Skip to main content
SpringerLink
Log in

A quantitative synchronization model for smooth pursuit target tracking

  • Original Paper
  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

We propose a quantitative model for human smooth pursuit tracking of a continuously moving visual target which is based on synchronization of an internal expectancy model of the target position coupled to the retinal target signal. The model predictions are tested in a smooth circular pursuit eye tracking experiment with transient target blanking of variable duration. In subjects with a high tracking accuracy, the model accounts for smooth pursuit and repeatedly reproduces quantitatively characteristic patterns of the eye dynamics during target blanking. In its simplest form, the model has only one free parameter, a coupling constant. An extended model with a second parameter, a time delay or memory term, accounts for predictive smooth pursuit eye movements which advance the target. The model constitutes an example of synchronization of a complex biological system with perceived sensory signals.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barborica A, Ferrera V (2003) Estimating invisible target speed from neuronal activity in monkey frontal eye field. Nat Neurosci 6:66–74

    Article  PubMed  CAS  Google Scholar 

  • Barnes GR, Donelan SF (1999) The remembered pursuit task: evidence for segregation of timing and velocity storage in predictive oculomotor control. Exp Brain Res 129:57–67

    Article  PubMed  CAS  Google Scholar 

  • Barnes GR, Barnes DM, Chakraborti SR (2000) Ocular pursuit responses to repeated, single-cycle sinusoids reveal behavior compatible with predictive pursuit. J Neurophysiol 84:2340–2355

    PubMed  CAS  Google Scholar 

  • Becker W, Fuchs AF (1985) Prediction in the oculomotor system: smooth pursuit during transient disappearance of a visual target. Exp Brain Res 57:565–575

    Article  Google Scholar 

  • Bennet S, Barnes G (2004a) Combined smooth and saccadic ocular pursuit during the transient occlusion of a moving visual object. Exp Brain Res 168:313–321

    Article  Google Scholar 

  • Bennet S, Barnes G (2004b) Predictive smooth ocular pursuit during the transient disappearance of a visual target. J Neurophysiol 92:578–590

    Article  Google Scholar 

  • de Brouwer S, Yuksel D, Blohm G, Missal M, Lefèvre P (2002) What triggers catch-up saccades during visual tracking? J Neurophysiol 87:1646–1650

    PubMed  Google Scholar 

  • Calvo O, Chialvo DR, Eguiluz VM, Mirasso C, Toral R (2004) Anticipated synchronization: a metaphorical linear view. Chaos 14:7–13

    Article  PubMed  Google Scholar 

  • Carey MR, Lisberger SG (2004) Signals that modulate gain control for smooth pursuit eye movements in monkeys. J Neurophysiol 91:623–631

    Article  PubMed  Google Scholar 

  • Carl JR, Gellman RS (1987) Human smooth pursuit: stimulus-dependent responses. J Neurophysiol 57:1446–1463

    PubMed  CAS  Google Scholar 

  • Churchland AK, Lisberger SG (2002) Gain control in human smooth-pursuit eye movements. J Neurophysiol 87:2936–2945

    PubMed  Google Scholar 

  • Churchland MM, Chou I, Lisberger SG (2003) Evidence for object permanence in the smooth-pursuit eye movements of monkeys. J Neurophysiol 90:2205–2218

    Article  PubMed  Google Scholar 

  • Cimponeriu L, Rosenblum M, Pikovsky A (2004) Estimation of delay in coupling from time series. Phys Rev E 70:046–213

    Article  Google Scholar 

  • Ciszak M, Toral R, Mirasso C (2004) Coupling and feedback effects in excitable systems: anticipated synchronization. Modern Phys Lett B 18:1135–1155

    Article  CAS  Google Scholar 

  • Dallos PJ, Jones RW (1963) Learning behaviour of the eye fixation control system. IEEE Trans Acoust 8:218–227

    Google Scholar 

  • Diekmann O, van Gils SA, Lunel SMV, Walther HO (1995) Delay equations. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Eurich CW et al. (2000) Delay adaptation in the nervous system. Neurocomputing 32–33:741–748

    Google Scholar 

  • Ferrera VP, Lisberger SG (1995) Attention and target selection for smooth pursuit eye movements. Neurosci 15:7472–7484

    CAS  Google Scholar 

  • Frank TD, Friedrich R, Beek PJ (2005) Identifying and comparing states of time-delayed systems: phase diagrams and applications to human motor control systems. Phys Lett A 338:74–80

    Article  CAS  Google Scholar 

  • Fukushima K et al. (2002) Coding of smooth eye movements in three-dimensional space by frontal cortex. Nature 419:157–162

    Article  PubMed  CAS  Google Scholar 

  • Glass L (2001) Synchronization and rhythmic processes in physiology. Nature 410:277–284

    Article  PubMed  CAS  Google Scholar 

  • Goldreich D, Krauzlis RJ, Lisberger SG (1992) Effect of changing feedback delay on spontaneous oscillations in smooth pursuit eye movements of monkeys. J Neurophysiol 67:625–638

    PubMed  CAS  Google Scholar 

  • Gopalsamy K (1992) Stability and oscillations in delay differential equations of population dynamics. Kluwer, Dordrecht

    Google Scholar 

  • Gottlieb J, MacAvoy M, Bruce C (1994) Neural responses related to smooth-pursuit eye movements and their correspondence with electrically elicited smooth eye movements in the primate frontal eye field. J Neurophysiol 72:1634–1653

    PubMed  CAS  Google Scholar 

  • Grimm RJ, Nashner LM (1975) Long loop dyscontrol. In: Desmedt JE (ed) Cerebral motor control in man: long loop mechanisms. Progr in Clin Neurophysiol, vol 4. Karger, Basel, pp 70–84

    Google Scholar 

  • Hale JK, Verduyn Lunel S (1993) Introduction to functional differential equations. Springer, Berlin HeidelBerg New York

    Google Scholar 

  • Heywood S, Churcher J (1971) Eye movements and the afterimage—1. Tracking the afterimage. Vision Res 11:1163–1168

    Article  PubMed  CAS  Google Scholar 

  • von Hofsten C (2004) An action perspective on motor development. Trends Cognit Sci 8:266–272

    Article  Google Scholar 

  • Horbelt W, Timmer J, Voss HU (2002) Parameter estimation in nonlinear delayed feedback systems from noisy data. Phys Lett A 299:513–521

    Article  CAS  Google Scholar 

  • Jones M (1976) Time, our lost dimension: toward a new theory of perception, attention, and memory. Psychol Rev 83:323–355

    Article  PubMed  CAS  Google Scholar 

  • Just W, Benner H, Scholl E (2003) Control of chaos by time-delayed feedback: a survey of theoretical and experimental aspects. Adv Solid State Phys 43:589–604

    Google Scholar 

  • Kahlon M, Lisberger SG (2000) Changes in the responses of Purkinje cells in the floccular complex of monkeys after motor learning in smooth pursuit eye movements. J Neurophysiol 84:2945–2960 (2000)

    PubMed  CAS  Google Scholar 

  • Kao GW, Morrow MJ (1994) The relationship of anticipatory smooth eye movement to smooth pursuit initiation. Vision Res 34:3027–3036

    Article  PubMed  CAS  Google Scholar 

  • Kettner RE, Suh M, Davis D, Leung HH (2002) Modeling cerebellar flocculus and paraflocculus involvement in complex predictive smooth eye pursuit in monkeys. Ann N Y Acad Sci 978:445–467

    Article  Google Scholar 

  • Kowler E, Steinman RM (1979) The effect of expectations on slow oculomotor control—I. Periodic target steps. Vision Res 19:619–632

    Article  PubMed  CAS  Google Scholar 

  • Krauzlis RJ (2004) Recasting the smooth pursuit eye movement system. J Neurophysiol 91:591–603

    Article  PubMed  Google Scholar 

  • Krauzlis RJ (2005) The control of voluntary eye movements: new perspectives. Neuroscientist 11:124–137

    Article  PubMed  Google Scholar 

  • Krauzlis RJ, Lisberger SG (1994) A model of visually-guided smooth pursuit eye movements based on behavioral observations. J Comp Neurosci 1:265–283

    Article  CAS  Google Scholar 

  • Lencer R, et al. (2004) Cortical mechanisms of smooth pursuit eye movements with target blanking. An fMRI study. Eur J Neurosci 19:1430–1436

    Article  Google Scholar 

  • Leung HC, Suh M, Kettner RE (2000) Cerebellar flocculus and paraflocculus Purkinje cell activity during circular pursuit in monkey. J Neurophysiol 83:13–30

    PubMed  CAS  Google Scholar 

  • Licklider JCR (1951) A duplex theory of pitch perception. Experimentia 7:128–134

    Article  CAS  Google Scholar 

  • Liston D, Krauzlis RJ (2003) Shared response preparation for pursuit and saccadic eye movements. J Neurosci 23:11,305–11,314 (2003)

  • van Loon EM, Hooge IT, van den Berg AV (2002) The timing of sequences of saccades in visual search. Proc R Soc Lond B Biol Sci 269:1571–1579

    Article  Google Scholar 

  • Madelain L, Krauzlis RJ (2003) Effects of learning on smooth pursuit during transient disappearance of a visual target. J Neurophysiol 90:972–982

    Article  PubMed  Google Scholar 

  • Malek-Zavarei M, Jamshidi M (1987) Time-delay systems: analysis, optimization and applications. North-Holland

  • Martin T, Egly R, Houck JM, Bish JP, Barrera BD, Lee DC, Tesche CD (2005) Chronometric evidence for entrained attention. Percept Psychophys 67:168–184

    PubMed  Google Scholar 

  • Medina JF, Carey MR, Lisberger SG (2005) The representation of time for motor learning. Neuron 45:157–167

    Article  PubMed  CAS  Google Scholar 

  • Mosekilde E, Maistrenko Y, Postnov D (2002) Chaotic synchronization: applications to living systems. World Scientific, Singapore

    Google Scholar 

  • von Norden GK, Mackensen G (1962) Pursuit movements of normal and amblyopic eyes. An electro-ophthalmographic study. I. Physiology of pursuit movements. Am J Ophthalmol 53:325–336

    Google Scholar 

  • Nudelman HB, Herberich KE, Hoyt BD, Rosenfield DB (1989) A neuroscience model of stuttering. J Fluency Disord 14: 399–427

    Article  Google Scholar 

  • Pikovsky A, Rosenblum M, Kurths J (2001) Synchronization—a universal concept in nonlinear science. Cambridge University Press, Cambridge

    Google Scholar 

  • Rashbass C (1961) The relationship between saccadic and smooth tracking eye movements. J Physiol 159:326–338

    PubMed  CAS  Google Scholar 

  • Reddy BAJ, Carpenter RHS (2000) The influence of urgency on decision time. Nat Neurosci 3:827–830

    Article  Google Scholar 

  • Ringach DL (1995) A ’tachometer’ feedback model of smooth pursuit eye movements. Biol Cybern 73:561–568

    PubMed  CAS  Google Scholar 

  • Robinson D (1965) The mechanics of human smooth-pursuit eye movement. J Physiol (London) 180:569–591

    CAS  Google Scholar 

  • Robinson DA (1989) Integrating with neurons. Ann Rev Neurosci 12:33–45

    Article  PubMed  CAS  Google Scholar 

  • Rosenbaum DA (2002) Time, space, and short-term memory. Brain Cognit 48:52–65

    Article  Google Scholar 

  • Siegert S, Friedrich R, Peinke J (1998) Analysis of data sets of stochastic systems. Phys Lett A 243:275–280

    Article  CAS  Google Scholar 

  • Stone LS, Krauzlis RJ (2003) Shared motion signals for human perceptual decisions and oculomotor actions. J Vis 3:725–736

    PubMed  Google Scholar 

  • Stone LS, Lisberger SG (1990a) Visual responses of Purkinje cells in the cerebellar flocculus during smooth-pursuit eye movements in monkeys. I. Simple spikes. J Neurophysiol 63:124–126

    Google Scholar 

  • Stone LS, Lisberger SG (1990b) Visual responses of Purkinje cells in the cerebellar flocculus during smooth-pursuit eye movements in monkeys. II. Complex spikes. J Neurophysiol 63:1262–1275

    PubMed  CAS  Google Scholar 

  • Strogatz SH (2001) Exploring complex networks. Nature 410:268–276

    Article  PubMed  CAS  Google Scholar 

  • Sturm AK, König P (2001) Mechanisms to synchronize neuronal activity. Biol Cybern 84:153–172

    Article  PubMed  CAS  Google Scholar 

  • Suh M, Leung HC, Kettner RE (2000) Cerebellar flocculus and ventral paraflocculus Purkinje cell activity during predictive and visually driven pursuit in monkey. J Neurophysiol 84:1835–1850

    PubMed  CAS  Google Scholar 

  • Tang S, Liu JM (2003) Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers. Phys Rev Lett 90:194–101

    Google Scholar 

  • Todorov E (2004) Optimality principles in sensorimotor control. Nat Neurosci 7:907–915

    Article  PubMed  CAS  Google Scholar 

  • Toral R et al. (2003) Characterization of the anticipated synchronization regime in the coupled FitzHugh-Nagumo model for neurons. Physica A 325:192–198

    Article  Google Scholar 

  • Varela F, Lachaux JP, Rodriguez E, Martinerie J (2001) The brainweb: phase synchronization and large–scale networks. Nat Rev Neurosci 2:229–239

    Article  PubMed  CAS  Google Scholar 

  • Voss HU (2000) Anticipating chaotic synchronization. Phys Rev E 61:5115–5119

    Article  CAS  Google Scholar 

  • Voss HU (2001a) A backward time shift filter for nonlinear delayed-feedback systems. Phys Lett A 279:207–214

    Article  CAS  Google Scholar 

  • Voss HU (2001b) Dynamic long-term anticipation of chaotic states. Phys Rev Lett 87:014–102

    Google Scholar 

  • Voss HU (2002a) Fast response by synchronization. In: Hoffmann KH (ed) 2nd Caesarium—coupling of biological and electronic systems. Springer, Berlin Heidelberg New York, pp 119–126

    Google Scholar 

  • Voss HU (2002b) Real-time anticipation of chaotic states of an electronic circuit. Int J Bifurcat Chaos 12:1619–1625

    Article  Google Scholar 

  • Voss HU (2003) Synchronization of reconstructed dynamical systems. Chaos 13:327–334

    Article  PubMed  CAS  Google Scholar 

  • Voss H, Kurths J (1997) Reconstruction of nonlinear time delay models from data by the use of optimal transformations. Phys Lett A 234:336–344

    Article  CAS  Google Scholar 

  • Wells SG, Barnes GR (1998) Fast, anticipatory smooth-pursuit eye movements appear to depend on a short-term store. Exp Brain Res 120:129–133

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Citigroup Biomedical Imaging Center, Weill Medical College of Cornell University, 1300 York Avenue, P.O. Box 234, New York, NY, 10021, USA

    Henning U. Voss

  2. Sackler Institute for Developmental Psychobiology, Weill Medical College of Cornell University, New York, NY, USA

    Bruce D. McCandliss

  3. Brain Trauma Foundation and Department of Neurological Surgery, Weill Medical College of Cornell University, New York, NY, USA

    Jamshid Ghajar

  4. Department of Neurological Surgery, Weill Medical College of Cornell University, New York, NY, USA

    Minah Suh

Authors
  1. Henning U. Voss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bruce D. McCandliss
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jamshid Ghajar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Minah Suh
    View author publications

    You can also search for this author in PubMed Google Scholar

Consortia

(CNRC-TBI)

Corresponding author

Correspondence to Henning U. Voss.

Additional information

Cognitive and Neurobiological Research Consortium in Traumatic Brain Injury (CNRC-TBI).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voss, H.U., McCandliss, B.D., Ghajar, J. et al. A quantitative synchronization model for smooth pursuit target tracking. Biol Cybern 96, 309–322 (2007). https://doi.org/10.1007/s00422-006-0116-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00422-006-0116-2

Keywords

Search

Navigation