Voluntary active head rotations produced vestibulo-ocular reflex eye movements (VOR) with the subject viewing a fixation target. When this target jumped, the size of the refixation saccades were a function of the ongoing initial velocity of the eye. Saccades made against the VOR were larger in magnitude. Simulation of a reciprocally innervated model eye movement provided results comparable to the experimental data. Most of the experimental effect appeared to be due to linear summation for saccades of 5 and 10 degree magnitude. For small saccades of 2.5 degrees, peripheral nonlinear interaction of state variables in the neuromuscular plant also played a role as proven by comparable behavior in the simulated model with known controller signals

Nam, M. H.

Stark, L.

Winters, J. M.

English

NASA Technical Reports Server

182-13712 i:
MODEL SIMULATION STUDIES TO CLARI_ THE EFFECT ON SACCADIC EYE
MOVEMENTS OF INITIAL CONDITION VELOCITIES SET BY THE VESTIBULAR
OCULAR REFLEX (VOR)
By Moon-hyon Nam, Jack M. Winters and La_rcence Stark
University of California, Berkeley
:
Acknowledgement: We are pleased to acknowledge partial support
from the NCC 2-86 Cooperative Agreement, NASA-
Ames Research Center and the Ministry of
, Education, Korea.
• 5
1982005792-528
https://ntrs.nasa.gov/search.jsp?R=19820005839 2020-03-21T15:57:55+00:00Z
SUMMARY
Voluntary active head rotations produced vestibulo-ocular reflex eye
movements (VOR) with the subject viewing a fixation target° When this
target Jumped, the size of the refixation saccades were a function of the
ongoing initial velocity of the eye. Saccades made against the VOR were
strikingly attenuated in magnitude while saccades going witn the VOR were
larger in magnitude. Simulation of a reciprorally innervated model eye
movement provided results comparable to the experimental data°
Most of the experimental effect appeared to be due to linear su_:ation
for saccades of 5 and I0 degree magnitude. 7or small saccade_ of 2.5
degrees, peripheral nonlinear interaction of state variables in the neuro-
muscular plant also played a role as proven by comparable behavior in the
simulated model with kno_ controller signals°
INTRODUCTION
Under natural conditions, it is well known that different types of
eye movements, generated by specialized subsystems of the CNS, may inter-
act temporally in a complex manner° In recent years, the interactions
between different types of eye movements has been studied in hv_mns and
primates in a number of different ways and the linear summation theory for
such movements has been proposed In particular, data on voluntary sac-
cades with compensatory movements (VOR) in monkeys (Morasso et al (19739,
saccade/vergence interactions in man (Kenyon et al (1980_; Ono et aI_1978_,
goal-directed saccades and VOR in man (Jurgens et al (1981)}ali support the
theory uf addltivity when two types of eye movements combine. Chun and
Robinson (1978) postulated switching off of slow command during the
execution of quick phase VOR in monkey Also, earlier work by Nam et al
(1981) presented some evidence for the 'Kenyon effect' in saccade and
VOR interactlon.
In this study, we examined our former hypothesis on linear sun_atio_
through the interaction between saccade and VOR eye movements by experi-
ments in humans and by computer simulation using a modified version of the
eye model described previously by Lehman and Stark (1979). Were the
observed phenomenon due to I) linear summation of VOR with the saccades,
2) peripheral nonlinear interaction of state variables in the neuro-
muscular plant, i.r., the 'Kenyon effect', 3) nonlinear interaction at
ocular motor neurons, the final common path that might ha_,e shown non-
linear squelching phenomena, or 4) higher level preprogrammed changes in
saccadic magnitude? By combining experimental results with simulation
findings, in which the latter has a known controllerslgnal, cases I) and
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1982005792-529
!L
_ 2) can be separated from cases 3) and 4), and significant insights can be
obtained.
[, •
METHOD
_ A. Experimental
Horizontal eye movements were measured using the infrared photo-
electric method which has a bandwidth of I kHz and a sensitivity of I0 min
of arc. Measurements were linear for a range of ± 25 degrees and
frequent calibrations guaranteed that recorded eye movements faithfully
reflected retinal orientation.
Horizontal head movements were measured with an electro-mechanical
transducer sy:,tem consisting of mechanical linkages using lignt-weight
universal joints and a sliding mechanism coupled to a low torque special
film potentiometero The linkage was _elf-allgning with the vertical
axis of the head and thus only rotational motion of the subject's head in
' the horizontal plane was measured by the potentiometer. This system
- allowed for flexible and natural head movements for the subject.
Data was obtained for five adult subjects. To generate the appropri-
ate VOR, the subject would rotate his head voluntarily at a frequency
between 0.8 and 1.5 Hz in a sinusoldal-like motion with a peak amplitude
between _ I0 and + 15 degrees relative to the center 'stralght-ahead'
position. Calibrations were performed on eye movements within + 25
degrees of the visual target using 5 equidistant points at a distance of
19 cm from the eye axis of rotation. After separate calibrations for the
eye and head movements to the same calibration target, the task of the
subject was to follow the Jumping targets as quickly as possible while
making the sinusoid-like head rotations.
The experimenter instructed the subject to carefully follow the visual ._
target and also gave the subject's various head rotatiou schemes ( ego
faster, slower, larger, smaller so as to obtain data with a variety of
head rotations), all the Li_e viewing the eye and head movement recordings_
Vision was monocular to avoid vergence effects. The data was classified
in terms of the initial velocity conditions as being 'with' (W) or
'aga;,,_t' (A) the VOR,
B. Simulatio_
The 'core' eye model algorithm has been described in detail previously
(Lehman and Stark, 1979) qm corresponding program represented
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1982005792-530
ma simulation of the eye mechanics for horizontal eye movements, i.e, of
the lateral and medial rectus muscle, involves the integration of a set
of six nonlinear differential equations°
The present program represents a significant extension of the _Jdel
so as to allow a sinusoid 'VOR' neurological signal---of specified
magnitude and frequency---to be the 'base t control signal. A saccade
(second ordez, of 2°5, 5, I0 or 20 degrees magnitude) can then be produced
at any time during a run, and consequently for different initial conditions
of VOR position, velocity, and acceleration. As presently set up, thelte is
both a left and a right saccade, with the left occurring first°
The main outputs of the program are the eye position and velocity _s
a function of time. In addition, a number of relevant data parameters
are calculated directly by the program, including the initial position and
velocity of the system at the start of the saccade, the apparent and
relative peak saccadlc velocities, and the duration and magnitude of the
resulting saccade (based on 'returning velocity' considerations).
RESULTS
Relative velocity distinguished from apparent velocity. Before pre-
senting the primary results, it is important to distinguish between the
apparent peak velocity, which is defined as the velocity with respect to
the absolute zero veloclty, and the relative peak velocity, i.e., the peak
velocity _elative to the initial velocity at the start of the saccade. The
difference between the two, which is due to the velocity of the compensatory
eye movement wL_n the saccade begins, can be up to approxlmately I00 deg/
sec, which is obviously significant relative to typical peak saccadic
velocities. As a limiting case, consider the difference between the abso-
lute and relative peak velocities for the small tcorrectlon' saccades
(Figures I and 2). In particular, notice that for the rlght-most saccade
in Figure 2, which has an amplitude of about I degree, the 'apparent' peak
velocity is -30 deg/seco while the 'relative' peak velocity is about 90
deg/sec---_ite a difference. Clearly, 90 deg/sec is the appropriate
velocity for this positive going, leftward saccade. This difference, of
course, is more noticeable for small saccades. Still, it is obvious that
there will be significant difference between figures using the two different
peak velocity definitions. To see this more explicitly, consider a typical
simulation run (Figure 3). Notice that the 'against' saccade, which by
definition has a uegaclve inltlal velocity, has a proportionally smaller
'absolute' versus 'relative' peak velocity. Conversely, for the 'with'
saccade, the 'absolute' peak velocity is proportionally larger. Notice
also that there is a linear relationship between the initial velocity and
the peak velocity measurements. Thus, an 'absolute' peak velocity versus
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1982005792-531
!initial velocity curve can be turned into a similar 'relative' graph Just
by adjusting the slope in an appropriate manner
Main effect of VOR velocity as an initial condition. The main effects
of the VOR initial conditions can be seen in a qualitative manner
(Figures I, 2 and 3). The magnitudes of the saecades are strikingly dif-
ferent depending upon whether they are on or against the initial conditiot_
velocity set by the VOR (Figure I). The saccades against are attenuated
and the saccades with are increased. It is interesting to note that sac-
cades against are attenuated with respect to saccades where the initial
condition is at 0 degree velocity (Figure 2). Similar results are found
in the simulation traces (Figure 3). These similaritles between experi-
mental and simulation traces will be shown in a more qualitative fashion
in later figures. Since the simulation results were obtained with a known
controller signal (CS), by comparing simulation versus experimental results
insights can be gained into the _echanism(s) responsible for the observed
eye interaction phenomena. Magnitude of a large number of experimental
and simulated saccades following I0 de_ree target Jump can be plotted as
a function of the initial eye velocity of the VOR (Figure 4)0 In addition
to the experimental and simulation curves, a line representing the pro-
jected system behavior if there was ideal linear summation of the two
controller signals is also shown. Notice the strong correlation between
the experimental and simulation data and the linear summation llne. This
provides very strong evidence for the linear summation hypotheses. A
similarly strong correlation also existed for 5 degree target saccades
(not illustrated).
Hysteresis. A secondary observation was that, in the simulation
results, a 'hysteresis' loop is apparent. This 'hysteresis' behavior
was due to the initial position and acceleration conditions at the start
of the saccade, which should be taken as implicit parameters in the
displayed curve. When a 'with' saccade is past the center 'zero" position
of ti_eeye, the initial position and acceleration conditions will both
tend to oppose eye motion, the former by virtue of the system elasticity i
and the latter by virtue of system inertia and its resulting deceleration. i
Thus, this could be called a 'wlth-against' case. By extension there are I
also 'with-with', 'agalnst-with', and 'agalnst-against' cases. These
simulation results indicate that some of the experimental scatter, which
is already not very large, may be due to the initial position and
acceleration conditions which are implicit parameters in the graph.
Saccadic masnltude as a function of initial condition velocit_ and of
intended saccadic size. Averaged experimental data for the four different
nominal saccade sizes is compared with the projected linear summation
case (as solid line) (Figure 5). Notice that, in general, the slope of
the experimental data is slightly lower. Part of this difference could be
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1982005792-532
directly due to the fact that average VOR velocity would be a better
representation than the initial velocity used. Normalized
magnitude is plotted versus the target magnitude so as to compare the
experimental magnitude data with the expected data based on linear sum-
mation for initial conditions of 40 and 80 degrees per second (Figure 6).
Again we see that linear summation accounts for a bulk of the effects.
However, experimental results show less effect than that expected from
linear summation. This could be due to the assumption that initial
condition velocity lasts throughout the saccade; there might be changes
during the saccade that would alter the summation calculations.
Saccadlc velocity as a factor of initial condition velocity. Addition-
al evidence for linear sun,natlon can be found through the analysis of
initial condition velocity and apparent peak velocity relationships.
Experimental data were compared with data from simulation using the
hypothetical linear summation model (Figure 7). 'l_e simulation results
also show the 'hystereses' effects of initial eye position and acceleration
(also seen in Figure 4). Notice that the apparent peak velocity is
graphed versus the initial VOR _elocity. For reasons explained above,
the relative peak velocity could also have been plotted. In the latter
case the linear sununation hypothesis would give a horizontal llne.
Naturally, the experimental and simulation data would change in a corre-
sponding manner. Differences between the experimental and simula21on data
were partly due to this difference of reference.
_in sequence relationships. The relationship between the saccadic
magnitude, duration and apparent pea_ velocity (Figure 8) shows further
evidence of interaction. Experimental and simulation data on apparent
velocity versus magnitude show different relative slopes for each saccade
size, crossing the normal main sequence (solid line) with a significant
shift in some cases. The amount of shift between the apparent and
relative peak velocity, which corresponds to the initial condition
velocity, could explain some of this shift. Mean values and 'with' and
'against' for 5 and 10 degree saccades fall on the main sequence. For
2.5 and 20 degree saccades, while the mean values fall on the main sequence,
the with and against initial condition velocity set by VOR lie off the
main sequence. The reason for the shift away from the main sequence might
be non-main sequence effects of VOR velocity and indicates there are non-
linear phenomena with these very small atldvery large saccade sizes.
1982005792-533
REFERENCES
,J
Morasso, Po, Bizzi, E., and DichEans, J. Adjustment of Saccade Character-
_ istlcs during Head Movement. Exp. Brain Re s,, 16: 492 cO0, 1973.
Kenyon, R.V., Ciuffreda, K.J. and Stark, L. Unequal Saccades during
Vergence. Am. J. Optom. & Physlo. Opt. 57(9): 586-594, 1980.
Ono, H., Naka_izo, S., _nd Steinbach, N.J. Nonaddttivity of Vergence and
Saccadic Eye Movement. Vision Reso, 18: 735-_39, !978.
Jurgens, R., Becker, W., Rieger, P., and Widderlch, A. Interaction between
Goal-directed Saccades and the Vestlbulo-ocular Reflex (VOR) is
Different fro_ Interaction between Quick Phases and the VO:_, In
Progress in Oculouotor Research, ed. by Fuchs, A. and Becks-, W.,
Elsevier, North Holland, t33, 1981.
Chun, K.S. and Robinson, D.A. A Model of Quick Fhase Generation in the
Vestlbulo-ocular Reflex. Biol. Cyber. 28: 209-221, 1978. i
Nam, M., Winter_. J. and S ,rk, L. Simulation and Nonlinear Interaction
of VOR with Saccadic Eye Movements. ONS 81, Jan. 18-21, 1981.
Lehman, S. and Stark, L. Simulation Analyses and Enumeration Studies of
Time Optimal Control. J. Cyber_ Inf. Scl. 2(2/4) 21-43, 1979.
.i
?
i - 543-
1982005792-534
F.
_J _ _-: %-/ ,._ I:
,""..I /....\ ,, .\ /- Ii
\ / \_/
t/ z
, ehea d t I sec J
!0_ .....
.... !iest
!
I01 Oeye A W " :
aoo_'_t _ T _+,., e,c
Figure I. Recordings of head position (eheai_))visualtarget (est),eye _'
position (_=y_= and eye velocity (_. In eye position trace,
A and W stand for against and with VOR_ and saccadic magnitude
(I_SaCl) and duratio_ are measured from saccadic portion. In
eye velocity record, _)_ initial velocity of VOR eye movements
at the instant of saccadic occurrence, (_ = apparent peak
velocity. "nlax
1982005792-535
O_GnVALPAGEIS
OF POOR QJAL|TY ,:_
[ 10o ,
510% :_
,&
Figure 2. Eye position and velocity record illustrating apparent and relative peak ilI
velocity.
go
° /
-.300 / '
_ o
t
200ms
t
Figure 3. Computer simulation trace for 5 degree saccade and I Hz, 35 degree slnusold
VOR controller signal.
-545-
1982005792-536
2O _*
r-_ f
OD
0
'-'15 , Oo,,,,..o ,
0 ** o._ " ' "
... •
dlO .,_. ' .
_; li _ •:experimental
_.:simulation
--: linear summation
0 " ' ' , (hypothesis)
-150 -I00 -50 0 50 I00 150
VOR Velocity, OIC (deg/sec) *:"
Figure 4. Magnitude vs initial condition velocity relationship for I0 degree target.
I Osac I
IS Ost
---: linear .eummation"0
= (hypothesis)
15 • experimental
.u !0 *
°
o ° _
0 ' ' ' ' 6
-100 -50 0 50 100 IC
VOR Velocity (deg/sec)
c
Figure 5. Averaged magnitude vs initial condition velocity relationship for four
nominal target Jump,
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1982005792-538
,4
MAIN SEOUENCE
I,O00
0
0(4
" .t,
m __ ._ ,.,,_4 ,t
"'""3::
= ,,,_
<>_ ,':. ,
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0
6
6
lOg " SIMULATION
: :EXPERIMENTAL
:®
!
i J i I A I t i i i I I
2,5 5 I0 20 40
I00 -
E
o_
• @ , .
. , • • ,,, oo_O • oeee •*!
, • . , •
I0 I ..-..-,L__J 5 i [ -L LL__ | L----__.2,5 I0 20 40
Magnitude, 10,,el (deg}
Figure 8. Main _equence relationship for apparent peak velocity, duration
vs magnitude.
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1982005792-539


Model simulation studies to clarify the effect on saccadic eye movements of initial condition velocities set by the Vestibular Ocular Reflex (VOR)

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