Biomedical Engineering Reference
In-Depth Information
human cells the erythrocytes undergo relatively large changes in volume result-
ing from blood pressure changes, in particular in the heart and the arteries.
However, in veins the changes in external pressure are significantly smaller
and we can treat water and solute exchange with blood plasma as stationary.
We can describe these processes applying methods similar to those used in
Section 8.5 for water transport in aqueous plants.
8.6.1 Regulation of Water Exchange between Erythrocytes
and Blood Plasma
To describe water permeation across erythrocyte membranes (Sha'afi and
Gary-Bobo 1973; Kargol et al. 2005) we use the mechanistic equations. We
replace the entire membrane by an equivalent membrane that contains all
water permeable pores ordered according to their sizes. Following the proce-
dure outlined in Section 8.5 we write the water influx through the equivalent
membrane as
J
vwa
=
L
p
σ
(
σ
−
1)∆Π =
L
p
σ
(
σ
−
1)
RT
(
c
si
−
c
s
0
)
(8.101)
and water eux as
J
vwb
=(1
−
σ
)[(1
−
c
s
V
s
)
σ
−
c
s
V
s
]
L
p
RT
(
c
si
−
c
s
0
)
(8.102)
We illustrate these equations using values of transport parameters for two
solutes (Table 8.3).
For concentrations
c
si
= 150 [mol/m
3
],
c
so
= 50 [mol/m
3
],
c
s
= 100
[mol/m
3
], and taking
R
=8
.
3[N
K],
T
= 300 [K] we calculated the
fluxes. For ethyl glycol we obtained
J
vwa
=
·
m/mol
·
10
−
8
[m/sec],
J
vwb
=
−
5.29
×
10
−
8
[m/sec], and for urea:
J
vwa
=
10
−
8
[m/sec],
J
vwb
=7
.
77
5
.
29
×
−
7
.
77
×
×
10
−
8
[m/sec] (Figure 8.6).
As these graphs show that the fluxes depend linearly on the internal solute
concentration. This concentration on the other hand depends on the active
transport,
J
vs
, required to maintain the stationary state. Similarly, the depen-
dence on the filtration coecient is linear while the largest changes of the
fluxes as functions of the reflection coecient occur for very small (near 0)
and very large (near 1) values of
σ
.
TABLE 8.3
Transport Parameters for Membranes of Human Erythrocytes
L
p
[m
3
/Ns]
V
s
[m
3
/mol]
Solute
σ
References
0.92
×
10
−
12
0.0566
×
10
−
3
Ethyl glycol
0.63
Katchalsky and Curran (1965)
1.27
×
10
−
12
0.042
×
10
−
3
Urea
0.55
Sha'afi and Gary-Bobo (1973)
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