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Home , Connectome, Connectomics

Ann. N.Y. Acad. Sci. ISSN 0077-8923

ANNALS OF THE NEW YORK ACADEMY OF SCIENCES Issue: The Year in Cognitive

The human : a

Olaf Sporns Department of Psychological and Sciences, Indiana University, Bloomington, Indiana

Address for correspondence: Olaf Sporns, Department of Psychological and Brain Sciences, Indiana University, Bloomington, Indiana 47405. [email protected]

The is a complex network. An important first step toward understanding the function of such a network is to map its elements and connections, to create a comprehensive structural description of the network architecture. This paper reviews current empirical efforts toward generating a network map of the human brain, the human connectome, and explores how the connectome can provide new insights into the organization of the brain’s structural connections and their role in shaping functional dynamics. Network studies of structural connectivity obtained from noninvasive have revealed a number of highly nonrandom network attributes, including high clustering and modularity combined with high efficiency and short path length. The combination of these attributes simultaneously promotes high specialization and high integration within a modular small-world architecture. Structural and functional networks share some of the same characteristics, although their relationship is complex and nonlinear. Future studies of the human connectome will greatly expand our knowledge of network topology and dynamics in the healthy, developing, aging, and diseased brain.

Keywords: networks; brain anatomy; neural dynamics; diffusion imaging; resting state; complex systems

cells6 to that of entire ecosystems.7 In neuroscience, Introduction the idea that the brain is a neural network has deep We live in the age of networks. Our social interac- historical roots. Yet the application of quantitative tions, be they personal relationships, political as- network theory to the brain is a recent develop- sociations, financial transactions, professional col- ment.8 This review will focus on the application laborations, the spreading of rumors or diseases, of network concepts and network thinking to the or physical transport and travel, increasingly occur human brain. I will survey the contributions of net- within networks that are evolving across time. All work science to our understanding of how human of these networks are examples of complex systems, brain function arises from the interactions of cells with highly structured connectivity patterns, mul- and systems. Throughout, I will attempt to chart a tiscale organization, nonlinear dynamics, resilient path into the future, extrapolating the current flow responses to external challenges, and the capac- of ideas and their potential impact on models and ity for self-organization that gives rise to collec- theories of the brain. tive or group phenomena. Modern developments A major driving force of recent progress has in and complex systems have delivered been the development of innovative methods for important insights into the structure and function mapping brain connectivity, at cellular and sys- of these diverse networks, as well as quantitative tems scales. In the human brain, the continued models that can both explain and predict network refinement of noninvasive diffusion imaging and phenomena.1–5 computational has begun to reveal Over the past decade, many studies across a range large-scale anatomical connections in unprece- of scientific disciplines have demonstrated that com- dented detail. For the first time, these methods al- plex networks pervade not only the social sciences, low the acquisition of comprehensive whole-brain but also biology, from the organization of single data sets from individual human subjects and their

doi: 10.1111/j.1749-6632.2010.05888.x Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. 109 The human connectome Sporns comparison with individual data on brain dynamics, series data can be processed to extract temporal cor- , behavior, and genetics. The mathemati- relations, spectral coherence, or measures of causal cal and theoretical framework of complex networks signal flow, with each approach representing differ- is an indispensable ingredient in the quantification, ent aspects of neural dynamics. Thus, the configu- analysis, and modeling of these challenging data sets. ration of a “functional connectome” depends crit- Driven by technological and theoretical develop- ically on the choice of empirical methodology and ments a new picture of the human brain is taking analysis. shape—a picture that views cognitive processes as Second, it is important to underline that the con- the result of collective and coordinate phenomena nectome is a description of brain connectivity. The unfolding within a complex network.8–12 term description implies compression of raw data As neuronal activity gives rise to dynamic patterns with the goal of extracting maximal information. and processes, anatomical or structural connections To use an analogy, an architectural description of play an important role in shaping these dynam- a physical structure summarizes the major features ics. Connectivity creates a structural skeleton for a of the design, but it does not offer a list of the di- dynamic regime conducive to flexible and robust mensions and positions of all the building blocks. neural computation. Comprehensive information In the case of the brain, it is not necessary to de- on structural connectivity is fundamental for the mand that the connectome be an exact replica of the formulation of mechanistic models of network pro- connectional anatomy down to the finest ramifica- cesses underlying human brain function. Hence, I tions of neurites and individual synaptic boutons. will begin with a discussion of recent progress in ob- Instead, the connectome should aim at a description taining a complete map of the brain’s connections, of brain architecture that ranges over multiple levels the human connectome. of organization, reflecting the multiscale nature of brain connectivity. This program may include the What is the human connectome? microscale of cells and , but it does not im- The human connectome is “a comprehensive struc- ply that all structural connectivity must be reduced tural description of the network of elements and to this level. Like any good road map, the human connections forming the human brain.”13,14 Three connectome should provide a multiscale description aspects of the connectome are central to this defini- of the topological and spatial layout of connectional tion, and they deserve to be emphasized here as they anatomy. Such a description will require the devel- have important theoretical ramifications. opment of sophisticated methods First, the connectome is principally about struc- and tools to represent information about connec- ture, about the extensive but finite set of phys- tivity across multiple spatial scales, for example, in ical links between neural elements. The physical the form of digital brain atlases.16 reality of structural connectivity provides an im- Third, the main thrust behind the concept of the portant point of methodological convergence— connectome is that it is the description of a network. different empirical methods for mapping structural Thehumanconnectomeisnotjustalargecollection connections should eventually provide a consistent of data. Instead it is a mathematical object that nat- anatomical description. In contrast, functional con- urally fits within a larger theoretical framework and nectivity, which unfolds within the structural net- thus links neuroscience to modern developments in work, is significantly more variable across time, re- and complex systems. Ongoing re- flecting changes in internal state or neural responses search in these rapidly evolving areas of science will to stimuli or task demand. Functional connectiv- be instrumental for enabling the connectome to re- ity is generally defined as a statistical dependence alize its full potential as a theoretical foundation for between remote neural elements or regions, and . New theoretical, mathemat- it can be measured with a number of rather dis- ical, and statistical approaches are urgently needed parate methods that offer different perspectives on to fully reveal the organization of the human con- brain dynamics.15 For example, electrophysiology nectome and its fundamental role in cognition. and magnetic resonance imaging (MRI) measure Some beginnings have been made, notably in graph very different physiological signals and operate on theory and dynamical systems, and it seems likely different time and spatial scales. Additionally, time that will continue to benefit from

110 Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. Sporns The human connectome efforts to map and model other complex biological interactions. Interestingly, the spatial arrangement systems. of chromatin within cell nuclei has been shown Connectome data sets are invaluable for linking to be associated with organized patterns of structure to function, a relationship that is of piv- expression.18 otal concern in the biological sciences and one of the This comparison suggests that neither central themes of this review. In biology, structure is nor should be viewed as rigid pro- encountered at many scales, from molecules to the grams or “blueprints” for biological function. Their morphology of cells and entire living forms. Struc- functions result not so much from the reading-out ture enables function, conservatively defined here as of encoded instructions but rather involves the col- the set of possible actions and interactions of a bio- lective and coordinated actions of genetic and neural logical system. For example, the three-dimensional elements in complex networks. The organization of structure of a macromolecule is critically important these networks enables the robustness and flexibil- for its interactions with other chemical , its ity of biological systems.19,20 Structural variations capacity to bind substrates or catalyze chemical re- can alter the dynamic expression of genomes and actions, and its localization within specific cellular connectomes and thus impact their functionality. compartments. Similarly, the connectivity structure The sensitivity of functional dynamics to structural of a neural system defines its internal dynamic states change is an important rationale for pursuing efforts and its range of responses to external perturbation. to catalogue and map and connectome data The importance of the connectome derives from sets. the fundamental role of the network of structural Empirical approaches to mapping the connectivity in shaping the rich and dynamic set human connectome of functional interactions of neural elements that underlie human cognition and behavior. The structural connectivity of the human brain is The term connectome was suggested in deliberate organized on multiple nested spatial scales. Roughly, analogy to the genome, and there are many paral- three scales of organization may be distinguished:13 lels between these two constructs. Both are funda- the microscale of single and synapses, the mental structural data sets that inform us about the macroscale of anatomically distinct brain regions possible “functions” (actions and interactions) of a and pathways, and the mesoscale of neuronal popu- biological system. Both involve structural elements lations and their interconnecting circuitry. Methods at different levels of scale (neurons, neuronal pop- for mapping the connectome exist at each of these ulations, and brain regions; base pairs, , and levels, and all of them are needed to achieve a com- genetic regulatory networks). Both exhibit variabil- plete representation of the human brain’s connec- ity across of the same, as well as dif- tions. At the microscale, there is significant progress ferent, species. Both give rise to complex system on mapping cellular connectivity and reconstruct- dynamics (firing patterns of neurons and neuronal ing neuronal processes and synapses with electron populations; spatiotemporal expression profiles of or light . At the mesoscale, tracing of gene products). Additional parallels have emerged axonal projections with neuroanatomical markers due to recent discoveries in gene modification and and histological sectioning are poised to deliver transcription. Structural units of the connectome as whole-brain connectional data in several nonhu- well as the genome can be modified by environmen- man species. At the macroscale, the development tal interactions. It is well known that brain connec- of noninvasive neuroimaging techniques allows the tivity is altered through various forms of neuronal observation of connectional anatomy across the plasticity, and recent work has shown that individ- whole brain in live human participants. ual genomes can be subject to epigenetic biochem- To this day, the mapping of the cellular connec- ical modification.17 Finally, both connectomes and tions in , accomplished 25 genomes are embedded in three-dimensional space, years ago,21 stands as the only complete connectome and the spatial proximity of their elements influ- of any . This unique data set was the result ences their functional dynamics. The location of of painstaking reconstruction of three-dimensional neural elements is crucially important for the devel- neuronal morphology and connectivity from thou- opment of connectivity and the resulting functional sands of ultrathin serial sections scanned by

Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. 111 The human connectome Sporns electron microscopy (EM). Extensive analysis of the on the local direction and inclination of axonal C. elegans has since provided im- fibers.31,32 The resulting distributions of vectors of portant insights into its wiring economy22 and con- fiber orientation can then be used to reconstruct nectional topology.23 In recent years, the advent of axonal pathways across the section, and possibly the new imaging, serial sectioning, and computational entire brain. The technique allows imaging of ax- reconstruction techniques has fueled renewed ef- ons at high spatial resolution, and it may become an forts to map cellular anatomy of neural tissue at important method for the verification and valida- extremely high, subcellular resolution. New compu- tion of fiber anatomy revealed by in vivo diffusion tational methods for automated three-dimensional imaging (see below). reconstruction of sectioned EM volumes are under The labeling of axonal projections with the aid development,24 an indispensable step given the size of neuroanatomical tracers has revealed the con- and complexity of serial EM data sets. EM recon- nectional anatomy of several mammalian in struction is currently the only approach with suf- extraordinary detail. The accuracy and sensitivity of ficient spatial resolution to trace individual axonal several of these tracers are well established, and the processes as well as dendritic spines, and it can in approach is particularly well suited for the mapping principle be used to map non-neuronal cell types of long-distance pathways. Collations of hundreds and reveal their relation to neurons. of individual anatomical reports on inter-regional Other approaches in microscopy involve the com- connections in the brains of several mammalian bination of optical fluorescence and scanning EM species33,34 have provided a wealth of insight into the of thin sections of neural tissue, or “array tomog- anatomical organization of functionally segregated raphy,”25 as well as the labeling of individual neu- brain regions and their hierarchical and clustered rons with immunofluorescent markers followed by arrangement.35–38 Bohland et al. have proposed a three-dimensional optical imaging.26,27 The latter connectome map for the be con- technique has been successfully applied to a set of structed through the systematic application of neu- neuromuscular connections in the mouse28 deliv- roanatomical tracers.39 While invasive anatomical ering important insights into the spatial layout of tracing techniques cannot be carried out in human axonal processes and their high degree of struc- brains, injection of lipophilic dyes in postmortem tural variability, both within and across individ- tissue have provided data on patterns of connec- uals. Imaging of neurons expressing fluorescent tional anatomy in at least some cortical regions.40,41 markers in a column of primary somatosen- Significant challenges remain before microscopy sory cortex has provided detailed information on methods can be deployed to fully map the human the number and spatial distribution of neuronal cell connectome at the microscale. Tracing individual bodies and the pattern of thalamic afferents.29 The human axons with EM or light microscopy will development of these and other fluorescence imag- require error-free tracing and reconstruction over ing techniques, particularly in combination with distances of many millimeters, from stacks of thou- genetic approaches,30 will undoubtedly yield un- sands of serial sections that individually cover an precedented quantitative data on the composition area of only a few square microns. Acquisition, stor- and connectivity of neural circuits in various animal age, and manipulation of raw data from even a sin- species. gle human-sized brain demands computational re- Histological sectioning and imaging of the whole sources far in excess of anything available today—it human brain is made difficult by its sheer size and has been estimated that a single microscale human volume. Modern refinements of histological tech- connectome would consist of one trillion gigabytes, niques allow the collection of complete sets of thin or one exabyte.42 While these challenges may seem histological sections from individual postmortem daunting at present, they may well be overcome as brains. Quantitative analysis of these sections can high-throughput automated microscopy and recon- visualize variations in cellular microarchitecture as struction become a reality. Other limitations, shared well as axonal connectivity. In a new technological by all ex vivo approaches to connectomics, concern development, histological sections of postmortem the difficulty of establishing links between anatomy human brains are examined with polarized light and function. For example, any connection diagram imaging, a technique that provides information derived at the cellular scale represents a snapshot in

112 Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. Sporns The human connectome time of a highly dynamic and variable architecture, humans, due to the lack of tract tracing data, but since changes in the morphology and connectivity is feasible in other species, including the macaque of individual neurons are not captured. And mi- monkey. Initial studies suggest that there is con- croscopy can only be carried out on sections from siderable agreement between diffusion imaging and postmortem tissue, which, in the case of humans, is tract tracing, at least with respect to a number of difficult to obtain and preserve, and the use of which long-range cerebral pathways.52,53 However, funda- eliminates the possibility of examining neural struc- mental limitations of diffusion imaging, for exam- ture in relation to neural dynamics or behavior. ple, its inability to resolve the direction of axonal MRI currently represents the best option for non- pathways and detect axonal branching, remain to be invasive mapping of large-scale structural connec- addressed. tions in the human brain.43 Some connectome maps The construction and analysis of structural and have been assembled on the basis of structural MRI functional brain networks from empirical data in- data. Correlations in the thickness or volume of volve a series of steps (Fig. 1).11 First, network nodes gray matter between two cortical areas, usually mea- must be defined, which, in the case of noninvasive sured across multiple participants, are partially pre- neuroimaging studies, generally involves a parcella- dictive of the presence of anatomical connections. tion into coherent regions on the basis of histologi- The mechanism that accounts for these correlations cal, connectional, or functional imaging data. Once is currently unknown but possibly involves corre- nodes are defined their mutual association is mea- lated metabolic or trophic processes, or genetic or sured, expressing their structural linkage or func- experience-related factors. Some of the very first tional coupling. These pair-wise measurements are whole-brain connection matrices were assembled then aggregated into a connection matrix, which on the basis of cross-subject correlations in cortical represents a graph or network. Finally, network thickness,44,45 and the approach continues to be of metrics can be computed to extract relevant char- use in clinical comparisons.46 acteristics of the graph’s topology, which can be Diffusion MRI provides information about the compared between individuals, subject groups, spatial orientation of myelinated fiber tracts in cere- recording modalities, or to random graphs con- bral .47 An important challenge is the structed according to specific null hypotheses. resolution of complex fiber architecture in parts While each step presents significant methodolog- of the brain where multiple fiber tracts intersect. ical challenges, perhaps the most important deci- Various imaging techniques that use multiple diffu- sion involves node definition. Noninvasive imaging sion directions48,49 can resolve heterogeneous fiber in humans does not allow the observation of in- orientations within single voxels. The subsequent dividual neurons and instead delivers measures of application of computational algorithms allows the neural population activity averaged over millimeter- inference of anatomical tracts from the observed dis- sized volume elements. The voxel partition is ar- tribution of diffusion anisotropy across the imaged bitrary and does not reflect any underlying bio- brain volume. Deterministic approaches to tractog- logical structure. Voxels need to be grouped into raphy rely on finding optimal streamlines within coherent regions to yield a biologically meaning- the diffusion tensor field, while probabilistic ap- ful partition of the brain volume. An ideal parti- proaches aim to provide statistical estimates for the tion should maximize the connectional informa- existence of fiber pathways. Various combinations of tion contained in the resulting graph achieving high diffusion imaging and tractography techniques have specificity and low redundancy of connection pat- been applied to the human brain and the brains of terns among discrete parcels or regions of the brain. other mammalian species, with continual improve- A partition that is too coarse will result in mixing ments in resolution and sensitivity. For example, of connection patterns and hence loss of informa- high-resolution diffusion spectrum imaging (DSI) tion about specific connections. An extremely fine- has recently mapped the complex fiber anatomy of grained partition will tend to contain a lot of redun- the human cerebellum,50 as well as the developing dant information, as many nodes are simply copies circuitry of the cat brain.51 Cross-validation of con- of each other. Random partitioning into roughly nectivity obtained from diffusion imaging against equal-sized brain nodes53,54 offers a trade-off be- histological tract tracing is difficult to carry out in tween coarse and fine parcellation since it allows the

Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. 113 The human connectome Sporns

Figure 1. Extraction of brain networks from empirical data follows along four steps: (1) parcellation of the brain volume into coherent regions on the basis of structural or connectional features (MRI), or node assignment by placement of sensors and/or recording sites (EEG, MEG); (2) structural or diffusion imaging to derive estimates of structural connectivity (left) or recording of time series data to estimate functional coupling (right); (3) construction of a connection matrix representing a structural (left) or functional network (right); shown here are data from the right , as reported previously;53,124 and (4) network analysis. exploration of network properties over a range of different connection profiles (“connectional fin- node scales. gerprints”),55 that is, different patterns of affer- Simple parcellation schemes based on anatom- ent and efferent anatomical connections, or dif- ical landmarks are imprecise and insufficient to ferent sets of functional linkages. Measurement of fully represent the true anatomical and func- the connection profiles of neural elements across tional diversity of the cortical architecture. More the brain volume (or cortical surface) delivers gra- sophisticated approaches use information about dients of connectional change with peaks corre- structural and/or functional connectivity to define sponding to putative regional boundaries. Alter- regions with a coherent connectivity profile, ob- natively, homogeneous groupings that correspond tained from individual brains. These approaches to segregated brain regions can be extracted us- build on the idea that different brain regions have ing clustering algorithms. Clustering of connectivity

114 Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. Sporns The human connectome profiles was used for segmentation of thalamic forts to map the human connectome, regardless of nuclei56 and definition of coherent cortical re- scale.64 gions in medial frontal cortex57 and inferior frontal Network architecture of the human cortex.58 connectome Correlations in spontaneous neural dynamics, for example, recorded in resting-state fMRI, exhibit lo- Parcellation allows the brain to be divided into a set cal differences and transitions across the cortical of discrete elements (nodes) and their mutual con- surface. Sharp boundaries between regions of co- nections (edges) that jointly form an object called herent resting-state functional connectivity can be a graph (Fig. 2). Commonly used in many scien- detected with image analysis tools applied to the tific disciplines, graphs are models of real systems cortical surface,59 thus allowing the noninvasive par- that offer a comprehensive map of how the sys- cellation of coherent functional regions in individ- tem’s elements are linked or associated with each ual subjects. Extending this approach, a detailed other. As models, graphs provide a description that parcellation of lateral parietal cortex was recently is highly compact and embodies numerous assump- carried out on the basis of functional connectivity tions about the nature of the real system that is be- obtained with resting-state fMRI, as well as task- ing represented.65 These assumptions must be taken evoked response profiles.60 Using a combination of into account in the analysis and functional interpre- gradient detection and network analysis techniques, tation of brain networks.66 the study identified a number of distinct parietal re- The structure of graphs or networks can be ana- gions that are arranged in network communities, lyzed with the help of a broad range of graph the- each of which maintains specific functional associ- oretical measures.67,68 A number of these measures ations. As these studies demonstrate, the combina- have already been applied to the analysis of struc- tion of multiple criteria for region definition includ- tural and functional brain networks.11,69,70 Based ing structural connectivity, resting-state functional on the information they provide about the biolog- connectivity, task-evoked activations, and possibly ical organization of brain networks, relevant graph cytoarchitectonic data greatly improves the robust- measures roughly fall into three classes: measures ness and sensitivity for defining network nodes, the of segregation, integration, and influence.66 Mea- building blocks of complex brain networks at the sures of segregation identify the degree to which large scale. the graph can be decomposed into local commu- Any effort to map the human connectome must nities or clusters of nodes that are highly intercon- go beyond the mapping of invariant structural pat- nected. Such network communities are often re- terns and also consider individual structural vari- ferred to as modules, a term that is used here only in ability and plasticity. Structural changes occur in the its graph-theoretical connotation. Measures of inte- courseofdevelopmentaswellasinrelationtoex- gration estimate the global efficiency of communi- perience. While the extent of experience-dependent cation among all nodes in the network. Measures of structural plasticity remains unknown in most neu- influence yield indices for the potential participa- ral systems, mounting evidence suggests that many tion of individual nodes and edges in dynamic pro- circuit elements (neurons and synapses) can un- cesses unfolding within the network, as expressed, dergo substantial structural modification on rela- for example, in the node/edge . Highly in- tively short time scales.61 Even at the large scale of fluential brain nodes are also referred to as hubs and interregional pathways, recent studies have demon- can be further classified according to their network strated changes in white matter architecture re- embedding and connection profiles.71 , lated to behavior.62 63 The interest in structural Graph metrics have proven to be useful analytic plasticity derives from its functional implications. tools for the study of brain networks. The generality Structural plasticity among neurons and brain re- of the mathematical framework of graph theory al- gions alters their dynamic interactions and func- lows its application in networks derived from a wide tional profiles. The importance of these structure– array of recording methods, from brain anatomy to function relationships (discussed in further detail functional connectivity, and in virtually all neural below) implies that dynamic changes of anatomi- systems. While most applications so far have been cal patterns should become an integral part of ef- at the large scale of whole-brain networks derived

Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. 115 The human connectome Sporns

Figure 2. Schematic representation of the basic concepts of graph theory. The diagram at the left shows an undirected weighted brain network such as might result from diffusion imaging and tractography. Thresholding removes weak connections, and further analysis reveals two network communities or modules that are interlinked via a highly connected and highly central hub node (a so-called connector hub, “C”). Each module also contains highly connected nodes with mainly intramodular connections, forming provincial hubs (“P”). The diagrams at the bottom show module 2 after the connections within it have been converted to a binary format, illustrating the concepts of a network path (between nodes 1 and 2) and clustering (around node 3). with diffusion or , cellular ties, or modules. This tendency toward modularity multielectrode recordings and optical imaging data is coupled with a high capacity for global infor- sets are increasingly modeled as graphs and com- mation flow, as indicated by high efficiency and plex networks.72–74 Graphmeasuresnotonlyhave short path length. The combination of high clus- a wide range of applications but also appear to be tering and short path length is one of the major robust and reliable. In large-scale systems, graph characteristics of small-world networks.78,79 Robust metrics have been shown to be robust across mul- small-world attributes were identified in several in- tiple imaging runs,75 given a suitable partition of dependent studies of whole-brain structural net- the brain into nodes and edges. Importantly, all works of human .53,54,80–82 The func- graph measures are sensitive to the choice of par- tional significance of the “small-world-ness” of the tition and parcellation,76,77 thus underscoring the human brain derives from the natural propensity importance of the initial node and edge definition. of this architecture to promote functional segre- More methodological work is needed in the area gation (local clustering) and functional integration of statistical comparison of graphs across imaging (global efficiency), a hallmark of complex neural dy- modalities, subjects, or subject groups. Such com- namics.83 Variations or disturbances of local and/or parisons can be challenging, especially if the graphs global anatomical or dynamic features may be sensi- contain an unequal number of network elements, or tively reflected in corresponding small-world mea- if the correspondence of nodes and/or edges across sures, and these measures may thus be of analytic different graphs cannot be established. importance. Graph analyses of structural and functional data The small world of the human cerebral cortex from the human brain have demonstrated an is composed of structural modules, or network abundance of characteristic, nonrandom attributes. communities. A modularity analysis45 performed Large-scale structural networks derived from non- on a connection matrix of human cortex previ- invasive diffusion imaging exhibit a high propensity ously derived from intersubject correlations in cor- for clustering of nodes into structural communi- tical thickness44 identified several internally densely

116 Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. Sporns The human connectome

Figure 3. Graphical layout and modularity of a human connectome. (A) The structural backbone of a structural connection matrix averaged over five participants was extracted, as previously described,53 resulting in a matrix containing roughly 25% of all pathways. This connection matrix was then embedded in two-dimensional space using the Kamada–Kawai force-based energy minimization algorithm.140 This algorithm assigns spring-like forces to the network’s edges and attempts to place all nodes such that an energy term is minimized, achieving an optimally balanced layout. Labels refer to the centers of mass of several brain regions. Note that the connection topology, when graphically arranged such that “tension” along edges is minimized, roughly reproduces the arrangement of these regions in anatomical space. Right and left hemispheres are clearly separated, and the major anterior–posterior and lateral-medial cortical axes can be recognized. Regions are abbreviated as follows: (r = right hemisphere, l = left hemisphere): BSTS = bank of the superior temporal ; CAC = caudal anterior cingulate cortex; IP = inferior parietal cortex; LOCC = lateral occipital cortex; LOF = lateral orbitofrontal cortex; LING = lingual ; MOF = medial orbitofrontal cortex; MT = middle temporal cortex; POPE = pars opercularis; PTRI = pars triangularis; PSTC = postcentral gyrus; PC = posterior cingulate cortex; PREC = precentral gyrus; PCUN = ; RAC = rostral anterior cingulate cortex; SF = superior frontal cortex; SP = superior parietal cortex. (B) Nodes are color coded by their assignment to one of six major structural modules, as previously reported.53 Note that modules comprise spatially coherent groupings of nodes. Plots at the right show anatomical locations of these modules in the right hemisphere. connected modules largely corresponding to func- identified six structurally distinct modules in the tionally distinct groups of areas related to vision, frontal, temporoparietal, and medial cortex (Fig. 3). movement or language, as well as a set of interlinking These modules mostly consisted of regions that hub regions including several areas of multimodal or were spatially close together, linked by a large num- association cortex. A study based on DSI data sets53 ber of short connection pathways found between

Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. 117 The human connectome Sporns adjacent areas. Particularly notable was a set of hubs Community detection is of special relevance for located along the anterior–posterior medial axis of studies of human brain networks because structural the brain that included highly connected regions and functional modules may coincide with sets of such as the rostral and caudal anterior cingulate brain regions and pathways that jointly participate cortex, the , and the precuneus. in specific cognitive tasks. For example, the appli- These regions were not only strongly interconnected cation of modularity to resting-state fMRI data has among each other but also maintained connections revealed several distinct networks engaged in dif- with regions in virtually all other major commu- ferent cognitive task domains.60,91 With the arrival nities in both right and left cerebral hemispheres. of robust parcellation strategies it is expected that A topologically central core of interconnected hub studies of communities in structural and functional regions was also described in a recent graph analy- brain networks will yield increasingly refined maps sis of large-scale structural connectivity of cat and of neurocognitive networks. macaque monkey.84 The prominent place of the posterior medial In parallel studies, functional modules have been cortex within the cortical network deserves closer derived from physiological brain recordings, includ- scrutiny. Several graph-theoretic analyses of in- ing resting-state fMRI. There are several common dependently acquired diffusion imaging data sets themes in the organization of structural and func- have reported high centrality for the precuneus tional networks. For example, in agreement with and posterior cingulate cortex, and neighboring re- structural network analysis, functional networks ex- gions.53,81,82,92 These regions form an aggregation of hibit a strong tendency toward modular small-world structural hubs (a structural core), combining a high architecture.85,86 Another common feature is the degree of connectedness as expressed in the graph existence of a nested hierarchy of structural87 and measures of node degree and strength, as well as functional modules.88 Thefullextentofthishierar- high . Interestingly, the same chy is only partially mapped and ranges from rel- set of regions occupies an equally central position atively coarse groupings—for example, the hemi- in functional networks, in particular those engaged spheres or major lobes of the cerebrum—to more during cognitive rest,89,93–96 and also corresponds fine-grained groupings, such as functional brain sys- to an area of extremely high baseline metabolic ac- tems (e.g., visual, auditory, somatomotor cortices), tivity.97 The precuneus, a central component of the individual segregated regions, gray matter nuclei, structural core, is activated during a wide variety of and even columnar arrangements of cells. An im- cognitive operations including self-referential pro- portant question for future network studies con- cessing, imagery, and episodic memory,98 its level cerns the relationship between structural and func- of baseline activation is associated with the level tional modules and their hierarchical arrangement. of ,99 and its functional connectivity Answering this question will require multimodal changes in the transition from waking to .100 imaging studies and network comparison across Activation studies and network analyses indicate a modalities. high degree of functional specialization within sub- Communities or modules are coupled via hub regions of the precuneus. The region exhibits dif- nodes, which represent highly connected and highly ferential patterns of activity during the processing central regions of the brain. Several studies of struc- of different kinds of social emotions.101 In addition, tural networks have pinpointed these regions within resting-state fMRI suggests that different subregions the parietal and frontal lobes of the cerebral cor- of the precuneus maintain distinct sets of func- tex.81,82 At least some hubs are mutually intercon- tional connections with other parts of the brain.102 nected or aggregated to form a prominent structural Taken together, the combination of physiological core, located in posteromedial cortex and compris- observations and network analysis has significantly ing several cortical regions including the precuneus, increased our understanding of the structure and posterior cingulate cortex, and superior parietal cor- function of this highly central brain region. tex.53 Large-scale functional networks exhibit a sim- Linking structure and function ilar organization, with several studies demonstrat- ing a set of functional clusters or modules,86 highly One of the main rationales for assembling the hu- connected hub nodes,89 and high global efficiency.90 man connectome is the importance of anatomical

118 Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. Sporns The human connectome structure for our understanding of neural dynam- dynamics in ever greater detail. Independent com- ics103 and, ultimately, cognition and behavior. As ponent analysis has demonstrated several distinct will become clear in this section, structural brain resting-state networks,114,115 some of which corre- connectivity does not rigidly determine neural in- spond to sets of brain regions that cooperate in teractions but acts as a set of constraints, a skeleton, specific cognitive domains such as vision, motor or scaffold that sharply reduces the dimensionality planning, or episodic memory. Their activation is of the neural state space. Within this reduced low- modulated by task demands and may have diagnos- dimensional space, neural dynamics remain fluid, tic value in at least some brain disorders.116 Dis- variable and sensitive to dynamic perturbations. tinct functional networks extracted from sponta- While this section of the chapter places emphasis neous (default mode) brain activity also resemble on how structure shapes function, it must be noted networks of coactive brain regions identified dur- that functional interactions and their expression in ing task-evoked activation studies.117 This suggests behavior at the level of the whole organisms can that resting brain activity partly reflects or rehearses profoundly influence structural patterns through a dynamic patterns that become differentially acti- variety of mechanisms of plasticity—thus, struc- vated in response to extrinsic task- and stimulus- tural and functional connectivity are reciprocally related perturbations. The systematic mapping of linked.104 resting-state functional connectivity has become Recent empirical studies and computational an integral part of the connectomics research models of the brain’s resting state have revealed program.118,119 the variable, yet robust, nature of spontaneous Thecharacteristicpatternsofneuraldynamics neural dynamics. Electrophysiological recordings observed during rest appear to have an anatomi- of spontaneous neural activity have demonstrated cal basis. Variations in the strength and integrity the presence of rapid transitions in global pat- of specific white matter tracts are correlated with terns of functional correlations, including periods of the strength of the corresponding functional con- intermittent phase locking and phase synchrony at nection observed in the resting state.120 Major multiple temporal and spatial scales,105 and broadly components of the default mode network121 and distributed synchronization times across multiple other resting-state networks122 are anatomically frequencies.106 Variable periods of phase locking connected. Perhaps the most compelling evidence have also been observed in magnetoencephalo- for structure–function relationships in brain con- graphic and fMRI recordings of resting-state brain nectivity comes from the direct comparison of activity,107 and further evidence suggests that scale- structural and functional networks within the same free neural dynamics involving multiple nested cohort of subjects.53,123,124 The comparison re- frequencies may have behavioral and cognitive veals significant positive correlations between the relevance.108 The scale-free nature of spontaneous strengths of structural connections identified with neural dynamics is potentially indicative of the pres- diffusion MRI and the strengths of functional ence of a “critical state,”109 a dynamic regime char- connections obtained with resting-state functional acterized by a highly diverse set of intrinsic neural MRI. This relationship is robust relative to effects states and a maximal dynamic range of responses to of spatial distance or variations in postprocessing of extrinsic perturbations. functional correlations. Another observation rein- Consistent patterns of activation and deactiva- forces an important point that was made in earlier tion among brain regions during transitions from studies of functional connectivity:125 alargenum- task evoked to resting activity led to the discov- ber of strong functional connections exist between ery of a coherent “default mode”110 whose par- regions that are not directly linked by an anatomical ticipating regions were linked into a default mode pathway. Because of the high base rate of structurally network.93 Neurophysiological correlates of default unconnected node pairs, it is impractical (indeed er- mode brain activity as observed in resting-state roneous) to infer structural connections from func- fMRI have been identified through combined imag- tional connections by simple means such as thresh- ing and electrophysiological recordings.111–113 Re- olding (Fig. 4). The network aspect of functional fined analysis and network modeling techniques connectivity is further underscored by the obser- have revealed the fine structure of resting-state brain vation that many functional connections between

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Figure 4. Inference of structural connectivity (SC) from resting-state functional connectivity (rsFC) is impractical. (A) Probability distribution of rsFC strengths between connected and unconnected node pairs. Note that node pairs that are directly connected, on average, maintain stronger rsFC than unconnected node pairs. (B) The corresponding receiver operating characteristic (ROC) curve shows the relation of false positives to true positives at thresholds ranging from −1to+1. (C) Thresholding the rsFC matrix such that 90% of all structural connections are correctly detected (≈ 16,100 out of 17,600) also falsely detects approximately 242,000 connections. For simplicity, the plot shows true and false positives in the right cerebral hemisphere only. Data as previously reported.124 unconnected region pairs can be partially predicted neural time series data, without interference from by the existence of indirect structural connections, physiological or scanner noise. Putative dynamic or indirect network paths (Fig. 5). This point crys- mechanisms can be fully explored by introducing tallizes one of the most fundamental insights about perturbations in structural coupling or physiology, the importance of a network perspective on human leading to predictions that can be empirically tested. brain function. All pair-wise dynamic interactions For example, a computational neural mass model of between two brain regions reflect a combination of the macaque cortex predicted that correlated fluctu- direct effects (if a direct structural link exists) and ations in BOLD responses were shaped by structural a blend of indirect effects that involve the flow of brain networks.127 Further, the model suggested that information through numerous network paths. A variations in BOLD amplitude were partially driven corollary of this observation is that the local per- by the transient synchronization of neural signals turbation (activation, deletion) of nodes or edges between sets of brain regions at fast time scales, a within the network can manifest itself as distur- prediction for which there is some supporting ev- bances of dynamic interactions in distant and seem- idence.113 Animportantfeatureofthisaswellas ingly unrelated brain systems.126 several related dynamic models128,129 is the highly Specific mechanisms of how the structure of variable nature of ongoing brain dynamics. While anatomical networks shapes functional connectivity anatomical connections play a key role in creating can be productively addressed by pursuing compu- large-scale functional networks, they also allow for tational modeling studies. Such models are useful significant and ongoing fluctuations within these because they allow the precise specification of struc- networks, thus giving rise to a repertoire of variable tural coupling and the computation of complete network states. Jointly, these models predict that a

120 Ann. N.Y. Acad. Sci. 1224 (2011) 109–125 c 2011 New York Academy of Sciences. Sporns The human connectome

Figure 5. Strengths of direct and indirect structural connections partially predict functional connections. (A) Correlation of direct SC and rsFC strengths at node pairs that are structurally connected. (B) Direct SC and indirect SC between node pairs are strongly correlated, that is, the presence of a strong, direct connection also predicts additional strong, indirect connections. This effect is due to the high degree of clustering present in the network. (C) Indirect SC weakly predicts rsFC between structurally unconnected node pairs. All correlations have P < 0.001. Indirect SC was computed as the sum of the product of SC strengths over all indirect paths of length 2. Direct and indirect SC was resampled to a Gaussian distribution. All data and analyses as previously reported.124 dynamic functional repertoire is essential for effi- significant progress has already been made in dis- cient neural processing.130 covering the network basis of common disorders of The availability of connectome data sets allows the brain,132 response to and recovery from brain the construction of neurocomputational models injury,126,133,134 individual differences,90,135,136 her- that can re-create key features and patterns of hu- itability,137 normal development and aging,138,139 man brain dynamics.124,131 Comparison of modeled as well as design principles of neural circuits that and empirically recorded patterns of functional con- derive from their spatial embedding and wiring nectivity suggest that dynamical models of neuronal economy.87 populations coupled by a structural connection ma- The arrival of brought significant trix can capture a large proportion of the observed change to the biological sciences and generated variance in large-scale resting-state neural activity. breathtaking technological and intellectual ad- More refined models that include better coverage of vances, many of which are still unfolding. It will subcortical regions, more accurate or more highly be some time before the impact of connectomics on resolved connectome data, and more sophisticated neuroscience has fully materialized. Going beyond neuronal physiology, are on the horizon. Such “vir- the collection of large data sets or the development tual brains”130 will offer increasingly detailed mod- of new empirical recording and mapping technolo- els that combine anatomy and physiology in silico, gies, connectomics has the potential to bring about thus contributing to our understanding of the net- a new conceptual understanding of human brain work dynamics of the human connectome. function. The human connectome refocuses an ur- gent need for a solid theoretical foundation to guide Outlook future empirical research in brain connectivity and Networks have become pervasive and adaptable dynamics. Network theory offers a fruitful begin- models to map and manage complex systems as di- ning and raises the tantalizing possibility that at verse as societies, ecosystems, cellular metabolism, least some of the principles underlying the func- and, finally, brains. Their considerable appeal and tioning of the human brain are held in common powerasmodelsofneuralsystemsderivesinno among a wide range of complex systems, biological small part from the insights they can deliver about and otherwise. the origin of dynamic brain activity unfolding within anatomical circuits, across multiple levels Acknowledgments of scale. This brief review cannot do justice to the full range of future applications of the human con- The author gratefully acknowledges support by a nectome. In addition to the aspects covered here, grant from the James S. McDonnell Foundation.

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