Biomedical Engineering Reference
In-Depth Information
and the quantity
XV
has been replaced by the equivalent quantity
WC
, where
C
is
the total ion-exchange capacity in milliliters per gram dry membrane.
Equation (1.11) can be partially solved to give:
1
2
Z
WC
4
2
RR
α=
−
+
+
(1.13)
where
H
WC
Z
WC
R
≡+−
1
(1.14)
can be computed numerically using equations (1.10) and
(1.13). All other parameters are known through experiments or membrane properties.
The differential equations describing time rate of change of hydrogen and salt
cations in the muscle membrane compartment with applied constant electric current
I
are given by:
Values of
s
and
α
dH
dt
µ
µµ
−
h
=
h
I
(1.15)
h
+
s
h
s
and
(
)
=−
dH S
dt
+
I
(1.16)
The multiplication factor for
I
in equation (1.15) is the fraction of the total
current, which is carried by hydrogen ions through the cation membrane.
µ
s
are the hydrogen-ion and salt-cation mobility, respectively. The positive direction
for
I
is taken to be from the anion-exchange to cation-exchange membranes. Sub-
stituting the total charge removed,
Q
=
It
and
µ
h
and
µ
s
/
µ
h
≡
p
, then:
(
)
=−1
dH S
dQ
+
dH
dQ
h
h p
−
+
=
and
(1.17)
These equations can be solved numerically for
H
and
S
as a function of
Q
.
MIT's Yannas and Grodzinsky (1973) were among the first to study the defor-
mation of collagen fiber from a rat-tail tendon in an electric field when constrained
at two ends and submerged in aqueous solution. They viewed their results as an
electrophoresis or electro-osmosis phenomenon. They reported that, except at the
isoelectric point, individual collagen molecules as well as macroscopic specimens
such as fibers and membranes constituted from such molecules carry a net electro-
static charge. This charge can give rise to a very intense electric field of the order
