A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics
By Krishna C. Garikipati, E. Arruda, Karl Grosh, H. Narayanan, S. Calve. 2003
256 citations recorded by the source corpus.
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.
Subfields: Biomedical Engineering, Cell Biology, Fluid Flow and Transfer Processes
View Paper: https://www.semanticscholar.org/paper/4cfd7a8675feb9a836bcb41a9968689d9a25b09d
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In Biomedical Engineering
In Fluid Flow and Transfer Processes
Citations in the corpus
- Remodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network (2004, background): “due to a surrounding liquid solvent, and is thus of isotropic nature, see Garikipati et al. (2004). The second term CðI1; I4Þ reflects the effective assembly of the individual eight chain energies c.”
- Stress-Modulated Growth (2007, background): “For this reason, some authors state a continuum mechanics theory for soft tissues in the framework of mixture theory [10], [11], [13], [17].”