Advertisement

Biological Cybernetics

, Volume 67, Issue 2, pp 191–194 | Cite as

The relationship between the Gabor elementary function and a stochastic model of the inter-spike interval distribution in the responses of visual cortex neurons

  • D. H. Berger
  • K. H. Pribram
Article

Abstract

In a previously reported study (Berger et al. 1990) we analyzed distributions of interspike intervals recorded extracellularly from cat visual cortex under four stimulus conditions. Stimuli were gratings differing in orientation and spatial frequency. The probability density function of first passage time for a random walk with drift process, which is defined by its barrier height and drift coefficient, was used to characterize the generating process of axonal discharge under resting and stimulus conditions. Drift coefficient and barrier height were derived from the sample mean and standard deviation of the measured inter-spike intervals. For cells with simple receptive fields, variations in spatial frequency produced changes only in drift coefficient. Variations in barrier height were produced only by changes in orientation of the stimulus. Currently, the method used to analyze these data was implemented in a simulation which displayed the relationship between the interval distribution of impulses, the random walk which represents the time series characteristic of the spike train model and the Gabor filter function which represents the geometry of the receptive field process.

Keywords

Random Walk Spatial Frequency Visual Cortex Barrier Height Receptive Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barker JL, Owens DG (1986) Electrophysiological pharmacology of GABA and diazepam in cultured CNS neurons. In: Olsen CW, Venter IC (eds) Benzoidiazepine/GABA receptors and chlorides channels: structural and functional properties. Liss, New York, pp 135–165Google Scholar
  2. Berger D, Pribram KH, Wild H, Bridges C (1990) An analysis of neural spike-train distributions: determinants of the response of visual cortex neurons to changes in orientation and spatial frequency. Exp Brain Res 80:129–134Google Scholar
  3. Campbell FW, Blakemore C (1969) On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images. J Physiol 203:237–260Google Scholar
  4. Cull-Candy SG, Usowicz MM (1989) Whole-cell current noise produced by excitatory and inhibitory amino acids in large cerebellar neurones of the rat. J Physiol 415:533–553Google Scholar
  5. Daugman JG (1980) Two-dimensional spectral analysis of cortical receptive field profiles. Vision Res 20:847–856Google Scholar
  6. Daugman JG (1985) Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. J Optom Soc Am A/2:1160–1169Google Scholar
  7. Daugman JG (1989) Complete discrete 2-d Gabor transforms by neural networks for image analysis and compression. IEEE Trans Acoust Speech Signal Process 36:1169–1179Google Scholar
  8. DeValois RL, Albrecht DG, Thorell LG, (1982) Spatial frequency selectivity of cells in the macaque visual cortex. Vision Res 22:545–559Google Scholar
  9. DeValois RL, Thorell LG, Albrecht DG (1985) Periodicity of striatecortex-cell receptive fields. J Optom Soc Am A/2:1115–1123Google Scholar
  10. Gerstein GL, Mandelbrot B (1964) Random walk models for the spike activity of a single neuron. Biophys J 4:41–68Google Scholar
  11. Kirilov AB, Borisyuk GN, Borisyuk RM, Kovalenko Yel, Makarenko VI, Chulaevsky VA, Kryukov Vi (1989) A model oscillator for a unified submodule. In: Touretzky DS (ed) Advances in neural information processing systems. Morgan Kaufmann, San Mateo Calif pp 560–567Google Scholar
  12. Kryukov VI (1978) Markov interaction processes and neuronal activity, In: Dold A, Eckmann B (ed) Lecture Notes in Mathematics, Vol 653: Locally interacting systems and their applications in biology. Springer, Berlin Heidelberg New York, pp 122–139Google Scholar
  13. Kulikowski JJ, Marcelja S, Bishop P (1982) Theory of spatial position and spatial frequency relation in the receptive fields of simple cells in the visual cortex. Biol Cybern 43:187–198Google Scholar
  14. Lassonde MC, Ptito M, Pribram Kh (1981) Intracerebral influences on the microstructure of visual cortex. Exp Brain Res 43:131–144Google Scholar
  15. Marcelja S (1980) Mathematical description of the responses of simple cortical cells. J Optom Soc Am 70:1297–1300Google Scholar
  16. Pribam KH (1991) Brain and perception: holonomy and structure in figurai processing. Erlbaum, Hillsdale NJGoogle Scholar
  17. Pribram KH, Carlton EH (1986) Holonomic brain theory in imaging and object perception. Act Psychol 63:174–210Google Scholar
  18. Romoa AS, Shalden M, Skottun BC, Freeman RD (1986) A comparison of inhibtion in orientation and spatial frequency of cat visual cortex. Nature 321:237–239Google Scholar
  19. Shapley R, Lennie P (1985) Spatial frequency analysis in the visual system. Ann Rev Neurosci 8:547–583Google Scholar
  20. Sillito AM, Kemp JA, Milson JA, Berardi N (1980) A re-evaluation of the mechanisms underlying simple cell orientation selectivity. Brain Res 194:517–520Google Scholar
  21. Tuckwell HC (1976) On the first-exit time problem for temporally homogeneous Markov processes. J Appl Prob 13:39–48Google Scholar
  22. Webster MA & DeValois RL (1985) Relationship between spatial-frequency and orientation tuning of striate-cortex cells. J Optom Soc Am A/2:1124–1132Google Scholar
  23. Williams PJ, MacVicar BA, Pittman QJ (1989) Identification of a GABA-activated chloride-mediated synaptic potential in rat pars intermedia. Brain Res 483:130–134Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • D. H. Berger
    • 1
  • K. H. Pribram
    • 1
  1. 1.Center for Brain Research and Informational SciencesRadford UniversityRadfordUSA

Personalised recommendations