Mathematical modeling of wound healing and subsequent scarring
Wietse Boon

Supervisor: D.C. (Daniel) Koppenol, F.J. (Fred) Vermolen

Site of the project: TU Delft

start of the project: May 2013

In November 2013 the Interim Thesis and a presentation has been given.

The Master project has been finished in June 2014 by the completion of the Masters Thesis and a final presentation has been given.

For working address etc. we refer to our alumnipage.

Summary of the master project:
One of the clinical problems regarding severe burns is the development of hypertrophic scars, which impair the natural topography of the effected skin region. The burns are classified on a scale of severeness that was developed by Guillaume Dupuytren (see image 1 and image 2) into first, second and third degree burns. The problem of a disturbed topography plays an important role in second and third degree burns (see image 3). During the healing of a burn, many complicated biological processes occur, and one of them is that fibroblasts (see picture 4) from the surrounding skin regions or from the fat region migrate into the damaged region, where they partly differentiate into myo-fibroblasts, and regenerate the extra cellular matrix which supports the skin tissue. Besides the regeneration of extra cellular matrix, the (myo-)fibroblasts contract, by which they induce an adjusted strain-pattern in the damaged region and its surroundings.

The extra cellular matrix, roughly consisting of fibres, in undamaged skin regions is ordered in a random way with very large orientational fluctuations over small distances. In the post-damaged region, however, the randomness of the arrangement of the fibres after repair of the damage, is much smaller and thereby this arrangement is very non-isotropic.

This project deals with the mathematical modeling of the development of the orientation of the fibres in relation to the present fibroblasts. Migration of fibroblasts is simulated on a cell-level where the migration of each individual fibroblast is modeled autonomously. In the migration of the cells, mechanical and chemical stimuli are incorporated, as well as a stochastic term to mimic local (unknown) fluctuations. The stochastic term is incorporated via a Wiener process. Further, chemical and mechanical signals are dealt with by solving reaction-transport partial differential equations, for which finite-element techniques are used to have as much as geometrical freedom as possible. We aim at a quantitative investigation of the biological and physiological factors that control the isotropy and randomness of the orientation of the fibroblast-formed post-damage extra cellular matrix. We will also scrutinize the interaction between the post-damage fibre orientation and the amount of contraction, where the latter may lead to an impaired skin surface topography.

Figuur 1: Guillaume Dupuytren

Figuur 2: Classification of the degree of a burn

Figuur 3: Third degree burn

Figuur 4: Fibroblasts

Contact information: Kees Vuik

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