Abstract

The work here described attempts to locate anatomically and to clarify the nature of dominant nonlinear operators in the human pupillary system for reflex to light. For this work an apparatus was constructed capable of stimulating both eyes simultaneously and recording the pupil diameter of one eye. Short light flashes were used as the input stimulus, and the maximum change in pupil diameter was chosen as the amplitude of response. Results of the experiments (1) confirmed the loglike dependence of response on input-light-flash energy, (2) demonstrated a dependence of response amplitude on duration between pulses in the double-pulse stimulating situation, (3) established the equivalence of response to double-pulse inputs in the cases of monocular and binocular double-pulse presentations, and (4) determined for the monocular and binocular cases the dependence of response amplitude on the amplitude of the second pulse in a double-pulse presentation. The similarity of results of the monocular and binocular cases suggests that the dominating nonlinear operation occurs after the summation of signals from the two eyes. The dependence of response amplitude on duration between pulses is discussed in terms of its implication of central mechanisms.

© 1963 Optical Society of America

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References

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  1. L. Stark and P. M. Sherman, J. Neurophysiol. 20, 17 (1957).
  2. J. Stegemann, Arch. Ges. Physiol. 264, 113 (1957).
    [CrossRef]
  3. M. Clynes, Ann. N. Y. Acad. Sci. 92, 946 (1961).
    [CrossRef] [PubMed]
  4. L. Stark and F. H. Baker, J. Neurophysiol. 22, 156 (1959).
    [PubMed]
  5. Note added in proof:L. Stark, Proc. Inst. Radio Engrs. 47, 1925 (1959).
    [PubMed]
  6. L. H. van der Tweel and J. J. D. van der Gon, Acta Physiol. Pharmacol. Neerl. 8, 52 (1959).
  7. S. A. Talbot, Ph.D. thesis, Department of Physics, Harvard, January1938.
  8. Strictly speaking, a physical system is driven. by a forcing function acting in time. It is only with acknowledged liberality that we adopt the convention callingenergy=∫0τF(t)dtthe driving function for input flux, F1 confined to sufficiently short durations, τ.
  9. G. Hakerem and S. Sutton, paper presented at the Second Pupil Colloquium, May 1962, MIT, Cambridge, Massachusetts.
  10. K. Weiler, Untersuchungen der Pupille und der Irisbewegungen beim Menschen (Julius Springer-Verlag, Berlin, 1910).
    [CrossRef]
  11. S. H. Bartley, J. Exptl. Psychol. 32, 110 (1943).
  12. L. Bellarminow, Arch. Ges. Physiol. 37 (1885).
    [CrossRef]
  13. H. K. Hartline, J. Cellular Comp. Physiol. 5, 229 (1934).
  14. J. C. Eccles and J. W. Magladerly, J. Physiol. (London) 90, 31 (1937).
  15. D. Whitteridge, J. Physiol. (London) 89, 99 (1937).
  16. I. H. Wagman and W. S. Battersby, Am. J. Physiol. 197, 1237 (1959).

1961 (1)

M. Clynes, Ann. N. Y. Acad. Sci. 92, 946 (1961).
[CrossRef] [PubMed]

1959 (4)

L. Stark and F. H. Baker, J. Neurophysiol. 22, 156 (1959).
[PubMed]

Note added in proof:L. Stark, Proc. Inst. Radio Engrs. 47, 1925 (1959).
[PubMed]

L. H. van der Tweel and J. J. D. van der Gon, Acta Physiol. Pharmacol. Neerl. 8, 52 (1959).

I. H. Wagman and W. S. Battersby, Am. J. Physiol. 197, 1237 (1959).

1957 (2)

L. Stark and P. M. Sherman, J. Neurophysiol. 20, 17 (1957).

J. Stegemann, Arch. Ges. Physiol. 264, 113 (1957).
[CrossRef]

1943 (1)

S. H. Bartley, J. Exptl. Psychol. 32, 110 (1943).

1937 (2)

J. C. Eccles and J. W. Magladerly, J. Physiol. (London) 90, 31 (1937).

D. Whitteridge, J. Physiol. (London) 89, 99 (1937).

1934 (1)

H. K. Hartline, J. Cellular Comp. Physiol. 5, 229 (1934).

1885 (1)

L. Bellarminow, Arch. Ges. Physiol. 37 (1885).
[CrossRef]

Baker, F. H.

L. Stark and F. H. Baker, J. Neurophysiol. 22, 156 (1959).
[PubMed]

Bartley, S. H.

S. H. Bartley, J. Exptl. Psychol. 32, 110 (1943).

Battersby, W. S.

I. H. Wagman and W. S. Battersby, Am. J. Physiol. 197, 1237 (1959).

Bellarminow, L.

L. Bellarminow, Arch. Ges. Physiol. 37 (1885).
[CrossRef]

Clynes, M.

M. Clynes, Ann. N. Y. Acad. Sci. 92, 946 (1961).
[CrossRef] [PubMed]

Eccles, J. C.

J. C. Eccles and J. W. Magladerly, J. Physiol. (London) 90, 31 (1937).

Hakerem, G.

G. Hakerem and S. Sutton, paper presented at the Second Pupil Colloquium, May 1962, MIT, Cambridge, Massachusetts.

Hartline, H. K.

H. K. Hartline, J. Cellular Comp. Physiol. 5, 229 (1934).

Magladerly, J. W.

J. C. Eccles and J. W. Magladerly, J. Physiol. (London) 90, 31 (1937).

Sherman, P. M.

L. Stark and P. M. Sherman, J. Neurophysiol. 20, 17 (1957).

Stark, L.

L. Stark and F. H. Baker, J. Neurophysiol. 22, 156 (1959).
[PubMed]

Note added in proof:L. Stark, Proc. Inst. Radio Engrs. 47, 1925 (1959).
[PubMed]

L. Stark and P. M. Sherman, J. Neurophysiol. 20, 17 (1957).

Stegemann, J.

J. Stegemann, Arch. Ges. Physiol. 264, 113 (1957).
[CrossRef]

Sutton, S.

G. Hakerem and S. Sutton, paper presented at the Second Pupil Colloquium, May 1962, MIT, Cambridge, Massachusetts.

Talbot, S. A.

S. A. Talbot, Ph.D. thesis, Department of Physics, Harvard, January1938.

van der Gon, J. J. D.

L. H. van der Tweel and J. J. D. van der Gon, Acta Physiol. Pharmacol. Neerl. 8, 52 (1959).

van der Tweel, L. H.

L. H. van der Tweel and J. J. D. van der Gon, Acta Physiol. Pharmacol. Neerl. 8, 52 (1959).

Wagman, I. H.

I. H. Wagman and W. S. Battersby, Am. J. Physiol. 197, 1237 (1959).

Weiler, K.

K. Weiler, Untersuchungen der Pupille und der Irisbewegungen beim Menschen (Julius Springer-Verlag, Berlin, 1910).
[CrossRef]

Whitteridge, D.

D. Whitteridge, J. Physiol. (London) 89, 99 (1937).

Acta Physiol. Pharmacol. Neerl. (1)

L. H. van der Tweel and J. J. D. van der Gon, Acta Physiol. Pharmacol. Neerl. 8, 52 (1959).

Am. J. Physiol. (1)

I. H. Wagman and W. S. Battersby, Am. J. Physiol. 197, 1237 (1959).

Ann. N. Y. Acad. Sci. (1)

M. Clynes, Ann. N. Y. Acad. Sci. 92, 946 (1961).
[CrossRef] [PubMed]

Arch. Ges. Physiol. (2)

J. Stegemann, Arch. Ges. Physiol. 264, 113 (1957).
[CrossRef]

L. Bellarminow, Arch. Ges. Physiol. 37 (1885).
[CrossRef]

J. Cellular Comp. Physiol. (1)

H. K. Hartline, J. Cellular Comp. Physiol. 5, 229 (1934).

J. Exptl. Psychol. (1)

S. H. Bartley, J. Exptl. Psychol. 32, 110 (1943).

J. Neurophysiol. (2)

L. Stark and P. M. Sherman, J. Neurophysiol. 20, 17 (1957).

L. Stark and F. H. Baker, J. Neurophysiol. 22, 156 (1959).
[PubMed]

J. Physiol. (London) (2)

J. C. Eccles and J. W. Magladerly, J. Physiol. (London) 90, 31 (1937).

D. Whitteridge, J. Physiol. (London) 89, 99 (1937).

Proc. Inst. Radio Engrs. (1)

Note added in proof:L. Stark, Proc. Inst. Radio Engrs. 47, 1925 (1959).
[PubMed]

Other (4)

S. A. Talbot, Ph.D. thesis, Department of Physics, Harvard, January1938.

Strictly speaking, a physical system is driven. by a forcing function acting in time. It is only with acknowledged liberality that we adopt the convention callingenergy=∫0τF(t)dtthe driving function for input flux, F1 confined to sufficiently short durations, τ.

G. Hakerem and S. Sutton, paper presented at the Second Pupil Colloquium, May 1962, MIT, Cambridge, Massachusetts.

K. Weiler, Untersuchungen der Pupille und der Irisbewegungen beim Menschen (Julius Springer-Verlag, Berlin, 1910).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of pupillometer used to stimulate the retina and record pupil area from one eye.

Fig. 2
Fig. 2

Dependence of the response as measured by maximum change in pupil diameter on the product of input flux amplitude and duration. Longest duration used was 10 msec; shortest was 0.1 msec.

Fig. 3
Fig. 3

Diagrammatic representation of the response to a double-pulse stimulus conceived as the summation of responses to two separate pulses. The function h(t) represents the increment in response due to the second pulse. A function r(t) is defined comparing h(t) with response to the second pulse given alone. In what follows we are only concerned with this comparison taken at the time of the response maximum, t m .

Fig. 4
Fig. 4

Typical pupil response to a light pulse of 10 msec duration and 10−2 mm amplitude.

Fig. 5
Fig. 5

(a) Response to a double pulse, both pulses presented to the same eye. Pulses were of 10 msec duration and 10−2 mm amplitude. (b) Response to a double pulse, second pulse presented to the contralateral eye. First pulse same as in 5(a); second pulse adjusted in amplitude to give same response when presented alone as response to first pulse.

Fig. 6
Fig. 6

Amplitude of response as measured by maximum diameter change to double pulse presented to one eye as function of duration between pulses. Pulse duration was 10 msec; amplitude was 10−2 mlm. Data represented by circles, and solid circle on ordinate indicates response to single pulse. Upper curve represents response in linear system which had a response to a single pulse similar to the pupil system. Inset gives data from separate experiment to determine maximum of functional relationship.

Fig. 7
Fig. 7

Data from an experiment similar to that illustrated in Fig. 6, but in which the second pulse presented to the contralateral eye. Response to second pulse presented alone approximately equal to response to first pulse.

Fig. 8
Fig. 8

Dependence of response, measured as maximum diameter change, on amplitude of second pulse, both pulses presented to the same eye. Intermediate value of F2 produced response when presented alone equal to response to first pulse. Data presented for two interpulse durations.

Fig. 9
Fig. 9

Data from experiment similar to that illustrated in Fig. 8, but in which second pulse presented to contralateral eye.

Tables (1)

Tables Icon

Table I Results from double-pulse experiment monocular and binocular inputs.

Equations (4)

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h ( t ) = Δ D F 2 ( t ) ,
r ( t ) = h ( t ) / Δ D F 2 ( t ) ,
r ( t ) = 1.
energy = 0 τ F ( t ) d t