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Minimal dynamical description of eye movements

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Abstract

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.

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References

  1. D.L. Sparks, Nat. Rev. Neurosci. 3, 952 (2002)

    Article  Google Scholar 

  2. M. Rolfs, Vision Res. 49, 2415 (2009)

    Article  Google Scholar 

  3. S. Martinez-Conde, J. Otero-Millan, S.L. Macknik, Nat. Rev. Neurosci. 14, 83 (2013)

    Article  Google Scholar 

  4. J. Otero-Millan, X.G. Troncoso, S.L. Macknik, I. Serrano-Pedraza, S. Martinez-Conde, J. Vision 8, 1 (2008)

    Article  Google Scholar 

  5. J. Otero-Millan, S.L. Macknik, A. Serra, R.J. Leigh, S. Martinez-Conde, Ann. N.Y. Acad. Sci. 1233, 107 (2011)

    Article  ADS  Google Scholar 

  6. L.J. Croner, E. Kaplan, Vision Res. 35, 7 (1995)

    Article  Google Scholar 

  7. J. Otero-Millan, S.L. Macknik, R.E. Langston, S. Martinez-Conde, Proc. Natl. Acad. Sci. USA 110, 6175 (2013)

    Article  ADS  Google Scholar 

  8. S. Martinez-Conde, S.L. Macknik, X.G. Troncoso, T.A. Dyar, Neuron 49, 297 (2006)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  10. M.B. McCamy, S.L. Macknik, S. Martinez-Conde, J. Physiol. 592, 4381 (2014)

    Article  Google Scholar 

  11. F.M. Costela, M.B. McCamy, S.L. Macknik, J. Otero-Millan, S. Martinez-Conde, PeerJ 1, e119 (2013)

    Article  Google Scholar 

  12. S. Martinez-Conde, S.L. Macknik, J. Vision 8, 1 (2008)

    Google Scholar 

  13. S. Martinez Conde, S.L. Macknik, D.H. Hubel, Nat. Rev. Neurosci. 5, 229 (2004)

    Article  Google Scholar 

  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)

  15. R. Engbert, J. Neurosci. 32, 8035 (2012)

    Article  Google Scholar 

  16. O. Komogortsev, C. Holland, S. Jayarathna, A. Karpov, ACM Trans. Appl. Percept. 10, 27 (2013)

    Article  Google Scholar 

  17. I.B. Wijayasinghe, Coordination and control of human eye and head: a classical mechanics approach, Ph.D. thesis, 2013

  18. B.K. Ghosh, I.B. Wijayasinghe, S.D. Kahagalage, IEEE Access 2, 316 (2014)

    Article  Google Scholar 

  19. W. Zhou, X. Chen, J. Enderle, Int. J. Neural Syst. 19, 309 (2009)

    Article  Google Scholar 

  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)

  21. J.D. Enderle, D.A. Sierra, Int. J. Neural Syst. 23, 1350002 (2013)

    Article  Google Scholar 

  22. M. Bettenbühl, C. Paladini, K. Mergenthaler, R. Kliegl, R. Engbert, M. Holschneider, J. Eye Mov. Res. 3, 1 (2010)

    Google Scholar 

  23. J.A. Del Punta, M.J. Ambrosio, G. Gasaneo, S.A. Zaytsev, L.U. Ancarani, J. Math. Phys. 55, 052101 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  24. R. Engbert, R. Kliegl, Vision Res. 43, 1035 (2003)

    Article  Google Scholar 

  25. A.T. Bahill, M.R. Clark, L. Stark, Math. Biosci. 24, 191 (1975)

    Article  Google Scholar 

  26. L. Matin, E. Matin, D.G. Pearce, Vision Res. 10, 837 (1970)

    Article  Google Scholar 

  27. J.-R. Liang, S. Moshel, A.Z. Zivotofsky, A. Caspi, R. Engbert, R. Kliegl, S. Havlin, Phys. Rev. E 71, 031909 (2005)

    Article  ADS  Google Scholar 

  28. K. Mergenthaler, R. Engbert, Phys. Rev. Lett. 98, 138104 (2007)

    Article  ADS  Google Scholar 

  29. R.H.S. Carpenter, Movements of the eyes, 2nd. edn. (Pion, London, 1988)

  30. N.M. Blachman, Information and Control 1, 56 (1957)

    Article  MathSciNet  Google Scholar 

  31. G. Rawitscher, J. Liss, Am. J. Phys. 79, 417 (2011)

    Article  ADS  Google Scholar 

  32. D.M. Mitnik, F.D. Colavecchia, G. Gasaneo, J.M. Randazzo, Comp. Phys. Commun. 182, 1145 (2011)

    Article  ADS  Google Scholar 

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Correspondence to Gustavo Gasaneo.

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Specht, J.I., Dimieri, L., Urdapilleta, E. et al. Minimal dynamical description of eye movements. Eur. Phys. J. B 90, 25 (2017). https://doi.org/10.1140/epjb/e2016-70472-0

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  • DOI: https://doi.org/10.1140/epjb/e2016-70472-0

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