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A parsimonious computational model of visual target position encoding in the superior colliculus

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Abstract

The superior colliculus (SC) is a brainstem structure at the crossroad of multiple functional pathways. Several neurophysiological studies suggest that the population of active neurons in the SC encodes the location of a visual target to foveate, pursue or attend to. Although extensive research has been carried out on computational modeling, most of the reported models are often based on complex mechanisms and explain a limited number of experimental results. This suggests that a key aspect may have been overlooked in the design of previous computational models. After a careful study of the literature, we hypothesized that the representation of the whole retinal stimulus (not only its center) might play an important role in the dynamics of SC activity. To test this hypothesis, we designed a model of the SC which is built upon three well-accepted principles: the log-polar representation of the visual field onto the SC, the interplay between a center excitation and a surround inhibition and a simple neuronal dynamics, like the one proposed by the dynamic neural field theory. Results show that the retinotopic organization of the collicular activity conveys an implicit computation that deeply impacts the target selection process.

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Notes

  1. i.e. activation = activation \(\times \) (\(1+\mathcal {N}(0,0.01)\))

  2. We do not consider the deformation of the projection from the visual field to the retina since we suppose the transformation used accounts already for that, see Fig 1 in Ottes et al. (1986) . Polar coordinates in \(\mathcal R\) are equivalent to polar coordinates in \(\mathcal V\),

References

  • Amari S (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybern 27(2):77–87

    Article  CAS  PubMed  Google Scholar 

  • Anderson RW, Keller EL, Gandhi NJ, Das S (1998) Two-dimensional saccade-related population activity in superior colliculus in monkey. J Neurophysiol 80(2):798–817

    CAS  PubMed  Google Scholar 

  • Arai K, Keller EL (2005) A model of the saccade-generating system that accounts for trajectory variations produced by competing visual stimuli. Biol Cybern 92(1):21–37

    Article  PubMed  Google Scholar 

  • Arai K, Keller EL, Edelman JA (1994) Two-dimensional neural networks model of the primate saccadis system. Neural Netw 7(6–7):1115–1135

    Article  Google Scholar 

  • Badler JB, Keller EL (2002) Decoding of a motor command vector from distributed activity in superior colliculus. Biol Cybern 86(3):179–189

    Article  PubMed  Google Scholar 

  • Chevalier G, Vacher S, Deniau JM, Desban M (1985) Disinhibition as a basic process in the expression of striatal functions. i. the striato-nigral influence on tecto-spinal/tecto-diencephalic neurons. Brain Res 334(2):215–226

    Article  CAS  PubMed  Google Scholar 

  • Coren S, Hoenig P (1972) Effect of non-target stimuli on the length of voluntary saccades. Percept Motor Skills 34:499–508

    Article  CAS  PubMed  Google Scholar 

  • Cowey A, Rolls ET (1974) Human cortical magnification factor and its relation to visual acuity. Exp Brain Res 21(5):447–454

    Article  CAS  PubMed  Google Scholar 

  • Daniel PM, Whitteridge D (1961) The representation of the visual field on the cerebral cortex in monkeys. J Physiol 159(2):203–221

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Deubel H, Wolf W, Hauske G (1984) The evaluation of the oculomotor error signal. In: Gale A, Johnson F (eds) Theoretical and applied aspects of eye movement research. Elsevier, Amsterdam, pp 55–62

    Google Scholar 

  • Dorris MC, Olivier E, Munoz DP (2007) Competitive integration of visual and preparatory signals in the superior colliculus during saccadic programming. J Neurosci 27:5053–5062

    Article  CAS  PubMed  Google Scholar 

  • Droulez J, Berthoz A (1991) A neural network model of sensoritopic maps with predictive short memory properties. Proc Natl Acad Sci 88(21):9653–9657

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Findlay JM (1982) Global visual processing for saccadic eye movements. Vis Res 22(8):1033–1045

    Article  CAS  PubMed  Google Scholar 

  • Findlay JM (1983) Visual information for saccadic eye movements. In: Hein A, Jeannerod M (eds) Spatially oriented behavior. Springer, New York

  • Freedman EG, Sparks DL (1997) Activity of cells in the deeper layers of the superior colliculus of the rhesus monkey: evidence for a gaze displacement command. J Neurophysiol 78(3):1669–1690

    CAS  PubMed  Google Scholar 

  • Gancarz G, Grossberg S (1999) A neural model of saccadic eye movement control explains task-specific adaptation. Vis Res 39(18):3123–3143

    Article  CAS  PubMed  Google Scholar 

  • Gandhi NJ, Katnani HA (2011) Motor functions of the superior colliculus. Annu Rev Neurosci 34:205–231

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Godijn R, Theeuwes J (2002) Programming of endogenous and exogenous saccades: evidence for a competitive integration model. J Exp Psychol 28(5):1038–1054

    Google Scholar 

  • Goffart L, Hafed ZM, Krauzlis RJ (2012) Visual fixation as equilibrium: evidence from superior colliculus inactivation. J Neurosci 32(31):10,627–10,636

    Article  CAS  Google Scholar 

  • Goossens HHLM, Van Opstal AJ (2006) Dynamic ensemble coding of saccades in the monkey superior colliculus. J Neurophysiol 95(4):2326–2341

    Article  CAS  PubMed  Google Scholar 

  • Hafed ZM, Krauzlis RJ (2008) Goal representations dominate superior colliculus activity during extrafoveal tracking. J Neurosci 28(38):9426–9439

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Hafed ZM, Goffart L, Krauzlis RJ (2008) Superior colliculus inactivation causes stable offsets in eye position during tracking. J Neurosci 28(32):8124–8137

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Hahnloser RHR, Seung HS, Slotine JJ (2003) Permitted and forbidden sets in symmetric threshold-linear networks. Neural Comput 15(3):621–638

    Article  PubMed  Google Scholar 

  • Hikosaka O, Wurtz RH (1985) Modification of saccadic eye movements by gaba-related substances. i. effect of muscimol and bicuculline in monkey superior colliculus. J Neurophysiol 53(1):266–291

    CAS  PubMed  Google Scholar 

  • Hikosaka O, Wurtz RH et al (1983) Visual and oculomotor functions of monkey substantia nigra pars reticulata. iv. relation of substantia nigra to superior colliculus. J Neurophysiol 49(5):1285–1301

    CAS  PubMed  Google Scholar 

  • Honda H (2005) The remote distractor effect of saccade latencies in fixation-offset and overlap conditions. Vis Res 45(21):2773–2779

    Article  PubMed  Google Scholar 

  • Johnston A (1986) A spatial property of the retino-cortical mapping. Spat Vis 1(4):319–331

    Article  CAS  PubMed  Google Scholar 

  • Kang I, Lee C (2000) Properties of saccade-related neurons in the cat superior colliculus: patterns of movement fields and discharge timing. Exp Brain Res 131(2):149–164

    Article  CAS  PubMed  Google Scholar 

  • Lee C, Rohrer WH, Sparks DL (1988) Population coding of saccadic eye movements by neurons in the superior colliculus. Nature 332(6162):357–360

    Article  CAS  PubMed  Google Scholar 

  • Lee P, Hall WC (2006) An in vitro study of horizontal connections in the intermediate layer of the superior colliculus. J Neurosci 26:4763–4768

    Article  CAS  PubMed  Google Scholar 

  • Lefèvre P, Galiana HL (1992) Dynamic feedback to the superior colliculus in a neural network model of the gaze control system. Neural Netw 5:871–890

    Article  Google Scholar 

  • Lefèvre P, Quaia C, Optican LM (1998) Distributed model of control of saccades by superior colliculus and cerebellum. Neural Netw 11(7–8):1175–1190

    Article  PubMed  Google Scholar 

  • Lévy-Schoen A (1969) Détermination et latence de la réponse oculo-motrice à deux stimulus simultanés ou successifs selon leur excentricité relative. L’Année Psychol 69(2):373–392

    Article  Google Scholar 

  • Lévy-Schoen A (1974) Le champ d’activité du regard: données expérimentales. L’Année Psychol 74:43–65

    Article  Google Scholar 

  • Marino RA, Rodgers CK, Levy R, Munoz DP (2008) Spatial relationships of visuomotor transformations in the superior colliculus map. J Neurophysiol 100(5):2564–2576

    Article  PubMed  Google Scholar 

  • Marino RA, Trappenberg TP, Dorris M, Munoz DP (2012) Spatial interactions in the superior colliculus predict saccade behavior in a neural field model. J Cognit Neurosci 24(2):315–336

    Article  Google Scholar 

  • McIlwain JT (1976) Large receptive fields and spatial transformations in the visual system. Int Rev Physiol 10:223–248

    Google Scholar 

  • Meredith MA, Ramoa AS (1998) Intrinsic circuitry of the superior colliculus: pharmacophysiological identification of horizontally oriented inhibitory interneurons. J Neurophysiol 79(3):1597–1602

    CAS  PubMed  Google Scholar 

  • Moschovakis A, Gregoriou G, Savaki H (2001) Functional imaging of the primate superior colliculus during saccades to visual targets. Nat Neurosci 4(10):1026–1031

    Article  CAS  PubMed  Google Scholar 

  • Munoz DP, Istvan PJ (1998) Lateral inhibitory interactions in the intermediate layers of the monkey superior colliculus. J Neurophysiol 79:1193–1209

    CAS  PubMed  Google Scholar 

  • Munoz DP, Wurtz RH (1995) Saccade-related activity in monkey superior colliculus. i. characteristics of burst and buildup cells. J Neurophysiol 73:2313–2333

    CAS  PubMed  Google Scholar 

  • Nakahara H, Morita K, Wurtz RH, Optican LM (2006) Saccade-related spread of activity across superior colliculus may arise from asymmetry of internal connections. J Neurophysiol 96(2):765–777

    Article  PubMed  Google Scholar 

  • Noton D, Stark L (1971) Scanpaths in eye movements during pattern perception. Science 171:308–311

    Article  CAS  PubMed  Google Scholar 

  • Olivier E, Porter JD, May PJ (1998) Comparison of the distribution and somatodendritic morphology of tectotectal neurons in the cat and monkey. Vis Neurosci 15(5):903–922

    Article  CAS  PubMed  Google Scholar 

  • Olivier E, Dorris MC, Munoz DP (1999) Lateral interactions in the superior colliculus, not an extended fixation zone, can account for the remote distractor effect. Behav Brain Sci 22(4):694–695

  • Optican LM (1995) A field theory of saccade generation: temporal-to-spatial transform in the superior colliculus. Vis Res 35(23–24):3313–3320

    Article  CAS  PubMed  Google Scholar 

  • Ottes FP, van Gisbergen JAM, Eggermont JJ (1984) Metrics of saccade responses to visual double stimuli: two different modes. Vis Res 24(10):1169–1179

    Article  CAS  PubMed  Google Scholar 

  • Ottes FP, van Gisbergen JAM, Eggermont JJ (1986) Visuomotor fields of the superior colliculus: a quantitative model. Vis Res 26(6):857–873

    Article  CAS  PubMed  Google Scholar 

  • Robinson DA (1972) Eye movements evoked by collicular stimulation in the alert monkey. Vis Res 12(11):1795–1808

    Article  CAS  PubMed  Google Scholar 

  • Rougier N, Vitay J (2006) Emergence of attention within a neural population. Neural Netw 19(5):573–581

    Article  PubMed  Google Scholar 

  • Salinas E, Abbott LF (1996) A model of multiplicative neural responses in parietal cortex. Proc Natl Acad Sci 93(21):11,956–11,961

    Article  CAS  Google Scholar 

  • Schiller PH, Stryker M (1972) Single-unit recording and stimulation in superior colliculus of the alert rhesus monkey. J Neurophysiol 35(6):915–924

    CAS  PubMed  Google Scholar 

  • Schneider S, Erlhagen W (2002) A neural field model for saccade planning in the superior colliculus: speed-accuracy tradeoff in the double-target paradigm. Neurocomputing 44–46:623–628

    Article  Google Scholar 

  • Short SJ, Enderle JD (2001) A model of the internal control system within the superior colliculus. Biomed Sci Instrum 37:349–354

    CAS  PubMed  Google Scholar 

  • Sparks DL, Mays LE (1980) Movement fields of saccade-related burst neurons in the monkey superior colliculus. Brain Res 190:39–50

    Article  CAS  PubMed  Google Scholar 

  • Sparks DL, Holland R, Guthrie BL (1976) Size and distribution of movement fields in the monkey superior colliculus. Brain Res 113(1):21–34

    Article  CAS  PubMed  Google Scholar 

  • Sparks DL, Lee C, Rohrer WH (1990) Population coding of the direction, amplitude, and velocity of saccadic eye movements by neurons in the superior colliculus. Cold Spring Harb Symp Quant Biol 55:805–811

    Article  CAS  PubMed  Google Scholar 

  • Taylor JG (1999) Neural bubble dynamics in two dimensions: foundations. Biol Cybern 80:393–409

    Article  Google Scholar 

  • Trappenberg TP, Dorris MC, Munoz DP, Klein RM (2001) A model of saccade initiation based on the competitive integration of exogenous and endogenous signals in the superior colliculus. J Cognit Neurosci 13(2):256–271

    Article  CAS  Google Scholar 

  • Van der Stigchel S, de Vries JP, Bethlehem R, Theeuwes J (2011) A global effect of capture saccades. Exp Brain Res 210(1):57–65

    Article  PubMed Central  PubMed  Google Scholar 

  • Walker R, Deubel H, Schneider WX, Findlay J (1997) Effect of remote distractors on saccade programming: evidence for an extended fixation zone. J Neurophysiol 78:1108–1119

    CAS  PubMed  Google Scholar 

  • Wang N, Warren S, May PJ (2010) The macaque midbrain reticular formation sends side-specific feedback to the superior colliculus. Exp Brain Res 201(4):701–717

    Article  PubMed Central  PubMed  Google Scholar 

  • Weber H, Fischer B (1994) Differential effects of non-target stimuli on the occurrence of express saccades in man. Vis Res 34(14):1883–1891

  • Wilson HR, Cowan JD (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Biol Cybern 13(2):55–80

    CAS  Google Scholar 

  • Wurtz RH, Goldberg ME (1972) Activity of superior colliculus in behaving monkey. iii. cells discharging before eye movements. J Neurophysiol 35(4):575–586

    CAS  PubMed  Google Scholar 

  • Yarbus AL (1967) Eye movements and vision. Plenum Press, New York

  • Zénon A, Krauzlis RJ (2012) Attention deficits without cortical neuronal deficits. Nature 489(7416):434–437

    Article  PubMed Central  PubMed  Google Scholar 

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Correspondence to Wahiba Taouali.

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This work was supported by the Institut National de la Recherche en Informatique et Automatique (INRIA), the Centre National de la Recherche Scientifique (CNRS) and the Agence Nationale de la Recherche : Grants MAPS (W.T., N.R., F.A. and L.G.) and VISAFIX (LG).

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Taouali, W., Goffart, L., Alexandre, F. et al. A parsimonious computational model of visual target position encoding in the superior colliculus. Biol Cybern 109, 549–559 (2015). https://doi.org/10.1007/s00422-015-0660-8

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  • DOI: https://doi.org/10.1007/s00422-015-0660-8

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