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Computational Neuroanatomy pp 295–335Cite as

Computational Methods for the Analysis of Brain Connectivity

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Abstract

The body of knowledge about the connectivity of brain networks on different structural scales is growing rapidly. This information is considered highly valuable for determining the neural organization underlying brain function, yet connectivity data are too extensive and too complex to be understood intuitively. Computational analysis is required to evaluate them. Here we review mathematical, statistical, and computational methods that have been used by ourselves and other investigators to assess the organization of brain connectivity networks.

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References

  1. Zeki S, Shipp S. The functional logic of cortical connections. Nature 1988; 335: 311–317.

    Article  PubMed  CAS  Google Scholar 

  2. Van Essen DC, Anderson CH, Felleman DJ. Information processing in the primate visual system-an integrated systems perspective. Science 1992; 255: 419–423.

    Article  PubMed  Google Scholar 

  3. Young MP. Objective analysis of the topological organization of the primate cortical visual system. Nature 1992; 358: 152–155.

    Article  PubMed  CAS  Google Scholar 

  4. Scannell JW, Burns GA, Hilgetag CC, O’Neil MA, Young MP. The connectional organization of the cortico-thalamic system of the cat. Cereb Cortex 1999; 9: 277–299.

    Article  PubMed  CAS  Google Scholar 

  5. Friston KJ. Functional and effective connectivity in neuroimaging: a synthesis. Hum Brain Mapp 1994; 2: 56–78.

    Article  Google Scholar 

  6. Felleman DJ, Van Essen DC. Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1991; 1: 1–47.

    Article  PubMed  CAS  Google Scholar 

  7. Young MP, Scannell JW, O’Neill MA, Hilgetag CC, Burns G, Blakemore C. Non-metric multidimensional scaling in the analysis of neuroanatomical connection data and the organization of the primate cortical visual system. Philos Trans R Soc Lond B Biol Sci 1995; 348: 281–308.

    Article  PubMed  CAS  Google Scholar 

  8. Hilgetag CC, O’Neill MA, Young MP. Indeterminate organization of the visual system. Science 1996; 271: 776–777.

    Article  PubMed  CAS  Google Scholar 

  9. Hilgetag CC, O’Neill MA, Young MP. Hierarchical organization of macaque and cat cortical sensory systems explored with a novel network processor. Philos Trans R Soc Lond B Biol Sci 2000; 355: 71–89.

    Article  PubMed  CAS  Google Scholar 

  10. Hilgetag CC, Burns GA, O’Neill MA, Scannell JW, Young MP. Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. Philos Trans R Soc Lond B Biol Sci 2000; 355: 91–110.

    Article  PubMed  CAS  Google Scholar 

  11. Jouve B, Rosenstiehl P, Imbert M. A mathematical approach to the connectivity between the cortical visual areas of the macaque monkey. Cereb Cortex 1998; 8: 28–39.

    Article  PubMed  CAS  Google Scholar 

  12. Sporns O, Tononi G, Edelman GM. Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb Cortex 2000; 10: 127–141.

    Article  PubMed  CAS  Google Scholar 

  13. Sporns O, Tononi G, Edelman GM. Connectivity and complexity: the relationship between neuroanatomy and brain dynamics. Neural Netw 2000; 13: 909–922.

    Article  PubMed  CAS  Google Scholar 

  14. Heimer L, Robards MJ. Neuroanatomical Tract Tracing Methods. Plenum Press, New York, 1981.

    Book  Google Scholar 

  15. Heimer L, Zaborszky L. Neuroanatomical Tract-Tracing Methods 2, Recent Progress. Plenum Press, New York, 1989.

    Google Scholar 

  16. Köbbert C, Apps R, Bechman I, Lanciego JL, Mey J, Thanos S. Current concepts in neuroanatomical tracing. Prog Neurobiol 2000; 62: 327–351.

    Article  PubMed  Google Scholar 

  17. Crick F, Jones E. Backwardness of human neuroanatomy. Nature 1993; 361: 109–110.

    Article  PubMed  CAS  Google Scholar 

  18. Mori S, Barker PB. Diffusion magnetic resonance imaging: Its principle and applications. Anat Rec (New Anat.) 1999; 257: 102–109.

    Article  CAS  Google Scholar 

  19. Conturo TE, Lori NF, Cull TS, et al. Tracking neuronal fiber pathways in the living human brain. Proc Natl Acad Sci USA 1999; 96: 10422–10427.

    Article  PubMed  CAS  Google Scholar 

  20. Van Essen DC. Functional organization of primate visual cortex. In: Cerebral Cortex, Vol. 3 ( Peters A, Rockland K, eds.). Plenum Press, New York, 1985, pp. 259–328.

    Google Scholar 

  21. Stephan KE, Zilles K, Kötter R. Coordinate-independent mapping of structural and functional data by objective relational transformation (ORT). Philos Trans R Soc Lond B Biol Sci 2000; 355: 37–54.

    Article  PubMed  CAS  Google Scholar 

  22. Stephan KE, Kamper L, Bozkurt A, Burns GA, Young MP, Kötter R. Advanced data base methodology for the Collation of Connectivity data on the Macaque brain (CoCoMac). Philos Trans R Soc Lond B Biol Sci 2001; 356: 1159–1186.

    Article  PubMed  CAS  Google Scholar 

  23. Burns GA. Knowledge management of the neuroscientific literature: the data model and underlying strategy of the NeuroScholar system. Philos Trans R Soc Lond B Biol Sci 2001; 356: 1187–1208.

    Article  PubMed  CAS  Google Scholar 

  24. Musil SY, Olson CR. Cortical areas in the medial frontal lobe of the cat delineated by quantitative analysis of thalamic afferents. J Comp Neurol 1991; 308: 457–466.

    Article  PubMed  CAS  Google Scholar 

  25. Barone P, Dehay C, Berland M, Bullier J, Kennedy H. Developmental remodeling of primate visual cortical pathways. Cereb Cortex 1995; 5: 22–38.

    Article  PubMed  CAS  Google Scholar 

  26. MacNeil MA, Lomber SG, Payne BR. Thalamic and cortical projections to middle suprasylvian cortex of cats: constancy and variation. Exp Brain Res 1997; 114: 24–32.

    Article  PubMed  CAS  Google Scholar 

  27. Barone P, Batardiere A, Knoblauch K, Kennedy H. Laminar distribution of neurons in extrastriate areas projecting to visual areas V1 and V4 correlates with the hierarchical rank and indicates the operation of a distance rule. J Neurosci 2000; 20: 3263–3281.

    PubMed  CAS  Google Scholar 

  28. Scannell JW, Grant S, Payne BR, Baddeley R. On variability in the density of corticocortical and thalamo-cortical connections. Philos Trans R Soc Lond B Biol Sci 2000; 355: 21–35.

    Article  PubMed  CAS  Google Scholar 

  29. Lennie P. Single units and visual cortex organization. Perception 1998; 27: 889–935.

    Article  PubMed  CAS  Google Scholar 

  30. Burns GAPC, Hilgetag CC. The computational representation and analysis of neuroanatomical knowledge: limiting the problem of information overload in neuroscience. FASEB J 2000; 14: A544.

    Google Scholar 

  31. Harary F. Graph Theory. Addison-Wesley, Reading, MA, 1969.

    Google Scholar 

  32. Nicolelis MAL, Yu C-H, Baccala LA. Structural characterization of the neural circuit responsible for control of cardiovascular functions in higher vertebrates. Comput Bio Med 1990; 20: 379–400.

    Article  CAS  Google Scholar 

  33. Young MP. The organization of neural systems in the primate cerebral cortex. Proc R Soc Lond B Biol Sci 1993; 252: 13–18.

    Article  CAS  Google Scholar 

  34. Scannell JW, Blakemore C, Young MP. Analysis of connectivity in the cat cerebral cortex. J Neurosci 1995; 15: 1463–1483.

    PubMed  CAS  Google Scholar 

  35. Patton PE, McNaughton B. Connection matrix of the hippocampal formation: I. The dentate gyrus. Hippocampus 1995; 5: 245–286.

    Article  PubMed  CAS  Google Scholar 

  36. Burns GAPC, Young MP. Analysis of the connectional organisation of neural systems associated with the hippocampus in rats. Philos Trans R Soc Lond B Biol Sci 2000; 355: 55–70.

    Article  PubMed  CAS  Google Scholar 

  37. Murre JM, Sturdy DP. The connectivity of the brain: multi-level quantitative analysis. Biol Cybern 1995; 73: 529–545.

    Article  PubMed  CAS  Google Scholar 

  38. Nicoll A, Blakemore C. Patterns of local connectivity in the neocortex. Neural Comput 1993; 5: 665–680.

    Article  Google Scholar 

  39. Stevens CF. How cortical interconnectedness varies with network size. Neural Comput 1989; 1: 473–479.

    Article  Google Scholar 

  40. Young MP, Hilgetag CC, Scannell JW. On imputing function to structure from the behavioural effects of brain lesions. Philos Trans R Soc Lond B Biol Sci 2000; 355: 147–161.

    Article  PubMed  CAS  Google Scholar 

  41. Kötter R, Hilgetag CC, Stephan KE. Connectional characteristics of areas in Walker’s map of primate prefrontal cortex. NeuroComputing 2001; 38–40: 741–746.

    Google Scholar 

  42. Zeki S. A Vision of the Brain. Blackwell, Oxford, 1993.

    Google Scholar 

  43. Barbas H, Rempel-Clower N. Cortical structure predicts the pattern of corticocortical connections. Cereb Cortex 1997; 7: 635–646.

    Article  PubMed  CAS  Google Scholar 

  44. Kötter R, Stephan KE, Palomero-Gallagher N, Geyer S, Schleicher A, Zilles K. Multimodal characterisation of cortical areas by multivariate analyses of receptor binding and connectivity data. Anat Embryol 2001; 204: 333–350.

    Article  PubMed  Google Scholar 

  45. Hilgetag CC. Mathematical approaches to the analysis of neural connectivity in the mammalian brain, PhD thesis, Faculty of Medicine, University of Newcastle upon Tyne, 1999.

    Google Scholar 

  46. Lagae L, Xiao DK, Raiquel S, Maes H, Orban GA. Position invariance of optic flow component selectivity differentiates monkey MST and FST cells from MT cells. Invest Ophthamol Vis Sci 1991; 32: 823.

    Google Scholar 

  47. Sporns O, Gally JA, Reeke GN, Jr, Edelman GM. Reentrant signaling among simulated neuronal groups leads to coherency in their oscillatory activity. Proc Natl Acad Sci USA 1989; 86: 7265–7269.

    Article  PubMed  CAS  Google Scholar 

  48. Sporns O, Tononi G, Edelman GM. Modeling perceptual grouping and figure-ground segregation by means of active reentrant connections. Proc Natl Acad Sci USA 1991; 88: 129–133.

    Article  PubMed  CAS  Google Scholar 

  49. Buckley F, Harary F. Distance in Graphs. Addison-Wesley, Redwood City, CA, 1990.

    Google Scholar 

  50. Floyd R. Algorithm 97: shortest path. Commun ACM 1962; 5: 345.

    Article  Google Scholar 

  51. Watts DJ, Strogatz SH. Collective dynamics of `small-world’ networks. Nature 1998; 393: 440–442.

    Article  PubMed  CAS  Google Scholar 

  52. Mitchison G. Neuronal branching patterns and the economy of cortical wiring. Proc R Soc Lond B Biol Sci 1991; 245: 151–158.

    Article  CAS  Google Scholar 

  53. Ringo JL, Doty RW, Demeter S, Simard PY. Time is of the essence: a conjecture that hemispheric specialization arises from interhemispheric conduction delays. Cereb Cortex 1994; 4: 331–343.

    Article  PubMed  CAS  Google Scholar 

  54. Young MP, Scannell JW. Component-placement optimization in the brain. Trends Neurosci 1996; 19: 413–415.

    PubMed  CAS  Google Scholar 

  55. Van Essen DC. A tension-based theory of morphogenesis and compact wiring in the central nervous system. Nature 1997; 385: 313–318.

    Article  PubMed  Google Scholar 

  56. Albert R, Jeong H, Barabasi AL. Error and attack tolerance of complex networks. Nature 2000; 406: 378–382.

    Article  PubMed  CAS  Google Scholar 

  57. Bollobas B. Random Graphs. Academic Press, London, 1985.

    Google Scholar 

  58. Erdös P, Rényi A. On the evolution of random graphs. Publ Math Inst Hung Acad Sci 1960; 5: 17–61.

    Google Scholar 

  59. Cohen JE. Threshold phenomena in random structures. Discr Appl Math 1988; 19: 113–128.

    Article  Google Scholar 

  60. Kauffman SA. The Origins of Order. Oxford University Press, 1993.

    Google Scholar 

  61. Rose G, Siebler M. Cooperative effects of neuronal ensembles. Exp Brain Res 1995; 106: 106–110.

    Article  PubMed  CAS  Google Scholar 

  62. Milgram S. The small world problem. Psychology Today 1967; 1: 61.

    Google Scholar 

  63. Watts DJ, Duncan J. Small Worlds. Princeton University Press, Princeton, NJ, 1999.

    Google Scholar 

  64. Stephan KE, Hilgetag CC, Burns GA., O’Neill MA, Young MP, Kötter R. Computational analysis of functional connectivity between areas of primate cerebral cortex. Philos Trans R Soc Lond B Biol Sci 2000; 355: 111–126.

    Article  PubMed  CAS  Google Scholar 

  65. Kötter R, Sommer FT, Global relationship between anatomical connectivity and activity propagation in the cerebral cortex. Philos Trans R Soc Lond B Biol Sci 2000; 355: 127–134.

    Article  PubMed  Google Scholar 

  66. Barabasi AL, Albert R. Emergence of scaling in random networks. Science 1999; 286: 509–512.

    Article  PubMed  Google Scholar 

  67. Jeong H, Tombor B, Albert R, Oltvai ZN, Barabasi AL. The large-scale organization of metabolic networks. Nature 2000; 407: 651–654.

    Article  PubMed  CAS  Google Scholar 

  68. Hilgetag CC, Grant S. Uniformity, specificity and variability of corticocortical connectivity. Philos Trans R Soc Lond B Biol Sci 2000; 355: 7–20.

    Article  PubMed  CAS  Google Scholar 

  69. Kruskal JB. Nonmetric multidimensional scaling: a numerical method. Psychometrika 1964; 29: 115–129.

    Article  Google Scholar 

  70. Kruskal JB. Multidimesional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 1964; 29: 1–27.

    Article  Google Scholar 

  71. Tenenbaum JB, de Silva V, Langford JC. A global geometric framework for nonlinear dimensionality reduction. Science 2000; 290: 2319–2323.

    Article  PubMed  CAS  Google Scholar 

  72. Roweis ST, Saul LK. Nonlinear dimensionality reduction by locally linear embedding. Science 2000; 290: 2323–2326.

    Article  PubMed  CAS  Google Scholar 

  73. Simmen MW., Goodhill GJ, Willshaw DJ. Scaling and brain connectivity. Nature 1994; 369: 448–449.

    Article  PubMed  CAS  Google Scholar 

  74. Young MP, Scannell JW, Burns GAPC, Blakemore C. Scaling and brain connectivity-reply. Nature 1994; 369: 449–450.

    Article  Google Scholar 

  75. Goodhill GJ, Simmen MW, Willshaw DJ. An evaluation of the use of multidimensional scaling for understanding brain connectivity. Philos Trans R Soc Lond B Biol Sci 1995; 348: 265–280.

    Article  PubMed  CAS  Google Scholar 

  76. Borg I, Lingoes J. Multidimensional Similarity Structure Analysis. Springer, New York, 1987.

    Book  Google Scholar 

  77. Guttmann L. A general nonmetric technique for finding the smallest coordinate space for a configuration of points. Pyrometrical 1968; 33: 469–506.

    Google Scholar 

  78. Cattell RB. The scree test for the number of factors. Multivariate Beh Res 1966; 1: 245–276.

    Article  Google Scholar 

  79. Ungerleider LG, Mishkin M. Two cortical visual systems. In: Analysis of Visual Behaviour ( Ingle DG, Goodale MA, Mansfield RJQ, eds.). MIT Press, Cambridge, MA, 1982, pp. 549–586.

    Google Scholar 

  80. Friston K. Characterising distributed functional systems. In: Human Brain Function ( Frackowiak R, Friston K, Frith C, Dolan R, Mazziotta J, eds.). Academic Press, San Diego, 1997, pp. 107–126.

    Google Scholar 

  81. Healy M. Matrices for Statistics. Clarendon Press, Oxford, 2000, pp. 93–96.

    Google Scholar 

  82. Greenacre M. Theory and Applications of Correspondence Analysis. Academic Press, London, 1984.

    Google Scholar 

  83. Shankle WR, Romney AK, Landing BH, Hara J. Developmental patterns in the cytoarchitecture of the human cerebral cortex from birth to 6 years examined by correspondence analysis. Proc Natl Acad Sci USA 1998; 95: 4023–4028.

    Article  PubMed  CAS  Google Scholar 

  84. Ringo JL. Neuronal interconnection as a function of brain size. Brain Behav Evol 1991; 38: 1–6.

    Article  PubMed  CAS  Google Scholar 

  85. Cherniak C. Local optimization of neuron arbors. Biol Cybernetics 1992; 66: 503–510.

    Article  CAS  Google Scholar 

  86. Cherniak C. Component placement optimization in the brain. J Neurosci 1994; 14: 2418–2427.

    PubMed  CAS  Google Scholar 

  87. Scannell JW. Determining cortical landscapes. Nature 1997; 386: 452.

    Article  PubMed  CAS  Google Scholar 

  88. Barbas H. Anatomic basis of cognitive-emotional interactions in the primate prefrontal cortex. Neurosci Biobehav Rev 1995; 19: 499–510.

    Article  PubMed  CAS  Google Scholar 

  89. Tononi G, Sporns O, Edelman GM. A measure for brain complexity: relating functional segregation and integration in the nervous system. Proc Natl Acad Sci USA 1994; 91: 5033–5037.

    Article  PubMed  CAS  Google Scholar 

  90. Tononi G, Sporns O, Edelman GM. A complexity measure for selective matching of signals by the brain. Proc Natl Acad Sci USA 1996; 93: 3422–3427.

    Article  PubMed  CAS  Google Scholar 

  91. Tononi G, McIntosh AR, Russell DP, Edelman GM. Functional clustering: identifying strongly interactive brain regions in neuroimaging data. Neuroimage 1998; 7: 133–149.

    Article  PubMed  CAS  Google Scholar 

  92. O’Neill MA, Hilgetag CC. The portable UNIX programming system (PUPS) and CANTOR: a computational environment for dynamical representation and analysis of complex neurobiological data. Philos Trans R Soc Lond B Biol Sci 2001; 356: 1259–1276.

    Article  PubMed  Google Scholar 

  93. Hilgetag CC, Burns GAPC, O’Neill MA, Young MP. Cluster structure of cortical systems in mammalian brains. In: Computational Neuroscience: Trends in Research, 1998 ( Bower JM, ed.). Plenum Press, New York, 1998, pp. 41–46.

    Google Scholar 

  94. Maunsell JH, Van Essen DC. The connections of the middle temporal visual area (MT) and their relationship to a cortical hierarchy in the macaque monkey. J Neurosci 1983; 3: 2563–2586.

    PubMed  CAS  Google Scholar 

  95. Hilgetag CC, Grant S. Uniformity and specificity of long-range corticocortical connections in the visual cortex of the Cat. Neurocomputing 2001; 38–40: 667–673.

    Article  Google Scholar 

  96. Milner AD, Goodale MA. The Visual Brain in Action. Oxford University Press, New York, 1996.

    Google Scholar 

  97. Petroni F, Panzeri S, Hilgetag CC, Kötter R, Young MP. Simultaneity of responses in a hierarchical visual network. Neuroreport 2001; 12: 2753–2759.

    Article  PubMed  CAS  Google Scholar 

  98. Grossberg S. How does the cerebral cortex work? Learning, attention, and grouping by the laminar circuits of visual cortex. Spat Vis 1999; 12: 163–185.

    Article  PubMed  CAS  Google Scholar 

  99. Grossberg S, Raizada RD. Contrast-sensitive perceptual grouping and object-based attention in the laminar circuits of primary visual cortex. Vision Res 2000; 40: 1413–1432.

    Article  PubMed  CAS  Google Scholar 

  100. Grossberg S, Williamson JR. A neural model of how horizontal and interlaminar connections of visual cortex develop into adult circuits that carry out perceptual grouping and learning. Cereb Cortex 2001; 11: 37–58.

    Article  PubMed  CAS  Google Scholar 

  101. Aharonov R, Meilijson I, Ruppin E. Measuring significance of neural elements: A quantitative approach. NeuroComputing 2002; in press.

    Google Scholar 

  102. McIntosh AR, Grady CL, Ungerleider LG, Haxby JV, Rapoport SI, Horwitz B. Network analysis of cortical visual pathways mapped with PET. J Neurosci 14: 655–666.

    Google Scholar 

  103. McIntosh A, Grady CL, Haxby JV, Ungerleider LG, and Horwitz B. Changes in limbic and prefrontal functional interactions in a working memory task for faces. Cereb Cortex 1996; 6: 571–584.

    Article  PubMed  CAS  Google Scholar 

  104. Büchel C, Friston KJ. Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modelling and fMRI. Cereb Cortex 1997; 7: 768–778.

    Article  PubMed  Google Scholar 

  105. Tagamets M-A, Horwitz B. Integrating electrophysiological and anatomical experimental data to create a large-scale model that simulates a delayed match-to-sample human brain imaging study. Cereb Cortex 1998; 8: 310–320.

    Article  PubMed  CAS  Google Scholar 

  106. Strogatz SH. Exploring complex networks. Nature 2001; 410: 268–276.

    Article  PubMed  CAS  Google Scholar 

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Authors
  1. Claus C. Hilgetag
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  2. Rolf Kötter
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  3. Klaas E. Stephan
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  4. Olaf Sporns
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Editors and Affiliations

  1. Krasnow Institute for Advanced Study and Psychology Department, George Mason University, Fairfax, VA, USA

    Giorgio A. Ascoli PhD

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Hilgetag, C.C., Kötter, R., Stephan, K.E., Sporns, O. (2002). Computational Methods for the Analysis of Brain Connectivity. In: Ascoli, G.A. (eds) Computational Neuroanatomy. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-59259-275-3_14

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  • DOI: https://doi.org/10.1007/978-1-59259-275-3_14

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