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University of Plymouth | Centre for Theoret. and Comput. Neuroscience | Home   

Neural Field Models of Cortical Receptive Fields

Neural field models are continuum models for extended cortical tissue comprising simple graded response or spiking neurons and (often) center-surround-type coupling schemes. They can beneficially be used to describe cortical tuning properties. In that case the continuous (spatial) variable describes a feature dimension in a stimulus set, and localised activity confined to only a certain region in the neural field reflects the different tuning of the cells. Different numbers of cell-types or cell-layers as well as various coupling schemes, parameters, and stimuli allow to reflect a variety of different anatomical, physiological, or experimental situations.

Non-linear neural field models are easy to simulate, but difficult to solve analytically. We have developed an approximation scheme particularly well suited for localized activity in these models. The scheme reduces the dynamics of the full system to just a low-dimensional set of ordinary differential equations for the amplitudes and tuning widths of the cells in the different network layers. These are in general the most interesting variables of the models. The reduced equations are much easier (and faster) to solve, but still provide significiant insight into the dynamics of the whole system. The method works for peaked solutions in models of arbitrary dimension and with possibly several neural layers.

The method greatly supports an understanding of the processes that shape responses in field models, and can be used in other contexts than receptive fields, too. It links localised solutions in neural field models to low-dimensional neural network equations like the Wilson-Cowan oscillator (T.W., 2001, 2002). It also provides a structure-function relationship that links components in the spatio-temporal activity of a neural field to its anatomical synaptic couplings (T.W., 2004). The works with Worgotter et al apply an early version of the method to concrete experimental data concerning the LGN-V1 projection.

Selected References

• Wennekers. T.:
  Separation of spatio-temporal receptives fields into sums of Gaussians component.
  Journal of Computational Neuroscience 16, 27-38, 2004.
  PDF File (207kBytes)


• Wennekers, T.:
  Dynamic approximation of spatio-temporal receptive fields in nonlinear neural field models.
  Neural Computation 14 (8): 1801-1825, 2002.
  PDF File (571kBytes)


• Suder, K.; Funke, K.; Zhao, Y.; Kerscher, N.; Wennekers, T.; Worgotter, F.:
  Spatial dynamics of receptive fields in cat primary visual cortex related to the temporal structure of thalamo-cortical feedforward activity - experiments and models.
  Experimental Brain Research 144 (4): 430-444, 2002.
  PDF File (175kBytes)


• Wennekers, T.:
  Orientation tuning properties of simple cells in Area V1 derived from an approximate analysis of nonlinear neural field models.
  Neural Computation 13 (8), 1721-1747, 2001.
  PDF File (286kBytes)


• Suder, K.; Worgotter, F.; Wennekers, T.:
  Neural field model of receptive field restructuring in primary visual cortex.
  Neural Computation 13, 139-159, 2001.
  PDF File (402kBytes)

   © 2004 by -thowe-