A switching multi-scale dynamical network model of EEG/MEG

Abstract

We introduce a new generative model of the Encephalography (EEG/MEG) data, the inversion of which allows for inferring the locations and temporal evolution of the underlying sources as well as their dynamical interactions. The proposed Switching Mesostate Space Model (SMSM) builds on the multi-scale generative model for EEG/MEG by Daunizeau and Friston (2007). SMSM inherits the assumptions that (1) bioelectromagnetic activity is generated by a set of distributed sources, (2) the dynamics of these sources can be modelled as random fluctuations about a small number of mesostates, and (3) the number of mesostates engaged by a cognitive task is small. Additionally, four generalising assumptions are now included: (4) the mesostates interact according to a full Dynamical Causal Network (DCN) that can be estimated; (5) the dynamics of the mesostates can switch between multiple approximately linear operating regimes; (6) each operating regime remains stable over finite periods of time (temporal clusters); and (7) the total number of times the mesostates' dynamics can switch is small. The proposed model adds, therefore, a level of flexibility by accommodating complex brain processes that cannot be characterised by purely linear and stationary Gaussian dynamics. Importantly, the SMSM furnishes a new interpretation of the EEG/MEG data in which the source activity may have multiple discrete modes of behaviour, each with approximately linear dynamics. This is modelled by assuming that the connection strengths of the underlying mesoscopic DCN are time-dependent but piecewise constant, i.e. they can undergo discrete changes over time. A Variational Bayes inversion scheme is derived to estimate all the parameters of the model by maximising a (Negative Free Energy) lower bound on the model evidence. This bound is used to select among different model choices that are defined by the number of mesostates as well as by the number of stationary linear regimes. The full model is compared to a simplified version that uses no dynamical assumptions as well as to a standard EEG inversion technique. The comparison is carried out using an extensive set of simulations, and the application of SMSM to a real data set is also demonstrated. Our results show that for experimental situations in which we have some a priori belief that there are multiple approximately linear dynamical regimes, the proposed SMSM provides a natural modelling tool.