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It's known (Hursh 1939) that myelinated axons exhibit the behavior $v = 6d$, where $v$ is the propagation speed [m/s] and $d$ is the axon diameter [μm].

A related relation for unmyelinated axons is (Malmivuo & Plonsey, eq. 2.1):

$$v = \sqrt{\frac{i_\text{Na max}}{r_i c_m^2 V_\mathrm{th}}}$$

I want to approximate the propagation speed that A-alpha nerve fibers would exhibit, if they were unmyelinated. How could I find values for the constants in the above equation? Is there an easier way to conduct these calculations, or has there already been a study done on this?

For the (myelinated) A-alpha fibers, d = 13-20 μm and v = 80-120 m/s according to Wikipedia.

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The provided relation for unmyelinated axons only holds up to certain diameter value of the axon and is valid only as long as the sodium conductance iNa is uniformly distributed along the cross-section of the axon. This explains why non-myelinated fibers are so thin, being only 0.2-1.5 μm in diameter.

In axons having a larger diameter the axon potential can only move between Ranvier nodes. If this fiber gets unmyelinated the axon potential just stops propagating, due to several reasons:

  1. Sodium concentration through the complete axon surface is too high so that it diffuses internally along the axon and reduces the concentration gradient in the direction of AP propagation.

  2. AP is propagated not only along the length of axon but also laterally, that leads to its flatenning over the axon surface, decreasing its amplitude etc.

Unfortunately I couldn't find the reprint of the original publication in Biofizika referenced by the webpage you provide the link to, so I cannot investigate the constraints of their model for AP propagation.

In order to estimate the propagation velocity in unmyelinated axons of large diameter I would take some theoretical papers investigating the properties of nerve fibers undergoing demyelination. Z. J. Koles and M. Rasminsky "A computer simulation of conduction in demyelinated nerve fibres", J Physiol. 1972 December; 227(2): 351–364. seems to be one of the earliest publications on this topic and it is freely available online.

In this paper the authors tried to simulate the conductance of demyelinated motor axon with diameter of 10μm and 5μm myelin sheath. They gradually decreases the amount of myelin width until 2.7% of the initial value where they saw the abolishment of AP propagation. The propagation time was 12.5 times higher than in normally myelinated fibers (for the distance where AP could travel). If we consider the initial propagation velocity being 80-120 m/s then after demyelination it is reduced down to 6-10 m/s and fade after a short travel.

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Is mkm being used as Micrometre (μm)? –  Rory M Jan 3 '12 at 10:41
    
Yes, thank you for your comment: I used it to copy the μ-symbol and substituted it in my answer! ;-) –  Alexander Galkin Jan 3 '12 at 11:08
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