Ex.lrimental
BrainResearch
Exp Brain Res (1988) 73:91-105
9 Springer-Verlag 1988
Eye movements induced by off-vertical axis rotation (OVAR)
at small angles of tilt
C. Darlot 1, P. Denise t, J. Droulez 1, B. Cohen 2, and A. Berthoz I
1 Laboratoire de PhysiologieNeurosensorielle du CNRS, 15, Rue de l'Ecole de M6decine, F-75270 Paris C6dex 06, France
2 Departments of Neurologyand Physiology,Mount Sinai School of Medicine, 1 East 100th Street, New York, NY 10029, USA
Summary. Off-vertical rotation (OVAR) in darkness
induced continuous horizontal nystagmus in humans
at small tilts of the rotation axis (5 to 30 degrees).
The horizontal slow eye velocity had two components: a mean velocity in the direction opposite to
head rotation and a sinusoidal modulation around
the mean. Mean velocity generally did not exceed
10 deg/s, and was less than or equal to the maximum
velocity of optokinetic after-nystagmus (OKAN).
Both the mean and modulation components of horizontal nystagmus increased with tilt angle and rotational velocity. Vertical slow eye velocity was also
modulated sinusoidally, generally around zero. The
amplitude of the vertical modulation increased with
tilt angle, but not with rotational velocity. In addition
to modulations in eye velocity, there were also
modulations in horizontal and vertical eye positions.
These would partially compensate for head position
changes in the yaw and pitch planes during each cycle
of OVAR. Modulations in vertical eye position were
regular, increased with increases in tilt angle and
were separated from eye velocity by 90 deg. These
results are compatible with the interpretation that,
during OVAR, mean slow velocity of horizontal
nystagmus is produced by the velocity storage mechanism in the vestibular system. In addition, they
indicate that the otolith organs induce compensatory
eye position changes with regard to gravity for tilts in
the pitch, yaw and probably also the roll planes. Such
compensatory changes could be utilized to study the
function of the otolith organs. A functional interpretation of these results is that nystagmus attempts to
stabilize the image on the retina of one point of the
surrounding world. Mean horizontal velocity would
then be opposite to the estimate of head rotational
velocity provided by the output of the velocity
Offprint requests to:
C. Darlot (address see above)
storage mechanism, as charged by an otolithic input
during OVAR. In spite of the lack of actual translation, an estimate of head translational velocity could,
in this condition, be constructed from the otolithic
signal. The modulation in horizontal eye position
would then be compensatory for the perceived head
translation. Modulation of vertical eye velocity
would compensate for actual changes in head orientation with respect to gravity.
Key words: Otolith - Nystagmus - Labyrinth - Eye
movements - Velocity storage mechanism
Introduction
Rotation of the head at constant velocity about a
vertical axis in darkness induces nystagmus and a
sense of motion. These disappear within 40-60 s.
However, if the axis of rotation is tilted with respect
to gravity (Off-Vertical Axis Rotation, OVAR),
nystagmus and the feeling of body movement last as
long as rotation continues (Guedry 1965; Benson and
Bodin 1966). Neuronal activity responsible for the
continuous response arises primarily from excitation
of the otolith organs by a component of gravity
orthogonal to the rotation axis (Guedry 1965; Correia and Money 1970; Stockwell et al. 1970; Raphan
et al. 1981; Goldberg and Fernfindez 1981, 1982;
Cohen et al. 1983; see Raphan and Cohen 1985 for
review).
The gravitY vector can be described in a stereotaxic set of orthogonal axes (Fig. 1). The X axis is the
intersection of sagittal and horizontal planes; the line
of sight coincides with this axis when the subject
looks ahead. The Y axis is the interaural axis at the
intersection of the horizontal and frontal planes, and
92
Fig. 1. Representation of the gravity vector in stereotaxic axes.
The origin of the three axes X, Y and Z is located between the two
labyrinths, at the intersectionof the frontal, sagittal and horizontal
planes. The gravity vector G is decomposedinto its components
along the axes: Gx, Gy and Gz. During OVAR, this latter
component does not vary with time, while the first two ones vary
sinusoidallyand in quadrature. Their sum, the gravitycomponent
GC, is fixedin space. When the head rotates about the Z axistilted
with respect to gravity (the rounded arrow indicates a clockwise
rotation), GC rotates, in head coordinates, in the opposite
direction (counterclockwise)
the Z axis is the intersection of frontal and sagittal
planes. To describe geometrically the otolithic stimulation due to O V A R , it is convenient to decompose
the gravity vector into three components, each along
one stereotaxic axis. The excitation level of each
sensory cell in the maculae of the utricle and saccule
is proportional to the scalar product of its polarization vector and linear acceleration. The polarization
vectors of most utricular cells are contained within
the horizontal stereotaxic plane and those of the
saccular cells within the sagittal plane (Goldberg and
Fernandez 1982).
During O V A R , subjects are rotated around the
Z axis. Therefore, the component of gravity along
this axis does not vary with time, and thus does not
induce any otolithic stimulation. The gravity components along the X and Y axes vary sinusoidaUy and in
quadrature during each turn. The extremes of the X
axis component occur when the head is in nose-down
and nose-up positions, and those of the Y axis
component when the head is laterally tilted.
The sum of the components along X and Z axes
lies within the sagittal plane. This vector sweeps the
maculae, alternately rotating forward and backward
during each half of one cycle. It particularly stimulates the saccular maculae and probably elicits vertical eye position changes and vertical nystagmus. The
sum of the components along Y and Z axes lies
within the frontal plane. This vector also alternately
rotates but sideways, and probably induces ocular
counter-rolling (Markham and Diamond 1983, 1985).
The sum of the components along the X and Y axes is
a vector located in the horizontal stereotaxic plane,
orthogonal to the rotation axis. Its magnitude is
proportional to the sine of the tilt angle of this axis.
This vector is fixed in space, but in head coordinates
it rotates at a velocity opposite to that of the head in
space. This is an equivalent way of saying that the
components along the two axes vary sinusoidally and
in quadrature. This "rotating vector" sequentially
excites the sensory cells of the maculae according to
the orientation of their polarization vector (Guedry
1966; Raphan et al. 1981a). The sequential activation
enables the Central Nervous System (CNS) to elaborate an estimate of rotational head velocity to elaborate an estimate of rotational head velocity (Raphan
and Schnalbok 1988). It is postulated that this
estimate is sent to the Velocity Storage Mechanism
(VSM) to activate neurons in the vestibulo-ocular
pathway (Raphan et al. 1981a; see Raphan and
Cohen 1985 for review). The resultant horizontal
slow phase eye velocity has two components (Guedry
1965; Benson and Bodin 1966; Harris 1987):
1. A mean eye velocity, which is compensatory to the
direction of head rotation. This velocity is probably
the output of the velocity storage mechanism (Cohen
et al. 1983).
2. A cyclic modulation in velocity at the frequency of
the head rotation, added to the mean velocity.
Several authors have described horizontal nystagmus
and perceptual effects induced by O V A R at 60-90
degrees of axis tilt and various head velocities
(Guedry 1965; Benson and Bodin 1966; Correia and
Guedry 1966; Stockwell et al. 1970; Young and Henn
1975; see Guedry 1974 and Benson 1974 for review).
Both components of horizontal eye velocity increase
with tilt of the axis of rotation and with head velocity.
The maximum of the modulation occurs about 30
degrees in advance of the nose-up position (Stockwell et al. 1970).
However, relatively little information is available
about the nystagmus induced by O V A R at small
angles of tilt of the axis of rotation, especially in man.
The present article reports observations and
measurements of eye movements induced by O V A R
at tilt angle up to 30 degrees.
93
OFF-VERTICAL AXIS ROTATION
CW 45 Deg/s
Tilt=15Degrees
Horizontaleyevelocity
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io
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An accompanying article describes motion sensations experienced by the subjects (Denise et al.
1988).
Methods
Subjects. Results were obtained from 27 subjects, from 21 to 45
years old. They had no history of auditory or vestibular disorder,
and they had neither spontaneous nystagmus nor a Romberg sign
in darkness. The integrity of the horizontal canals was checked by
post-rotatory nystagmus. Five subjects became nauseated so
quickly that their oculomotor responses could not be measured.
Nevertheless, their sensation of body motion was similar to that of
other subjects (see Denise et al. 1988).
Recording technique. Horizontal and vertical eye movements were
recorded with DC electrooculography (EOG). Care was taken to
avoid cross-coupling between the horizontal and vertical electrodes by placing them at right angles to each other. Subjects were
adapted for 15 min in darkness before their eye movements were
calibrated in dim red light.
Pretesting. Per-rotatory nystagmus was induced by a step increase
in head velocity from 0 to 45 deg/s. Maximum accelerations and
decelerations at the onset and end of rotation were approximately
500 deg/sz. The dim red lights were then switched on, and OKN
Fig. 2. Nystagmic pattern during
OVAR. This nystagmus was induced
by clockwise OVAR at 45~ about
an axis tilted 15 degrees from the
vertical. The traces are, from top to
bottom: horizontal eye velocity,
horizontal eye position, vertical eye
velocity, vertical eye position, and
head position about the yaw (Z) axis.
Eye movements to the fight and up,
and clockwise (rightward) head rotation, caused upward trace deflections. Head position was measured
from chair position, by a potentiometer in a bridge circuit that
resets after each turn. The sudden
drop in this trace coincides with
origin of phases (nose-down position). The position of the subject at
various times during the rotational
cycle is shown diagrammatically at
bottom left, and the correspondence
between the phase of rotation and
time at bottom right
was measured during two minutes of constant velocity rotation.
The lights were switched off again, and at the end of the test,
rotation was stopped, and post-rotatory nystagmus was recorded
in darkness. Gains and time constants of these responses were
within normal limits in all subjects.
Stimulation. OVAR nystagmus was induced by rotating the
subjects, in darkness, at constant rotational velocity, around an
axis tilted with respect to gravity.
The apparatus was a rotating chair driven by a torque motor
(Toennies) on a platform that could be tilted by hydraulic jacks
placed at one side. Tilting from zero to 30 degrees or vice versa
was achieved in about 10 s. To avoid any influence of canal
stimulation, two minutes were allowed to elapse after every
change in tilt angle or rotational velocity, to let canal activity
subside. Then nystagmus was recorded for two to five minutes,
depending on the velocity. There was a slight sinusoidal modulation of rotational velocity~ but its amplitude did not exceed
0.1 deg/s at 45 deg/s and 30 degrees of tilt. The corresponding
acceleration is below canal threshold; thus eye movements
resulted only from otolith stimulation.
Subjects were instructed to maintain their heads stationary
upright, keep their eyes open in darkness, look straight ahead at
an imaginary horizon, and not to try to follow imaginary points or
noises in the room. Experimenters kept silent except when asking
subjects to describe their feelings. The experiment was terminated
whenever the subjects wished.
Six angles of tilt were used: 5, 10, 15, 20, 25 and 30 degrees.
The tilt angle was varied randomly in three subjects. This led to
94
Subject 3
HORIZONTAL
Deg.
10-
45~
Velocity modulation
Deg/s
Right
10
Position
Right
~
. 25 ~
9 ~ ~176149
9 9149
5
l_e
:,
0
:::t
Left
.
:.
%
r
t
I
1
I
I
I'
I
I
I
0
90
180
270
360
0
90
180
270
360
VERTICAL
Deg/s
5
Up
Deg.
10
Up
9 o9
.." . ; ;
Down
0
;
9t0
o9
I
180
99
I
270
-5
I
360
Down
~
0
9t0
r
180
I
270
i
360
Phase in degrees.
Fig. 3. Results of record processing. Cyclic modulations of horizontal (upper row) and vertical (lower row) eye position (left column) and
velocity (right column) are shown during OVAR at 45~ and 25 degrees of axis tilt. 20 cycles were sampled and averaged, with 120 points
per cycle. Each point represents the average value of eye position or velocity during the time required for the head to rotate by 3 degrees.
The origin of the phase plots is the nose-down position. The phase scale is drawn at the bottom line. Sinusoidal curve fitted to each set of
points is drawn with a solid line, and mean value of velocity with an interrupted line
early development of nausea. Consequently, in the other subjects
the angle of tilt was progressively increased.
All subjects were tested at the standard velocity of 45 deg/s.
Nine were successively rotated at 30, 45 and 60 deg/s, at one or
several tilt angles from 5 to 20 degrees.
Three subjects were also rotated at 90, 120 and 140 deg/s at 10
degrees of tilt. Sixteen subjects were rotated in only one direction.
The other six subjects had successive clockwise and counterclockwise rotation. The results were not different in the two groups.
Most subjects asked that the experiment be terminated before
completion of all velocities and tilt angles. This was frequently not
because of nausea, but because the whole experiment lasted for an
hour and a half. Consequently, sets of measurements were
satisfactorily large only for tilt angles from 5 to 20 degrees, and
conclusions on effects of larger tilt angles are based on fewer
observations.
All subjects leaned their head on a concave head-rest, in
similar positions with regard to the rotational axis. Thus, otolithic
95
A
Deg/s
10
Subject 1
Mean velocity
DegYs
10
8
HORIZONTAL
Velocity modulation
Analysis of eye movements. Signals representing horizontal and
Position modulation
[3eg
6
9
6
6
4
4
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1;
i;
~legYs
Deg/s
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VERTICAL
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A n g l e of tilt in d e g r e e s
B
Dog/s
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Subject 2
Mean velocity
Deg/s
l
8
4
6
3
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2
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1'o
a'o
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o
Deg/s
5
Deg/s
5
HORIZONTAL
Velocity modulation
Position modulation
Deg
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Results
9
9
1'o
2'o
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~'o
VERTICAL
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310
vertical eye position, chair position and velocity, sensation of body
acceleration and velocity or position felt by the subject (see
accompanying article) were displayed on an oscillograph and
simultaneously recorded by a computer (HP 1000) for off-line
processing. Eye position was digitally differentiated to obtain eye
velocity. Saccades and quick phases were identified and eliminated
from the record. Each cycle was divided into 120 bins, each 3
degrees wide, and 20 cycles were averaged. Position and velocity
data were fitted with least square sinusoids. An example is shown
in Fig. 3. From this, mean horizontal and vertical eye position and
velocity, together with amplitude of their modulations (half of
peak to peak modulation) and the phase with respect to chair
position were determined. The nose-down position was taken as
the origin of the phase plots (Stockwell et al. 1970). Estimates of
the means and amplitudes of modulation around the mean were
not independent, so that a sudden change of one could reduce the
accuracy of measurement of the other. Results obtained by
computer processing were compared to measurements made by
hand on the paper records. There were only minimal differences.
Phase measurements were accurate to no more than + 25
degrees, due to the inherent irregularity in the eye movement
patterns. This was determined by recording the same subject
several times on the same and on different days.
[]
0
[]
110
O
[3
0
210
3tO
o
~'0
A n g l e of tilt in d e g r e e s
Fig. 4A, B. Effects of tilt angle on nystgmus. Abscissa: axis tilt
angle in degrees. Ordinates, from left to right: mean value (first
column, circles), modulation amplitude of slow phase eye velocity
(second column, squares), and modulation amplitude of eye
position (third column, diamonds) of horizontal (upper row, filled
symbols) and vertical (lower row, empty symbols) eye movements.
Results are shown for two subjects. Subject 2 is the same as in
Fig. 3, but the record was made on another day
Horizontal and vertical nystagmus were induced by
OVAR (Fig. 2). It was necessary to keep the eyes
open in darkness to maintain the nystagmus. When
they were closed, the nystagmus became altered and
soon disappeared. There was considerable variation
in the responses, both among and between individuals. This made it difficult to tabulate group averages.
Among the 22 subjects studied, 15 had regular eye
movements with similar characteristics. Sample values from this group are shown in Fig. 4 and pooled
values are presented in Fig. 5. The other 7 subjects
had irregular movements, with sudden changes unrelated to stimulus, that were analyzed separately.
Eye velocity
Horizontal eye velocity
stimulation should not have been different from subject to subject.
Slight transient head tilts could have occurred, but the resulting
canal stimulation would have been weak and could not have
modified the low frequency ocular responses. In two subjects the
head was fixed to the head rest with a strip of cloth. This soon
became painful and was abandoned. In two other subjects the
head was stabilized with a bite-board. The results in these four
subjects were similar to those observed in subjects whose heads
were simply leaning on the head-rest.
The chair was a bucket seat with arm and foot rests and a
security harness. Since important tactile cues were felt during
OVAR, for two subjects the seat was fitted with a depression
mattress that was firmly molded to the body. This did not change
the results.
Horizontal slow phase velocity had two components
(Figs. 2 and 3), a sinusoidal modulation at the
frequency of rotation, superimposed on a mean eye
velocity. This was considered compensatory in that it
was in a direction opposite to head rotation. Both
components generally ranged up to 8 deg/s. However, mean velocities up to 20 deg/s and amplitudes
of modulation of 25 deg/s were encountered occasionally.
Effect of tilt of the rotation axis on horizontal eye
velocity. Weak nystagmic movements could be distin-
96
HORIZONTAL
Meanvelocity
Velocity modulation
8I
68 I Deg/s
4
0
PHASE1
6
~'X ~
Rotation
6
4
TTT
l
4
t
2
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180 NU
270/
LED~ ~ 9 0
Deg/s
Position modulation
= 20 I
8
0 Phasebead
ND
T
110 I 210 I
Deg/sVERTICAL ,
T 648 I Deg
1
RED2
T
0
l Ti
i 1~0 2~0 i
Angleof tilt indegrees
T *
0 i 1~0 i 2t0
Fig. 5. Summary of the results on 15 subjects with regular eye
movements. Same presentation as in Fig. 4, except that the polar
plot on the bottom left, is similar to that of Fig. 5. Each point in
the diagram stands for the average of the measurements made on
the 15 subjects. Standard deviations are represented by vertical
segments. The polar plot is divided into sectors identified by
numbers. Each sector represents the range of the maximum of the
modulation of one nystagmic variable. 1: Vertical upwardmost eye
position - 2: Horizontal compensatory eye position - 3: Vertical
upwardmost eye velocity - 4: Horizontal compensatory eye
velocity. The compensatory direction is toward the left in this
figure, as rotation has been conventionally figured clockwise
guished from baseline for tilts of the axis of rotation
of 5 degrees and above.
The relationship between eye velocity and tilt
angle is illustrated in Fig. 4 for 2 subjects, and in
Fig. 5 for the 15 subjects with regular eye movements. In most subjects, mean velocity and modulation amplitude increased with tilt angle. However,
for the group as a whole, mean velocity varied
around 3 deg/s for tilts of the axis of rotation up to 20
degrees, and increased thereafter. This is due to the
large spread of the responses.
In some subjects, at a given tilt angle, mean eye
velocity diminished with time, and was sometimes
smaller at the end of the experiment than at the
beginning, even if the tilt angle was greater. Exceptionally, amplitude of eye velocity modulation was
also reduced, as the tilt angle was increased. Generally, malaise or a drop of attention occurred simultaneously.
Effects of rotation velocity. For all subjects, both
components of horizontal eye velocity increased with
rotation velocity. At a tilt angle of 10 degrees, in the
10 subjects with regular eye movements that were
tested at several velocities, average values of mean
velocity and velocity modulation increased respectively from 2 to 8 deg/s and from 2 to 6 deg/s when
head rotational velocity increased from 30 to 60 deg/s.
In the three subjects tested at higher velocities, mean
eye velocity showed sudden variations within the
range 4-8 deg/s, and decreased when rotation velocity was further increased. In the two subjects that
were rotated at 120 and 140 dens, mean eye velocity
decreased to 0 after about two minutes, and only a
cyclic modulation of slow phase eye velocity
remained. For one of these subjects, whose eye
movements were especially fast, amplitude of modulation increased linearly from 5 to 20 deg/s when
rotational velocity was increased from 30 to 140 deg/s
(R-sq = 0.8).
Vertical eye velocity
OVAR also induced a cyclical modulation of vertical
eye velocity (Figs. 2 and 3). The amplitude of
modulation varied from 0 to 25 deg/s, depending on
the subject and the tilt angle, but most often ranged
between 0 and 12 deg/s. For the 15 subjects with
regular eye movements, the average amplitude of
modulation of vertical eye velocity increased proportionally with tilt angle, from 2.3 deg/s at 10 degrees to
7.4 deg/s at 25 degrees of tilt. This held true both for
individual subjects (Fig. 4) and for the group as a
whole (Fig. 5, R-sq = 0.9).
The mean vertical eye velocity was equal to zero
in most subjects. In some individuals it could be
directed either upward or downward. It never
exceeded 4 deg/s, and was the same at all tilt angles
and velocities for the same subject on the same day.
In one subject with downward beating nystagmus,
mean vertical slow eye velocity increased from 3 to
16 deg/s when the velocity of rotation was increased
from 30 to 120 deg/s. The amplitude of modulation of
the velocity did not change, however. Another
subject, recorded twice at an interval of several
months, had a downward beating nystagmus on one
occasion and upward beating nystagmus the second
time. On both occasions, mean horizontal eye velocity was opposite to head rotation.
Slow phase eye velocity and nausea
Subjects suffering from nausea often made smaller
and slower eye movements than those without symptoms. Mean eye velocity was strongly reduced. The
modulation in eye velocity was usually, but not
necessarily, reduced. One subject, who performed
the whole experiment, suffered from malaise from
97
OFF-VERTICAL AXIS ROTATION CW 45 Deg/s
41' Position left
In Velocity left
Subject.1
Nose up
180
() Position up
[ ] Velocity up
Subject 2
Nose up
180
210
7
Fo
/
150
.I
25
20
9^
\o.oo
oeo,,
Deg or Deg/s
300 \
I
,
25
25\
j
6o
o2s
.ot~t~o~~~ ~ o
Nose down
Degrees
Nose down
~Ph~selead
Degrees
Fig. 6. Polar plots showing the phases and modulation amplitudes of the oculomotor responses represented in Fig. 4, when axis tilt angle
was increased, at 45~ of clockwise head rotational velocity. Same symbols as in Fig. 4: squares for velocity and diamonds for position;
open symbols for horizontal movements, filled symbols for vertical movements. Values of axis tilt angles are written in small numbers
beside the points. The scale in degrees or degrees per second is drawn on the radius. Rotation progressed from nose-down position (0 deg)
to left ear down position (270 deg) and so on, as indicated by the thin rounded arrow below 330 degrees. Phase leads are counted positively
in the trigonometric (counterclockwise) direction, as indicated by the thin rounded arrow below 30 degrees. Each point is the tip of a vector
whose origin is the center of the diagram, whose magnitude is proportional to the amplitude of modulation of the variable, and whose phase
is that of the maximum of the variable. Subject 1 had regular and Subject 2 irregular eye movements. Note that vertical position and
velocity (open symbols) were about 90 degrees apart, but that the phase angle between horizontal position and velocity (filled symbols) was
more variable, but always greater than 90 degrees
the beginning. He had no modulation in eye velocity,
but nystagmus with mean velocities between 2.3 and
5.3 deg/s was present for rotational velocities between 30 and 90 deg/s. At 120 deg/s, a modulation in
eye velocity of 24 deg/s suddenly appeared. At that
time the mean eye velocity was 46 deg/s. He was
considered to be in the irregular group.
Eye position changes
Absolute eye position could not be accurately measured, particularly in the vertical direction, due to
slow drift of the E O G signal. However, :there were
clear shifts of average eye position in the direction of
the slow phases of horizontal nystagmus, as welt as
shifts of vertical eye position (Figs. 2 and 3).
The amplitude of the cyclical shift in horizontal
eye position could vary from 0 to 12 degrees at any
tilt angle, depending on the subject (Figs. 2 and 3).
In individual subjects, amplitude of eye position
modulation increased with tilt angle (Fig. 4B).
Group averages were about 2 degrees for tilts of the
rotational axis of 5 degrees, increasing to about
4 degrees for tilts of 25 degrees (Fig. 5). Changes in
the beating field of nystagmus were particularly large
in two subjects, varying up to 16 degrees. The
relationship between head velocity and change in the
beating field varied from one subject to another, but
remained regular for each subject.
The amplitude of the shift in vertical eye position
ranged from 0 to 16 degrees at any tilt angle, with
considerable intersubject variability (Figs. 2 and 3).
For the subjects shown in Fig. 4, it increased monotonically with tilt angle. For the group as whole,
there was also an increase in the amplitude of the
modulation in eye position, going from 1 degree at 5
degrees of tilt of the rotation axis to 4.5 degrees at 25
degrees of tilt (Fig. 5).
When rotation velocity was increased, whatever
the initial value and at any tilt angle, the cyclical
shifts in horizontal and vertical position increased by
about 20% during the next 10 s. Then, they slowly
dropped back to the previous steady state value,
which was stable for each subject. A change in head
rotation velocity, therefore, had no long-lasting
effect on eye position, which was a gravity-dependent
response.
98
Subject2
~
~
N=6
45~'s
Amplitudeof saccades
L
l
N=IO
45~
Amplitudeof saccades
1(~ig15.
~
0
90
180
270 360
[- ' - 7 ~ ~ ] ~ N u mofbsctccades
er
- ~ ] 010
0
Subject 3
90
180 270
Cumulativepositionshift
0
560
go
180 , 270
Numberof saccades
360
go
360
180
i
270
100
g
eg
0
90
180
Phase
in degrees
270
560
~
0
90
180 I
~
270
J
360
Phase in degrees
Fig. 7. Average distributionof horizontal components of nystagmicfast phases within a cycle,for two subjects. Abscissa: Phase, from 0 to
360 degrees. Ordinates, from top to bottom: - Amplitudesof saccades, each vertical segmentrepresentingthe amplitude of one saccade, at
its phase of occurrencewithinthe cycle- Number of saccades. Average number of saccadesoccurringin each time interval during whichthe
head has rotated by 30 degrees- Cumulativeeye position. Sum of the amplitudesof the saccades occurringduring each time interval. For
each subject, peaks in beating-frequency, amplitude and velocity of horizontal components of nystagmic fast phases occurred
simultaneouslywith maximumslow eye velocity.Subject 2 was representative of the most commonlyobserved pattern. Fast phases were
unevenlydistributed in all subjects. Averages of 6 cyclesfor Subject 2 and 10 cyclesfor Subject 3, are shown on these graphs
Phase relations
Phases of eye velocity and eye position modulations
in horizontal and vertical directions are plotted in
Fig. 6, in polar coordinates, for two subjects rotated
clockwise at 45 deg/s. Each point on the diagram
represents the maximum positive value of a sinusoid
fitted to horizontal or vertical eye velocity or position. The number beside the point shows the tilt
angle of the axis of rotation. Upward and leftward
movements (i.e., in the direction opposite to head
rotation) are denoted as positive values. The distance
from the center of the diagram represents the
amplitude of the response. Its angular position with
respect to the origin represents the phase with
respect to the nose-down position (Stockwell et al.
1970). Phase angles were incremented positively in
the trigonometric (counterclockwise) direction. For
instance, a point whose phase is 60 deg represents a
response whose positive maximum leads the nosedown position by 60 deg. The polar diagram at the
bottom left of Fig. 5 shows the range of the phases of
velocity and position for the group with regular eye
movements.
The phase of the maximum compensatory horizontal eye velocity, i.e., in the direction opposite to
that of head rotation, ranged between 150 and
260 deg, depending on the subject (Fig. 6). Most
commonly, it ranged within 180-240 deg and was
about 210 deg for subjects with regular eye movements (Fig. 5). All subjects did not behave in the
same way. There were large variations of phase, that
increased with increasing tilt angles in many subjects
with irregular eye movements (e.g. Fig. 6, Subject 2).
The phase of maximum compensatory horizontal
eye position, in the direction opposite to lateral head
tilt, was regularly about 70 deg in advance of the
nose-down position (range 60-100 deg) in subjects
with regular eye movements (Fig. 6, Subject 1).
Occasionally, other subjects showed phases out of
this range (Fig. 6, Subject 2). The modulation in
horizontal eye position was measured for the 3 subjects rotated at 30, 45, 60 and 90 deg/s at 10 degrees
of tilt. At each rotation velocity, the amplitude was
multiplied by the pulsation. This gave the amplitudes
of the derivative of the position modulation. These
were always smaller than the amplitude of modulation in velocity. This difference must be due to the
variation in beating frequency and size of the saccades during each cycle.
In contrast, the maxima of the modulations in
upward eye velocity and eye position were tightly
phase-locked. For all subjects, at any tilt angle, the
99
phase of the maximum upward eye velocity occurred
regularly about 90 deg in advance of the nose-down
position (range 80-110 deg). Moreover, the phase of
the upwardmost position remained around zero deg,
never leading the nose-down position by more than
10 deg nor lagging behind it by more than 30 deg.
Vertical eye position shifts during O V A R were,
therefore, compensatory for head tilt in the pitch
plane.
An estimate of the amplitude of the derivative of
the modulation in vertical position was calculated
and compared to the modulation in velocity. The
actual modulation was greater than the estimated
derivative.
Distribution of the fast phases of nystagmus
Fast phases were not evenly distributed throughout
the cycle. As illustrated for two subjects in Fig. 7, the
amplitude and number of saccades and the cumulative shift in eye position tended to occur at the same
phase angle as the maximum slow eye velocity. As
slow eye velocity increased with tilt angle or rotation
velocity, these values also increased.
Discussion
The continuous nystagmus induced by yaw rotation
about axes tilted at small angles from the vertical,
consisted of changes in horizontal and vertical eye
position and velocity, with broad variability between
and among subjects.
The different variables will be successively considered.
Mean slow phase eye. velocity
Mean horizontal slow phase eye velocities elicited by
OVAR were invariably compensatory, i.e. in the
direction opposite to that of head rotation. In most
subjects, the threshold for the appearance of a
nystagmic response was at a tilt angle between 10 and
15 degrees (Fig. 4), although it can be lower, at
about 5 degrees for some individuals. The latency of
appearance of the response could not be determined
because of the slow dynamics of the hydraulic jacks
that moved the axis of rotation. In the monkey it is
about one second (Raphan et al. 1981).
In monkeys, mean horizontal velocities of
40-50 deg/s are commonly achieved during O V A R at
60 deg/s and 30 degrees of tilt (Raphan et al. 1981).
In contrast, mean compensatory velocities reached
by our subjects never exceeded 20 deg/s and generally ranged between 0 and 8 deg/s at a rotational
velocity of 45 deg/s (Fig. 5). Similar results were
obtained by Stockwell et al. (1970) and Harris and
Barnes (1986) during O V A R at higher tilt angles,
and by Benson and Barnes (1973) during counterrotation: Thus, in humans, the gain of the eye
velocity that compensates for head velocity during
OVAR seems to never exceed 0.2 and be often
lower.
The interpretation that, velocity storage mechanism produces horizontal mean eye velocity, during
OVAR, is supported by the observation that this
velocity was always equal to or less than the peak
velocity of OKAN induced by OKN at the same
rotation velocity. VSM saturates at 10-15 deg/s in
most humans (Cohen et al. 1981; Jell et al. 1985);
since mean eye velocity varies in the range 2-8 deg/s,
its measurement during O V A R could give an adequate index of functioning of VSM. A tilt angle of no
more than 15 degrees would be enough for this test,
as Young and Henn (1975) showed that mean eye
velocity tended to saturate at tilt angles greater than
30 degrees.
The magnitude of the rotating vector, which is
the driving force activating the otolith organs,
increases proportionally to the sine of the tilt angle.
Therefore, a likely possibility would be that the
components of horizontal eye velocity would follow
the same rule. For the tilt angles that were used, the
values of the angle in radians and its sine are very
dose. As a result, the increase in mean velocity
should have been close to linear. Despite a large
spread, this was the case in many subjects. In other
subjects, the slope of the increase was greater at 10
than at 30 degrees of tilt angle. This could be due to
the decrease of VSM gain with increases in tilt angle
(Raphan and Cohen 1985).
During barbecue rotation, horizontal mean eye
velocity increased when rotation velocity was
increased from 0 to 100 deg/s, and then decreased to
0 when rotation velocity was further increased to
180 deg/s (Correia and Guedry 1966; Guedry 1970).
During OVAR, as Stockwell et al. (1970) observed,
mean velocity decreased to zero after two minutes of
rotation at high velocities (120 and 140 deg/s). Thus,
a neural circuit behaving as a low-pass filter should
exist in the otolith-ocular pathway (Mayne 1974).
Raphan and Schnalbok (1988) have proposed a
mechanism for estimation of velocity during OVAR.
They postulate that the CNS calculates a velocity by
comparing a pattern of input from the otolith organs
with a previous pattern. Their model outputs an
estimate of velocity that falls to zero at high speeds of
rotation. In addition, high rotational velocities shorten the dominant time constant of the velocity storage
mechanism (Raphan et al. 1979). Thus, there could
100
either be a reduction in the ability to estimate the
velocity of head rotation and a drop in the signal
driving the VSM, or a reduction in the saturation
velocity and output of the VSM itself, which, in turn,
would cause lower mean slow phase velocities.
Vertical mean eye velocity (i.e. mean velocity in
the sagittal plane) was absent or very small during
O V A R in humans and in monkeys (Raphan et al.
1981). This is consistent with the finding of Harris
and Barnes (1986). Although velocity storage in the
sagittal plane is present during forward-downward
head movements in the cat (Darlot et al. 1981) and
monkey (Matsuo and Cohen 1984). It supports the
interpretation that, during O V A R , storage would
require a sustained sweeping of the maculae by an
acceleration vector rotating for at least one minute in
the same direction. Indeed, polarization vectors of
most saccular sensory ceils are aligned with the
sagittal plane (Fernfindez et ai. 1972; Fernfindez and
Goldberg 1976b; Goldberg and Fernfindez 1982).
The vector which stimulates these cells is, therefore,
the sum of the constant vector along the Z axis and
the component along the X axis. It is this latter
component which actually changes with time, and
stimulates the sensory cells. It sweeps the saccular
maculae from forward to backward during a half
cycle (4 s at a rotation velocity of 45 deg/s, and in the
reverse direction during the other half cycle. In terms
of system analysis, assuming that a vertical VSM
exists; having similar dynamics as horizontal VSM, it
should behave as a first order low-pass filter, with a
time constant of 15 s, its corner frequency should be
0.067 Hz. The neural activity induced in the sensory
cells by a rotation at 45 deg/s corresponding to a
frequency of 0.125 Hz, would therefore be completely filtered out, so that the output of the VSM
would be zero. In contrast, Harris and Barnes (1986),
recording with a search coil, observed in humans and
cats a small vertical mean velocity in the upward
direction, which might reflect the functioning of the
direct pathway, by-passing the VSM, to the ocular
motoneurons. Indeed, although a small vertical mean
velocity recorded by E O G could just be the result of
some minute artefactual coupling between horizontal
and vertical traces, this should not occur with a
search coil.
Modulation in eye velocity and eye position
Amplitudes of horizontal eye velocity modulation
measured in this study were comparable to those
observed during O V A R by Stockwell et al. (1970),
and slightly greater than those observed by Harris
and Barnes (1986). They are consistent with the
observations of Benson and Barnes (1973) during
counter-rotation, Correia and Guedry (1966) and
Guedry (1970) during barbecue rotation, and Buizza
et al. (1980) during lateral oscillations. They were
twice greater than most L-nystagmus amplitudes
(Young 1967, 1972).
Maxima in horizontal slow eye velocity in the
direction opposite to head rotation occurred in most
subjects 30 deg in advance of the nose-up position.
This phase angle matches with previous measurements (Stockwell et al. 1970), and also coincides with
the phase of perception that the force vector is acting
backward in the sagittal plane during O V A R (Benson et ah 1975) and counter-rotation (Benson and
Barnes 1973).
Velocity storage does not appear to be involved
in the modulation of horizontal eye velocity during
OVAR. Indeed, modulations persisted at high velocities of rotation, when mean eye velocity had dropped to zero. This is consistent with the observation by
Niven et al. (1966) that during sinusoidal translational oscillations along the Y axis, the decay of the
nystagmus was immediate after removal of the
stimulus. It is neither likely that velocity storage be
involved in producing modulations in vertical eye
velocity.
For rotation at 45 deg/s and 30 degrees of tilt, the
peak angular velocity in the sagittal plane to which
our subjects were submitted was 23.6 deg/s. There
was little or no mean velocity, but the average
modulation amplitude in vertical velocity was about
8 deg/s, or a gain of 0.34. This modulation did not
change when rotation velocity was increased, indicating that the two were independent. The amplitude of
vertical eye velocity modulation was found to be
smaller by Harris and Barnes, in man: the gain was
0.06 at a rotation velocity of 60 deg/s and 30 degrees
of tilt angle.
The question arises whether the otolithic signals
which produce eye velocity modulations are related
to head position or to head velocity. During O V A R
at 60, 45 and 30 deg/s, head position rotates with
regard to gravity each 6, 9 or 12 s at frequencies of
0.17, 0.11 or 0.08 Hz, respectively. The output of the
otolith organs would be mainly related to head
position at these frequencies (Fernfindez and Goldberg 1976a-c).
The vertical eye position changes were surprisingly regular, and compensated for changes in head
position in the pitch plane. As their amplitude was
dependent on the angle of tilt of the axis of rotation,
but not on rotational velocity, they were probably
driven by an eye position signal.
The change in horizontal eye position was more
complex. During rotation about a vertical axis, in the
absence of an otolith induced change in eye position,
101
the beating field of nystagmus depends on the
distribution of saccade frequency and amplitude,
which, in turn, is prominently controlled by slow
phase eye velocity (Chun and Robinson 1978; Guitton and Voile 1987). During OVAR, on the other
hand, the modulation in slow phase velocity was not
the derivative of the modulation of position (Fig. 5).
A double control in velocity and position could
therefore exist, and the adjustment be made by
saccade amplitude and distribution.
Positional changes in the yaw and pitch plane that
compensate for head position with regard to gravity
are well known in lateral eyed animals, but have not
been noted before in humans to our knowledge.
During OVAR, in the absence of vision or canal
input, they could arise either from otolithic or
somatosensory informations. There is little information about somatosensory effect on eye position in
humans, but in the monkey, the weak eye position
changes induced by tilt with respect to gravity are
mainly due to otolithic inputs (Krejcova et al. 1971).
Therefore, in humans, the horizontal and vertical
positional changes induced by O V A R probably also
arise mainly from the otolith organs.
Ocular counter-rolling is not registered by EOG,
and therefore was not measured in this study.
Diamond and Markham (1983) showed that counterrolling is the same whatever way the ear-down
position is reached, either by tilting from the upright
to the side-down position, or by rotating, as during
OVAR. In the present experiment it would be
expected that tilts of the rotation axis would have
induced 4 to 8 degrees of counter-rolling. By analogy
with vertical eye position changes, counter-rolling
would be independent of rotational velocity. Thus,
compensatory eye position shifts are probably present during OVAR, with the eyes moving up and
down, side to side and counter-rolling, as the head
moves through each cycle of rotation.
During ocular counter-rolling, the e y e rolls
around the line of sight. Horizontal and vertical
EOG traces could therefore have been affected by
counter-rolling when the line of sight did not coincide
with the X axis. Whether this actually occurred is not
known, but contamination of E O G traces by
counter-rolling could perhaps explain the difference
in amplitude of modulation and in the phases
between our results and those of Harris (1985)
obtained with search coils.
Causes of variation
Several factors could be responsible for the variability of the obtained results. First, sensations of
discomfort were induced in many subjects, even at
small angles of tilt, after 10 to 20 min of OVAR.
Malaise and a loss of attention could have affected
slow phase velocities. Since testing proceeded from
lower to higher velocities of rotation in most subjects, this could have reduced the mean and modulation values of the responses at higher stimulus
velocities. Moreover, when the rotation axis is vertical, exposure to passive rotation reduces the dominant time constant and the saturation velocity of the
velocity storage mechanism. If habituation were to
occur over the course of testing, it could also have
reduced mean eye velocities at the higher stimulus
velocities, which were usually tested last. All these
factors, and also the fact that canals were not
stimulated while otoliths were, could explain why
maximum values of mean eye velocities during
OVAR were somewhat lower than peak OKAN
values in the same subjects. In addition, the visual
task given to the subject, which was not precisely
controlled here, is probably also an important factor
(see below).
In summary, slow velocity of nystagmus induced
in human subjects by rotation about an axis tilted at
small angles from the vertical, show cyclical modulations around a mean value probably produced by the
velocity storage mechanism. Cyclical modulations in
vertical eye position and velocity probably compensate for changes in head position with regard to
gravity. Their regularity and magnitude suggest that
they could be used to check otolith function.
Functional interpretation of nystagmus induced by
OVAR
We hereafter present a theoretical analysis that could
account for the observed eye movements.
As any movement can be, at any time, decomposed into the sum of a translation and a rotation, a
head displacement generally stimulates simultaneously the semi-circular canals and the otoliths. In a
re-examination of the gain of the vestibulo-ocular
reflex, Viirre et al. (1986) established that perfect
stabilization of a point image on the retina requires
the gain of the V O R to follow the equation:
E'R = - H'R q- H'T X P / p2
(1)
E'R: angular eye velocity.
H'R: angular head velocity.
H'T: translational head velocity.
P : vector having as origin the eye, and as tip the
point of the surrounding world whose image is
stabilized.
x : cross product.
102
1) The CNS estimates H'R, via the VSM (Raphan
and Cohen 1981, 1983, 1985; Hain 1986).
2) The CNS estimates translational head velocity
from the otolithic signal, via an unknown neural
circuit. This is likely, as translational head velocity
can be estimated by subjects submitted to translational accelerations (Meiry 1965; Young and Meiry
1968).
I
I-i T
/
/
/
D
Fig. 8. Valueof eyevelocitycompensatingfor headtranslation.To
stabilize one point on the retina duringhead translation,the eye is
to rotate at a velocitydepending,througha vectorialrelationship
(see text) on head translationalvelocity(H'x), and distance (D)
along the line of sight (LS) of the target (T). E is a unitaryvector
along LS
All these quantities are vectorial and expressed in
head coordinates. This equation gives the angular
velocity needed for a cyclopean eye having the same
center of rotation as the head to stabilize the image of
one point on the retina, not necessarily on the fovea.
The rotation centers of the head and eye are considered to be coinciding. The transformation described
by the second term of the right member is illustrated
by Fig. 8. This term does not account for any
counter-rolling, i.e. eye rotation around the direction
of P, as the cross product of two vectors of which one
is P itself has no component along P. This equation is
valid instantaneously; to describe eye velocity during
vestibular stimulation, one must also know how the
central nervous system (CNS) estimates H'R and H'T.
This equation simplifies to the classical VOR equation E' R = - H'R when the translational head velocity is zero, or when the distance of the stabilized
point is infinite.
Results obtained during simultaneous stimulation
of canals and otoliths are quantitatively accounted
for by this equation (Gresty and Bronstein 1986;
Gresty et al. 1987). Assuming that it describes the
actual functioning of the VOR, there remains the
questions of the head coordinates used by the CNS
(Raphan and Cohen 1985), and how cross products
are performed.
A differential equation gives the change of P
which results from an actual head displacement:
d P / d t = ' H ' T - H ' R X P.
(2)
To interpret the results of OVAR, we propose
adding several hypotheses:
3) P is the gaze vector, given by the relation:
P=E.D
The direction of this vector is the line of sight, and its
magnitude is the distance of a target, actual or
imaginary. In this latter case, for instance in darkness, VOR gain can be modified by a mental
resetting of the imaginary target (Barr et al. 1976;
Baloh et al. 1984; Melvill-Jones et al. 1984). When
no clearly located imaginary target can be evoked, D
is set to a default value, which is neither zero nor
infinite. An argument in favor of this hypothesis is
that the gain of the eye velocity modulation decreases
when the eyes are closed, due perhaps to cancellation
of the second term of the right side of Eq. (3), or to
the setting of D to infinite.
Equation (1) then becomes Eq. (3), valid even in
darkness, (and in which ocular counter-rolling is also
given only by the first term of the right side).
E'R = - H ' R + (H'TX E) / D
(3)
D: distance between the eye and the target.
E: eye position vector i.e. vector of unit length,
having the direction of the line of sight.
Another differential equation links E'R and E:
dE / dT = E'rt x E.
(4)
During OVAR, the components of the rotating
vector on X and Y vary in quadrature, and so would
H'T, the estimate of head translational velocity, with
a lag % depending on stimulation frequency. Its
three components on the stereotaxic axes would be:
On X axis:
On Y axis:
On Z axis:
[H'T] cos (cot + c9)
]H'a-[ sin (cot + q~)
0.
The three components of the eye position vector are:
On X axis:
On Y axis:
OnZaxis:
Ex
Ey
E z.
103
As the subjects look forward, IExl is great with
respect to IEyl and lEvi. The components of the cross
product H'T x E are then:
On X axis: IH'TI " Ez 9 sin (cot + q~)
On Y axis: - [H'T[ 9 Ez 9 cos (cot + q))
On Z axis: IH'TI " (Ey 9 cos (cot + qg) - Ex 9 sin
(cot +
O r : - IH'T[ 9 ~/Ex2 + Ey2- sin (cot + qo - |
With: @ = Arctg (By / Ex).
O is therefore equal to the angle between the straight
ahead direction and the gaze direction, in the horizontal plane, and is small if the subjects look ahead.
The phase of the horizontal eye velocity modulation
should therefore be very close to %
Division of these three components by D gives
respectively the velocity of rotation of the eye around
the X, Y and Z axis. Rotation around X axis is not
counter-roUing, which is rotation around P.
Horizontal eye velocity modulation
Rotation of the eye around the Z axis describes
horizontal eye velocity modulation. Its gain is:
IH'z[ 9 ~/Ex2 + Ey 2 / D.
Each term is potential source of variation:
1) Estimate of translational head velocity may vary
with time, especially if it derives from the combination of several sensory inputs (vestibular, tactile and
proprioceptive).
2) Gaze orientation changes when it is reset to a new
target. This could occur often in darkness, when the
target is imaginary. The resulting gain variation
should be small if the subject keeps looking ahead,
i.e. if IEyl remains small with respect to [Ex[; but
could be large if considerable gaze shifts would
occur.
3) The distance of the target, D, may also be reset.
To estimate the default value of D, one must know
how the CNS estimates H'T from an acceleration
signal. Assuming that translational head velocity is
accurately estimated during lateral oscillations, and
that the subjects were looking straight ahead, default
value may be estimated at 27 + 9 m from the results
of Niven et al. (1965), and at 18 + 9 m from those of
Buizza et al. (1980). These values are so large, that
they perhaps represent a resting position of the eye
rather than the distance of an imaginary target.
According to Eq. (3), the cross product of the
estimate of H'T and E should be maximal when
horizontal slow eye velocity is maximal. These two
vectors should therefore be orthogonal at a phase
angle of about 210 degrees. Provided the subjects
were looking straight ahead, the estimate of H'ashould then be in the frontal plane. During barbecue
nystagmus, maximum compensatory slow eye velocity occurs when the gravity vector is aligned with the
Y axis (Benson and Bodin 1966; Correia and Guedry
1966; Saito et al. 1968; Wall and Black 1984). This
leads the response during O V A R by 30 to 50
degrees. Hence, the phase lead could possibly
increase with tilt angle (see also subject 2 in Fig. 5).
Vertical eye velocity modulation
Rotation of the eye around the Y axis describes
vertical eye velocity modulation. Its expression,
derived from the second term of the right side of
Eq. (3), is:
-IH'T] 9 E z . cos (cot +
/ D.
The result of this expression is small, as Ez is far
smaller than 1. Its sign depends on that of Ez, and
therefore, its phase can change by any angle between
0 and n radians, depending whether the subject's
gaze is upward or downward. These characteristics
are not consistent with the experimental results.
Therefore vertical eye velocity modulation cannot be
accounted for by this expression. It can on the
contrary be described by the first term of the right
side of Eq. (3): - H'R. Head velocity in the sagittal
plane could thus be sensed through the change in
orientation of the gravity vector, and would elicit
vertical eye movements, via the direct vestibuloocular pathway which has no storage, and would
have a gain smaller than 1.
Acknowledgements, The authors thank M. Ehrette for his technical help, Dr. Vidville for the acquisition program, and Dr. M.
Smith for help with the English text. This study has been
supported by the CNRS LP002, CNES 51003 and NS 00294. A
preliminary report has been presented at the meeting of the
Barany Society, Ann Arbor, Michigan, May 21-24, 1985.
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Received March 25, 1987 / Accepted April 22, 1988