Traveling-wave solutions of a modified Hodgkin-Huxley type neural model via Novel analytical results for nonlinear transmission lines with arbitrary I(V) characteristics

Abstract

Herein an enhanced Hodgkin-Huxley (H-H) type model of neuron dynamics is solved analytically via formal methods. Our model is a variant of an earlier one by M.A. Mahrous and H.Y. Alkahby [1]. Their modified model is realized by a hyperbolic quasi-linear diffusion operator with time-delay parameters; this compared to the original H-H model with standard parabolic quasi-linear diffusion operator and no time-delay parameters. Besides these features, the present model also incorporates terms describing signal dissipation into the background substrate (e.g., conductance to ground), making it more experimentally amenable. The solutions which results via the present scheme are of traveling-wave profile, which agree qualitatively with those observed in actual electro-physiological measurements made on the neural systems originally studied by H-H These results confirm the physiological soundness of the enhanced model and of the preliminary assumptions which motivated the present solution strategy; the comparison of the present results with actual electro-physiological data displays shall appear in later publications.

Keywords

• Hodgkin-Huxley
• hyperbolic quasilinear diffusion operator
• non-linear transmission line
• analytical solution.