Author(s)

N. G. Gulko¹, I. T. Selezov²

¹Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
²Institute of Hydromechanics, NAS of Ukraine, Kiev, Ukraine.

The problem of excitation and the propagation of a nerve impulse by an axon (nerve fiber) for the case of a noninstantaneous function is studied. The application of no instantaneous step function of the Heaviside type takes into account the time of delay. This generalizes the problem of the propagation of axon excitation to the case of an input impulse function’s noninstantaneous action with some increasing excitation. An exact analytical solution to the problem is constructed based on the Laplace integral transform and Ephros theorem. The propagation of the transmembrane potential was studied, in response to the switching on and off, for impulse of a constant current pulse delivered intracellularly at different points in time. The time analysis of excitation propagation along axon at different distances from the excitation point was performed.

Noninstantaneous, Excitation, Heaviside Function, Transmembrane Potential, Ephros Theorem, Laplace Transform

Gulko, N. and Selezov, I. (2021) How Does the Slow Injection of a Medicine under the Influence of a Magnetic Field Affects the Spreading of Medical Substances. Journal of Applied Mathematics and Physics, 9, 3115-3121. doi: 10.4236/jamp.2021.912203.