Biomedical Engineering Reference
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Fig. 4
Modeling spatiality in viral dynamics:
(1)
Spatial grid where viral dynamics on each of the
different grid sites is described by a model based on ordinary differential equations [see Eq. (
2
)].
The pictures show the viral load at equilibrium on each of the different grid sites for different
degrees of spatial coupling between the sites (Reproduced with permission from [
34
] c
(2005)
Elsevier Ltd.).
(2)
Sketch of the development of an infection in solid tissue modeled in a 2D
cellular automaton [
9
]. Target cells can become infected by their infected neighboring cells that
can infect other cells or die. Modeling infection by cell-to-cell transmission will lead to a wavelike
pattern for the spread of the infection.
(3)
Snapshots of a simulation modeling spread of infection
in a solid tissue with a 2D cellular automaton using different rules for the replacement of dead cells
[
8
]: (
a
) replacement of cells independent of the location of uninfected target cells, (
b
) replacement
of dead cells by proliferation of neighboring uninfected cells, (
c
) immune cells have to breach the
infection wave to allow the replacement of dead cells. Cells shown in the screenshots are either
uninfected (
white
), dead (
black
), infected or represent immune cells (Reproduced with permission
from [
7
]
c
(2009) Elsevier Ltd.)
discretized the lymphocyte and antigen concentration in space using a regular grid as
done by Funk et al. [
34
]. Instead of using rates, the authors calculate the probability
for each reaction at each grid site and randomly perform the proliferation or death
of lymphocytes according to these probabilities. Using this stochastic simulation,
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