Biomedical Engineering Reference
In-Depth Information
(b) The sum of the cation concentrations does not equal the chloride concen-
tration on either side of the membrane. Why?
3.16
The potential difference across a cell membrane from outside to inside is ini-
tially
90 mV (when in its resting phase). When a stimulus is applied, Na
+
ions
are allowed to move into the cell such that the potential on the inside changes
to
−
+
20 mV for a short amount of time (depolarization time).
(a) If the membrane capacitance per unit area is 1 mF/cm
2
, how much charge
moves through a membrane of area 0.05 cm
2
during the depolarization
time?
(b) The charge on a Na
+
ion is positive. How many ions move through the
membrane?
(c) How much energy is expended in moving these ions through the
membrane to create this change in potential (called the action potential)?
3.17
If the time constant of a typical axon is 10 ms, what would be the resistance
of one square centimeter of its membrane? The membrane capacitance of a
typical axon is 1 mF/cm
2
.
3.18
Dr. Shingo Yashu is studying a neuromusclular interaction using voltage clamp
measurements. He is interested in using tetraethylammonium (TEA) to block
potassium conductance.
(a) To understand the output, he needs to derive a potassium conductance
equation using the Hodgkin-Huxley model. Please help him.
(b) A part of a muscle cell membrane was studied with the voltage clamp
measurements with a 30-mV positive voltage step input. He measured the
membrane current as 0.5 mA/cm
2
after 5 ms of step input. When the
potassium current was blocked with TEA the current was 1 mA/cm
2
after
5 ms of step input. Also, he observed that the flow of K
+
ions could be
stopped with a 100-mV increase in resting membrane potential. What is
the potassium ion conductance
g
K
?
3.19
The axons of the myelinated nerve fibers are completely encased in a my-
elin sheath. Their neural conduction rates are faster than those of the un-
myelinated nerve fibers. Myelinated nerve fibers are present in somatic and
autonomic nerves. In a patient, one of the myelinated nerves was damaged in
their right arm, which reduced the propagation speed to 65% of the original.
Damaged and healthy nerves are stimulated with a similar stimulus current.
If the smallest current adequate to initiate activation is considered to remain
unchanged, how much longer is stimulus needed with the damaged nerve? The
propagation speed is inversely proportional to the square root of the mem-
brane capacitance
−
1
2
(())
m
Θ
α
C
.
A membrane has 75 Na
+
ion channels/mm
2
with a conductance of 4 pS/chan-
nel. The capacitance of the membrane is 0.01 pF/mm
2
. Calculate the flow and
the time of sodium ions across the membrane of surface area of 1 mm
2
with
V
M
= −
3.20
65 mV, V
M
'
=
35 mV, and V
Na
=
62 mV.
3.21
A defibrillator detects ventricular fibrillation, and shocks the heart to restore
the normal rhythm. Phillips is interested in manufacturing a new defibrillator
