Biological Cybernetics

, Volume 97, Issue 4, pp 279–292 | Cite as

Geometry of the superior colliculus mapping and efficient oculomotor computation

  • Nicolas Tabareau
  • Daniel Bennequin
  • Alain Berthoz
  • Jean-Jacques Slotine
  • Benoît Girard
Original Paper

Abstract

Numerous brain regions encode variables using spatial distribution of activity in neuronal maps. Their specific geometry is usually explained by sensory considerations only. We provide here, for the first time, a theory involving the motor function of the superior colliculus to explain the geometry of its maps. We use six hypotheses in accordance with neurobiology to show that linear and logarithmic mappings are the only ones compatible with the generation of saccadic motor command. This mathematical proof gives a global coherence to the neurobiological studies on which it is based. Moreover, a new solution to the problem of saccades involving both colliculi is proposed. Comparative simulations show that it is more precise than the classical one.

Keywords

Saccades Superior colliculus Spatio-temporal transformation Computational model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson R, Keller E, Gandhi N, Das S (1998) Two-dimensional saccade-related population activity in superior colliculus in monkey. J Neurophysiol 80(2):798–817PubMedGoogle Scholar
  2. Arai K, Keller E, Edelman J (1994) Two-dimensional neural network model of the primate saccadic system. Neural Netw 7:1115–1135CrossRefGoogle Scholar
  3. Arai K, Das S, Keller E, Aiyoshi E (1999) A distributed model of the saccade system: simulations of temporally perturbed saccades using position and velocity feedback. Neural Netw 12(10):1359–1375PubMedCrossRefGoogle Scholar
  4. Badler J, Keller E (2002) Decoding of a motor command vector from distributed activity in superior colliculus. Biol Cybern 86(3): 179–189PubMedCrossRefGoogle Scholar
  5. Bourbaki N (1972) Groupes et algèbres de Lie, Chapitres 2 et 3. Dunod, ParisGoogle Scholar
  6. Dräger U, Hugel D (1976) Topography of visual and somatosensory projections to mouse superior colliculus. J Neurophysiol 39:91–101PubMedGoogle Scholar
  7. Feldon S, Feldon P, Kruger L (1970) Topography of the retinal projection upon the superior colliculus of the cat. Vision Res 10:135–143PubMedCrossRefGoogle Scholar
  8. Girard B, Berthoz A (2005) From brainstem to cortex: computational models of saccade generation circuitry. Prog Neurobiol 77:215–251PubMedGoogle Scholar
  9. van Gisbergen J, van Opstal A, Tax A (1987) Collicular ensemble coding of saccades based on vector summation. Neuroscience 21(2):541–555PubMedCrossRefGoogle Scholar
  10. Goffart L, Pélisson D (1998) Orienting gaze shifts during muscimol inactivation of caudal fastigial nucleus in the cat. I. Gaze dysmetria. J Neurophysiol 79:1942–1958PubMedGoogle Scholar
  11. Goossens H, van Opstal A (2000) Blink-perturbed saccades in monkey. II. superior colliculus activity. J Neurophysiol 83:3430–3452PubMedGoogle Scholar
  12. Goossens H, van Opstal A (2006) Dynamic ensemble coding of saccades in the monkey superior colliculus. J Neurophysiol 95:2326–2341PubMedCrossRefGoogle Scholar
  13. Grantyn A, Moschovakis A (2003) Structure–function relationships in the superior colliculus of higher mammals. In: Hall W, Moschovakis V (eds) The superior colliculus: new approaches for studying sensorimotor integration, methods & new frontiers in neuroscience, chap 5. CRC Press, Boca Raton, pp 107–145Google Scholar
  14. Grantyn A, Brandi AM, Dubayle D, Graf W, Ugolini G, Hadjidimitrakis K, Moschovakis A (2002) Density gradients of trans-synaptically labeled collicular neurons after injections of rabbies virus in the lateral rectus muscle of the rhesus monkey. J Comp Neurol 451:346–361PubMedCrossRefGoogle Scholar
  15. Groh J (2001) Converting neural signals from place codes to rate codes. Biol Cybern 85(3):159–165PubMedCrossRefGoogle Scholar
  16. Herrero L, Rodríguez F, Salas C, Torres B (1998) Tail and eye movememnts evoked by electrical microstimulation of the optic tectum in goldfish. Exp Brain Res 120:291–05PubMedCrossRefGoogle Scholar
  17. Hirsch H (1976) Differential topology. Springer, New YorkGoogle Scholar
  18. Hörmander L (1983) The Analysis of linear partial differential operators I. No 256. In: Grundlehren der mathematischen Wissenschaften. Springer, BerlinGoogle Scholar
  19. Iwamoto Y, Yoshida K (2002) Saccadic dysmetria following inactivation of the primate fastigial oculomotor region. Neurosci Lett 325:211–215PubMedCrossRefGoogle Scholar
  20. Kaneko C, Evinger C, Fuchs A (1981) Role of the cat pontine burst neurons in generation of saccadic eye movements. J Neurophysiol 46(3):387–408PubMedGoogle Scholar
  21. Keller E (1974) Participation of medial pontine reticular formation in eye movement generation in monkey. J Neurophysiol 37(2): 316–332PubMedGoogle Scholar
  22. King W, Fuchs F (1979) Reticular control of vertical saccadic eye movements by mesencephalic burst neurons. J Neurophysiol 42(3): 861–876PubMedGoogle Scholar
  23. Knudsen E (1982) Auditory and visual maps of space in the optic tectum of the owl. J Neurosci 2(9):1177–1194PubMedGoogle Scholar
  24. Lee C, Rohrer W, Sparks D (1988) Population coding of saccadic eye movements by neurons in the superior colliculus. Nature 332: 357–360PubMedCrossRefGoogle Scholar
  25. McIlwain J (1976) Large receptive fields and spatial transformations in the visual system. In: Porter R (eds) Neurophysiology II, Int Rev Physiol, vol 10. University Park Press, Baltimore, pp 223–248Google Scholar
  26. McIlwain J (1983) Representation of the visual streak in visuotopic maps of the cat’s superior colliculus: influence of the mapping variable. Vision Res 23(5):507–516PubMedCrossRefGoogle Scholar
  27. Moschovakis A, Kitama T, Dalezios Y, Petit J, Brandi A, Grantyn A (1998) An anatomical substrate for the spatiotemporal transformation. J Neurosci 18(23):10219–10229PubMedGoogle Scholar
  28. Munoz D, Waitzman D, Wurtz R (1996) Activity of neurons in monkey superior colliculus during interrupted saccades. J Neurphysiol 75(6):2562–2580Google Scholar
  29. Olivier E, Porter J, May P (1998) Comparison of the distribution and somatodendritic morphology of tectotecal neurons in the cat and monkey. Vis Neurosci 15:903–922PubMedCrossRefGoogle Scholar
  30. van Opstal A, van Gisbergen J (1989) A nonlinear model for collicular spatial interactions underlying the metrical properties of electrically elicited saccades. Biol Cybern 60(3):171–183PubMedCrossRefGoogle Scholar
  31. Optican L (2005) Sensorimotor transformation for visually guided saccades. Ann NY Acad Sci 1039:132–148PubMedCrossRefGoogle Scholar
  32. Ottes F, van Gisbergen JA, Eggermont J (1986) Visuomotor fields of the superior colliculus: a quantitative model. Vision Res 26(6): 857–873PubMedCrossRefGoogle Scholar
  33. Robinson D (1972) Eye movements evoked by collicular stimulation in the alert monkey. Vision Res 12:1795–1808PubMedCrossRefGoogle Scholar
  34. Rosa M, Schmid L (1994) Topography and extent of visual-field representation in the superior colliculus of the megachiropteran Pteropus. Vis Neurosci 11:1037–1057PubMedCrossRefGoogle Scholar
  35. Schwarz E (1980) Computational anatomy and functional architecture of striate cortex: a spatial mapping approach to perceptual coding. Vision Res 20:645–669CrossRefGoogle Scholar
  36. Siminoff R, Schwassmann H, Kruger L (1966) An electrophysiological study of the visual projection to the superior colliculus of the rat. J Comp Neurol 127:435–444PubMedCrossRefGoogle Scholar
  37. Soetedjo R, Kaneko C, Fuchs A (2000) Evidence that the superior colliculus participates in the feedback control of saccadic eye movements. J Neurophysiol 87:679–695Google Scholar
  38. Sparks D, Holland R, Guthrie B (1976) Size and distribution of movement fields in the monkey superior colliculus. Brain Res 113:21–34PubMedCrossRefGoogle Scholar
  39. Yoshida K, McCrea R, Berthoz A, Vidal P (1982) Morphological and physiological characteristics of inhibitory burst neurons controlling horizontal rapid eye movements in the alert cat. J Neurophysiol 48(3):761–784PubMedGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Nicolas Tabareau
    • 1
  • Daniel Bennequin
    • 2
  • Alain Berthoz
    • 1
  • Jean-Jacques Slotine
    • 3
  • Benoît Girard
    • 1
  1. 1.UMR 7152, Laboratoire de Physiologie de la Perception et de l’ActionCNRS-Collège de FranceParisFrance
  2. 2.UMR 7586, Equipe Géométrie et DynamiqueUniversité Paris Diderot-CNRS, Paris, FranceParisFrance
  3. 3.Nonlinear Systems LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations