Nonlinear Dynamic Causal Models for fMRI

By Klaas E. Stephan, Lars Kasper, Lee M. Harrison, Jean Daunizeau, H. D. den Ouden, Michael Breakspear, Karl J. Friston. NeuroImage, 2008

441 citations recorded by the source corpus.

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 attention-induced 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.

Subfields: Cellular and Molecular Neuroscience, Cognitive Neuroscience

View Paper: https://www.semanticscholar.org/paper/7fb8beaf79137ce4114122860ddb2e2b8f07ea72

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cellular and Molecular Neuroscience

In Cognitive Neuroscience

Citations in the corpus

Behavioral / Systems / Cognitive Striatal Prediction Error Modulates Cortical Coupling (2010, positive): “Finally, the D (j ) matrices encode how connection strengths are modulated or gated by activity in area j (for details, see Stephan et al., 2008).”
Health, USA Reviewed by: (2010, positive): “If so, then dynamic causal modeling (DCM) (Friston et al., 2003; Penny et al., 2004a; Sonty et al., 2007; Stephan et al., 2008; Rowe et al., 2010), SEM (McIntosh and Gonzalez-Lima, 1994; Buchel and Friston, 1997; Rowe et al., 2002b; Sharma et al., 2009) or Granger causality modeling (GCM)…”
Ten Simple Rules for Dynamic Causal Modelling (2009, neutral): “Although inference can be about any aspect of model structure or any parameter in a DCM, the focus of DCM studies is typically on context-dependent changes in coupling.”
Graph analysis of the human connectome: Promise, progress, and pitfalls (2013, neutral): “The resulting edge weights are typically scalar, continuous and symmetric and can be used to quantify both positive and negative covariations in regional activity.”
VBA: A Probabilistic Treatment of Nonlinear Models for Neurobiological and Behavioural Data (2014, background): “This is typically written in the form of Equation 1 (first line), where the neural evolution function is given by [27]:”
Handbook of Functional MRI Data Analysis: Index (2011, background): “DCM is often referred to as a bilinear model because it involves the interaction of two linear effects; however, the DCM model has also been extended to nonlinear cases in which connections are modulated by a third region (Stephan et al., 2008).”
Analysing connectivity with Granger causality and dynamic causal modelling (2013, methodology): “GC applied within a statespace framework incorporating explicit observation equations for modelling hemodynamic responses [49]”
The salience network is responsible for switching between the default mode network and the central executive network: Replication from DCM (2014, methodology): “Recent advances in methodology mean it is now possible to compare families of DCMs (Penny et al., 2010), to use a random effects method for model selection (Stephan et al., 2009) and to specify nonlinear and stochastic models (Li et al., 2011; Stephan et al., 2008).”
Dynamic models of large-scale brain activity (2017, methodology): “This Bayesian approach is now well established for magnetoencephalography (MEG), EEG and fMRI data within the framework of dynamic causal modeling 100,101 .”
Bayesian model reduction and empirical Bayes for group (DCM) studies (2016, methodology): “First, Bayesian model reduction is restricted to comparing nested models; this prohibits a comparison of models which differ in the functional form of the likelihood; for example, comparisons of bilinear versus nonlinear DCMs for fMRI (Stephan et al., 2008), neural mass versus mean field models of e”
Functional and Effective Connectivity: A Review (2011, positive): “These sorts of effects have motivated the development of nonlinear models of effective connectivity that consider explicitly interactions among synaptic inputs (e.g., Friston et al., 1995; Stephan et al., 2008).”
Effective connectivity: Influence, causality and biophysical modeling (2011, methodology): “and Körding, 2010; Witt and Meyerand, 2009). Others have shown advantages for Bayes-Net methods in short time series and for GCM for longer time series (Zou et al., 2009). An extensive set of simulations (NETSIM) has been carried out by Smith et al. (2010b) using non-stationary (Poisson-type) neural”
On the Definition of Signal-To-Noise Ratio and Contrast-To-Noise Ratio for fMRI Data (2013, background): “Another possibility is to model the strength of the signal based on the standard deviation of the activation signal [29–35],”
Bayesian Model Selection for Group Studies (2009, neutral): “The difference in log-evidences for all twenty data sets is plotted as a bar chart. the synthetic data sets described by Stephan et al. (2008), consisting of twenty synthetic BOLD time-series that were generated using a three-area nonlinear DCM with fixed parameters and adding Gaussian observation…”