This is not the same computation as the 3D version — it doesn't look up the Hursh/Rushton formulas. Every number below comes out of two small numerical solvers running live:
Healthy internode (saltatory hop):
finite-difference solve of the passive cable PDE
c·∂V/∂t = (1/r_axial)·∂²V/∂x² − g_leak·V
from a decaying node waveform to the V=20mV
threshold at the next node. r_axial, c and
g_leak are derived from real axon geometry
(axoplasm resistivity, membrane capacitance,
and myelin-wrap count from the g-ratio).
Demyelinated internode (continuous conduction):
Nagumo bistable reaction-diffusion wave,
∂V/∂t = D·∂²V/∂x² + k·V(V−a)(1−V),
whose wavefront speed θ = √(kD/2)·(1−2a) was
cross-checked against a direct finite-difference
solve of the same PDE (see the verification
script) before being used here.
- Fiber diameter slider — the total myelinated fiber diameter (axon + all wraps). This — not the bare axon diameter alone — is what sets internode length in real myelinated fibers, and it's the quantity Hursh's and Rushton's original derivations actually held fixed while varying g. Holding it fixed here is what makes the g-ratio optimum below emerge from the solver instead of being asserted: at fixed fiber diameter, more myelin (lower g) always improves the electrotonic space constant, but it also shrinks the axon core inside that same fiber (r_axial ∝ 1/axonD²) and lengthens the internode — the numeric solve is what finds where those two effects balance.
- g-ratio slider — the axon-diameter / fiber-diameter ratio. The optimum marker is found by sweeping the cable solve over g for the current fiber diameter — it is not hard-coded, and it lands close to but not exactly on the textbook asymptotic value of g≈0.6065, because the finite-difference solve keeps the full nonlinear cable behaviour that the closed-form approximation discards.
- Demyelination severity — the fraction of internodes shown loses its myelin and switches solvers entirely, from the cable relay to the Nagumo wave, using the same axon core diameter (g × fiber Ø) the segment already had. Because that wave is roughly one to two orders of magnitude slower per micron, even modest severities drag the average down hard — matching the real clinical picture of conduction slowing/block in demyelinating disease.