Dynamic causal modelling for EEG and MEG

Abstract

Dynamic Causal Modelling (DCM) is an approach first introduced for the analysis of functional magnetic resonance imaging (fMRI) to quantify effective connectivity between brain areas. Recently, this framework has been extended and established in the magneto/encephalography (M/EEG) domain. DCM for M/EEG entails the inversion a full spatiotemporal model of evoked responses, over multiple conditions. This model rests on a biophysical and neurobiological generative model for electrophysiological data. A generative model is a prescription of how data are generated. The inversion of a DCM provides conditional densities on the model parameters and, indeed on the model itself. These densities enable one to answer key questions about the underlying system. A DCM comprises two parts; one part describes the dynamics within and among neuronal sources, and the second describes how source dynamics generate data in the sensors, using the lead-field. The parameters of this spatiotemporal model are estimated using a single (iterative) Bayesian procedure. In this paper, we will motivate and describe the current DCM framework. Two examples show how the approach can be applied to M/EEG experiments.

Fig. 1

Neuronal state-equations. A source consists of three neuronal subpopulations, which are connected by four intrinsic connections with weights γ _1,2,3,4. Mean firing rates (Eq. 3) from other sources arrive via forward A ^F, backward A ^B and lateral connections A ^L. Similarly, exogenous input Cu enters receiving sources. The output of each subpopulation is its trans-membrane potential (Eq. 2)

Fig. 2

Model specification. The sources comprising the network are connected with forward (dark grey), backward (grey) or lateral (light grey) connections as shown. A1: primary auditory cortex, STG: superior temporal gyrus, IFG: inferior temporal gyrus. Three different models were tested within the same architecture (a–c), allowing for learning-related changes in forward F, backward B and forward and backward FB connections, respectively. The broken lines indicate the connections we allowed to change. (d) Sources of activity, modelled as dipoles (estimated posterior moments and locations), are superimposed in an MRI of a standard brain in MNI space

Fig. 3

Bayesian model selection among DCMs for the three models, F, B and FB, expressed relative to a DCM in which no connections were allowed to change (null model). The graphs show the free energy approximation to the log-evidence. (a) Log-evidence for models F, B and FB for each subject (relative to the null model). The diamond attributed to each subject identifies the best model on the basis of the subject’s highest log-evidence. (b) Log-evidence at the group level, i.e., pooled over subjects, for the three models

Fig. 4

DCM results for a single subject [subject 9] (FB model). (a) Reconstructed responses for each source and changes in coupling during oddball processing relative to standards. The numbers next to each connection are the gain modulation in connection strength and the posterior probability that the modulation is different from one. The mismatch response is expressed in nearly every source. (b) Predicted (solid) and observed (broken) responses in measurement space, which result from a projection of the scalp data onto their first three spatial modes

Fig. 5

Coupling gains and their posterior probability estimated over subjects for each connection in the network for models F (a) and FB (b). There are widespread learning-related changes in all connections, expressed as modulations of coupling for deviants relative to standards

Fig. 6

Social (left) and isolated (right) parameter estimates from the steady-state LFP data analysis. The top panels illustrate the predicted and actual (dashed line) spectra. The bottom panels show the prior (in white) and posterior (in black) mean for each parameter. Parameters here are see also Fig. 7

Fig. 7

Results of steady-state LFP data analysis. The left panel shows the connection parameters of the different cell groups within the modelled source. Parameters were inferred with inhibitory connectivity (and impulse response) prior parameter variances set to zero. The mean estimates of the connectivity’s γ ₁, γ ₂, γ ₃ are shown with the associated p-values. The right panels display the expected excitatory impulse response functions and sigmoid firing functions for both groups. These are constructed using the maximum a posteriori (MAP) estimates of the excitatory synaptic kernel amplitude and time-constant (H _e, τ _e) in the former and the MAP estimate of ρ ₂ in the latter. The control group estimates are shown in blue and the isolated animals in red, with p-values in parentheses. Note that for steady-state models, we have added an inhibitory–inhibitory connection (γ ₅), which is not used for the evoked response models