Biomedical Engineering Reference
In-Depth Information
z
v
F
RT
pF
2
c
1
e
−
v
c
2
−
I
i
=
(7.2)
RT
z
v
F
RT
e
−
1
−
In this equation,
c
2
is the extracellular concentration, while
c
1
symbolizes the intracel-
lular concentrations. The paracellular shunt or the tight junctions are also described
using the GHK equations. The basolateral potassium channels use an inward recti-
fying factor along with the GHK equation. The basolateral Na/K/2Cl cotransporter
is defined by a single constant trCl, assuming no voltage dependence and no depen-
dence with regards to the ion concentrations.
The model simulates ion transport under current- or voltage-clamp conditions
and allows monitoring of individual ionic membrane currents, membrane potentials,
and intracellular ion concentrations. Using a set of transport parameters, the model
reproduces the effects of conductance inhibition on transepithelial transport.
I
a
(
V
a
)
=
iT
j
(
V
a
)
(7.3)
j
I
b
(
V
b
)
=
iT
j
(
V
b
)
(7.4)
j
These equations [
18
] represent the sum of currents flowing through different channels
in the apical and the basolateral membranes, respectively. These equations are used
to solve for
V
a
and
V
b
. Under the voltage-clamp condition, the model solves the
following set of equations:
I
a
(
V
a
)
=
I
b
(
V
b
)
(7.5)
V
a
+
V
b
=
V
te
(7.6)
The following equations are solved under current-clamp conditions:
I
t
=
I
a
(
V
a
)
+
I
s
(
V
te
)
(7.7)
I
a
(
V
a
)
=
I
b
(
V
b
)
(7.8)
V
te
=
V
a
+
V
b
(7.9)
Horisberger's model produces steady-state results.
Y. Sohma, M.A. Gray, Y. Imai, and B.E. Argent [
41
] modeled ion transport in
the pancreatic ductal epithelium cells using a model which was similar to that of
Horisberger. As Fig.
7.8
shows, it includes many more ion channels and multiple
co-transporters [
41
]. Furthermore, the model incorporates ions besides Na
+
,K
+
,
and Cl
−
. It also includes transportation of bicarbonate (HCO
3
) and hydrogen (H
+
)
ions.
Sohma et al. proposed an equation for the turnover rate for the Na
+
−
n
HCO
3
cotransporter [
41
]:
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