Abstract
A thermodynamic theory has previously been introduced for explaining the formation of ocular dominance columns in the visual cortex. This paper extends the theory to account for the variation in patterns of ocular dominance columns as a phase transition phenomenon. For this purpose, an “Order parameter” is calculated by Monte Carlo simulation. On a phase diagram representing a two-dimensional parameter space, the conditions in which abnormal ocular dominance columns arise are visualized, and several visual deprivation experiments are successfully explained.
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References
Anderson PA, Olavarria J, Van Sluyters RC (1988) The overall pattern of ocular dominance bands in the cat visual cortex. J Neurosci 8:2183–2200
Binder K, Stauffer D (1986) Monte Carlo studies of systems with disorder. In: Binder K (ed) Monte Carlo methods in statistical physics. Springer, Berlin Heidelberg New York
Garel T, Doniach S (1982) Phase transitions with spontaneous modulation the dipolar Ising ferromagnet. Phys Rev B 26:325–329
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
Mastronarde DN (1983) Correlated firing of cat retinal ganglion cells. II. Responses of X-and Y-cells to single quantal events. J Neurophysiol 49:325–349
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
Miller KD, Keller JB, Stryker MP (1989) Ocular dominance column development: analysis and simulation. Science 245:605–615.
Stryker MP, Strickland SL (1984) Physiological segregation of ocular dominance columns depends on the pattern of afferent electrical activity. Invest Ophthalmol [Suppl] 25:278
Swindale NV (1981) Absence of ocular dominance patches in darkreared cats. Nature (London) 290:332–333
Swindale NV (1982) A model for the formation of ocular dominance stripes. Proc R Soc Lond B 208:243–264
Tanaka S (1989) Theory of self-organization of cortical maps. In: Touretzky DS (ed) Advances in neural information processing system 1. Morgan Kaufmann, San Mateo, pp 451–458
Tanaka S (1990a) Theory of self-organization of cortical maps: mathematical framework. Neural Networks 3:625–640
Tanaka S (1990b) Experience-dependent self-organization of biological neural networks. NEC Res Dev 98:1–14
Tanaka S (1991) Theory of ocular dominance column formation: Mathematical basis and computer simulation. Biol Cybern 64:263–272
Von der Malsburg C (1979) Development of ocularity domains and growth behaviour of axon terminals. Biol Cybern 32:49–62
Wiesel TN, Hubel DH (1974) Ordered arrangement of orientation columns in monkeys lacking visual experience. J Comp Neurol 158:307–318
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Tanaka, S. Phase transition theory for abnormal ocular dominance column formation. Biol. Cybern. 65, 91–98 (1991). https://doi.org/10.1007/BF00202383
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DOI: https://doi.org/10.1007/BF00202383