The discrete logic of the Brain - Explicit modelling of Brain State durations in EEG and MEG

We consider the detection and characterisation of brain state transitions, based on ongoing Magneto and Electroencephalography (M/EEG). Here a brain state represents a specific brain dynamical regime or mode of operation, which produces a characteristic quasi-stable pattern of activity at topography, sources or network levels. These states and their transitions over time can reflect fundamental computational properties of the brain, shaping human behaviour and brain function. The Hidden Markov Model (HMM) has emerged as a useful model-based approach for uncovering the hidden dynamics of brain state transitions based on observed data. However, the Geometric distribution of state duration (dwell time) implicit in HMM places highest probability on very short durations, which makes it inappropriate for the accurate modelling of brain states in M/EEG. We propose using Hidden Semi Markov Models (HSMM), a generalisation of HMM that models the brain state duration distribution explicitly. We present a Bayesian formulation of HSMM and use the Variational Bayes framework to efficiently estimate the HSMM parameters, the number of brain states and select among alternative brain state duration distributions. We assess HSMM performance against HMM on simulated data and demonstrate that the accurate modelling of state duration is paramount for accurately and robustly modelling non-Markovian EEG brain state features. Finally, we used actual resting-state EEG data to demonstrate the approach in practice and conclude that it provides a flexible parameterised framework that permits closer interrogation of possible generative mechanisms.