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A mathematical model for cell-induced gel compaction in vitro

journal contribution
posted on 2023-05-18, 15:44 authored by Green, JEF, Andrew BassomAndrew Bassom, Friedman, A
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.

History

Publication title

Mathematical Models and Methods in Applied Sciences

Volume

23

Pagination

127-163

ISSN

0218-2025

Department/School

School of Natural Sciences

Publisher

World Scientific Publ Co Pte Ltd

Place of publication

Journal Dept Po Box 128 Farrer Road, Singapore, Singapore, 912805

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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