Canard solutions in neural mass models: consequences on critical regimes - Laboratoire Traitement du Signal et de l'Image Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Neuroscience Année : 2021

Canard solutions in neural mass models: consequences on critical regimes

Résumé

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.
Fichier principal
Vignette du fichier
s13408-021-00109-z (3.41 Mo) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte

Dates et versions

hal-03366319 , version 1 (05-10-2021)

Licence

Paternité

Identifiants

Citer

Elif Köksal Ersöz, Fabrice Wendling. Canard solutions in neural mass models: consequences on critical regimes. Journal of Mathematical Neuroscience, 2021, 11 (1), pp.11. ⟨10.1186/s13408-021-00109-z⟩. ⟨hal-03366319⟩
18 Consultations
18 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More