The Chronnectome: Time-Varying Connectivity Networks as the Next Frontier in fMRI Data Discovery

Recent years have witnessed a rapid growth of interest in moving functional magnetic resonance imaging (fMRI) beyond simple scan-length averages and into approaches that capture time-varying properties of connectivity. In this Perspective we use the term “chronnectome” to describe metrics that allow a dynamic view of coupling. In the chronnectome, coupling refers to possibly time-varying levels of correlated or mutually informed activity between brain regions whose spatial properties may also be temporally evolving. We primarily focus on multivariate approaches developed in our group and review a number of approaches with an emphasis on matrix decompositions such as principle component analysis and independent component analysis. We also discuss the potential these approaches offer to improve characterization and understanding of brain function. There are a number of methodological directions that need to be developed further, but chronnectome approaches already show great promise for the study of both the healthy and the diseased brain. Recent years have witnessed a rapid growth of interest in moving functional magnetic resonance imaging (fMRI) beyond simple scan-length averages and into approaches that capture time-varying properties of connectivity. In this Perspective we use the term “chronnectome” to describe metrics that allow a dynamic view of coupling. In the chronnectome, coupling refers to possibly time-varying levels of correlated or mutually informed activity between brain regions whose spatial properties may also be temporally evolving. We primarily focus on multivariate approaches developed in our group and review a number of approaches with an emphasis on matrix decompositions such as principle component analysis and independent component analysis. We also discuss the potential these approaches offer to improve characterization and understanding of brain function. There are a number of methodological directions that need to be developed further, but chronnectome approaches already show great promise for the study of both the healthy and the diseased brain. The human connectome is of great current interest and has received renewed attention recently with the NIH-funded human connectome projects (http://www.neuroscienceblueprint.nih.gov/connectome/), which focus on generating a large amount of functional and structural data from a variety of brain imaging modalities, and the BRAIN initiative (http://www.whitehouse.gov/share/brain-initiative), which focuses on developing new technologies to provide more detailed access to connectivity information within the brain. The connectome is a term that is used primarily to describe the wiring diagram of the brain (Sporns et al., 2005Sporns O. Tononi G. Kötter R. The human connectome: A structural description of the human brain.PLoS Comput. Biol. 2005; 1: e42Crossref PubMed Scopus (2131) Google Scholar). However, we would suggest that a wiring diagram absent of function is unlikely to be a sufficient tool to understand how the brain works, even in relatively simple systems, due to the impact of modulatory effects and issues like the numbers and kinds of membrane currents in each of the neurons (Bargmann and Marder, 2013Bargmann C.I. Marder E. From the connectome to brain function.Nat. Methods. 2013; 10: 483-490Crossref PubMed Scopus (323) Google Scholar). The term “connectome” has now been nuanced in multiple ways including scale (e.g., micro, meso, macro) and modality (e.g., structure, function). For both structure and function, one can also consider a spectrum of different scales of change in connectivity (slow, fast). It is also possible to consider the impact of disease on the healthy connectome, in order to derive characteristic signatures of connectivity that may be specific to certain brain illnesses (Calhoun et al., 2012Calhoun V.D. Sui J. Kiehl K.A. Turner J.A. Allen E.A. Pearlson G.D. Exploring the psychosis functional connectome: aberrant intrinsic networks in schizophrenia and bipolar disorder.Front. Psychiatry. 2012; 2: 75Crossref PubMed Scopus (168) Google Scholar). One of the key aspects of the “omic” expansion of terminology in our view is that such categorizations describe objects or states that are not random and can be categorized into collections of objects that describe some useful features of function, structure, or dynamics, various aspects of which may interact with disease. Thus, genomics, metabolomics, proteomics, connectomics, and our introduction of chronnectomics all have the common goal of providing a canonical set of descriptors that can be drawn upon to understand the healthy and diseased human organism. The term chronnectome is used to describe a focus on identifying time-varying, but reoccurring, patterns of coupling among brain regions. Of note, the term “dynome” has also recently been introduced (Kopell et al., 2014Kopell N.J. Gritton H.J. Whittington M.A. Kramer M.A. Beyond the Connectome: The Dynome.Neuron. 2014; 83: 1319-1328Abstract Full Text Full Text PDF PubMed Scopus (209) Google Scholar); however, the focus of the dynome is on time-varying (oscillatory) activity whose basic characteristics (frequency, phase, amplitude, etc.) are generally assumed to be static. The chronnectome is a model of the brain in which nodal activity and connectivity patterns are changing in fundamental ways through time. In the context of this paper, “dynamics” is thus referring to intrinsic nonstationarities rather than to the behavior of model oscillators with effectively static activation and coupling parameters. Thus the chronnectome, as we define it, is making the specific assumption that the dynamics are nonstationary in interesting ways, whereas the dynome does not make any such assumption. Spontaneous fluctuations are a hallmark of neural signals. To date, macro functional human connectome work has largely been based on functional connectivity maps derived from functional magnetic resonance imaging (fMRI) data. However, such maps are most commonly derived from an fMRI experiment spanning from 5 to 30 min and represent an implicit assumption that the functional connectivity (or chronnectome) over this period of time is relatively static. This assumption was challenged in work focused on time-varying multivariate connectivity patterns (Sakoğlu et al., 2010Sakoğlu U. Pearlson G.D. Kiehl K.A. Wang Y.M. Michael A.M. Calhoun V.D. A method for evaluating dynamic functional network connectivity and task-modulation: application to schizophrenia.MAGMA. 2010; 23: 351-366Crossref PubMed Scopus (435) Google Scholar) and in other work focused on time-frequency analysis methods (Chang and Glover, 2010Chang C. Glover G.H. Time-frequency dynamics of resting-state brain connectivity measured with fMRI.Neuroimage. 2010; 50: 81-98Crossref PubMed Scopus (1259) Google Scholar). Since then, multiple chronnectomic studies have appeared (for a recent review, see Hutchison et al., 2013aHutchison R.M. Womelsdorf T. Allen E.A. Bandettini P.A. Calhoun V.D. Corbetta M. Della Penna S. Duyn J.H. Glover G.H. Gonzalez-Castillo J. et al.Dynamic functional connectivity: promise, issues, and interpretations.Neuroimage. 2013; 80: 360-378Crossref PubMed Scopus (1682) Google Scholar). The brain itself is clearly highly dynamic, but the chronnectome refers not to the dynamics within a single region, but rather to the dynamics in the connectivity (coupling) among two or more regions. The concept of dynamic connectivity also has been used in various ways in the field, including (static) functional connectivity, regional (but detailed) modeling of the dynamic changes between a small number of regions with many parameters (typically assuming the same response for each stimulus [Friston et al., 2003Friston K.J. Harrison L. Penny W. Dynamic causal modelling.Neuroimage. 2003; 19: 1273-1302Crossref PubMed Scopus (3205) Google Scholar] or at rest [Havlicek et al., 2011Havlicek M. Friston K.J. Jan J. Brazdil M. Calhoun V.D. Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering.Neuroimage. 2011; 56: 2109-2128Crossref PubMed Scopus (139) Google Scholar], so-called effective [dynamic] connectivity), or time-varying whole brain functional connectivity patterns (Allen et al., 2014Allen E.A. Damaraju E. Plis S.M. Erhardt E.B. Eichele T. Calhoun V.D. Tracking whole-brain connectivity dynamics in the resting state.Cereb. Cortex. 2014; 24: 663-676Crossref PubMed Scopus (1687) Google Scholar). In the following, we focus on the whole-brain approaches in this work rather than approaches that focus on only a few regions. The most fundamental element of the chronnectome is its dynamic view of coupling (e.g., connectivity) in which two or more regions or sets of regions, all possibly evolving spatially in time, are coupled with connective strengths measured as explicit functions of time. This can include temporal coupling (i.e., traditional connectivity), spatial coupling, or spatiotemporal coupling. The time dependence ranging from slow (years) to fast (milliseconds) is also a useful property. In addition, the property of scale (micro, macro, or meso) is important (for fMRI data we are at the macro scale). Another property is modality—e.g., structural MRI, diffusion, functional MRI, electroencephalography (EEG), magnetoencephalography (MEG), or even genetics. Finally, the chronnectome may vary as a function of condition (e.g., health, disease, behavior). These are just a few examples. Because there are multiple ways to define connectome (e.g., a neuron-level wiring diagram, a set of possibly modulatory factors on said diagram, a statistical summary of many-to-many macroscopic connectivity, etc.), it is important to provide a definition of the term as it is being used in the local context. This is also true of the term “network,” which can refer to diagrams based on graph metrics, unthresholded correlation maps, diffusion tract tracing, or regional brain image covariation among subjects (Erhardt et al., 2011aErhardt E.B. Allen E.A. Damaraju E. Calhoun V.D. On network derivation, classification, and visualization: a response to Habeck and Moeller.Brain Connect. 2011; 1: 1-19Crossref PubMed Scopus (11) Google Scholar). In this work we focus upon whole-brain (statistical) connectivity patterns assessed within the relatively faster timescale of the macro functional connectome (i.e., seconds versus minutes) as measured by fMRI. Note that there is also extensive work in EEG/MEG microstates on the scale of milliseconds, which is relevant but will not be fully reviewed here (Koenig et al., 2002Koenig T. Prichep L. Lehmann D. Sosa P.V. Braeker E. Kleinlogel H. Isenhart R. John E.R. Millisecond by millisecond, year by year: normative EEG microstates and developmental stages.Neuroimage. 2002; 16: 41-48Crossref PubMed Scopus (402) Google Scholar, Musso et al., 2010Musso F. Brinkmeyer J. Mobascher A. Warbrick T. Winterer G. Spontaneous brain activity and EEG microstates. A novel EEG/fMRI analysis approach to explore resting-state networks.Neuroimage. 2010; 52: 1149-1161Crossref PubMed Scopus (247) Google Scholar, Pascual-Marqui et al., 1995Pascual-Marqui R.D. Michel C.M. Lehmann D. Segmentation of brain electrical activity into microstates: model estimation and validation.IEEE Trans. Biomed. Eng. 1995; 42: 658-665Crossref PubMed Scopus (631) Google Scholar). Based on the rapid increase in journal papers focused on dynamic connectivity (Allen et al., 2014Allen E.A. Damaraju E. Plis S.M. Erhardt E.B. Eichele T. Calhoun V.D. Tracking whole-brain connectivity dynamics in the resting state.Cereb. Cortex. 2014; 24: 663-676Crossref PubMed Scopus (1687) Google Scholar, Calhoun et al., 2013bCalhoun V.D. Yaesoubi M. Rashid B. Miller R. Characterization of Connectivity Dynamics in Intrinsic Brain Networks GlobalSIP.2013https://doi.org/10.1109/GlobalSIP.2013.6737020Crossref Scopus (4) Google Scholar, Chang and Glover, 2010Chang C. Glover G.H. Time-frequency dynamics of resting-state brain connectivity measured with fMRI.Neuroimage. 2010; 50: 81-98Crossref PubMed Scopus (1259) Google Scholar, Hutchison et al., 2013aHutchison R.M. Womelsdorf T. Allen E.A. Bandettini P.A. Calhoun V.D. Corbetta M. Della Penna S. Duyn J.H. Glover G.H. Gonzalez-Castillo J. et al.Dynamic functional connectivity: promise, issues, and interpretations.Neuroimage. 2013; 80: 360-378Crossref PubMed Scopus (1682) Google Scholar, Hutchison et al., 2013bHutchison R.M. Womelsdorf T. Gati J.S. Everling S. Menon R.S. Resting-state networks show dynamic functional connectivity in awake humans and anesthetized macaques.Hum. Brain Mapp. 2013; 34: 2154-2177Crossref PubMed Scopus (524) Google Scholar, Keilholz, 2014Keilholz S.D. The neural basis of time-varying resting state functional connectivity.Brain Connect. 2014; (Published online July 31, 2014)https://doi.org/10.1089/brain.2014.0250Crossref Scopus (83) Google Scholar, Keilholz et al., 2013Keilholz S.D. Magnuson M.E. Pan W.J. Willis M. Thompson G.J. Dynamic properties of functional connectivity in the rodent.Brain Connect. 2013; 3: 31-40https://doi.org/10.1089/brain.2012.0115Crossref PubMed Scopus (107) Google Scholar, Leonardi et al., 2013Leonardi N. Richiardi J. Gschwind M. Simioni S. Annoni J.M. Schluep M. Vuilleumier P. Van De Ville D. Principal components of functional connectivity: a new approach to study dynamic brain connectivity during rest.Neuroimage. 2013; 83: 937-950Crossref PubMed Scopus (298) Google Scholar, Sakoğlu et al., 2010Sakoğlu U. Pearlson G.D. Kiehl K.A. Wang Y.M. Michael A.M. Calhoun V.D. A method for evaluating dynamic functional network connectivity and task-modulation: application to schizophrenia.MAGMA. 2010; 23: 351-366Crossref PubMed Scopus (435) Google Scholar), including recent work showing that metastable states correspond to stages of consciousness (Hudson et al., 2014Hudson A.E. Calderon D.P. Pfaff D.W. Proekt A. Recovery of consciousness is mediated by a network of discrete metastable activity states.Proc. Natl. Acad. Sci. USA. 2014; 111: 9283-9288Crossref PubMed Scopus (108) Google Scholar), the fMRI community has quickly grasped that assessment of functional connectivity has been limited by the assumption of spatial and temporal stationarity throughout the measurement period. Existing approaches have demonstrated the importance of studying the chronnectome using analyses based on windowed (or gradually tapered) correlations between regions of interest (Di and Biswal, 2013Di X. Biswal B.B. Dynamic brain functional connectivity modulated by resting-state networks.Brain Struct. Funct. 2013; https://doi.org/10.1007/s00429-013-0634-3Crossref PubMed Scopus (108) Google Scholar, Kucyi and Davis, 2014Kucyi A. Davis K.D. Dynamic functional connectivity of the default mode network tracks daydreaming.Neuroimage. 2014; 100: 471-480Crossref PubMed Scopus (247) Google Scholar, Lindquist et al., 2014Lindquist M.A. Xu Y. Nebel M.B. Caffo B.S. Evaluating dynamic bivariate correlations in resting-state fMRI: A comparison study and a new approach.Neuroimage. 2014; 101: 531-546Crossref PubMed Scopus (232) Google Scholar, Zalesky et al., 2014Zalesky A. Fornito A. Cocchi L. Gollo L.L. Breakspear M. Time-resolved resting-state brain networks.Proc. Natl. Acad. Sci. USA. 2014; 111: 10341-10346Crossref PubMed Scopus (501) Google Scholar) or between temporally coherent networks captured with multivariate approaches (Allen et al., 2014Allen E.A. Damaraju E. Plis S.M. Erhardt E.B. Eichele T. Calhoun V.D. Tracking whole-brain connectivity dynamics in the resting state.Cereb. Cortex. 2014; 24: 663-676Crossref PubMed Scopus (1687) Google Scholar, Damaraju et al., 2014Damaraju E. Allen E.A. Belger A. Ford J.M. McEwen S.C. Mathalon D.H. Mueller B.A. Pearlson G.D. Potkin S.G. Preda A. et al.Dynamic functional connectivity analysis reveals transient states of dysconnectivity in schizophrenia.Neuroimage Clin. 2014; 5: 298-308Crossref Scopus (681) Google Scholar, Sakoğlu et al., 2010Sakoğlu U. Pearlson G.D. Kiehl K.A. Wang Y.M. Michael A.M. Calhoun V.D. A method for evaluating dynamic functional network connectivity and task-modulation: application to schizophrenia.MAGMA. 2010; 23: 351-366Crossref PubMed Scopus (435) Google Scholar), change-point analysis (Cribben et al., 2012Cribben I. Haraldsdottir R. Atlas L.Y. Wager T.D. Lindquist M.A. Dynamic connectivity regression: determining state-related changes in brain connectivity.Neuroimage. 2012; 61: 907-920https://doi.org/10.1016/j.neuroimage.2012.03.070Crossref PubMed Scopus (208) Google Scholar), or time-frequency analyses (Chang and Glover, 2010Chang C. Glover G.H. Time-frequency dynamics of resting-state brain connectivity measured with fMRI.Neuroimage. 2010; 50: 81-98Crossref PubMed Scopus (1259) Google Scholar). Multivariate methods in particular have proven quite powerful for both identifying intrinsic connectivity networks and for evaluating dependencies among these networks either in time (Allen et al., 2011Allen E.A. Erhardt E.B. Damaraju E. Gruner W. Segall J.M. Silva R.F. Havlicek M. Rachakonda S. Fries J. Kalyanam R. et al.A baseline for the multivariate comparison of resting-state networks.Front Syst Neurosci. 2011; 5: 2Crossref PubMed Scopus (63) Google Scholar, Jafri et al., 2008Jafri M.J. Pearlson G.D. Stevens M. Calhoun V.D. A method for functional network connectivity among spatially independent resting-state components in schizophrenia.Neuroimage. 2008; 39: 1666-1681Crossref PubMed Scopus (721) Google Scholar) or in space (Ma et al., 2011Ma S. Correa N.M. Li X.L. Eichele T. Calhoun V.D. Adalı T. Automatic identification of functional clusters in FMRI data using spatial dependence.IEEE Trans. Biomed. Eng. 2011; 58: 3406-3417Crossref PubMed Scopus (14) Google Scholar). In the subsequent sections we first provide examples of different chronnectomic approaches that emphasize various aspects of connectivity that change in time (e.g., temporal coupling, spatial coupling, and graph metrics) in addition to discussing the importance and need for validation. Next, we highlight a bit more the underlying assumptions and approaches for defining a connectivity “state” and the considerable differences that result followed by a higher-order approach that shows promise in unifying some of this information. Finally, we give specific examples of how chronnectomic work from our group has been applied to study mental illness, demonstrating the importance of the chronnectome in assessing the impact of mental illness on the brain. Underscoring this is data showing important differences in dynamic connectivity related to various mental illnesses, including schizophrenia and bipolar disorder. Such an approach provides new hope that we can find powerful biomarkers from fMRI data that are probably currently getting “diluted” through the use of an average connectivity map. Finally, we briefly mention some newer additional approaches that show promise for the future followed by some broader closing comments. Here we review several key approaches that have been used to identify dynamic states. The chronnectomic field is relatively young, but there are multiple ways to evaluate different aspects of changes in brain connectivity over time. In this section we start with the most common approach, which is to characterize changes in correlation over time (i.e., temporal coupling) assuming fixed regions. Next, we discuss an approach that models changes in the spatial patterns over time (i.e., spatial coupling). In the third section we discuss graphical models that can reconfigure in time. Each of these approaches provides a useful perspective and highlights different aspects of how brain connectivity is changing over time. Finally, we discuss the important topic of validating the various approaches. It is critical to understand how robust each approach is to noise and to understand their limitations. One of the first proposed approaches to characterize chronnectomic changes is called dynamic functional network connectivity (Sakoğlu et al., 2010Sakoğlu U. Pearlson G.D. Kiehl K.A. Wang Y.M. Michael A.M. Calhoun V.D. A method for evaluating dynamic functional network connectivity and task-modulation: application to schizophrenia.MAGMA. 2010; 23: 351-366Crossref PubMed Scopus (435) Google Scholar). In this, an approach called group independent component analysis (ICA) (Calhoun and Adalı, 2012Calhoun V.D. Adalı T. Multisubject independent component analysis of fMRI: a decade of intrinsic networks, default mode, and neurodiagnostic discovery.IEEE. Rev. Biomed. Eng. 2012; 5: 60-73Crossref PubMed Scopus (392) Google Scholar) is used to parcellate the brain into networks, each of which has its own characteristic time course. Next, time-varying changes among component time courses, called functional network connectivity (FNC) (Jafri et al., 2008Jafri M.J. Pearlson G.D. Stevens M. Calhoun V.D. A method for functional network connectivity among spatially independent resting-state components in schizophrenia.Neuroimage. 2008; 39: 1666-1681Crossref PubMed Scopus (721) Google Scholar), is captured by calculating cross-correlations between brain networks (components) over time using a tapered windowing (Allen et al., 2014Allen E.A. Damaraju E. Plis S.M. Erhardt E.B. Eichele T. Calhoun V.D. Tracking whole-brain connectivity dynamics in the resting state.Cereb. Cortex. 2014; 24: 663-676Crossref PubMed Scopus (1687) Google Scholar, Sakoğlu et al., 2010Sakoğlu U. Pearlson G.D. Kiehl K.A. Wang Y.M. Michael A.M. Calhoun V.D. A method for evaluating dynamic functional network connectivity and task-modulation: application to schizophrenia.MAGMA. 2010; 23: 351-366Crossref PubMed Scopus (435) Google Scholar). An example of this can be seen in Figure 1 in which group ICA is run on multiple subjects, followed by selection of components of interest and estimation of among-component time course correlations. Following this, a k-means clustering is performed (one of several methods that have been proposed) on the time series of correlation patterns to identify connectivity “state” matrices (these can be thought of as average patterns that subjects tend to return to during the course of the experiment). These can then be summarized based on the patterns of connectivity within each state as well as high-level summaries such as the dwell time each individual subject spends in each state (Allen et al., 2014Allen E.A. Damaraju E. Plis S.M. Erhardt E.B. Eichele T. Calhoun V.D. Tracking whole-brain connectivity dynamics in the resting state.Cereb. Cortex. 2014; 24: 663-676Crossref PubMed Scopus (1687) Google Scholar). A similar approach, except using regions of interest instead of components, has been used to show that sleep states can be predicted based on their connectivity pattern at a given time (Larson-Prior et al., 2011Larson-Prior L.J. Power J.D. Vincent J.L. Nolan T.S. Coalson R.S. Zempel J. Snyder A.Z. Schlaggar B.L. Raichle M.E. Petersen S.E. Modulation of the brain’s functional network architecture in the transition from wake to sleep.Prog. Brain Res. 2011; 193: 277-294Crossref PubMed Scopus (93) Google Scholar, Tagliazucchi and Laufs, 2014Tagliazucchi E. Laufs H. Decoding wakefulness levels from typical fMRI resting-state data reveals reliable drifts between wakefulness and sleep.Neuron. 2014; 82: 695-708Abstract Full Text Full Text PDF PubMed Scopus (403) Google Scholar). This is quite exciting, as it suggests that these state patterns may be useful for prediction. They also appear to be useful for characterizing disease, and an example of this appears in a recent paper focused on schizophrenia (Damaraju et al., 2014Damaraju E. Allen E.A. Belger A. Ford J.M. McEwen S.C. Mathalon D.H. Mueller B.A. Pearlson G.D. Potkin S.G. Preda A. et al.Dynamic functional connectivity analysis reveals transient states of dysconnectivity in schizophrenia.Neuroimage Clin. 2014; 5: 298-308Crossref Scopus (681) Google Scholar). One striking finding is that patterns that appear to characterize disease are only present in some of the states, and thus they are best estimated with a chronnectomic approach. Another very interesting direction is the focus on variation over time in spatial coupling. Because fMRI data are spatiotemporal, one can conceive of chronnectomic changes as the spatial patterns of correlated networks themselves instead of a focus on the connectivity among fixed spatial networks. In an early example of this an ICA was run on subsets of data over time to evaluate changes in the default mode network (Kiviniemi et al., 2011Kiviniemi V. Vire T. Remes J. Elseoud A.A. Starck T. Tervonen O. Nikkinen J. A sliding time-window ICA reveals spatial variability of the default mode network in time.Brain Connect. 2011; 1: 339-347Crossref PubMed Scopus (194) Google Scholar). A newer approach using independent vector analysis (IVA), which generalizes ICA to multiple data sets and performs a joint source separation such that the statistical dependence across them is fully taken into account (Anderson et al., 2014Anderson M. Fu G. Phlypo R. Adalı T. Independent vector analysis: identification conditions and performance bounds.IEEE Trans. Signal Process. 2014; 62: 4399-4410Crossref Scopus (49) Google Scholar, Kim et al., 2006Kim T. Attias H. Lee T.W. Independent vector analysis: definition and algorithms.Proc. 40th Asilomar Conf. Signals Systems Comput. 2006; : 1393-1396Google Scholar). A key advantage of this for studying dynamics is the ability to analyze short records of data, as joint processing enables better performance in the estimation without imposing additional constraints. IVA maximizes independence among temporal subsets of the data (called source component values or SCVs) rather than among the full data set, which is the case for ICA. The IVA approach also captures the dependence across time windows within a network so that changes over time in a given network can be tracked. We can capture chronnectomic changes in spatial coupling by again using overlapping windows of data and organizing the window from each subject as shown in Figure 2A. The SCVs that are highly dependent across the data sets will be those that are approximately static and those with more variability (less dependence among the source components within the source vector) will report on the dynamic spatial components. Because neither the temporal nor the spatial domain is constrained, the resulting decomposition successfully identifies the spatiotemporal dynamics in a data-driven manner. We analyzed healthy controls and patients with schizophrenia using the windowed IVA approach shown in Figure 2A with seven windows, each of which overlapped by 50% to cover a 200 time point resting fMRI data set (Ma et al., 2014Ma S. Calhoun V.D. Phlypo R. Adalı T. Dynamic changes of spatial functional network connectivity in healthy individuals and schizophrenia patients using independent vector analysis.Neuroimage. 2014; 90: 196-206Crossref PubMed Scopus (140) Google Scholar). Thirty components were estimated, of which 12 were determined to be BOLD related. Networks revealed very different spatial variation in patients versus controls (Figure 2B). We next computed probabilities to capture the spatial coupling by characterizing the transition probabilities for each state, which tells us whether a subject with a certain spatial pattern at a certain time is more or less likely to transition to another spatial pattern at a future time. Results indicated that controls show significantly less probability of transition between states (see example showing that patient temporal lobe state [state 3] is more likely to transition to another state [state 1] in Figure 2C). This provides a nice way to summarize changes in spatial patterns over time and to track differences in disease. One can also evaluate changes in the dependencies between pairs of spatial networks over time. To estimate spatial dependencies we can compute a mutual information matrix for each subject and each window (this is a matrix that indicates how similar each spatial pattern is to another spatial pattern over time). The schizophrenia patients show considerably more dependence among state 3 to other states than do the controls. This is a simple summary measure of only seven windows but it indicates that spatial dynamics can be sensitive measures of disease state. A full assessment of the spatial dynamics for each TR hence promises to more fully characterize the changes. Graph theory has become an important and widely used approach to summarize brain function (Sporns, 2011Sporns O. The human connectome: a complex network.Ann. N Y Acad. Sci. 2011; 1224: 109-125Crossref PubMed Scopus (930) Google Scholar). In addition, concepts such as “small-worldness” and “rich club networks” have already been studied extensively in the context of schizophrenia (Bullmore and Sporns, 2009Bullmore E. Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems.Nat. Rev. Neurosci. 2009; 10: 186-198Crossref PubMed Scopus (7367) Google Scholar, Zalesky et al., 2012Zalesky A. Fornito A. Egan G.F. Pantelis C. Bullmore E.T. The relationship between regional and inter-regional functional connectivity deficits in schizophrenia.Hum. Brain Mapp. 2012; 33: 2535-2549Crossref PubMed Scopus (85) Google Scholar). Extensions to time-varying graphs can be accomplished by incorporating multilayer network approaches, which attempt to quantify temporal variation in graph structure by constricting adjacency tensors to estimate multilayer graph statistics. This has been applied to examine brain network changes (over the span of days to hours to several minutes) in learning (Bassett et al., 2011Bassett D.S. Wymbs N.F. Porter M.A. Mucha P.J. Carlson J.M. Grafton S.T. Dynamic reconfiguration of human brain networks during learning.Proc. Natl. Acad. Sci. USA. 2011; 108: 7641-7646Cross