Canard solutions in neural mass models: consequences on critical regimes.

IF 2.3 4区 医学 Q1 Neuroscience
Elif Köksal Ersöz, Fabrice Wendling
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引用次数: 2

Abstract

Mathematical models at multiple temporal and spatial scales can unveil the fundamental mechanisms of critical transitions in brain activities. Neural mass models (NMMs) consider the average temporal dynamics of interconnected neuronal subpopulations without explicitly representing the underlying cellular activity. The mesoscopic level offered by the neural mass formulation has been used to model electroencephalographic (EEG) recordings and to investigate various cerebral mechanisms, such as the generation of physiological and pathological brain activities. In this work, we consider a NMM widely accepted in the context of epilepsy, which includes four interacting neuronal subpopulations with different synaptic kinetics. Due to the resulting three-time-scale structure, the model yields complex oscillations of relaxation and bursting types. By applying the principles of geometric singular perturbation theory, we unveil the existence of the canard solutions and detail how they organize the complex oscillations and excitability properties of the model. In particular, we show that boundaries between pathological epileptic discharges and physiological background activity are determined by the canard solutions. Finally we report the existence of canard-mediated small-amplitude frequency-specific oscillations in simulated local field potentials for decreased inhibition conditions. Interestingly, such oscillations are actually observed in intracerebral EEG signals recorded in epileptic patients during pre-ictal periods, close to seizure onsets.

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神经质量模型中的鸭式解:临界状态的后果。
在多个时间和空间尺度上的数学模型可以揭示大脑活动关键转变的基本机制。神经质量模型(nmm)考虑相互连接的神经元亚群的平均时间动态,而没有明确表示潜在的细胞活动。神经团的形成所提供的介观水平已被用于模拟脑电图(EEG)记录,并研究各种大脑机制,如生理和病理脑活动的产生。在这项工作中,我们考虑了在癫痫背景下广泛接受的NMM,其中包括四个相互作用的神经元亚群,它们具有不同的突触动力学。由于所产生的三时间尺度结构,该模型产生了松弛型和破裂型的复杂振荡。利用几何奇异摄动理论的原理,揭示了鸭尔德解的存在性,并详细说明了鸭尔德解如何组织模型的复振荡和可激性。特别是,我们表明病理性癫痫放电和生理背景活动之间的界限是由鸭式溶液决定的。最后,我们报告了鸭翼介导的小幅度频率特异性振荡在抑制条件下降的模拟局部场电位中存在。有趣的是,这种振荡实际上是在癫痫患者在癫痫发作前的脑电图信号中观察到的。
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来源期刊
Journal of Mathematical Neuroscience
Journal of Mathematical Neuroscience Neuroscience-Neuroscience (miscellaneous)
自引率
0.00%
发文量
0
审稿时长
13 weeks
期刊介绍: The Journal of Mathematical Neuroscience (JMN) publishes research articles on the mathematical modeling and analysis of all areas of neuroscience, i.e., the study of the nervous system and its dysfunctions. The focus is on using mathematics as the primary tool for elucidating the fundamental mechanisms responsible for experimentally observed behaviours in neuroscience at all relevant scales, from the molecular world to that of cognition. The aim is to publish work that uses advanced mathematical techniques to illuminate these questions. It publishes full length original papers, rapid communications and review articles. Papers that combine theoretical results supported by convincing numerical experiments are especially encouraged. Papers that introduce and help develop those new pieces of mathematical theory which are likely to be relevant to future studies of the nervous system in general and the human brain in particular are also welcome.
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