[Nerve impulse conduction along myelinated fibers while internodal vary (mathematical model)]

The mathematical model of a myelinated fibre (Hille, 1971) was used to study the dependence of the velocity of nerve impulse propagation (theta) and of some parameters of the action potential on the properties of internodes. Calculations have shown that with increasing of the length (L) of internodes over the range of 0.75-3 mm, theta rises and then declines; in the fibre with the external diameter, D = 14 mu the maximum of theta falls on L = 1.5 mm. With decreasing of d/D (d = internal diameter of the fibre) at expense of D (simulation of the myelin sheath thickening) theta grows up monotonically, while the safety factor N (defined as the ratio of the potential (V) in the 6th node to V in the 8th node at a moment when V in the 8th node reaches its maximum) rises steeply only up to d/D approximately 0.75; with further increasing of D, N increases insignificantly. The raising of the longitudinal resistance (ri + r0) leads to the gradual decrease of theta; at ri + r0 = 70 mohm/cm the nerve impulse propagation ceased. The estimation of the longitudinal resistance of the intercellular clefts suggests that in the nerve trunks with a compact packing of nerve fibres the flow of the local currents through the axoplasm of the neighbouring fibres is a prerequisite for impulse conduction. The possibility of electrical (electronical) interaction between the membranes of nodes and internodes has been studied. Calculations have shown that if the generation of a membrane potential in the internode were absent, the resting potential of the node would by 10 mv lower than the potential created by the nodal "generator".