Biomedical Engineering Reference
In-Depth Information
Next, they inserted two electrodes (Ag/AgCl) in the ion-exchange compartments
and applied a voltage gradient to enable them to change the pH of the solution
surrounding the muscle membrane through an electrodialysis process. In effect, they
were activating a pH-sensitive muscle by varying the pH of the surrounding solution
electrically. They studied muscle membrane response as a function of pH, solution
concentration, compartment size, certain cations, and membrane fabrication.
The next section details a formulation used by Fragala et al. (1972) to develop
analytical relations among applied field, hydrogen ion, and salt concentration that
affects the pH and, ultimately, the muscle contraction and expansion.
The dissociation constant
K
of the acid groups in the muscle membrane is given by:
+
−
(
HA
HA
)(
)
h
α
α
(1.1)
K
=
=
(
)
1
−
where
HA
represents the acid group
α
is the degree of dissociation
h
is the hydrogen-ion concentration
the bar over the variable here and in what follows indicates values within the
membrane
The hydrogen-ion concentration inside the membrane can then be written as:
h
=−
(
1
αα
)
K
(1.2)
Assuming equilibrium is established between the interior of the muscle mem-
brane and the surrounding solution instantaneously, we have:
hs
=
hs
(1.3)
where
s
is the concentration of the salt cation.
Concentrations within the membrane are referred to the water volume absorbed
in the membrane structure. Assuming that the Donnan equilibrium principle governs
the distribution of free electrolytes between the interior of the muscle membrane
and the surrounding solution,
1
2
)
+
(
2
α
X
s
s
s
α
X
s
(1.4)
+≡
(
)
=
1
Ds
α
,
2
4
2
in which
X
is the total concentration (dissociated and undissociated) of weak acid
groups in the membrane. This expression reduces to unity for
α
= 0 and
X
/
s
for
