Wound Healing: Multi-Scale Modeling - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 335

In this way, the quality of the tissue can be evaluated over time within a certain
region, which also gives a useful indication of how the wound heals. This can be
applied to more complicated models based on the solution of PDEs. We note that
the computational model is extremely simple, and we refer for more complicated
mathematical models to Vermolen and Javierre [ 29 ].
3 The Relation Between the Scales Involved
The three model classes give insights in their own way in their own scales. The cell-
level models tell us how the shape of the cell actually behaves during the process of
migration, which plays a major role in wound closure, wound contraction, but also in
processes like tumor growth, as well as in the immune system. The measure of how
much a cell can deform depends on its stiffness. Diseases that impair the cell stiffness
(by for instance making the cell stiffer), will influence how the cell deforms when it
is moving. In the case of the immune system, more elastic cells need to migrate over
an only smaller distance to engulf a bacterium or any other harmful agent, see Fig. 4 .
This means that the bacteria or agents are neutralized within less time, and that less
energy is consumed if the cell is flexible. In future studies, we will analyze the
energy consumption of the immune system. Thereby, it can be concluded that the
cell stiffness influences the efficiency of the immune system, next to the known
parameters like the blood vessel stiffness and the number of white blood cells in the
sense that if the cells are stiffer for some reason then the immunity response becomes
less efficient. This holds for the immune system but also for the cells (for instance
fibroblasts) that converge during processes like wound healing. The reason is that if
cells converge to each other and if cells are relatively stiff, then it will take more time
until cells are in physical contact. During the early stages of wound healing, flexible
cells will be elongated as they move towards each other. Hence at the earliest stages
at which the wound is closed, the cells are elongated if they are flexible. In the course
of time as more cells have appeared due to cell division, the cells will get their
cobble-stone shape. An example of a micrograph with different cell shapes in a cell
colony is shown in Fig. 8 .
If the cells are very stiff, then wound closure will be retarded since the cells are
not able to elongate and hence the state of wound closure with elongated cells,
which is the first stage of the wound being fully or partly closed, does not exist.
Hence, the cell deformation model is very helpful in predicting the macroscopic
closure rate of the wound. This issue will be investigated quantitatively in future.
The results from the cell colony model describe the nature how large numbers
of cells converge, divide and die during processes like wound healing or tumor
growth. In these models cell velocities, as well as cell division and death rates are
used. These quantities are relatively easy to measure and thereby a good estimate
of the wound healing kinetics can be obtained. Furthermore, the biological nature
of wound healing is evaluated by monitoring the shape of the wound edge, and a