Biomedical Engineering Reference
In-Depth Information
Figure 5.38
Diffusion distance from the point source in an isotropic cell cluster.
where
L
is obtained by averaging the distance of each particle between their loca-
tion at time
t
and at time
t
= 0 .
In Figure 5.39, we have plotted the normalized diffusion length versus time
for different cluster morphologies: ordered (square and hexagonal cells) and dis-
ordered, with narrow ECS. A narrow ECS is defined here by a constant width less
than 1/10 of the average size of the cells but larger than about three times the mean
free path of the particles.
On very rare occassions, the diffusing particles execute random walk inside a
small region of the ECS where the particles are initially placed, so that the value of
b
is that of free diffusion:
b
= 1 at
t
= 0. After a short time, the particles have ex-
plored all the available initial space and start diffusing inside the ECS. They are now
constrained inside the ECS by the cells' boundaries, and
b
reaches a nearly constant
Figure 5.39
Normalized diffusion length versus time for different (regular and irregular) clusters.
