Wound Healing: Multi-Scale Modeling - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 336

Fig. 8 Two time-sequence
micrographs, taken 4 h apart,
which demonstrate shape
changes in NIH3T3
fibroblasts which cover a
local damage site: A oval
elongated shape of migrating
cells. B Multi-polar cell
shapes when cells are resting
and well-spread at a sub-
confluent density; note the 4-
poles cell in the center of the
magnified frame.
C Polygonal cell shapes in
dense confluent sites. The
scale-bar represents 100 lm

B

close link to in-vitro experiments with one-layer cell colonies can be established
easily. Note that in the cell deformation model we considered a chemical signal
driving cell edge mobility. Without any complication, it is mentioned that the
mathematical nature of this signal is very generic and hence that this signal can
also represented by a strain energy density as in the cell colony model. This
generic nature of course also applies for the cell colony model where we could use
a chemical signal using the same mathematical principles. Both the cell-scale and
colony-scale models can model processes like chemotaxis and tensotaxis.
The transfer of the information from the cell colony model and hence also from
the cellular model, in a certain sense is done by considering the theory outlined in
Sect. 2.1.1 in case of random walk with a well-defined drift component. It can be
seen that the cell diffusivity is related to the average cell velocity. This, however,
only holds for the treatment of cells as so-called point sources that move inde-
pendently. Incorporating the cell areas or volumes will make the treatment more
challenging. However, if the cells or bacteria are sufficiently small compared to the
mean distance they travel over a certain amount of time, then the approach in
Sect. 2.1.1 is quite reasonable. The incorporation of chemotaxis, or analogously
tensotaxis, the amount of biomass per unit area or volume that moves over a
certain distance within a unit of time is proportional to the number of cells per unit
volume or area, that is the cell density, times the concentration gradient scaled by a
factor of proportionality. This is how the classical linear version of the Keller-
Segell model for chemotaxis results. The continuum-based scale allows the use of
larger tissue areas and hence allows to consider realistic in-vivo wound sizes. The
transfer from colony models to PDE models, also strongly depends on the modes