Skip to main content

Development of Columnar Structures in Visual Cortex

  • Chapter
  • 302 Accesses

Abstract

Many features of visual scenes are represented in the visual cortex in the form of maps. The best studied of these are the maps of features such as ocular dominance and orientation in primary visual cortex (V1). The beautifully regular structure of these maps and their dependence on patterns of neural activity have inspired several different computational models. In this chapter, we focus on what can be explained by models based on the idea of optimizing a trade-off between coverage and continuity, in particular, the elastic net (EN).

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Swindale NV. The development of topography in the visual cortex: a review of models. Network 1996; 7:161–247.

    Google Scholar 

  2. Swindale NV. Development of ocular dominance stripes, orientation selectivity and orientation columns. In: Modelling Neural Development Ch. 12. ( van Ooyen A, ed.). MIT Press, Cambridge, MA, 2001.

    Google Scholar 

  3. Das A, Gilbert CD. Distortions of visuotopic map match orientation singularities in primary visual cortex. Nature 1997; 387: 594–598.

    Article  PubMed  CAS  Google Scholar 

  4. Hubel DH, Wiesel TN. Functional architecture of the macaque monkey visual cortex. Proc R Soc Lond B Biol Sci 1977; 198: 1–59.

    Article  PubMed  CAS  Google Scholar 

  5. Blasdel GG, Salama G. Voltage-sensitive dyes reveal a modular organization in monkey striate cortex. Nature 1986; 321: 579–585.

    Article  PubMed  CAS  Google Scholar 

  6. Bonhoeffer T, Grinvald A. Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns. Nature 1991; 353: 429–431.

    Article  PubMed  CAS  Google Scholar 

  7. Issa NP, Trepel C, Stryker MP. Spatial frequency maps in cat visual cortex. J Neurosci 2000; 20: 8504–8514.

    PubMed  CAS  Google Scholar 

  8. Shoham D, Hübener M, Schulze S, Grinvald A, Bonhoeffer T. Spatio-temporal frequency domains and their relation to cytochrome oxidase staining in cat visual cortex. Nature 1997; 385: 529–533.

    Article  PubMed  CAS  Google Scholar 

  9. Hübener M, Shoham D, Grinvald A, Bonhoeffer T. Spatial relationships among three columnar systems in cat area 17. J Neurosci 1997; 17: 9270–9284.

    PubMed  Google Scholar 

  10. Everson RM, Prashanth AK, Gabbay M, Knight BW, Sirovich L, Kaplan E. Representation of spatial frequency and orientation in the visual cortex. Proc Natl Acad Sci USA 1998; 95: 8334–8338.

    Article  PubMed  CAS  Google Scholar 

  11. Bartfeld E, Grinvald, A. Relationships between orientation-preference pinwheels, cytochrome oxidase blobs, and ocular-dominance columns in primate striate cortex. Proc Natl Acad Sci USA 1992; 89: 11905–11909.

    Article  PubMed  CAS  Google Scholar 

  12. Obermayer K, Blasdel GG. Geometry of orientation and ocular dominance columns in monkey striate cortex. J Neurosci 1993; 13: 4114–4129.

    PubMed  CAS  Google Scholar 

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

    PubMed  CAS  Google Scholar 

  14. Horton JC, Hocking DR. Intrinsic variability of ocular dominance column periodicity in normal macaque monkeys. J Neurosci 1996; 16: 7228–7339.

    PubMed  CAS  Google Scholar 

  15. Obermayer K, Blasdel GG. Singularities in primate orientation maps. Neural Comput 1997; 9: 555–575.

    Article  PubMed  CAS  Google Scholar 

  16. Löwel S, Schmidt KE, Kim D-S, et al. The layout of orientation and ocular dominance domains in area 17 of strabismic cats. Eur J Neurosci 1998; 10: 2629–2643.

    Article  PubMed  Google Scholar 

  17. Müller T, Stetter M, Hübener M, et al. An analysis of orientation and ocular dominance patterns in the visual cortex of cats and ferrets. Neural Comput 2000; 12: 2573–2595.

    Article  PubMed  Google Scholar 

  18. Kaschube M, Wolf F, Geisel T, Löwel, S. Quantifying the variability of patterns of orientation domains in the visual cortex of cats. Neurocomputing 2000; 32–33: 415–423.

    Article  Google Scholar 

  19. Hubel DH, Wiesel TN, LeVay S. Plasticity of ocular dominance columns in monkey striate cortex. Philos Trans R Soc Lond B Biol Sci 1977; 278: 377–409.

    Article  PubMed  CAS  Google Scholar 

  20. Shatz CJ. Impulse activity and the patterning of connections during CNS development. Neuron 1990; 5: 745–756.

    Article  PubMed  CAS  Google Scholar 

  21. Katz LC, Shatz CJ. Synaptic activity and the construction of cortical circuits. Science 1996; 274: 1133–1138.

    Article  PubMed  CAS  Google Scholar 

  22. Stryker MP, Harris WA. Binocular impulse blockade prevents the formation of ocular dominance columns in cat visual cortex. J Neurosci 1986; 6: 2117–2133.

    PubMed  CAS  Google Scholar 

  23. Shatz CJ, Stryker MP. Ocular dominance in layer IV of the cat’s visual cortex and the effects of monocular deprivation. J Physiol 1978; 281: 267–283.

    PubMed  CAS  Google Scholar 

  24. LeVay, S, Wiesel TN, Hubel DH. The development of ocular dominance columns in normal and visually deprived monkeys. J Comp Neurol 1980; 191: 1–51.

    Article  PubMed  CAS  Google Scholar 

  25. Chapman B, Jacobson MD, Reiter HO, Stryker MP. Ocular dominance shift in kitten visual cortex caused by imbalance in retinal electrical activity. Nature 1986; 324: 154–156.

    Article  PubMed  CAS  Google Scholar 

  26. Rittenhouse CD, Shouval HZ, Paradiso MA, Bear MF. Monocular deprivation induces homosynaptic long-term depression in visual cortex. Nature 1999; 397: 347–350.

    Article  PubMed  CAS  Google Scholar 

  27. Hubel DH, Wiesel TN. Binocular interaction in striate cortex of kittens reared with artificial squint. J Neurophysiol 1965; 28: 1041–1059.

    PubMed  CAS  Google Scholar 

  28. Löwel S. Ocular dominance column development: Strabismus changes the spacing of adjacent columns in cat visual cortex. J Neurosci 1994; 14: 7451–7468.

    PubMed  Google Scholar 

  29. Sengpiel F, Gödecke I, Stawinski P, Hübener M, Löwel S, Bonhoeffer T. Intrinsic and environmental factors in the development of functional maps in cat visual cortex. Neuropharmacology 1998; 37: 607–621.

    Article  PubMed  CAS  Google Scholar 

  30. Durbin R, Mitchison G. A dimension reduction framework for understanding cortical maps. Nature 1990; 343: 644–647.

    Article  PubMed  CAS  Google Scholar 

  31. Durbin R, Willshaw D. An analog approach to the traveling salesman problem using an elastic net method. Nature 1987; 326: 689–691.

    Article  PubMed  CAS  Google Scholar 

  32. Goodhill GJ, Willshaw DJ. Application of the elastic net algorithm to the formation of ocular dominance stripes. Network 1990; 1: 41–59.

    Article  Google Scholar 

  33. Kohonen TK. Self-organized formation of topologically correct feature maps. Biol Cybern 1982; 43: 59–59.

    Article  Google Scholar 

  34. Kohonen TK. Self-Organizing Maps. Springer-Verlag, Berlin, 1995.

    Book  Google Scholar 

  35. Erwin E, Obermayer K, Schulten K. Models of orientation and ocular dominance columns in the visual cortex: A critical comparison. Neural Comput 1995; 7: 425–468.

    Article  PubMed  CAS  Google Scholar 

  36. Tikhonov AN, Arsenin, VY. Solutions of Ill-Posed Problems. Scripta Series in Mathematics. (Translation editor: Fritz John)John Wiley & Sons, New York, 1977.

    Google Scholar 

  37. Erwin E, Obermayer K, Schulten K. Self-organizing maps: Ordering, convergence properties and energy functions. Biol Cybern 1992; 67: 47–55.

    Article  PubMed  CAS  Google Scholar 

  38. Utsugi A. Hyperparameter selection for self-organizing maps. Neural Comput 1997; 9: 623–635.

    Article  Google Scholar 

  39. Dayan P. Arbitrary elastic topologies and ocular dominance. Neural Comput 1993; 5: 392–401.

    Article  Google Scholar 

  40. Swindale NV. Coverage and the design of striate cortex. Biol Cybern. 1991; 65: 415–424.

    Article  PubMed  CAS  Google Scholar 

  41. Swindale NV, Shoham D, Grinvald A, Bonhoeffer T, and Hübener M. Visual cortex maps are optimised for uniform coverage. Nat Neurosci 2000; 3:822–826.

    Google Scholar 

  42. Silverman BW. Density Estimation for Statistics and Data Analysis. Chapman & Hall, London, 1986.

    Google Scholar 

  43. Bishop CM, Svensén M, Williams CKI. GTM: the generative topographic mapping. Neural Comput 1998; 10: 215–234.

    Article  Google Scholar 

  44. Goodhill GJ, Sejnowski TJ. A unifying objective function for topographic mappings. Neural Comput 1997; 9;1291–1303.

    Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  46. Goodhill GJ. The influence of neural activity and intracortical connectivity on the periodicity of ocular dominance stripes. Network 1998; 9: 419–432.

    Article  PubMed  CAS  Google Scholar 

  47. Lawler EL, Lenstra JK, Rinnooy Kan AHG, Shmoys DB. The Travelling Salesman Problem. John Wiley & Sons, Chichester, England, 1986.

    Google Scholar 

  48. Willshaw DJ, von der Malsburg C. How patterned neural connections can be set up by self-organization. Proc R Soc Lond B Biol Sci 1976; 194: 431–445.

    Article  PubMed  CAS  Google Scholar 

  49. Willshaw DJ, von der Malsburg C. A marker induction mechanism for the establishment of ordered neural mappings: its application to the retinotectal problem. Philos Trans R Soc Lond B Biol Sci 1979; 287: 203–243.

    Article  PubMed  CAS  Google Scholar 

  50. Durbin R, Szeliski R, Yuille A. An analysis of the elastic net approach to the traveling salesman problem. Neural Comput 1989; 1: 348–358.

    Article  Google Scholar 

  51. Rose K. Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proc of the IEEE 1998; 86:2210–2239.

    Google Scholar 

  52. Goodhill GJ. Correlations, competition, and optimality: modelling the development of topography and ocular dominance. Cognitive Science Research Paper CSRP 226, Sussex University, 1992.

    Google Scholar 

  53. Goodhill GJ, Richards Li. Retinotectal maps: molecules, models and misplaced data. Trends Neurosci 1999; 22: 529–534.

    Article  PubMed  CAS  Google Scholar 

  54. Yuille AL, Kolodny JA, Lee CW. Dimension reduction, generalized deformable models and the development of ocularity and orientation. Neural Networks 1996; 9:309–319.

    Google Scholar 

  55. Goodhill GJ. Topography and ocular dominance: a model exploring positive correlations. Biol Cybern 1993; 69:109–118.

    Google Scholar 

  56. Goodhill GJ, Löwel S. Theory meets experiment: correlated neural activity helps determine ocular dominance column periodicity. Trends Neurosci 1995; 18: 437–439.

    Article  PubMed  CAS  Google Scholar 

  57. Goodhill GJ, Willshaw DJ. Elastic net model of ocular dominance: overall stripe pattern and monocular deprivation. Neural Comput 1994; 6:615–621.

    Google Scholar 

  58. Goodhill GJ, Bates KR, Montague PR. Influences on the global structure of cortical maps. Proc R Soc Lond B Biol Sci 1997; 264: 649–655.

    Article  CAS  Google Scholar 

  59. Goodhill GJ, Cimponeriu A. Analysis of the elastic net applied to the formation of ocular dominance and orientation columns. Network 2000; 11:153–168.

    Google Scholar 

  60. Hoffsümmer F, Wolf F, Geisel T, Löwel S, Schmidt K. Sequential bifurcation of orientation-and ocular dominance maps. In: Proc of the Fifth Int Conf on Artificial Neural Networks (ICANN95) Vol. 1. (Fogelman-Soulie F, Gallinari R, eds.). EC2 & Cie, Paris, France, 1995, pp. 535–540.

    Google Scholar 

  61. Hoffsümmer F, Wolf F, Geisel T, Löwel S, Schmidt K. Sequential bifurcation and dynamic rearrangement of columnar patterns during cortical development. In: Computational Neuroscience: Trends in Research 1995. ( Bower TM, ed.). Academic Press, New York, 1996, pp. 197–202.

    Google Scholar 

  62. Wolf F, Geisel T. Spontaneous pinwheel annihilation during visual development. Nature 1998; 395: 73–78.

    Article  PubMed  CAS  Google Scholar 

  63. Schwartz EL. Computational studies of the spatial architecture of primate visual cortex: columns, maps, and protomaps. In: Primary Visual Cortex in Primates Vol. 10 of Cerebral Cortex, Ch. 9. ( Peters A, Rockland KS, eds.). Plenum Press, New York, 1994, 359–411.

    Google Scholar 

  64. Wolf F, Bauer H-U, Geisel T. Formation of field discontinuities and islands in visual cortical maps. Biol. Cybern 1994; 70: 525–531.

    Article  PubMed  CAS  Google Scholar 

  65. Hetherington PA, Swindale NV. Receptive field and orientation scatter studied by tetrode recordings in cat area 17. Vis Neurosci 1999; 16: 637–652.

    Article  PubMed  CAS  Google Scholar 

  66. Tessier-Lavigne M., Goodman CS. The molecular biology of axon guidance. Science 1996; 274: 1123–1133.

    Article  PubMed  CAS  Google Scholar 

  67. Mueller BK. Growth cone guidance: first steps towards a deeper understanding. Annu Rev Neurosci 1999; 22: 351–388.

    Article  PubMed  CAS  Google Scholar 

  68. Cheng HJ, Nakamoto M, Bergemann AD, Flanagan JG. Complementary gradients in expression and binding of ELF-1 and Mek4 in development of the topographic retinotectal projection map. Cell 1995; 82: 371–381.

    Article  PubMed  CAS  Google Scholar 

  69. Drescher U, Kremoser C, Handwerker C, Loschinger J, Noda M, Bonhoeffer F. In vitro guidance of retinal ganglion cell axons by RAGS, a 25 KDa tectal protein related to ligands for Eph receptor tyrosine kinases. Cell 1995; 82: 359–370.

    Article  PubMed  CAS  Google Scholar 

  70. Feldheim DA, Kim Y-I, Bergemann AD, Frisén J, Barbacid M, Flanagan JG. Genetic analysis of Ephrin-A2 and Ephrin-A5 shows their requirement in multiple aspects of retinocollicular mapping. Neuron 2000; 25: 563–574.

    Article  PubMed  CAS  Google Scholar 

  71. Goodhill GJ. Dating behavior of the retinal ganglion cell. Neuron 2000; 25: 501–503.

    Article  PubMed  CAS  Google Scholar 

  72. Flanagan JG, Vanderhaeghen P. The ephrins and Eph receptors in neural development. Annu Rev Neurosci 1998; 21: 309–345.

    Article  PubMed  CAS  Google Scholar 

  73. Feldheim DA, Vanderhaeghen P, Hansen MJ, et al. Topographic guidance labels in a sensory projection to the forebrain. Neuron 1998; 21: 1303–1313.

    Article  PubMed  CAS  Google Scholar 

  74. Vanderhaeghen P, Lu Q, Prakash N, et al. A mapping label required for normal scale of body representation in the cortex. Nat Neurosci 2000; 3: 358–365.

    Article  PubMed  CAS  Google Scholar 

  75. Crowley JC, Katz LC. Development of ocular dominance columns in the absence of retinal input. Nat Neurosci 1999; 2: 1125–1130.

    Article  PubMed  CAS  Google Scholar 

  76. Crowley JC, Katz LC. Early development of ocular dominance columns. Science 2000; 290: 1321–1324.

    Article  PubMed  CAS  Google Scholar 

  77. Crair, MC, Gillespie DC, Stryker MP. The role of visual experience in the development of columns in cat visual cortex. Science 1998; 279: 566–570.

    Article  PubMed  CAS  Google Scholar 

  78. Gödecke I, Bonhoeffer T. Development of identical orientation maps for two eyes without common visual experience. Nature 1996; 379: 251–254.

    Article  PubMed  Google Scholar 

  79. Wolf F, Bauer H-U, Pawelzik K, Geisel T. Organization of the visual cortex. Nature 1996; 382: 306–307.

    Article  PubMed  CAS  Google Scholar 

  80. Weliky M, Katz LC. Disruption of orientation tuning in visual cortex by artificially correlated neuronal activity. Nature 1997; 386: 680–685.

    Article  PubMed  CAS  Google Scholar 

  81. Goodhill GJ. Stimulating issues in cortical map development. Trends Neurosci 1997; 20: 375–376.

    Article  PubMed  CAS  Google Scholar 

  82. Weliky M, Katz LC. Correlational structure of spontaneous neuronal activity in the developing lateral geniculate nucleus in vivo. Science 1999; 285: 599–604.

    Article  PubMed  CAS  Google Scholar 

  83. Smolen P, Baxter DA, Byrne JH. Mathematical modeling of gene networks. Neuron 2000; 26: 567–580.

    Article  PubMed  CAS  Google Scholar 

  84. Sharp DH, Reinitz J. Prediction of mutant expression patterns using gene circuits. 1998; Biosystems 47: 79–90.

    Article  PubMed  CAS  Google Scholar 

  85. von Dassow G, Meir E, Munro EM, Odell GM. The segment polarity network is a robust developmental module. Nature 2000; 406: 188–192.

    Article  PubMed  CAS  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media New York

About this chapter

Cite this chapter

Carreira-Perpiñán, M.Á., Goodhill, G.J. (2002). Development of Columnar Structures in Visual Cortex. In: Ascoli, G.A. (eds) Computational Neuroanatomy. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-59259-275-3_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-59259-275-3_15

  • Publisher Name: Humana Press, Totowa, NJ

  • Print ISBN: 978-1-61737-297-1

  • Online ISBN: 978-1-59259-275-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics