Biomedical Engineering Reference
In-Depth Information
effective area of pores
∆
V
A
tp
∆
t
J
v
=
(8.109)
where
A
tp
=
i
=1
A
i
is the total effective area of pores in the membrane. In
analogy to (8.109) the dependence of the flux
J
v
on the pressure stimulus can
be expressed as
J
v
=
L
v
∆
P
(8.110)
where
L
p
is the total filtration coecient of the pores (a measure of the total
hydraulic conductivity of pores in the membrane). Experimentally measurable
are the rate of the volume flow ∆
V/
∆
t
and the membrane surface
A
tm
from
which the values of
J
v
and
L
p
can be determined. The values of filtration
coecients given in literature refer thus to quantities defined by equations
(8.108). On the other hand a comparison of equations (8.108-8.109) shows
that
L
p
=
A
tm
A
tp
L
p
(8.111)
From equations (8.111) and (8.37) we have
A
tp
=
8
ηπlA
tm
L
p
(8.112)
where
L
p
is the filtration coecient from the KK formalism. This formula
allows computations of the total pore area,
A
tp
,
provided
η
,
l
,
A
tm
, and
L
p
are
known. On the other hand
,
knowing values of
s
and
A
tp
the number of pores
can be found as
N
=
A
tp
/s
. We computed the values based on the following
data: viscosity of human blood plasma,
η
=1
.
81
10
−
21
[Ns/nm
2
] (Kane and
Sternheim 1988); filtration coecient of human erythrocytes membrane,
L
p
=
1
.
27
×
10
−
12
[m
3
/Ns] (Sha'afi and Gary-Bobo 1973); total surface area of a
human erythrocyte,
A
tm
= 167
×
10
6
[nm
2
] (Sha'afi et al. 1970; Milgram and
Solomon 1977); thickness of a human eryth
r
ocyte membrane,
l
=7
.
5 [nm]
(Stryer 2000); mean pore cross-section area,
s
=0
.
137 [nm
2
]. We found that
for such an erythrocyte the total pore cross-section area is
A
tp
= 268
.
9 [nm
2
],
which gives the number of pores at
N
= 1.9
×
10
3
. That is, on the average
×
10
3
[nm
2
] of cell surface area.
there is one pore per 87
×
8.7 Comparison of Transport Formalisms: KK,
ME, and 2P
The main aim of this chapter is to compare various formalisms for mem-
brane transport of binary solutions. As mentioned in the introduction they
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