dorsal/arxiv
View SchemaThe micromechanics of fluid-solid interactions during growth in porous soft biological tissue
| Authors | H. Narayanan, E. M. Arruda, K. Grosh, K. Garikipati |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0701003 |
| URL | https://arxiv.org/abs/q-bio/0701003 |
Abstract
In this paper we address some modelling issues related to biological growth. Our treatment is based on a recently-proposed, general formulation for growth within the context of Mixture Theory (Journal of the Mechanics and Physics of Solids, 52, 2004, 1595--1625). We aim to enhance this treatment by making it more appropriate for the biophysics of growth in porous soft tissue, specifically tendon. This involves several modifications to the mathematical formulation to represent the reactions, transport and mechanics, and their interactions. We also reformulate the governing differential equations for reaction-transport to represent the incompressibility constraint on the fluid phase of the tissue. This revision enables a straightforward implementation of numerical stabilisation for the hyperbolic, or advection-dominated, limit. A finite element implementation employing an operator splitting scheme is used to solve the coupled, non-linear partial differential equations that arise from the theory. Motivated by our experimental model, an in vitro scaffold-free engineered tendon formed by self-assembly of tendon fibroblasts (Tissue Engineering, 10, 2004, 755--761), we solve several numerical examples demonstrating biophysical aspects of tissue growth, and the improved numerical performance of the models.
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"abstract": "In this paper we address some modelling issues related to biological growth.\nOur treatment is based on a recently-proposed, general formulation for growth\nwithin the context of Mixture Theory (Journal of the Mechanics and Physics of\nSolids, 52, 2004, 1595--1625). We aim to enhance this treatment by making it\nmore appropriate for the biophysics of growth in porous soft tissue,\nspecifically tendon. This involves several modifications to the mathematical\nformulation to represent the reactions, transport and mechanics, and their\ninteractions. We also reformulate the governing differential equations for\nreaction-transport to represent the incompressibility constraint on the fluid\nphase of the tissue. This revision enables a straightforward implementation of\nnumerical stabilisation for the hyperbolic, or advection-dominated, limit. A\nfinite element implementation employing an operator splitting scheme is used to\nsolve the coupled, non-linear partial differential equations that arise from\nthe theory. Motivated by our experimental model, an in vitro scaffold-free\nengineered tendon formed by self-assembly of tendon fibroblasts (Tissue\nEngineering, 10, 2004, 755--761), we solve several numerical examples\ndemonstrating biophysical aspects of tissue growth, and the improved numerical\nperformance of the models.",
"arxiv_id": "q-bio/0701003",
"authors": [
"H. Narayanan",
"E. M. Arruda",
"K. Grosh",
"K. Garikipati"
],
"categories": [
"q-bio.TO"
],
"title": "The micromechanics of fluid-solid interactions during growth in porous soft biological tissue",
"url": "https://arxiv.org/abs/q-bio/0701003"
},
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