Fig 1.
Illustration of the Canonical Microcircuit Model (CMC) model.
Each source (V1, rV5 and lV5) comprises 4 neural subpopulations: spiny stellate cells (SS), superficial pyramidal cells (SP), deep pyramidal cells (DP) and inhibitory interneurons (II). Neural populations within a source are coupled with intrinsic connections (full arrows; bottom figure), while coupling between neural populations of different sources are extrinsic connections (dotted arrows). Red and blue arrows denote inhibitory and excitatory connections, respectively. The dynamics of the hidden (neuronal) states of each population can be described with the pairs of differential equations shown. There are four extrinsic connections: from SP to SS and DP (forward). Also, from DP to SP and II (backward). Intrinsic couplings are parametrized by G1,..,10. Three regions comprise the network that is assumed to generate observed cross-spectral densities: V1 and left and right V5. These are shown on the top right. Forward connections were specified from V1 to V5 while backward connections were specified from V5 to V1. σ(xi) is a sigmoidal activation function which transforms post-synaptic potential into average spiking output, with r a parameter controlling the steepness. Finally, the external input to a brain source is denoted with u and enters SS. The free parameters shown in the figure are also listed in Table 1.
Table 1.
Parameters of neural model (see Fig 1 for an illustration of the neural model).
Fig 2.
Results of the power spectral analysis.
Panel A shows the topographic plot of the mean power difference (Δ Power; power = Db/frequency)) at 10.6 Hz. The FDR-thresholded t-values of all Channels x Frequencies are shown in image format in panel B. The mean power spectrum and 0.95 standard error intervals about the mean over channels PO7, Oz, O2 and PO8 for EO and EC are plotted in panel C.
Fig 3.
The bar graph of the free energy (i.e., log evidence) differences from the full model (i.e. the model with extrinsic, V1 and V5 connectivity modulations) are shown for the 8 PEB models considered. The models were formed by creating combinations with or without the following three parameters sets: extrinsic modulations (Ext), V1 intrinsic modulations (V1) and V5 intrinsic modulations (V5). We observe that the full model has the highest (approximate) model evidence. In addition, models without V5 intrinsic modulation have smaller evidence compared to models that included V5 intrinsic modulation.
Fig 4.
Extrinsic connectivity modulations.
This figure shows the group-level results of the extrinsic connectivity modulations associated with EC states (relative to EO). More specifically, the mean posterior and 90% Bayesian confidence intervals (pink) after the greedy search algorithm and Bayesian model averaging are shown. Note that the estimated parameters are log-scale parameters (i.e., the parameters in the right column of Table 1 (θB), but here we used different x-axis labelling for clarity.). The right panel shows the posterior probabilities of the extrinsic connections. increase during EC. The backwards connections appear to increase as well, however, the evidence is not conclusive (Pp<0.95). The posterior probabilities (Pp) are 100%, 100%, 90% and 72% for V1 → lV5, V1 → rV5, lV5 → V1 and rV5 → V1, respectively.
Fig 5.
Intrinsic connectivity modulations.
The figure reports the group-level results of the intrinsic connectivity modulations associated with EC states (relative to EO) in the three sources of interest. More specifically, the mean posterior and 90% Bayesian confidence interval (pink error bars) after the greedy search algorithm and Bayesian model averaging are shown in the top row. The middle row shows the corresponding posterior probabilities of the intrinsic modulations, the pink dotted lines correspond to a Pp of .95. Finally, the bottom is a schematic presentation of the modulation with Pp>.95 and the direction of the effect. Inhibitory connections are shown in red and excitatory in blue.
Fig 6.
The results of the sensitivity analysis—averaged across subjects—are shown in image format. The group BMA results (i.e. the middle panels of Figs 4 and 5) are provided in the lower part for comparison. Simply put, positive (red) values indicate that an increase of a parameter at the posterior mean would result in increased power at that specific frequency bin. A negative value (in blue) means an increase of a particular parameter results in a decreased power. The arrows indicate the sensitivities for the significant intrinsic connectivity modulations that are shown in the lower part of the figure. is the Jacobian of the power spectrum of the generative model with respect to the model parameters of interest (intrinsic and extrinsic) which are shown for all modelled frequency bins.