Biological Cybernetics

, Volume 55, Issue 1, pp 43–57 | Cite as

A model of the smooth pursuit eye movement system

  • D. A. Robinson
  • J. L. Gordon
  • S. E. Gordon


Human, horizontal, smooth-pursuit eye movements were recorded by the search coil method in response to Rashbass step-ramp stimuli of 5 to 30 deg/s. Eye velocity records were analyzed by measuring features such as the time, velocity and acceleration of the point of peak acceleration, the time and velocity of the peaks and troughs of ringing and steady-state velocity. These values were averaged and mean responses reconstructed. Three normal subjects were studied and their responses averaged. All showed a peak acceleration-velocity saturation. All had ringing frequencies near 3.8 Hz and the mean steady-state gain was 0.95.

It is argued that a single, linear forward path with any transfer function G(s) and a 100 ms delay (latency) cannot simultaneously simulate the initial rise of acceleration and ring at 3.8 Hz based on a Bode analysis. Also such a simple negative feedback model cannot have a steady-state gain greater than 1.0; a situation that occurs frequently experimentally. L.R. Young's model, which employs internal positive feedback to eliminate the built-in unity negative feedback, was felt necessary to resolve this problem and a modification of that model is proposed which simulates the data base. Acceleration saturation is achieved by borrowing the idea of the local feedback model for saccades so that one nonlinearity can account for the acceleration-velocity saturation: the main sequence for pursuit. Motor plasticity or motor learning, recently demonstrated for pursuit, is also incorporated and simulated.

It was noticed that the offset of pursuit did not show the ringing seen in the onset so this was quantified in one subject. Offset velocity could be characterized by a single exponential with a time constant of about 90 ms. This observation suggests that fixation is not pursuit at zero velocity and that the pursuit system is turned on when needed and off during fixation.


Smooth Pursuit Feedback Model Motor Plasticity Offset Velocity Negative Feedback Model 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bahill AT, Clark RM, Stark L (1975) The main sequence, a tool for studying human eye movements. Math Biosci 24:191–204Google Scholar
  2. Becker W, Fuchs AF (1985) Prediction in the oculomotor system: smooth pursuit during transient disappearance of a visual target. Exp Brain Res 57:562–575Google Scholar
  3. Boghen D, Troost BT, Daroff RB, Dell'Osso LF, Birkett JE (1974) Velocity characteristics of normal human saccades. Invest Ophthalmol 13:619–623Google Scholar
  4. Cannon SC, Robinson DA (1986) The final common integrator is in the prepositus and vestibular nuclei. In: Keller EL, Zee DS (eds) Adaptive processes in eye movements and vision. Pergamon Press, Oxford (in press)Google Scholar
  5. Carl JR, Gellman RS (1985) Human smooth pursuit: the response to conflicting velocity and position stimuli. Soc Neurosci Abstr vol 11, part 1, p 78Google Scholar
  6. Demer JL (1981) The variable gain element of the vestibuloocular reflex is common to the optokinetic system of the cat. Brain Res 229:1–13Google Scholar
  7. Fuchs AF, Luschei ES (1970) Firing patterns of abducens neurons of alert monkeys in relationship to horizontal eye movement. J Neurophysiol 33:382–392Google Scholar
  8. Fuchs AF, Kaneko CRS, Scudder CA (1985) Brain stem control of saccadic eye movements. Annu Rev Neurosci 8:307–337Google Scholar
  9. Gisbergen JAM van, Robinson DA, Gielen S (1981) A quantitative analysis of the generation of saccadic eye movements by burst neurons. J Neurophysiol 45:417–442Google Scholar
  10. Gellman RS, Carl JR (1985) Human smooth pursuit: early responses to sudden changes in target velocity. Soc Neurosci Abstr, vol 11, part 1, p 79Google Scholar
  11. Gonshor A, Melvill Jones G (1976) Extreme vestibulo-ocular adaptation induced by prolonged optical reversal of vision. J Physiol (London) 256: 381–414Google Scholar
  12. Holst E von, Mittelstaedt H (1950) Das reafferenzprincip. Naturwissenschaften 37:464–476Google Scholar
  13. Ito M (1982) Cerebellar control of the vestibulo-ocular reflex-around the flocculus hypothesis. Annu Rev Neurosci 5:275–296Google Scholar
  14. Jürgens R, Becker W, Kornhuber HH (1981) Natural and drug-induced variations of velocity and duration of human saccadic eye movements: evidence for a control of the neural pulse generator by local feedback. Biol Cybern 39:87–96Google Scholar
  15. Keller EL (1973) Accommodative vergence in the alert monkey. Vision Res 13:1565–1575Google Scholar
  16. Lisberger SG, Fuchs AF (1978) Role of primate flocculus during rapid behavioral modification of vestibuloocular reflex. I. Purkinje cell activity during visually guided horizontal smooth-pursuit eye movements and passive head rotation. J Neurophysiol 41:733–763Google Scholar
  17. Lisberger SG, Evinger C, Johanson GW, Fuchs AF (1981) Relationship between eye acceleration and retinal image velocity during foveal smooth pursuit in man and monkey. J Neurophysiol 46:229–249Google Scholar
  18. Lynch JC, Mountcastle VB, Talbot WH, Yin TCT (1977) Parietal lobe mechanisms for directed visual attention. J Neurophysiol 40:362–389Google Scholar
  19. Mays LE, Sparks DL (1980) Saccades are spatially, not retinocentrically coded. Science 208:1163–1165Google Scholar
  20. Meyer CH, Lasker AG, Robinson DA (1985) The upper limit of human smooth pursuit velocity. Vision Res 25:561–563Google Scholar
  21. Michael JA, Melvill Jones G (1966) Dependence of visual tracking capability upon stimulus predictability. Vision Res 6:707–716Google Scholar
  22. Miles FA, Fuller JH (1975) Visual tracking and the primate flocculus. Science 189:1000–1002Google Scholar
  23. Morris EJ, Lisberger SG (1983) Signals used to maintain smooth pursuit eye movements in monkeys: effects of small retinal position and velocity errors. Soc Neurosci Abstr, vol 9, part 2, p 866Google Scholar
  24. Mustari MJ, Fuchs AF, Wallman J (1984) Smooth-pursuit-related units in the dorsolateral pons of the rhesus macaque. Soc Neurosci Abstr, vol 10, part 2, p 987Google Scholar
  25. Newsome WT, Wurtz RH, Dürsteler MR, Mikami A (1985) Deficits in visual motion processing following ibotenic acid lesions of the middle temporal visual area of the macaque monkey. J Neurosci 5:825–840Google Scholar
  26. Optican LM, Zee DS, Chu FC (1985) Adaptive responses to ocular muscle weakness in human pursuit and saccadic eye movements. J Neurophysiol 54:110–122Google Scholar
  27. Rashbass C (1961) The relationship between saccadic and smooth tracking eye movements. J Physiol (London) 159:326–338Google Scholar
  28. Robinson DA (1965) The mechanics of human smooth pursuit eye movement. J Physiol (London) 180:569–591Google Scholar
  29. Robinson DA (1972) Eye movements evoked by collicular stimulation in the alert monkey. Vision Res 12:1795–1808Google Scholar
  30. Robinson DA (1975) Oculomotor control signals. In: Lennerstrand G, Bach-y-Rita P (eds) Basic mechanisms of ocular motility and their clinical implications. Pergamon Press, Oxford, pp 337–374Google Scholar
  31. Robinson DA (1976) Adaptive gain control of vestibuloocular reflex by the cerebellum. J Neurophysiol 39:954–969Google Scholar
  32. Ron S, Robinson DA (1973) Eye movements evoked by cerebellar stimulation in the alert monkey. J Neurophysiol 36:1004–1022Google Scholar
  33. Schalén L (1980) Quantification of tracking eye movements in normal subjects. Acta Otolaryngol 90:404–413Google Scholar
  34. Sperry RW (1950) Neural basis of spontaneous optokinetic response produced by visual inversion. J Comp Physiol Psychol 43:482–489Google Scholar
  35. Steinbach MJ (1969) Eye tracking of self-moved targets: the role of efference. J Exp Psychol 82:366–376Google Scholar
  36. Steinbach MJ (1976) Pursuing the perceptual rather than the retinal stimulus. Vision Res 16:1371–1376Google Scholar
  37. Suzuki DA, Keller EL (1983) Sensory-oculomotor interactions in primate cerebellar vermis: a role in smooth pursuit control. Soc Neurosci Abstr, vol 9, part 1, p 606Google Scholar
  38. Suzuki DA, Noda H, Kase M (1981) Visual and pursuit eye movement-related activity in posterior vermis of monkey cerebellum. J Neurophysiol 46:1120–1139Google Scholar
  39. Wyatt HJ, Pola J (1981) Slow eye movements to eccentric targets. Invest Ophthalmol Vis Sci 21:477–483Google Scholar
  40. Yasui S, Young LR (1975) Eye movements during after-image tracking under sinusoidal and random vestibular stimulation. In: Lennerstrand G, Bach-y-Rita P (eds) Basic mechanisms of ocular motility and their clinical implications. Pergamon Press, Oxford, pp 509–513Google Scholar
  41. Young LR (1971) Pursuit eye tracking movements. In: Bach-y-Rita P, Collins CC, Hyde JE (eds) Control of eye movements. Academic Press, New York, pp 429–443Google Scholar
  42. Young LR (1977) Pursuit eye movement — what is being pursued? In: Baker R, Berthoz A (eds) Control of gaze by brain stem neurons, Elsevier, Amsterdam, pp 29–36Google Scholar
  43. Young LR, Forster JD, van Houtte N (1968) A revised stochastic sampled data model for eye tracking movements. Fourth Ann NASA-University Conference on Manual Control, University of Michigan, Ann Arbor, MichiganGoogle Scholar
  44. Zee DS, Robinson DA (1979) An hypothetical explanation of saccadic oscillations. Ann Neurol 5:405–414Google Scholar
  45. Zee DS, Butler PH, Optican LM, Tusa RJ, Gücer G (1982) Effects of bilateral occipital lobectomies on eye movements in monkeys: preliminary observations. In: Roucoux A, Crommelinck M (eds) Physiological and pathological aspects of eye movements. Junk, The Hague, pp 225–232Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • D. A. Robinson
    • 1
  • J. L. Gordon
    • 1
  • S. E. Gordon
    • 1
  1. 1.Departments of Ophthalmology and NeurologyThe Johns Hopkins University, School of MedicineBaltimoreUSA

Personalised recommendations