One dimensional elastic continuum model of epidermal wound healing

Qi Mi
University of Pittsburgh

Diseases of necrotizing enterocolitis(NEC) results after an injury to
the mucosal lining of the intestine,leading to translocation of
bacteria and endotoxin.Intestinal mucosal defects are repaired by the
process of intestinal restitution, during which enterocytes migrate
from healthy areas to sites of injury.

In this paper,we developed a mathematical model for the migration and
proliferation of enterocytes occuring in the necrotizing enterocolitis
disease. The model is based on a novel assumption of elastic
deformation of the cell layer and incorporates the following three
components (i) motility promoting force due to lamellipod formation,
(ii) motility impeding friction due to the adhesion to the cell matrix
and (iii) enterocyte proliferation. Our model successfully reproduces
the behavior observed for enterocyte migration on glass coverslips,
namely the dependence of migration speed on the distance from the
wound edge and the finite propagation distance in the absence of
proliferation which results in an occasional failure to close the
wound.

The model can be used to describe the dynamics of closure of a wound
with a linear edge and can be used to predict the effect of chemical
agents on the three main individual components of wound healing:
mobility (force applied by lamellipods), friction (strength of
adhesion to the cell matrix), and proliferation.