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A Nonlinear Model of the Behavior of Simple Cells in Visual Cortex

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Abstract

Despite their structured receptive fields (RFs) and the strong linear components in their responses, most simple cells in mammalian visual cortex exhibit nonlinear behaviors. Besides the contrast-response function, nonlinearities are evident in various types of failure at superposition tasks, in the disagreement between direction indices computed from drifting and counterphase flickering gratings, in various forms of response suppression (including end- and side-stopping, spatial-frequency-specific inhibition and cross-orientation inhibition), in the advance of phase with increasing contrast, and in phase-insensitive and frequency-doubled responses to counterphase flickering gratings. These behaviors suggest that nonlinearities are involved in the operation of simple cells, but current models fail to explain them. A quantitative model is presented here that purports to describe basic and common principles of operation for all visual cortical cells. Simple cells are described as receiving afferents from multiple subunits that differ in their individual RFs and temporal impulse responses (TIRs). Subunits are independent and perform a spatial integration across their RFs followed by halfwave rectification and temporal convolution with their TIRs. This parallel operation yields a set of temporal functions representing each subunit's contribution to the membrane potential of the host cell, whose final form is given by the weighted sum of all subunits' contributions. By varying the number of subunits and their particular characteristics, different instances of the model are obtained each of which displays a different set of behaviors. Extensive simulation results are presented that illustrate how all of the reported nonlinear behaviors of simple cells arise from these multi-subunit organizations.

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References

  • Ahmed B, Allison JD, Douglas RJ, Martin KAC (1997) An intracellular study of the contrast-dependence of neuronal activity in cat visual cortex. Cerebral Cortex 7: 559–570.

    Google Scholar 

  • Albrecht DG (1995) Visual cortex neurons in monkey and cat: Effect of contrast on the spatial and temporal phase transfer functions. Visual Neurosci. 12: 1191–1210.

    Google Scholar 

  • Albrecht DG, De Valois RL (1981) Striate cortex responses to periodic patterns with and without the fundamental harmonics. J. Physiol. 319: 497–514.

    Google Scholar 

  • Albrecht DG, Geisler WS(1991) Motion selectivity and the contrast-response function of simple cells in the visual cortex. Visual Neurosci. 7: 531–546.

    Google Scholar 

  • Albrecht DG, Hamilton DB (1982) Striate cortex of monkey and cat: Contrast response function. J. Neurophysiol. 48: 217–237.

    Google Scholar 

  • Anderson JS, Carandini M, Ferster D (2000) Orientation tuning of input conductance, excitation, and inhibition in cat primary visual cortex. J. Neurophysiol. 84: 909–926.

    Google Scholar 

  • Bauman LA, Bonds AB (1991) Inhibitory refinement of spatial frequency selectivity in single cells of the cat striate cortex. Vision Research 31: 933–944.

    Google Scholar 

  • Bergen JR, Wilson HR (1985) Prediction of flicker sensitivities from temporal three-pulse data. Vision Research 25: 577–582.

    Google Scholar 

  • Berman NJ, Douglas RJ, Martin KAC, Whitteridge D (1991) Mechanisms of inhibition in cat visual cortex. J. Physiol. 440: 697–722.

    Google Scholar 

  • Bishop PO, Coombs JS, Henry GH (1971a) Responses to visual contours: Spatiotemporal aspects of excitation in the receptive fields of simple striate neurones. J. Physiol. 219: 625–657.

    Google Scholar 

  • Bishop PO, Coombs JS, Henry GH (1971b) Interaction effects of visual contours on the discharge frequency of simple striate neurones. J. Physiol. 219: 659–687.

    Google Scholar 

  • Bolz J, Gilbert CD (1986) Generation of end-inhibition in the visual cortex via interlaminar connections. Nature 320: 362–365.

    Google Scholar 

  • Bonds AB(1989) Role of inhibition in the specification of orientation selectivity of cells in cat striate cortex. Visual Neurosci. 2: 41–55.

    Google Scholar 

  • Bracewell RN (1978) The Fourier Transform and its Applications. McGraw-Hill, New York.

  • Camarda RM, Peterhans E, Bishop PO (1985) Simple cells in cat striate cortex: Responses to stationary flashing and to moving light bars. Exp. Brain Res. 60: 151–158.

    Google Scholar 

  • Carandini M, Heeger DJ (1994) Summation and division by neurons in primate visual cortex. Science 264: 1333–1336.

    Google Scholar 

  • Carandini M, Heeger DJ, Movshon JA (1997) Linearity and normalization in simple cells of the macaque primary visual cortex. J. Neurosci. 17: 8621–8644.

    Google Scholar 

  • Casanova C, Nordmann JP, Ohzawa I, Freeman RD (1992) Direction selectivity of cells in the cat's striate cortex: Differences between bar and grating stimuli. Visual Neurosci. 9: 505–513.

    Google Scholar 

  • Cavanaugh JR, Bair W, Movshon JA (2002a) Nature and interaction of signals from the receptive field center and surround in macaque V1 neurons. J. Neurophysiol. 88: 2530–2546.

    Google Scholar 

  • Cavanaugh JR, Bair W, Movshon JA (2002b) Selectivity and spatial distribution of signals from the receptive field surround in macaque V1 neurons. J. Neurophysiol. 88: 2547–2556.

    Google Scholar 

  • Dahari R, Spitzer H (1996) Spatiotemporal adaptation model for retinal ganglion cells. Journal of the Optical Society of America A 13: 419–435.

    Google Scholar 

  • Daugman JG (1980) Two-dimensional spectral analysis of cortical receptive field profiles. Vision Research 20: 847–856.

    Google Scholar 

  • Dawis S, Shapley R, Kaplan E, Tranchina D (1984) The receptive field organization of X-cells in the cat: Spatiotemporal coupling and asymmetry. Vision Research 24: 549–564.

    Google Scholar 

  • Dean AF, Tolhurst DJ (1986) Factors influencing the temporal phase of response to bar and grating stimuli for simple cells in the cat striate cortex. Exp. Brain Res. 62: 143–151.

    Google Scholar 

  • Dean AF, Tolhurst DJ, Walker NS (1982) Non-linear temporal summation by simple cells in cat striate cortex demonstrated by failure of superposition. Exp. Brain Res. 45: 456–458.

    Google Scholar 

  • DeAngelis GC, Robson JG, Ohzawa I, Freeman RD (1992) Organization of suppression in receptive fields of neurons in cat visual cortex. J. Neurophysiol. 68: 144–163.

    Google Scholar 

  • DeAngelis GC, Ohzawa I, Freeman RD (1993) Spatiotemporal organization of simple-cell receptive fields in the cat's striate cortex. I. General characteristics and postnatal development. J. Neurophysiol. 69: 1091–1117.

    Google Scholar 

  • DeAngelis GC, Freeman RD, Ohzawa I (1994) Length and width tuning of neurons in the cat's primary visual cortex. J. Neurophysiol. 71: 347–374.

    Google Scholar 

  • DeAngelis GC, Ohzawa I, Freeman RD (1995) Receptive-field dynamics in the central visual pathways. Trends Neurosci. 18: 451–45

    Google Scholar 

  • De Valois RL, Cottaris NP (1998) Inputs to directionally selectivity simple cells in macaque striate cortex. Proceedings of the National Academy of Sciences (USA) 95: 14488–14493

    Google Scholar 

  • De Valois KK, Tootell RBH (1983) Spatial-frequency-specific inhi bition in cat striate cortex cells. J. Physiol. 336: 359–376.

    Google Scholar 

  • De Valois RL, Albrecht DG, Thorell LG (1982) Spatial frequency selectivity of cells in macaque visual cortex. Vision Research 22: 545–559.

    Google Scholar 

  • De Valois RL, Thorell LG, Albrecht DG(1985) Periodicity of striate-cortex-cell receptive fields. Journal of the Optical Society of America A 2: 1115–1123.

    Google Scholar 

  • De Valois RL, Cottaris NP, Mahon LE, Elfar SD, Wilson JA (2000) Spatial and temporal receptive fields of geniculate and cortical cells and directional selectivity. Vision Research 40: 3685–3702.

    Google Scholar 

  • Dobbins A, Zucker SW, Cynader MS (1989) End-stopping and curvature. Vision Research 29: 1371–1387.

    Google Scholar 

  • Douglas RJ, Martin KAC, Whitteridge D (1988) Selective responses of visual cortical cells do not depend on shunting inhibition. Nature 332: 642–644.

    Google Scholar 

  • Duysens J (1987) Is direction selectivity of cat area 17 cells always independent of contrast and dependent on short-distance interactions? Exp. Brain Res. 67: 663–666

    Google Scholar 

  • Duysens J, Gulyís B, Maes H (1991) Temporal integration in cat visual cortex: A test of Bloch's law. Vision Research 31: 1517–1528.

    Google Scholar 

  • Emerson RC (1988) A linear model for symmetric receptive fields: Implications for classification tests with flashed and moving images. Spatial Vision 3: 159–177.

    Google Scholar 

  • Emerson RC (1997) Quadrature subunits in directionally selective simple cells: Spatiotemporal interactions. Visual Neurosci. 14: 357–371.

    Google Scholar 

  • Emerson RC, Coleman L (1981) Does image movement have a special nature for neurons in the cat's striate cortex? Investigative Ophthalmology and Visual Science 20: 766–783.

    Google Scholar 

  • Emerson RC, Gerstein GL (1977) Simple striate neurons in the cat. II. Mechanisms underlying directional asymmetry and directional selectivity. J. Neurophysiol. 40: 136–155.

    Google Scholar 

  • Emerson RC, Huang MC (1997) Quadrature subunits in directionally selective simple cells: Counterphase and drifting grating responses. Visual Neurosci. 14: 373–385.

    Google Scholar 

  • Enroth-Cugell C, Robson JG, Schweitzer-Tong DE, Watson AB (1983) Spatiotemporal interactions in cat retinal ganglion cells showing linear spatial summation. J. Physiol. 341: 279–307.

    Google Scholar 

  • Ferster D (1986) Orientation selectivity of synaptic potentials in cat primary visual cortex. J. Neurosci. 6: 1284–1301.

    Google Scholar 

  • Ferster D, Jagadeesh B (1991) Nonlinearity of spatial summation in simple cells of areas 17 and 18 of cat visual cortex. J. Neurophysiol. 66: 1667–1679.

    Google Scholar 

  • Ferster D, Jagadeesh B (1992) EPSP-IPSP interactions in cat visual cortex studied with in vivo whole-cell patch recording. J. Neurosci. 12: 1262–1274.

    Google Scholar 

  • Foster KH, Gaska JP, Nagler M, Pollen DA (1985) Spatial and temporal frequency selectivity of neurones in visual cortical areas V1 and V2 of the macaque monkey. J. Physiol. 365: 331–363.

    Google Scholar 

  • Ganz L, Felder R (1984) Mechanism of directional selectivity in simple neurons of the cat's visual cortex analyzed with stationary flash sequences. J. Neurophysiol. 51: 294–324.

    Google Scholar 

  • García-Pérez MA (1999a) Complex cells as linear mechanisms receiving sequential afferents. Neuro Report 10: 3815–3819.

    Google Scholar 

  • García-Pérez MA (1999b) Direction selectivity and spatiotemporal separability in simple cortical cells. J. Comput. Neurosci. 7: 173–189.

    Google Scholar 

  • García-Pérez MA, Peli E (2001) Intrasaccadic perception. J. Neurosci. 21: 7313–7322.

    Google Scholar 

  • Goodwin AW, Henry GH, Bishop PO (1975) Direction selectivity of simple striate cells: Properties and mechanisms. J. Neurophysiol. 38: 1500–1523.

    Google Scholar 

  • Gradshteyn IS, Ryzhik IM (1994) Table of integrals, series, and products (5th ed.). Academic Press, San Diego, CA.

    Google Scholar 

  • Gray CM, McCormick DA (1996) Chattering cells: Superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science 274: 109–113.

    Google Scholar 

  • Hamada T, Yamashima M, Kato K (1997) A ring model for spatiotemporal properties of simple cells in the visual cortex. Biol. Cyber. 77: 225–233.

    Google Scholar 

  • Hawken MJ, Parker AJ (1987) Spatial properties of neurons in the monkey striate cortex. Proceedings of the Royal Society of London B 231: 251–288.

    Google Scholar 

  • Heeger DJ (1991) Nonlinear model of neural responses in cat visual cortex. In: MS Landy, JA Movshon, eds. Computational Models of Visual Processing. MIT Press, Cambridge, MA. pp. 119–133.

    Google Scholar 

  • Heeger DJ (1992a) Normalization of cell responses in cat striate cortex. Visual Neurosci. 9: 181–197.

    Google Scholar 

  • Heeger DJ (1992b) Half-squaring in responses of cat striate cells. Visual Neurosci. 9: 427–443.

    Google Scholar 

  • Heeger DJ (1993) Modeling simple-cell direction selectivity with normalized, half-squared, linear operators. J. Neurophysiol. 70: 1885–1898.

    Google Scholar 

  • Heggelund P, Krekling S, Skottun BC (1984) Spatial summation in subregions of simple-cell receptive fields in cat striate cortex as a function of slit length. J. Physiol. 352: 327–337.

    Google Scholar 

  • Henry GH, Bishop PO (1972) Striate neurons: Receptive field organization. Investigative Ophthalmology 11: 357–368.

    Google Scholar 

  • Holub RA, Morton-Gibson M(1981) Response of visual cortical neurons of the cat to moving sinusoidal gratings: Response-contrast functions and spatiotemporal interactions. J. Neurophysiol. 46: 1244–1259.

    Google Scholar 

  • Hubel DH, Wiesel TN (1962) Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. J. Physiol. 160: 106–154.

    Google Scholar 

  • Hubel DH, Wiesel TN (1965) Receptive fields and functional architecture in two non-striate visual areas (18 and 19) of the cat. J. Neurophysiol. 28: 229–289.

    Google Scholar 

  • Hubel DH, Wiesel TN (1968) Receptive fields and functional architecture of monkey striate cortex. J. Physiol. 195: 215–243.

    Google Scholar 

  • Ikeda H, Wright MJ (1975) Spatial and temporal properties of 'sustained' and 'transient' neurones in area 17 of the cat's visual cortex. Exp. Brain Res. 22: 363–383.

    Google Scholar 

  • Jacobson LD, Gaska JP, Chen H-W, Pollen DA (1993) Structural testing of multi-input linear-nonlinear cascade models for cells in macaque striate cortex. Vision Research 33: 609–626.

    Google Scholar 

  • Jagadeesh B, Wheat HS, Ferster D (1993) Linearity of summation of synaptic potentials underlying direction selectivity in simple cells of the cat visual cortex. Science 262: 1901–1904.

    Google Scholar 

  • Jagadeesh B, Wheat HS, Kontsevich LL, Tyler CW, Ferster D (1997) Direction selectivity of synaptic potentials in simple cells of the cat visual cortex. J. Neurophysiol. 78: 2772–2789.

    Google Scholar 

  • Jones HE, Grieve KL, Wang W, Sillito AM (2001) Surround suppression in primate V1. J. Neurophysiol. 86: 2011–2028.

    Google Scholar 

  • Jones JP, Stepnoski A, Palmer LA (1987) The two-dimensional spectral structure of simple receptive fields in cat striate cortex. J. Neurophysiol. 58: 1212–1232.

    Google Scholar 

  • Kagan I, Gur M, Snodderly DM (2002) Spatial organization of receptive fields of V1 neurons of alert monkeys: Comparison with responses to gratings. J. Neurophysiol. 88: 2557–2574.

    Google Scholar 

  • Kapadia MK, Westheimer G, Gilbert CD (1999) Dynamics of spatial summation in primary visual cortex of alert monkeys. Proceedings of the National Academy of Sciences (USA) 96: 12073–12078.

    Google Scholar 

  • Kato H, Bishop PO, Orban GA (1978) Hypercomplex and simple/ complex cell classifications in cat striate cortex. J. Neurophysiol. 41: 1071–1095.

    Google Scholar 

  • Kayser A, Priebe NJ, Miller KD (2001) Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning. J. Neurophysiol. 85: 2130–2149.

    Google Scholar 

  • Knight BW (1972) Dynamics of enconding in a population of neurons. J. Gen. Physiol. 59: 734–76

    Google Scholar 

  • Kulikowski JJ, Bishop PO, Kato H (1981) Spatial arrangements of responses by cells in the cat visual cortex to light and dark bars and edges. Exp. Brain Res. 44: 371–385.

    Google Scholar 

  • Lauritzen TZ, Krukowski AE, Miller KD (2001) Local correlation-based circuitry can account for responses to multi-grating stimuli in a model of cat V1. J. Neurophysiol. 86: 1803–1815.

    Google Scholar 

  • Levitt JB, Sanchez RM, Smith III EL, Movshon JA (1990) Spatiotemporal interactions and the spatial phase preferences of visual neurons. Exp. Brain Res. 80: 441–445.

    Google Scholar 

  • Li CY, Li W (1994) Extensive integration field beyond the classical receptive field of cat's striate cortical neurons-Classification and tuning properties. Vision Research 34: 2337–2355.

    Google Scholar 

  • (1973) The visual cortex as a spatial frequency analyser. Vision Research 13: 1255–1267.

  • Maske R, Yamane S, Bishop PO (1985) Simple and B-cells in cat striate cortex. Complementarity of responses to moving light and dark bars. J. Neurophysiol. 53: 670–685.

    Google Scholar 

  • McLean J, Palmer LA (1989) Contribution of linear spatiotemporal receptive field structure to velocity selectivity of simple cells in area 17 of cat. Vision Research 29: 675–679.

    Google Scholar 

  • McLean J, Raab S, Palmer LA (1994) Contribution of linear mechanisms to the specification of local motion by simple cells in areas 17 and 18 of the cat. Visual Neurosci. 11: 271–294.

    Google Scholar 

  • Mechler F, Ringach DL (2002) On the classification of simple and complex cells. Vision Research 42: 1017–1033.

    Google Scholar 

  • Morrone MC, Burr DC, Maffei L (1982) Functional implications of cross-orientation inhibition of cortical visual cells. I. Neurophysiological evidence. Proceedings of the Royal Society of London B 216: 335–354.

    Google Scholar 

  • Movshon JA, Thompson ID, Tolhurst DJ (1978) Spatial summation in the receptive fields of simple cells in the cat's striate cortex. J. Physiol. 283: 53–77.

    Google Scholar 

  • Mullikin WH, Jones JP, Palmer LA (1984) Receptive-field properties and laminar distribution of X-like and Y-like simple cells in cat area 17. J. Neurophysiol. 52: 350–371.

    Google Scholar 

  • Murthy A, Humphrey AL, Saul AB, Feidler JC (1998) Laminar differences in the spatiotemporal structure of simple cell receptive fields in cat area 17. Visual Neurosci. 15: 239–256.

    Google Scholar 

  • Nestares O, Heeger DJ (1997) Modeling the apparent frequency-specific suppression in simple cell responses. Vision Research 37: 1535–1543.

    Google Scholar 

  • Orban GA (1991) Quantitative electrophysiology of visual cortical neurones. In: AG Leventhal, ed. Vision and Visual. Dysfunction. Vol. 4. The Neural Basis of Visual Function. MacMillan, Basingstoke, UK. pp. 173–222.

    Google Scholar 

  • Orban GA, Kennedy H, Maes H (1981) Response to movement of neurons in areas 17 and 18 of the cat: Direction selectivity. J. Neurophysiol. 45: 1059–1073.

    Google Scholar 

  • Palmer LA, Davis TL (1981a) Receptive-field structure in cat striate cortex. J. Neurophysiol. 46: 260–276.

    Google Scholar 

  • Palmer LA, Davis TL (1981b) Comparison of responses to moving and stationary stimuli in cat striate cortex. J. Neurophysiol. 46: 277–295.

    Google Scholar 

  • Palmer LA, Gottschalk A, Jones JP (1987) Constraints on the estimation of spatial receptive field profiles of simple cells in visual cortex. In: VZ Marmarelis, ed. Advanced Methods of Physiological System Modelling. Biomedical Simulation Resources, Los Angeles, CA. pp. 205–216.

    Google Scholar 

  • Palmer LA, Jones JP, Stepnoski RA (1991) Striate receptive fields as linear filters: Characterization in two dimensions of space. In: AG Leventhal, ed. Vision and Visual Dysfunction. Vol. 4. The Neural Basis of Visual Function. MacMillan, Basingstoke, UK. pp. 246–265.

    Google Scholar 

  • Peli E, García-Pérez MA (2003) Motion perception under involuntary eye vibration. Exp. Brain Res. 149: 431–438.

    Google Scholar 

  • Petrov AP, Pigarev IN, Zenkin GM (1980) Some evidence against Fourier analysis as a function of the receptive fields in cat's striate cortex. Vision Research 20: 1023–1025.

    Google Scholar 

  • (1997) Response variability and timing precision of neuronal spike trains in vivo. J. Neurophysiol. 77: 2836–2841.

  • Reid RC, Soodak RE, Shapley RM (1987) Linear mechanisms of directional selectivity in simple cells of cat striate cortex. Proceedings of the National Academy of Sciences (USA) 84: 8740–8744.

    Google Scholar 

  • Reid RC, Soodak RE, Shapley RM(1991) Directional selectivity and spatiotemporal structure of receptive fields of simple cells in cat striate cortex. J. Neurophysiol. 66: 505–529.

    Google Scholar 

  • Reid RC, Victor JD, Shapley RM(1992) Broadband temporal stimuli decrease the integration time of neurons in cat striate cortex. Visual Neurosci. 9: 39-45.

    Google Scholar 

  • Rodieck RW(1965) Quantitative analysis of cat retinal ganglion cell response to visual stimuli. Vision Research 5: 583–601.

    Google Scholar 

  • Saul AB, Humphrey AL (1992a) Evidence of input from lagged cells in the lateral geniculate nucleus to simple cells in cortical area 17 of the cat. J. Neurophysiol. 68: 1190–1208.

    Google Scholar 

  • Saul AB, Humphrey AL (1992b) Temporal-frequency tuning of direction selectivity in cat visual cortex. Visual Neurosci. 8: 365–372.

    Google Scholar 

  • Sceniak MP, Ringach D, Hawken MJ, Shapley R (1999) Contrast's effect on spatial summation by macaque V1 neurons. Nature Neurosci. 2: 733–739.

    Google Scholar 

  • Sceniak MP, Hawken MJ, Shapley R (2002) Contrast-dependent changes in spatial frequency tuning of macaque V1 neurons: Effects of a changing receptive field size. J. Neurophysiol. 88: 1363–1373.

    Google Scholar 

  • Schumer R, Movshon JA (1984) A spatiotemporal model of simple cell responses (Abstract). Investigative Ophthalmology and Visual Science 25: 32.

    Google Scholar 

  • Sengpiel F, Sen A, Blakemore C (1997) Characteristics of surround inhibition in cat area 17. Exp. Brain Res. 116: 216–228.

    Google Scholar 

  • Sengpiel F, Baddeley RJ, Freeman TCB, Harrad R, Blakemore C (1998) Different mechanisms underlie three inhibitory phenomena in cat area 17. Vision Research 38: 2067–2080.

    Google Scholar 

  • Skottun BC (1998) A model for end-stopping in the visual cortex. Vision Research 38: 2023–2035.

    Google Scholar 

  • Skottun BC, De Valois RL, Grosof DH, Movshon JA, Albrecht DG, Bonds AB (1991) Classifying simple and complex cells on the basis of response modulation. Vision Research 31: 1079–1086.

    Google Scholar 

  • Soodak RE (1986) Two-dimensional modeling of visual receptive fields using Gaussian subunits. Proceedings of the National Academy of Sciences (USA) 83: 9259–9263.

    Google Scholar 

  • Soodak RE, Shapley RM, Kaplan E (1991) Fine structure of receptive-field centers of X and Y cells of the cat. Visual Neurosci. 6: 621–628.

    Google Scholar 

  • Spitzer H, Hochstein S (1985) Simple-and complex-cell response dependences on stimulation parameters. J. Neurophysiol. 53: 1244–1265.

    Google Scholar 

  • Sun M, Bonds AB (1994) Two-dimensional receptive-field organization in striate cortical neurons of the cat. Visual Neurosci. 11: 703–720.

    Google Scholar 

  • Tatian B (1965) Method for obtaining the transfer function from the edge response function. Journal of the Optical Society of America 55: 1014–1019.

    Google Scholar 

  • Tolhurst DJ, Dean AF (1987) Spatial summation by simple cells in the striate cortex of the cat. Exp. Brain Res. 66: 607–620.

    Google Scholar 

  • Tolhurst DJ, Dean AF (1990) The effects of contrast on the linearity of spatial summation of simple cells in the cat's striate cortex. Exp. Brain Res. 79: 582–588.

    Google Scholar 

  • Tolhurst DJ, Dean AF (1991) Evaluation of a linear model of directional selectivity in simple cells of the cat's striate cortex. Visual Neurosci. 6: 421–428.

    Google Scholar 

  • Tolhurst DJ, Heeger DJ (1997a) Contrast normalization and a linear model for the directional selectivity of simple cells in cat striate cortex. Visual Neurosci. 14: 19-25.

    Google Scholar 

  • Tolhurst DJ, Heeger DJ (1997b) Comparison of contrast-normalization and threshold models of the responses of simple cells in cat striate cortex. Visual Neurosci. 14: 293–309.

    Google Scholar 

  • Tolhurst DJ, Walker NS, Thompson ID, Dean AF (1980) Nonlinearities of temporal summation in neurones in area 17 of the cat. Exp. Brain Res. 38: 431–435.

    Google Scholar 

  • Tolhurst DJ, Movshon JA, Thompson ID (1981) The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast. Exp. Brain Res. 41: 414–419.

    Google Scholar 

  • Walker GA, Ohzawa I, Freeman RD (1999) Asymmetric suppression outside the classical receptive field of the visual cortex. J. Neurosci. 19: 10536–10553.

    Google Scholar 

  • Walker GA, Ohzawa I, Freeman RD (2000) Suppression outside the classical cortical receptive field. Visual Neurosci. 17: 369–379.

    Google Scholar 

  • Walker GA, Ohzawa I, Freeman RD (2002) Disinhibition outside receptive fields in the visual cortex. J. Neurosci. 22: 5659–5668.

    Google Scholar 

  • Watson AB, Ahumada AJ (1985) Model of human visual-motion sensing. Journal of the Optical Society of America A 2: 322–342.

    Google Scholar 

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  1. Departamento de Metodología, Facultad de Psicología, Universidad Complutense, Campus de Somosaguas, 28223, Madrid, Spain

    Miguel A. García-Pérez

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García-Pérez, M.A. A Nonlinear Model of the Behavior of Simple Cells in Visual Cortex. J Comput Neurosci 17, 289–325 (2004). https://doi.org/10.1023/B:JCNS.0000044874.24421.48

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