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. 2014 Nov 1;101:796–808. doi: 10.1016/j.neuroimage.2014.06.062

Fig. 2.

Fig. 2

This schematic illustrates the state-space or dynamic causal model that we used to generate expected cross spectra and simulated data. Left panel: this shows the differential equations governing the evolution of depolarisation in four populations constituting a single electromagnetic source (of EEG, MEG or LFP measurements). These equations are expressed in terms of second-order differential equations that can be rewritten as pairs of first order equations, which describe postsynaptic currents and depolarisation in each population. These populations are divided into input cells in granular layers of the cortex, inhibitory interneurons and (superficial and deep) principal or pyramidal cell populations that constitute the output populations. The equations of motion are based upon standard convolution models for synaptic transformations, while coupling among populations is mediated by a sigmoid function of (delayed) mean depolarisation. The slope of the sigmoid function corresponds to the intrinsic gain of each population. Intrinsic (within-source) connections couple the different populations, while extrinsic (between-source) connections couple populations from different sources. The extrinsic influences (not shown) enter the equations in the same way as the intrinsic influences but in a laminar specific fashion (as shown in the right panel). Right panel: this shows the simple two source architecture used in the current paper. This comprises one lower source that sends forward connections to a higher source (but does not receive reciprocal backward connections). The intrinsic connectivity (dotted lines) and extrinsic connectivity (solid line) conform to the connectivity of the canonical microcircuit and the known laminar specificity of extrinsic connections (Bastos et al., 2012). Excitatory connections are in red and inhibitory connections are in black. Random fluctuations drive the input cells and measurements are based on the depolarisation of superficial pyramidal cells. See Table 2 for a list of key parameters and a brief description.