The speed of corneal epithelial wound healing

We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically the role of epidermal growth factor. We determine an analytic approximation for the speed of travelling wave solutions of the model and verify the result numerically. The predicted speed compares very well with experimentally measured healing rates

Analysis of travelling waves associated with the modelling of aerosolised skin grafts

A previous model developed by the authors investigates the growth patterns of keratinocyte cell colonies after they have been applied to a burn site using a spray technique. In this paper, we investigate a simplified one-dimensional version of the model. This model yields travelling wave solutions and we analyse the behaviour of the travelling waves. Approximations for the rate of healing and maximum values for both the active healing and the healed cell densities are obtained

Effect of initial conditions on the speed of reaction-diffusion fronts

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

Mathematical models of wound healing

Available from British Library Document Supply Centre- DSC:D95157 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

Lipoprotein oxidation and its significance for atherosclerosis: a mathematical approach

Atherosclerosis is a chronic disease which involves the build up of cholesterol and fatty deposits within the arterial wall. This results in the narrowing of the vessel lumen, which eventually restricts blood flow to vital organs such as the heart and lungs. These events may culminate in a heart attack or stroke, the commonest causes of death in the U.K. population. In this paper we study the early stages of atherosclerosis which include the build up of cholesterol within subendothelial cells to form what is known as a fatty streak, the earliest identifiable evidence of atherosclerosis. The deposition of cholesterol is believed to be a consequence of oxidation of circulating cholesterol-rich lipoproteins, in particular low density lipoproteins (LDLs). Via a mathematical model we investigate this process of oxidation within the context of an in vitro framework. We first recreate existing experimental results and then extend the model to investigate phenomenon not studied by current experimental protocols. We find that the model displays hysteresis which reveals some interesting insights into possible in vivo events. Mathematical analysis of this behaviour predicts that vitamin E supplementation is not as beneficial as high density lipoproteins (HDLs) and vitamin C. Furthermore, the scavenging of oxidants by HDL can provide an important first line of defence against LDL oxidation

A Mechanochemical Model for Adult Dermal Wound Contraction and the Permanence of the Contracted Tissue Displacement Profile

this paper is on investigating the model to acquire a greater understanding of the contracted wound state. A subsequent report will address pathological transitions of fibrocontractive disease states as predicted by the model discussed below (L. Olsen et al., submitted