Nonlinear dynamic causal models for fMRI

Abstract

Models of effective connectivity characterize the influence that neuronal populations exert over each other. Additionally, some approaches, for example Dynamic Causal Modelling (DCM) and variants of Structural Equation Modelling, describe how effective connectivity is modulated by experimental manipulations. Mathematically, both are based on bilinear equations, where the bilinear term models the effect of experimental manipulations on neuronal interactions. The bilinear framework, however, precludes an important aspect of neuronal interactions that has been established with invasive electrophysiological recording studies; i.e., how the connection between two neuronal units is enabled or gated by activity in other units. These gating processes are critical for controlling the gain of neuronal populations and are mediated through interactions between synaptic inputs (e.g. by means of voltage-sensitive ion channels). They represent a key mechanism for various neurobiological processes, including top-down (e.g. attentional) modulation, learning and neuromodulation. This paper presents a nonlinear extension of DCM that models such processes (to second order) at the neuronal population level. In this way, the modulation of network interactions can be assigned to an explicit neuronal population. We present simulations and empirical results that demonstrate the validity and usefulness of this model. Analyses of synthetic data showed that nonlinear and bilinear mechanisms can be distinguished by our extended DCM. When applying the model to empirical fMRI data from a blocked attention to motion paradigm, we found that attentioninduced increases in V5 responses could be best explained as a gating of the V1→V5 connection by activity in posterior parietal cortex. Furthermore, we analysed fMRI data from an event-related binocular rivalry paradigm and found that interactions amongst percept-selective visual areas were modulated by activity in the middle frontal gyrus. In both practical examples, Bayesian model selection favoured the nonlinear models over corresponding bilinear ones.

Generalised filtering and stochastic DCM for fMRI

“…These data were acquired during an attention to visual motion paradigm and have been used to illustrate psychophysiological interactions, structural equation modelling, multivariate autoregressive models, Kalman filtering, variational filtering, EM and DEM Friston, 1997, 1998;Friston et al, 2003Friston et al, , 2008Harrison et al, 2003;Stephan et al, 2008). Here, we revisit questions about the generation of distributed responses by analysing the data using conventional deterministic DCMs (EM), stochastic DCMs under the mean-field approximation (DEM) and generalised filtering (GF).…”

“…This paper comprises four sections. In the first, we present an illustrative application of generalised filtering to the same fMRI data set (attention to motion) that we have used previously to demonstrate DCM using EM Stephan et al, 2008) and DEM . This section serves to illustrate the nature of the GF scheme and the results it produces.…”

Depression alters “top-down” visual attention: A dynamic causal modeling comparison between depressed and healthy subjects

“…We could thus, within a Bayesian framework, characterize the brain connectivity of the two groups of subjects, as well as their differences. We hypothesized that controls would display a connectivity network compatible with the Load Theory (Lavie et al, 2004) with a reduced drive of the activity in V4 in high attentional load mediated either by a direct action of P on V4 or by an indirect decrease of the gating from V1 to V4 (Schwartz et al, 2005;Stephan et al, 2008). We hypothesized that the connectivity of this visuo-attentional system would differ between MDD and controls in two distinct ways.…”

The impact of hemodynamic variability and signal mixing on the identifiability of effective connectivity structures in BOLD fMRI

“…Over the past decade, multiple generative models have been proposed in the context of the DCM (Friston, Kahan, Biswal, & Razi, 2011; Friston et al., 2003; Havlicek et al., 2015; Kiebel, Kloppel, Weiskopf, & Friston, 2007; Li et al., 2011; Marreiros, Kiebel, & Friston, 2008; Seth, Chorley, & Barnett, 2013; Smith et al., 2011; Stephan, Weiskopf, Drysdale, Robinson, & Friston, 2007; Stephan et al., 2008). In this study, we chose the original, single‐node per region DCM (Friston et al., 2003; Smith et al., 2011).…”