Abstract
We present a generic model to investigate alignment due to cell movement with spefic application to collagen fibre alignment in wound healing. In particular, alignment in two orthogonal directions is considered. Numerical simulation are presented to show how alignment is affected by key parameter min the model. from a travelling wave analysis of a simplified one‐dimensional version of the model we derive a first order ordinary differential equation to describe the time evolution of aligment. We conclude that in the wound healing context,faster healing wounds result in more aligment and hence more serve scarring. It is shown how the model can be extended to included orientation dependent Kinetics,multipkle cell types and several extracellular matrix materials.
Highlights
AND BIOLOGICAL BACKGROUNDDermal wound healing is an extremely complex process
Dermal fibroblasts invade the wound space, synthesizing structural proteins including collagen, at the same time as reorganising the existing extracellular matrix (ECM). These fibroblasts convert reversibly into a contractile phenotype known as myofibroblasts, which are responsible for the process of active 'wound contraction'
We begin by introducing a simple, highly generic mathematical model which represents the basic process of cells moving through extracellular matrix. We extend this isotropic model to account for ECM fibre orientation, and numerical simulations are presented in two space dimensions
Summary
Dermal wound healing is an extremely complex process. The initial response to a full thickness skin injury is bleeding and the formation of a blood clot, and the progression from this into a contracted scar involves a series of interacting and only partially understood biological processes. An important prototype biological system is colonies of fibroblasts in vitro, in which cellular orientation is mediated by direct cellcell contacts, giving rise to orientation patterns This was first modelled by (Edelstein-Keshet and Ermentrout, 1990) and a number of subsequent models have been proposed, typically formulated as integrodifferential equations for the density of cells oriented at a particular angle as a function of space and time (Mogilner and Edelstein-Keshet, 1996). Another biological alignment system that has been extensively modelled is the intracellular actin filament network, which shows pronounced alignment patterns in response to the local stress field; stress can be either self-generated or externally applied.
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