Skip to main content
SpringerLink
Log in

Theory of ocular dominance column formation

Mathematical basis and computer simulation

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

A general theory previously proposed by the author which describes synaptic stabilization on the basis of three basic assumptions is employed for the understanding of ocular dominance column formation. A reduced mathematical model is constructed based on the thermodynamics in the Ising spin variables representing the afferent synaptic connection distribution. The results of Monte Carlo simulations on the segregation of ipsilateral and contralateral synaptic terminals in the input layer of the primary visual cortex suggest the existence of phase transition phenomena. Three types of ocular dominance column patterns — stripe, blob, and uniform — are visualized according to the values of the correlation strength and the degree of imbalance in activity between the left and right retinas. The theory presented here successfully explains how ocular dominance columns are developed.

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

  • Changeux JP, Danchin A (1976) Selective stabilization of developing synapses as a mechanism for the specification of neuronal networks, Nature 264:705–712

    Google Scholar 

  • Collingridge GL, Bliss TVP (1987) NMDA receptors — their role in long-term potentiation, Trends Neurosci 10:288–293

    Google Scholar 

  • Frank E (1987) The influence of neuronal activity on patterns of synaptic connections. Trends Neurosci 10:188–190

    Google Scholar 

  • Hubel DH, Wiesel TN (1962) Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. J Physiol 160:106–154

    Google Scholar 

  • Hubel DH, Wiesel TN (1977) Functional architecture of macaque monkey visual cortex. Proc R Soc Lond B198:1–59

    Google Scholar 

  • Hubel DH, Wiesel TN, LeVay S (1977) Plasticity of ocular dominance columns in monkey striate cortex. Phil Trans R Soc Lond B278:377–409

    Google Scholar 

  • Hubel DH, Wiesel TN, Stryker MP (1978) Anatomical demonstration of orientation columns in macaque monkey. J Comp Neurol 177:361–380

    Google Scholar 

  • Kaas JH, Merzenich MM, Killackey HP (1983) The organization of somatosensory cortex following peripheral nerve damage in adult and developing mammals. Ann Rev Neurosci 6:325–356

    Google Scholar 

  • Kirkpatric S, Gellat CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Google Scholar 

  • Knudsen EI, DuLac S, Esterly SD (1987) Computational maps in the brain. Ann Rev Neurosci 10:41–65

    Google Scholar 

  • LeVay S, Connolly M, Houde J, Van Essen DC (1985) The complete pattern of ocular dominance stripes in the striate cortex and visual field of the macaque monkey. J Neurosci 5:486–501

    Google Scholar 

  • Linsker R (1986) From basic network principles to neural architecture: Emergence of spatial-opponent cells. Proc Natl Acad Sci USA 83:7508–7512

    Google Scholar 

  • Livingstone MS, Hubel DH (1984) Anatomy and physiology of a colorsystem in the primate visual cortex. J Neurosci 4:309–356

    Google Scholar 

  • Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092

    Google Scholar 

  • Miller KD, Keller JB, Stryker MP (1989) Ocular dominance column development: analysis and simulation. Science 245:605–615

    Google Scholar 

  • Rakic P (1977) Prenatal development of the visual system in Rhesus monkey. Phil Trans R Soc Lond B278:245–260

    Google Scholar 

  • Swindale NV (1980) A model for the formation of ocular dominance stripes. Proc R Soc Lond B208:243–264

    Google Scholar 

  • Tanaka S (1988) Theory of self-organization of cortical maps. In: The proceeding of SICE '88, ESS2–5:1069–1072

    Google Scholar 

  • Tanaka S (1989) Theory of self-organization of cortical maps. In: Touretzky DS (eds) Advances in neural information processing system, Vol 1. Morgan Kaufmann, San Mateo Calif, pp 451–458

    Google Scholar 

  • Tanaka S (1990a) Theory of self-organization of cortical maps: mathematical framework. Neural Networks: (to be published)

  • Tanaka S (1990b) Experience-dependent self-organization of biological neural networks. NEC Res Dev 98:1–14

    Google Scholar 

  • Von der Malsburg C (1979) Development of ocularity domains and growth behavior of axon terminals. Biol Cybern 32:49–62

    Google Scholar 

  • Wu FY (1982) The Potts model. Rev Mod Phys 54:235–268

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fundamental Research Laboratories, NEC Corporation, 34 Miyukigaoka, Tsukuba, 305, Ibaraki, Japan

    Shigeru Tanaka

  2. Laboratory for Neural Networks, RIKEN Frontier Research Program, Hirosawa 2-1, Wako, 351-01, Saitama, Japan

    Shigeru Tanaka

Authors
  1. Shigeru Tanaka
    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

Tanaka, S. Theory of ocular dominance column formation. Biol. Cybern. 64, 263–272 (1991). https://doi.org/10.1007/BF00199589

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00199589

Keywords

Search

Navigation