Dynamical causal modelling for M/EEG: spatial and temporal symmetry constraints.

We describe the use of spatial and temporal constraints in dynamic causal modelling (DCM) of magneto- and electroencephalography (M/EEG) data. DCM for M/EEG is based on a spatiotemporal, generative model of electromagnetic brain activity. The temporal dynamics are described by neural-mass models of equivalent current dipole (ECD) sources and their spatial expression is modelled by parameterized lead-field functions. Often, in classical ECD models, symmetry constraints are used to model homologous pairs of dipoles in both hemispheres. These constraints are motivated by assumptions about symmetric activation of bilateral sensory sources. In classical approaches, these constraints are 'hard'; i.e. the parameters of homologous dipoles are shared. Here, in the context of DCM, we illustrate the use of informed Bayesian priors to implement 'soft' symmetry constraints that are expressed in the posterior estimates only when supported by the data. Critically, with DCM one can deploy symmetry constraints in either the temporal or spatial components of the model. This enables one to test for symmetry in temporal (neural-mass) parameters in the presence of non-symmetric spatial expressions of homologous sources (and vice versa). Furthermore, we demonstrate that Bayesian model comparison can be used to identify the best models among a range of symmetric and non-symmetric variants. Our main finding is that the use of 'soft' symmetry priors is recommended for evoked responses to bilateral sensory input. We illustrate the use of symmetry constraints in DCM on synthetic and real EEG data.