EIGENSLOPE METHOD FOR SECOND-ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS AND THE SPECIAL CASE OF CYLINDRICAL CELLULAR STRUCTURES WITH SPATIAL GRADIENTS IN MEMBRANE CAPACITANCE - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 267

Table 2. Eigenvalues and Fourier coecients for decomposed exper-
imental waveform (voltage responses to current step) and for model
with exponentially-distributed membrane capacitance. Experimental
data came from a selected spinal motoneuron from Glenn and others
(1987). Amplitude coecients are reported as a fraction of the steady
state value, V = 0:01266

Experimental Data Model Prediction Deviation

0 5.28 ms 5.28 ms 0%

1 0.787 ms 0.866 ms 10%

A 0 0.4779 0.4826 ms 1%

A 1 0.3791 0.2891 ms -23.7%

Fig. 3. Experimental data (solid line) t with a recording from the exponentially varying
membrane capacity model (dashed line), from 1 ms to 10 ms.

5. Comparison of Model Responses to Experimental
Responses

The question addressed was whether a single membrane cylinder model
with sealed ends and a point or exponential distribution of C m could ac-
count for the voltage response of single quasi-cylindrical cells to a cur-
rent pulse. Experimental data from studies on spinal motoneurons (stim-
ulation and response determined at X = 0) were used for this purpose.
The values of C; R m , C m , and L were chosen from empirical studies on