Electronic Journal of Differential Equations,
Conference 02 (1999), pp. 133-136.

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


Author: Valentino Anthony Simpao (Math. Consultant Services, Greenville, KY, USA)

 
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.


Published January 21, 2000.
Math Subject Classifications: 35L70, 92C20, 35K57.
Key Words: Hodgkin-Huxley; hyperbolic quasilinear diffusion operator; 
 non-linear transmission line; analytical solution.