Different Epileptiform Regimes in the Neural Population Modelled by the Generalized Telegraph Equation
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Keywords:
Neural Population, Epileptiform Behavior, Cattaneo Equation, Factorization Procedure, Traveling WavesAbstract
The field-type approach to the neural cortical activities serves as a good alternative to the
ANN-type models. It represents different states of the spiking and bursting neurons as a continuous field
with a certain initial spatial distribution. The evolution of the neural populations is described with the
generalized telegraph partial differential equations. In this paper, we use the Cattaneo generalization of
Fick’s model to describe the evolution of the epileptiform behavior in the small- and middle-scale neural
clusters. We study the factorization procedure for the generalized telegraph equation and investigate the
exact particular solutions to different dynamical regimes, which depend on the separation constant
playing the role of a control parameter in our model. Additionally, we derive the traveling wave solutions
and discuss briefly their properties.
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References
Yakar, M., Yılmaz, H. M., & Mutluoglu, O. (2014). Performance of photogrammetric and terrestrial laser scanning methods in volume computing of excavation and filling areas. Arabian Journal for Science and Engineering, 39, 387-394.
Alptekin, A., & Yakar, M. (2020). Determination of pond volume with using an unmanned aerial vehicle. Mersin Photogrammetry Journal, 2(2), 59-63.
Karataş, L., Alptekin, A., & Yakar, M. (2022). Mardin historical Kuyumcular (Jewelers) Bazaar restoration evaluation. Advanced Engineering Days (AED), 5, 15-17.
Maune, D. F. (2001). Digital elevation model technologies and applications: The DEM user manual. The American Society for Photogrammetry and Remote Sensing. ISBN:1-57083-064-9
Kim, J. W., Roberts, J. A., & Robinson, P. A. (2009). Dynamics of epileptic seizures: evolution, spreading, and suppression. Journal of Theoretical Biology, 257(4), 527-532.
Depannemaecker, D., Destexhe, A., Jirsa, V., & Bernard, C. (2021). Modeling seizures: From single neurons to networks. Seizure, 90, 4-8.
Depannemaecker, D., Ezzati, A., Wang, H. E., Jirsa, V., & Bernard, C. (2023). From phenomenological to biophysical models of seizures. Neurobiology of Disease, 182, 106131.
Stefanescu, R. A., Shivakeshavan, R. G., & Talathi, S. S. (2012). Computational models of epilepsy. Seizure, 21(10), 748-759.
Sanz, C. M. Navarro, M. M., Diaz, D. C., Sanchez-Elexpuru, G., & Di Donato, V. (2023). Toward the use of novel alternative methods in epilepsy modeling and drug discovery. Frontiers in Neurology, 14, 1213969.
Ohmori, I., Ouchida, M., Shinohara, M., Kobayashi, K., Ishida, S., & Mashimo, T. (2022). Novel animal model of combined generalized and focal epilepsy. Epilepsia, 63, e80-e85.
Cattaneo, C. (1948) Sulla conduzione del calore. Attidel Seminario Matematico e Fisicodella Università di Modena, 3, 83-101.
Ahmed, E. (2018). Some simple mathematical models in epilepsy. Current Trends in Biostatistics and Biometrics, 1(2), 48.
Abdusalam, H. A., & Fahmy, E. S. (2009). Exact solution for the generalized Telegraph Fisher’s equation. Chaos, Solitons and Fractals, 41, 1550-1556.
Fick, A. (1855). On liquid diffusion. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 10(63), 30-39.
Guzmán-Lastra, F., Löwen, H., & Mathijssen, A. J. T. M. (2021). Active carpets drive non-equilibrium diffusion and enhanced molecular fluxes. Nature Communications, 12, 1906.
Sohanian Haghighi, H., Markazi, A. H. D. (2017).A new description of epileptic seizures based on dynamic analysis of a thalamocortical model. Scientific Reports, 7, 13615.
