Rosch Richard E, Scheid Brittany, Davis Kathryn A, Litt Brian, Ashourvan Arian
Departments of Pediatrics and Neurology, Columbia University Irving Medical Center, New York, NY, 10032, USA.
Department of Basic and Clinical Neuroscience, Institute of Psychiatry, Psychology and Neuroscience, King's College London, Cutcombe Road, London, SE5 9RT, UK.
Adv Sci (Weinh). 2025 Jun;12(23):e2411829. doi: 10.1002/advs.202411829. Epub 2025 Apr 7.
Many biological systems display circadian and slow multi-day rhythms, such as hormonal and cardiac cycles. In patients with epilepsy, these cycles also manifest as slow cyclical fluctuations in seizure propensity. However, such fluctuations in symptoms are consequences of the complex interactions between the underlying physiological, pathophysiological, and external causes. Therefore, identifying an accurate model of the underlying system that governs the multi-day rhythms allows for a more reliable seizure risk forecast and targeted interventions. The primary aim is to develop a personalized strategy for inferring long-term trajectories of epileptiform activity and, consequently, seizure risk for individual patients undergoing long-term ECoG sampling via implantable neurostimulation devices. To achieve this goal, the Hankel alternative view of Koopman (HAVOK) analysis is adopted to approximate a linear representation of nonlinear seizure propensity dynamics. The HAVOK framework leverages Koopman theory and delay-embedding to decompose chaotic dynamics into a linear system of leading delay-embedded coordinates driven by the low-energy coordinate (i.e., forcing). The findings reveal the topology of attractors underlying multi-day seizure cycles, showing that seizures tend to occur in regions of the manifold with strongly nonlinear dynamics. Moreover, it is demonstrated that the identified system driven by forcings with short periods up to a few days accurately predicts patients' slower multi-day rhythms, which improves seizure risk forecasting.
许多生物系统呈现出昼夜节律和持续数天的缓慢节律，如激素和心脏周期。在癫痫患者中，这些周期也表现为癫痫发作倾向的缓慢周期性波动。然而，症状的这种波动是潜在生理、病理生理和外部原因之间复杂相互作用的结果。因此，识别出控制多日节律的潜在系统的准确模型，有助于进行更可靠的癫痫发作风险预测和有针对性的干预。主要目标是制定一种个性化策略，用于推断癫痫样活动的长期轨迹，进而推断通过植入式神经刺激装置进行长期皮层脑电图（ECoG）采样的个体患者的癫痫发作风险。为实现这一目标，采用了基于柯普曼算子的汉克尔替代视图（HAVOK）分析来近似非线性癫痫发作倾向动力学的线性表示。HAVOK框架利用柯普曼理论和延迟嵌入，将混沌动力学分解为由低能量坐标（即强迫）驱动的领先延迟嵌入坐标的线性系统。研究结果揭示了多日癫痫发作周期背后吸引子的拓扑结构，表明癫痫发作倾向于发生在具有强非线性动力学的流形区域。此外，研究表明，由周期短至几天的强迫驱动的已识别系统能够准确预测患者较慢的多日节律，从而改善癫痫发作风险预测。
