Biomedical Engineering Reference
In-Depth Information
18.
The following steady-state concentrations and permeabilities are given for a membrane. Note
that
A
þ
is not permeable. The ion channel resistances are
R
K
¼
1
:
7k
O
,
R
Na
¼
9
:
09 k
O
, and
R
Cl
¼
3
:
125 k
O
.
Ion
Cytoplasm (mM)
Extracellular Fluid (mM)
Ratio of Permeabilities
K
þ
168
6
1.0
Na
þ
50
337
0.019
Cl
41
340
0.381
A
þ
64
12
—
(a) Find the Nernst potential for each ion. (b) Draw a circuit model for this membrane. (Hint:
See Figure 12.13.) (c) Find the membrane resting potential using the circuit in part (b).
(d) Find the Thevenin's equivalent circuit for the circuit in part (b).
19.
Suppose the membrane in Figure 12.13 is given with
R
K
¼
0
:
1k
O
,
R
Na
¼
2k
O
,
R
Cl
¼
0
:
25 k
O
,
E
K
¼
74 mV,
E
Na
¼
55 mV, and
E
Cl
¼
68 mV. (a) Find
V
m
. (b) Find the Thevenin's
equivalent circuit.
20.
Suppose a membrane has an active
Na-K
pump with
R
K
¼
0
:
1k
O
,
R
Na
¼
2k
O
,
R
Cl
¼
0
:
25 k
O
,
E
K
¼
74 mV,
E
Na
¼
55 mV, and
E
Cl
¼
68 mV, as shown in Figure 12.14. Find
I
Na
and
I
K
for the active pump.
21.
The following steady-state concentrations and permeabilities are given for a membrane. Note
that
A
þ
is not permeable.
Ion
Cytoplasm (mM)
Extracellular Fluid (mM)
Ratio of Permeabilities
K
þ
140
2.5
1.0
Na
þ
13
110
0.019
Cl
3
90
0.381
A
þ
64
12
—
(a) If
R
K
¼
1
:
7k
O
and R
Cl
¼
3
:
125 k
O
, then find
R
Na
. (b) Find the Thevenin's equivalent
circuit model.
22.
Suppose that a membrane that has an active
Na-K
pump with
R
K
¼
0
:
1k
O
,
R
Na
¼
2k
O
,
R
Cl
¼
0
:
25 k
O
,
E
K
¼
74 mV,
E
Na
¼
55 mV,
E
Cl
¼
68 mV, and
C
m
¼
1 mF, as shown in
Figure 12.15, is stimulated by a current pulse of 10 m
A
V
m
. (b) Find the
capacitive current. (c) Calculate the size of the current pulse applied at 6 ms for 1 ms,
necessary to raise
for 6 ms
:
(a) Find
40 mV and the stimulus is
applied as in part (c), then explain whether an action potential occurs.
23.
Suppose that a membrane that has an active
V
m
to
40 mV
.
(d) If the threshold voltage is
Na-K
pump with
R
K
¼
2
:
727 k
O
,
R
Na
¼
94
:
34 k
O
,
R
Cl
¼
3
:
33 k
O
,
E
K
¼
72 mV,
E
Na
¼
55 mV,
E
Cl
¼
49
:
5 mV, and
C
m
¼
1mF, shown in
Figure 12.15, is stimulated by a current pulse of 13 mA for 6 ms
:
Find (a)
V
m
, (b)
I
K
, and
(c) the capacitive current.
24.
Suppose a membrane has an active
Na-K
pump with
R
K
¼
1
:
75 k
O
,
R
Na
¼
9
:
09 k
O
,
R
Cl
¼
1mFas
shown in Figure 12.15. (a) Find the predicted resting membrane potential. (b) Find
3
:
125 k
O
,
E
K
¼
85
:
9 mV,
E
Na
¼
54
:
6 mV,
E
Cl
¼
9
:
4 mV, and
C
m
¼
V
m
if a small subthreshold current pulse is used to stimulate the membrane.
