Biomedical Engineering Reference
In-Depth Information
25. Suppose a membrane has an active
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
1 mF, as shown in
Figure 12.15. Design a stimulus that will drive
V m to threshold at 3 ms. Assume that the
threshold potential is
40 mV. (a) Find the current pulse magnitude and duration. (b) Find
V m .
26. Suppose a current pulse of 20 mA is passed through the membrane of a squid giant axon. The
and sketch
1
R l ¼
10 3 S,
Hodgkin-Huxley parameter values for the squid giant axon are
G l ¼
0
:
3
G K ¼
G Na ¼
10 3 S,
10 3 S,
10 3 V,
10 3 V,
36
120
E K ¼
72
E l ¼
49
:
4
10 3 V and
10 6 F
E Na ¼
55
C m ¼
1
:
Simulate the action potential. Plot (a)
V m ,
G Na , and
G K versus time, (b)
V m ,
and
versus time, and (c)
V m ,
I Na ,
I K ,
I c , and
n, m,
h
I l
versus time.
27. Suppose a current pulse of 20 mA is passed through an axon membrane. The parameter
1
R l ¼
G K ¼
10 3 S,
10 3 S,
10 3 V,
values for the axon are
G l ¼
0
:
3
36
E K ¼
12
10 3 V,
10 3 V, and
10 6 F
E l ¼
10
:
6
E Na ¼
115
C m ¼
1
:
Assume that Eqs. (12.41) to
(12.48) describe the axon. Simulate the action potential. Plot (a)
V m ,
G Na , and
G K versus time,
I l versus time.
28. This exercise examines the effect of the threshold potential on an action potential for the squid
giant axon. The Hodgkin-Huxley parameter values for the squid giant axon are
(b)
V m ,
n, m,
and
h
versus time, and (c)
V m ,
I Na ,
I K ,
I c , and
1
R l ¼
G K ¼
G Na ¼
10 3 S,
10 3 S,
10 3 S,
10 3 V,
G l ¼
0
:
3
36
120
E K ¼
72
10 3 V,
10 3 V, and
10 6 F
E l ¼
49
:
4
E Na ¼
55
C m ¼
1
:
(a) Suppose a current pulse
of
10 mA, which hyperpolarizes the membrane, is passed through the membrane of a squid
giant axon for a very long time. At time
0, the current pulse is removed. Simulate the
resultant action potential. (b) The value of the threshold potential is defined as when
I Na > I K þ I l :
t ¼
Changes in threshold potential can be easily implemented by changing the
value of 25 in the equation for a m to a lower value. Suppose the value of 25 is changed to 10 in
the equation defining a m and a current pulse of
10 mA (hyperpolarizes the membrane) is
passed through the membrane of a squid giant axon for a very long time. At time
t ¼
0, the
current pulse is removed. Simulate the resultant action potential.
29. Simulate the plots shown in Figures 12.20 to 12.22 in the voltage clamp mode.
30. Select an input current waveform necessary to investigate the refractory period that
follows an action potential. (Hint: Use a two-pulse current input.) What is the minimum
refractory period? If the second pulse is applied before the minimum refractory period,
how much larger is the stimulus magnitude that is needed to generate an action
potential?
31. Explain whether the following circuit allows the investigator to conduct a voltage clamp
experiment. The unmyelinated axon is sealed at both ends. A silver wire is inserted inside
the axon that eliminates
R a :
Clearly state any assumptions.
Continued
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