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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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| 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 |