Akademik Veri Yönetim Sistemi
Recent Progress in Science and Engineering, cilt.1, sa.2, ss.11, 2025 (Hakemli Dergi)
The spatial evolution of the epileptiform regime in neural networks can be alternatively described in terms of a statistical approach, dealing with average smooth, differentiable fields rather than discrete neural elements. After a brief review of mathematical methods for modeling epilepsy (the condensed matter vs. the neural mass models) together with their pros and cons, we introduce our continuous-space model for the pre-ictal scalar field and the ictal epileptiform vector flux in the form of the diffusion equation and Cattaneo’s equation, correspondingly. For the radially symmetric case, we derive the exact analytical solution that describes the spread of seizures at the mesoscopic level. Then we study the long-range asymptotes of our solution. To conclude, we discuss the possibility of controlling the epileptiform spatial evolution and briefly focus on the future development of the proposed model.
Modeling epilepsy; continuous-space approach; diffusion equation; Cattaneo’s law; mesoscopic spatial dynamics; analytical solution