XVII.
G.
M.
R.
P.
A.
J.
L. Stark
F. H. Baker
Julia R. Bristol
H. T. Hermann
J. C. Houk, Jr.
E. Mudama
F. Navas
A.
ACCOMMODATION
NEUROLOGY
I. Sobel
S. F. Stanten
Y. Takahashi
E. Van Horn
P. A. Willis
S. Yasui
L. R. Young
P. Nelson
Okajima
C. Payne
R. Samson
A. Sandberg
Simpson
TRACKING
Accommodation is most often seen in association with convergence,
and it is well
known that a variety of clues, particularly binocular fusion, drives convergence.
there a monocular accommodation reflex, and if so, what is its stimulus?
Is
It is impor-
tant to try to understand such a physiological error mechanism - a widely distributed,
unlearned, involuntary mechanism present in restricted monocular viewing without complex perceptual clues -
which might drive the lens control system.
It is also of interest
to understand the mechanism for sensing not only the magnitude of the error signal but
its directional sense because blur is rather similar in both directions of error.
Several suggestions,
have been put forward.
with rather incomplete experimental evidence to support them,
These include astigmatic asymmetry and spherical abberation,I
chromatic abberation and the Stiles-Crawford effect,
ments (monocular parallax).2
secondary to small fixation move-
There is also a trial-and-error mechanism in the 2-cps
oscillation of the lens which could act as a phase-sensitive detector.
1.
3
Experiment
The experimental arrangement used in our tracking experiment is
Fig. XVII-1,
described in
which is essentially the same as Campbell and Westheimer's.1
The sub-
ject looks at a target through a convergent lens L 2 that is placed so that its second principal focal plane is at the plane of the pupil of the subject (second principal focal plane
This geometrical disposition eliminates the dependence of the size of the target on its position. The luminance of the target is also kept unchanged by means of lens
L 1 that collimates the illuminating light beam. The subject's eye is instilled with I per
cent homatropine, which paralyzes the ciliary muscle; thus he can see the target clearly
method).
only when its distance from the eye is at a certain value.
ments both for drugged and undrugged subjects.)
(We have carried out experi-
The target is moved back and forth
by successive steps of various amplitudes (measured in diopters) of either positive or
This research is supported in part by the U.S. Public Health Service (B-3055,
B-3090), the Office of Naval Research (Nonr-1841 (70)), the Air Force (AF33(616)-7588,
AF49(638)-1130), and the Army Chemical Corps (DA-18-108-405-Cml-942); and in part
by the National Science Foundation (Grant G-16526).
QPR No. 67
205
(XVII.
NEUROLOGY)
D
L1
T
L2
S
M
H
A
P
+E
Fig. XVII-1.
-E
Scheme of the tracking experiment.
Lens L
makes light beam from
is placed so that its second princi1
the source S parallel, and lens L 2
pal focus is on the pupil of the subject's eye. The target T is a pin
and is moved back and forth by a servomechanism.
negative sign which are chosen with equal probability but quite randomly. As the target
moves from the original position of clear vision, the subject is told to bring the target
back into focus by turning the knob of a potentiometer. The target position is servocontrolled so that it is proportional to the sum of the random-step input and the potentiometer output.
The random-step input and the voltage of the potentiometer are recorded on a Sanborn
pen recorder. An example of such a recording is shown in Fig. XVII-2.
Campbell and Westheimer studied the initial direction in which the subject moved
the target in tracking to determine whether or not a directionally sensitive error detector is present in the subject's lens control system.
They tried this tracking experiment
for four subjects and reported that all of them could track the target movement correctly
after a few trials under normal conditions. One subject experienced difficulty when
monochromatic light was used, but soon learned to overcome this and thereafter tracked
without error. When spherical abberation is removed by means of an annular pupil,
Campbell and Westheimer's four subjects were "not always correct" in their tracking
task. This error followed completely correct tracking with a normal pupil, perhaps
after some learning. Fincham, however, showed no effect of an annular pupil.
Our experimental evidence indicates that even with a normal pupil, no error-free
initial tracking or learning of tracking occurs. We feel that the main difference between
QPR No. 67
206
NEUROLOGY)
(XVII.
LT
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t Iv %
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i i
Record of random-step function (upper traces) and the
output of subject-operated potentiometer (lower traces).
Campbell and Westheimer's and our results is
that we controlled the randomness
of the target more carefully.
2.
Experimental Findings
Figure XVII-3 shows one of the results of our experiment. The number of failed
initial-tracking moves in each successive 10 trials is plotted against the number of succeeding sets of 10 trials.
There is no obvious decreasing initial-error tendency, in
contrast with the almost perfect responses mentioned by Campbell and Westheimer.
We have performed the experiment for several subjects with their eyes either homFixing the subject's eye lens by the drug does not always seem to
be necessary as long as the subject turns the potentiometer quickly after target moves
atropinized or not.
QPR No. 67
207
6
4-
2
O
10
1
2
Fig. XVII-4.
QPR
No. 67
25
30
35
Number of erroneous initial tracking attempts (ordinate) in successive
10 trials vs sequence of sets of 10 trials (abscissa).
Fig. XVII-3.
0
20
15
3
4
5
6
7
2
3
4
5
6
Probability density of successive correct trackings. (a) Data
obtained for the first 100 trials. (b) Data for last 100 trials
of 290 trials. The solid line is the theoretical probability distribution for purely random events.
208
7
(XVII.
NEUROLOGY)
because the time required for the subject to decide which way he should turn the potentiometer is obviously much shorter than the time lag of accommodation.
As a matter of
fact, the results are not very different in either case.
Quantitatively, to confirm the randomness of our results, the distribution of the number of intervals between successive failed trackings was investigated.
Figure XVII-4
shows the distributions obtained for the first and the last hundered trials in a total of
290 trials.
It is clear that there is no significant difference between the two distribu-
tions.
By assuming that the occurrence of false tracking is random (Poisson distribution)
and that its average occurrence is a, the probability that the time interval between two
successive occurrences of the false tracking is T is given by
P(T) : ae
-aT
The straight lines in Fig. XVII-4 represent this equation.
The coincidence of the data
to this line suggests that the tracking occurred randomly.
Three necessary features in the control of the experimental stimulus condition must
be stressed.
First, the size and intensity of the target should be constant as it is moved
nearer and farther away.
This can be accomplished by placing a second principal focus
Second, lateral movement of the target
of the target image at the plane of the pupil.
will occur if any of the optics are slightly off axis.
lateral directions with near and far movement.
The target will move in opposite
As soon as this happens,
a subject may
8
SUBJECT : J.B.
EYE
: NORMAL
TARGET : BLACK PIN
6
INPUT
: SUCCESSIVE STEPS OF 1 D
4
2
0
5
10
15
20
25
30
Fig. XVII- 5. Number of erroneous initial tracking in successive 10 trials vs sequence
of set of 10 trials. After 160 trials the subject apparently noticed either
lateral movement or size change resulting from imperfect arrangement
of optics. Ordinate and abscissa scales same as in Fig. XVII-3.
QPR No. 67
209
(XVII.
NEUROLOGY)
quickly learn to appreciate this clue and to track a random target correctly. The experiments shown in Fig. XVII-5 furnish an example. In the seventeenth group of 10 trials,
the subject evidently quickly learned to track correctly, and on inquiry was about to point
out a lateral movement present as a clue. Different published experiments may be judged
on the following basis: the least demonstrated ability to track a random target should be
the most accurate and carefully controlled experiment, since any error in apparatus
will provide unwanted clues. The third important factor of control is the randomness
of input step changes of target position.
3.
Discussion
Astigmatic affects can certainly be used as clues for voluntary accommodative
tracking. In addition to a usual asymmetrical blur that is due to common astigmatic
faults in most persons' lenses, 4 these effects can be exaggerated with the use of cylindrical lenses. 5 However, we feel that it is not a good candidate for the physiological
sensor, since it is such a variable factor, and possibly is absent in many normal persons. Its effect is, of course, quite dependent upon image characteristics. A bright
self-illuminated target will accentuate this effect, whereas an opaque, less brightly lit
target such as we have used will decrease this effect. Fincham has shown that small
targets often remove whatever clues have been previously used for accommodative
responses.
Fixation movement was found to be necessary by Fincham 2 for four of the subjects
who were experienced enough to subjectively control their eye fixation. The effect of
small fixation movements would be to increase the contrast of the image's light distribution on the retina because the spatial differentiation that occurs with movement counteracts the smear of the image's light distribution (produced by convolving the object's
light distribution with the quasi-Gaussian spread function of the optics of the eye6). A
fixation movement also has the effect of removing adaptation to a stationary target which
8
6
4
2
GREEN
0
Fig. XVII-6.
QPR No. 67
W]lH
ITE
100
CGREEN1
200
WHITE
300
400
Record of random target motion and the tracking by a subject whose eye
is not drugged. Ordinate, number of errors in 10 successive trials;
abscissa, number of trials. Change of target lighting from white to monochromatic has no obvious effect.
210
(XVII.
NEUROLOGY)
7
causes disappearance of a stabilized image. ' 8
The lens control system is remarkably insensitive to chromatic abberation. The
inability of our subjects to track in initial direction better than randomly was unaffected
It thus
by their having or not having chromatic abberation information (Fig. XVII-6).
seems doubtful whether or not chromatic abberation can be the physiological stimulus
to an accommodative reflex.
The 2-cps oscillation might act as a trial-and-error phase-sensitive direction device
for the accommodative stimulus.9
In operating conditions of low-amplitude error signal,
as in a stationary state driven by noise alone, the lens servo is
undamped,1
0
and 2-cps oscillations are produced.
unstable or highly
Nonlinearities stabilize the system,
These oscillations are just below the correct ampli-
however, for large input signals.10
tude range for threshold sensitivity.
11
However, it still requires an effective utiliza-
tion of the appreciated blur at a level of 0.2 diopter which is below amplitudes of 0. 3
diopter, where we have shown that no nonrandom tracking occurs if careful attention
is paid to the three experimental control conditions.
2
consciously and be unable to use it to track.
4.
It is possible to appreciate blur
Conclusion
We began these experiments to confirm published suggestions concerning the physiological image operating mechanism which acts as a stimulus to the accommodative
We were interested in obtaining evidence to decide between an odd error
function such as chromatic abberation and a phase-sensitive detection scheme such as
the 2-cps oscillation as a trial-and-error method. After several runs of tracking experresponse.
iments of the type described here,
with careful re-evaluation of published data,
we have
arrived at the tentative position that no physiological mechanism for monocularly driving
accommodation has been clearly demonstrated to act at an unlearned reflex-stimulus
a variety of perceptual clues voluntarily learned or
appreciated may be used to track targets or correct for blur. However, if care is taken
to eliminate gross perceptual clues, such as lateral movements of a target in off-axis
optical system, size and intensity clues often present in experimental systems conlevel of neural function.
However,
structed without use of the second principal focus method, and nonrandom predictable
target movements, and furthermore, if no additional clues are supplied by cylindrical
lenses emphasizing astigmatic asymmetries,
brightly illuminated targets emphasizing
other lens asymmetries, and large target movements, then the ability to track targets
seems to be rather meager and, in fact, closely approaches random tracking.
L. Stark, Y.
Takahashi
References
1. F. W. Campbell and G. Westheimer, Factors influencing
responses of the human eye, J. Opt. Soc. Am. 49, 568-571 (1959).
QPR No. 67
211
accommodation
(XVII.
NEUROLOGY)
2. E.
Opthalmol.
F. Fincham, The accommodation
35, 381-393 (1951).
3.
F. W. Campbell and G. Westheimer,
dation, J. Opt. Soc. Am. 48, 669 (1958).
reflex
and its
stimulus,
British
J.
Significance of fluctuations of accommo-
4. R. E. Bannon, H. Cooley, and R. Textor, The stigmatoscopy method of determining the binocular refractory status, Am. J. Opt. Arch. Am. Acad. Opt. 27, 8 (1950).
5. We wish to thank Professor G. Westheimer for calling our attention to reference 4.
6. E. L. O'Neill, Selected Topics in Optics and Communication Theory, ITEK Corporation reprint (September, 1958).
7. R. W. Ditchburn and B. L. Ginsborg, Vision with stabilized retinal image,
Nature 170, 36-37 (1952).
8. L. Riggs, F. Ratliff, J. Cornsweet, and T. Cornsweet, The disappearance of
steadily fixated visual test objects, J. Opt. Soc. Am. 43, 495-501, (1953).
9. F. W. Campbell, G. Westheimer, and J. G. Robson, Fluctuations of accommodation under steady viewing condition, J. Physiol. 145, 579-594 (1959).
10. L. Stark, Y. Takahashi, and G. Zames, The dynamics of the human lens system, Quarterly Progress Report No. 66, Research Laboratory of Electronics, M.I.T.,
July 15, 1962, pp. 337-351.
11. F. W. Campbell and G. Westheimer, Sensitivity of the eye to difference in
focus, J. Physiol. 143, 18 (1958).
B.
DEPENDENCE OF ACCURACY OF EYE MOVEMENTS ON PREDICTION
Measurements of the horizontal eye movements of subjects following square-wave
patterns of target position reveal that after several cycles the subjects begin to predict
the target movement. The normal minimum reaction time of approximately 130 msec
is decreased and often becomes negative during such prediction of the time, direction,
and magnitude of the next target step.
1
In observing the rapid saccadic responses to a square wave of target position it was
noticed that, for predictions, the amplitude of the initial saccadic response was often
in error by a considerable angle, and a large corrective saccade was required later to
position the eye on the new target angle. This error was in contrast to the accuracy of
the responses that occurred after a normal reaction time, for which the amplitude of the
initial saccade was generally accurate within better than 5 per cent of the angle
of the target step.
Examples of these responses are shown in Fig. XVII-7a.
Notice that
the accurate corrective saccade does not occur until 130 msec after the target has
reached its new position.
One interpretation of this observation is that in the nonpre-
dictive case the input to the control system is the new target position, whereas in the
predictive saccade case the input is the remembered target position, and the accuracy
of this remembered position is low.
To test this observation in a controlled manner,
QPR No. 67
212
a series of experiments were run
(XVII. NEUROLOGY)
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A
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RESPONSE TIME (M SEC.)
.
200
---
(a) Normal and predictive saccadic responses.
of initial error vs response time.
with constant-amplitude 0.4-cps square waves -
(b)
Percentage
a target function that has yielded
Figure XVII-7b
a high percentage of predictions, as well as normal delayed responses.
is a typical plot of the percentage of error of the initial saccadic movement versus
response time.
The frequency of errors greater than 5 per cent increases sharply for
predictive movements (X = 21.9, p<0.
00 1
). Of particular interest are saccadic responses
occurring from 0-130 msec after the target step.
Since this is less than a minimum
reaction time, the decision to make the saccadic jump must have been initiated before the
target step, and its intended magnitude based on the remembered angle of the alternate
QPR No. 67
213
(XVII.
NEUROLOGY)
target position.
Before the response actually took place, however, the target switched
to its new position and visual information was available to modify the amplitude of the
intended saccade. The data indicate that no such modification takes place. The frequency of percentage errors greater than 5 per cent in response is significantly higher
for all responses occurring earlier than 130 msec before the target step than for those
occurring after 130 msec (X2= 7.08, p<0.01).
The significance of this result is that once
a decision to make a saccadic movement has been initiated, no new visual information
can affect the course of this movement. 2
L. R. Young, L. Stark
References
1. L. Stark, G. Vossius, and L. R. Young, Predictive control of eye movements,
Trans. IRE, PGHFE (in press).
2. L. R. Young, A Sampled Data Model for Eye Tracking Movements, Sc.D.
Thesis, Department of Aeronautics and Astronautics, M.I.T., May 11, 1962.
C.
PHOTOTUBE GLASSES FOR MEASURING EYE MOVEMENTS
The eye-position monitor described previously
1
is of limited use for some investigations because of the slow rise time of its Clairex CdS photosensors. This problem
is further complicated by the influence of the intensity of illumination on the frequency
response.
To avoid these effects, a new eye-position monitor has been built which
employs RCA 1P42 miniature vacuum phototubes.
This monitor operates on the scleral reflection principle, as does the Clairex device,
but has an added degree of flexibility afforded by the adjustable optometrist's eye-glass
frames on which the elements are mounted. This frame serves as a support for the
1P42
-
5 MEG
+
OUTPUT TO HIGH Z
DIFFERENTIAL
AMPLIFIER
I
-1P42
GE224
22.5V
------
I
4.7 MEG
AT 1.5V
GE224
Fig. XVII-8.
QPR No. 67
Schematic diagram of phototube glasses.
214
Oeye
dOeye
dt
~mtr :
:::
i
--ipn~
i~h -r
ir
:
9
eye
=~i
:ii~i~f~
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I
+I
i
rte
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i ---~....~
-'-.. ......
.,. _ -r:; ~t:~flf
CfdIi
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= .~
i
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rl
F:
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-'~i~-~-~-~-~~
~
ri
R
r ~ ni h ?~if~t-irt-Lt'~i- ~ r
i~:
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=I
d e ye
i,t
r
3
' r -~Y=~:i'
-w
dt
"rrr- ; rr;
m~~~~ tt
3wllu;rr:
...
:. 3
r fC
-lirf:: tt:
i
TIME-sec
(b)
Fig. XVII-9.
QPR No. 67
Recordings of eye movement taken with phototube glasses.
(a) Optokinetic nystagmus response to target moving laterally
in visual field, with derivative of eye motion. (b) Response
to ±50 steps, with derivative of eye motion.
215
(XVII.
NEUROLOGY)
two GE 224 bulbs and 1P42 phototubes and may be easily adjusted to fit any subject.
Figure XVII-8 shows the schematic diagram of these glasses.
Since the output level from the phototubes is quite low, special care must be exercised to avoid noise pickup.
At present, the peak-to-peak amplitude of 60-cps pickup
has been reduced to a level corresponding to an eye-deflection arc of less than 20',
a
quite satisfactory level.
is
Calibration
shifts his
another
gaze
made
from
fixation
point.
the
by recording
one
of the monitor
a
fixation point through
small
The
output
calibration is
linear
known
as the
visual
of eye
for an angle
subject
to
angle
deflection
of ±60.
Figure XVII-9
Fig. XVII-9a
shows
taneous
the
the
subject
record
shows
subject
samples
is
response
of the
exhibiting
to
time
of two records
50
optokinetic
steps as
derivative
taken
by these
position
is
glasses.
Figure
nystagmus.
recorded
of eye
with these
also
XVII-9b
glasses.
shown
In
in
A
simul-
each
figure.
G. P.
Nelson, L. Stark, L. R.
Young
References
1. L. Stark and A. Sandberg, A simple instrument for measuring eye movements,
Quarterly Progress Report No. 62, Research Laboratory of Electronics, M.I.T.,
July 15, 1961, pp. 268-270.
D.
FINGER TREMOR
For
some time finger
tremor
has
been studied
with the
hopes
of applying
the information so obtained to the analysis of the nature of the control system for
human movement and for possible use as a diagnostic test.
Some examples of finger
tremor in Parkinson's disease have been previously recorded. 1
Recent published reports
have suggested that the ballistocardiographic impulsive force plays a role in the generation of physiological finger tremor.2
We have developed an apparatus for the measurement of finger tremor which uses
the optical lever principle and is
schematic
sensitive and reliable.
diagram of this apparatus,
obtained with a micrometer movement.
Figure XVII-10 shows a
and Fig. XVII-11 shows a calibration curve
Some examples of data obtained under different
weight and tension conditions are shown in Figs. XVII-12 and XVII-13.
that there is some variability from subject to subject.
in altering the spectra of the tremor.
It can be seen
Of interest is the effect of load
Voluntary tension seems to yield a greater low-
frequency portion of the spectra, and weighting the finger appears to sharpen the spectra.
QPR No. 67
216
REFLECTING MIRRORS
-
-
FINGER POSITION
-Q-
'
LIGHT BEAM
7
/I
LIGHT
LIGHT SOURCE
I
SLIT LENS
/ I
/
/ I
7
(/T
12 .6 V
Fig. XVII-10.
Schematic diagram of optical tremor measuring device.
3.4 3.3
3.2
I---
3.1
3.0
2.92.82.7-
Fig.
XVII-11
2.62.5
0.5
I
1.0
1.5
2.0
2.5
TARGET EDGE MOTION (MM)
Calibration curve of optical tremor measuring device.
QPR No. 67
217
41
I
~
I-_
I r-
I
~ffitL~
(b)
(C)
20mm/sec
(i)
Fig. XVII-12.
QPR No. 67
Finger tremor from Subject A with finger (a) relaxed, (b) tense,
and (c) weighted (50 grams); Subject B with finger (d) relaxed,
(e) tense, and (f) weighted (50 grams); and Subject C with finger
(g) relaxed, (h) tense, and (i) weighted (50 grams).
218
--
I
a~ I
-
I
11~~1
a
L-
-
LI
iW
(b)
(c)
-7-C
(d)
(e)
20 mm / sec
Fig. XVII-13.
QPR No. 67
Finger tremor for (a) Subject A, finger relaxed; (b) Subject B, finger
relaxed; (c) Subject C, finger relaxed; (d) Subject A, finger tense;
(e) Subject B, finger tense; (f) Subject C, finger tense; (g) Subject A,
finger weighted (50 grams); (h) Subject B, finger weighted (50 grams);
and (i) Subject C, finger weighted (50 grams).
219
--
-~-
(XVII.
NEUROLOGY)
Of course, it is necessary to apply spectral analysis to these data in order to make
quantitative statements, and such studies are under way; one example is found in
Section XVII-G.
E. Mudama, P.
A. Willis, L. Stark
References
1i. L. Stark and M. Iida, Dynamical response of the movement coordination system
of patients with Parkinson syndrome, Quarterly Progress Report No. 63, Research
Laboratory of Electronics, M.I.T., October 15, 1961, pp. 204-213.
2. C. Van Buskirk and R. A.
Neurology 12, 361-369 (1962).
E.
SAMPLED-DATA
Fink, Physiologic tremor, An experimental study,
PROPERTIES OF THE HUMAN MOTOR COORDINATION
SYSTEM
Recent studies have suggested that both the eye-movement tracking system and the
hand-movement tracking system can be treated as sampled-data control systems.
This report will present some data that may be used in support of this analysis of the
human motor coordination system.
When slowly moving ramps are used as input target signals, and the subject is
tracking this input with a device that offers very small mechanical impedance, a response
that is similar to that of Fig. XVII-14 is seen.
The output response consists of step-
like changes of position which occur with irregular intervals and amplitudes.
The output
signal rotary motion transducer had an effectively infinite resolution, and neither friction
CW20*
Zco,
CCW20O
CW20'
a.w
00'
CCW20'I
TIMF
-
Fig. XVII-14.
QPR
No. 67
20 SECONDS
-
Response to slow ramp input signals.
220
(XVII.
NEUROLOGY)
nor any other component of the mechanical impedance of the transducer was of sufficient
magnitude to play an important role in the dynamics of the system. Early studies utilizing this input suggested the possibility that the known sampled-data properties of the
eye-tracking system were possibly related to these steplike responses, but recent experiments have failed to confirm this conjecture.4
When pulses of varying width are used as input target signals and are presented
irregularly in time, a response that is similar to that shown in Fig. XVII-15a is
obtained. There are delays of approximately 150-250 msec before the rapid response
motions occur for both leading and trailing edges of the input target motion. This delay
in response has several components in addition to nerve conduction time and is sometimes called the psychological refractory time. When a pulse of extremely narrow width
is supplied unpredictably as an input target motion, a normal delay occurs before the
response movement to the leading edge of the input motion, as shown in Fig. XVII-15b.
CW20'
CW20*
(a)
r,
°
CW20
TIME-
Fig. XVII-15.
(a) Typical long
inputs.
pulse
to unpredictable
Response
response.
impulse
(b) Typical
response.
pulse
pulse response.
QPR No. 67
SECOND
I
(b) Typical impulse response.
221
(XVII.
NEUROLOGY)
UNPREDICTABLE
INPUT
0 AMPLITUDE OF CENTRAL FREQUENCY
A
+
50
AMPLITUDE OF CENTRAL FREQUENCY± I 0'
2.0-
z
\
0.5 -
0.2-
0.1 -
0.2
0.5
1.0
5.0
2.0
FREQUENCY
Fig. XVII-16.
However,
IN
10.0
CPS
Frequency response gain data.
the response motion to the trailing edge of the input motion has a much pro-
longed delay, 400 msec in the case illustrated in Fig. XVII-15b.
This prolonged delay
can be accounted for as a normal refractory period that starts with the initial response
motion, rather than being triggered by the trailing edge of the input target. This behavior would be characteristic of a sampled-data system.
Similar evidence has been shown
for the eye-movement control system, in which, because of the relative power of the
eye musculature compared with the low mechanical impedance of the eyeball, the load
and muscle dynamics are negligible compared to the shaping of the response waveform
by the sampled-data control dynamics.
For a motor coordination sampled-data system with the transient responses shown
in Figs. XVII-14 and XVII-15, the frequency response to wide bandwidth inputs would
demonstrate a peak at one-half the sampling frequency, or at approximately 2-3 cps,
as well as an absence of coherent tracking characteristics at frequencies greater
than .this peaking frequency.
The eye-movement system has been more fully treated
experimentally and theoretically by Young.
tem,
however,
occurrence
l
For the manual tracking control sys-
there exists very little experimental data that clearly support the
of this suggested peaking frequency,
since most of these experiments
have used input bandwidths with either much lower frequencies than 3 cps or else
too little power at these higher frequencies to obtain effective responses necessary
to demonstrate
frequency
the peak.
response
QPR No. 67
Stark,
experiments
lida,
that
and Willis
were
222
not
5
have described
limited by these
steady-state
undesirable
input
(XVII.
NEUROLOGY)
spectrum characteristics (see Fig. XVII-16).
This clearly defined peak in the response spectrum supports the transient data and
the idea that the human motor coordination system can be treated as a sampled-data
control system.
L. Stark, Y. Okabe, P. A. Willis
References
1. L. R. Young, A Sampled Data Model for Eye Tracking Movements, Sc.D. Thesis,
Department of Aeronautics and Astronautics, M.I. T., May 11, 1962.
2. L. R. Young and L. Stark, A sampled-data model for eye-tracking movements,
Quarterly Progress Report No. 66, Research Laboratory of Electronics, M.I.T.,
July 15, 1962, pp. 370-384.
3. G. A. Bekey, Sampled Data Models of the Human Operator in a Control System,
Ph. D. Thesis, Department of Electrical Engineering, U. C. L. A., 1962.
4. Y. Okabe, H. Rhodes, L. Stark, and P. A. Willis, Simultaneous hand and eye
tracking movements, Quarterly Progress Report No. 66, Research Laboratory of Electronics, M.I.T., July 15, 1962, pp. 395-401.
5. L. Stark, M. lida, and P. A. Willis, Dynamic characteristics of the motor coordination system in man, Biophys. J. 1, pp. 279-300 (1961).
F.
FREQUENCY RESPONSE OF A SPINDLE RECEPTOR
To establish a firmer basis for the model of a spindle receptor which was presented
in Quarterly Progress Report No. 66 (pp. 384-389), a sinusoidal analysis of the stretch
receptors in the frog's extensor longitus digitus IV muscle was undertaken. This preparation contains 3-7 spindle bags with as many as 3 occurring on a single intrafusal
fiber. No attempt was made to obtain single-unit responses; rather the average
response of all of the units associated with this unifunctional muscle were judged to be
more useful for justifying a model of this transducer which is suitable for simulating
1,2
motor coordination.
Fig. XVII-17.
QPR No. 67
Response of spindle
lines in top record
nerve pulses from
frequency, ~40 pps.
spindle stretch, the
receptor to sinusoidal drive. Length of vertical
is proportional to interval between successive
spindle; peak-to-peak change in instantaneous
Bottom record shows sinusoidal component of
input (frequency, =0.03 cps).
223
__
(XVII.
1.
NEUROLOGY)
Procedure
The preparation was stretched sinusoidally in position about a dc level that was
chosen to eliminate saturations at either maximum frequency of nerve pulses or a minimum frequency of no pulses.
The peak-to-peak stretch was 0.4 mm which should corre-
spond to a small-signal input to this 17-mm long muscle. The nerve impulses triggered
a linear sweep circuit; a trace whose length was proportional to the pulse interval
The record was calibrated in pulses per second so that the results might be
resulted.
evaluated in terms of instantaneous frequency of firing.
A sample record is shown in
Fig. XVII-17.
2.
Results
Figure XVII-18 shows that the phase vs frequency plot is only roughly proportional
to the slope of the amplitude vs frequency plot, an exact proportionality being required
of a linear system.
Figure XVII-19 shows a step response of this preparation.
As
another check on linearity it was desired to compare this step response with that predicted from the sinusoidal analysis.
The break frequencies of rough asymptotes drawn
on the gain plot of Fig. XVII-18 were used to form the transfer function
600
400
20 Ij"
~,,
_20@
1jI~r27~Tt.
_40o
-60.001
0.001
-.-
0.01
0.1
FREQUENCY
Fig. XVII-18.
1.0
224
_ __
7
10
(CPS)
Frequency response of a frog spindle receptor.
have been drawn on the gain curve.
QPR No. 67
_ _
A
4.i
. . . . . . . . . . . . .1. . . . 't
_I
Rough asymptotes
(XVII.
H(s) =
NEUROLOGY)
K(30s+l)
(5s+l)(0. 35S+1)
K was evaluated from the lowest frequency point of Fig. XVII-18 to be K = 27 (pps/mm
The unit step response was calculated
stretch).
S(t) = 27 + 143 e
0
2t - 170 e
3
t
and is superimposed on the record in Fig. XVII-19.
The rise time is rather slow, but
decay is approximately correct.
01234
5
10
20
TIME (sec)
Fig.
XVII-19.
Step response of a frog spindle receptor. The step response
predicted from the frequency response data is shown by the
solid line. The step input occurred at t = 0.
interesting to see what constraints are placed on the parameters of the
model developed in (1) and shown in Fig. XVII-20 by the values of the time constants
It is
XSB
LUMPED TENDON STIFFNESS
Fig. XVII-20.
LUMPED INTRAFUSAL
FIBER STIFFNESS
AND VISCOSITY
NUCLEAR BAG VISCOSITY
AND STIFFNESS
Mechanical model of a spindle receptor. Inputs are Xm (length of
the muscle) and X (artificial length caused by an input to the intrafusal fiber); the output is XSB (length of the nuclear bag).
QPR No. 67
225
(XVII.
NEUROLOGY)
in H(s).
The equations that relate the time constants to the physical parameters
are
Bf
T
1
Kf
Bf + Bb
T2
= Kf
+ Kb
T3
BfB b
BB
(3)
Kt(B +Bb
K is not included, since part of its value is contributed by the unknown gain of the transducer that converts stretch of the nuclear bag to nerve pulses.
Even though the K's and B's represent five unknowns in the three equations (3),
interesting relations may be obtained by demanding that these mechanical parameters be
positive.
If Bb > 0, then Kb
approach infinity.
> 4.7 Kf. If we allow the equality, then Bb = 0 and Kt must
Instead, assuming K b = 4.8 Kf leads to B b = 0.5,
independently of units of measure.
Also, K t = 3 Kf/(ZKf+0.035),
2 Kf >>0.035, then Kt = 3/2 (force/length).
spring constant than the intrafusal fiber.
(force-time/length)
and if we assume that
But the tendon should have a much larger
Kt > 10 Kf.
All of these requirements would be satisfied if
Kf = 0. 1 kg/m, K b = 0.48 kg/m, Kt = 1.3 kg/m,
B b = 0.5 kg-sec/m, and Bf = 2.9 kg-sec/m.
3.
Conclusions
Three factors prevent us from drawing any strong conclusions.
First, the analysis
was conducted with only two preparations, and the range of frequencies used was barely
sufficient.
More experimental work should be done.
mathematical analysis was the assumption of linearity.
Second, underlying all of our
Both the failure of correct
correspondence between gain and phase Bode plots and an error in the rise time of step
response as computed from the transfer function indicate nonlinearities,
small signal inputs that were used.
even for the
Third, values of the mechanical parameters of the
spindle receptor were suggested without strong justification for the model to which these
parameters apply.
Nevertheless, these findings add support to the model presented in
Quarterly Progress Report No. 66 (pp. 384-389) and provide some feeling for the functional significance of the anatomical structure of spindle receptors.
We wish to thank Dr. Jos6 del Castillo for his valuable suggestions and for making
his facilities at the University of Puerto Rico, School of Tropical Medicine, available
to us.
J.
C. Houk,
Jr.,
V. Sanchez,
P.
Wells
References
1. J. C. Houk, Jr. and L. Stark, An analytical model of a muscle spindle receptor
for simulation of motor coordination, Quarterly Progress Report No. 66, Research
Laboratory of Electronics, M.I.T., July 15, 1962, pp. 384-389.
QPR No. 67
226
(XVII.
NEUROLOGY)
2. J. Atwood, J. Elkind, J. C. Houk, M. King, L. Stark, and P. A. Willis, Digital
computer simulation of a neurological system, Quarterly Progress Report No. 63,
Research Laboratory of Electronics, M.I.T., November 15, 1961, pp. 215-217.
G.
ON-LINE USE OF A GENERAL-PURPOSE
DIGITAL COMPUTER
FOR
BIOLOGICAL EXPERIMENTS
The use of computers in attempting to assimilate large amounts of information concerning biological systems has been widely stressed.1
A useful development has been
the application of on-line digital computers that rapidly present digestive, analytical
results of a complex,
perhaps statistically designed, experiment to the experimenter
while the experiment is in progress or shortly afterward.
This reduction of feedback
time in experiments is one important advantage of the utilization of a digital computer
in this fashion.
Examples of these on-line computers include the special-purpose Aver-
age Response Computer,
2
the Analog Electronic Averager,
3
and the TX-0 computer,
4
all of which are used in the Research Laboratory of Electronics.
We have previously described our use of a digital computer for the generation of
comb spectra input functions and for gain- and phase-shift analysis of the experimental
system response.5
Three other types of data analysis methods have been programmed
for the GE 225; these are the average response program, the impulse response program,
and the autocorrelation and power spectrum programs.
1.
Average Response Program
A digital-computer program has been written and successfully used which accepts
on-line response data evoked by repetitive excitation and automatically computes the
average response as an analog voltage output.
following three parameters:
The program is fully specified by the
(a) Input sampling rate - max value,
4.7 kcps; (b) Output
sampling rate - max value, 4.7 kcps; (c) Number of points in response - max value,
7, 000.
Separate specification of an input and output sampling rate enables the computer to
time-scale in order to suit auxiliary equipment, for instance, the X-Y recorder.
At
present, the number of responses averaged must be less than 256, although the precise
number does not have to be specified at the beginning of an experiment.
In a typical
experiment responses to a particular input are obtained repeatedly until various experimental factors prohibit the taking of more data, for instance, subject fatigue, at which
time the experimenter signals the computer that the experiment has been completed.
Previously, analytic studies of the deterministic portion of the pupil servomechanism
have been delayed with respect to transient data because of a lack of adequate signal-tonoise ratio and variability in single responses.
QPR No. 67
227
This is now less of a barrier, as can
-il
- --
I
---
I
C
I
(a)
(b)
Fig. XVII-21.
Average pupil responses (solid line) and model response
(dashed line) to (a) Positive pulse of light and (b) Positive
ramp of light.
4
ww
Oj
a--Fzhi
Ua.
.
wzI-"
a-
TIME-
Fig. XVII-22.
QPR No. 67
-sec-]
TIME-
TIME-
Typical single pupil responses.
(b) Ramp responses.
228
i.
10 sec
(a) Pulse responses.
(XVII.
NEUROLOGY)
be seen by comparing Figs. XVII-21 and XVII-22.
The averager program has been used to obtain reliable and consistent pupil response
data to use in formulating models for the human pupil reflex to light. Figure XVII-21
shows examples of averaged responses.
Typical single pupil responses are shown in
Fig. XVII-22 for comparison.
2.
Impulse Response Program
A general second-order model is stored in the GE 225,
and the coefficients and
parameters of this model are adjusted by the program to give a second-order fit to the
150
V
-5
Fig. XVII-23.
input time record.
Mechanical impulse response and second-order fit.
Figure XVII-23 shows
response of the human motor coordination system
obtained by the computer.
of the mechanical
an example
impulse
and also the second-order
Higher-order fits, which are obviously necessary,
fit
are
under development.
3.
Autocorrelation and Power Spectrum Program
An autocorrelation program that allows a maximum
infinite string of input data has been written.
(total points) (Tmax).
T
shift of 650 and will take an
The computation time is T = (.02 sec)
Figure XVII-24a shows the autocorrelation function obtained
from a finger tremor record,
a section of which is
shown in
Fig. XVII-24b.
The cosine transform program accepts this autocorrelation as input and yields
both unsmoothed and smoothed power density spectra as an output.
Both the auto-
correlation and the power spectra are obtained as output plots on an X-Y plotter.
QPR
No. 67
229
-S
SEC
-
TIME
TIME
(b)
Fig. XVII-24.
(a) Autocorrelation of the section of finger tremor
time record shown in (b).
Fig. XVII-25.
Power density spectra obtained from Fig. XVII-28a.
(a) Unsmoothed spectrum.
QPR No. 67
230
(b) Smoothed spectrum.
(XVII.
NEUROLOGY)
Figure XVII-25 shows the unsmoothed and smoothed power density spectra obtained
from the autocorrelation function of Fig. XVII-24a.
Julia R. Bristol, R.
C. Payne, P.
A. A. Sandberg,
L. Stark, P.
R.
Samson
A. Willis
References
1. W. A. Rosenblith (ed.), Sensory Communication (The M.I.T. Press, Cambridge,
Mass., and John Wiley and Sons, Inc., New York, 1961).
2. W. A. Clark, R. M. Brown, M. H. Goldstein, Jr., C. E. Molnar, D. F. O'Brien,
and H. E. Ziemann, The Average Response Computer (ARC): A digital device for computing averages and amplitude and time histograms of electrophysiological response,
Trans. IRE, Vol. BME-8, No. 1, pp. 46-51, January 1961.
3. J. S. Barlow and R. M. Brown, An Analog Correlator System for Brain Potentials, Technical Report 300, Research Laboratory of Electronics, M.I.T., July 14,
1955; see also J. S. Barlow and M. A. B. Brazier, A note on a correlator for electroencephalographic work, EEG Clin. Neurophysiol. 6, 321 (1954).
4. Communications Biophysics Group of Research Laboratory of Electronics and
W. M. Siebert, Processing Electronic Data (The Technology Press of the Massachusetts
Institute of Technology, Cambridge, Mass., 1959), pp. 39-45; see also J. L. Mitchell
and K. H. Olsen, TX-0, A transistor computer with a 256 X 256 memory, Proc. Eastern
Joint Computer Conference, New York, December 10-12, 1956 (American Institute of
Electrical Engineers, New York, 1957), pp. 93-101.
5. Y. Okabe, R. C. Payne, H. Rhodes, L. Stark, and P. A. Willis, Use of on-line
digital computer for measurement of a neurological control system, Quarterly Progress
Report No. 61, Research Laboratory of Electronics, M.I.T., April 15, 1961, pp. 219222.
H.
EFFECT OF PHARMACOLOGICAL AGENTS ON CONTROL OF EYE
MOVEMENTS
Our program of research into neurological control systems has partly relied upon
an input-output, black-box analysis, with several varients, such as experimental manipulation of input signal characteristics and artificial environmental clamping of feedback
gain, to aid in this analysis.
The dissection of the black box of a neurological control
system is made possible by means of studying patients with different neurological syndromes (defective subsystems) and also the use of pharmacological agents that have
differential effects on the loops and mechanisms in the system under study.
This report
represents initial application of the latter method to the eye movement control system.
1.
Pharmacological Agents
Barbiturates are common sedatives widely used as sleeping pills.
We used seco-
barbital (35 mg intravenously) in smaller doses than employed in normal sedation since
it has been known that certain features of eye movements are very sensitive to these
QPR No. 67
231
(XVII.
NEUROLOGY)
barbiturates.
1-3
Another drug, methamphetamine (10 mg intravenously),
and is related to drugs commonly taken to resist sleepiness.
its effect of reducing appetite.
is a stimulant
At times it is given for
These drugs were administerd by a licensed physician
under carefully supervised medical conditions to normal, healthy subjects.
2.
Measurement and Target Techniques
The subject was positioned with his head fixed in a catcher's mask and a set of photo-
cell goggles, which have been described, for measuring eye position in various directions of horizontal gaze.
The target was either a vertical bar of light or a series of
stripes moving across a television screen that was behind the fixation point.
Calibra-
tion and recording have also been previously described.
3.
Performance Tasks
A rather varied set of tasks was required to be performed by the subjects in order
to survey drug effects on many aspects of the complex sampled-data multiloop system that controls normal human eye movements.
These included (a) Directed gaze in
darkness - lateral and forward, (b) Compensatory movements to passive head rotation,
(c) Gaze directed at fixation point, (d) Conjugate eye movements following moving targets
of (i) steps, (ii)
constant velocity, (iii) constant acceleration, and (iv)
sinusoids; and
(e) Optokinetic nystagmus.
These tasks are designed to elucidate the various types of eye movements - saccades,
pursuit, fixation stability, and nystagmus.
4.
Results
Normal tracking of a sinusoidal target movement generally results in a rather smooth
eye position recording similar to that shown in the middle trace of Fig. XVII-26.
Occa-
sionally, discontinuous changes of position occur which can be more clearly seen in the
rate or derivative recording shown in the top trace of Fig. XVII-26.
These discontinuous
spikes of velocity were found to occur at a rate of 2. 8 saccades per cycle when the input
signal is a 0.5-cps sinusoid.
The same subject under the influence of 35 mg of seco-
barbital administered intravenously shows a very scalloped eye position recording
(middle trace of Fig. XVII-27).
This is produced by an increased saccadic rate of 6.4
saccades per cycle, which is clearly shown in the top trace of Fig. XVII-27 as a frequent series of velocity spikes.
It is clear that the pursuit control loop 8,9 has been
grossly affected by the drug, yet at the same time the subject is obviously alert enough
to perform fairly accurate tracking and, indeed, to have his saccadic position-control
loop operate at greater than normal rates in order to compensate for the affected pursuit system.
The normal response to a series of moving stripes when the subject is attempting
QPR No. 67
232
(XVII.
NEUROLOGY)
50*/ SEC.
/
50'•SEC
.
T
Fig. XVII-26.
Fig. XVII-27.
Eye rate and eye position when
tracking 0.5-cps sinusoid in top and
Bottom trace, eye
middle trace.
position in response to a moving
pattern of stripes behind the fixation
point. (Time, 25 mm = 1 sec.)
Same subject as in Fig. XVII-25,
under 35 mm secobarbital.
This is
to maintain fixation on a stationary point is a pattern of optokinetic nystagmus.
shown in the bottom trace of Fig. XVII-26, in which approximately 1.2 jumps per second
occur to produce an irregular saw-tooth waveform.
The constant-velocity slower portion
of the saw tooth represents the action of the pursuit system, which is involuntarily influenced by the moving stripes. The eye drifts produced by the moving stripe pattern are
compensated for by the saccadic fixation system.
The effect of barbiturates is striking,
removing almost all trace of the optokinetic nystagmus, as shown in the bottom trace
of Fig. XVII-27.
In agreement with this evidence of the resistance of the saccadic system to barbiturates is the response to unpredictable steps shown in Fig. XVII-28. Here, we see
that when the subject has been administered barbiturates no significant changes occur
in the accuracy of large saccades. In fact, there is only a suggestive decrease in accuracy shown in the middle trace of Fig. XVII-28,
as compared with the top trace of
The result is the same for the subject following unpredictable steps after
having had methamphetamine administered. When statistical analysis is applied to the
data, however, it is found that methamphetamine decreases and secobarbital increases
Fig. XVII-28.
QPR No. 67
233
(XVII.
NEUROLOGY)
/
&i
Fig. XVII-28.
Fig. XVII-29.
Eye position in response to
unpredictable step changes
of target for (a) control,
(b) barbiturate, (c) methamphetamine conditions.
Eye position with instructions for forward gaze without fixation point (complete
darkness). Same conditions
as for Fig. XVII-28.
the normal response latent time of 250 msec by 10 per cent.
When the subject is placed in complete darkness and is instructed to direct his gaze
at a fixation point, which is extinguished at the beginning of the run, another interesting
set of effects is noted, as shown in Fig. XVII-29.
were measured and analyzed:
Two characteristics of the record
Average saccadic frequency and average saccade angle.
These quantities should represent the instability of the eye control system in maintaining
fixation in darkness. Barbiturates were found to increase the average frequency from
1.1 to 3.0 saccades per second, whereas methamphetamine decreased the average saccade angle from 1.6' to 0.80.
Discussion
It is felt that these results, although preliminary, suggest the power of combining
an input-output analysis with a pharmacological dissection method.
H. T. Hermann, G. P.
QPR No. 67
234
Nelson, L.
Stark, L.
R. Young
(XVII.
NEUROLOGY)
References
1. C. Rashbass, Barbiturate nystagmus and the mechanisms of visual fixation,
Nature 183, 897-898 (1959).
2. G. Westheimer and C.
833-834 (1961).
Rashbass, Barbiturates and eye vergence,
Nature 191,
3. P. Bergman, M. Nathanson, and M. Bender, Electrical recordings of normal
and abnormal eye movements modified by drugs, A. M. A. Arch. Neurol. Psych. 67,
357-374 (1952).
4. L. Stark and A. Sandberg, A simple instrument for measuring eye movements,
Quarterly Progress Report No. 62, Research Laboratory of Electronics, M.I.T.,
July 15, 1961, pp. 268-270.
L. R. Young, Tracking projection for tracking experiments, Quarterly Progress
5.
Report No. 62, Research Laboratory of Electronics, M.I.T., July 15, 1961, pp. 270-271.
6.
L. Stark, G. Vossius, and L. R. Young, Predictive control of eye movements,
Quarterly Progress Report No. 62, Research Laboratory of Electronics, M.I.T.,
July 15, 1961, pp. 271-281.
L. Stark and G. Nelson, Optokinetic nystagmus, Quarterly Progress Report
7.
No. 64, Research Laboratory of Electronics, M.I.T., January 15, 1962, pp. 326-328.
8. G. P. Nelson and L. Stark, Optokinetic nystagmus in man, Quarterly Progress
Report No. 66, Research Laboratory of Electronics, M.I.T., July 15, 1962, pp. 366369.
L. R. Young and L. Stark, A sampled-data model for eye-tracking movement,
9.
Quarterly Progress Report No. 66, Research Laboratory of Electronics, M.I.T.,
July 15, 1962, pp. 370-384.
QPR No. 67
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I