Minimal dynamical description of eye movements

  • Juan I. Specht
  • Leonardo Dimieri
  • Eugenio Urdapilleta
  • Gustavo Gasaneo
Regular Article


In this paper we have addressed the question of whether a simple set of functions being the solution of a model, namely the damped harmonic oscillator with a general driving force, can satisfactorily describe data corresponding to ocular movements produced during a visual search task. Taking advantage of its mathematical tractability, we first focused on the simplest driving force compatible to the experimental data, a step-like activation. Under this hypothesis we were able to further simplify the system, once data from several experiments were fitted, producing an essentially parameter-free model that we plan to use in future applications. To increase the quality of the description of individual movements, we expanded the complexity in the forcing term and solved the inverse problem by using a proper mathematical formalism. Furthermore, additional terms, those arising from ocular drift and tremor, may be included within the same mathematical approach.


Statistical and Nonlinear Physics 


  1. 1.
    D.L. Sparks, Nat. Rev. Neurosci. 3, 952 (2002)CrossRefGoogle Scholar
  2. 2.
    M. Rolfs, Vision Res. 49, 2415 (2009)CrossRefGoogle Scholar
  3. 3.
    S. Martinez-Conde, J. Otero-Millan, S.L. Macknik, Nat. Rev. Neurosci. 14, 83 (2013)CrossRefGoogle Scholar
  4. 4.
    J. Otero-Millan, X.G. Troncoso, S.L. Macknik, I. Serrano-Pedraza, S. Martinez-Conde, J. Vision 8, 1 (2008)CrossRefGoogle Scholar
  5. 5.
    J. Otero-Millan, S.L. Macknik, A. Serra, R.J. Leigh, S. Martinez-Conde, Ann. N.Y. Acad. Sci. 1233, 107 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    L.J. Croner, E. Kaplan, Vision Res. 35, 7 (1995)CrossRefGoogle Scholar
  7. 7.
    J. Otero-Millan, S.L. Macknik, R.E. Langston, S. Martinez-Conde, Proc. Natl. Acad. Sci. USA 110, 6175 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    S. Martinez-Conde, S.L. Macknik, X.G. Troncoso, T.A. Dyar, Neuron 49, 297 (2006)CrossRefGoogle Scholar
  9. 9.
    M.B. McCamy, J. Otero-Millan, S.L. Macknik, Y. Yang, X.G. Troncoso, S.M. Baer, S.M. Crook, S. Martinez-Conde, J. Neurosci. 32, 9194 (2012)CrossRefGoogle Scholar
  10. 10.
    M.B. McCamy, S.L. Macknik, S. Martinez-Conde, J. Physiol. 592, 4381 (2014)CrossRefGoogle Scholar
  11. 11.
    F.M. Costela, M.B. McCamy, S.L. Macknik, J. Otero-Millan, S. Martinez-Conde, PeerJ 1, e119 (2013)CrossRefGoogle Scholar
  12. 12.
    S. Martinez-Conde, S.L. Macknik, J. Vision 8, 1 (2008)Google Scholar
  13. 13.
    S. Martinez Conde, S.L. Macknik, D.H. Hubel, Nat. Rev. Neurosci. 5, 229 (2004)CrossRefGoogle Scholar
  14. 14.
    C.F. Martin, L. Schovanec, in Dynamical Systems, Control, Coding, Computer Vision, edited by G. Picci, D.S. Gilliam, Progress in Systems and Control Theory 25, 173 (1999)Google Scholar
  15. 15.
    R. Engbert, J. Neurosci. 32, 8035 (2012)CrossRefGoogle Scholar
  16. 16.
    O. Komogortsev, C. Holland, S. Jayarathna, A. Karpov, ACM Trans. Appl. Percept. 10, 27 (2013)CrossRefGoogle Scholar
  17. 17.
    I.B. Wijayasinghe, Coordination and control of human eye and head: a classical mechanics approach, Ph.D. thesis, 2013Google Scholar
  18. 18.
    B.K. Ghosh, I.B. Wijayasinghe, S.D. Kahagalage, IEEE Access 2, 316 (2014)CrossRefGoogle Scholar
  19. 19.
    W. Zhou, X. Chen, J. Enderle, Int. J. Neural Syst. 19, 309 (2009)CrossRefGoogle Scholar
  20. 20.
    J.D. Enderle, W. Zhou, Models of Horizontal Eye Movements. Part 2: A 3rd-Order Linear Saccade Model (Morgan and Claypool Publishers, San Rafael, CA, 2010)Google Scholar
  21. 21.
    J.D. Enderle, D.A. Sierra, Int. J. Neural Syst. 23, 1350002 (2013)CrossRefGoogle Scholar
  22. 22.
    M. Bettenbühl, C. Paladini, K. Mergenthaler, R. Kliegl, R. Engbert, M. Holschneider, J. Eye Mov. Res. 3, 1 (2010)Google Scholar
  23. 23.
    J.A. Del Punta, M.J. Ambrosio, G. Gasaneo, S.A. Zaytsev, L.U. Ancarani, J. Math. Phys. 55, 052101 (2014)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    R. Engbert, R. Kliegl, Vision Res. 43, 1035 (2003)CrossRefGoogle Scholar
  25. 25.
    A.T. Bahill, M.R. Clark, L. Stark, Math. Biosci. 24, 191 (1975)CrossRefGoogle Scholar
  26. 26.
    L. Matin, E. Matin, D.G. Pearce, Vision Res. 10, 837 (1970)CrossRefGoogle Scholar
  27. 27.
    J.-R. Liang, S. Moshel, A.Z. Zivotofsky, A. Caspi, R. Engbert, R. Kliegl, S. Havlin, Phys. Rev. E 71, 031909 (2005)ADSCrossRefGoogle Scholar
  28. 28.
    K. Mergenthaler, R. Engbert, Phys. Rev. Lett. 98, 138104 (2007)ADSCrossRefGoogle Scholar
  29. 29.
    R.H.S. Carpenter, Movements of the eyes, 2nd. edn. (Pion, London, 1988)Google Scholar
  30. 30.
    N.M. Blachman, Information and Control 1, 56 (1957)MathSciNetCrossRefGoogle Scholar
  31. 31.
    G. Rawitscher, J. Liss, Am. J. Phys. 79, 417 (2011)ADSCrossRefGoogle Scholar
  32. 32.
    D.M. Mitnik, F.D. Colavecchia, G. Gasaneo, J.M. Randazzo, Comp. Phys. Commun. 182, 1145 (2011)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Juan I. Specht
    • 1
  • Leonardo Dimieri
    • 2
    • 4
  • Eugenio Urdapilleta
    • 3
    • 4
  • Gustavo Gasaneo
    • 1
    • 4
  1. 1.Departamento de Física, Universidad Nacional del Sur – IFISURBuenos AiresArgentina
  2. 2.Instituto de Investigaciones en Ingeniería Eléctrica – IIIEBuenos AiresArgentina
  3. 3.División de Física Estadística e Interdisciplinaria, Centro Atómico Bariloche, S. C. de Bariloche (8400)Río NegroArgentina
  4. 4.Consejo Nacional de Investigaciones Científicas y Técnicas, CONICETBuenos AiresArgentina

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