Biomedical Engineering Reference
In-Depth Information
TABLE 9.1
Description of
SC
Tortuosity and Porosity Based on Brick and Mortar
Structures of Figure 9.2.
Reference
Porosity (
ε
)
Tortuosity (
τ
)
d
h
+
g
2
g
d
h
2
1+
g
h
Michaels
et al. (1975)
1+
1)
d
+
g
4
Nh
+(
N
−
g
g
+
d
Cussler et al.
(1988)
L
g
+
d
2
2
d
2
2
1)
d
+
g
2
−
L
+(
N
−
Lange-
Lieckfeldt
and Lee
(1992)
d
2
2
L
1)
ω
(1 +
ω
)
2
d
Nh
+(
N
−
g
(
g
+
d
)
Johnson
et al. (1997)
L
ω
(1 +
ω
)
2
d
Nh
+(
N
−
1)
g
+(
N
−
1)
g
(
g
+
d
)
Kusner et al.
(2007)
τ
flux
=
Nh
+(
N
−
1)
g
τ
volume
=
Nh
+(
N
−
1)
g
+(
N
−
1)
d
Nh
+(
N
−
1)
g
Source: Adapted from Compendium provided in Kushner et al. 2007.
study compares the model predictions of
D
b
, the solute-
SC
diffusion coe-
cient, and
K
b
, the solute-lipid bilayer partition coe
cient (a measure of the
solute's solubility within the lipid bilayers). To do this, the permeability of
equation (9.3) is defined as
P
=
ε
τ
D
b
K
b
L
(9.4)
where
ε
and
τ
are, respectively, the porosity and the tortuosity of the inter-
cellular paths (lipid-filled spaces between the corneocytes).
Should the porosity and tortuosity be known, it is then possible to find
accurate values for the
D
b
, the solute-
SC
diffusion coecient, and
K
b
, the
solute-lipid bilayer partition coecient. These values are found by combining
analytic solutions with experimental results (Kushner et al. 2007a). This is
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