Biomedical Engineering Reference
In-Depth Information
Fig. 3 Evolution of the oxygen density (top left), MDGF density (top right), capillary density
(bottom left) and fibroblasts density (bottom right) in the centre of the wound
The computational domain consists of two different parts: the undamaged tissue
and the wound. The initial concentration of every species in the wound site is null.
The undamaged tissue is full of all the species except MDGF, which is not present.
We have solved the resulting problem using a finite element analysis. The
primary unknowns are interpolated from nodal values through shape functions and
the times derivatives are approximated with a trapezoidal method. The resulting
nonlinear system of equations is solved using a standard explicit method. This
numerical method is analogue to the one used in Javierre et al. [ 62 ] for wound
contraction alone. The interested reader is referred to [ 62 ] to find the details of the
implementation.
4.1.2 Numerical Results
A circular wound of radius 1 cm has been studied. We present the obtained results,
showing the evolution of the species concentration in the wound centre along time
(see Fig. 3 ).
We observe how the oxygen concentration regulates the rest of the variables.
When there is no oxygen in the centre of the wound the level of MDGF increases
rapidly, which causes the appearance of capillaries. When the capillary density
grows, more oxygen is supplied to the wound centre and the MDGF decreases. The
capillary density grows rapidly to the capillary density of undamaged tissue (u e 3 )
when the oxygen begins to increase. Finally, it is clear from the results that oxygen
affects the fibroblasts concentration (see Fig. 4 ). When oxygen is not included in
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