Causality in Time Series - ClopiNet

JMLR: Workshop and Conference Proceedings 12:65–94, 2011Causality in Time SeriesCausal Time Series Analysis of functional MagneticResonance Imaging DataAlard RoebroeckFaculty of Psychology & NeuroscienceMaastricht University, the NetherlandsAnil K. SethSackler Centre for Consciousness ScienceUniversity of Sussex, UKPedro Valdes-SosaCuban Neuroscience Centre, Playa, Cubaa.roebroeck@maastrichtuniversity.nla.k.seth@sussex.ac.ukpeter@cneuro.edu.cuEditors: Florin Popescu and Isabelle GuyonAbstractThis review focuses on dynamic causal analysis of functional magnetic resonance(fMRI) data to infer brain connectivity from a time series analysis and dynamicalsystems perspective. Causal influence is expressed in the Wiener-Akaike-Granger-Schweder (WAGS) tradition and dynamical systems are treated in a state space modelingframework. The nature of the fMRI signal is reviewed with emphasis on theinvolved neuronal, physiological and physical processes and their modeling as dynamicalsystems. In this context, two streams of development in modeling causalbrain connectivity using fMRI are discussed: time series approaches to causality in adiscrete time tradition and dynamic systems and control theory approaches in a continuoustime tradition. This review closes with discussion of ongoing work and futureperspectives on the integration of the two approaches.Keywords: fMRI, hemodynamics, state space model, Granger causality, WAGS influence1. IntroductionUnderstanding how interactions between brain structures support the performance ofspecific cognitive tasks or perceptual and motor processes is a prominent goal in cognitiveneuroscience. Neuroimaging methods, such as Electroencephalography (EEG),Magnetoencephalography (MEG) and functional Magnetic Resonance Imaging (fMRI)are employed more and more to address questions of functional connectivity, interregioncoupling and networked computation that go beyond the ‘where’ and ‘when’ oftask-related activity (Friston, 2002; Horwitz et al., 2000; McIntosh, 2004; Salmelin andKujala, 2006; Valdes-Sosa et al., 2005a). A network perspective onto the parallel anddistributed processing in the brain - even on the large scale accessible by neuroimagingmethods - is a promising approach to enlarge our understanding of perceptual, cognitiveand motor functions. Functional Magnetic Resonance Imaging (fMRI) in particular isc○ 2011 A. Roebroeck, A.K. Seth & P. Valdes-Sosa.