Canard solutions in neural mass models: consequences on critical regimes

Area of Science:

• Computational neuroscience
• Mathematical biology
• Epilepsy research

Background:

• Neural mass models (NMMs) simulate average neuronal population dynamics at a mesoscopic level.
• NMMs are used to model electroencephalographic (EEG) recordings and study brain activity, including physiological and pathological states.
• Understanding critical transitions in brain activity is key to deciphering neurological disorders.

Purpose of the Study:

• To investigate a specific four-subpopulation Neural Mass Model (NMM) with complex dynamics relevant to epilepsy.
• To apply geometric singular perturbation theory to understand the model's oscillations and excitability.
• To identify the role of canard solutions in organizing brain activity and distinguishing between normal and pathological states.

Main Methods:

• Utilized a well-established NMM with four interacting neuronal subpopulations and distinct synaptic kinetics.
• Employed geometric singular perturbation theory to analyze the model's three-time-scale structure.
• Investigated the emergence and organization of complex oscillations, including relaxation and bursting types.

Main Results:

• Unveiled the existence and organizing role of canard solutions within the NMM.
• Demonstrated that canard solutions define the boundaries between physiological brain activity and pathological epileptic discharges.
• Identified canard-mediated, frequency-specific oscillations in simulated local field potentials under reduced inhibition, mirroring pre-ictal signals in epilepsy patients.

Conclusions:

• Canard solutions are crucial for understanding the complex dynamics of the studied NMM, particularly in the context of epilepsy.
• The findings provide a theoretical framework for the observed pre-ictal oscillations in epileptic patients.
• This research highlights the utility of mathematical modeling and perturbation theory in neuroscience and epilepsy research.