Biomedical Engineering Reference
In-Depth Information
• Phenomenological models where the wound healing is modeled as a moving
boundary problem where the interface moves as a result of a growth factor and
local curvature.
The first approach involves very complicated models where many badly known
biological input-parameters are needed. A big advantage is the fact that these models
take relatively many biological parameters and subprocesses into account and that
large tissue areas and large wounds can be modeled. This class of models can be
applied to real-like in-vivo wounds of the order of centimeters or even larger. The
domain of computation needs to be discretized to obtain a finite-element (or any
other discretization) discretization in order to approximate the solution of the
resulting boundary value problems formulated in terms of partial differential
equations and its initial/boundary conditions. The parameter space and limited
availability of appropriate values is a serious drawback of this class of models.
An example concerns the availability of diffusion coefficients (i.e. random walk) or
chemotactic coefficients or proliferation coefficients, see [
3
-
6
,
7
-
10
,
11
,
12
,
13
,
14
,
15
,
16
] to mention a few of them. The second class of models only takes few
parameters into account, but stays close to biology if one models in-vitro experi-
ments. An extension to in-vivo cases is not straightforward since one typically will
need to consider a large domain of computation and thereby making the number of
cells or lattice points to be considered extraordinarily large. However, information
from experiments concerning cell motility as a function of the acidity for instance,
can be incorporated in a relatively straightforward manner. Examples are the studies
presented in [
1
,
2
,
17
,
18
,
19
,
20
]. The third model class takes few parameters as well,
however, there is not much biology involved. An advantage of this class of models
is, if the model has been set up in a clever way, that the small number of parameters
involved can be adjusted such that experimental cases can be modeled in both
in-vitro and in-vivo situations. See for the instance [
21
,
9
,
22
,
23
].
In the manuscript, we will describe these classes of models and discuss their
applicability. We will mainly focus on a recently developed continuity-based
model from the second class on cellular level. Of course the models from the
cellular automata-class, such as the cellular Potts model, can be positioned in the
same kind of models. This continuous-based model mimics the migration of a
collection of cells on a planar substrate, where we also take into account a bac-
terially infected zone where an increased acidity, resulting from the competition of
cells and bacteria on oxygen and nutrients, impairs cellular mobility without the
use of a predefined computational lattice. We will show some examples of sim-
ulations. In this model cell motion is a partly stochastic process. Cell death and cell
division are modeled as stochastic processes. The original formulation of the
model can be found in Vermolen and Gefen [
1
]. Furthermore, we will show some
results from a newly constructed cell deformation model under the influence of
chemotaxis. Finally, we address how the results from a small scale model can be
used as input for a large scale model.
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