A switching multi-scale dynamical network model of EEG/MEG Iván Olier a , Nelson J. Trujillo-Barreto b, ⁎, Wael El-Deredy a a School of Psychological Sciences, University of Manchester, Manchester, United Kingdom b Cuban Neuroscience Center, Havana, Cuba abstract article info Article history: Accepted 9 April 2013 Available online 21 April 2013 Keywords: Source localisation Inverse problem Electromagnetic tomography State-space models Variational Bayes Clustering Dynamical Causal Models Negative Free Energy 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 pro- posed 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 interpre- tation 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. © 2013 Elsevier Inc. All rights reserved. Introduction The most straightforward manifestations of neuronal activations and their interactions at the macroscopic level are primarily of elec- tromagnetic origin and can be recorded in the form of Electroenceph- alography (EEG) or Magnetoencephalography (MEG) signals with a resolution of milliseconds. It is well established that EEG and MEG are due to the local macroscopic average of intra and extracellular ionic currents produced by the postsynaptic activity of masses of neu- rons synchronised in time and space. Nevertheless, uniquely inferring the underlying source activity given the encephalographic data (the so called EEG/MEG Inverse Problem) is not possible unless prior infor- mation or constraints about the physiologically meaningful solutions is considered. The available methods to solve this inverse problem include Dipolar Solutions (DS) (Korvenoja and Aronen, 2001; Korvenoja et al., 1999; Scherg and Von Cramon, 1985; Wagner et al., 2000), Distrib- uted Linear Solutions (DLS) (Dale and Sereno, 1993; Hämäläinen and Ilmoniemi, 1994) as well as more flexible approaches which cast DS and DLS methods into a common framework (Daunizeau et al., 2006). Importantly, additional constraints are usually necessary to assure uniqueness and stability of the inverse solution, which include purely spatial constraints (Bosch-Bayard et al., 2001; Dale and Sereno, 1993; Friston et al., 2008; Fuchs et al., 1999; Hämäläinen and Ilmoniemi, 1994; Pascual-Marqui et al., 1994; Trujillo-Barreto et al., 2004; Vega-Hernández et al., 2008; Wipf and Nagarajan, 2009), as well as spatio-temporal (ST) constraints (Baillet and Garnero, 1997; Daunizeau et al., 2006; Ou et al., 2009; Phillips et al., 2002; Trujillo-Barreto et al., 2008; Valdés-Sosa et al., 2009; Zumer et al., 2008). These methods have allowed us to address questions about where and when EEG/MEG-related neuronal events occur in the brain, with reasonable accuracy. Nevertheless, it has been argued that it is not NeuroImage 83 (2013) 262–287 ⁎ Corresponding author at: Cuban Neuroscience Centre, Ave 25, Esq. 158, No. 15202, Cubanacán, Playa, La Habana, Cuba. Fax: +53 7 2086707. E-mail address: trujillo@cneuro.edu.cu (N.J. Trujillo-Barreto). 1053-8119/$ – see front matter © 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.neuroimage.2013.04.046 Contents lists available at ScienceDirect NeuroImage journal homepage: www.elsevier.com/locate/ynimg