Modeling Epileptic Seizure: An Alternative Perspective Through Integral Equation Reformulation

Epileptic seizures, characterized by abnormal electrical activity in the brain, pose a significant challenge for diagnosis and treatment. Electroencephalography (EEG), measuring the brain's electrical activity, plays a crucial role in understanding these events. However, analysing epileptic EEG signals, often resembling a complex storm of electrical activity, can be challenging. Usually, these signals have been modelled using integral equations, but the limitations remain in capturing the full dynamics of seizures. This study proposes a novel approach to analysing EEG data during epileptic seizures by reformulating the integral equation. Instead of viewing the chaotic patterns as mere noise, the study proposes an alternative perspective that delves deeper into the underlying structure. By reformulating the integral equation, it is aimed at to capturing not just the individual components of the electrical activity but also the intricate relationships between them, potentially revealing hidden patterns and dynamics associated with epileptic seizures. This new approach holds the potential for a deeper understanding of seizure mechanisms. By uncovering the hidden order amidst the seemingly chaotic EEG signals, we might gain valuable insights into the brain's behaviour during seizures. This understanding could pave the way for enhanced diagnostics, more effective treatment strategies, and ultimately, better outcomes for patients suffering from epilepsy. Keywords: Epileptic seizures, EEG signals, Integral Equation, convolution equation.