Biomedical Engineering Reference
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Figure 5.37  Estimation of the tortuosity in the case of convex, isotropic, porous media.
2
2
2
L
4
n
D
x
2
AB
AB
τ
=
=
=
2
2
2
2
d
2
n
D
x
Finally
L
d
AB
AB
τ =
= 2
The same reasoning may be applied to the 3D case.
It has been also shown that there is a very simple relation between the effective
and free diffusion coefficient involving the tortuosity
D
D
1
eff
=
(5.52)
2
τ
Thus, if the width of the ECS is narrow and remains uniformly constant in the
2D cluster, the value of the effective diffusion coefficient is half that of the free dif-
fusion coefficient
D
D
= 1
2
eff
Assuming the same conditions for the ECS (isotropy and convexity), the Monte-
Carlo numerical model shows that (5.50) and (5.52) also apply for any isotropic
cluster of irregular cells. Figure 5.38 shows the location of the diffusing particles
initially starting from the injection point after a time interval of 15 seconds ( D =
10 -10 m 2 /s).
Let us introduce the normalized diffusion length b by
L
Dt
β =
(5.53)
4
 
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