Email updates

Keep up to date with the latest news and content from BMC Neuroscience and BioMed Central.

This article is part of the supplement: Eighteenth Annual Computational Neuroscience Meeting: CNS*2009

Open Access Poster presentation

Pinwheel crystallization in a dimension reduction model of visual cortical development

Wolfgang Keil1234* and Fred Wolf12

Author Affiliations

1 Department of Nonlinear Dynamics, Max-Planck-Institute for Dynamics and Self-Organization, D37073 Göttingen, Germany

2 Bernstein Center for Computational Neuroscience, D37073 Göttingen, Germany

3 Faculty of Physics, University of Göttingen, D37073 Göttingen, Germany

4 IMPRS, Physics of Biological and Complex Systems, D37077 Göttingen, Germany

For all author emails, please log on.

BMC Neuroscience 2009, 10(Suppl 1):P63  doi:10.1186/1471-2202-10-S1-P63


The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/10/S1/P63


Published:13 July 2009

© 2009 Keil and Wolf; licensee BioMed Central Ltd.

Poster presentation

The primary visual cortex (V1) of higher mammals contains a topographic representation of visual space in which neighborhood-preserving maps of several variables describing visual features such as position in visual space, line orientation, movement direction, and ocularity are embedded [1]. It has been hypothesized that the complex spatial layouts of these representations can be interpreted as ground states of a smooth mapping of a high-dimensional space of visual stimulus features to an effectively two dimensional array of neurons [2,3]. Competitive Hebbian models of cortical development have been widely used to numerically study the properties of such mappings [2-5], but no analytical results about their ground states have been obtained so far. A classical example of such dimension reducing mappings is the Elastic Network Model (EN), which was proposed in [2].

Here we use a perturbative approach to compute the ground states of the EN for the joint mapping of two visual features: (i) position in visual space, represented in a retinotopic map and (ii) line orientation, represented in an orientation preference map (OPM). In this framework, the EN incooporates a mapping from a four-dimensional feature space to the twodimensional cortical sheet of neurons. We show that the dynamics of both feature representations can be treated within a general theory for the stability of OPMs [6]. We find various ground states as a function of the lateral intracortical interactions and external stimulus distribution properties. However, in all parameter regimes, the grounds states of the Elastic Network Model are either stripe-like, or crystalline representation of the two visual features. We present a complete phase diagram of the model, summarizing pattern selection. Analytical predictions are confirmed by direct numerical simulations. Our results question previous studies (see [5] and references therein) concluding that the EN correctly reproduces the spatially aperiodic arrangement of visual cortical processing modules.

References

  1. Blasdel G, Salama G: Voltage-sensitive dyes reveal a modular organization in monkey striate cortex.

    Nature 1986, 321:579-585. PubMed Abstract | Publisher Full Text OpenURL

  2. Durbin R, Mitchison G: A dimension reduction framework for understanding cortical maps.

    Nature 1990, 343:644-646. PubMed Abstract | Publisher Full Text OpenURL

  3. Obermayer K, Ritter H, Schulten K: A principle for the formation of the spatial structure of cortical feature maps.

    PNAS 1990, 87:8345-8349. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  4. Kohonen T: Self-organization and associative memory. New York: Springer-Verlag; 1983.

  5. Goodhill RG: Contributions of theoretical modeling to the understanding of neural map development.

    Neuron 2007, 56:301-311. PubMed Abstract | Publisher Full Text OpenURL

  6. Wolf F: Symmetry, multistability, and long-range interactions in brain development.

    PRL 2005, 95:208701. Publisher Full Text OpenURL