Global dynamics of neural mass models.

Area of Science:

• Computational neuroscience
• Theoretical neuroscience
• Mathematical modeling of brain dynamics

Background:

• Neural mass models simulate cortical activity and explain electroencephalography (EEG) and magnetoencephalography (MEG) data.
• These models exhibit complex dynamics, including bifurcations and transitions, crucial for describing brain activity itinerancy.
• Fitting complex neural mass models to empirical data is challenging, often requiring simplifying assumptions like linear perturbations around fixed points.

Purpose of the Study:

• To provide a mathematical analysis of neural mass models, specifically the canonical microcircuit model.
• To derive analytical solutions for slow changes in cortical activity (dynamical itinerancy).
• To enable model inversion beyond fixed points, encompassing transitions between semi-stable or multi-stable states.

Main Methods:

• Mathematical analysis of the canonical microcircuit model.
• Derivation of a second-order perturbation analysis of the phase flow.
• Application of adiabatic approximations to describe amplitude modulations.

Main Results:

• Analytical solutions describing dynamical itinerancy in neural mass models.
• Proof-of-principle for semi-stable states in cortical dynamics at the column scale.
• A framework for model inversion across regions of phase space, including transitions between oscillatory states.

Conclusions:

• The developed mathematical framework allows for more accurate model inversion of neural mass models.
• This approach is applicable to understanding transitions between multiple semi-stable brain states, such as those observed in epilepsy (interictal, pre-ictal, ictal).
• The findings advance the ability to model and interpret complex, dynamic brain activity from empirical measurements.