Chapter 2. Introduction

Mapping the structural and active functional properties of brain networks is a key goal of basic and clinical neuroscience and medicine. The novelty and importance of this transformative research was recently emphasized by the U.S. National Institute of Health in their 2010 announcement for the Human Connectome Project:

Knowledge of human brain connectivity will transform human neuroscience by providing not only a qualitatively novel class of data, but also by providing the basic framework necessary to synthesize diverse data and, ultimately, elucidate how our brains work in health, illness, youth, and old age.

The study of human brain connectivity generally falls under one or more of three categories: structural, functional, and effective (Bullmore and Sporns, 2009).

Structural connectivity denotes networks of anatomical (e.g., axonal) links. Here the primary goal is to understand what brain structures are capable of influencing each other via direct or indirect axonal connections. This might be studied in vivo using invasive axonal labeling techniques or noninvasive MRI-based diffusion weighted imaging (DWI/DTI) methods.

Functional connectivity denotes (symmetrical) correlations in activity between brain regions during information processing. Here the primary goal is to understand what regions are functionally related through correlations in their activity, as measured by some imaging technique. A popular form of functional connectivity analysis using functional magnetic resonance imaging (fMRI) has been to compute the pairwise correlation (or partial correlation) in BOLD activity for a large number of voxels or regions of interest within the brain volume.

In contrast to the symmetric nature of functional connectivity, effective connectivity denotes asymmetric or causal dependencies between brain regions. Here the primary goal is to identify which brain structures in a functional network are (causally) influencing other elements of the network during some stage or form of information processing. Often the term “information flow” is used to indicate directionally specific (although not necessarily causal) effective connectivity between neuronal structures. Popular effective connectivity methods, applied to fMRI and/or electrophysiological (EEG, iEEG, MEG) imaging data, include dynamic causal modeling, structural equation modeling, transfer entropy, and Granger-causal methods.

Contemporary research on building a human ‘connectome’ (complete map of human brain connectivity) has typically focused on structural connectivity using MRI and diffusion-weighted imaging (DWI) and/or on functional connectivity using fMRI. However, the brain is a highly dynamic system, with networks constantly adapting and responding to environmental influences so as to best suit the needs of the individual. A complete description of the human connectome necessarily requires accurate mapping and modeling of transient directed information flow or causal dynamics within distributed anatomical networks. Efforts to examine transient dynamics of effective connectivity (causality or directed information flow) using fMRI are complicated by low temporal resolution, assumptions regarding the spatial stationarity of the hemodynamic response, and smoothing transforms introduced in standard fMRI signal processing (Deshpande et al., 2009a; Deshpande et al., 2009b). While electro- and magneto-encephalography (EEG/MEG) affords high temporal resolution, the traditional approach of estimating connectivity between EEG electrode channels (or MEG sensors) suffers from a high risk of false positives from volume conduction and non-brain artifacts. Furthermore, severe limitations in spatial resolution when using surface sensors further limits the physiological interpretability of observed connectivity. Although precisely identifying the anatomical locations of sources of observed electrical activity (the inverse problem) is mathematically ill-posed, recent improvements in source separation and localization techniques may allow approximate identification of such anatomical coordinates with sufficient accuracy to yield anatomical insight invaluable to a wide range of cognitive neuroscience and neuroengineering applications (Michel et al., 2004). In limited circumstances it is also possible to obtain human intracranially-recorded EEG (ICE, ECoG, iEEG) that, although highly invasive, affords high spatiotemporal resolution and (often) reduced susceptibility to non-brain artifacts.

Once activity in specific brain areas have been identified using source separation and localization, it is possible to look for transient changes in dependence between these different brain source processes. Advanced methods for non-invasively detecting and modeling distributed network events contained in high-density EEG data are highly desirable for basic and clinical studies of distributed brain activity supporting behavior and experience. In recent years, Granger Causality (GC) and its extensions have increasingly been used to explore ‘effective’ connectivity (directed information flow, or causality) in the brain based on analysis of prediction errors of autoregressive models fit to channel (or source) waveforms. GC has enjoyed substantial recent success in the neuroscience community, with over 1200 citations in the last decade (Google Scholar). This is in part due to the relative simplicity and interpretability of GC – it is a data-driven approach based on linear regressive models requiring only a few basic a priori assumptions regarding the generating statistics of the data. However, it is also a powerful technique for system identification and causal analysis. While many landmark studies have applied GC to invasively recorded local field potentials and spike trains, a growing number of studies have successfully applied GC to non-invasively recorded human EEG and MEG data (as reviewed in (Bressler and Seth, 2010)). Application of these methods in the EEG source domain is also being seen in an increasing number of studies (Hui and Leahy, 2006; Supp et al., 2007; Astolfi et al., 2007; Haufe et al., 2010).

In the last decade an increasing number of effective connectivity measures, closely related to Granger’s definition of causality, have been proposed. Like classic GC, these measures can be derived from (multivariate) autoregressive models fit to observed data time-series. These measures can describe different aspects of network dynamics and thus comprise a complementary set of tools for effective connectivity or causal analysis.

Several toolboxes affording various forms of Granger-causal (or related) connectivity analysis are currently available in full or beta-release. Table 1 provides a list of several of these toolboxes, along with the website, release version, and license. Although these toolboxes provide a number of well-written and useful functions, most lack integration within a more comprehensive framework for EEG signal processing (the exceptions being Fieldtrip's routines, and TSA, which integrates into the Biosig EEG/MEG processing suite). Furthermore, many of these may implement only one or two (often bivariate) connectivity measures, lack tools for sophisticated visualization, or lack robust statistics or multi-subject (group) analysis. Finally, to our knowledge, with the exception of E-Connectome, none of these toolboxes directly support analysis and visualization of connectivity in the EEG source domain. These are all factors that our Source Information Flow Toolbox (SIFT), combined with the EEGLAB software suite, hopes to address.

Table 1. A list of free Matlab-based toolboxes for granger-causal connectivity analysis in neural data.

Toolbox Name	Primary Author	Website	License
Granger Causality Connectivity Analysis (GCCA) Toolbox	Anil Seth	https://www.sussex.ac.uk/research/centres/sussex-centre-for-consciousness-science/resources/connectivity	GPL 3
Time-Series Analysis (TSA) Toolbox	Alois Schloegl	https://sourceforge.net/p/octave/tsa/ci/default/tree/	GPL 2
E-Connectome	Bin He	https://www.nitrc.org/projects/econnectome	GPL 3
Fieldtrip	Robert Oosteveld	http://fieldtrip.fcdonders.nl/	GPL 2
Brain-System for Multivariate AutoRegressive Timeseries (BSMART)	Jie Cui	http://www.brain-smart.org/	--

SIFT is an open-source Matlab (The Mathworks, Inc.) toolbox for analysis and visualization of multivariate information flow and causality, primarily in EEG/iEEG/MEG datasets following source separation and localization. The toolbox supports both command-line (scripting) and graphical user interface (GUI) interaction and is integrated into the widely used open-source EEGLAB software environment for electrophysiological data analysis (sccn.ucsd.edu/eeglab). There are currently four modules: data preprocessing, model fitting and connectivity estimation, statistical analysis, and visualization. A fifth group analysis module, affording connectivity analysis and statistics over a cohort of datasets, will be included in the upcoming beta release. First methods implemented include a large number of popular frequency-domain granger-causal and coherence measures, obtained from adaptive multivariate autoregressive models, surrogate and analytic statistics, and a suite of tools for interactive visualization of information flow dynamics across time, frequency, and (standard or personal MRI co-registered) anatomical source locations.

In this tutorial, I will outline the theory underlying multivariate autoregressive modeling and granger-causal analysis. Practical considerations, such as data length, parameter selection, and non-stationarities are addressed throughout the text, and useful tests for estimating statistical significance are outlined. This theory section is followed by a hands-on walkthrough of the use of the SIFT toolbox for analyzing source information flow dynamics in an EEG dataset. Here we will walk through a typical data processing pipeline culminating with the demonstration of some of SIFT’s powerful tools for interactive visualization of time- and frequency-dependent directed information flow between localized EEG sources in an anatomically-coregistered 3D space. Theory boxes through the chapter will provide additional insight on various aspects of model fitting and parameter selection.