Conduction in bundles of demyelinated nerve fibers: computer simulation

Abstract

This study presents a model of action potential propagation in bundles of myelinated nerve fibers. The model combines the single-cable formulation of Goldman and Albus (1967) with a basic representation of the ephaptic interaction among the fibers. We analyze first the behavior of the conduction velocity (CV) under the change of the various conductance parameters and temperature. The main parameter influencing the CV is the fast sodium conductance, and the dependence of CV on the temperature is linear up to 30 degrees C. The increase of myelin thickness above its normal value (5 microm) gives a slight increase in CV. The CV of the single fiber decreases monotonically with the disruption of myelin, but the breakdown is abrupt. There is always conduction until the thickness is larger than 2% of its original value, at which with at this point a sharp transition of CV to zero occurs. Also, the increase of temperature can block conduction. At 5% of the original thickness there is still spike propagation, but an increase of 2 degrees C causes conduction block. These results are consistent with clinical observations. Computer simulations are performed to show how the CV is affected by local damage to the myelin sheath, temperature alterations, and increased ephaptic coupling (i.e., coupling of electrical origin due to the electric neutrality of all the nerve) in the case of fiber bundles. The ephaptic interaction is included in the model. Synchronous impulse transmission and the formation of "condensed" pulse states are found. Electric impulses with a delay of 0.5 ms are presented to the system, and the numerical results show that, for increasing coupling, the impulses tend to adjust their speed and become synchronized. Other interesting phenomena are that spurious spikes are likely to be generated when ephaptic interaction is raised and that damaged axons suffering conduction block can be brought into conduction by the normal functioning fibers surrounding them. This is seen also in the case of a large number of fibers (N=500). When all the fibers are stimulated simultaneously, the conduction velocity is found to be strongly dependent on the level of ephaptic coupling and a sensible reduction is observed with respect to the propagation along an isolated axon even for low coupling level. As in the case of three fibers, spikes tend to lock and form collective impulses that propagate slowly in the nerve. On the other hand, if only 10% of fibers are stimulated by an external input, the conduction velocity is only 2% less than that along a single axon. We found a threshold value for the ephaptic coupling such that for lower values it is impossible to recruit the damaged fibers into conduction, for values of the coupling equal to this threshold only one fiber can be restored by the nondamaged fibers, and for values larger than the threshold an increasing number of fibers can return to normal functioning. We get values of the ephaptic coupling such that 25% of axons can be damaged without change of the collective conduction.

Information processing in the axon

“…There is no evidence for this yet, but modelling studies indicate that the relative location of nodes of Ranvier on two adjacent myelinated axons might also determine the degree of temporal synchrony between fibres 113,114 . On small unmyelinated axons, ephaptic interaction between axons is predicted to be minimal 115 but future research might reveal a powerful means to thoroughly synchronize neuronal activity downstream of the site of action potential initiation.…”

Evoked membrane potential change in rat optic nerve fiber: Computer simulation

“…However, for long stimuli train, [Na + ] in variations may not be negligible. In our model, the persistent A-current strongly maintain the membrane between myelinated nerve fibers [35,36] must be modeled.…”

Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations

“…The work [20,21] considers two types of coupling at once, ephaptic and ohmetric, and that approach may provide further insight into the dynamics of our present problem. The work in [3] is concerned with ephaptic coupling in nonmyelinated nerve fibers that might be modeled with (1.1) with large D. In [16], the authors focus on the effects of demyelination of nerve fibers in large bundles and observe a reduction in the speed of action potential propagation when the nodes of Ranvier are aligned. In addition, we have shown that for any value of A, there is a value of β such that a 1 = a 2 .…”

“…Although our particular model is motivated by this neurological application, similar models may also be used to study action potentials in cardiac cells, among other things (see [3,16,20,21]). The authors in [1] also mention the possible application of coupled two-dimensional lattices to the study of image processing.…”