I have not read the much-referred to pages by Dr. Koester, but several things
are certain:
First, the situation in an axon CAN NOT be treated as a parallel-plate
capacitor with an Area equal to the outer circumference. The geometry
is simply not correct.
Second, it SHOULD be treated as a cylindrical capacitor with the plate
surfaces being the inside wall of the membrane and the outside of the
myelin.
Third, in this case, the capacitance is given by C = k*L/ln(b/a) where
a is the inner radius (the axoplasm), and b is the outer radius (the
axoplasm + the membrane thickness + the thickening due to the myelin).
Fourth, it is clear that as the amount of myelin INCREASES, b INCREASES
and C DECREASES, as postulated.
Fifth, it can be shown by playing with the math (this is an exercise that
can be done at home) that, if we look at the ratios (dR/dx)/R and
(dC/dx)/C, i.e. the *relative* changes in R and C for changes in x,
C DECREASES MORE RAPIDLY in the myelin situation than does R for the
increasing the axon radius case.
Sixth, all that jive about myelin being a more efficient means of increasing
conduction velocity than is increasing the fiber radius can be VALIDATED
MATHEMATICALLY, if the right equations are used.
-----
brp
dr bruce parnas
brp at psychomo.arc.nasa.gov
/usr/local/Std.Disclaimer: The opinions expressed here are mine and
not those of NASA, but you probably could have guessed that.
It's not my fault. Not all of us here at NASA are Rocket Scientists