Effective connectivity: Influence, causality and biophysical modeling

Abstract

This is the final paper in a Comments and Controversies series dedicated to “The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution”. We argue that discovering effective connectivity depends critically on state-space models with biophysically informed observation and state equations. These models have to be endowed with priors on unknown parameters and afford checks for model Identifiability. We consider the similarities and differences among Dynamic Causal Modeling, Granger Causal Modeling and other approaches. We establish links between past and current statistical causal modeling, in terms of Bayesian dependency graphs and Wiener–Akaike–Granger–Schweder influence measures. We show that some of the challenges faced in this field have promising solutions and speculate on future developments.

The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference

“…If, conversely, the past of Y does convey information about the future of X above and beyond all information contained in the past of X then we say that Y G-causes X. Much has been made of the fact that this notion of "causality" does not necessarily tally with more conventional (and perhaps more physically intuitive) notions (Pearl, 2009;Valdes-Sosa et al, 2011;Friston, 2011;Roebroeck et al, 2009Roebroeck et al, , 2010) (note, for example, that the processes must be strictly non-deterministic for the above definition even to make sense). We do not engage this debate here; throughout this paper the term "causal" is used exclusively in the Wiener-Granger sense just described.…”

“…Application of G-causality to fMRI BOLD data has been highly controversial for apparently good reasons; e.g., David et al (2008); Valdes-Sosa et al (2011). First, the BOLD signal (as captured by the hemodynamic response function, HRF) is an indirect, sluggish, and variable (inter-regionally and inter-subjectively), transformation of underlying neural activity (Handwerker et al, 2012).…”

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

“…On the other hand, we have state‐space models which infer effective connectivity on the basis of the temporal patterns in the dynamics [e.g., Dynamic Causal Modeling, DCM (Friston, Harrison, & Penny, 2003), Granger Causality, GC, (Granger, 1969; Roebroeck, Formisano, & Goebel, 2011; Seth, Barrett, & Barnett, 2015; Solo, 2016), Transfer Entropy, TE (Lizier, Heinzle, Horstmann, Haynes, & Prokopenko, 2011; Vicente, Wibral, Lindner, & Pipa, 2011)]. There is an ongoing debate upon which class of models is better suited for this research problem (Valdes‐Sosa, Roebroeck, Daunizeau, & Friston, 2011). …”

Causal discourse in a game of incomplete information

“…Further, the generality of topological settable systems makes them broadly useful for application in economics, as well as in other quite di¤erent …elds. For example, topological settable systems may apply to the study of causality in the spatial-temporal manifolds used to analyze neural activity in the brain (Valdés-Sosa, BornotSánchez, et al, 2011;Valdés-Sosa, Roebroeck, et al, 2011).…”