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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