Biomedical Engineering Reference
In-Depth Information
A current pulses of 6 ms duration, with the onsets
occurring at 0, 2, 4, 6, and 8 ms. Since the pulses occur within 5t of the previous pulses, the effect
of each on
The following figure is due to a series of 15
m
V
m
is additive, allowing the membrane to depolarize to approximately
45 mV. If the
pulses are spaced at intervals greater than 5t, then
V
m
would be a series of pulse responses, as
previously illustrated.
−
40
−
45
−
50
55
−
−
60
−
65
−
70
−
75
−
80
−
85
−
90
0
0.005
0.01
0.015
0.02
0.025
Time (s)
12.5.3 Changes in Membrane Potential with Distance
The circuit model in Figure 12.15 or 12.16 describes a small area or section of the mem-
brane. In Example Problem 12.6, a current pulse was injected into the membrane and
resulted in a change in
in this section of the membrane causes current
to flow into the adjacent membrane sections, which causes a change in
V
m
. The change in
V
m
in each section
and so on, continuing throughout the surface of the membrane. Since the volume inside
the dendrite is much smaller than the extracellular space, there is significant resistance to
the flow of current in the cytoplasm from one membrane section to the next as compared
with the flow of current in the extracellular space. The larger the diameter of the dendrite,
the smaller the resistance to the spread of current from one section to the next. To model
this effect, a resistor,
V
m
, is placed in the cytoplasm connecting each section together, as
shown in Figure 12.17. This model is actually a three-dimensional surface and continues
in the x, y, and z directions. The outside resistance is negligible, since it has a greater
volume and is modeled as a short circuit.
Suppose a current is injected into a section of the dendrite as shown in Figure 12.18, sim-
ilar to the situation in Example Problem 12.6, where
R
a
t
0
is large. At steady state, the transient
response due to
C
m
has expired, and only current through the resistance is important. Most
of the current flows out through the section into which the current was injected, since it has
