A Biologically Constrained, Mathematical Model of Cortical Wave Propagation Preceding Seizure Termination

Epilepsy—the condition of recurrent, unprovoked seizures—manifests in brain voltage activity with characteristic spatiotemporal patterns. These patterns include stereotyped semi-rhythmic activity produced by aggregate neuronal populations, and organized spatiotemporal phenomena, including waves. To assess these spatiotemporal patterns, we develop a mathematical model consistent with the observed neuronal population activity and determine analytically the parameter configurations that support traveling wave solutions. We then utilize high-density local field potential data recorded in vivo from human cortex preceding seizure termination from three patients to constrain the model parameters, and propose basic mechanisms that contribute to the observed traveling waves. We conclude that a relatively simple and abstract mathematical model consisting of localized interactions between excitatory cells with slow adaptation captures the quantitative features of wave propagation observed in the human local field potential preceding seizure termination.

癫痫是一类以反复发作、无明确诱因的痫性发作为特征的神经系统疾病，其脑电压活动呈现特征性的时空模式。这类模式包括神经元集群产生的刻板半节律性活动，以及包含波在内的有序时空现象。为了表征此类时空模式，本研究构建了与观测到的神经元集群活动相符的数学模型，并通过解析方法确定了支持行波（traveling wave）解的参数配置。随后，本研究利用3名患者癫痫发作终止前颅内皮层记录的高密度局部场电位（local field potential, LFP）数据对模型参数进行约束，并提出了与观测到的行波相关的核心机制。研究最终得出结论：仅包含兴奋性神经元间局部相互作用与慢适应过程的简约抽象数学模型，能够复现人类癫痫发作终止前局部场电位中观测到的行波传播定量特征。