ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

size. The model is used for two dimensional wounds.
3. MATERIALS AND METHODS
In this work, we propose a continuous angiogenesis model that incorporates biological,
chemical and mechanical factors, consisting of a number of coupled reaction-diffusion
equations. The primary variables of the model are the concentrations of oxygen (u1),
macrophage-derived growth factors -such as VEGF (vascular endothelial growth factor)
or others, henceforth MDGF (u2), capillary density (u3) and fibroblasts (n). We have
modified the model proposed by Javierre et al. [6], based on the model of Maggelakis
[5], in order to introduce the effect of fibroblasts in the process.
The evolution of the biological and biochemical species stated above follows a
conservation law
where Q denotes the species (u1, u2, u3 or n), JQ its net flux (which takes into account
the dragging term due to ECM deformation) and fQ its net production [9].
We have also implemented the mechanical behaviour of the skin and cells. Fibroblasts
can exert traction forces due to their actomyosin mechanism [3]. The net stress of one
fibroblasts cell per unit of extra-cellular matrix is evaluated as
where pcell is a piecewise linear function depending on the tissue volumetric strain of the
tissue, ρecm is the density of the extra-cellular matrix and Rτ the traction inhibition
collagen density.
In this work we assume that skin behaves as a hyperelastic material, which is more
suitable [10, 11] than a viscoelastic approach, which has been usually used to model
skin in the wound healing process [7]. We assumed an Ogden energy function.
We have solved the resulting problem using a finite element analysis. It has been
implemented through an Abaqus user subroutine.
In this work two wounds with different geometries were studied. The first one is a
circular wound with a diameter of 2 cm and the second one is an elliptical wound with
the same area and with aspect ratio of 5. Both wounds are surrounded by a sufficiently
large circumference of undamaged skin to avoid boundary effects and are evaluated
during 30 days.
4. RESULTS
In first place we observe the evolution of the wound area during the studied time. The
contraction in both wounds is similar, the circular wound contracts by around 27% of its
original size and the elliptical wound around 24% of its original size. We show the
initial and the final geometry of both wounds after 30 days in Figure 1. The contraction