Figure 2.

A, Model specification: the three DCMs used for Bayesian model comparison. Sources in each model receive endogenous neuronal fluctuations or innovations (modeled as a mixture of pink and white noise) that elicit neural responses characterized by a power spectrum that depends upon the model parameters. Random-effects Bayesian model selection showed that the model with a common thalamic source (Model 2) had the greatest evidence (with a 92% posterior probability). Model 2 was thus selected for subsequent quantitative analysis of effective connectivity changes across the three experimental conditions. B, Equations of motion describing neuronal interactions in thalamic, posterior cingulate, and anterior cingulate regions. These dynamics are based on a neural mass model that has been used extensively in the causal modeling of electromagnetic data (Jansen and Rit, 1995; David and Friston, 2003; David et al., 2005; Moran et al., 2008). It represents a minimal description of synaptic processing in multiple populations, in terms of synaptic convolution of presynaptic inputs and a nonlinear mapping between the resulting depolarization and firing rates. The kernels, from which we derive the transfer functions, obtain analytically from the Jacobian ℑ = ∂f/∂x describing the stability of motion ẋ = f(x,u,θ) of hidden neuronal states, x(t) and a mapping (forward model) s(x,θ : x→s that couples hidden states to the observed signals in PCC and ACC. Neuronal fluctuations or input are denoted by u(t). For region i, and input or innovation k, the kernel is:

The Jacobian is augmented by a matrix of inter-regional delays D, ℑ ← (I + Dℑ)⁻¹ℑ. The kernels are hence functions of the model's equations of motion and output mapping. The output here is determined largely by pyramidal cell activity (∼80%) in each cortical area. See Tables 1 and 2 in Moran et al. (2009) for the prior values of model parameters.