Functional Connectivity

This article was originally published in Brain Mapping: An Encyclopedic Reference, published by Elsevier, and the attached copy is provided by Elsevier for the author's benefit and for the benefit of the author's institution, for non-commercial research and educational use including without limitation use in instruction at your institution, sending it to specific colleagues who you know, and providing a copy to your institution’s administrator.

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Functional Connectivity SB Eickhoff and VI Mu¨ller, Research Centre Ju¨lich, Ju¨lich, Germany; HHU Du¨sseldorf, Du¨sseldorf, Germany ã 2015 Elsevier Inc. All rights reserved.

Glossary Network-based functional connectivity analysis Analysis to delineate functional connectivity within an a prioridefined network of regions. Resting-state functional connectivity Time series correlation in BOLD fMRI data acquired during the absence of an externally purported task.

Brain Organization and the Different Aspects of Connectivity The human brain is organized along two fundamental principles, functional segregation and functional integration (Friston, 2002). Here, functional segregation refers to the fact that the brain, in particular, the cerebral cortex, is not a homogeneous entity but can be subdivided into regionally distinct modules. Such modules, for example, cortical areas or subcortical nuclei, may be defined based on microstructural properties such as cyto-, myelo-, or receptor architecture, resulting in anatomical brain maps detailing the structural heterogeneity of the cerebral cortex. Additionally, functional criteria, that is, response properties as investigated by functional neuroimaging approaches such as fMRI, likewise suggest a regional specialization for the processing of specific stimuli or the performance of particular cognitive operations. Structural and functional mapping approaches thus emphasize the segregation of gray matter into distinct modules that are distinguished from each other in terms of microanatomy and response characteristics. The concept of functional integration, on the other hand, highlights that no brain region is by itself sufficient to perform a particular cognitive, sensory, or motor process. Rather, all of these mental capacities or ‘functions’ in the psychological sense have to rely on a dynamic interplay and exchange of information between different regions (Friston, 2002). Furthermore, a particular cortical area may be engaged by many different cognitive tasks; that is, there is no one-to-one mapping between brain regions and mental functions. From a conceptual point of view, it has thus been argued that the recruitment and dynamics within distributed brain networks are the most important foundation for the implementation of mental operations. However, it should be noted that functional integration and segregation are not necessarily in contrast, but rather complement each other, as functional integration can be conceptualized as the interaction between specialized regions, each performing a distinct computational subprocess (Eickhoff & Grefkes, 2011; Friston, 2002). Nevertheless, in recent years, there has been a substantial shift in our concepts of the brain organization and the neurobiology of higher mental operations away from a mainly localizing approach toward a view that stresses the role of

Brain Mapping: An Encyclopedic Reference

Seed-based functional connectivity analysis Analysis to delineate functional connectivity of one (or more) seed region with the rest of the brain. Task-based functional connectivity Above chance coactivations of brain regions across a large set of different neuroimaging studies.

networks and thus brain connectivity in understanding mental functions. In spite of the now pivotal role of connectivity analyses in functional systems neuroscience, the concept of brain connectivity in itself has remained somewhat enigmatic. Most importantly, there is no such thing as ‘the’ connectivity of a particular brain area. Rather, several conceptually different aspects of brain connectivity may be distinguished. Among them, a major, natural dividing line is that between anatomical connectivity and functional connectivity. The former represents the hard-wired connections between different brain areas formed by fiber tracts containing multiple individual axons, that is, a structural property of the brain. Evidently, such structural connections are a necessary prerequisite for any interaction between different parts of the brain but not in themselves sufficient to characterize these interactions giving rise to cognitive functions (Friston, 2011). Anatomical or structural connectivity, as investigated at the axonal level in nonhuman primates using invasive tracing approaches or approximated in vivo by means of diffusion-weighted imaging, thus represents the scaffold on which any transfer of information may take place but does not reflect the coupling and dynamic interactions between different parts of the brain. In contrast to structural connectivity, functional connectivity in a broader sense thus denotes the interactions between regional activity and hence the dynamic within the respective networks. Within this broad category that may be used to summarize any functional relationships between different parts of the brain independently of the anatomical connections by which they are implemented, two different concepts may be distinguished. One is effective connectivity, which denotes the influence that one node within a particular neuronal system exerts over another (Friston, 1994) and hence comes closest to the intuitive notion of functional interactions. It assesses the directed, either excitatory or inhibitory, effects that one particular area causes in another remote one. Given the fact that such interactions are rarely static, effective connectivity is usually considered in a dynamic, that is, time- and often context-dependent manner. Since such causal influences may not be directly measured using today’s neuroimaging techniques, investigating effective connectivity usually depends on models of functional interactions that estimate the influences between brain regions based on dependencies, temporal precedence, and other

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Brain Mapping: An Encyclopedic Reference, (2015), vol. 2, pp. 187-201

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INTRODUCTION TO ANATOMY AND PHYSIOLOGY | Functional Connectivity

aspects. The other aspect in the description of functional interactions in the brain networks that is also the most widely employed approach to the investigation of brain connectivity at the moment is functional connectivity in the more confined sense.

Functional Connectivity: Definition and Conceptual Implications Functional connectivity is defined as the temporal coincidence of spatially distant neurophysiological events (Friston, 1994). That is, two regions are considered to show functional connectivity if there is a statistical relationship between the measures of activity recorded for them. The notion behind this connectivity approach is that areas are presumed to be coupled or are components of the same network if their functional behavior is consistently correlated with each other. In contrast to effective connectivity analyses, which rest on numerous assumptions regarding both the underlying neurobiology and the model chosen to estimate it, functional connectivity represents a much more direct approach to the analysis of functional networks. In particular, it concurs with the intuitive notion that when two things happen together, these two things should be related to each other. By relying very little on a priori assumptions, functional connectivity analysis thus rather reflects a straightforward, observational measure of functional relationships. This definition, however, already clearly reveals two key aspects that need to be considered when dealing with functional connectivity analyses. The first is the important caveat that functional connectivity per se is purely correlative in nature. As just noted, two regions show functional connectivity, if increased activity in one region is associated above chance with activity in another. As always with correlations, however, this does not imply any causal relationship or even any sort of direct connection between these two regions. Correlated activity in two regions may, for example, be mediated via additional structures relaying information from the first area to the second. Such relay processes could moreover be transmitted through cascades of several intermediates or via cortical–subcortical loops involving, for example, the basal ganglia or the cerebellum. In such cases, activity in one area may represent the ultimate drive of activity in the other even in the absence of a structural connection, that is, fibers running between the two areas. Strong functional connectivity may hence be observed even if structural connections are weak or absent, although in most cases, these two aspects of brain connectivity show at least some level of convergence (Eickhoff et al., 2010). Furthermore, it is also possible that a third area induces correlated activation between regions that actually do not have any form of direct interaction. Therefore, functional connectivity may be driven by an external source inducing concurrent activity in both areas. An example of such situation would be the feedforward of stimulus-driven activity in early sensory areas that is forwarded to parietal sensory areas for perceptual analysis and, in parallel, to premotor cortex for response preparation. Even if both would be implemented in completely segregated streams, this scenario would lead to correlated activity changes in higher sensory areas and motor regions, that is, functional connectivity

between them. Thus, functional connectivity may be observed even between regions that are not functionally interacting with each other due to effects of the experimental setup. A similar consideration also holds for structured noise or confounds, such as motion or physiological effects (Birn, 2012; Duncan & Northoff, 2013). If their influence is not removed from the data or accommodated in the analysis, spurious correlations will arise. It follows that while functional connectivity investigations themselves require much less elaborate modeling and a priori assumptions than most approaches to effective connectivity analyses, they at the same time are much more susceptible to biological and technical confounds that may influence the noise spectrum of the data and induce spurious correlations that may be mistaken as functional interactions. Consequently, as will be detailed in the succeeding text, removing or accounting for potential confounds has become a major aspect not only of development but also of conjecture, in particular, with respect to resting-state functional connectivity analyses. Secondly, it should be remarked that the notion of functional connectivity may pertain to any form of neurophysiological events. That is, any above-chance coincidence of brain activity signals recorded in different parts of the brain may be considered as evidence for coupling between them, which may be direct, indirect, or spurious, and hence functional connectivity. Restingstate analyses, that is, time-series correlations in BOLD fMRI data acquired in a task-free state, may thus be used to assess functional connectivity in the brain. However, it must be remembered that functional connectivity represents a much broader concept that may not be equated with such resting-state analyses. Rather, functional connectivity may, for example, also be realized as correlated spiking patterns or field potentials. This application of functional connectivity analysis is commonly found in electrophysiological experiments in nonhuman species, where direct recordings of individual cells or multiunit activity may be correlated among different recording sites (Aertsen, Erb, & Palm, 1994; Gerstein & Perkel, 1969). In humans, it may also be applied to direct recordings during deep brain stimulation by correlating electrophysiological recordings from the implanted electrodes between different sites or contacts or by correlating them with cortical signals as measured, for example, by magnetoencephalography (MEG) or electroencephalography (EEG) (e.g., Hohlefeld et al., 2013; Lourens et al., 2013). Another non-fMRI application of functional connectivity analyses is the delineation of correlations or more precisely coherence between EEG sensors, which due to the high temporal resolution of EEG may be computed as broadband correlations or specific for particular frequency bands. In these instances, functional connectivity analyses indicate coherent oscillations, that is, neuronal mass activity, between different regions of the brain reflecting synchronous activity (Ruchkin, 2005). In terms of fMRI data, functional connectivity may be investigated on measurements that are obtained while the subject is passively lying in the scanner (resting state) or on fMRI data recorded during a particular task (e.g., Ebisch et al., 2013). Finally, the analysis of the coactivation patterns across many different task-based fMRI experiments can likewise be used to investigate functional connectivity in the brain (Eickhoff et al., 2010). In such analyses, the individual experiments represent the units of observation, and the analysis aims at identifying the above-chance coincidence of reported activations across different experiments. In summary,


Author's personal copy INTRODUCTION TO ANATOMY AND PHYSIOLOGY | Functional Connectivity

functional connectivity may thus be assessed using various data modalities and analysis approaches, rendering it a broad concept rather than a particular method.

Functional Connectivity in fMRI The currently most widely applied strategy for the examination of functional connectivity is based on the assessment of correlated signal changes in fMRI time series. In this approach, the functional connectivity between two locations of the brain is estimated by the (linear) correlation coefficient between their fMRI time series. The idea underlying ‘functional connectivity MRI’ thus confines to the fundamental concept of functional connectivity analyses, that is, coincidence of signals between different brain areas as outlined in the preceding text. The popularity of functional connectivity MRI data then stems from the fact that, given the richness of fMRI data, which usually consists of several hundred time points of wholebrain voxel-wise data, this approach has the perspective to yield information on functional connectivity across the entire brain at the level of individual subjects.

Functional Connectivity in fMRI Data on Specific Experimental Paradigms Analyses of functional connectivity by the correlation of regional BOLD signal intensities may be performed on fMRI time series obtained during the performance of experimental paradigms, that is, while subjects are engaged in a particular cognitive or perceptual experiment. In these cases, however, the major predicament is the immanent presence of taskdriven correlations. That is, all those regions that are activated by the particular experimental condition at hand will necessarily show functional connectivity due to common stimulusevoked modulations. Importantly, these effects may not easily be discarded as spurious or trivial. Rather, the common recruitment by a particular condition in fact follows precisely the idea of functional connectivity as the coincidence of neurophysiological events. Nevertheless, it is often regarded as not adding substantial new information above the observation of jointly activated regions in a conventional fMRI analysis. However, functional connectivity analysis by correlation of voxel- or region-wise fMRI time series obtained during the performance of an experimental paradigm that entails multiple conditions may provide insight into how closely different regions interact during the assessed experimental condition and how this coupling may change as a function of the condition at hand. In the context of more complex experiments consisting of multiple contextual sets, functional connectivity describes to which degree two regions are commonly corecruited and hence presumably coupled. When performed across the entire time series, that is, across all conditions, the correlation of regional fMRI signals may thus be regarded as a measure of the overall functional connectivity between the regions at hand across the entire experimental setting. If, however, functional connectivity measures are computed separately for a condition, task- or context-specific differences may be assessed. For example, assuming an experiment with two conditions presented in a block design, the correlation

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between the local BOLD time series of two regions may be computed independently for those blocks where one or the other condition was present and then contrasted with each other. While representing an easy window into paradigmrelated changes in interregional coupling, these approaches have become largely obsolete today. In particular, one of the key problems associated with computing functional connectivity during the performance of experimental paradigms is the delay and dispersion of task-related neuronal activity by the hemodynamic response function. Consequently, time-series correlation estimated from those scans taken during the presence of the respective experimental condition may not reflect the functional coupling during its performance. Rather, functional connectivity during that particular condition would be observable later (but with potentially variable delay between regions) in the time series. These problems posed by hemodynamic coupling render condition-specific functional connectivity problematic outside of cases in which very long, for example, minutes, blocks are employed for each condition. Consequently, the assessment of condition- and context-specific effects in fMRI time series obtained during experimental paradigms is now primarily the domain of analyses, in which both the presence of each particular condition of context and the hemodynamic response are explicitly modeled. Effective connectivity models such as dynamic causal modeling or Granger causality mapping (Goebel, Roebroeck, Kim, & Formisano, 2003) have thus by now largely superseded functional connectivity analyses as the method of choice to investigate connectivity during the performance of experimental paradigms. One of the key advantages of these effective connectivity models over straight time-series correlations is that they investigate context-specific influences between different brain regions while explicitly accommodating the delay of condition-related fMRI changes caused by the hemodynamic response function. In other words, if the timing of experimental manipulations is known, which is the case in fMRI data obtained during the performance of an experimental paradigm, effective connectivity models represent a substantially more specific approach to investigating context-dependent couplings than the analysis of functional connectivity.

Functional Connectivity in Resting-State fMRI Data In contrast to connectivity analyses in the context of experimental paradigms, where the timing is known, the situation is completely different, if there are no experimentally controlled manipulations, that is, when the timing of the underlying mental activity is unknown. In this case, functional connectivity analyses by fMRI time-series correlations thus represent the main avenue toward analyzing the interactions between different brain regions. Therefore, the currently most widely used application of functional connectivity analysis pertains to the assessment of ‘resting-state’ fMRI data. In such acquisitions, fMRI images are obtained using the same BOLD-sensitive sequences as in fMRI activation studies, usually with a time of repetition (TR) of 2–3 s, for about 5–10 min. Importantly, and in contrast to classical fMRI approaches using experimental paradigms, the subjects are lying in the scanner without being challenged by a particular task. That is, resting-state fMRI is based on BOLD time series consisting of several hundreds of




individual BOLD-sensitive images that are obtained while the subjects do not perform any externally purported task but are rather instructed to let their mind wander and not think about anything specific. It should be self-evident that the content and timing in the flow of thought are individual and hence different for each subject as they are not externally triggered. Consequently, no predefined time points are available, which would allow modeling of the associated hemodynamic response; that is, there is no condition- or context-related activity. Likewise, any methods for effective connectivity modeling, which also depend on an experimental input function describing the relevant timing of events, are not applicable in a straightforward manner. The beginning of resting-state functional connectivity analyses thus mainly goes back to positron emission tomography (PET) studies more than a decade ago, which showed that metabolic activity at ‘rest’ was not random but rather seemed to have a discernible structure. In particular, it was observed that local fludeoxyglucose (FDG)-activity counts of different, distant brain regions were significantly correlated across subjects (Horwitz, Duara, & Rapoport, 1984; Moeller, Strother, Sidtis, & Rottenberg, 1987). In other words, these studies indicated that spatially structured patterns of functional connectivity are accessible in the unstructured task-free state. In a seminar paper, Biswal, Yetkin, Haughton, and Hyde (1995) then showed in an individual subject that by testing for regions whose resting-state time series are significantly correlated with that of the primary motor cortex, they could identify many core regions of the brain’s motor network. This paper thus revealed that meaningful functional connectivity may be inferred from single-subject fMRI images acquired in a task-free state by the analysis of time-series correlations. In the following, restingstate fMRI has risen to remarkable popularity due to the combination of several key properties. First of all, it poses very low demands on subjects’ compliance, given that these do not need to complete any paradigm and consequently do not have to execute an experiment with a sufficient performance. Rather, all that is required is to remain still in the scanner for 5–10 min, which makes these acquisitions well suited for larger cohorts of subjects that would otherwise feature a high dropout rate, for example, clinical populations or children. Resting-state fMRI thus represents an approach, which allows most insights into the functional organization of the brain requiring least participation by the subjects. Additionally, multiple analyses are possible on the same data, as it is not constrained by task-specific effects. Functional connectivity analysis is therefore a procedure that is not dependent on knowing the timing of mental operations and that reduces the (subject-specific) time-series information to parametric information about the strength of interactions, which may additionally be aggregated across subjects. Consequently, resting-state functional connectivity analysis has become an important approach in basic and clinical neuroscience. In parallel to its growing popularity and importance, there has been an increasing awareness and discussion on potential confounding effects in resting-state functional connectivity analyses. In particular, it has been noted that the raw fMRI signal time courses are noisy due to scanner artifacts, motioninduced effects, and physiological sources such as cardiac and respiratory cycles (Birn, 2012; Duncan & Northoff, 2013).

While some of this noise is unstructured and hence only increases unexplained variance in the data, other sources of noise represent systematic confounds that may induce spurious correlations between the time courses of different brain regions. For example, let us assume changes in the global fMRI signal, be it due to scanner drifts or physiological effects that affect all voxels in the same manner. If these global signal changes over time are large enough, relative to the region-specific changes in BOLD activity that reflect the signal of interest, the correlation between pairs of regions will be close to perfect. Given the potential dominance of this effect over the relatively subtle functionally relevant fluctuations of the regional BOLD signal, there is a danger that global signal changes may strongly influence the overall level of functional connectivity as estimated from a subject’s fMRI time series. Several approaches to deal with this problem have been proposed (Murphy, Birn, & Bandettini, 2013). In a very simplistic approach, one could just extract the time series of a sphere placed in the ventricles and/or the deep white matter to represent the global signal change, following the logic that these will not contain regionally specific patterns of activity changes. These time courses may then be entered as regressors of no interest in a general linear model (GLM) or removed from the regional time series of interest prior to the correlation analysis. Alternatively, the time courses for global gray and white matter and cerebrospinal fluid may be computed by averaging across all voxels in that particular tissue class, reducing the influence of any subjective placement of the reference time series. In this context, however, it remains debated whether the mean gray-matter signal should actually be removed as it may reflect meaningful neurobiological information. Moreover, as another alternative approach, the mean signal time course may also be computed in a wholebrain mask, that is, averaged across the entire image. While all of these approaches are useful to remove spurious (positive) correlations from the data, it has been a matter of conjecture and argument whether global signal removal in itself may actually induce an artificial anticorrelation structure in the data, that is, replace spuriously high correlations with potentially likewise spurious anticorrelations (Murphy, Birn, Handwerker, Jones, & Bandettini, 2009). Besides these issues related to global signal changes, which affect the whole brain similarly, it is still a matter of debate how best to remove the effects of noise that is related to head motion and cardiovascular and respiratory effects. Importantly, however, in contrast to global signal changes, these effects may be specific to a particular type of connection, a particular direction, or a particular group of subjects. As one example, it has been shown that head motion may lead to an apparent increase in local functional connectivity, while the connectivity between more distant regions becomes attenuated (Satterthwaite et al., 2013). Likewise, cardiorespiratory effects do not affect the entire brain in the same fashion but seem to have a regional preponderance, for example, near the brainstem (Dagli, Ingeholm, & Haxby, 1999). While a complete coverage of the various approaches and aspects of correcting for physiological confounds in resting-state imaging is well beyond the scope of this overview and at the same time these methods are still rapidly evolving, they can be roughly divided into two classes (Murphy et al., 2013). Some approaches make



use of recorded (heartbeat and respiration) or estimated (head motion) time courses detailing these confounds, which are then used to remove the influence of the confounding factors in a model-based fashion. Other approaches are based on datadriven decomposition of the data using, for example, principle or independent component analyses (ICA). In these, either a certain set of dominant components in the data, reflecting global signal and systematic sources of variation, are blindly subtracted or components that have spatiotemporal characteristics incompatible with neurobiological activity are identified and removed from the data. Finally, it needs to be considered that due to the noise spectrum of fMRI data and the fact that the hemodynamic response function acts as a low-pass filter, correlations in BOLD signal that are indicative of functional connectivity between neuronal processes in different regions are predominantly present in a particular frequency range, usually assumed to be located between 0.01 and 0.1 Hz (Fox & Raichle, 2007; Greicius, Krasnow, Reiss, & Menon, 2003). In order to focus the analyses on these neurobiologically meaningful frequencies, temporal band-pass filtering is usually applied. In summary, there is thus an important need to reduce both global and biased spurious correlations by multiple processing steps such as spatial and temporal filtering and removal of signal contributions from motion, physiological noise, and global signal fluctuations before meaningful functional connectivity may be estimated from task-free data. There is also an ongoing debate on the physiological basis of BOLD signal correlations in the absence of an externally purported task. For example, it has been suggested that these fluctuations are driven by intrinsic activity events constrained by anatomical connections between the respective areas (Fox & Raichle, 2007). In this concept, resting-state functional connectivity may thus be regarded to be largely a reflection of the anatomical connectivity between different brain regions in the absence of an external task. Supporting this view, simulation studies show that one may generate patterns similar to restingstate fluctuations by injecting stochastic activity in structural networks defined by anatomical connectivity information (Honey, Kotter, Breakspear, & Sporns, 2007). On the other hand, some patterns of functional ‘resting-state’ connectivity exist, which cannot be explained by known, direct anatomical connections. As noted in the preceding text, indirect connections, cascades, or loops could mediate these indirect effects, and hence, functional dynamics may extend well beyond known, major fiber connections. However, it remains unresolved what drives these interactions in a physiological sense, that is, why there should be stochastic fluctuations of sufficient magnitude to propagate along anatomical connections. In particular, it would be unlikely that stochastic activity changes having an emergent structure due to the anatomical connectivity architecture should be present without a psychological correlate. This predicament has motivated a modified view on the psychophysiology of the ‘resting-state networks,’ which deempathizes the ‘resting’ aspect. Rather, it is assumed that the brain is never at rest (Buckner & Vincent, 2007) as there is always a large amount of ongoing activity composed of a vast variety of mental functions, even when a subject is lying still in the scanner. These range from bodily perception and

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somatosensation to memories and reflections, emotions and feelings, and explicit cognitive reasoning and planning including inner speech. That is, when lying in an MRI scanner without a specific paradigm to focus on, we are not thus resting but rather performing all sorts of mental operations in succession or parallel. The correlation in the MR signal time course between two regions should thus reflect the degree to which these jointly participate in the various networks engaged in the absence of an externally preset task. ‘Resting-state’ activity would hence consist of a, more or less random, sampling of all the different task-related networks that the brain is capable of, with a certain preponderance for introspective and interpersonal aspects (Schilbach et al., 2012). This view not only presents a plausible explanation for the apparent presence of networks resembling those seen in task-based fMRI but also reconciles the psychological experience of ‘rest’ with the hypothesis of coordinated stochastic fluctuations in brain activity. In particular, while these fluctuation would look random to the outside observer as the activity change in a particular region follows no specifiable temporal pattern, these would not be generated stochastically but rather reflect the ongoing, unconstrained train of thought of the subject. It has thus been proposed to avoid the term ‘resting state’ in favor of ‘task-free functional connectivity’ or ‘functional connectivity in the absence of an external structured task set’ (Buckner & Vincent, 2007; Schilbach et al., 2012), given that rest may not be an adequate term to describe the ongoing mental operations during ‘mind wandering’ or unconstrained, endogenously controlled cognition in an fMRI scanner.

Task-Based Functional Connectivity and Coactivations The notion that functional connectivity can be computed in the absence of an external structured task set easily leads to the complementary aspect of task-dependent functional connectivity, which is the correlation of neurophysiological responses during the performance of externally purported experimental tasks. As noted in the preceding text, functional connectivity may be inferred from correlation analysis between fMRI time series from different brain regions during the performance of a particular task. In this case, however, functional connectivity analysis is limited to the task at hand or – more precisely – to the particular experimental implementation of a given task. While such an approach may reveal new insight into the functional network underlying that particular experimental paradigm, it does not allow, however, answering the core question about task-based functional connectivity: Which other regions does a particular area in question work with? Or in other words, if a particular area is activated, which other brain regions are then more likely to be coactivated than it would be expected by chance? In order to answer this question comprehensively, task-based functional connectivity analysis needs to be performed across a large number of different tasks and implementations. Moreover, ideally, such data-driven definition of task-interacting brain networks should cover a broad range of functional domains in order to reveal associations between regions beyond a particular mental function. That is, the key question for task-based functional connectivity may not be resolved by the investigation of interactions during a




particular experimental setup but can only be addressed by investigating above-chance coactivations between different parts of the brain across a large set of functional neuroimaging studies. The possibility of actually implementing this idea has emerged from the advent of large-scale databases on functional neuroimaging results. Such resources, like the BrainMap (http://brainmap.org), the SumsDB (http://sumsdb.wustl. edu/sums/index.jsp), and Neurosynth (http://neurosynth. org) databases, have been developed in parallel to the growth of the functional neuroimaging field in order to keep up with the vast amount of fMRI findings published each year. In addition to these, several other database projects have been present over the course of the last decade, including the initially successful but ultimately short-lived fMRIDC (Van Horn et al., 2001), the European NeuroGenerator project (Roland et al., 2001), and many smaller initiatives, often representing the work of a single individual. It turned out that storage of raw neuroimaging data or even full statistical parametric maps seems impossible at the moment for several reasons. These range from the amount of storage space needed; to the reluctance of many researchers to make their data, collected with great investment of time and resources, freely available; to problems in backfilling older experiments. Consequently, all of the current approaches listed in the preceding text have been developed as coordinate-based databases. That is, they usually contain, for each included study, the location of the local maxima reported for each particular contrast (which may be retrieved from the published paper without any help from the original authors) and associated meta-data describing the experimental design, that is, the neuropsychological context of the experiment and the aspects that are to be isolated by the respective contrast. They thus make use of the high standardization of neuroimaging data, reported as tables of maxima coordinates and in particular of the ubiquitous adherence to standard coordinate systems such as the Montreal Neurological Institute (MNI) system. Importantly, the assembled data in these databases now allow testing for significant convergence of reported findings on a particular task, that is, topicbased meta-analyses. Rather, the results reported across all different kinds of tasks and experiments may be readily compared with each other and integrated with respect to the spatial location of significant neural activity. Neuroimaging databases thus provide the aforementioned broad pool of neuroimaging data across many different mental states that is needed to assess functional connectivity in terms of above-chance coactivation probabilities between different areas. Databases of several thousands of fMRI studies thus enable us to ask if two regions in the brain are more likely to show coactivation than one would expect by chance, that is, if there is a coincidence of reported activity in these two regions across many different experiments. In practice, task-based functional connectivity of a given region is established by retrieving all experiments from a database that feature at least one focus of activation within this region of interest. Coordinate-based meta-analysis is then performed over all activation foci reported in these experiments in order to test for significant convergence. As the experiments entered into such an analysis are selected based on the presence of an activation in a given seed region, any significant convergence of coordinates outside that seed would reflect

above-chance coactivation (Eickhoff et al., 2010). Importantly, such meta-analytic connectivity modeling (MACM) does not differentiate between different experimental paradigms or other factors, but rather is solely based on the likelihood of observing activation in a target region (or voxel). Consequently, it avoids any a priori bias based on potentially premature taxonomic considerations but represents a completely data-driven approach to the identification of functionally interacting brain networks during the performance of activation experiments. It is also of note that MACM, in spite of all its differences to the currently much more popular resting-state functional connectivity analysis, exactly follows the definition of functional connectivity by testing for coincidences of neurophysiological events. More precisely, MACM tests for the coincidence (joint reporting within a given contrast) of taskevoked activation in different brain regions (representing the neurophysiological events). Importantly, it has to be noted that MACM in particular differs from other functional connectivity measures such as not only resting-state connectivity but also, for example, MEG/EEG coherence, with regard to timescales. While other approaches are based on temporal dynamics in individual subjects, in task-based functional connectivity analysis via coactivation mapping, the unit of observation is not a specific point in an acquired time series but rather a particular neuroimaging experiment (cf. Jakobs et al., 2012 for a more detailed discussion of the conceptual commonalities and differences). Also, connectivity is not being estimated for a given subject but in a pool of many different experiments, each involving multiple subjects. Thus, task-based (MACM) functional connectivity is not expressed as coherent fluctuation across time but rather as coherent activation across experiments. Compared to resting-state functional connectivity analysis, MACM holds advantages and disadvantages. Probably, the biggest drawback of MACM is, as mentioned in the preceding text, that it is per definition not applicable to individual subjects. Consequently, there is no straightforward approach to integrate information from MACM task-based functional connectivity with measures of performance and establish brain–behavior relationships. Therefore, MACM findings may primarily serve as priors for future studies investigating functional or structural connectivity in a set of new subjects. MACM may thus be particularly useful as an independent, hypothesisforming approach that may then be tested using, for example, resting-state functional connectivity or fiber tract analysis from diffusion-weighted imaging. In turn, compared with task-free functional connectivity measures, MACM task-based functional connectivity analysis features two distinct advantages. First, MACM delineates networks that are conjointly recruited by a broad range of tasks and should hence reflect robust, that is, meaningful patterns of coordinated activity in response to an external challenge. Second, the MACM approach can also be used to investigate what kinds of experiments yield coactivation between two regions (Mu¨ller et al., 2013). While, as noted in the preceding text, MACM does not allow any inference on brain–behavior relationships, as it is not suitable for individual subject analysis, it thus allows establishing a link between functional connectivity and particular mental operations. In other words, MACM does not provide an answer to the question, how does connectivity in a particular



network relate to performance but instead provide inference on the mental operations, which recruit that particular connection, that is, functional inference. Evidently, these two aspects are highly complementary on each other, and together, they may allow a comprehensive inference on what kind of tasks recruit a given connection and how its strength relates to individual measures of performance. The complementarity between MACM and resting-state functional connectivity analysis, however, expands beyond this aspect. In contrast to resting-state functional connectivity, MACM analyses are based on task-related neural activity and therefore reflect functional connectivity in response to external challenges and largely miss spontaneous networks related to self-initiated behavior and thought. Thus, MACM (based on published activation coordinates for various neuropsychological tasks across many papers) and resting-state correlations (based on BOLD time series of individual subjects in the absence of an external task) are based on two completely independent sources of data, each of which not only provides insight into brain network organization in a different mental state but most likely also holds its own pattern of confounds and noise. A comprehensive assessment of the functional connectivity patterns of a particular seed region may thus consist of performing a meta-analysis both identifying significant coactivation in all experiments activating that seed region (MACM) and identifying all voxels in the brain whose time series in a task-free state (resting state) shows significant correlation with the reference time course extracted from that seed (Mu¨ller et al., 2013). In a comparison of both functional connectivity maps, two situations may arise. Either, regions are congruently implicated as being functionally connected with the seed in both analyses. Such convergent evidence across fundamentally different states (presence and absence of tasks) may be regarded as a very strong indication of a functional coupling with the seed. A mismatch between both analyses in turn must always carefully be examined for the potential effects of confounds and noise, which should be quite different across these two approaches and result in different spurious functional connectivity findings. On the other hand, however, strong but nonmatching evidence obtained from both analyses may also relate to the fundamental differences between the two states (Jakobs et al., 2012). In particular, it is well conceivable that a given brain region interacts with a particular set of areas (related, e.g., to planning and internal goals) during spontaneous, selfinitiated mental operations and with another distinct set of areas (related, e.g., to sensory processing) during the performance of externally presented experimental paradigms. Both convergence and divergence of results may hence contribute to our understanding of functionally connected networks in the brain. In addition and as noted in the preceding text, they may provide complementary information on the kind of tasks corecruiting two functionally connected areas and the relationship with interindividual variability of neurocognitive measures, respectively. While there has yet been little to no research along these lines, the prospect of differentiating internally and externally driven functional connectivity networks and their relation to a broad range of cognitive paradigms and individual performance measures may hold an important potential for understanding the physiology of the

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two main states of brain function, reaction to the external world and reflection on our inner states.

How to Analyze FC: Seed Correlations A very straightforward approach to functional connectivity analysis, independently of the actual data modality at hand, for example, resting-state fMRI time series or databases of activation experiments for coactivation mapping, is to perform seed region correlation. These analyses are founded on one or more a priori defined regions of interest (seeds), whose functional connectivity pattern is then delineated across the rest of the brain. In particular, seed-based functional connectivity analyses first involve extracting the signal of interest from the seed region, that is, the identification of the neurophysiological events for that region whose connectivity is to be examined. In time series-based approaches, such as resting-state fMRI, this involves the extraction of a characteristic time series (usually the first eigenvariate) for the seed region, which then represents the signal of interest. Subsequently, the local time series of all other locations of the brain (typically all voxels in a 3-D dataset, although regional or sensor-space measures are likewise possible) are compared with this seed time series. As noted previously, one of the main problems associated with time series-based functional connectivity analyses is spurious correlations introduced by structured noise or confounds in the data that may influence the observed relationship between the assessed signal time series and hence bias the results. Thus, confounding effects must be removed either using knowledge on these confounds in an explicit mode or by data-driven denoising (cf. the preceding text) from the time series of the seed and those of all other locations. Functional connectivity between the seed and each other location may then be quantified and statistically tested based on these denoised data using bivariate approaches, in particular linear correlation coefficients, which in most cases are subsequently transformed into Fisher Z-scores for standardization. Alternatively, functional connectivity may be assessed by setting up and estimating a GLM for each location in the brain in which the time series of the seed represents the explanatory variable of interest, while the confounds are added as covariates of no interest. In either case, single-subject estimates of functional connectivity with the seed for each location of the brain are then subjected to a second-level analysis testing for the consistency of effects across subjects. Task-based functional connectivity by meta-analytic connectivity modeling, in turn, takes a slightly different approach. First, all experiments (in a database) that feature at least one focus of activation in the seed region are identified. Here, the search may be restricted to specific kinds of studies, for example, only to studies on healthy subjects. All coordinates reported in the respective experiments are then extracted. Next, quantitative coordinate-based meta-analysis is conducted in order to test for convergence of reported coactivation in those experiments by, for example, using the activation likelihood estimation algorithm. Evidently, as experiments were defined by the activation within the seed region, all experiments included in the analysis feature at least one focus of activation in that region. In turn, the seed will always show the highest




(a) Resting-state FC

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Figure 1 Example of seed-based functional connectivity analyses: based on a functionally defined seed in the hand area of the left primary motor cortex (blue), functional connectivity was delineated by resting-state (a) and task-based functional connectivity analyses (b). Both analyses are thresholded at the same level of significance (p < 0.05, corrected for multiple comparisons). Note that using of the same seed region and threshold, both approaches to functional connectivity show a fundamentally similar motor-related network. Yet, several divergences between both approaches are also apparent, indicating that resting-state and task-based functional connectivity analyses provide complementary information.

convergence of activity. Significant convergence of the reported foci outside the seed in turn indicates above-chance coactivation and hence task-based functional connectivity. Importantly, in spite of the different analytic approach investigating convergence of spatially sparse signals rather than computing the correlation of spatially continuous data, MACM has the same localizing properties with resting-state functional connectivity analyses. Consequently, both may be applied to the same seed region in order to delineate its functional connectivity pattern in two complementary approaches using completely independent datasets and reflecting coupling in different mental states. This is illustrated in Figure 1 showing seed-based functional connectivity mapping using restingstate and meta-analytic connectivity analyses seeded in the hand area of the left primary motor cortex. The main advantage of seed-based functional connectivity analysis is that it represents an approach toward functional network mapping by delineating those regions in the brain showing functional connectivity with the seed. Importantly, these approaches are thus spatially localizing; that is, they provide information about where in the brain functional connectivity with the seed is found. They perform this spatial inference, however, in an indirect fashion. Rather than using an explicit spatial model and performing a statistical inference on the model parameters pertaining to spatial locations, the functional connectivity with the seed is analyzed and statistically tested independently for each location (voxel) in the brain. By plotting those locations at which the respective test became significant, following correction for multiple comparisons, the spatial pattern of regions showing functional connectivity is then recovered. This approach is thus analogous to the standard approach in task-based fMRI analysis in which regions of significant activation are identified by plotting those locations where the inference using a GLM-based mass-

univariate approach became significant. Moreover, seedbased analyses may also be used to localize regions showing significant differences in functional connectivity with the regions of interest. In the context of resting-state functional connectivity, such contrasts may, for example, be used to identify regions, which show a significant difference in functional connectivity with the seed between patients and controls, that is, regions that show a disease-dependent dys-connectivity with that seed. In task-based functional connectivity analyses, coactivation patterns with a seed between different tasks and behavioral domains may be compared. That is, additional contextual filters may be applied when identifying those experiments in the database that feature activation within the seed and the ensuing whole-brain coactivation patterns may then be compared. This allows, for example, identifying those regions, which show significantly more consistent coactivation with the seed in cognitive tasks as compared with motor tasks. Thus, there are various applications for seed-based functional connectivity analyses based on resting-state fMRI or analyses of coactivations, which may be applied independently but can also be combined. In particular, when performed for more several, conceptually related, seed regions of interest, such analyses may represent a powerful approach to the delineation of functional networks interacting (differentially) with a set of a priori defined regions. In this case, the seed regions would in turn provide the functional context for the interpretation of the observed connectivity patterns. On the downside, it must be acknowledged that the results of seed-based functional connectivity analyses strongly depend on the precise localization of the seed. Consequently, the quantitative definition of the seed, that is, the operationalization of the scientific question by a binary mask, is crucial to the entire endeavor. As an example, suppose one wants to investigate the functional connectivity of the hand area within the



primary motor cortex. In this case, the seed region could be drawn by the investigator using anatomical landmarks (hand knob), but it could also be based on a significant cluster of activation in a previous fMRI experiment of hand movements or a significant cluster of convergence in a meta-analysis of such tasks. In either of these cases, the next question would be if the seed is defined by an a priori defined functional cluster or a sphere around the local maxima coordinate and/or additionally masked by an anatomical mask of the primary motor cortex, constructed either from macroanatomy (posterior wall of the precentral gyrus) or from probabilistic cytoarchitectonic maps (e.g., areas 4a and 4p). All of these approaches, and potentially many more, could be considered valid representations of the hand area of the primary motor cortex, even though they most likely will differ notably in their precise location and extent and consequently also in their functional connectivity pattern. The seed definition hence provides an important initial constraint and potential bias in these kinds of functional connectivity analyses. As an unrelated but likewise important consideration, seedbased functional connectivity analyses may become difficult to manage if the number of seeds grows, as each individual seed will result in at least one whole-brain connectivity map, with additional statistical maps coming from contrast or conjunction analyses of different populations or task settings. In particular, if the effects for the different seeds do not overlap, such analyses may easily end up without a clearly interpretable result. Moreover, while the choice of the seed may provide a functional context for the interpretation of functional connectivity or dys-connectivity maps, it must be considered that the ensuing interpretation often requires a (potentially overly simplified) one-to-one mapping between a spatial location and an associated mental process. In particular, the interpretation of the established functional connectivity map or the regions showing abnormal connectivity in a patient sample will often be focused on a particular functional context that was associated with the seed when planning the respective study. Often, however, a region of the brain may be associated with several different functional properties, rendering the (subjective) reverse inference and focus on one functional aspect open to potential bias. The final drawback worth mentioning is that seed-based functional connectivity analyses may be particularly sensitive to the influence of confounds, in particular those that have a spatial structure. One example for such spatially structured confounds in resting-state functional connectivity analyses may be the heterogeneous effects of motion on short- versus long-range connections’ strengths, where the former are accentuated and the latter reduced (Satterthwaite et al., 2013). If moreover motion is also not homogeneously or randomly present in two different samples, for example, in patients versus controls, a contrast of seed-based functional connectivity measures between the two groups would reveal a significant difference in long-range connections with weaker connectivity shown for the group that had shown more motion. In taskbased (MACM) functional connectivity, the unequal sampling of the entire brain by experimental tasks, that is, the fact that a lot of experiments use a similar (visual) input, mental operation, and (hand) motor output structure and hence show in particular frequent activation in the visual, parietal, and

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posterior frontal cortices but rather infrequently report regions like the middle temporal gyrus, may likewise be considered a spatially structured confound.

How to Analyze FC: Network Analysis Another approach that is less focused on localization is the investigation of functional connectivity within an a priori defined network of regions. In this kind of analysis, included regions may be considered as the nodes of the ensuing brain network, whereas the estimated functional connectivity would represent the edges between these (Behrens & Sporns, 2012). Independent of the use of resting-state fMRI time series or taskbased connectivity modeling (MACM), a network-based analysis of functional connectivity in a predefined network first always involves the extraction of the signal of interest from each of the a priori defined regions. In resting-state functional connectivity analyses, the most common approach would be to compute the characteristic time series for each region, for example, the mean or first eigenvariate of all voxels that are part of the respective region. Secondly, these signals need to be processed, for example, by removing variance that can be explained by global signals or physiological confounds. Following this preprocessing, a vector representing the signal (time series) of the neurobiological feature of interest will be obtained for each of the a priori defined regions. From these, the cross correlation between the individual regions then readily assembles a functional connectivity matrix. That is, the similarity in the signal vector is computed between each pair of regions or nodes, usually by means of Fisher Z-transformed linear correlation coefficients. The full set of values for all pairs or regions then represents the functional connectivity within the assessed network. Each edge in the resulting network is characterized by a single value and would be computed for each subject individually. These values, one per connection, that is, pair of regions, and the subject may then be subjected to various kinds of follow-up analyses. In contrast, in task-based coactivation analyses, the signal would usually be provided by a vector detailing the involvement of a region in all experiments stored in the employed database. That is, a vector will be obtained for every region of the network, containing for every experiment of the database the information if the respective region is reported or not. In a next step, in most cases, noninformative aspects such as experiments that activate none of the predefined regions will be removed. Then, the similarity of the vectors will be computed for all pairs of regions in the respective network, which again will result in a single value for every edge of the network. These values that would represent the likelihood of coactivation potentially corrected for overall biases in activation probability may then again be used for follow-up analyses. For example, the functional resting-state connectivity along each edge may be compared between two groups of subjects such as patients and controls. Likewise, when phenotypic measures of the subjects are available, the individual, subject-specific strength of the functional connectivity along each connection may be correlated with the behavioral covariate of interest. This thus allows investigating the relationship between the connectivity in a predefined network and the respective phenotype (see Figure 2 for an example).




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Figure 2 Example of network-based functional connectivity analyses investigating a specific network: In this case, functional connectivity was investigated in a motor network identified in a previous fMRI study (a). By using resting-state functional connectivity analyses, the connectivity strength between each pair of nodes was computed and then subsequently related to behavioral measurements. This analysis revealed a significant positive correlation between functional connectivity between the left cerebellum and right basal ganglia and the interindividual variability of performance in a finger-tapping test (b). In contrast, by using task-based coactivation analysis and functional decoding using the BrainMap database, it could be shown that coactivation of the left cerebellum with the right basal ganglia was significantly associated to experiments related to action execution and to tasks like finger tapping, recitation/repetition, and flexion/extension (c). The integration of task-based and resting-state functional connectivity analyses thus allows both functional decoding of mental operations associated with a particular connection and its relation to interindividual differences in phenotype.

In particular, in larger networks covering multiple individual regions, this approach may likewise become localizing by testing which connections within the examined network show a relationship to a neurocognitive measure of interest or a difference between patients and controls. These kinds of analyses may thus be seen as an extension of the localizing framework for seed-based functional connectivity analyses or brain–behavior correlations using other imaging modalities to the network level. Finally, the properties of individual nodes or the entire network may be summarized using network measures derived from graph theory such as the average degree, the average shortest path length, and the presence of hubs. These graph theoretical analyses, although outside the scope of this overview, have the appeal that they allow the characterization of complex networks or the role of individual nodes within these by a few characteristic numbers. They come, however, with the downside that these measures are usually fairly abstract, making them at time difficult to interpret in a neurobiological sense. Moreover, they also represent a highly reduced characterization of usually complex connectivity patterns. Similarly, as in seed-based analyses, how to set up the regions of interest, that is, the nodes making up the investigated network, has an important influence on the ensuing functional connectivity measures and any follow-up analyses. Evidently, these regions of interest may be assembled in many different ways, reflecting different ideas and goals for the functional connectivity

network analysis. Broadly, however, the various approaches and definition of networks should fall into two classes, one referring to whole-brain networks and the other to specific (functional) networks not covering the entire brain. In the former, the entire brain is subdivided into regions of interest (see Figure 3(a) for an example), which can be performed by a number of different ways, with the most prevalent being a subdivision based on (macro)anatomical atlases or a geometric division into parcels of roughly equal size (Behrens & Sporns, 2012). Alternatively, the parcels may also be estimated from the data itself, for example, by spatially constrained ward clustering to identify patches that feature a homogeneous (resting-state) functional connectivity pattern (Behrens & Sporns, 2012). Independently of the method used to define these regions, if the investigated nodes cover the entire brain, the ensuing network will evidently also represent the complete brain-wide functional connectivity pattern or functional connectome (Sporns, Tononi, & Kotter, 2005). While analyses of the full functional connectome have received much attention recently, it needs to be cautioned that this does not represent a singular, well-defined property of a particular individual, but may rather depend on the way the brain is divided into separate regions, the preprocessing steps, and the confound removal, among other factors. One of the major advantages of connectome-style analysis is the fact that it does not rely on a priori hypotheses outside of the assumptions going into the definition of the individual regions. It thus allows the investigation of all functional connections and the localization



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Figure 3 Example of a network-based, ‘connectome-style’ functional connectivity analysis covering the entire brain. The whole brain was subdivided into 1600 equally sized regions of interests (a). Resting-state functional connectivity was then determined by correlating all 1600 nodes with each other resulting in a full connectivity matrix for the entire brain (b).

of those interactions that, for example, differ between two populations or that relate to a particular phenotype. This advantage, however, comes with a potentially severe multiple comparison problem. For example, at a granularity of 1000 regions of interest (which would be equivalent to each cortical region covering roughly 2–3 cm2 of cortex, i.e., probably more than an individual functional module), any statistical inference on the ensuing functional connectome would need to deal correcting for almost half a million parallel tests. Increasing the granularity in order to arrive at more specific coverage of functional units substantially worsens the problem as the number of parallel tests increases to the second degree with the number of regions. Conversely, reducing the number of regions ameliorates the multiple comparison problem but in turn dramatically reduces the specificity of any findings. In particular, it may be argued that these larger regions, which would result from a parcellation of lower granularity, would contain multiple functional modules, each showing a potentially specific pattern of functional connectivity. Averaging across these may thus obscure relevant features in the functional connectome. In other words, choosing a finegrained parcellation – with the extreme case of considering each voxel individually – will allow a more specific analysis and localization of effects but comes at a rapidly increasing multiple comparison problem. In turn, choosing a broader parcellation will lead to less problems in statistical inference but entails lower specificity and probably also validity of the findings. This predicament has more recently started an interest in the use of multivariate pattern-analysis approaches for the investigation of connectome data (e.g., Sripada et al., 2013). These avoid the problem of multiple independent tests but rather use the entire pattern of functional connectivity measures, that is, the strengths along all edges of the whole-brain network, to identify patterns that are predictive of, for example, clinical classifications (health vs. disease) or phenotypic variables such as cognitive performance. Referring the reader to the respective section on pattern analyses for further details, we would thus summarize that network-based analyses in which the regions of interest cover the entire brain have the intriguing potential of characterizing the entire functional connectome but are still faced with

open questions on how to parcel the brain into distinct regions and challenged by the necessary trade-off between specificity and validity on one hand and data reduction on the other. Alternatively and falling into the other class of network definition (those not covering the entire brain), the investigated regions may also represent a set of brain locations that are considered to form a functional network based on information other than functional connectivity, for example, a previous fMRI study or a meta-analysis of activation findings. As an example, the regions of interest for a network-based analysis of functional connectivity of the motor system may be defined by those brain areas, which are involved in hand movements. This would restrict the analysis to a particular functional system and thus increase the interpretability of findings. In contrast to the investigation of the full functional connectome, such analyses may be regarded as hypothesis-driven investigations of functional connectivity in which the definition of the network represents the operationalization of the neurobiological hypothesis. In the case of the motor system and as shown in Figure 2, this approach would, for example, allow to assess whether interindividual differences in the functional connectivity between different cortical and subcortical motor areas are related to phenotypic differences in motor behavior. Such hypothesis-driven approach obviously has the main advantage that the analysis is focused on those regions that have a functional relevance to the behavior at hand. In addition to better interpretability, those analyses also avoid incidental findings in other parts of the brain that may be driven by residual confounding effects or represent false positives. At the same time, such functional definition will, in most cases, keep the number of regions and hence the multiple comparison problem limited. This in turn increases the sensitivity of the analysis, as less severe correction is required. Using a priori knowledge on a functional system of interest in order to investigate functional connectivity within that system has thus two main advantages: the obtained findings are functionally more specific and also more sensitive due to a lower number of parallel comparisons. In turn, one potential disadvantage is (again) the dependency on the exact definition of the seeds. As detailed in the preceding text in the section on seed-based




functional connectivity, there is no general standard for this definition, which represents the operationalization of the neurobiological hypothesis, that is, the investigated system, into a set of regions of interest. Rather, the same neurobiological entity, for example, the motor system, may be parameterized into a set of regions or nodes by many different approaches, which most likely will have an influence on the obtained network measures. In other words, whereas the functional connectivity analyses in a priori defined network should represent a largely, though not completely, unbiased approach, the definition of the respective nodes is potentially much more open to bias. A second potential drawback that is shared with all hypothesis-driven analysis approaches is the fact that such investigations are blind to effects outside the hypothesized network. As connectivity is only assessed between an a priori defined set of regions, even the most substantial or relevant influence of an outside region, that is, one that was not part of the predefined set of nodes, will be missed. Consequently, the validity of network-based approaches focusing on a particular functional system is crucially determined by both the completeness of the a priori network model and the quality by which the chosen regions of interest reflect the relevant nodes. There is, however, a justified hope that the recent emergence of meta-analytic approaches, which have by now already resulted in robust definitions of several cognitive systems, may provide a solution to these problems. In particular, defining the nodes of functional brain networks by those regions that show convergent evidence for functional involvement in a specific neurobiological system, computing the functional connectivity between these network nodes, and relating the interindividual differences in functional connectivity strength to phenotypic measures that probe the respective neurobiological system at the behavioral level may represent a promising approach to bridging functional localization, connectivity, and behavior.

How to Analyze FC: Independent Component Analysis As can be inferred from the preceding text, functional connectivity analyses may be performed by different approaches, such as correlations on time series from resting-state fMRI data and task-driven coactivations across a large number of functional neuroimaging experiments. Beyond that, the different analysis methods for functional connectivity also show a continuum ranging from strongly hypothesis-driven approaches (networkbased analyses in confined a priori defined sets of nodes), to analyses that investigate the whole-brain connectivity of one or a few predefined regions of interest (seed-based analyses), to those that investigate the functional connectivity between any pair of a large set of regions covering the entire brain (connectome-style analyses). All of these approaches, however, rely on some a priori definition of brain regions or nodes. ICA in turn represents an alternative, completely data-driven approach to functional connectivity analysis. The key idea behind ICA is to separate a signal provided by a time series (or a large set of findings from previous neuroimaging studies) into a set of mutually independent and associated time courses. In other words, ICA identifies sets of voxels or regions that cofluctuate across time (in resting-state or task-based fMRI data) or that are coactivated across experiments. Each

component thus represents a system of regions that show functional connectivity with each other (see Figure 4 for an example of a component derived by ICA). In this context, it is interesting to note that the ICA decomposition of resting-state fMRI time series and the BrainMap database have yielded highly convergent sets of components, indicating that a similar decomposition into functional systems may be achieved by applying it to data across many tasks and experiments and resting-state data (Smith et al., 2009). In itself, however, ICA is a purely decomposing approach, which only enables the identification of mutually independent sets of regions of high within-component functional connectivity. By using dualregression approaches though, subject-specific versions of the spatial maps determined at the group level and their associated time series may be computed. Statistical analysis may then be sought by testing for differences in the expression of a particular component at each voxel between two groups or be related to a particular phenotype. The ensuing results, which are specific for a given component and consist of voxels in which there is, for example, a significant group difference, have sometimes been mislabeled as ‘differences in functional connectivity within region A.’ However, there is obviously no connectivity within a region. These results thus denote a difference in the functional coupling between the identified set of voxels and the rest of the component. That is, a significant group difference in the analysis of a specific component reveals that the ensuing voxels are more or less tightly integrated into that component in one group of subjects compared with the other. While the technical details of ICA, in particular with respect to its application toward resting-state fMRI data, are detailed in a separate part of this book, some advantages and drawbacks of ICA-based analyses relative to the other functional connectivity approaches should be considered. Evidently, a main strength of ICA-based functional connectivity analyses is that it is a completely data-driven approach that does not require any a priori choice of regions or network nodes. Rather, not only the components themselves but also their number may be estimated from the data at hand, resulting in an unbiased definition of functional connectivity networks. Moreover, by decomposing the entire dataset, the different estimated components provide the possibility of investigating multiple functional systems at once. They thus represent a ‘middle road’ between the two classes of network-based functional connectivity approaches outlined in the preceding text. While being much more complete than a priori networks covering a particular functional system, they provide a data-driven grouping into such systems of coherent connectivity that is not intrinsically given by connectome analyses. Finally, ICAs have been shown to be highly robust, not only across different experimental states such as task and rest (Smith et al., 2009) but also across subjects. In particular, the identification of many common components is possible even on the level of individual subjects (Zuo et al., 2010). There are, however, also several drawbacks that need to be considered in the context of ICA to assess functional connectivity. One of them is the direct flip side of one of the main strengths, namely, the completely data-driven approach lacking any a priori knowledge. While this property is advantageous when investigating the functional organization of the human brain without any constraints, it does also have



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Figure 4 Example of a component derived by independent component analyses using resting-state fMRI data. Here, the color scale indicates how strongly each voxel is associated with this particular component (thresholded at p > .5 for displaying purposes). Using dual regression, subject-specific versions of this group-level spatial map and their associated time series may be computed and subsequently subjected to statistical inference testing for differences across subjects or groups in the expression of that particular component at each voxel.

limitations. In particular, as the components are estimated from the data, they do not represent a standardized ‘test set’ that may be employed to probe functional connectivity in a specific prespecified network. This makes it difficult to directly compare findings across studies or populations. Moreover, conventional ICAs usually focus on the assessment of between-group effects of brain–behavior correlations within each component, that is, test whether a set of voxels are more strongly or weakly integrated into the respective component and, if so, where these voxels are more strongly or weakly integrated. Once estimated, the identified components thus represent rather strong constraints on the statistical analysis of the data. For example, it is easy to test if a voxel in the primary motor cortex is more or less integrated into the ICA component representing the motor system in a group of patients, and the findings should be well interpretable. In contrast, a change in the integration of this voxel with a different component, for example, the visual system, is technically equally feasible but may be much more difficult to interpret as that particular voxel is not per se significantly associated with the respective component. Finally, given a considerable degree of consistency between datasets, ICA studies have presented converging evidence for the existence of several distinct components (i.e., functional networks) in fMRI datasets obtained during a task-free, ‘resting’ state. Moreover, as noted in the preceding text, most of these ‘resting-state networks’ closely resemble networks that are commonly engaged in task-based fMRI studies (Smith et al., 2009). This has led to the intuitive but still not fully validated notion that virtually, any functional system in the brain is discernible by ICA decomposition. It has also contributed to the now widely established functional labeling of these components as ‘dorsal attention network,’ ‘visual network,’ ‘auditory network,’ ‘sensorimotor network,’ ‘central-executive network,’ ‘core network,’ and so on. While intuitive and certainly convenient in reporting ICA findings, these labels are unfortunately primarily an example of largely subjective reverse inference. Just because a component looks spatially ‘similar’ to a set of regions that have been found in task-based fMRI studies does not yet implicate that these networks are associated with the respective cognitive function. Moreover, one needs to consider that, due to

the simplicity and consequent recent popularity of ICA-based resting-state functional connectivity analyses, many of these labels have become associated with sets of connotations that may have become somewhat detached from task-based cognitive psychology. Terms like ‘saliency network’ and ‘default mode network’ may provide useful vehicles to denoting a particular spatial component consisting of the bilateral anterior insula and the midcingulate cortex/SMA and a bilateral posterior inferior parietal and anterior and posterior midline network, respectively. They have, however, evolved to carry functional connotations that may or may not be valid and in any case hinder an unbiased investigation into their functional roles.

Summary and Conceptual Considerations Understanding the organization of the human brain will necessarily be a multimodal endeavor that requires the consideration of both the regional specialization (using structural and functional brain mapping) and the integration between specialized regions, that is, the integrated analysis of structure, function, and connectivity. In this context, functional connectivity analyses should hold a crucial position as they may provide a bridge between structural connectivity, representing the scaffold of fiber connections between remote brain regions, and functional specialization as revealed by the pattern of taskrelated activity. Investigating functional connectivity allows the delineation of interacting networks and the amount of functional coupling between the respective regions in a robust fashion using rather limited assumptions. It must be acknowledged, though, that functional connectivity is per se a correlative approach, which entails several important caveats. Probably, the most important implication from this correlative nature is the consideration that functional connectivity between two regions does not imply any direct interaction between them. Rather, several different routes such as relays or loops may realize not only the required coincidence of neurophysiological events but also the common influences by the third region. Moreover, given the straightforward but rather nondiscriminative nature of functional connectivity analyses, they may be particularly sensitive to confounding




factors, that is, aspects other than the effects of interest, which affect the correlation structure in the data. Keeping these caveats in mind, however, functional connectivity analyses have a unique role in multimodal brain mapping that is complementary to functional and structural mapping and anatomical connectivity analyses. It must also be noted that functional connectivity represents a very broad concept that comprises multiple different possible analysis approaches. These range from hypothesis-driven investigations of interregional coupling among a set of predefined regions, usually from a particular functional system; to seed-based analyses testing for regions showing significant functional connectivity with that particular seed; to connectome analyses investigating the full functional connectivity pattern between a large set of regions covering the entire brain; to finally ICAs decomposing the signal in a completely data-driven fashion. Moreover, functional connectivity estimated on resting-state fMRI time series represents not only the most widely used approach but also the probably most feasible method to obtain functional network information in larger or less compliant cohorts of subjects. In the spectrum of functional connectivity modalities, however, it only represents one possible aspect. In turn, investigation of task-based coactivation patterns and cross correlation analyses of MEG/ EEG time series may provide valuable and most important complementary information in functional interactions during a different mental state, that is, the performance of externally structured tasks, and at a higher temporal resolution, respectively. In this context, one important question for further research is the relationship between different aspects of functional connectivity and their relation to measures of structural connectivity and functional specialization.

See also: INTRODUCTION TO ANATOMY AND PHYSIOLOGY: Cytoarchitectonics, Receptorarchitectonics, and Network Topology of Language; Cytoarchitecture and Maps of the Human Cerebral Cortex; Myeloarchitecture and Maps of the Cerebral Cortex; Transmitter Receptor Distribution in the Human Brain; INTRODUCTION TO METHODS AND MODELING: BrainMap Database as a Resource for Computational Modeling; Dynamic Causal Models for fMRI; Effective Connectivity; Graph-Theoretical Analysis of Brain Networks; MetaAnalyses in Functional Neuroimaging; Multi-voxel Pattern Analysis; Resting-State Functional Connectivity.

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