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Updated: Aug 5, 2026

Electric Cell-substrate Impedance Sensing for the Quantification of Endothelial Proliferation, Barrier Function, and Motility
Published on: March 28, 2014
Abstract:
A continuum model of diffusion-coupled cells that more accurately reflects the presence of low-permeability gap junctions between cells is analyzed. It is shown by a multi-scale analysis that to lowest order the slow evolution of the mean concentration is described by the usual ordinary differential equations for a discrete model. Furthermore, stable non-uniform steady solutions are shown to exist in the continuum model of a one component system, whereas this is impossible for the standard reaction-diffusion model of this system. It is also shown how to average the equations in this continuum model to obtain a system of reaction-diffusion equations with constant coefficients.
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