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Functional Analysis of Pupil Nonlinearities

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Neurological Control Systems

Abstract

In attempting to describe mathematically or to characterize the black box input-output behavior of the human pupil light reflex, we investigated three different basic formulations of the system. The Wiener G-functionals, a recently developed mathematical characterization of systems, will be discussed in detail but we will first briefly present two other, more standard approaches to the problem, describing functions and heuristic modeling [30]. Neglecting the experimental details — some of which will be presented later — let us assume that the experimenter has available transducers capable of generating input light stimuli as wave forms of arbitrary time dependence and monitoring an analog voltage proportional to the output, which is pupil area of a normal awake human subject.

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References and Further Reading

  1. Baker, F. H.: Pupillary response to double pulse stimulation: A study of nonlinearity in the human pupil system. J. Opt. Soc. Am. 53: 1430 (1963).

    Article  Google Scholar 

  2. Baker, F., Emmerich, G. W., Tyler, V., and Stark, L.: Unpublished experiments (1957).

    Google Scholar 

  3. Bower, J. L., and Schultheiss, P. M.: Introduction to the Design of Servomechanisms, Wiley, New York (1958).

    Google Scholar 

  4. Boynton, R. M.: Some temporal factors in vision. In: Sensory Communication, W. A. Rosenblith, ed., Massachusetts Institute of Technology, Cambridge, Mass. (1961), pp. 739–756.

    Google Scholar 

  5. Campbell, F. W., and Robson, J. G.: Unpublished experiments (1958).

    Google Scholar 

  6. Campbell, F. W.,and Whiteside, T. C. D.: Induced pupillary oscillations. Brit. J. Ophthalmol. 34: 180–189 (1950).

    Google Scholar 

  7. Clynes, M.: Computer dynamic analysis of the pupil light reflex: A unidirectional rate sensitive sensor. Third International Conference on Medical Electronics, London (1960).

    Google Scholar 

  8. Clynes, M.: Unidirectional rate sensitivity: A biocybernetic law of reflex and humoral systems as physiologic channels of control and communication. Ann. N. Y. Acad. Sci., Pavlovian Conference Monograph on Higher Nervous Activity (1961).

    Google Scholar 

  9. Clynes, M.: The non-linear biological dynamics of unidirectional rate sensitivity illustrated by analog computer analysis, pupillary reflex to light and sound, and heart rate behavior. Ann. N. Y. Acad. Sci. 98: 806–845 (1962), Article 4.

    Google Scholar 

  10. Cole, K. S.: Dynamic electrical characteristics of the squid axon membrane. Arch. Sci. Physiol. 3: 253–258 (1949).

    Google Scholar 

  11. Cornsweet, T. N.: Determination of the stimuli for involuntary drifts and saccadic eye movements. J. Opt. Soc. Am. 46: 987–994 (1956).

    Article  Google Scholar 

  12. Davenport, W. B., Jr., and Root, W. L.: An Introduction to the Theory of Random Signals and Noise, McGraw-Hill, New York (1958).

    MATH  Google Scholar 

  13. Elkind, J. I.: Characteristics of simple manual control systems. Lincoln Laboratory Tech. Rept., M.I.T., Number III: 1–145 (1956).

    Google Scholar 

  14. Evans, W. R.: Control System Dynamics, McGraw-Hill, New York (1954).

    Google Scholar 

  15. Hartline, H. K.: A quantitative and descriptive study of the electrical response to illumination of the arthropod eye. Am. J. Physiol. 83: 466–483 (1928).

    Google Scholar 

  16. James, H. M., Nichols, V. B., and Phillips, R. S.: Theory of Servomechanisms, McGraw-Hill, New York (1947).

    Google Scholar 

  17. Katznelson, J.: Synthesis of nonlinear filters. Sc. D. Thesis, Elect. Eng. Dept., Massachusetts Institute of Technology, Cambridge, Mass. (1963).

    Google Scholar 

  18. Lee, Y. W.: Statistical theory of nonlinear systems. Class Notes for Massachusetts Institute of Technology Elect. Eng. Course 6. 572.

    Google Scholar 

  19. Lee, Y. W.: Statistical Theory of Communication, Wiley, New York (1960).

    MATH  Google Scholar 

  20. Lee, Y. W., and Schetzen, M.: Measurement of the kernels of a nonlinear system by cross correlation. Quart. Prog. Rept., Research Laboratory of Electronics, M.I.T. 60: 118–130 (1961).

    Google Scholar 

  21. Lowenstein, O. L.: Pupillary reflex shapes and topical clinical diagnosis. Neurology 5: 631–644 (1955).

    Google Scholar 

  22. Lowenstein, O., and Givner, I.: Pupillary reflex to darkness. Arch. Ophthalmol. 30: 603–609 (1943).

    Article  Google Scholar 

  23. Lowenstein, O., and Loewenfeld, I. E.: Role of sympathetic and parasympathetic systems in reflex dilatation of the pupil. Arch. Neurol. Psychiat. 64: 313–340 (1950).

    Google Scholar 

  24. MacColl, L.: Fundamental Theory of Servomechanisms, Van Nostrand, Princeton, N. J. (1945), p. 107.

    Google Scholar 

  25. Marmont, G.: Electrode clamp for squid axon. J. Cellular Comp. Physiol. 34: 351 (1949).

    Article  Google Scholar 

  26. Mason, S. J., and Zimmermann, H.: Electronic Circuits, Signals, and Systems, Wiley, New York (1960).

    Google Scholar 

  27. McCulloch, W. S.: Why the mind is in the head. In: Cerebral Mechanisms in Behavior, The Hixon Symposium, Wiley, New York (1951), pp. 42–57.

    Google Scholar 

  28. McRuer, D. T., and Krendel, E. S.: Dynamic response of human operators. WADC Tech. Report 56: 524 (1957).

    Google Scholar 

  29. Newton, G. C., Gould, L. A., and Kaiser, J. F.: Analytical Design of Linear Feedback Controls, Wiley, New York (1957).

    Google Scholar 

  30. Sandberg, A.A., and Stark, L.: Wiener G-function analysis as an approach to nonlinear characteristics of human pupil light reflex. IEEE Trans. Biomedical Engineering (1966).

    Google Scholar 

  31. Schetzen, M.: Measurement of the kernels of a nonlinear system by cross correlation with Gaussian non-white inputs. Quart. Prog. Rept., Research Laboratory of Electronics, M.I.T. 63: 113–117 (1961).

    Google Scholar 

  32. Schultheiss, P. M., and Bower, J. L.: An Introduction to the Design of Servomechanisms, Wiley, New York (1958), 500 pp.

    Google Scholar 

  33. Stanten, S. F., and Stark, L.: A biological stochastic process (pupil noise). Transactions of the 4th Colloquium on the Pupil, May 11–12, 1966.

    Google Scholar 

  34. Stark, L.: Stability, oscillations, and noise in the human pupil servomechanism. Proc. Inst. Radio Eng. 47: 1925–1939 (1959).

    Google Scholar 

  35. Stark, L.: Oscillations of a neurological servomechanism predicted by the Nyquist stability criterion. In: Selected Papers in Biophysics, Yale University Press, New Haven, Conn. (1960).

    Google Scholar 

  36. Stark, L.: Environmental clamping of biological systems. Quart. Prog. Rept., Research Laboratory of Electronics, M.I.T. 66: 229–230 (1961).

    Google Scholar 

  37. Stark, L.: Biological rhythms, noise, and asymmetry in the pupil-retinal control system. Ann. N.Y. Acad. Sci. 98: 1096–1108 (1962), Article 4.

    Google Scholar 

  38. Stark, L., and Baker, F.: Stability and oscillations in a neurological servomechanism. J. Neurophysiol. 22: 156–164 (1959).

    Google Scholar 

  39. Stark, L., Campbell, F. W., and Atwood, J.: Pupil unrest: An example of noise in a biological servomechanism. Nature (London) 182: 857–858 (1958).

    Article  Google Scholar 

  40. Stark, L., and Cornsweet, T. N.: Testing a servoanalytic hypothesis for pupil oscillations. Science 127: 588 (1958).

    Article  Google Scholar 

  41. Stark, L., fida, M., and Willis, P. A.: Dynamic characteristics of the motor coordination system in man. Quart. Prog. Rept., Research Laboratory of Electronics, M.I.T. 60: 229 (1961).

    Google Scholar 

  42. Stark, L., and Kuhl, F.: Analysis of pupil response and noise. Quart. Prog. Rept., Research Laboratory of Electronics, M.I.T. 62: 255–262 (1961).

    Google Scholar 

  43. Stark, L., Redhead, J., and Payne, R. C.: Asymmetrical behavior in the pupil system. Quart. Prog. Rept., Research Laboratory of Electronics, M.I.T. 61: 223–230 (1961).

    Google Scholar 

  44. Stark, L., and Sherman, P. M.: A servoanalytic study of the consensual pupil reflex to light. J. Neurophysiol. 20: 17–26 (1957).

    Google Scholar 

  45. Stark, L., Vossius, G., and Young, L. R.: Predictive control of eye tracking movements. IRE Trans. Human Factors Electron. HFE-3(2): 52–57 (1962).

    Google Scholar 

  46. Stegemann, J.: On the influence of sinusoidal variations in brightness upon pupillary size. Pflügers Arch. Ges. Physiol. 264: 113–122 (1957).

    Article  Google Scholar 

  47. Stern, H. J.: Simple method for early diagnosis of abnormalities of pupillary reaction. Brit. J. Ophthalmol. 28: 276–278 (1944).

    Google Scholar 

  48. Talbot, S. A.: Pupillography and pupillary transient. Doctoral Dissertation, Dept. of Physics, Harvard University, Cambridge, Mass. (1938).

    Google Scholar 

  49. Tustin, A.: The nature of the operator’s response in manual control and its implications for controller design. J. IEE 94(11A), No. 2 (1947).

    Google Scholar 

  50. Van Der Tweel, L.H., and Denior Van Der Gon, J. J.: The light reflex of the normal pupil of man. Acta Physiol. Pharmacol. Neerl. 8: 69 (1959), Fig. 15.

    Google Scholar 

  51. Wiener, N.: Cybernetics, Wiley, New York (1948).

    Google Scholar 

  52. Wiener, N.: Nonlinear Problems in Random Theory, The Technology Press, Massachusetts Institute of Technology, and Wiley, New York (1958).

    Google Scholar 

  53. Wybar, K. C.: Ocular manifestations of disseminated sclerosis. Proc. Roy. Soc. Med. 45: 315–320 (1952).

    Google Scholar 

  54. Young, F. A., and Biersdorf, W. R.: Pupillary contraction and dilatation in light and darkness. J. Comp. Physiol. Psychol. 47: 264–268 (1954).

    Article  Google Scholar 

  55. Young, L. R.: A sampled data model for eye tracking movements. Doctoral Dissertation, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Mass. (1962).

    Google Scholar 

  56. Young, L. R., Green, D. M., Elkind, J. L., and Kelly, J. A.: Adaptive characteristics of manual tracking. Fourth National Symposium on Human Factors in Electronics, Washington, D.C. (1963).

    Google Scholar 

  57. Young, L. R., and Stark, L.: Variable feedback experiments supporting a discrete model for eye tracking movements. IEEE Trans. Human Factors Electron. HFE-4(1): 38–51 (1963).

    Google Scholar 

  58. Blackman, R. B., and Tukey, J. W.: The Measurement of Power Spectra, Dover, New York (1959).

    MATH  Google Scholar 

  59. Edwards, L. F.: Concise Anatomy, McGraw-Hill, New York (1956), Chaps. 53 and 54.

    Google Scholar 

  60. Laning, J. H., Jr., andBattin, R. H.: Random Processes in Automatic Control, McGraw-Hill, New York (1956).

    Google Scholar 

  61. Parzen, E.: Stochastic Processes, Holden Day, San Francisco (1962).

    MATH  Google Scholar 

  62. Sandberg, A. A.: Sinusoidal light stimulation of the human pupil servomechanism. Quart. Prog. Rept., Research Laboratory of Electronics, M.I.T. 74: 261–265 (1964).

    Google Scholar 

  63. Stark, L., Sandberg, A. A., Stanten, S. F., Willis, P. A., and Dickson, J. F.: On-line digital computers used in biological experiments and modeling. Ann. N.Y. Acad. Sci. 115: 738–762 (1964).

    MATH  Google Scholar 

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Authors and Affiliations

  1. University of California, Berkeley, USA

    Lawrence Stark M.D. (Professor of Physiological Optics)

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  1. Lawrence Stark M.D.
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© 1968 Plenum Press

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Stark, L. (1968). Functional Analysis of Pupil Nonlinearities. In: Neurological Control Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-0706-8_7

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  • DOI: https://doi.org/10.1007/978-1-4684-0706-8_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-0708-2

  • Online ISBN: 978-1-4684-0706-8

  • eBook Packages: Springer Book Archive

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