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Unformatted text preview: Network architecture of the long-distance pathways in the macaque brain Dharmendra S. Modhaa,1 and Raghavendra Singhb a IBM Research-Almaden, San Jose, CA 95120; and bIBM Research-India, New Delhi 110070, India Communicated by Mortimer Mishkin, National Institute of Mental Health, Bethesda, MD, June 11, 2010 (received for review March 27, 2009) 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 ber 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 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 World-Wide Web (18, 19). Model: Deriving the Network Description Collation of Connectivity data on the Macaque brain (CoCoMac), a seminal contribution to neuroinformatics, is a publicly available database (20–22). 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 rst 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 con icting 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, uni ed, hierarchical brain map that recursively partitions brain and its constituents into | brain network | network analysis | structural | functional I n 1669, Nicolaus Steno (1) referred to white matter as “nature’s nest masterpiece.” White matter pathways in the brain mediate information ow 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 identi cation and classi cation (13). However, even the largest previous network (6) completely lacks edges corresponding to corticosubcortical and subcortico-subcortical longdistance connections and has signi cant gaps even among corticocortical long-distance connections (SI Appendix, Fig. S1). Author contributions: D.S.M. and R.S. designed research, performed research, analyzed data, and wrote the paper. The authors declare no con ict of interest. Freely available online through the PNAS open access option. 1 To whom correspondence should be addressed. E-mail: [email protected] This article contains supporting information online at 1073/pnas.1008054107/-/DCSupplemental. † 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. PNAS | July 27, 2010 | vol. 107 | no. 30 | 13485–13490 NEUROSCIENCE *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. Fig. 1. Macaque brain long-distance network. Each vertex of the network corresponds to a brain region in the hierarchical brain map of SI Appendix, Fig. S6, and each edge encodes the presence of long-distance connection between corresponding brain regions. Edges are drawn using algorithmically bundled splines (25). SI Appendix, Tables S2 and S3 provide a summary of the number of edges in major corticocortical and corticosubcortical subnetworks. A color wheel is used for better discrimination amongst brain regions. For the leaf brain regions in the two outermost circles, the color wheel is rotated by 120° and 240°. The edges are drawn in black. SI Appendix, Table S1 enumerates the entire hierarchical brain map and provides a complete index to acronyms of the brain regions; it has been color-coded for wider accessibility. progressively smaller physical regions.‡ The brain map can provide a natural frame of reference within which to correlate, aggregate, and understand various merged brain regions. Conceptually, merging brain regions and extracting a hierarchy can be carried out according to logical and formal calculus developed by CoCoMac curators (20–22, 24). In practice, the tasks are made formidable by a number of factors. For example, (i ) there are partially over- ‡ This usage of physical hierarchical partition of brain into its constituent parts is different from logical hierarchical information processing in visual cortex, as discussed in the article by Felleman and Van Essen (2). lapping brain regions (SI Appendix, Fig. S5); (ii ) there are direct con icts between mapping relations (SI Appendix, Fig. S3); (iii ) there are implied indirect con icts that are far too numerous and inherently insidious (SI Appendix, Fig. S3); and (iv) there are errors and omissions in the underlying database, which itself is large. Although it is dif cult to de ne a formal metric against which a single hierarchical brain map can be defensibly constructed, reassuringly, any hierarchical brain map built on the same set of merged regions will at most affect the resolution of the networktheoretical analysis. In this study, we have constructed one hierarchical brain map, at the highest resolution that the data can meaningfully support, toward our goal of network analysis Modha and Singh 13486 | (SI Appendix). The entire set of merged brain regions and our hierarchical brain map are explicitly detailed in the multipage SI Appendix, Table S1 to provide complete transparency and to permit future additions, deletions, and modi cations as data with ner resolution become available. SI Appendix, Fig. S6 visualizes our hierarchical brain map. It can be seen that the brain is divided into cortex, diencephalon, and basal ganglia, which are themselves divided into smaller regions, such as temporal lobe, frontal lobe, parietal lobe, occipital lobe, insula, and cingulate cortex. With the brain regions in the hierarchical brain map as vertices, our network contains 6,602 edges, wherein an edge encodes the presence of long-distance connection between corresponding brain regions. Fig. 1 displays the network on the hierarchical brain map, where each edge is visualized by a spline curve. Visualizing 6,602 edges directly leads to a highly cluttered gure in which no details are discernible (SI Appendix, Fig. S17A). To improve clarity, splines with a common origin or destination are bundled algorithmically (25) (SI Appendix and SI Appendix, Figs. S16 and S17). The gure succinctly captures many aspects of the cumulative contribution of a whole community of neuroanatomists over the past half century into a single illustration. The long distance network dataset consists of three text les: Macaque_LongDistance_Network.nameslist, Macaque_LongDistance_Network_connectivity.edgelist, and Macaque_LongDistance_Network_mapping.edgelist. The les are publicly available and are described in SI Appendix. Our network is (i ) comprehensive in that it incorporates every study included in CoCoMac; (ii ) consistent in that every edge can be tracked back to an underlying tracer study; (iii ) concise in that identical brain regions (e.g., V1, 17, striate cortex) are merged and their connectivity is aggregated, thus reducing brain regions to 383 from 6,877 in the original database; (iv) coherent in that brain regions are organized in a uni ed hierarchical parcellation or brain map; and, nally, (v) colossal in that it is roughly three times larger than the largest previous such network (6) (compare Fig. 1 with SI Appendix, Fig. S1). The comprehensiveness of our network is underscored by the fact that it contains logical subnetworks corresponding to a number of important physical ber systems, namely, the visual system (2); dorsal-ventral pathways (3); thalamocortical relays (26); and numerous corticocortical, corticosubcortical, and subcorticosubcortical ber systems (4). The brain regions involved in these ber systems are enumerated in SI Appendix, Table S4, and the corresponding subnetworks are illustrated in SI Appendix, Figs. S18–21. It is important to note that strength, trajectory, and laminar source/target of projections are missing from our network, which only encodes the presence of connections. Preliminary analysis (SI Appendix) con rms that the network is sparse, reciprocal, and small-world (27, 11) and reveals that the network has the proverbial six degrees of separation (28). As our main contributions, we rst characterize the degree distribution, that is, the probability distribution of the number of connections that each brain region makes. Second, we study topologically central regions and subnetworks in the brain and, in the process, reveal two remarkable anatomical substrates of behavior via network-theory and web-searching algorithms. Results Degree Distribution of the Brain Network. In a network, degree of a vertex is the total number of edges that it touches. The tail behavior of the frequency distribution of degrees is a key signature of how connectivity is spread among vertices. A scale-free network follows a power law; that is, asymptotically, the probability that a vertex is connected with k other vertices is proportional to k−γ for some positive power γ. Scale-free networks naturally arise via mechanisms of growth and preferential attachment (29). For an exponential network, asymptotically, the probability that a vertex is connected with k other vertices is proportional to e−k/λ, for some positive constant λ. Exponential networks can arise via random network evolution (30) or via a mechanism that hinders preferential attachment (31), such as Modha and Singh Fig. 2. Our network is directed, meaning that each edge is an ordered pair of vertices. By keeping the connectivity but removing direction, we created the undirected version of our network that has 383 vertices and 5,208 edges. The undirected network has an average degree of λ = 27.2. Following Keller (39), we analyze the behavior of the empirical complementary cumulative degree distribution (also known as survival function), which is drawn using circles on both of the above plots. The dashed line in the top log-log plot shows the complementary cumulative distribution of the maximum likelihood power law t, ∼x−3.15, x ≥ 33, which was derived using the software provided with Clauset et al. (37). Moreover, the P value is extremely small ( 0:1); hence, the maximum likelihood power law hypothesis is rejected (37, box 1). The dashed line in the bottom log-linear plot shows the complementary cumulative distribution of the maximum entropy exponential distribution t, λ−1 exp(−x/λ), over the entire range of data. The bottom plot is also shown using the linear-linear scale in SI Appendix, Fig. S22. These plots suggest that the hypothesis of the maximum entropy exponential distribution is consistent with the data. the cost of adding links to the vertices or the limited capacity of a vertex. The World-Wide Web, the Internet (15), some social networks, and the metabolic networks are all scale-free (16), whereas power grids, air traf c networks, and collaboration networks of company directors (31, 16) are all exponential. A simple but fundamental unanswered question is whether the degree distribution of the brain network is scale-free, exponential, or neither? In related work, Humphries et al. (32) reported that the brainstem reticular formation is not a scale-free network. For the smaller brain networks, Sporns and Zwi (11) did not nd evidence for power law distribution but left open the possibility that a large-scale network may uncover such structure. PNAS | July 27, 2010 | vol. 107 | no. 30 | 13487 NEUROSCIENCE Fig. 3. Innermost core for the undirected version of our network. The innermost core is a central subnetwork that is far more tightly integrated than the overall network. Information likely spreads more swiftly within the innermost core than through the overall network, the overall network communicates with itself mainly through the innermost core, and the innermost core contains major components of the task-positive and task-negative networks derived via functional imaging research (43). Further confusing the matter, Eguíluz et al. (33) found that functional networks of the human brain are scale-free, but Achard et al. (34) argued that at the level of resting state networks between cortical areas, these same networks are not scale-free. Restricted by the small size of available networks, Kaiser et al. (35) pursued an indirect approach based on simulated lesion studies (36) and concluded that “cortical networks are affected in ways similar to scale-free networks concerning the elimination of nodes or connections. However, a direct comparison of degree distributions has been impossible.” Armed with our network, we provide a fresh perspective on the controversy. Based on the recipe for analyzing power law distributions in the study by Clauset et al. (37), Fig. 2A demonstrates 13488 | that the maximum likelihood scale-free hypothesis is untenable. Fig. 2B and SI Appendix, Fig. S22 demonstrate that over the nite range of available data, the maximum entropy exponential distribution ts the data well. It is noteworthy that for the 302-neuron network in the worm Caenorhabditis elegans (38), the tail of the degree distribution is also well approximated by exponential decays (31). Prefrontal Cortex Is Topologically Central. We have seen that vertices in our network have differing degrees of connectivity. We now introduce a number of widely studied metrics of topological centrality that take into account how vertices are interconnected. Modha and Singh Table 1. Top 10 brain regions according to several metrics of topological centrality for our network Characteristic Integrator Rank → In-degree In-closeness Authorities Out-degree Out-closeness Hubs Betweenness PageRank 1 32 46 32 46 46 46 24 32 2 46 12o 12o 24 24 24 46 MD 3 12o 32,11 46 TF TF 9 LIP 46 4 12l 24 11 9 TE TF 13a 36r 5 11 12l 12l 13 9 TE MD PIT 6 24 MD 24 13a TH TH 32 12o 7 F7 8A 14 TH LIP 13 TF 24 8 14 23c F7 TE, LIP PGm 32 PIT 23c 9 8A 8B MD PGm 23, PM#3, 45 23 13 12l 10 LIP LIP, F7 9 V2 12 PM#3 PS 11 Distributor Intermediary The regions in prefrontal cortex are shown in bold. SI Appendix, Table S1 provides an index of acronyms for the brain regions. The table was computed using Pajek (42). In- and out-degrees, respectively, are direct measures of how much information a vertex receives and sends. For each vertex, de ne out-closeness as its average shortest path to every other vertex and its in-closeness as the average shortest path to it from every other vertex (40). For each vertex, de ne betweenness centrality as the number of shortest paths that pass through it (41, 40). PageRank was developed in the context of Web searching to nd how often a vertex will be visited during random network traversal (18). Betweenness centrality and PageRank, which take both inand out-connections into account, measure the ef cacy of vertices in information intermediation. Hubs and authorities were also developed in the context of Web searching, and are de ned relative to each other. They are recursively, circularly, and iteratively computed: A good hub links to many good authorities, and a good authority is one that is linked to by many good hubs (19). Hubs distribute information, whereas authorities aggregate information. Table 1 shows the top 10 brain regions according to the above metrics of topological centrality. Roughly, 70% of the top 10 regions according to in-degree, in-closeness, and authorities reside primarily in prefrontal cortex (32, 46, 12o, 12l, 11, 14, 8A, 8B, 14, 9), suggesting that it serves as an integrator of information. The top out-degree, out-closeness, and hub regions are distributed across prefrontal cortex (46, 9, 13, 13a, 45, 12, and 32), temporal lobe (TH, TF, and TE), parietal lobe (LIP and PGm), cingulate cortex (24 and 23), occipital lobe (V2), and thalamus (PM#3), with prefrontal cortex claiming 40% of the top 10 regions. This indicates that prefrontal cortex may also serve as a distributor of information. The top 10 regions according to betweenness and PageRank are distributed across prefrontal cortex (46, 13a, 32, 13, PS, 12o, 12l, and 11), temporal lobe (TF, PIT, and 36r), cingulate cortex (24 and 23c), parietal lobe (LIP), and thalamus (MD), with roughly half of the top regions residing in prefrontal cortex. Together, in a precise, quantitative, and multidimensional fashion, these facts strengthen the hypothesis that prefrontal cortex is an ef cient intermediary of information serving both as an integrator and a distributor. Is the topological centrality of prefrontal cortex an artifact of prefrontal regions being studied more often? Our investigation (SI Appendix, Figs. S23–28) did not nd that prefrontal cortex (and its subregions) was studied more often than other brain regions in CoCoMac data, nor did it nd a correlation between how often a region is studied and its degree. On the other hand, as expected, SI Appendix, Fig. S29 nds that degree is correlated with centrality. Together, these facts imply that topological centrality of prefrontal cortex is not attributable to it being studied more often. Anatomy Meets Physiology and Behavior. Topological centrality indicates that some vertices are more special than others. A logical ensuing question is whether the brain network contains special subnetworks. Now, we demonstrate that the brain network indeed contains a special subnetwork that captures its topological essence. Core decomposition is a computationally ef cient algorithm (17) that recursively peels off the least connected vertices to reveal progressively more closely connected subnetworks. In the rst step, the algorithm recursively peels off all vertices with only Modha and Singh one edge until only vertices with at least two edges remain. In the second step, the algorithm recursively peels off all the vertices with only two edges until only vertices with at least three edges remain. The algorithm continues in like manner until all vertices are peeled off. Each peeling step de nes a core. Each core is a subset of the previous core; hence, the cores constitute a nested hierarchy (SI Appendix, Fig. S31). Progressing along the hierarchy yields successive cores that are ever more tightly interconnected. The last or the innermost core is the top of this hierarchy and constitutes a topologically central subnetwork. We found the innermost core for the undirected version of our network (Fig. 3), and it turned out to be a remarkable topological structure. The innermost core is deeply nested (SI Appendix, Fig. S31), such that each vertex in the innermost core touches at least 29 other vertices in the innermost core. The innermost core has 122 vertices. Let us refer to the set of remaining 261 vertices as the crust. There are 2,872 edges from the innermost core to itself, 1,707 edges from the crust to the innermost core, and 1,230 edges from the innermost core to the crust. There are only 793 edges from the crust to itself. Thus, 88% of all edges either originate or terminate in the innermost core, although it contains only 32% of the vertices. The longest shortest path (namely, diameter) for the innermost core is only 4, whereas for the overall network, it is signi cantly higher, namely, 6. Similarly, the average shortest path between any two vertices in the innermost core is only 1.95, whereas for the overall network, it is signi cantly higher, namely, 2.62. Further, the innermost core contains the vast majority of topological central vertices in Table 1 (SI Appendix, Fig. S32). Thus, the innermost core is a central subnetwork that is far more tightly integrated than the overall network, information likely spreads more swiftly within the innermost core than through the overall network, and the overall network communicates with itself mainly through the innermost core. Although the innermost core is structurally interesting, it is functionally even more intriguing. The innermost core spans premotor and prefrontal cortex (42 regions), temporal lobe (23 regions), parietal lobe (16 regions), thalamus (15 regions), basal ganglia (12 regions), cingulate cortex (7 regions), insula (6 regions), and V4 in visual cortex. SI Appendix enumerates all brain regions in the innermost core. Three decades of functional brain imaging research in humans has culminated in the de nition of two dynamically anticorrelated functional networks: a task-positive network activated during goal-directed performance and a tasknegative network implicated in self-referential processing (43). Assuming a plausible set of homologies between human and macaque cortical organization,§ we found that the innermost core contains major components of both of these networks (SI Appendix § Establishing homology between human and macaque cortical organization remains an ongoing and active research area (23, 44–46), and it has been clearly noted that “homology cannot be proven but must be ‘inferred’” (47). Nonetheless, building on the conclusion in the article by Orban et al. (47) that “Despite several functional differences, many areas are homologous, especially at early levels of the visual hierarchy. In higherorder cortex, ‘regional’ homology still largely applies” and emboldened by the early functional MRI studies in mapping task-positive and task-negative networks in macaque (48), here, we assume that homology indeed holds. PNAS | July 27, 2010 | vol. 107 | no. 30 | 13489 NEUROSCIENCE and SI Appendix, Fig. S33). The innermost core constitutes the anatomical substrate that mediates temporally coordinated correlations within each network and anticorrelations between the networks and upholds physiological correlates underlying behavior. Given the structural and functional centrality of the innermost core, it is natural to ask if it is sensitive to changes in the network. Quite reassuringly, precise analysis has revealed that the innermost core cannot change dramatically, given modest additions or deletion of edges in the network (SI Appendix, Tables S5 and S6); hence, it is an extremely stable and robust signature of the network. Discussion We have collated a comprehensive, consistent, concise, coherent, and colossal network spanning the entire brain and grounded in anatomical tracing studies that is a stepping stone to both fundamental and applied research in neuroscience and cognitive computing (14). What was previously scattered across 410 papers, 10,681 connectivity relations, and 16,712 mapping relations and limited to neuroanatomists specializing in the wetware of the experimental animals is now uni ed and accessible to network scientists who can unleash their algorithmic software toolkits (20–22). We have begun to uncover remarkable global topological regularities of the network. The maximum entropy exponential distribution 1. Steno N (1669) Dissertatio de cerebri anatome, spectatissimis viris dd Societatis apud dominum Thevenot collectae, dictata, atque é gallico exemplari (Latinitate donata, opera and studio Guidonis Fanosii, Paris). 2. Felleman DJ, Van Essen DC (1991) Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1:1–47. 3. Ungerleider LG, Mishkin M (1982) Analysis of Visual Behavior, eds Ingle DJ, Goodale MA, Mans eld RJ (MIT Press, Cambridge, MA), pp 549–586. 4. Schmahmann JD, Pandya DN (2006) Fiber Pathways of the Brain (Oxford Univ Press, New York). 5. Young MP (1993) The organization of neural systems in the primate cerebral cortex. Proc Biol Sci 252:13–18. 6. Kaiser M, Hilgetag CC (2006) Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLOS Comput Biol 2:e95. 7. Scannell JW, Burns GA, Hilgetag CC, O’Neil MA, Young MP (1999) The connectional organization of the cortico-thalamic system of the cat. Cereb Cortex 9:277–299. 8. Young MP (1992) Objective analysis of the topological organization of the primate cortical visual system. Nature 358:152–155. 9. Hilgetag CC, O’Neill MA, Young MP (1996) Indeterminate organization of the visual system. Science 271:776–777. 10. Stephan KE, et al. (2000) Computational analysis of functional connectivity between areas of primate cerebral cortex. Philos Trans R Soc Lond B Biol Sci 355:111–126. 11. Sporns O, Zwi JD (2004) The small world of the cerebral cortex. Neuroinformatics 2: 145–162. 12. Sporns O, Kötter R (2004) Motifs in brain networks. PLoS Biol 2:e369. 13. Sporns O, Honey CJ, Kötter R (2007) Identi cation and classi cation of hubs in brain networks. PLoS ONE 2:e1049. 14. Bohland JW, et al. (2009) A proposal for a coordinated effort for the determination of brainwide neuroanatomical connectivity in model organisms at a mesoscopic scale. PLOS Comput Biol 5:e1000334. 15. Faloutsos M, Faloutsos P, Faloutsos C (1999) On power-law relationships of the Internet topology. Proceedings of SIGCOMM’99 (Association for Computing Machinery, New York), pp 251–262. 16. Newman MEJ, Barabási AL, Watts DJ (2006) The Structure and Dynamics of Networks (Princeton Univ Press, Princeton). 17. Seidman SB (1983) Network structure and minimum degree. Soc Networks 5:269–287. 18. Brin S, Page L (1998) The anatomy of a large-scale hypertextual web search engine. Comput Netw ISDN Syst 30:107–117. 19. Kleinberg JM (1999) Authoritative sources in a hyperlinked environment. J ACM 46: 604–632. 20. Stephan KE, Zilles K, Kötter R (2000) Coordinate-independent mapping of structural and functional data by objective relational transformation (ORT). Philos Trans R Soc Lond B Biol Sci 355:37–54. 21. Stephan KE, et al. (2001) Advanced database methodology for the Collation of Connectivity data on the Macaque brain (CoCoMac). Philos Trans R Soc Lond B Biol Sci 356:1159–1186. 22. Kötter R (2004) Online retrieval, processing, and visualization of primate connectivity data from the CoCoMac database. Neuroinformatics 2:127–144. 23. Van Essen DC (2004) The Visual Neurosciences, eds Chalupa L, Werner J (MIT Press, Cambridge, MA), pp 507–521. ðaverage degreeÞÀ1 exp½ − x=ðaverage degreeފ characterizes the degree distribution of the network surprisingly well. Prefrontal cortex claims a disproportionately large share of topologically central brain regions according to a variety of ranking schemes, and thus serves as both an integrator and a distributor of information in the brain. We have found a deeply nested and tightly integrated core circuit spanning the entire brain that contains both the task-positive and task-negative networks. Assuming homology, it is indeed reassuring that the core circuit computed using structural data from a half century of anatomical tracing data in nonhuman primates corresponds so well with 3 decades of behavioral imaging research in humans. This hints at an evolutionarily preserved core circuit of the brain that may be a key to the age-old question of how the mind arises from the brain. ACKNOWLEDGMENTS. We thank four anonymous reviewers for a number of constructive suggestions that greatly improved and expanded our original submission. We thank curators of the CoCoMac databases, most notably, Rolf Kötter, for making the database publicly available. The research reported in this paper was sponsored by the Defense Advanced Research Projects Agency, Defense Sciences Of ce, Program: Systems of Neuromorphic Adaptive Plastic Scalable Electronics, under Contract HR0011-09-C-0002. 24. Kötter R, Wanke E (2005) Mapping brains without coordinates. Philos Trans R Soc Lond B Biol Sci 360:751–766. 25. Holten D (2006) Hierarchical edge bundles: Visualization of adjacency relations in hierarchical data. IEEE Trans Vis Comput Graph 12:741–748. 26. Sherman SM, Guillery RW (2006) Exploring the Thalamus and Its Role in Cortical Function (MIT Press, Cambridge, MA). 27. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442. 28. Milgram S (1967) Small-world problem. Psychol Today 1:61–67. 29. Barabási AL, Bonabeau E (2003) Scale-free networks. Sci Am 288:60–69. 30. Erdös P, Rényi A (1960) On the evolution of random graphs. A Publ Math Inst Hung Acad Sci 5:17–61. 31. Amaral LA, Scala A, Barthelemy M, Stanley HE (2000) Classes of small-world networks. Proc Natl Acad Sci USA 97:11149–11152. 32. Humphries MD, Gurney K, Prescott TJ (2006) The brainstem reticular formation is a small-world, not scale-free, network. Proc Biol Sci 273:503–511. 33. Eguíluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV (2005) Scale-free brain functional networks. Phys Rev Lett 94:018102. 34. Achard S, Salvador R, Whitcher B, Suckling J, Bullmore E (2006) A resilient, lowfrequency, small-world human brain functional network with highly connected association cortical hubs. J Neurosci 26:63–72. 35. Kaiser M, Martin R, Andras P, Young MP (2007) Simulation of robustness against lesions of cortical networks. Eur J Neurosci 25:3185–3192. 36. Albert R, Jeong H, Barabási AL (2000) Error and attack tolerance of complex networks. Nature 406:378–382. 37. Clauset A, Shalizi C, Newman MEJ (2009) Power-law distributions in empirical data. SIAM Rev 51:661–703. 38. White JG, Southgate E, Thomson JN, Brenner S (1996) The structure of the nervous system of the nematode Caenorhabditis elegans. Philos Trans R Soc Lond B Biol Sci 314:1–340. 39. Keller EF (2005) Revisiting “scale-free” networks. Bioessays 27:1060–1068. 40. Newman MEJ (2005) A measure of betweenness centrality based on random walks. Soc Networks 27:39–54. 41. Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40:35–41. 42. de Nooy W, Mrvar A, Batagelj V (2005) Exploratory Social Network Analysis with Pajek (Cambridge Univ Press, New York). 43. Fox MD, et al. (2005) The human brain is intrinsically organized into dynamic, anticorrelated functional networks. Proc Natl Acad Sci USA 102:9673–9678. 44. Orban GA, et al. (2003) Similarities and differences in motion processing between the human and macaque brain: evidence from fMRI. Neuropsychologia 41:1757–1768. 45. Asta ev SV, et al. (2003) Functional organization of human intraparietal and frontal cortex for attending, looking, and pointing. J Neurosci 23:4689–4699. 46. Orban GA, Van Essen DC, Vanduffel W (2004) Comparative mapping of higher visual areas in monkeys and humans. Trends Cogn Sci 8:315–324. 47. Orban GA, et al. (2006) Mapping the parietal cortex of human and non-human primates. Neuropsychologia 44:2647–2667. 48. Vincent JL, et al. (2007) Intrinsic functional architecture in the anaesthetized monkey brain. Nature 447:83–86. 13490 | Modha and Singh ...
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