Speed of spread of excitation in the reduced Hodgkin-Huxley model-I. Rapid relaxation of the sodium current

The paper considers the problem of calculating the speed of spread of excitation in the Hodgkin-Huxley model on the assumption of rapid activation of the sodium current. In view of the slowness of the potassium activation and sodium inactivation it is considered that in the region influencing the formation of the speed of the pulse, the dynamics of these processes may be disregarded. Through a bit-linear approximation fo the voltage-current characteristic obtained the authors find an analytical solution of the problem passing at different limits into the Kolmogorov and Scott solutions. The dependence of the speed of the pulse on the parameters is analysed.