of the coupled formulation. |
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Keywords: | Chemo-mechanical processes Mass transport Stress-enhanced diffusion Tendon and muscle mechanics Tumor growth |
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