Date: Apr. 22, 2018
In modern biology, epithelial spreading is considered to be the leading biological mechanism during wound healing and embryonic development. The dynamics of epithelial spreading is dominated by collective cell migrations, which, in the case of wound healing, is a result of chemo-mechanical interactions between cell deformation and intracellular signaling. The deformation of the tissue layer triggers the emission of a diffusing active chemical species which generates an active force (Kopf and Pismen, 2013).
The goal of this study is to construct a mathematical model for epithelial spreading that allows us to predict the deformation of epithelial tissues, the concentration of active chemical species, and how they interact with other. We proposed a two dimensional linear model by describing the epithelial tissue as a thin layer and modeling the planar deformation using Hookean elasticity. We also employed reaction-diffusion equations to model the concentration of the active chemical species. Furthermore, we constructed a nonlinear model to predict the dynamic spreading of an epithelial tissue on a 1D substrate. We introduced feedback loops between tissue deformation and chemical concentration, which represents the chemo-mechanical interaction that prompts the collective migration of epithelial cells (Kopf and Pismen, 2013).
Tissue deformation and concentration of active chemical species predicted by the 2D linear model:
Reference
Köpf, Michael H., and Len M. Pismen. “A Continuum Model of Epithelial Spreading.” Soft matter 9.14 (2013): 3727–3734. Web.
Carrier, Patrick et al. “Characterization of Wound Reepithelialization Using a New Human Tissue-Engineered Corneal Wound Healing Model.” Investigative ophthalmology & visual science 49.4 (2008): 1376–1385. Web.