Köksal Ersöz Elif, Wendling Fabrice
Univ Rennes, INSERM, LTSI-U1099, Campus de Beaulieu, F - 35000, Rennes, France.
J Math Neurosci. 2021 Sep 16;11(1):11. doi: 10.1186/s13408-021-00109-z.
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.
多时空尺度的数学模型能够揭示大脑活动中临界转变的基本机制。神经质量模型（NMMs）考虑相互连接的神经元亚群的平均时间动态，而不明确表示潜在的细胞活动。神经质量公式提供的介观水平已被用于对脑电图（EEG）记录进行建模，并研究各种大脑机制，如生理和病理性大脑活动的产生。在这项工作中，我们考虑一种在癫痫背景下被广泛接受的神经质量模型，它包括四个具有不同突触动力学的相互作用神经元亚群。由于由此产生的三时间尺度结构，该模型产生了弛豫和爆发类型的复杂振荡。通过应用几何奇异摄动理论的原理，我们揭示了鸭解的存在，并详细说明了它们如何组织模型的复杂振荡和兴奋性特性。特别是，我们表明病理性癫痫放电和生理背景活动之间的边界由鸭解决定。最后，我们报告了在模拟局部场电位中，对于抑制降低的情况，存在由鸭介导的小幅度频率特异性振荡。有趣的是，在癫痫患者发作前期接近发作开始时记录的脑内EEG信号中实际观察到了这种振荡。
