Biomedical Engineering Reference
In-Depth Information
α
= 1. Combining equations (1.3) and (1.4) gives the external solution hydrogen-ion
concentration as:
(
)
(
)
h
=−
1
ααα
K
D
,
s
(1.5)
The total amount of hydrogen ion
H
(including undissociated) in the muscle
compartment is:
(
)
(1.6)
H VhV
=++−
1
α
XV
where
V
represents water volume. The first and third terms are the dissociated and
undissociated hydrogen ions in the muscle membrane, respectively. The second term
gives the acid added to the external solution. The total amount of salt cation
S
is then:
SsVsV
=+
(1.7)
Assuming water absorption by the membrane depends linearly on the degree of
dissociation, then:
(
)
(1.8)
VWw k
=
+
α
0
where
W
is the dry weight of the muscle membrane,
w
0
its water content in milliliters
per gram dry membrane, and
k
is a proportionality constant. In terms of the total
volume
V
T
, we also have:
(
)
VV Ww k
T
=−
+
α
(1.9)
0
Substituting in equation (1.7) and rearranging yields
(
)
(
)
+−
(
)
SsD sWw k
=
α
,
+
α
VWwk
T
+
α
(1.10)
0
0
Substituting for
h
,
V
, and
V
in equation (1.6) from equations (1.5), (1.8), and
(1.9) gives:
1
−
α
(
)
H
=
Z
+
α
WC
(1.11)
α
where
(
)
Ww k
Ds
+
α
(
)
+−
0
ZKWw k
≡
+
α
V
(1.12)
(
)
0
T
α
,
