Biomedical Engineering Reference
In-Depth Information
value. The numerical results of Figure 5.39 are very similar to that of de Sousa et al.
[26] obtained experimentally for regular triangle and square lattices.
The asymptotic value of
b
is 0.7, thus
L
Dt
1
(5.54)
β
=
»
0.7
»
4
2
By definition, the apparent diffusion coefficient satisfies
L
D t
» 1
(5.55)
4
eff
From (5.54) and (5.55), we find
D
D
1
1
2
eff
2
(5.56)
=
β
=
»
2
τ
leading to the value
τ
= 2
.
5.4.2.5 Intercleft Spaces and Channel Restrictions
Real ECSs in the human body are often more complex than those of a uniformly
narrow gap between the cells, which we analyzed in the preceding section. Very
often the spacing of the cells' lattice is not uniform and there are intercleft spaces. It
is shown that diffusion speed may be reduced by entrapment when the dimensions
of the residual spaces are large and the connecting exits are sufficiently small. By
“sufficiently small” we mean that the mean free path of the particle inside the car-
rier fluid is of the order of the cross dimensions of the ECS.
An idealized example is that of a cluster of round cells. If the dimension of
the gaps between the cells is decreased, the apparent diffusion coefficient becomes
smaller than the value predicted by (5.6). In the case defined in Figure 5.40, we
D
D
»
1
4
eff
obtain
.
Figure 5.40
Normalized diffusion length versus time for a cluster of round cells with small gaps.
