Rate of excitation propagation in a reduced Hodgkins-Huxley model. I. Rapid relaxation of the sodium current]

The question of calculating excitation propagation velocity is analyzed on the basis of the Hodgkin-Huxley model. The activation of the sodium current is assumed to be rapid as compared to the rate of potential variation. Because of slow variation of potassium activation and sodium inactivation the dynamics of these processes is assumed to be of negligible effect in the region of impulse velocity formation. By means of pieace-wise linear approximation of thus obtained voltage-current characteristics the characteristics the analytical solution of the problem was found. In two limiting cases this solution coincides with the solutions of Kolmogorov and Scott. The dependence of impulse velocity on parameters is analyzed and illustrated graphically.