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A mathematical model for cell-induced gel compaction in vitro


Green, JEF and Bassom, AP and Friedman, A, A mathematical model for cell-induced gel compaction in vitro, Mathematical Models and Methods in Applied Sciences, 23, (1) pp. 127-163. ISSN 0218-2025 (2013) [Refereed Article]

DOI: doi:10.1142/S0218202512500479


We present a mathematical model for cell-induced gel contraction in vitro. The core of the model consists of conservation equations for the mass of the gel and the number of cells, coupled to a force balance on the gel. On the basis of previously reported experimental findings for collagen gels, which are frequently used experimentally, the gel is treated as a compressible viscous fluid while inertial effects are neglected. The flow is assumed to be isothermal, and a linear pressure–density relation is adopted. The force exerted on the gel by cells is assumed to depend upon the local environment surrounding the cell: influences can include the cell and extracellular matrix density, and the concentration of a diffusible chemical produced by the cells. We consider the simple, but experimentally relevant, case of spherically symmetric gels. For cell-free gels, we show how simple experiments might be used to determine the parameters in the model. When the cell-derived forces are given by a prescribed function of position, we are able to obtain the early time and steady-state behavior of the solution analytically. We perform numerical simulations which generate predictions of how the gel density evolves during compaction under differing assumptions concerning the factors influencing the force exerted by the cells. These results are compared with some previous observations reported in the literature.

Item Details

Item Type:Refereed Article
Keywords:compressible fluid, extracellular matrix, non-local
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:105694
Year Published:2013
Web of Science® Times Cited:3
Deposited By:Mathematics and Physics
Deposited On:2016-01-13
Last Modified:2017-11-01

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