Computation of Impulse Conduction in Myelinated Fibers; Theoretical Basis of the Velocity-Diameter Relation

Abstract

For myelinated fibers, it is experimentally well established that spike conduction velocity is proportional to fiber diameter. However no really satisfactory theoretical treatment has been proposed. To treat this problem a theoretical axon was described consisting of lengths of passive leaky cable (internode) regularly interrupted by short isopotential patches of excitable membrane (node). The nodal membrane was assumed to obey the Frankenhaeuser-Huxley equations. The explicit diameter dependencies of the various parameters were incorporated into the equations. The fiber diameter to axon diameter ratio was taken to be constant, and the internode length was taken to be proportional to the fiber diameter. Both these conditions reflect the situation that exists in real, experimental fibers. Dimensional analysis shows that these anatomical conditions are equivalent to Rushton's (1951) assumption of corresponding states. Hence, conduction velocity will be proportional to fiber diameter, in complete agreement with the experimental findings. Digital computer solutions of these equations were made in order to compute a set of actual velocities. Computations made with constant internode length or constant myelin thickness (i.e., nonconstant fiber diameter to axon diameter ratio) did not show linearity of the velocity-diameter relation.

Neuronal Birth Order Identifies a Dimorphic Sensorineural Map

“…We show that in the zebrafish larva, terminal neuromasts are innervated by large-diameter afferent axons. The conduction velocity of myelinated axons in vertebrates increases linearly with their diameter (Hursh, 1939;Holmes, 1941;Goldman and Albus, 1968). Therefore, early-born neurons projecting from terminal neuromasts are likely to be fast conducing, making them well suited to produce the first and fastest lateral-line stimulus for the C-start response.…”

Electron Microscopy of the Mouse Optic Nerve: A Quantitative Study of the Total Optic Nerve Fibers

“…In spite of a wide variety of experimental animals and methods among these investigators, there is a general agreement that the distribution of the fiber diameter is unimodal, the mode in the frequency distribution is skewed toward the fiber diameter including the myelin sheath, because of the physiological evidence that the conduction velocity of the myelinated fiber is proportional to its external diameter, as suggested by RUSTON (1951) and GOLDMAN (1968). DONOVAN (1967) initially pointed out the heterogeneous construction of the nerve fibers in the cat optic nerve, since she observed a greater percentage of small fibers in the peripheral area than in the central area.…”

No Evidence for Chronic Demyelination in Spared Axons after Spinal Cord Injury in a Mouse

“…This simpler model, available from the NEURON database, represents the axon and myelin sheath as a single conductor. Membrane dynamics in the internodes are a function of myelin conductance and capacitance, which is estimated from the relationship between the capacitance and conductance of a coaxial cable (Goldman and Albus, 1968).…”