Finite volume modeling of neural communication: Exploring electrical signaling in biological systems

This article investigates neuronal dynamics in neuroscience, employing mathematical frameworks such as the Hodgkin Huxley model to describe them. Action potentials electrical signals generated by neurons are crucial for communication within the nervous system. The Hodgkin–Huxley model offers an anal...

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Main Authors: Muzammal Saleem, Muhammad Saqib, Badar Saad Alshammari, Shahid Hasnain, Amjad Ayesha
Format: Article
Language:English
Published: Elsevier 2025-03-01
Series:Partial Differential Equations in Applied Mathematics
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S2666818125000105
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author Muzammal Saleem
Muhammad Saqib
Badar Saad Alshammari
Shahid Hasnain
Amjad Ayesha
author_facet Muzammal Saleem
Muhammad Saqib
Badar Saad Alshammari
Shahid Hasnain
Amjad Ayesha
author_sort Muzammal Saleem
collection DOAJ
description This article investigates neuronal dynamics in neuroscience, employing mathematical frameworks such as the Hodgkin Huxley model to describe them. Action potentials electrical signals generated by neurons are crucial for communication within the nervous system. The Hodgkin–Huxley model offers an analytically representation of how neurons produce and propagate these action potentials by accounting for key factors, including membrane potential variations influenced by ion channel conductances. These ion channels regulate ion movement across cell membranes, which is essential for neuronal activity. The model has been widely applied to study phenomena such as neural network behavior and the impact of drugs on neuronal function. The proposed numerical approach, based on a hyperbolic tangent (tanh) function, is shown to be second-order accurate and unconditionally stable. Validation through comparison with existing literature and computational simulations demonstrates strong agreement between predicted outcomes and those generated by the model. The numerical method proves to be a reliable and precise tool for modeling the dynamics of physical systems, with potential applications in fields such as electromagnetism, acoustics, and fluid mechanics.
format Article
id doaj-art-5b6141f7459f499fa8c95c46d4e3e4fd
institution Kabale University
issn 2666-8181
language English
publishDate 2025-03-01
publisher Elsevier
record_format Article
series Partial Differential Equations in Applied Mathematics
spelling doaj-art-5b6141f7459f499fa8c95c46d4e3e4fd2025-01-19T06:26:47ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101082Finite volume modeling of neural communication: Exploring electrical signaling in biological systemsMuzammal Saleem0Muhammad Saqib1Badar Saad Alshammari2Shahid Hasnain3Amjad Ayesha4Institute of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, PakistanInstitute of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan; Corresponding author.Department of Mathematics, College of Science, Northern Border University, Arar, Saudi ArabiaDepartment of Mathematics, University of Chakwal, 48800, PakistanJoint Doctoral School, Silesian university of Technology, Gliwice, PolandThis article investigates neuronal dynamics in neuroscience, employing mathematical frameworks such as the Hodgkin Huxley model to describe them. Action potentials electrical signals generated by neurons are crucial for communication within the nervous system. The Hodgkin–Huxley model offers an analytically representation of how neurons produce and propagate these action potentials by accounting for key factors, including membrane potential variations influenced by ion channel conductances. These ion channels regulate ion movement across cell membranes, which is essential for neuronal activity. The model has been widely applied to study phenomena such as neural network behavior and the impact of drugs on neuronal function. The proposed numerical approach, based on a hyperbolic tangent (tanh) function, is shown to be second-order accurate and unconditionally stable. Validation through comparison with existing literature and computational simulations demonstrates strong agreement between predicted outcomes and those generated by the model. The numerical method proves to be a reliable and precise tool for modeling the dynamics of physical systems, with potential applications in fields such as electromagnetism, acoustics, and fluid mechanics.http://www.sciencedirect.com/science/article/pii/S2666818125000105Nonlinear biological modelTanh-coth methodFinite volume schemesStability analysisPhase plane analysis
spellingShingle Muzammal Saleem
Muhammad Saqib
Badar Saad Alshammari
Shahid Hasnain
Amjad Ayesha
Finite volume modeling of neural communication: Exploring electrical signaling in biological systems
Partial Differential Equations in Applied Mathematics
Nonlinear biological model
Tanh-coth method
Finite volume schemes
Stability analysis
Phase plane analysis
title Finite volume modeling of neural communication: Exploring electrical signaling in biological systems
title_full Finite volume modeling of neural communication: Exploring electrical signaling in biological systems
title_fullStr Finite volume modeling of neural communication: Exploring electrical signaling in biological systems
title_full_unstemmed Finite volume modeling of neural communication: Exploring electrical signaling in biological systems
title_short Finite volume modeling of neural communication: Exploring electrical signaling in biological systems
title_sort finite volume modeling of neural communication exploring electrical signaling in biological systems
topic Nonlinear biological model
Tanh-coth method
Finite volume schemes
Stability analysis
Phase plane analysis
url http://www.sciencedirect.com/science/article/pii/S2666818125000105
work_keys_str_mv AT muzammalsaleem finitevolumemodelingofneuralcommunicationexploringelectricalsignalinginbiologicalsystems
AT muhammadsaqib finitevolumemodelingofneuralcommunicationexploringelectricalsignalinginbiologicalsystems
AT badarsaadalshammari finitevolumemodelingofneuralcommunicationexploringelectricalsignalinginbiologicalsystems
AT shahidhasnain finitevolumemodelingofneuralcommunicationexploringelectricalsignalinginbiologicalsystems
AT amjadayesha finitevolumemodelingofneuralcommunicationexploringelectricalsignalinginbiologicalsystems