Wound Healing: Multi-Scale Modeling - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 337

that are incorporated in the modeling. If migration of cells is not only random, nor
determined by any chemical signals, then, the tensotaxis could be modeled, which
results into a completely different model where the diffusivity-tensor depends on
the local strains. We note that the total local strain-tensor at any point within the
domain of computation is determined by taking summing over the contributions of
all individual cells. In a PDE-setting, one has to evaluate the cell density, which is
the number of cells per unit of area or volume, and the forces that they exhibit. In
our colony model, the strain energy density is evaluated as a result of adding the
contributions of all individual cells that are present in the colony. To upscale this
tensotaxis is by all means less trivial to carry out then upscaling processes like
chemotaxis or random walk, and hence this is a challenge for future research.
Though, it is tempting to upscale the models and many processes, though in some
cases it is very difficult to incorporate all the information from the models. An
example is the size of the cells in the colony models. The cell size certainly has an
influence on the modeling outcomes in the sense that if large cells disappear then a
relatively large gap arises. This enlargement of the cell radius makes the profile
more prone to noise.
4 Modeling Several Processes in Wound Healing
The models that we considered here are very generic of nature and until here the
presentation has mainly focused on wound closure or gap closure. Apart from gap
closure, infections are very common to occur in clinical or real-world wounds. To
this extent, we also plan to model bacterial infections, in which bacteria compete
with the basis cells, such as fibroblasts or keratinocytes, on nutrients and oxygen,
and thereby increase the tension of biotic lactates, which increase the acidity. The
colony model has been extended with bacteria that move around and divide ran-
domly. Bacterial motion is purely modeled as a Wiener process, by the use of
equation ( Sect. 2.1.1 ) with a certain division and death probability and release rate
of biotic lactates. This chemical release is modeled by the use of Green's Fun-
damental solutions to the diffusion equation, and therewith in fact, the concen-
tration of lactates as a result of a score of bacteria is determined using a
superposition argument. A pilot study has been carried out in Vermolen and Gefen
[ 18 ]. In this work, it is assumed that the cellular mobility decreases with increasing
concentration of biotic lactates. A final conclusion of this work is that the decrease
of motility causes gaps not to close anymore, hence the initial wound does no
longer close entirely and that 'micro-gaps', which result from local cell death, and
which would normally be occupied by newly appearing daughter cells from cell
division, are no longer filled up due to decreased cellular motility. Hence the
decrease of cellular motility leaves the gap open (for a long time) and can also be
held responsible for the decrease of the quality of tissue. In principle white blood
cells clear up contaminants and bacteria, and therefore we are working on a