Conduction velocity - SK versus KR theory
Conduction velocity in a transmission line is a function
of the effective R, L, G, C, and radian frequency of that line (hatted
values under S-K theory, unhatted values under K-R theory.) See
A new passive neural
equation: Part a, derivation Equation
1 below is (13) in this reference.
Writing (1) out, velocity is:
In the K-R case, L is negligible, and (2) becomes
If membrane conductance, G, is set to 0, this simplifies
In the K-R case, with membrane conductance G set to 0,
velocity is proportional to the square root of frequency. R and C are fixed
for a particular line.
For the S-K case, the relevant values are the hatted values
that include crossterms, and effective inductance is large, rather than
In the case where G is negligible, G hat is negligible
and (6) reduces to
For small neural lines, the numerical value of L is much
larger than R, and as frequency increases, the velocity function gets closer
and closer to
So under S-K theory, velocity for small neural lines,
with G very low, is INDEPENDENT of frequency, because frequency effects
in numerator and denominator cancel.
The proportional relations of velocity to frequency are shown below:. K-R calculates a line with R and C, and negligible L. S-K calculates a line with R, C, and L, with L large. The vertical and horizontal scales are arbitrary linear scales to illustrate the shape of the curve.