Abstract

Cope et al. [J. Opt. Soc. Am. A 30, 2401 (2013)] proposed a class of models for lateral geniculate nucleus (LGN) ON-cell behavior consisting of a linear response with divisive normalization by local stimulus contrast. Here, we analyze a specific model with the linear response defined by a difference-of-Gaussians filter, and a circular Gaussian for the gain pool weighting function. For sinusoidal grating stimuli, the parameter region for bandpass behavior of the linear response is determined, and the gain control response is shown to act as a switch (changing from “off” to “on” with increasing spatial frequency). It is also shown that large gain pools stabilize the optimal spatial frequency of the total nonlinear response at a fixed value independent of contrast and stimulus magnitude. Under- and super-saturation, as well as contrast saturation, occur as typical effects of stimulus magnitude. For circular spot stimuli, it is shown that large gain pools stabilize the spot size that yields the maximum response.

© 2014 Optical Society of America

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  1. D. Cope, B. Blakeslee, and M. E. McCourt, “Modeling lateral geniculate nucleus response with contrast gain control. part 1: formulation,” J. Opt. Soc. Am. A 30, 2401–2408 (2013).
    [CrossRef]
  2. J. G. Robson, “Neural images: the physiological basis of spatial vision,” in Visual Coding and Adaptability, C. S. Harris, ed. (Lawrence Erlbaum Associates, 1980), pp. 177–214.
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    [CrossRef]
  4. A. M. Derrington and P. Lennie, “Spatial and temporal contrast sensitivities of neurons in lateral geniculate nucleus of macaque,” J. Physiol. 357, 219–240 (1984).
  5. E. Kaplan, K. Purpura, and R. M. Shapley, “Contrast affects the transmission of visual information through the mammalian lateral geniculate nucleus,” J. Physiol. 391, 267–288 (1987).
  6. T. Shou, X. Li, Y. Zhou, and B. Hu, “Adaptation of visually evoked responses of relay cells in the dorsal lateral geniculate nucleus of the cat following prolonged exposure to drifting gratings,” Vis. Neurosci. 13, 605–613 (1996).
    [CrossRef]
  7. A. Kayser, N. J. Priebe, and K. D. Miller, “Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning,” J. Neurophysiol. 85, 2130–2149 (2001).
  8. V. Bonin, V. Mante, and M. Carandini, “Nonlinear processing in LGN neurons,” in Advances in Neural Information Processing Systems 16, S. Thrun, L. Saul, and B. Schölkopf, eds. (MIT, 2004), pp. 1443–1450.
  9. S. G. Solomon, J. W. Peirce, N. T. Dhruv, and P. Lennie, “Profound contrast adaptation early in the visual pathway,” Neuron 42, 155–162 (2004).
    [CrossRef]
  10. V. Bonin, V. Mante, and M. Carandini, “The suppressive field of neurons in lateral geniculate nucleus,” J. Neurosci. 25, 10844–10856 (2005).
    [CrossRef]
  11. T. Duong and R. D. Freeman, “Spatial frequency-specific contrast adaptation originates in primary visual cortex,” J. Neurophysiol. 98, 187–195 (2007).
    [CrossRef]
  12. V. Mante, V. Bonin, and M. Carandini, “Functional mechanisms shaping lateral geniculate responses to artificial and natural stimuli,” Neuron 58, 625–638 (2008).
    [CrossRef]
  13. D. H. Hubel, “Single unit activity in the lateral geniculate body and optic tract of unrestrained cats,” J. Physiol. 150, 91–104 (1960).
  14. D. H. Hubel and T. N. Wiesel, “Integrative action in the cat’s lateral geniculate body,” J. Physiol. 155, 385–398 (1961).
  15. G. H. Jacobs and R. L. Yolton, “Center-surround balance in receptive fields of cells in the lateral geniculate nucleus,” Vis. Res. 10, 1127–1144 (1970).
    [CrossRef]
  16. R. T. Marrocco, “Maintained activity of monkey optic tract fibers and lateral geniculate nucleus cells,” Vis. Res. 12, 1175–1181 (1972).
    [CrossRef]
  17. J. Papaioannou and A. White, “Maintained activity of lateral geniculate nucleus neurons as a function of background luminance,” Exp. Neurol. 34, 558–566 (1972).
    [CrossRef]
  18. R. T. Marrocco, “Possible neural basis for brightness magnitude estimates,” Brain Res. 86, 128–133 (1975).
    [CrossRef]
  19. R. B. Barlow and R. Verillo, “Brightness sensation in a ganzfeld,” Vis. Res. 16, 1291–1297 (1976).
    [CrossRef]
  20. R. W. Doty, “Tonic retinal influences in primates,” Ann. NY Acad. Sci. 290, 139–151 (1977).
    [CrossRef]
  21. P. D. Spear, D. C. Smith, and L. L. Williams, “Visual receptive-field properties of single neurons in cat’s ventral lateral geniculate nucleus,” J. Neurophysiol. 40, 390–409 (1977).
  22. R. B. Barlow, D. M. Snodderly, and H. A. Swadlow, “Intensity coding in primate visual system,” Exp. Brain Res. 31, 163–177 (1978).
    [CrossRef]
  23. Y. Kayama, R. R. Riso, J. R. Bartlett, and R. W. Doty, “Luxotonic responses of units in macaque striate cortex,” J. Neurophysiol. 42, 1495–1517 (1979).
  24. P. D. Spear, R. J. Moore, C. B. Y. Kim, J.-T. Xue, and N. Tumosa, “Effects of aging on the primate visual system: spatial and temporal processing by lateral geniculate neurons in young adult and old Rhesus monkeys,” J. Neurophysiol. 72, 402–420 (1994).
  25. S. D. Van Hooser, J. Alexander, F. Heimel, and S. B. Nelson, “Receptive field properties and laminar organization of lateral geniculate nucleus in the gray squirrel (Sciurus carolinesis),” J. Neurophysiol. 90, 3398–3418 (2003).
    [CrossRef]
  26. T. R. Tucker and D. Fitzpatrick, “Luminance-evoked inhibition in primary visual cortex: a transient veto of simultaneous and ongoing response,” J. Neurosci. 26, 13537–13547 (2006).
    [CrossRef]
  27. H. J. Alitto, B. D. Moore, D. L. Rathburn, and W. M. Ursey, “A comparison of visual responses in the lateral geniculate nucleus of alert and anaesthetized macaque monkeys,” J. Physiol. 589, 87–99 (2011).
    [CrossRef]
  28. J. W. Pierce, “The potential importance of saturating and supersaturating contrast response functions in visual cortex,” J. Vis. 7(6):1, 1–10 (2007).
    [CrossRef]
  29. D. Cope, B. Blakeslee, and M. E. McCourt, “Analysis of multidimensional difference-of-Gaussians filters in terms of directly observable parameters,” J. Opt. Soc. Am. A 30, 1002–1012 (2013).
    [CrossRef]
  30. L. J. Croner and E. Kaplan, “Receptive fields of P and M ganglion cells across the primate retina,” Vis. Res. 35, 7–24 (1995).
    [CrossRef]
  31. G. Winterer and D. R. Weinberger, “Genes, dopamine and cortical signal-to-noise ratio in schizophrenia,” Trends Neurosci. 27, 683–690 (2004).
    [CrossRef]
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    [CrossRef]

2013 (2)

2012 (1)

M. Carandini and D. J. Heeger, “Normalization as a canonical neural computation,” Nat. Rev. Neurosci. 13, 51–62 (2012).
[CrossRef]

2011 (1)

H. J. Alitto, B. D. Moore, D. L. Rathburn, and W. M. Ursey, “A comparison of visual responses in the lateral geniculate nucleus of alert and anaesthetized macaque monkeys,” J. Physiol. 589, 87–99 (2011).
[CrossRef]

2008 (1)

V. Mante, V. Bonin, and M. Carandini, “Functional mechanisms shaping lateral geniculate responses to artificial and natural stimuli,” Neuron 58, 625–638 (2008).
[CrossRef]

2007 (2)

T. Duong and R. D. Freeman, “Spatial frequency-specific contrast adaptation originates in primary visual cortex,” J. Neurophysiol. 98, 187–195 (2007).
[CrossRef]

J. W. Pierce, “The potential importance of saturating and supersaturating contrast response functions in visual cortex,” J. Vis. 7(6):1, 1–10 (2007).
[CrossRef]

2006 (1)

T. R. Tucker and D. Fitzpatrick, “Luminance-evoked inhibition in primary visual cortex: a transient veto of simultaneous and ongoing response,” J. Neurosci. 26, 13537–13547 (2006).
[CrossRef]

2005 (1)

V. Bonin, V. Mante, and M. Carandini, “The suppressive field of neurons in lateral geniculate nucleus,” J. Neurosci. 25, 10844–10856 (2005).
[CrossRef]

2004 (2)

S. G. Solomon, J. W. Peirce, N. T. Dhruv, and P. Lennie, “Profound contrast adaptation early in the visual pathway,” Neuron 42, 155–162 (2004).
[CrossRef]

G. Winterer and D. R. Weinberger, “Genes, dopamine and cortical signal-to-noise ratio in schizophrenia,” Trends Neurosci. 27, 683–690 (2004).
[CrossRef]

2003 (2)

A. G. Leventhal, Y. Wang, M. Pu, Y. Zhou, and Y. Ma, “GABA and its agonists improved visual cortical function in senescent monkeys,” Science 300, 812–815 (2003).
[CrossRef]

S. D. Van Hooser, J. Alexander, F. Heimel, and S. B. Nelson, “Receptive field properties and laminar organization of lateral geniculate nucleus in the gray squirrel (Sciurus carolinesis),” J. Neurophysiol. 90, 3398–3418 (2003).
[CrossRef]

2001 (1)

A. Kayser, N. J. Priebe, and K. D. Miller, “Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning,” J. Neurophysiol. 85, 2130–2149 (2001).

1996 (1)

T. Shou, X. Li, Y. Zhou, and B. Hu, “Adaptation of visually evoked responses of relay cells in the dorsal lateral geniculate nucleus of the cat following prolonged exposure to drifting gratings,” Vis. Neurosci. 13, 605–613 (1996).
[CrossRef]

1995 (1)

L. J. Croner and E. Kaplan, “Receptive fields of P and M ganglion cells across the primate retina,” Vis. Res. 35, 7–24 (1995).
[CrossRef]

1994 (1)

P. D. Spear, R. J. Moore, C. B. Y. Kim, J.-T. Xue, and N. Tumosa, “Effects of aging on the primate visual system: spatial and temporal processing by lateral geniculate neurons in young adult and old Rhesus monkeys,” J. Neurophysiol. 72, 402–420 (1994).

1987 (1)

E. Kaplan, K. Purpura, and R. M. Shapley, “Contrast affects the transmission of visual information through the mammalian lateral geniculate nucleus,” J. Physiol. 391, 267–288 (1987).

1984 (1)

A. M. Derrington and P. Lennie, “Spatial and temporal contrast sensitivities of neurons in lateral geniculate nucleus of macaque,” J. Physiol. 357, 219–240 (1984).

1979 (1)

Y. Kayama, R. R. Riso, J. R. Bartlett, and R. W. Doty, “Luxotonic responses of units in macaque striate cortex,” J. Neurophysiol. 42, 1495–1517 (1979).

1978 (1)

R. B. Barlow, D. M. Snodderly, and H. A. Swadlow, “Intensity coding in primate visual system,” Exp. Brain Res. 31, 163–177 (1978).
[CrossRef]

1977 (2)

R. W. Doty, “Tonic retinal influences in primates,” Ann. NY Acad. Sci. 290, 139–151 (1977).
[CrossRef]

P. D. Spear, D. C. Smith, and L. L. Williams, “Visual receptive-field properties of single neurons in cat’s ventral lateral geniculate nucleus,” J. Neurophysiol. 40, 390–409 (1977).

1976 (1)

R. B. Barlow and R. Verillo, “Brightness sensation in a ganzfeld,” Vis. Res. 16, 1291–1297 (1976).
[CrossRef]

1975 (1)

R. T. Marrocco, “Possible neural basis for brightness magnitude estimates,” Brain Res. 86, 128–133 (1975).
[CrossRef]

1972 (2)

R. T. Marrocco, “Maintained activity of monkey optic tract fibers and lateral geniculate nucleus cells,” Vis. Res. 12, 1175–1181 (1972).
[CrossRef]

J. Papaioannou and A. White, “Maintained activity of lateral geniculate nucleus neurons as a function of background luminance,” Exp. Neurol. 34, 558–566 (1972).
[CrossRef]

1970 (1)

G. H. Jacobs and R. L. Yolton, “Center-surround balance in receptive fields of cells in the lateral geniculate nucleus,” Vis. Res. 10, 1127–1144 (1970).
[CrossRef]

1961 (1)

D. H. Hubel and T. N. Wiesel, “Integrative action in the cat’s lateral geniculate body,” J. Physiol. 155, 385–398 (1961).

1960 (1)

D. H. Hubel, “Single unit activity in the lateral geniculate body and optic tract of unrestrained cats,” J. Physiol. 150, 91–104 (1960).

Alexander, J.

S. D. Van Hooser, J. Alexander, F. Heimel, and S. B. Nelson, “Receptive field properties and laminar organization of lateral geniculate nucleus in the gray squirrel (Sciurus carolinesis),” J. Neurophysiol. 90, 3398–3418 (2003).
[CrossRef]

Alitto, H. J.

H. J. Alitto, B. D. Moore, D. L. Rathburn, and W. M. Ursey, “A comparison of visual responses in the lateral geniculate nucleus of alert and anaesthetized macaque monkeys,” J. Physiol. 589, 87–99 (2011).
[CrossRef]

Barlow, R. B.

R. B. Barlow, D. M. Snodderly, and H. A. Swadlow, “Intensity coding in primate visual system,” Exp. Brain Res. 31, 163–177 (1978).
[CrossRef]

R. B. Barlow and R. Verillo, “Brightness sensation in a ganzfeld,” Vis. Res. 16, 1291–1297 (1976).
[CrossRef]

Bartlett, J. R.

Y. Kayama, R. R. Riso, J. R. Bartlett, and R. W. Doty, “Luxotonic responses of units in macaque striate cortex,” J. Neurophysiol. 42, 1495–1517 (1979).

Blakeslee, B.

Bonin, V.

V. Mante, V. Bonin, and M. Carandini, “Functional mechanisms shaping lateral geniculate responses to artificial and natural stimuli,” Neuron 58, 625–638 (2008).
[CrossRef]

V. Bonin, V. Mante, and M. Carandini, “The suppressive field of neurons in lateral geniculate nucleus,” J. Neurosci. 25, 10844–10856 (2005).
[CrossRef]

V. Bonin, V. Mante, and M. Carandini, “Nonlinear processing in LGN neurons,” in Advances in Neural Information Processing Systems 16, S. Thrun, L. Saul, and B. Schölkopf, eds. (MIT, 2004), pp. 1443–1450.

Carandini, M.

M. Carandini and D. J. Heeger, “Normalization as a canonical neural computation,” Nat. Rev. Neurosci. 13, 51–62 (2012).
[CrossRef]

V. Mante, V. Bonin, and M. Carandini, “Functional mechanisms shaping lateral geniculate responses to artificial and natural stimuli,” Neuron 58, 625–638 (2008).
[CrossRef]

V. Bonin, V. Mante, and M. Carandini, “The suppressive field of neurons in lateral geniculate nucleus,” J. Neurosci. 25, 10844–10856 (2005).
[CrossRef]

V. Bonin, V. Mante, and M. Carandini, “Nonlinear processing in LGN neurons,” in Advances in Neural Information Processing Systems 16, S. Thrun, L. Saul, and B. Schölkopf, eds. (MIT, 2004), pp. 1443–1450.

Cope, D.

Croner, L. J.

L. J. Croner and E. Kaplan, “Receptive fields of P and M ganglion cells across the primate retina,” Vis. Res. 35, 7–24 (1995).
[CrossRef]

Derrington, A. M.

A. M. Derrington and P. Lennie, “Spatial and temporal contrast sensitivities of neurons in lateral geniculate nucleus of macaque,” J. Physiol. 357, 219–240 (1984).

Dhruv, N. T.

S. G. Solomon, J. W. Peirce, N. T. Dhruv, and P. Lennie, “Profound contrast adaptation early in the visual pathway,” Neuron 42, 155–162 (2004).
[CrossRef]

Doty, R. W.

Y. Kayama, R. R. Riso, J. R. Bartlett, and R. W. Doty, “Luxotonic responses of units in macaque striate cortex,” J. Neurophysiol. 42, 1495–1517 (1979).

R. W. Doty, “Tonic retinal influences in primates,” Ann. NY Acad. Sci. 290, 139–151 (1977).
[CrossRef]

Duong, T.

T. Duong and R. D. Freeman, “Spatial frequency-specific contrast adaptation originates in primary visual cortex,” J. Neurophysiol. 98, 187–195 (2007).
[CrossRef]

Fitzpatrick, D.

T. R. Tucker and D. Fitzpatrick, “Luminance-evoked inhibition in primary visual cortex: a transient veto of simultaneous and ongoing response,” J. Neurosci. 26, 13537–13547 (2006).
[CrossRef]

Freeman, R. D.

T. Duong and R. D. Freeman, “Spatial frequency-specific contrast adaptation originates in primary visual cortex,” J. Neurophysiol. 98, 187–195 (2007).
[CrossRef]

Heeger, D. J.

M. Carandini and D. J. Heeger, “Normalization as a canonical neural computation,” Nat. Rev. Neurosci. 13, 51–62 (2012).
[CrossRef]

Heimel, F.

S. D. Van Hooser, J. Alexander, F. Heimel, and S. B. Nelson, “Receptive field properties and laminar organization of lateral geniculate nucleus in the gray squirrel (Sciurus carolinesis),” J. Neurophysiol. 90, 3398–3418 (2003).
[CrossRef]

Hu, B.

T. Shou, X. Li, Y. Zhou, and B. Hu, “Adaptation of visually evoked responses of relay cells in the dorsal lateral geniculate nucleus of the cat following prolonged exposure to drifting gratings,” Vis. Neurosci. 13, 605–613 (1996).
[CrossRef]

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, “Integrative action in the cat’s lateral geniculate body,” J. Physiol. 155, 385–398 (1961).

D. H. Hubel, “Single unit activity in the lateral geniculate body and optic tract of unrestrained cats,” J. Physiol. 150, 91–104 (1960).

Jacobs, G. H.

G. H. Jacobs and R. L. Yolton, “Center-surround balance in receptive fields of cells in the lateral geniculate nucleus,” Vis. Res. 10, 1127–1144 (1970).
[CrossRef]

Kaplan, E.

L. J. Croner and E. Kaplan, “Receptive fields of P and M ganglion cells across the primate retina,” Vis. Res. 35, 7–24 (1995).
[CrossRef]

E. Kaplan, K. Purpura, and R. M. Shapley, “Contrast affects the transmission of visual information through the mammalian lateral geniculate nucleus,” J. Physiol. 391, 267–288 (1987).

Kayama, Y.

Y. Kayama, R. R. Riso, J. R. Bartlett, and R. W. Doty, “Luxotonic responses of units in macaque striate cortex,” J. Neurophysiol. 42, 1495–1517 (1979).

Kayser, A.

A. Kayser, N. J. Priebe, and K. D. Miller, “Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning,” J. Neurophysiol. 85, 2130–2149 (2001).

Kim, C. B. Y.

P. D. Spear, R. J. Moore, C. B. Y. Kim, J.-T. Xue, and N. Tumosa, “Effects of aging on the primate visual system: spatial and temporal processing by lateral geniculate neurons in young adult and old Rhesus monkeys,” J. Neurophysiol. 72, 402–420 (1994).

Lennie, P.

S. G. Solomon, J. W. Peirce, N. T. Dhruv, and P. Lennie, “Profound contrast adaptation early in the visual pathway,” Neuron 42, 155–162 (2004).
[CrossRef]

A. M. Derrington and P. Lennie, “Spatial and temporal contrast sensitivities of neurons in lateral geniculate nucleus of macaque,” J. Physiol. 357, 219–240 (1984).

Leventhal, A. G.

A. G. Leventhal, Y. Wang, M. Pu, Y. Zhou, and Y. Ma, “GABA and its agonists improved visual cortical function in senescent monkeys,” Science 300, 812–815 (2003).
[CrossRef]

Li, X.

T. Shou, X. Li, Y. Zhou, and B. Hu, “Adaptation of visually evoked responses of relay cells in the dorsal lateral geniculate nucleus of the cat following prolonged exposure to drifting gratings,” Vis. Neurosci. 13, 605–613 (1996).
[CrossRef]

Ma, Y.

A. G. Leventhal, Y. Wang, M. Pu, Y. Zhou, and Y. Ma, “GABA and its agonists improved visual cortical function in senescent monkeys,” Science 300, 812–815 (2003).
[CrossRef]

Mante, V.

V. Mante, V. Bonin, and M. Carandini, “Functional mechanisms shaping lateral geniculate responses to artificial and natural stimuli,” Neuron 58, 625–638 (2008).
[CrossRef]

V. Bonin, V. Mante, and M. Carandini, “The suppressive field of neurons in lateral geniculate nucleus,” J. Neurosci. 25, 10844–10856 (2005).
[CrossRef]

V. Bonin, V. Mante, and M. Carandini, “Nonlinear processing in LGN neurons,” in Advances in Neural Information Processing Systems 16, S. Thrun, L. Saul, and B. Schölkopf, eds. (MIT, 2004), pp. 1443–1450.

Marrocco, R. T.

R. T. Marrocco, “Possible neural basis for brightness magnitude estimates,” Brain Res. 86, 128–133 (1975).
[CrossRef]

R. T. Marrocco, “Maintained activity of monkey optic tract fibers and lateral geniculate nucleus cells,” Vis. Res. 12, 1175–1181 (1972).
[CrossRef]

McCourt, M. E.

Miller, K. D.

A. Kayser, N. J. Priebe, and K. D. Miller, “Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning,” J. Neurophysiol. 85, 2130–2149 (2001).

Moore, B. D.

H. J. Alitto, B. D. Moore, D. L. Rathburn, and W. M. Ursey, “A comparison of visual responses in the lateral geniculate nucleus of alert and anaesthetized macaque monkeys,” J. Physiol. 589, 87–99 (2011).
[CrossRef]

Moore, R. J.

P. D. Spear, R. J. Moore, C. B. Y. Kim, J.-T. Xue, and N. Tumosa, “Effects of aging on the primate visual system: spatial and temporal processing by lateral geniculate neurons in young adult and old Rhesus monkeys,” J. Neurophysiol. 72, 402–420 (1994).

Nelson, S. B.

S. D. Van Hooser, J. Alexander, F. Heimel, and S. B. Nelson, “Receptive field properties and laminar organization of lateral geniculate nucleus in the gray squirrel (Sciurus carolinesis),” J. Neurophysiol. 90, 3398–3418 (2003).
[CrossRef]

Papaioannou, J.

J. Papaioannou and A. White, “Maintained activity of lateral geniculate nucleus neurons as a function of background luminance,” Exp. Neurol. 34, 558–566 (1972).
[CrossRef]

Peirce, J. W.

S. G. Solomon, J. W. Peirce, N. T. Dhruv, and P. Lennie, “Profound contrast adaptation early in the visual pathway,” Neuron 42, 155–162 (2004).
[CrossRef]

Pierce, J. W.

J. W. Pierce, “The potential importance of saturating and supersaturating contrast response functions in visual cortex,” J. Vis. 7(6):1, 1–10 (2007).
[CrossRef]

Priebe, N. J.

A. Kayser, N. J. Priebe, and K. D. Miller, “Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning,” J. Neurophysiol. 85, 2130–2149 (2001).

Pu, M.

A. G. Leventhal, Y. Wang, M. Pu, Y. Zhou, and Y. Ma, “GABA and its agonists improved visual cortical function in senescent monkeys,” Science 300, 812–815 (2003).
[CrossRef]

Purpura, K.

E. Kaplan, K. Purpura, and R. M. Shapley, “Contrast affects the transmission of visual information through the mammalian lateral geniculate nucleus,” J. Physiol. 391, 267–288 (1987).

Rathburn, D. L.

H. J. Alitto, B. D. Moore, D. L. Rathburn, and W. M. Ursey, “A comparison of visual responses in the lateral geniculate nucleus of alert and anaesthetized macaque monkeys,” J. Physiol. 589, 87–99 (2011).
[CrossRef]

Riso, R. R.

Y. Kayama, R. R. Riso, J. R. Bartlett, and R. W. Doty, “Luxotonic responses of units in macaque striate cortex,” J. Neurophysiol. 42, 1495–1517 (1979).

Robson, J. G.

J. G. Robson, “Neural images: the physiological basis of spatial vision,” in Visual Coding and Adaptability, C. S. Harris, ed. (Lawrence Erlbaum Associates, 1980), pp. 177–214.

Shapley, R. M.

E. Kaplan, K. Purpura, and R. M. Shapley, “Contrast affects the transmission of visual information through the mammalian lateral geniculate nucleus,” J. Physiol. 391, 267–288 (1987).

Shou, T.

T. Shou, X. Li, Y. Zhou, and B. Hu, “Adaptation of visually evoked responses of relay cells in the dorsal lateral geniculate nucleus of the cat following prolonged exposure to drifting gratings,” Vis. Neurosci. 13, 605–613 (1996).
[CrossRef]

Smith, D. C.

P. D. Spear, D. C. Smith, and L. L. Williams, “Visual receptive-field properties of single neurons in cat’s ventral lateral geniculate nucleus,” J. Neurophysiol. 40, 390–409 (1977).

Snodderly, D. M.

R. B. Barlow, D. M. Snodderly, and H. A. Swadlow, “Intensity coding in primate visual system,” Exp. Brain Res. 31, 163–177 (1978).
[CrossRef]

Solomon, S. G.

S. G. Solomon, J. W. Peirce, N. T. Dhruv, and P. Lennie, “Profound contrast adaptation early in the visual pathway,” Neuron 42, 155–162 (2004).
[CrossRef]

Spear, P. D.

P. D. Spear, R. J. Moore, C. B. Y. Kim, J.-T. Xue, and N. Tumosa, “Effects of aging on the primate visual system: spatial and temporal processing by lateral geniculate neurons in young adult and old Rhesus monkeys,” J. Neurophysiol. 72, 402–420 (1994).

P. D. Spear, D. C. Smith, and L. L. Williams, “Visual receptive-field properties of single neurons in cat’s ventral lateral geniculate nucleus,” J. Neurophysiol. 40, 390–409 (1977).

Swadlow, H. A.

R. B. Barlow, D. M. Snodderly, and H. A. Swadlow, “Intensity coding in primate visual system,” Exp. Brain Res. 31, 163–177 (1978).
[CrossRef]

Tucker, T. R.

T. R. Tucker and D. Fitzpatrick, “Luminance-evoked inhibition in primary visual cortex: a transient veto of simultaneous and ongoing response,” J. Neurosci. 26, 13537–13547 (2006).
[CrossRef]

Tumosa, N.

P. D. Spear, R. J. Moore, C. B. Y. Kim, J.-T. Xue, and N. Tumosa, “Effects of aging on the primate visual system: spatial and temporal processing by lateral geniculate neurons in young adult and old Rhesus monkeys,” J. Neurophysiol. 72, 402–420 (1994).

Ursey, W. M.

H. J. Alitto, B. D. Moore, D. L. Rathburn, and W. M. Ursey, “A comparison of visual responses in the lateral geniculate nucleus of alert and anaesthetized macaque monkeys,” J. Physiol. 589, 87–99 (2011).
[CrossRef]

Van Hooser, S. D.

S. D. Van Hooser, J. Alexander, F. Heimel, and S. B. Nelson, “Receptive field properties and laminar organization of lateral geniculate nucleus in the gray squirrel (Sciurus carolinesis),” J. Neurophysiol. 90, 3398–3418 (2003).
[CrossRef]

Verillo, R.

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Figures (15)

Fig. 1.
Fig. 1.

Cross sections of linear field functions R(x1,0) versus x1/ρ0 and gain control function 10G(x1,0) versus x1/ρ0, where ρ0 is the LGN excitatory center radius (Section 3), and the gain control has been scaled by 10 to better reveal its shape over the plot interval. Parameter values: (1) σC2=0.1292ρ02, σS2=4.651ρ02, βCS=0.836 (strong band-pass); (2) σC2=0.1130ρ02, σS2=4.070ρ02, βCS=0.488 (moderate band-pass); (3) σC2=0.0798ρ02, σS2=2.873ρ02, βCS=0.081 (weak band-pass); (4) σC2=0.0646ρ02, σS2=2.326ρ02, βCS=0.019 (low-pass); and σG2=9.0ρ02 (gain control). The maximum for each curve is (1/σC2βCS/σS2)/2π.

Fig. 2.
Fig. 2.

Parameter space, Region AB, for new parameters αC2, αS2 with sample βCS-contours. The boundary is given by Curves A and B corresponding to βCS=1. Region AB is partitioned by the βCS-contours; that is, each point of the region lies on one and only one contour for 0<βCS<1. Notice that maximum αC2 on each βCS-contour occurs at αS2=0.5, which allows the range of αC2 associated with a given βCS value to be determined from the plot. The indicated points (1)–(4) correspond to the parameter pairs in Fig. 1.

Fig. 3.
Fig. 3.

Sinusoidal grating linear field response maximum (R[P]/νG)max versus normalized spatial frequency log10(πρ0sP) for the parameter pairs of Fig. 1, using SNR=4 and maximum grating contrast, cP=1. The figure illustrates (1) strong, (2) moderate, (3) weak bandpass behavior and, finally, (4) low-pass behavior. For case (1), the optimal frequency πρ0sLIN=0.614 is marked by a vertical dashed line.

Fig. 4.
Fig. 4.

Sinusoidal grating linear field response maximum (R[P]/νG)max versus normalized spatial frequency log10(πρ0sP) for the strong bandpass case of Fig. 1 and levels SNR=1 (short dashing), SNR=2 (medium dashing), SNR=4 (long dashing), SNR=8 (solid), at maximum grating contrast, cP=1. The linear response is scaled by the SNR value; in particular, there is no change in the optimal frequency (vertical dashed line) as SNR varies. The low-frequency and high-frequency limits are evident and illustrate that the low-frequency limit is twice the high-frequency limit for cP=1.

Fig. 5.
Fig. 5.

Region AB of Fig. 2 with optimal linear spatial frequency contours shown (pink lines) for πρ0sLIN=0.9,0.8,0.7,0.6,0.5 and the boundary contour πρ0sLIN=0.0 (Curve C). Region AC (bounded by Curves A and C) corresponds to linear field responses with no optimal spatial frequency (low-pass filter region). Region ABC (bounded by Curves A, B, and C) corresponds to linear field responses with a unique optimal spatial frequency sLIN (bandpass filter region). The limit πρ0sLIN=1 corresponds to the corner point (αC2,αS2)=(0.5,0.5).

Fig. 6.
Fig. 6.

Sinusoidal grating gain control response minimum (G[P]/νG)min versus normalized spatial frequency log10(πρ0sP) for gain control parameters αG2=1 (thin lines), αG2=4 (medium lines), and αG2=9 (thick lines). Each gain control response is shown for contrast cP=1 and SNR=1,2,4,8, matching Fig. 4. The gain control response turns from “off” at low frequencies to “on” at higher frequencies, with nominal “on” values πρ0sGAIN=1.15,0.575,0.383 shown as vertical lines of corresponding thickness. The plateau level is proportional to SNR, but is essentially independent of αG2, which determines where the plateau begins.

Fig. 7.
Fig. 7.

Sinusoidal grating total response maximum (LGN[P]/νLGN)max versus normalized spatial frequency log10(πρ0sP) for the four linear responses of Fig. 4 (strong bandpass), combined with the three gain control responses of Fig. 6. “On” values πρ0sGAIN=1.15,0.575,0.383 are shown as vertical lines of corresponding thickness. For αG2=1 (thin lines), gain control is ineffective at the linear optimal spatial frequency sLIN, and the resulting nonlinear optimal spatial frequency sLGN varies with SNR. For αG2=9 (thick lines), gain control is fully effective at the linear optimal frequency sLIN, and the nonlinear optimal frequency sLGN remains stable as SNR varies [πρ0sLGN=πρ0sLIN=0.614 (vertical dashed line)].

Fig. 8.
Fig. 8.

Sinusoidal grating total response maximum (LGN[P]/νLGN)max versus normalized spatial frequency log10(πρ0sP) for the four linear responses of Fig. 4 [strong bandpass case of Fig. 1 at levels SNR=1 (short dashing), SNR=2 (medium dashing), SNR=4 (long dashing), SNR=8 (solid), and the saturated response SNR= (solid)], combined with increasingly effective gain control levels [gain parameter αG2=9 (thin), αG2=16 (medium), and αG2=25 (thick)]. In all cases, gain control is fully effective at the linear optimal spatial frequency sLIN, and the nonlinear optimal spatial frequency sLGN remains stable as SNR varies [πρ0sLGN=πρ0sLIN=0.614 (vertical dashed line)].

Fig. 9.
Fig. 9.

Sinusoidal grating total response maximum (LGN[P]/νLGN)max versus contrast cP for the strong bandpass case of Fig. 1, with spatial frequency at the optimal value (πρ0sLGN=πρ0sLIN=0.614) and gain parameter αG2=9. The curves correspond to SNR=1,2,4,8 and the saturated response limit SNR=. Notice the contrast saturation at, SNR=4 and super-saturation at SNR=8. The model predicts super-saturation in the sinusoidal grating response as a general effect with increasing SNR.

Fig. 10.
Fig. 10.

Sinusoidal grating total response maximum (LGN[P]/νLGN)max for the strong bandpass case of Fig. 1, with gain parameter αG2=9 and SNR=4 versus contrast cP and normalized spatial frequency log10(πρ0sP). The contrast saturation curve in Fig. 9 is a cross section of this plot at the vertical plane marking the optimal spatial frequency (πρ0sLGN=πρ0sLIN=0.614). Notice the optimal frequency is independent of contrast.

Fig. 11.
Fig. 11.

Sinusoidal grating saturated response |cP|(LGN[P]/νLGN)max,sat versus normalized frequency log10(πρ0sP) for the strong bandpass case of Fig. 1, with gain parameter αG2=9 at different contrast values. Optimal frequency is πρ0sLGN=0.614 (vertical dashed line) and gain control “on” value is πρ0sGAIN=0.383 (vertical solid line). The limiting value at cP=0 cannot be measured directly and is indicated by the dotted line.

Fig. 12.
Fig. 12.

Circular spot linear field response R[P]/νG versus normalized spot radius ρP/ρ0 for the strong bandpass case of Fig. 1, at levels SNR=1 (short dashing), SNR=2 (medium dashing), SNR=4 (long dashing), and SNR=8 (solid). The responses are proportional to SNR with maxima where the spot sizes match the excitatory center ρP/ρ0=1 (vertical dashed line).

Fig. 13.
Fig. 13.

Circular spot gain control response G[P]/νG versus normalized spot radius ρP/ρ0 for gain control parameters αG2=0.36 (gain maximum inside excitatory center, thin line), αG2=0.72 (gain maximum at excitatory center boundary, medium line), αG2=9.0 (gain maximum outside excitatory center, thick line), and excitatory center boundary ρP/ρ0=1 (vertical dashed line). Each gain control case is shown for the levels SNR=1,2,4,8 of Fig. 12. In each case, the spot size for maximum gain control is independent of SNR.

Fig. 14.
Fig. 14.

Circular spot total response LGN[P]/νLGN versus normalized spot radius ρP/ρ0 for the strong bandpass case of Fig. 1, with the levels (SNR=1,2,4,8) of Fig. 12, and the gain control parameters αG2=0.36,0.72,9.0 of Fig. 13. For weak gain control (αG2=0.36,0.72), the (local) maximum response occurs for spot sizes on or outside the excitatory center, and the position varies strongly with SNR. Excitatory center boundary ρP/ρ0=1 (vertical dashed line). For strong gain control (αG2=9.0), the (local) maximum response occurs inside the excitatory center, and is increasingly localized as SNR increases.

Fig. 15.
Fig. 15.

Circular spot saturated response (LGN[P]/νLGN)sat versus normalized spot radius ρP/ρ0 for the strong bandpass case of Fig. 1 and gain control parameters αG2=0.36,0.72,1.0,4.0,9.0, where the increasing thickness of the lines corresponds to increasing αG2. For αG2>0.72, the saturated response has a local maximum inside the excitatory center; that is, the spot size for the local maximum of the response remains stable as SNR increases.

Equations (49)

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LGN[P]νLGNPos(R[P]G[P]),
R[P]R×RR(y)P(y)dy,
R(x)12πσC2exp(x12+x222σC2)βCS2πσS2exp(x12+x222σS2).
R×RR(x)dx=1βCS.
G[P](R×RG(y)(P(y)μG[P]+νG)2dy)1/2,
μG[P]R×RG(y)P(y)dy,
G(x)12πσG2exp(x12+x222σG2),
VarG[P]R×RG(y)(P(y)μG[P])2dy=R×RG(y)P(y)2dyμG[P]2,
G[P]=(VarG[P]+νG2)1/2.
P(x)=νMAGp(x),
R[P]=νMAGR[p]VarG[P]=νMAG2VarG[p]G[P]=νG(1+νMAG2νG2VarG[p])1/2.
LGN[P]νLGN=Pos(R[P]/νGG[P]/νG)=νMAGνGPos(R[p])(1+νMAG2νG2VarG[p])1/2.
(LGN[P]νLGN)satlimνMAGνG(LGN[P]νLGN)=Pos(R[p])VarG[p].
LGN[P]νLGN=νPνG(1βCS).
0<σC<σSand0<βCS1.
αCσC/ρ0andαSσS/ρ0.
βCS=αS2αC2exp(12αS212αC2).
αS2=(2PL(exp(1/(2αC2))2αC2))1for0<αC2<12,
P(x)=νP(1+cPcos(2πsPd(αP)·xϕP)),
R[P]/νG=νPνG(1βCS+cPcos(ϕP)TC(sP)),
TC(sP)=exp(2αC2(πρ0sP)2)βCSexp(2αS2(πρ0sP)2).
TC(sP)=R×RR(x1,x2)exp(2πi(s1x1+s2x2))dx1dx2,
(R[P]νG)maxmaxϕP(R[P]νG)=νPνG(1βCS+|cP|TC(sP))0.
limsP0(R[P]νG)max=νPνG(1βCS)(1+|cP|)limsP(R[P]νG)max=νPνG(1βCS).
(πρ0sLIN)2=ln(αS2βCS/αC2)2(αS2αC2).
αS2=(4PL(exp(1/(4αC2))4αC2))1for0<αC2<14.
0πρ0sLIN1
μG[P]=νG(1+cPcos(ϕP)exp(2αG2(πρ0sP)2))whereαGσG/ρ0,
G[P]/νG=[1+12(νPcPνG)2(1exp(4αG2(πρ0sP)2))C(ϕP)]1/2C(ϕP)(1cos(2ϕP)exp(4αG2(πρ0sP)2)).
(G[P]νG)minminϕP(G[P]νG)=[1+cP22(νPνG)2(1exp(4(αGπρ0sP)2))2]1/2.
limsP0(G[P]νG)min=1andlimsP(G[P]νG)min=[1+cP22(νPνG)2]1/2.
sPsGAINimplies0.99(1exp(4(αGπρ0sP)2))2<1that is,πρ0sGAIN=1.15/αG.
LGN[P]νLGN=Pos(R[P]/νG)G[P]/νG.
(LGN[P]νLGN)maxmaxϕP(Pos(R[P]/νG)G[P]/νG)=(R[P]/νG)max(G[P]/νG)min,
limsP0(LGN[P]νLGN)max=νPνG(1βCS)(1+|cP|)limsP(LGN[P]νLGN)max=νPνG(1βCS)[1+cP22(νPνG)2]1/2.
(LGN[P]νLGN)max,satlimνPνG(LGN[P]νLGN)max=2|cP|1βCS+|cP|TC(sP)1exp(4αG2(πρ0sP)2).
(LGN[P]νLGN)max,sat=2/|cP|1exp(4αG2(πρ0sP)2)(R[P]/νG)maxSNR
(LGN[P]νLGN)max,sat2|cP|(R[P]/νG)maxSNRforsP>sGAIN.
|cP|(LGN[P]νLGN)max,sat=2(1βCS)1exp(4αG2(πρ0sP)2)(1+|cP|TC(sP)1βCS).
limcP0|cP|(LGN[P]νLGN)max,sat=2(1βCS)1exp(4αG2(πρ0sP)2).
P(x){νSP0x12+x22<ρP20otherwise.
R[P]νG=νSPνG[1exp(ρP22αC2ρ02)βCS(1exp(ρP22αS2ρ02))]>0.
limρP/ρ00(R[P]νG)=0maxρP/ρ0(R[P]νG)=(R[P]νG)ρPρ0=1limρP/ρ0(R[P]νG)=νSPνG(1βCS).
μG[P]=νSP(1exp(ρP22αG2ρ02)),
G[P]νG=[1+νSP2νG2(1exp(ρP22αG2ρ02))exp(ρP22αG2ρ02)]1/2.
ρG/ρ0=2ln(2)αG=1.18αG.
limρP/ρ00(G[P]νG)=1maxρP/ρ0(G[P]νG)=(G[P]νG)ρPρ0=ρGρ0limρP/ρ0(G[P]νG)=1.
limρP/ρ00(LGN[P]νLGN)=0,limρP/ρ0(LGN[P]νLGN)=νSPνG(1βCS).
(LGN[P]νLGN)sat=exp(ρP22αG2ρ02)[exp(ρP22αG2ρ02)1]1/2·[1exp(ρP22αC2ρ02)βCS(1exp(ρP22αS2ρ02))].

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