Measuring functional and effective connectivity

Functional connectivity can be measured either during rest or during a task. During rest, things are fairly straightforward - provided that we have adequately controlled for physiological noise, head motion etc (see “fMRI fundamentals” note), we can measure it using e.g., a correlation of fMRI signals.

During task its a little more complex. Typically we want to isolate the aspect of functional connectivity that is task-dependent. This can be done in different ways. This note outlines some of the issue in measuring functional connectivity under different circumstances.

Electrophysiological concepts of functional coupling

Most of fMRI focuses on correlations in BOLD signals and stops there. If we really want to understand neuronal communication, we need to understand what is happening at the physiological level. This is best accessed with (invasive and non-invasive) electrophysiological recording techniques that have the spatial resolution required to measure neural activity at appropriate time scales (i.e., fMRI is too slow). These articles provide some overviews of current models of how neurons synchronise their activity. That is, they explain what we should be actually thinking about when considering communication in brain networks.

Synchronisation and communication through coherence

• Wolf Singer 2013 - Cortical dynamics revisited
• Wolf Singer 1999 - Neuronal Synchrony: A Versatile Code for the Definition of Relations?
• Pascal Fries 2005 - A mechanism for cognitive dynamics: neuronal communication through neuronal coherence
• Pascal Fries 2005 - Rhythms for Cognition: Communication through Coherence

Dominant coupling modes

• Engel et al. 2013 - Intrinsic Coupling Modes: Multiscale Interactions in Ongoing Brain Activity
• Siegel et al. 2012 - Spectral fingerprints of large-scale neuronal interactions

Cross-frequency coupling

• Canolty and Knight 2010 - The functional role of cross-frequency coupling

Neuronal oscillations

• Gyorgy Buzsaki 2006 - Rhythms of the Brain
• Buzsaki and Draguhn 2004 - Neuronal Oscillations in Cortical Networks
• Buzsaki et al. 2013 - Scaling Brain Size, Keeping Timing: Evolutionary Preservation of Brain Rhythms

General overviews

• Karl Friston 1994 - Functional and Effective Connectivity in Neuroimaging: A Synthesis
• Karl Friston 2011 - Functional and Effective Connectivity: A Review
• Stephen Smith 2012 - The future of FMRI connectivity
• Smith et al. 2010 - Network modelling methods for FMRI
  • Note: one limitation of the model architecture used in this article is that it is not small-world (contrary to the statements in the paper) - it lacks closed triangles and is thus not clustered.
• Bastos and Schoffelen 2016 - A Tutorial Review of Functional Connectivity Analysis Methods and Their Interpretational Pitfalls
• Basti et al. 2020 - Multi-dimensional connectivity: a conceptual and mathematical review
  • Accompanying MATLAB toolbox

Measuring task-related FC

Psychophysiological interactions

• Friston et al. 1997 - Psychophysiological and Modulatory Interactions in Neuroimaging
• Gitelman et al. 2003 - Modeling regional and psychophysiologic interactions in fMRI: the importance of hemodynamic deconvolution
• Notes and resources from FSL team (zip download)
• McLaren et al. 2012 - A generalized form of context-dependent psychophysiological interactions (gPPI): A comparison to standard approaches
• Mumford Brain Stats video tutorial
• Cisler et al. 2014 - A comparison of statistical methods for detecting context-modulated functional connectivity connectivity in fMRI
• Fornito et al. 2012 - Competitive and cooperative dynamics of large-scale brain functional networks supporting recollection
  • Accompanying MATLAB toolbox

Beta series regression

• Rissman et al. 2004 - Measuring functional connectivity during distinct stages of a cognitive task
• Fornito et al. 2011 - General and Specific Functional Connectivity Disturbances in First-Episode Schizophrenia During Cognitive Control Performance

Activity flow toolbox

Effective connectivity

Functional connectivity is a statistical dependence between recorded brain signals (e.g., BOLD). Effective connectivity is the influence that one neuronal system exerts over another. Influence is highlighted because we are talking about causal interaction. Neuronal is highlighted because we are no longer concerned with the measured signals - we aim to infer the causal structure of interactions at the neuronal level. To do this, we need some mapping from neural activity to the measure signal; e.g., from neuronal dynamics to BOLD.

Dynamic causal modelling (DCM) is the best-developed framework for measuring effective connectivity. Below are some key articles. This is not an exhaustive list as DCM is currently not widely used in the lab (this will likely change in future), but this is a start anyway.

General considerations

• Karl Friston 2009 - Causal Modelling and Brain Connectivity in Functional Magnetic Resonance Imaging
• Friston et al. 2012 - Analysing connectivity with Granger causality and dynamic causal modelling

Key methodological papers

• Friston et al. 2003 - Dynamic causal modelling
• Stephan et al. 2010 - Ten simple rules for dynamic causal modeling
• Li et al. 2011 - Generalised filtering and stochastic DCM for fMRI
• Seghier and Friston 2013 - Network discovery with large DCMs
• Friston et al. 2011 - Network discovery with DCM
• Zeidman et al. 2019 - A guide to group effective connectivity analysis, part 1: First level analysis with DCM for fMRI