This paper explores the internal dynamical mechanisms of epileptic seizures through quantitative modeling based on full brain electroencephalogram (EEG) signals. Our goal is to provide seizure prediction and facilitate treatment for epileptic patients. Motivated by an earlier mathematical model with incorporated synaptic plasticity, we studied the nonlinear dynamics of inherited seizures through a differential equation model. First, driven by a set of clinical inherited electroencephalogram data recorded from a patient with diagnosed Glucose Transporter Deficiency, we developed a dynamic seizure model on a system of ordinary differential equations. The model was reduced in complexity after considering and removing redundancy of each EEG channel. Then we verified that the proposed model produces qualitatively relevant behavior which matches the basic experimental observations of inherited seizure, including synchronization index and frequency. Meanwhile, the rationality of the connectivity structure hypothesis in the modeling process was verified. Further, through varying the threshold condition and excitation strength of synaptic plasticity, we elucidated the effect of synaptic plasticity to our seizure model. Results suggest that synaptic plasticity has great effect on the duration of seizure activities, which support the plausibility of therapeutic interventions for seizure control.

本文通过基于全脑脑电图（EEG）信号的定量建模探索了癫痫发作的内部动力学机制。我们的目标是提供癫痫发作预测并促进癫痫患者的治疗。受具有合并突触可塑性的早期数学模型的启发，我们通过微分方程模型研究了遗传性癫痫发作的非线性动力学。首先，根据从诊断为葡萄糖转运蛋白缺乏症患者记录的一组临床遗传脑电图数据，我们在常微分方程组上建立了动态​​癫痫发作模型。在考虑并消除了每个EEG通道的冗余之后，该模型的复杂性降低了。然后我们验证了该模型产生的定性相关行为与遗传性癫痫发作的基本实验观察结果相符，包括同步指数和频率。同时，验证了建模过程中连通性结构假说的合理性。此外，通过改变阈值条件和突触可塑性的激发强度，我们阐明了突触可塑性对癫痫发作模型的影响。结果表明，突触可塑性对癫痫发作的持续时间有很大影响，这支持了控制癫痫发作的治疗干预措施的合理性。此外，通过改变阈值条件和突触可塑性的激发强度，我们阐明了突触可塑性对癫痫发作模型的影响。结果表明，突触可塑性对癫痫发作的持续时间有很大影响，这支持了控制癫痫发作的治疗干预措施的合理性。此外，通过改变阈值条件和突触可塑性的激发强度，我们阐明了突触可塑性对癫痫发作模型的影响。结果表明，突触可塑性对癫痫发作的持续时间有很大影响，这支持了控制癫痫发作的治疗干预措施的合理性。