Skip to main content
SpringerLink
Log in

How Does Connectivity Between Cortical Areas Depend on Brain Size? Implications for Efficient Computation

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

A formula for an average connectivity between cortical areas in mammals is derived. Based on comparative neuroanatomical data, it is found, surprisingly, that this connectivity is either only weakly dependent or independent of brain size. It is discussed how this formula can be used to estimate the average length of axons in white matter. Other allometric relations, such as cortical patches and area sizes vs. brain size, are also provided. Finally, some functional implications, with an emphasis on efficient cortical computation, are discussed as well.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allman JM (1999) Evolving Brains. Freeman, New York.

    Google Scholar 

  • Amir Y, Harel M, Malach R (1993) Cortical hierarchy reflected in the organization of intrinsic connections in macaque monkey visual cortex. J. Comp. Neurol. 334: 19-46.

    Google Scholar 

  • Attwell D, Laughlin SB (2001) An energy budget for signaling in the gray matter of the brain. J. Cerebral Blood Flow and Metabolism 21: 1133-1145.

    Google Scholar 

  • Barton RA, Harvey PH (2000) Mosaic evolution of brain structure in mammals. Nature 405: 1055-1058.

    Google Scholar 

  • Braitenberg V (1978a) Cell assemblies in the cerebral cortex. In: R Heim, G Palm, eds. Theoretical Approaches to Complex Systems. Springer-Verlag, Berlin.

    Google Scholar 

  • Braitenberg V (1978b) Cortical architectonics: General and areal. In: MAB Brazier, H Petsche, eds. Architectonics of the Cerebral Cortex. Raven, New York, pp. 443-465.

    Google Scholar 

  • Braitenberg V (2001) Brain size and number of neurons: An exercise in synthetic neuroanatomy. J. Comput. Neurosci. 10: 71-77.

    Google Scholar 

  • Braitenberg V, Schüz A (1998) Cortex: Statistics and Geometry of Neuronal Connectivity. Springer, Berlin

    Google Scholar 

  • Burkhalter A, Bernardo KL (1989) Organization of corticocortical connections in human visual cortex. Proc. Natl. Acad. Sci. USA 86,1071-1075.

    Google Scholar 

  • Cajal SR (1995) Histology of the Nervous System of Man and Vertebrates. Oxford Univ. Press, New York, Vol. 1.

    Google Scholar 

  • Caviness VS (1975) Architectonic map of neocortex of the normal mouse. J. Comp. Neurol. 164: 247-264.

    Google Scholar 

  • Changizi MA (2001) Principles underlying mammalian neocortical scaling. Biol. Cybern. 84: 207-215.

    Google Scholar 

  • Cherniak C (1995) Neural component placement. Trends Neurosci. 18: 522-527.

    Google Scholar 

  • Chklovskii D, Stevens CF (1999) Wiring optimization in the brain. In: SA Solla, ed. Advances in Neural Information Processing Systems. MIT Press, Cambridge, Vol. 12, pp. 103-107.

    Google Scholar 

  • Douglas RJ, Martin KAC (1991) Opening the grey box. Trends Neurosci. 14: 286-293.

    Google Scholar 

  • Felleman DJ, Van Essen DC (1991) Distributed hierarchical processing in the primate cerebral cortex. Cereb. Cortex 1: 1-47.

    Google Scholar 

  • Frahm HD, Stephan H, Stephan M (1982) Comparison of brain structure volumes in insectivora and primates. I. Neocortex. J. Hirnforsch. 23: 375-389.

    Google Scholar 

  • Greilich H (1984) Quantitative Analyse der cortico-corticalen Fernverbindungen bei der Maus. Thesis, Univ. of Tuebingen.

  • Hofman MA (1983) Energy metabolism, brain size and longevity in mammals. Quarterly Review of Biology 58: 495-512.

    Google Scholar 

  • Hofman MA (1985) Size and shape of the cerebral cortex in mammals. I. The cortical surface. Brain Behav. Evol. 27: 28-40.

    Google Scholar 

  • Hofman MA (1989) On the evolution and geometry of the brain in mammals. Prog. Neurobiol. 32: 137-158.

    Google Scholar 

  • Hursh JB (1939) Conduction velocity and diameter of nerve fibers. Amer. J. Physiol. 127: 131-139.

    Google Scholar 

  • Jerison HJ (1973) Evolution of the Brain and Intelligence. Academic Press, New York.

    Google Scholar 

  • Jerison HJ (1991) Brain Size and the Evolution of Mind. Am. Mus. Natl. Hist., New York.

  • Kaas JH (1987) The organization of neocortex in mammals: Implications for theories of brain function. Ann. Rev. Psychol. 38: 129-151.

    Google Scholar 

  • Kaas JH (1995) The evolution of isocortex. Brain Behav. Evol. 46: 187-196.

    Google Scholar 

  • Kaas JH (2000) Why is brain size so important: Design problems and solutions as neocortex gets bigger or smaller. Brain Mind 1: 7-23.

    Google Scholar 

  • Karbowski J (2001) Optimal wiring principle and plateaus in the degree of separation for cortical neurons. Phys. Rev. Lett. 86: 3674-3677.

    Google Scholar 

  • Karbowski J (2002) Optimal wiring in the cortex and neuronal degree of separation. Neurocomputing 44-46: 875-879.

    Google Scholar 

  • Kolb B(1990) Organization of the neocortex of the rat. In:B Kolb, RC Tees, eds. The Cerebral Cortex of the Rat. MIT Press, Cambridge, pp. 21-33.

  • Krubitzer L (1995) The organization of neocortex in mammals: Are species differences really so different? Trends Neurosci. 18: 408- 417.

    Google Scholar 

  • Krubitzer L, Huffman KJ (2000) Arealization of the neocortex in mammals: Genetic and epigenetic contributions to the phenotype. Brain Behav. Evol. 55: 322-335.

    Google Scholar 

  • Krubitzer L, Kunzle H, Kaas J (1997) Organization of sensory cortex in Madagascan insectivore, the tenrec (Echinops telfairi). J. Comp. Neurol. 379: 399-414.

    Google Scholar 

  • Laughlin SB, de Ruyter van Steveninck RR, Anderson JC (1998) The metabolic cost of neural information. Nature Neurosci. 1: 36- 41.

    Google Scholar 

  • Levy WB, Baxter RA (1996) Energy-efficient neural codes. Neural Comput. 8: 531-543.

    Google Scholar 

  • Luhmann HJ, Martinez-Millan L, Singer W (1986) Development of horizontal intrinsic connections in cat striate cortex. Exp. Brain Res. 63: 443-448.

    Google Scholar 

  • Mitchison G (1992) Axonal trees and cortical architecture. Trends Neurosci. 15: 122-126.

    Google Scholar 

  • Murre JMJ, Sturdy DPF (1995) The connectivity of the brain: Multilevel quantitative analysis. Biol. Cybern. 73: 529-545.

    Google Scholar 

  • Olivares R, Montiel J, Aboitiz F (2001) Species differences and similarities in the fine structure of the mammalian corpus callosum. Brain Behav. Evol. 57: 98-105.

    Google Scholar 

  • Pandya DN, Yeterian EH (1985) Architecture and connections of cortical association areas. In: A Peters, EG Jones, eds. Cerebral Cortex. Plenum, New York, Vol. 4, pp. 3-61.

    Google Scholar 

  • Prothero JW, Sundsten JW (1984) Folding of the cerebral cortex in mammals. Brain Behav. Evol. 24: 152-167.

    Google Scholar 

  • Ringo JL (1991) Neuronal interconnection as a function of brain size. Brain Behav. Evol. 38: 1-6.

    Google Scholar 

  • Ringo JL, Doty RW, Demeter S, Simard PY (1994) Time is of the essence: A conjecture that hemispheric specialization arises from interhemispheric conduction delay. Cereb. Cortex 4: 331-343.

    Google Scholar 

  • Rockel AJ, Hiorns RW, Powell TPS (1980) The basic uniformity in structure of the neocortex. Brain 103: 221-244.

    Google Scholar 

  • Rockland KS, Lund JS, Humphrey AL (1982) Anatomical binding of intrinsic connections in the striate cortex of tree shrews (Tupaia glis). J. Comp. Neurol. 209: 41-58.

    Google Scholar 

  • Rumberger A, Tyler CJ, Lund JS (2001) Intra-and inter-areal connections between the primary visual cortex V1 and the area immediately surrounding V1 in the rat. Neuroscience 102: 35-52.

    Google Scholar 

  • Rushton WAH (1951) A theory of the effects of fiber size in medullated nerve. J. Physiol. 115: 101-122.

    Google Scholar 

  • Scannell JW, Young MP (1993) The connectional organization of neural systems in the cat cerebral cortex. Current Biology 3: 191- 200.

    Google Scholar 

  • Scannell JW, Young MP, Blakemore C (1995) Analysis of connectivity in the cat cerebral cortex. J. Neurosci. 15: 1463-1483.

    Google Scholar 

  • Schüz A (2001) Private communication.

  • Schüz A, Demianenko G(1995) Constancy and variability in cortical structure. A study on synapses and dendritic spines in hedgehog and monkey. J. Brain Res. 36: 113-122.

    Google Scholar 

  • Schüz A, Liewald D(2001) Patterns of cortico-cortical connections in the mouse. In: N Elsner, GW Kreutzberg, eds. The Neurosciences at the Turn of the Century. Thieme, Vol. II, p. 624.

  • Schüz A, Preissl H (1996) Basic connectivity of the cerebral cortex and some considerations on the corpus callosum. Neurosci. Biobehav. Rev. 20: 567-570.

    Google Scholar 

  • Shulman RG, Rothman DL (1998) Interpreting functional imaging studies in terms of neurotransmitter cycling. Proc. Natl. Acad. Sci. USA 95: 11993-11998.

    Google Scholar 

  • Sibson NR, Dhankar A, Mason GF, Rothman DL, Behar KL, Shulman RG (1998) Stoichiometric coupling of brain glucose metabolism and glutamatergic neuronal activity. Proc. Natl. Acad. Sci. USA 95: 316-321.

    Google Scholar 

  • Sporns O, Tononi G, Edelman GM (2000) Theoretical Neuroanatomy: Relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb. Cortex 10: 127-141.

    Google Scholar 

  • Stephan H, Frahm H, Baron G (1981) New and revised data on volumes of brain structures in insectivores and primates. Folia Primatol. (Basel) 35: 1-29.

    Google Scholar 

  • Stevens CF (1989) How cortical interconnectedness varies with network size. Neural Comput 1: 473-479.

    Google Scholar 

  • Wong-Riley MTT (1989) Cytochrome oxidase: An endogenous metabolic marker for neuronal activity. Trends Neurosci. 12: 94-101.

    Google Scholar 

  • Young MP (1992) Objective analysis of the topological organization of the primate cortical visual system. Nature 358: 152- 155.

    Google Scholar 

  • Young MP (1993) The organization of neural systems in the primate cerebral cortex. Proc. Roy. Soc. B 252: 13-18.

    Google Scholar 

  • Young MP, Scannell JW, Burns G. (1995) The Analysis of Cortical Connectivity. Landes, Austin, TX.

    Google Scholar 

  • Zeki S, Shipp S (1988) The functional logic of cortical connections. Nature 335: 311-317.

    Google Scholar 

  • Zhang K, Sejnowski TJ (2000) A universal scaling law between gray matter and white matter of cerebral cortex. Proc. Natl. Acad. Sci. USA 97: 5621-5626.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sloan-Swartz Center for Theoretical Neurobiology, Division of Biology 216-76, California Institute of Technology, Pasadena, CA, 91125, USA

    Jan Karbowski

Authors
  1. Jan Karbowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karbowski, J. How Does Connectivity Between Cortical Areas Depend on Brain Size? Implications for Efficient Computation. J Comput Neurosci 15, 347–356 (2003). https://doi.org/10.1023/A:1027467911225

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1027467911225

Search

Navigation