Computational methods for a mathematical model of propagation of nerve impulses in myelinated axons

Lima, Pedro M.; Ford, Neville J.; Lumb, Patricia M.

doi:10.1016/j.apnum.2014.06.004

Cited by 12 publications

(4 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such functions determine computational characteristics of the required action of the receptors by the sent impulses [21]. Such plots also represent the experimental verification of the stimulated response as nerve impulses in the form of electric charges that owns a definite propagating potential and computational biological parameters [22].…”

Section: Proper Nature Of the Nerve Impulsesmentioning

confidence: 99%

Proper Understanding of the Nerve Impulses and the Action Potential

Abdelhady¹

2023

WJNS

View full text Add to dashboard Cite

Neurologists define the transmission of nerve impulses across the membranes of the neural cells as a result of difference in the concentration of ions while they measured an electric potential, called as an action potential, which allows the propagation of such nerve impulses as electrical signals. Such measurements should guide them to a logical explanation of the nerve impulses as electric charges driven by the measured action potential. However, such logical conclusion, or explanation, is ignored due to a wrong definition of the flow of electric charges as a flow of electrons that cannot pass through neural networks. According to recent studies, electric charges are properly defined as electromagnetic (EM) waves whose energy is expressed as the product of its propagating electric potential times their entropy flow which is adhered to the flow of such energy. Such definition matches the logical conclusion of the nerve impulses as electric charges, as previously explained, and defines the entropy of the neural network, measured by Ammeters, in Watt or Joule/Volt. The measured entropy represents a neurodiagnostic property of the neural networks that measures its capacity to allow the flow of energy per unit action potential. Theoretical verification of the innovative definition of nerve impulses is presented by following an advanced entropy approach. A proper review of the machine records of the stimulating electric charges, used in the diagnosis of the neural networks, and the stimulated nerve impulses or stimulated responses, represents practical verifications of the innovative definitions of the electric charges and the nerve impulses. Comparing the functioning of the thermoelectric generators and the brain neurons, such neurons are defined as thermoelectric generators of the electric nerve impulses and their propagating, or action, potential.

show abstract

Section: Proper Nature Of the Nerve Impulsesmentioning

confidence: 99%

Proper Understanding of the Nerve Impulses and the Action Potential

Abdelhady¹

2023

WJNS

View full text Add to dashboard Cite

show abstract

“…Differential equations with fractional derivatives are used for modeling non-Markovian processes in various areas of science such as Physics, Biology and Economics [1][2][3][4][5]. The methods for analytical solution of ordinary and partial fractional differential equations can be applied to only special types of equations and initial conditions.…”

Section: Introductionmentioning

confidence: 99%

A New Method for Numerical Solution of the Fractional Relaxation and Subdiffusion Equations Using Fractional Taylor Polynomials

Dimitrov

2015

Preprint

View full text Add to dashboard Cite

The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional differential equations often have a singularity at the initial point, which may result in a lower accuracy of the numerical solutions. We propose a method for improving the accuracy of the numerical solutions of the fractional relaxation and subdiffusion equations based on the fractional Taylor polynomials of the solution at the initial point.

show abstract

“…Fractional calculus is a rapidly growing field of science. Differential equations with the Caputo and Riemann-Liouville fractional derivatives are used for modeling processes in economics, physics and engineering [6,26,37,40,43]. The Caputo fractional derivative and the fractional integral of arbitrary order are defined as a convolution of the derivatives of the function and the power function.…”

Section: Introductionmentioning

confidence: 99%