人类和实验动物模型中记录的大多数癫痫发作可以通过通用现象学数学模型来描述,癫痫.在这个模型中,癫痫发作样事件(SLE)由缓慢变量驱动,并在癫痫发作开始和偏移时通过鞍状节点(SN)和同临床分叉发生,分别。在这里,我们使用生物物理相关的神经元模型研究了单细胞水平的SLE,该模型包括四个方程式的慢/快系统。慢速子系统的两个方程描述了离子浓度变化,而快速子系统的两个方程描述了神经元的电生理活动。使用细胞外K+作为慢变量,我们报告说,当细胞外K达到临界值时,具有SN/同斜分支的SLE很容易在单细胞水平上发生。在患者和实验模型中,癫痫发作也可以演变成持续发作性活动(SIA)和去极化阻滞(DB),这些活动也是Epileptor动态曲目的一部分。将模型中的细胞外K浓度增加到实验癫痫持续状态和DB期间发现的值,我们表明SIA和DB也可以发生在单个单元级别。因此,癫痫发作,SIA,DB,最初被确定为网络事件,可以在单个神经元水平上存在于生物物理模型的统一框架中,并表现出与在Epileeptor中观察到的相似的动力学。作者摘要:癫痫是一种以癫痫发作为特征的神经系统疾病。使用电生理记录在宏观和微观尺度的实验模型中对患者的癫痫发作进行了表征。实验工作允许建立详细的缉获分类法,这可以用数学模型来描述。我们可以区分两种主要类型的模型。现象学(通用)模型的参数和变量很少,并且可以进行详细的动力学研究,通常可以捕获在实验条件下观察到的大多数活动。但它们也有抽象的参数,使生物学解释变得困难。生物物理模型,另一方面,使用大量的变量和参数,因为它们所代表的生物系统的复杂性。因为解的多重性,很难提取一般的动力学规则。在目前的工作中,我们整合了这两种方法,并将详细的生物物理模型简化为足够的低维方程,从而保持了通用模型的优势。我们提议,在单细胞水平,不同病理活动的统一框架是癫痫发作,去极化块,和持续的ictal活动。
The majority of seizures recorded in humans and experimental animal models can be described by a generic phenomenological mathematical model, the Epileptor. In this model, seizure-like events (SLEs) are driven by a slow variable and occur via saddle node (SN) and homoclinic bifurcations at seizure onset and offset, respectively. Here we investigated SLEs at the single cell level using a biophysically relevant neuron model including a slow/fast system of four equations. The two equations for the slow subsystem describe ion concentration variations and the two equations of the fast subsystem delineate the electrophysiological activities of the neuron. Using extracellular K+ as a slow variable, we report that SLEs with SN/homoclinic bifurcations can readily occur at the single cell level when extracellular K+ reaches a critical value. In patients and experimental models, seizures can also evolve into sustained ictal activity (SIA) and depolarization block (DB), activities which are also parts of the dynamic repertoire of the Epileptor. Increasing extracellular concentration of K+ in the model to values found during experimental status epilepticus and DB, we show that SIA and DB can also occur at the single cell level. Thus, seizures, SIA, and DB, which have been first identified as network events, can exist in a unified framework of a biophysical model at the single neuron level and exhibit similar dynamics as observed in the Epileptor.Author Summary: Epilepsy is a neurological disorder characterized by the occurrence of seizures. Seizures have been characterized in patients in experimental models at both macroscopic and microscopic scales using electrophysiological recordings. Experimental works allowed the establishment of a detailed taxonomy of seizures, which can be described by mathematical models. We can distinguish two main types of models. Phenomenological (generic) models have few parameters and variables and permit detailed dynamical studies often capturing a majority of activities observed in experimental conditions. But they also have abstract parameters, making biological interpretation difficult. Biophysical models, on the other hand, use a large number of variables and parameters due to the complexity of the biological systems they represent. Because of the multiplicity of solutions, it is difficult to extract general dynamical rules. In the present work, we integrate both approaches and reduce a detailed biophysical model to sufficiently low-dimensional equations, and thus maintaining the advantages of a generic model. We propose, at the single cell level, a unified framework of different pathological activities that are seizures, depolarization block, and sustained ictal activity.