Biomedical Engineering Reference
In-Depth Information
spinal motoneurons
24;32;33;34;35
. The multiexponential decomposition algo-
rithm described in Knisley and Glenn
36
was used to estimate
0
,
1
, A
0
,
and A
1
for representative experimental response data from a series of spinal
motoneurons taken from the study of Glenn et al
32
. Fig. 3 shows the results
of a best t procedure between the experimental voltage recording and the
theoretical response in the exponential model. Table 2 shows the rst two
eigenvalues and initial amplitudes for the two waveforms. The parameters
for the best t under the above assumption were C
m
= 1F , C = 0:34F ,
R
m
= 7; 000, L = 1:55, and V
ss
= 0:01266 .
Voltage transients produced by constant current pulses in the soma of
neurons are more closely approximated the exponential model than a point
or stepped model. In experimental waveforms analyzed, A0 varied from 34%
to 75% of the steady state value and had only rarely come close to 90%
of steady state. The point capacitance model could not produce responses
consistent with experimentally-derived curves of electrotonic responses in
the neurons. The stepped model produce similar responses to the neurons
within the range 0:4 < Z < :6, and thus a stepped capacitance change could
account for the empirical ndings under this condition. The range condition
has an interesting correlation: It is also the range under which response of
the step model most closely approximated the exponential model (Table 1),
arguing indirectly for the greater applicability of the exponential model.
6. The Constant Membrane Capacitance Assumption
6.1. Errors Produced by Assumption of Constant C
m
In this section, the exponential model developed with the eigenslope
method will nally be applied to the long-standing problem of whether
or not the assumption of constant capacitance is justied. The response
of a membrane cylinder with constant C
m
was compared to a cylinder with
an exponential gradient in C
m
under the conditions that the average C
m
is the same in both models and the variation in C
m
is within the range
measured in recent studies. As shown in the responses of Fig. 4 and in
measurements of decay rate derived from those responses in Table 3, a 2%
gradient in membrane capacitance causes about a 1.0% error in the time to
decay to 90% of the initial value, a 0.5% error in time to 50% decay, and a
0.3% error in time to 90% decay. A 10% gradient causes about a 7% change
in time to decay to 90% of the initial value, a 3.5% error in time to 50%
decay, an a 2.4% error in time to 90% decay.
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