Skip to main content

Three-neuron model of compensatory eye movements in response to vestibular stimulation

Abstract

Generation of compensatory eye movements which arise in response to vestibular stimulation is described in the framework of a three-neuron pathway, by which the vestibulo-ocular reflex is conducted. A mathematical model of the reflex based on the literature is presented in the paper. All parameters and variables of the model proposed have a clear physiological meaning. Incompleteness of the vestibulo-ocular interconnections described in the literature is shown. For the particular case of head rotation about the vertical axis, an experiment is proposed and performed; the results of the experiment allow one to identify unknown parameters of the model. The torsional vestibulo-ocular reflex readaptation process to usual earth gravity conditions after long-term orbital flight was experimentally investigated.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    V. V. Alexandrov, T. B. Alexandrova, T. G. Astakhova, E. Soto, and A. G. Yakushev, “Equations of dynamics of the cupulo-endolymphatic system of vestibular canals,” Differ. Uravn., 35, No. 4, 71–77 (1999).

    Google Scholar 

  2. 2.

    E. V. Alexandrovich, Mathematical Model of Eye Muscle Apparatus Functioning [in Russian], Ph.D. Thesis, Moscow State University, 1994.

  3. 3.

    D. E. Angelaki, A. M. Green, and J. D. Dickman, “Differential sensorimotor processing of vestibulo-ocular signals during rotation and translation,” J. Neuroscience, 21, No. 11, 3968–3985 (2001).

    Google Scholar 

  4. 4.

    O. Bergamin and D. Straumann, “Three-dimensional binocular kinematics of torsionnal vestibular nystagmus during convergence on head-fixed targets in humans,” J. Neurophysiol., 86, No. 1, 113–122 (2001).

    Google Scholar 

  5. 5.

    A. Brodal, O. Pompeiano, and F. Walberg, in: The Vestibular Nuclei and Their Connections, Anatomy and Functional Correlations, Charles C. Thomas, ed., Springfield, Illinois (1962).

    Google Scholar 

  6. 6.

    M. Egerstedt and C. F. Martin, “A control theoretic model of the muscular actions in human head-eye coordination,” J. Math. Systems Estim. Control, 8, No. 2, 234–248 (1998).

    MathSciNet  Google Scholar 

  7. 7.

    R. J. Jacobs, “Visual resolution and contour interaction in the fovea and periphery,” Vision Research, 19, No. 11, 1187–1195 (1979).

    Article  Google Scholar 

  8. 8.

    A. V. Kondrachuk and M. D. Ross, “Modeling of the otolith structure behavior under static loads (inertial forces and endolymphatic pressure),” Abstracts of the 20th Annual Midwinter Meeting, Association for Research in Otolaryngology, St. Petersburg, Florida, USA, 1997, p. 154.

  9. 9.

    L. N. Kornilova, V. Grigorova, and G. Bodo, “Vestibular function and sensory interaction in space flight,” J. Vest. Res., 3, 219–230 (1993).

    Google Scholar 

  10. 10.

    R. Lorente de No, “Vestibulo-ocular reflex arc,” Arch. Neurol. Psychiat., 30, 245–291 (1933).

    Google Scholar 

  11. 11.

    G. Metta and P. Fitzpatrick, “Better vision through experimental manipulation,” in: EPSRC/BBSRC Int. Workshop, Biologically-Inspired Robotics: The Legasy of W. Grey Walter, Bristol, UK, August 2002.

  12. 12.

    E. A. Muratova and A. G. Yakushev, “Mathematical model of vestibular-ocular reaction of a human on a rotation about a vertical axis,” in: Proc. VIIth Russian Conf. Biomech, Nigny Novgorod, May 24–28, 2004 [in Russian].

  13. 13.

    C. M. Oman, E. N. Marcus, and I. S. Curthoys, “The influence of semicircular canal morphology on endolymph flow dynamics: An anatomically descriptive mathematical model,” Acta Otolaryngol., 103, 1–13 (1987).

    Google Scholar 

  14. 14.

    C. M. Oman and L. R. Young, “The physiological range of pressure difference and cupula deflections in the human semicircular duct,” Acta Otolaryngol., 74, 324–331 (1972).

    Google Scholar 

  15. 15.

    I. V. Orlov, Vestibular Function [in Russian], Nauka, St. Petersburg (1998).

    Google Scholar 

  16. 16.

    A. Pellionisz, “Tensorial aspects of the multidimensional approach to the vestibulo-oculomotor reflex and gaze,” in: A. Berthoz and G. Melvill-Jones, eds., Reviews of Oculomotor Research-I. Adaptive Mechanisms in Gaze Control, Elsevier, Amsterdam (1985), pp. 281–296.

    Google Scholar 

  17. 17.

    A. Pellionisz, “Tensor network theory and its application in computer modeling of the metaorganization of sensorimotor hierarchies of gaze,” in: Proc. “Neuronal Networks for Computing,” AIP 151, American Institute of Physics, New York (1986), pp. 339–344.

    Google Scholar 

  18. 18.

    S. V. Petukhov, Biomechanics, Bionics, and Symmetry [in Russian], Nauka, Moscow (1981).

    MATH  Google Scholar 

  19. 19.

    R. D. Rabbitt and E. R. Damiano, “A hydroelastic model of macromechanics in the endolymphatic vestibular canal,” J. Fluid Mech., 238, 337–369 (1992).

    MATH  Article  Google Scholar 

  20. 20.

    V. A. Sadovnichiy, V. V. Alexandrov, T. B. Alexandrova, S. S. Lemak, and A. M. Shkel, “Vestibular function in the extremal conditions of personal navigation and its correction,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 4, 25–35 (2003).

  21. 21.

    I. Yu. Sarkisov, “Reaction of hydrodynamically interacted semicircular canals on adequate stimulus,” Probl. Kosmich. Biol., 31, 714 (1975).

    Google Scholar 

  22. 22.

    A. A. Shipov, A. V. Kondrachuk, and S. P. Sirenko, Biomechanics of Vestibular Apparatus [in Russian], Slovo, Moscow (1997).

    Google Scholar 

  23. 23.

    E. Soto, A. Flores, and R. Vega, “NMDA mediated potentiation of inner ear afferent synapse,” Neuroreport, 5, 1963–1965 (1994).

    Article  Google Scholar 

  24. 24.

    W. Steinhausen, “Über die Beobachtung der Cupula in den Bogengangsampullen des Labirinthes des lebenden Hechts,” Phlug. Arch., 232, 500–512 (1933).

    Article  Google Scholar 

  25. 25.

    J. Szentagothai, “The elementary vestibulo-ocular reflex arc,” J. Neurophysiol., 13, 395–407 (1950).

    Google Scholar 

  26. 26.

    J. Szentagothai, Die Rolle der einzelnen Labyrithrezeptoren bei der Orientation von Augen und Kopf in Raume, Akademiai Kiado, Budapest (1952).

    Google Scholar 

  27. 27.

    V. I. Usachev, “Interaction of vestibular, optic, and proprioceptive sensor systems in the process of rotational nystagmus,” Sensornye Sistemy, 9, No. 4, 42–47 (1995).

    Google Scholar 

  28. 28.

    A. J. Van-Egmond, J. J. Groen, and L. B. W. Jongkees, “The mechanics of the semicircular canal,” J. Physiol., 110, 1–17 (1949).

    Google Scholar 

  29. 29.

    Ya. F. Vinnikov, O. G. Gazenko, and L. K. Titova, Receptor of Gravity [in Russian], Nauka, Leningrad (1971).

    Google Scholar 

  30. 30.

    H. de Vries, “The mechanics of the labyrinth otoliths,” Acta Otolaryngol., 38, No. 3, 262–273 (1950).

    Google Scholar 

  31. 31.

    A. L. Yarbus, The Role of Eye Movements in the Vision Process [in Russian], Nauka, Moscow (1965).

    Google Scholar 

Download references

Author information

Affiliations

Authors

Additional information

__________

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 8, pp. 175–193, 2005.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Muratova, E.A., Yakushev, A.G. Three-neuron model of compensatory eye movements in response to vestibular stimulation. J Math Sci 147, 6668–6681 (2007). https://doi.org/10.1007/s10958-007-0504-8

Download citation

Keywords

  • Hair Cell
  • Semicircular Canal
  • Vestibular Nucleus
  • Extraocular Muscle
  • Vestibular Stimulation