Wound Healing: Multi-Scale Modeling - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 338

colony-model that also clears up the bacteria by introducing white blood cells into
the model.
We extended the simulations that we showed here for the three-dimensional
cells that deform and migrate to the case of white blood cells (leukocytes) that
leave a small blood vessel to head for an infection to neutralize the bacteria
present. This modeling is currently done by the use of colony models and cell
deformation models. Here a translation to the use of PDEs for continuum models is
also to be made. We are also in the process of doing this and the results will appear
in future papers. A final stage is the remodeling stage where the tissue remodels to
transform from a scarred state into the fully undamaged state. To simulate this
remodeling process, which is important in the context of hypertrophic scar for-
mation as a result of burns, both the cellular and PDE-based models will be very
useful

since fibroblasts having several properties due to various chemico-

mechanical environments will be taken into account.
Until now, we described the modeling of several biological processes: cell
division, cell migration (due to random walk, tensotaxis or chemotaxis). Immobile
processes like maturation towards cell division or cell differentiation can be
modeled in cell colonies like stochastic processes. In fact, if the entire history path
in terms of the chemical and mechanical environment is known then the time at
which the cell differentiates or divides is determined. This advocates for a
deterministic approach for cell division or differentiation processes. An example of
such a model can be found in the age-structured model by de Vries et al. [ 31 ] for
the computation of age-distributions in population dynamics or Prokharau et al.
[ 32 ] for the modeling of cell differentiation with a maturation space variable
(which corresponds to complete differentiation whenever this variable is one and
to a fully undifferentiated state whenever the value zero holds). The latter model
also contains biological processes like cell migration and cell division. This
modeling class is based on solving an advection equation for the cell density per
unit of maturation and can be extended to the incorporation of the physical space
to model cell migration. In real-world situations, the entire history path of the cells
is not exactly known or even hardly known. To this extent, the hypothesis of
deterministic modeling is violated and one has to rely on stochastic processes. In
the current paper we limited ourselves to modeling cell division as a purely ran-
dom process. Probably it is more accurate to model cell differentiation by means of
both a stochastic and deterministic component.

5 Conclusions

We presented a review of our ongoing work in simulation of wound healing on
various scales. All scales give their own bits of information: The cell-based model
for cell deformation can be used to analyze the shape changes a cell experiences
under the influence of an attracting or repulsing chemical or under the influence of
a local strain pattern. The cell-colony models can be used to look at the dynamics