Advertisement

Annals of Biomedical Engineering

, Volume 23, Issue 4, pp 375–387 | Cite as

Estimation of autonomic nervous activity using the inverse dynamic model of the pupil muscle plant

  • Shiro Usui
  • Yutaka Hirata
Starkfest: Vision & Movement in Man and Machines Modeling Motor Control Processes

Abstract

In order to elucidate the mechanism of the pupillary control system, the internal property of the pupillary muscle plant, as well as the autonomic nervous input to the muscle plant, must be analyzed. In this study, we approach the problem first by constructing a new homeomorphic biomechanical model for the human pupillary muscle plant (forward dynamic model). We showed that the model is able not only to reproduce various experimental results that exhibit various nonlinearities but also to explain how such nonlinear responses are generated in terms of the internal property of the model. Then, we contrive a possible method to estimate the autonomic nervous input to the muscle plant. This method utilizes the inverse dynamic model of the pupillary muscle plant so that the autonomic nervous input can be estimated from the pupillary response. We applied this method to the experimental step responses, and showed that the estimated neural input indicates characteristics quite similar to the results of the physiological experiment. Last, we discuss the origin of the pupillary escape and capture as well as the sustained and transient components of the pupillary response, based on the analysis of the forward and/or inverse dynamic model.

Keywords

Pupil Light reflex Biomechanical model Inverse dynamic model Pupillary escape Pupillary capture 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Clynes, M. Uniderectional rate sensitivity.Ann. N.Y. Acad. Sci. 92:946–969, 1961.PubMedCrossRefGoogle Scholar
  2. 2.
    Dennison, L. A. Mathematical Model for the Motor Activity of the Cat Iris. Worchester: Worcester Polytechnic Institute, Ph.D. Thesis, 1967.Google Scholar
  3. 3.
    Fletcher, R., and M. Powell. A rapidly convergent descent method for minimization.Computer J. 6:163–168, 1963.Google Scholar
  4. 4.
    Hannaford, B., W. S. Kim, S. H. Lee, and L. Stark. Neurological control of head movements: inverse modeling and electromyographic evidence.Math. Bio. Sci. 78:159–178, 1986.CrossRefGoogle Scholar
  5. 5.
    Hansmann, D Human pupillary mechanics: physiology and control. Berkeley: University of California, Ph.D. Thesis, 1972.Google Scholar
  6. 6.
    Hirata, Y., and S. Usui. Nonlinear dynamical model for human pupillary muscle plant.IEICE J77-DII. 1:170–180, 1994.Google Scholar
  7. 7.
    Inoue, T. The response of rabbit ciliary nerve to luminance intensity.Brain Res. 201:206–209, 1980.PubMedCrossRefGoogle Scholar
  8. 8.
    Inoue, T., and T. Kiribuchi. Cortical and subcortical pathway for pupillary reactions in rabbits.Jpn. J. Ophthalmol. 29:63–70, 1985.PubMedGoogle Scholar
  9. 9.
    Kohn, M., and M. Clynes. Color dynamics of the pupil.Ann. N.Y. Acad. Sci. 15:931–950, 1969.CrossRefGoogle Scholar
  10. 10.
    Krenz, W., and L. Stark. Neuronal population model for the pupil-size effect.Math. Biosci. 68:247–265, 1983.CrossRefGoogle Scholar
  11. 11.
    Krenz, W., M. Robin, S. Barez, and L. Stark. Neurophysiological model of the normal and abnormal human pupil.IEEE Trans. Biomed. Eng. BME-32:817–825, 1985.CrossRefGoogle Scholar
  12. 12.
    Krenz, W., and L. Stark. System model for pupil size effect. Feedback model.Biol. Cybern. 51:391–397, 1985.PubMedCrossRefGoogle Scholar
  13. 13.
    Loewenfeld, I. Central inhibitory influences upon pupillary movements.Neuro-ophthalmol. 3-3:217–225, 1986.Google Scholar
  14. 14.
    Loewenfeld, I.The Pupil—Anatomy, Physiology and Clinical Applications. Iowa: Iowa State University Press, 1993. 1590 pp.Google Scholar
  15. 15.
    Meiss, A. Some mechanical properties of cat intestinal muscle.Am. J. Physiol. 220:2000–2007, 1971.PubMedGoogle Scholar
  16. 16.
    Nishida, I., and H. Okada. The activity of the pupilloconstrictory centers.Jpn. J. Physiol. 10:64–72, 1960.Google Scholar
  17. 17.
    Sandberg, A., and L. Stark. Wiener G-functional analysis as an approach to non-linear characteristics of human pupil light reflex.Brain Res. 11:194–211, 1968.PubMedCrossRefGoogle Scholar
  18. 18.
    Semmlow, J., and L. Stark. Simulation of a biomechanical model of the human pupil.Math. Biosci. 11:109–128, 1971.CrossRefGoogle Scholar
  19. 19.
    Semmlow, J., and D. Chen. A simulation model of the human pupil light reflex.Math. Biol. 11:109–128, 1977.CrossRefGoogle Scholar
  20. 20.
    Stark L., and P. Sherman A servoanalytic study of consensual pupil reflex to light.J. Neurophysiol. 20:17–26, 1957.PubMedGoogle Scholar
  21. 21.
    Stark, L., and F. Baker. Stability and oscillations in a neurological servomechanism.J. Neurophysiol. 22:156–164, 1959.PubMedGoogle Scholar
  22. 22.
    Sun, F., P., Tauchi, and L. Stark. Dynamic pupillary response controlled by the pupil size effect.Exp. Neurol. 82:313–324, 1983.PubMedCrossRefGoogle Scholar
  23. 23.
    Terdiman, J., J. Smith, and L. Stark. Dynamic analysis of the pupil with light and electrical stimulation.IEEE Trans. Syst. Man, Cybern SMC-1:239–251, 1971.CrossRefGoogle Scholar
  24. 24.
    Thompson, S. The pupil. In:Adler's Physiology of the Eye (ninth edition), edited by W. M. Hart, Jr. St. Louis: Mosby Year Book, 1992, pp. 412–441.Google Scholar
  25. 25.
    Tsujisawa, I., K. Mukuno, and S. Ishikawa. The pupillary change in the course of brain death.Auton. Nerv. Syst. 26:63–70, 1989.Google Scholar
  26. 26.
    Usui, S., and L. Stark. A model for nonlinear stochastic behavior of the pupil.Biol. Cybern. 45:13–21, 1982.PubMedCrossRefGoogle Scholar
  27. 27.
    Usui, S., R. Matsuda, H. Ikeno, and H. Miyachi. Continuous system simulator (SIGMA) on personal computer.Proc. of JSST Int. Conf. 135–140, 1986.Google Scholar
  28. 28.
    Usui, S., Y. Hirata, and S. Nagaoka. Pupillary light response during a parabolic flight.Proc. of 40th Int. Cong. Aviation Space Med. 141, 1992.Google Scholar
  29. 29.
    Watanabe, A., and L. Stark. Kernel method for nonlinear analysis: identification of a biological control system.Math. Biosci. 27:99–108, 1975.CrossRefGoogle Scholar
  30. 30.
    Watanabe, I., and K. Niimi.Illustration Ophthalmology. Tokyo: Bunkoudon, 1987, 370 pp.Google Scholar
  31. 31.
    Yoshitomi, T., Y. Ito, and H. Inomata. Autonomic innervations of the dog and human iris sphincter and dilator muscles.J. Eye (Atarashii Ganka). 4-4:531–533, 1987.Google Scholar
  32. 32.
    Young, L., B., Han, and P. Wu. Transient and sustained components of the pupillary responses evoked by luminance and color.Vision Res. 33:437–446, 1993.PubMedCrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 1995

Authors and Affiliations

  • Shiro Usui
    • 1
  • Yutaka Hirata
    • 1
  1. 1.Department of Information and Computer SciencesToyohashi University of TechnologyToyahashiJapan

Personalised recommendations