Ann. N.Y. Acad. Sci. ISSN 0077-8923 ANNALS OF THE NEW YORK ACADEMY OF SCIENCES Issue: The Year in Cognitive Neuroscience The human connectome: a complex network Olaf Sporns Department of Psychological and Brain Sciences, Indiana University, Bloomington, Indiana Address for correspondence: Olaf Sporns, Department of Psychological and Brain Sciences, Indiana University, Bloomington, Indiana 47405. [email protected] The human brain 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 neuroimaging 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 graph theory 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 tractography 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- cognition, 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 synapses, 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 neuroinformatics 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- network science 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 cognitive neuroscience. 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 connectomics 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 gene 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 genomes central themes of this review. In biology, structure is nor connectomes should be viewed as rigid pro- encountered at many scales, from