Understanding the network structure of white matter communication pathways is essential for unraveling the mysteries of the brain's function, organization, and evolution. To this end, we derive a unique network incorporating 410 anatomical tracing studies of the macaque brain from the Collation of Connectivity data on the Macaque brain (CoCoMac) neuroinformatic database. Our network consists of 383 hierarchically organized regions spanning cortex, thalamus, and basal ganglia; models the presence of 6,602 directed long-distance connections; is three times larger than any previously derived brain network; and contains subnetworks corresponding to classic corticocortical, corticosubcortical, and subcortico-subcortical fiber systems. We found that the empirical degree distribution of the network is consistent with the hypothesis of the maximum entropy exponential distribution and discovered two remarkable bridges between the brain's structure and function via networktheoretical analysis. First, prefrontal cortex contains a disproportionate share of topologically central regions. Second, there exists a tightly integrated core circuit, spanning parts of premotor cortex, prefrontal cortex, temporal lobe, parietal lobe, thalamus, basal ganglia, cingulate cortex, insula, and visual cortex, that includes much of the task-positive and task-negative networks and might play a special role in higher cognition and consciousness. neuroanatomy | brain network | network analysis | structural | functional I n 1669, Nicolaus Steno (1) referred to white matter as "nature's finest masterpiece." White matter pathways in the brain mediate information flow and facilitate information integration and cooperation across functionally differentiated distributed centers of sensation, perception, action, cognition, and emotion. Uncovering the global topological regularities of the logical longdistance connections that are subserved by the physical white matter pathways is a key prerequisite to any theory of brain function, dysfunction, organization, dynamics, and evolution. Anatomical tracing in experimental animals has historically been the pervasive technique for mapping long-distance white matter projections (2-4). Given the resolution of anatomical tracing experiments, they typically furnish data at a macroscale of cortical areas or, more generally, brain regions. The associated network description* models brain regions as vertices and the presence of reported long-distance connections as directed edges between them. The most well-known network of the macaque monkey visual cortex consists of 32 vertices and 305 edges (2). Other networks of the macaque cortex consist of 70 vertices and 700 edges (5) and 95 vertices and 2,402 edges (6). The largest network of the cat cortex has 95 vertices and 1,500 edges (7). Network-theoretical analyses have uncovered a number of remarkable insights: distributed and hierarchical structure of cortex (2); topological organization of cortex (8); indeterminacy of unique hierarchy (9); functional smallworld characteristics, optimal set analysis, and multidimensional scaling (10); small-world characteristics (11); nonoptimal component placement for wire length (6); structural and functional motifs (12); and hub identification and classification (13). However, even the largest previous network (6) completely lacks edges corresponding to corticosubcortical and subcortico-subcortical longdistance connections and has significant gaps even among corticocortical long-distance connections (SI Appendix, Fig. S1 ). To gain a better understanding of the structure and organization of the brain, a network spanning the entire brain would be extremely useful. Such a network will be an indispensable foundation for clinical, systems, cognitive, and computational neurosciences (14) . No such network has been reported. We undertake the challenge of constructing, visualizing, and analyzing such a network. Our network opens the door to the application of large-scale network-theoretical analysis that has been so successful in understanding the Internet (15), metabolic networks, protein interaction networks (16), various social networks (17), and searching the 19) . Collation of Connectivity data on the Macaque brain (CoCoMac), a seminal contribution to neuroinformatics, is a publicly available database (20) (21) (22) . Conscientiously and meticulously, the database curators have collated and annotated information on over 2,500 anatomical tracer injections from over 400 published experimental studies. CoCoMac is an objective, coordinate-independent collection of annotations that captures two relationships between pairs of brain regions, where each brain region refers to cortical and subcortical subdivisions as well as to combinations of such subdivisions into sulci, gyri, and other large ensembles. The first relationship is connectivity-whether a brain region in one study projects to another region in (possibly) a different study. There are 10,681 connectivity relations. † The second relationship is mapping-whether a brain region in one study is identical to, a substructure of, or a suprastructure of another region in (possibly) a different study. There are 16,712 mapping relations. Unfortunately, because of a multiplicity of brain maps, divergent nomenclature, boundary uncertainty, and differing resolutions in different studies, mapping relations are often conflicting and connectivity information is typically scattered across related brain regions. The situation is aptly described by Van Essen (23): "Our fragmentary and rapidly evolving understanding is reminiscent of the situation faced by cartographers of the earth's surface many centuries ago, when maps were replete with uncertainties and divergent portrayals of most of the planet's surface." Consolidating connectivity information by merging logically equivalent brain regions and aggregating their connectivity is a necessary prerequisite to any network-analytical study. Further, it is desirable to place the merged brain regions into a coherent, unified, hierarchical brain map that recursively partitions brain and its constituents into To whom correspondence should be addressed. E-mail: dmodha@us.ibm.com. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1008054107/-/DCSupplemental. *It is important to draw a distinction between the actual physical network in a macaque brain and its logical description in network-theoretical terminology using reported data. Because we are primarily concerned with the latter usage in this paper, we will refer to network description as network. † CoCoMac also reports 13,498 plausible connections that were tested for but were not found. This substantially reduces the possibility that projections present in the brain are dramatically undersampled or underreported. www.pnas.org/cgi
Macaque brain white matters of Long-Distance Pathways (LDP) are successfully found and mapped REF .
Network architecture of the long-distance pathways in the macaque brain
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Biology Medicine