Biomedical Engineering Reference
In-Depth Information
EXAMPLE PROBLEM 12.4
Find
Cl
channels are ignored. Use
V
m
for the frog skeletal muscle (Table 12.2) if the
R
K
¼
1
:
7k
O
and
R
Na
¼
15
:
67 k
O:
Solution
The following diagram depicts the membrane circuit with mesh current
I
,current
I
Na
through the
sodium channel, and current
I
K
through the potassium channel. Current
I
is found using mesh analysis:
E
Na
þ
IR
Na
þ
IR
K
E
K
¼
0
Outside
I
Na
R
Na
R
K
I
K
V
m
-
-
I
E
Na
E
K
+
+
Inside
and then solving for
I
,
10
3
I
¼
E
K
E
Na
R
Na
þ
R
K
¼
ð
105
56
Þ
10
3
¼
9
:
27 m
A
ð
15
:
67
þ
1
:
7
Þ
yields
V
m
¼
E
Na
þ
IR
Na
¼
89
mV
Notice that
I
¼
I
Na
and
I
¼
I
K
,or
I
Na
¼
I
K
as expected. Physiologically, this implies that the
Na
þ
current is exactly balanced by the outward bound
K
þ
current.
inward
EXAMPLE PROBLEM 12.5
Find V
m
for the frog skeletal muscle if
R
Cl
¼
3
:
125 k
O
.
Solution
To solve, first find a Thevenin's equivalent circuit for the circuit in Example Problem 12.4:
V
TH
¼
V
m
¼
89 mV
and
R
TH
¼
R
Na
R
K
R
Na
þ
R
K
¼
1
:
534 k
O
Continued
