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16.6 SOME APPLICATIONS OF INTEREST 337

FIG. 16.10 Surfaces where Dirichlet boundary conditions are applied.

16.6.2.3 Boundary Conditions
All faces of the chip are considered impervious to chemical species and cells, except for the supply surfaces that are
marked in red in Fig. 16.10. Therefore, the boundary conditions are of the Neumann type in the rest of the contour of
the chamber such that cell and oxygen flux are specified to be 0. In the red-marked surfaces, we assume Dirichlet
boundary conditions. These boundary conditions depend on the desired microenvironment conditions (oxygen sup-
ply and oxygen gradient) and vary from one experiment to another. As an example, suppose that cell concentration is
s
set to 0 for both alive and dead phenotypes and oxygen supply is fixed to O ¼ 2 mmHg.
2
16.6.2.4 Initial Conditions
As initial conditions, we assume that, at the beginning, there are no dead cells at the culture chamber, and the con-
0
6
centration of alive cells is homogeneous and equal to C ¼ 1 10 cell/mL. Finally, it is assumed that oxygen pressure
0
is homogeneous at t ¼ 0 and equal O ¼ 2 mmHg.
2
16.6.2.5 Results and Discussion
Fig. 16.11 shows the evolution over time of alive cells and Fig. 16.12 shows the evolution of dead cells on the culture
chamber. As expected, the cell concentration remains high next to the supply channels and decreases in the central part
of the chamber, where oxygen consumption induces anoxia. Therefore, once the oxygen threshold of O ¼ 1:6 mmHg is
∗
2
achieved, cell death is promoted. This explains, analogously, why dead cell concentration increases at the same
regions. However, cell chemotaxis explains why alive cells are even more concentrated at oxygen supply points: cells
migrate in the direction of the oxygen gradient and when they arrive to a well-oxygenated point, proliferation occurs
normally because the conditions are now favorable and the cell concentration is below the capacity limit.
The results of the simulation show how the cell culture is going to evolve during the virtual experiment. With the
presented parameters and boundary conditions, the lack of oxygen diffusion along the culture chamber results in the
fast appearance of a necrotic core occupying almost the entire chamber. The researcher should, therefore, consider
whether the dimensions of the chip, the hydrogel diffusivity properties, or the initial cell concentration are appropriate
for the experiment carried out and assess whether other conditions would be preferable. This kind of in silico predic-
tion can be extrapolated to other cell populations and tissues, other geometries, and other mechanical frameworks
relative to the experiment. Moreover, the simulation of the different processes allows access to all field value variables,
which can, in turn, be interesting for the disclosure of correlation between phenomena or variables of clinical or phys-
iological interest that would be inaccessible from an experimental point of view due to technical considerations (dif-
ficulty or impossibility of field variable monitorization).
It is important to note, however, that model and parameter characterization is always a very complicated task. Even
if frequently simplified, the multiphysics nature of the TME is very complex: many different phenomena are coupled
and many scales are involved, resulting in a hard nonlinear problem where even the semiquantitative analysis is often
complicated. Too-simplistic models lead to the failure of predictive simulation models while complex and sophisti-
cated ones result in a difficult parameter estimation (due to both numerical and experimental difficulties and valida-
tion). Moreover, highly nonlinear and coupled models in different physical scales may involve very expensive
simulations from the computational point of view.

II. MECHANOBIOLOGY AND TISSUE REGENERATION