Interocular yoking in human saccades examined by mutual information analysis.

Abstract

Saccadic eye movements align the two eyes precisely to foveate a target. Trial-by-trial variance of eye movement is always observed within an identical experimental condition. This has often been treated as experimental error without addressing its significance. The present study examined statistical linkages between the two eyes' movements, namely interocular yoking, for the variance of eye position and velocity.
Horizontal saccadic movements were recorded from twelve right-eye-dominant subjects while they decided on saccade direction in Go-Only sessions and on both saccade execution and direction in Go/NoGo sessions. We used infrared corneal reflection to record simultaneously and independently the movement of each eye. Quantitative measures of yoking were provided by mutual information analysis of eye position or velocity, which is sensitive to both linear and non-linear relationships between the eyes' movements. Our mutual information analysis relied on the variance of the eyes movements in each experimental condition. The range of movements for each eye varies for different conditions so yoking was further studied by comparing GO-Only vs. Go/NoGo sessions, leftward vs. rightward saccades.
Mutual information analysis showed that velocity yoking preceded positional yoking. Cognitive load increased trial variances of velocity with no increase in velocity yoking, suggesting that cognitive load may alter neural processes in areas to which oculomotor control is not tightly linked. The comparison between experimental conditions showed that interocular linkage in velocity variance of the right eye lagged that of the left eye during saccades.
We conclude quantitative measure of interocular yoking based on trial-to-trial variance within a condition, as well as variance between conditions, provides a powerful tool for studying the binocular movement mechanism.

Full text

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PROCEEDINGSOpen Access
Interocular yoking in human saccades examined
by mutual information analysis
Masaki Maruyama1,2*, Peter BC Fenwick3, Andreas A Ioannides3,1
From Consciousness and its Measures: Joint Workshop for COST Actions NeuroMath and Consciousness
Limassol, Cyprus. 29 November – 1 December 2009
Abstract
Background: Saccadic eye movements align the two eyes precisely to foveate a target. Trial-by-trial variance of
eye movement is always observed within an identical experimental condition. This has often been treated as
experimental error without addressing its significance. The present study examined statistical linkages between the
two eyes’ movements, namely interocular yoking, for the variance of eye position and velocity.
Methods: Horizontal saccadic movements were recorded from twelve right-eye-dominant subjects while they
decided on saccade direction in Go-Only sessions and on both saccade execution and direction in Go/NoGo
sessions. We used infrared corneal reflection to record simultaneously and independently the movement of each
eye. Quantitative measures of yoking were provided by mutual information analysis of eye position or velocity,
which is sensitive to both linear and non-linear relationships between the eyes’ movements. Our mutual
information analysis relied on the variance of the eyes movements in each experimental condition. The range of
movements for each eye varies for different conditions so yoking was further studied by comparing GO-Only vs.
Go/NoGo sessions, leftward vs. rightward saccades.
Results: Mutual information analysis showed that velocity yoking preceded positional yoking. Cognitive load
increased trial variances of velocity with no increase in velocity yoking, suggesting that cognitive load may alter
neural processes in areas to which oculomotor control is not tightly linked. The comparison between experimental
conditions showed that interocular linkage in velocity variance of the right eye lagged that of the left eye during
saccades.
Conclusions: We conclude quantitative measure of interocular yoking based on trial-to-trial variance within a condition,
as well as variance between conditions, provides a powerful tool for studying the binocular movement mechanism.
Background
Saccadic eye movements are rapid shifts of gaze onto a
new point in the visual field so that the image of the
object at that point falls on the fovea. When the two eyes
foveate the same object, visual performance is improved
in dim light [1], and the two eyes allow stereopsis
through detailed comparison of the retinal images from
the two eyes. The linking together of the movement of
the two eyes, usually by opposite muscle pairs is ‘yoking’,
one of the simplest statements of Herings Law or the law
of equal innervation. With horizontal saccades to the left
the yoked pair are predominantly the lateral rectus of
the left eye and medial rectus of the right. Yoking during
saccades has to be maintained in the presence of
an asymmetry of muscle strength and media stiffness.
Collins et al [2], have shown that for maintaining extreme
horizontal gaze the medial rectus developed a force 26%
greater than the lateral rectus. There is also an asymme-
try of the media, as the stiffness of tissues restraining
globe motion for the adducting eye was 11% greater than
for the eye in the abducting movement.
When a subject makes saccades from an identical
fixation point to an identical target, we always observe
variation of eye movements among the saccades. This
trial-to-trial variation has often been treated as just
* Correspondence: mmasaki1974@gmail.com
1Laboratory for Human Brain Dynamics, RIKEN Brain Science Institute, 2-1
Hirosawa, Wakoshi, Saitama 351-0198, Japan
Maruyama et al. Nonlinear Biomedical Physics 2010, 4(Suppl 1):S10
http://www.nonlinearbiomedphys.com/content/4/S1/S10
© 2010 Maruyama et al; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.

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experimental noise and cancelled out by averaging over
trials. However, Erkelens and Sloot [3] indicated by the
often-used correlation coefficient analysis that statistical
relatedness in trial-to-trial variance is strong between
the eyes’ saccade directions. A further paper looked at
trial to trial variation in peak velocity, saccade duration,
and curvature (angular velocity over time) and noted
that high variances in these measures were compatible
with saccade accuracy. They found the interocular cor-
relation of trial-to-trial variance was also high for peak
velocity, saccade duration and saccade curvature [4].
Their findings suggested the presence of a common sac-
cade generator for the eyes, which fluctuates among
trials. They also commented that assuming a local feed-
back loop was guiding saccades then the high correla-
tion between duration and curvature raised the
possibility of common feed back from the two eyes.
Their finding implies that intensive analysis of variance
will yield new insight into interocular yoking. In addi-
tion extracting maximum information from limited
sampled data could be valuable in clinical environments
because a short time for eye movement recording
reduces the stress for patients.
In this study we set out to examine interocular yoking
in horizontal saccades by looking at the variance
of movement for each eye across trials. The degree of
yoking was quantified by the technique of Mutual Infor-
mation (MI) analysis [5] which unlike correlation coeffi-
cient analysis, is sensitive to both linear and non-linear
relationships between the eyes movements. We wanted
to know if MI analysis might provide new evidence for
the functioning of the oculomotor system beyond that
given by classical correlation coefficient analysis. We
also used experimental differences in the averages and
standard deviations (SD) amongst trials for each eye.
The averages and SDs modulated by a common motor
driver for both eyes could also indicate the course of
interocular yoking.
Although eye position in horizontal saccades is a sim-
ple integration of velocity in each trial [6], non-linear
calculation of MI analysis over trials could in principle
provide different aspects of how position and velocity
are controlled. Therefore we compared the yoking in
the eyes’ positions with respect to velocity.
Finally we wanted to know if the degree of yoking can
assist studies on the effects of cognitive load. Our pre-
vious magnetoencephalographic (MEG) study in humans
observed an increase in interactive activity between the
brainstem and cerebellum during saccades with a high
cognitive-load task [7]. In the current study, we used a
subset of the identical saccade tasks used in the MEG
study and examined whether altering the cognitive load
influences the degree of yoking.
Methods
Subjects
Twelve healthy right-handed men participated in the
experiment. Their ages ranged from 19 to 39 years, with
a mean age of 27 years. All subjects had right eye domi-
nance, normal visual acuity and had neither ophthalmo-
logical nor neurological abnormalities. Right-handedness
was determined by the 10-item Edinburgh handedness
inventory [8] and eye dominance with the near-far align-
ment eye test. Six subjects were Japanese fluent in up/
down reading and the others were Caucasian with little
or no Japanese reading skills. Before starting the experi-
ment, the protocol and the recording method of eye
movements were explained, and participants gave
informed consent. All procedures were approved by the
RIKEN Ethical Committee.
Oculomotor task
Different tasks had different cognitive load, depending on
how the information about the movements and direc-
tions were given to the subject. Every trial started with
the illumination of a fixation point, a small cross, at the
centre of the screen (Fig. 1). While the subjects main-
tained fixation, two squares were simultaneously illumi-
nated on the horizontal axis to the left and right of the
fixation point at an angular distance of 12 deg. After an
interval of 1 – 3 s, an arrowhead was displayed at the
fixation point. The arrowhead’s direction indicated which
square was to be a target for the saccade. For the Go trial
the subjects made a saccade towards the target as soon as
they could after the appearance of the arrowhead and
then fixated the target until the squares disappeared and
the fixation cross reappeared in the centre of the screen.
In the NoGo trial, if the direction of the arrowhead was
downward, they were instructed to keep their fixation at
the centre and not to make a saccade. The trial ended
and the next trial began when the central fixation point
reappeared. The arrowhead always contained information
about the direction to move which was not available
before the trial. The degree of cognitive load was
increased in a Go/NoGo trial when the subject had to
process the Go/NoGo information.
Each subject had 12 sessions on two consecutive days
lasting about one hour for each day. Half of the sessions
contained only Go trials (Go-Only session) and the
other half contained Go and NoGo trials (Go/NoGo ses-
sion). Each session contained five leftward and five
rightward saccade trials in the Go-Only session and five
extra NoGo trials in the Go/NoGo session. Thus Go-
Only and Go/NoGo sessions consisted of 10 and
15 trials, respectively. These two types of sessions were
alternated and in each session the left and right direc-
tions were randomized. Before starting each session, the
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subjects were informed which session was to follow. The
total number of trials was 30 for each saccade task, left-
ward, rightward in Go-Only (total 60) and an additional
30 NoGo trials in Go/NoGo (total 90). The session
types were Go-Only, Go/NoGo and experiment days
were 1stand 2nd.
Visual stimuli
The visual stimuli were presented on a 21-in. flat CRT dis-
play placed 58 cm distant from the subjects. The squares,
arrowheads and the fixation cross subtended 0.85 deg.
The display had a frame refresh rate of 85 Hz. The stimuli
were generated by Presentation software (Neurobehavioral
systems, Inc., version 0.80, Albany, CA, USA).
Recording and preprocessing
Eye movements were recorded with an infrared reflec-
tion system (Takei; TKK2901). Before starting each ses-
sion, the system was calibrated by asking the subjects to
fixate several times at 12 positions around the edge of a
square (24 × 24 deg) and at the center. This procedure
was repeated until the calibration was adequately per-
formed. The subject’s head was stabilized by supports
for the chin and forehead. Eye position was recorded
from both eyes independently and simultaneously at
a frequency of 1000 Hz. The system had a noise level
of 0.13 deg. The horizontal eye position and the image
signals were stored on a computer for off-line analyses.
Eye velocity was calculated by off-line differentiation of
the position records between neighboring time slices.
Our approach was to characterize each saccade by
three latency features. The first feature defined the start
of the saccade and it is called the saccade initiation time.
The second feature corresponded to the latency with
maximum eye velocity and it is called the peak-velocity
time. The third feature defined the end of the saccade
and it is called the saccade end time. These parameters
were defined automatically based on eye velocity criteria.
For the details of the automatic procedures, please see
the Supplementary Materials in Additional file 1. The
Go/NoGo
Go-Only
No saccade
Leftward
saccade
Rightward
saccade
Fixation
Fixation
Rightward
saccade
Fixation
Fixation
2 s
1-3 s
1 s
2 s
1-3 s
1 s
Figure 1 Schematic representations of the stimulus display sequence and the oculomotor task in the Go-Only sessions and in the
Go/NoGo sessions. Every trial started with the fixation of a small central cross. Two squares, targets for the saccade, were then presented
simultaneously on both left and right sides of the fixation cross. The direction of the saccade was shown by the pointing of an arrowhead
which then appeared in place of the fixation cross. In the Go-Only sessions, the subjects made a saccade to one target in each trial. The
Go/NoGo sessions contained trials in which the arrowhead pointed downward instructing the subjects to hold the fixation.
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initiation time was used to align the saccades’ data over
the trials for the analyses of average and standard devia-
tion (SD), and also for MI and correlation coefficient
analyses.
Eye positions and velocities for each trial were seg-
mented for 50 ms before and 100 ms after the detected
saccadic initiation. Trials were excluded that contained
too early onset, <150 ms after the start of the cue
image, or too late >800 ms, or a saccade toward the
opposite direction, or were contaminated by blinks.
Between 9 and 30 trials were obtained for each saccade
direction, session type, experiment day and subject (25
trials on average).
Statistical analysis of average eye movement
Each eye can show different movements by varying the
experimental conditions (leftward vs. rightward, Go-
Only vs. Go/NoGo, 1stday vs. 2ndday). The differential
effect of the condition on the eyes indicates the yoking.
We first tested each condition’s effect on each eye’s
velocity by the examination of the velocity from each
time slice using an analysis of variance (ANOVA) SPSS
15.0 (SPSS Inc., Chicago, Illinois, USA). We identified
significant effects in the velocity that were common
between the eyes. The ANOVA was set up to examine
differences in average velocity, thus this approach
showed yoking based on the average velocity changes
following the different experimental conditions.
Because of the number of slices analysed many Type 1
errors were expected to occur by chance, so the effects
were defined only as significant when they continuously
satisfied the criterion for a Type 1 error of p<0.05 for
10 ms or more. When interactions were significant,
post-hoc multiple comparisons were performed using
Scheffe’s procedure. An identical method was also used
for the analysis of eye positions.
Mutual information analysis
In MI analysis, the key measurement for quantification
of relationships among variables is entropy [5]. For
example, the entropy of the left eye can be partitioned
into NLEpossible states defined as
H LE
(
pipi
LE
i
N
=∑
LE
LE
)( )ln( )
= −
1
(1)
where pLE(i) is the probability that the left eye will be
in state i and pLE(i) = 1. The entropy for events of the
right eye can be correspondingly defined as
H RE
(
pjpj
RE
j
N
=∑
RE
RE
) ( )ln( )
= −
1
(2)
Simultaneous recordings of the two eyes’ movements,
as in this study, allowed the measurement of the joint
probability, p(i,j), that the left and right eyes will be in
state i and j. The entropy of joint events is
H LE RE
(
p i j
( , )ln ( , )
p i j
j
N
i
N
∑
RE LE
=∑
1
,)
= −
=
1
(3)
where ΣΣ p(i,j) = 1. If statistical interactions or com-
mon influences exist between the two eye’s movements,
i.e., p(i,j) ≠ pLE(i)pRE(j), information on the right (left)
eye’s state can reduce the uncertainty on the left (right)
eye’s state, which can be represented by a reduction of
the joint entropy. The MI quantifies this reduction as
I LE RE
(
H LE
(
H RE
(
H LE RE
(,))),)
=+−≥ 0
(4)
The MI vanishes only if the two eye’s states are com-
pletely independent. In this study, eye velocity and posi-
tion served as measures of ocular state for the purpose
of MI analysis. We analyzed two relationships: between
left eye velocity and right eye velocity (velocity MI) and
between left eye position and right eye position (posi-
tional MI).
The joint probability was estimated from the paired
samples by the following procedure. First, the position
and velocity of each trial were aligned to the timing of
saccade initiation. Next, a short analysis window of 11
ms was set for the left and right eye between –50 and
100 ms from the initiation of the saccade. The samples
within the windows were paired between the eyes. Then,
the joint probability distribution was estimated by apply-
ing a Gaussian kernel to the paired samples. The
smoothing length of the kernel was optimized, based on
the samples, using a likelihood cross validation method
[9]. This is a completely automatic method for choosing
the smoothing length. It minimizes the difference
between the estimated probability distribution and the
true one in terms of information distance that has been
constructed from the samples. For details of the opti-
mized Gaussian kernel method, please see the Supple-
mentary Materials in Additional file 1. Finally, MI was
calculated by using Eq. (1) ~ (4). The analysis window
was shifted in steps of 5 ms, which gave enough time
resolution to find out fluctuation in yoking during the
saccade.
Measurements of MI can overestimate weak relation-
ship because of limited sample sizes. We therefore esti-
mated the overestimation by a randomization procedure.
The pairs of the two eyes’ data were randomized across
trials and across time slices within the analysis window,
MI was then calculated in the same way described above
for 100 times and averaged, producing the mean MI of
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the randomized data (MIRan). In all MI results, we used
the corrected MI value, MICordefined as the difference
between the MI value obtained from the original data,
MIOriand the mean across the 100 randomizations:
MICor= MIOri– MIRan. The preliminary simulation with
computer generated samples confirmed that this
removed the overestimation and also showed a reduction
in the standard deviation when there was no statistical
relationship (Supplementary Fig. 1A and B in Additional
file 2).
The association of velocity MI with positional MI was
studied using the differences between the experimental
conditions. This was tested by an ANOVA (direction ×
session type × day × subject). The effects were defined
as significant only when they continuously satisfied a
criterion for Type 1 error of p<0.05 for 10 ms or more.
The latencies for significant differences in velocity MI
with respect to those in positional MI were compared.
The MI estimation was influenced by sample size.
Smaller sample sizes produced lower MI estimations
(Supplementary Fig. 1C in Additional file 2). While
there was the possibility of significant MI differences
derived only from the sample size difference, the
ANOVA set up to show such changes did not find any
significant difference in sample size between the condi-
tions (p > 0.05). Although the different sample sizes
increased the standard deviation of MI among the sub-
jects and thus decreases the sensitivity of the ANOVA,
there were sufficient significant differences for the asso-
ciation between velocity and positional MI to support
the validity of this analysis method.
Spearman’s rank correlation coefficient (CR) analysis
was also included in order to be compared with MI ana-
lysis and highlight any of MI’s advantages or disadvan-
tages. The preparation of the paired samples and the
statistical test for CR analysis were identical to those for
the MI analysis.
Eye movement variances
MI analysis relied on the variance of the eyes move-
ments to show the interocular statistical relationships. A
decrease of MI could reflect both a variance decrease
and/or a weak relationship in yoking between the eyes.
To distinguish the two cases, we examined the SD of
samples from each eye among the trials and within the
analysis window, set in steps of 5 ms. The differences in
SD between the experimental conditions were tested for
each eye by ANOVA. The effects were significant when
they satisfied the criterion of Type 1 error of p<0.05 for
10 ms or more.
Any common significant differences in SD between
the eyes were also used to show the interocular relation-
ships, as was done for the differences in the averages.
The ANOVA was set up to examine differences in the
variance of the eyes’ movements, thus this approach
showed yoking based on variance changes following the
different experimental conditions.
Results
Latencies of saccades
Figure 2 shows representative eye position and velocity
obtained from one single trial of rightward saccade (1st
day, GoOnly session). During the saccade from the cen-
ter (0 deg) to the target position (12 deg), the right eye
(dotted line in Fig. 2A) led the left eye (solid line). The
eye velocities in Fig. 2B also show that the right eye’s
saccade was slightly earlier with respect to the left eye.
This result is consistent with previous studies in which
the abducting saccades led the adducting ones [10-12].
In figure 2C, the arrow heads indicate the time at initia-
tion, peak-velocity and the end in this trial, given by the
average velocity between the eyes.
Initiation times from the onset of the cue image were
compared between saccade directions, session types and
days in Fig. 3A. A four-way ANOVA (direction × type ×
day × subject) shows that the initiation times in the Go-
Only sessions were significantly shorter than in the
Go/NoGo sessions (i in Fig. 3A; F1,12=249, p<0.001).
The initiation times on the 2ndday were significantly
shorter than on the 1stday (ii; F1,11=20.4, p<0.001),
representing a practice effect. A significant interaction
between the direction effect and the type effect was
found (F1,12=6.14, p<0.05). Next, peak-velocity latency
from the time of initiation were examined. The ANOVA
showed that latencies of the peak velocity of the right-
ward saccades, mean 20 ms, were significantly shorter
than for leftward ones (22 ms) (iv in Fig. 3B; F1,11=4.92,
p<0.05). The length of saccade duration obtained by
subtraction of the initiation time from the end time was
studied (Fig. 3C). The ANOVA did not show any signifi-
cant differences (p>0.05) except for individual variances.
The grand average of the duration was 57 ms. Hereafter,
we use the average latencies of the peak velocity (21 ms)
and the end (57 ms) for the reference of saccadic key
events.
Average eye velocities
The averages of eye velocity over all subjects are shown
for the left eye in Fig. 4A. Positive deviations denote eye
movements toward the saccadic target for either leftward
or rightward movements. The left eye velocity of leftward
saccades (red lines) was significantly higher relative to
the rightward ones (blue lines) in a period from the
initiation to the peak velocity (between 0 and 22 ms from
the saccade initiation; red square brackets), as shown by
an ANOVA (direction × type × day × subject) for each
time slice. Likewise an ANOVA for the right eye found a
significant difference in velocity between the directions,
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but this was after the peak velocity (between 29 and 69
ms; red square brackets in Fig. 4B). The ANOVAs also
identified latencies of significantly higher velocities on
the 2ndday (dashed lines) relative to the 1stday (solid
lines) in both eyes (left eye: between 17 and 36 ms, right
eye: between 34 and 45 ms; cyan square brackets), repre-
senting a practice effect. The onsets of significant differ-
ences are linked between the eyes in Fig. 4C. Both effects
of direction (red line) and day (cyan line) were earlier in
the left eye.
ANOVAs for position found significant differences
between the abducting and adducting saccades, between
the Go-Only and Go/NoGo sessions in both eyes and
between the days for the left eye (Supplementary Fig. 2
in Additional file 3). The leading eye based on the direc-
tion effect (right eye leading) was not consistent with
that based on the session type effect (left eye leading).
Variances of eye velocities
The SD of eye velocity is shown for the left eye in Fig.
5A and for the right eye in 5B. Averages of SDs over all
subjects are shown for each experimental condition. The
SD increased steeply at the initiation of the saccade and
decreased after 15 ms, and then increased again in some
conditions before the end of the saccade.
An ANOVA for the left eye’s velocity found signifi-
cantly larger variance in the leftward saccades (red lines)
than the rightward (blue lines) in a period between – 5
and 30 ms. On the other hand, an ANOVA for the right
eye’s velocity identified the reverse difference, i.e., larger
variance in the rightward saccades than the leftward
from 0 to 10 ms. Taken together, the abducting eye
exhibited larger variance relative to the adducting eye.
The latencies of the abducting-adducting effect are
denoted by black square brackets. Also, in both eyes,
the ANOVAs identified significantly larger variance in
the Go/NoGo sessions (dashed lines) than the Go-Only
sessions (solid lines) (left eye: between – 10 and 0 ms
and between 10 and 30 ms; right eye: between 5 and 20
ms; green square brackets), and larger variance near the
end of leftward saccades (red lines) relative to the right-
ward saccades (blue lines) (left eye: between 60 and 70
ms, right eye: between 50 and 65 ms). To see the effect
of abducting-adducting and the cognitive load, see Sup-
plementary Fig. 3A and B in Additional file 3.
The onsets of significant differences are shown linked
between the eyes in Fig. 5C. The abducting-adducting
effect (black line) and the cognitive load effect (green
line) were earlier in the left eye than the right eye,
though the leftward-rightward effect was identified ear-
lier in the right eye relative to the left eye.
Results of statistical tests for the variance of position
are shown in Supplementary Fig. 4 in Additional file 3.
ANOVAs on positions found significantly larger variance
for the abducting saccades than the adducting ones, in
the Go/NoGo sessions than the Go-Only sessions, and
on the 2ndday than the 1stday in both eyes. The leading
eyes based on these effects were not consistent.
Joint probability distribution
Representative joint probability distributions, used for
MI analysis, are shown in Fig. 6 for the leftward
Version
Latency from cue onset (ms)
Eye velocity (deg/s)
0
200
400
C
325300350375 400
Left eye
Right eye
Eye position (deg)A
5
0
10
0
200
400
Eye velocity (deg/s)B
Figure 2 A, B. Example of different time courses in position
and velocity between the left eye (solid lines) and the right
eye (dotted lines), obtained from a single trial in which the
saccadic target was on the right side. Positive deflections shown on
the vertical axis of A, B and C denote rightward movements, and
thus indicate the eye movement toward the target. C. Version
velocity, i.e., the averaged velocity between the eyes. The saccade
initiation, peak-velocity and end of the trial are indicated by
arrowheads, based on the version velocity. Horizontal axis is taken
from the onset of the arrowhead cue image (see Fig. 1).
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Figure 3 Averaged times for: A. Saccade initiation from the onset of cue image; B. Peak-velocity from the saccade initiation; C. Saccade
duration. The average was performed separately for the 1stday (left panels) and the 2ndday (right panels), for the Go-Only sessions (open bars)
and the Go/NoGo sessions (filled bars), for the leftward saccades (left paired-bars in each panel) and the rightward saccades (right paired-bars).
Error bars represent ± 1 SE. The saccades initiated significantly earlier: i. in the Go-Only than in the Go/NoGo sessions (p<0.001); ii. on the
2ndday than on the 1stday (p<0.001); iii. The peak-velocity was significantly earlier for the rightward than the leftward saccades (p<0.05).
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GoOnlyGo/NoGo
Leftward, 1
Rightward, 1
day
day
st
st
Leftward, 2
Righttward, 2
day
nd
day
nd
A Left eye
B Right eye
0 50100
Latency from saccade initiation (ms)
0
100
200
300
050100
Latency from saccade initiation (ms)
050100
Latency from saccade initiation (ms)
0
100
200
300
050 100
Latency from saccade initiation (ms)
Right eye velocity Right eye velocity
0 ms
Initiation
21 ms
Peak velocity
57 ms
End
Leftward > Rightward
2 day >
nd
1 day
st
Left eye velocityLeft eye velocity
C Interocular yoking
Average velocity (deg/s)
Average velocity (deg/s)
Figure 4 Dependence of averaged eye velocities on experimental conditions:A. Left eye; B. Right eye. Averages among all subjects are
shown for the saccade toward the left (red lines) and right (blue lines) in the sessions of Go-Only (left panels) and Go/NoGo (right panels), on
the 1stday (solid lines) and 2ndday (dashed lines). Positive deflections of velocity of eye movements toward saccadic target. Horizontal axes are
the latency from the saccade initiation. The latencies of significantly faster movements are denoted by red square brackets for the leftward
saccade relative to the rightward, and by cyan square brackets for the saccades on the 2ndday than 1stday. The significant differences were
revealed by ANOVA factoring the saccade direction, the session type, the experiment day and the subject (p < 0.05 for 10 ms or more). C. Time
courses comparisons between the eyes based on the significant differences. The latencies of significant difference with respect to the saccade
directions are indicated by red horizontal bars. The onsets of the significant difference are linked between the eyes by a thin red line, showing
eye yoking. Cyan horizontal bars linked by a thin line indicated the yoking found based on the significant day effect.
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1 day
st
2 day
nd
Leftward, Go-Only
Rightward, Go-Only
Leftward, Go/NoGo
Rightward, Go/NoGo
A Left eye
B Right eye
0 50100
Latency from saccade initiation (ms)
SD of velocity (deg/s)
0
-50
50
100
0 50100
050100
Latency from saccade initiation (ms)
SD of velocity (deg/s)
0
-50
50
100
0 50100
Right eye velocityRight eye velocity
0 ms
Initiation
21 ms
Peak velocity
57 ms
End
Abducting > Adducting
Go/NoGo > Go-Only
Leftward > Rightward
Left eye velocityLeft eye velocity
C Interocular yoking
Latency from saccade initiation (ms)
Latency from saccade initiation (ms)
-50
-50
Figure 5 Trial-to-trial variances related to eye velocities and experimental conditions:A. Left eye; B. Right eye. Standard deviation (SD)
within each subject is averaged among all subjects for the saccade toward the left (red lines) and right (blue lines) for the sessions of Go-Only
(solid lines) and Go/NoGo (dashed lines), on the 1stday (left panels) and 2ndday (right panels). Horizontal axes are the latency from saccade
initiation. The latencies of significantly larger variances are denoted by black square brackets for the abducting saccade relative to the adducting,
by red square brackets for the leftward saccade relative to the rightward, and by green square brackets for the saccades in the Go/NoGo
sessions than the Go-Only. The significant differences were calculated by ANOVA factoring the saccade direction, the session type, the
experiment day and the subject (p < 0.05 for 10 ms or more). To see the difference between the Go/NoGo and Go-Only sessions, see
Supplementary figure 3A and B in Additional file 3. C. Time course comparisons between the eyes were based on the significant differences. The
latency of significant differences between the abducting and adducting saccades are shown by black horizontal bars. The onsets of the
significant dependencies are linked between the eyes by a thin black line, showing eye yoking. Linked horizontal bars in red indicate the yoking
found based on the significant difference between the leftward and rightward saccades, and that in green showed the significant effect of
cognitive load.
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Left eye position (deg)
0
1432
Right eye position (deg)
0
4
3
2
1
0
2
1
Left eye position (deg)
01432
Right eye position (deg)
0
4
3
2
1
0
0.4
0.2
MI
CR
CR
= 1.59
= 0.99
= 0.99
Ori
Ori
Ori
MI= 1.59
Ori
MI
CR
CR
= 0.17
= 0.05
= 0.05
Ran
Ran
Ran
MI = 0.17
Ran
Left eye velocity (deg/s)
C Position, 90 - 100 ms
0500250
Right eye velocity (deg/s)
0
500
250
0
6X10
-5
3
0
Right eye velocity (deg/s)
0
0
2
1
MI
CR
CR
= 1.12
= 0.96
= 0.96
Ori
Ori
Ori
MI= 1.12
Ori
MI
CR
CR
= 0.12
= 0.01
= 0.01
Ran
Ran
Ran
MI= 0.12
Ran
Left eye position (deg)
81014 12
Right eye position (deg)
8
14
12
10
0
2
1
Left eye position (deg)
Right eye position (deg)
0
0.4
0.2
Left eye velocity (deg/s)
-40-20 40200
Right eye velocity (deg/s)
-40
40
20
0
-20
0
0.5
Left eye velocity (deg/s)
-40-2040200
Right eye velocity (deg/s)
-40
40
20
0
-20
0
4
MI
CR
CR
= 0.02
= 0.09
= 0.09
Ori
Ori
Ori
MI = 0.02
Ori
MI
CR
CR
= 0.02
= 0.02
= 0.02
Ran
Ran
Ran
MI= 0.02
Ran
Left eye velocity (deg/s)
250 500
500
250
3X10
-5
1412108
8
14
12
10
8X10
-3
1X10
-2
0.6
MI
CR
CR
= 1.24
= -0.01
= -0.01
Ran
Ran
Ran
MI= 1.24
Ran
MI
CR
CR
= 2.51
= 0.86
= 0.86
Ori
Ori
Ori
MI= 2.51
Ori
0.8
A Position, 5 - 15 ms
B Velocity, 5 - 15 ms
D Velocity, 90 - 100 ms
Figure 6 Examples of joint probability density distributions, used for computation of mutual information (MI). The distributions were
estimated by applying a Gaussian kernel to: A. Eye position samples between 5 and 10 ms from saccade initiation; B. Eye velocity samples
between 5 and 10 ms; C. Eye position samples between 90 and 100 ms; D. Eye velocity samples between 90 and 100 ms. The smoothing
length of the kernel was optimized based on the samples by the likelihood cross validation method. The distributions are for a leftward saccade,
Go/NoGo session on the 1stday. Left panel: The samples were paired between the eyes in each trial with no delay. The MI of the original paired
samples (MIOri) and its correlation coefficient (CROri) are noted on the top left of each panel. Right panel: The pairs were randomized among
trials within the time window of 11 ms. Because of the finite sample size (330 pairs). the MI of randomized samples (MIRan) was often
significantly larger than zero in spite of the randomization procedure. The MIRanwas used to estimate the overestimation of relationship. The
CROridid not overestimate the relationship as shown by the correlation coefficient of the randomized samples (CRRan). The probability densities
are indicated by the colors, as specified in the color scales. The units of velocity are (deg/s)-2and position deg-2.
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saccades in the Go/NoGo sessions on the 1stday. The
eyes’ positions (Fig. 6A, left panel) and velocities (6B,
left panel) were obtained between 5 and 15 ms. Here,
we refer to the center of this time window as latency.
The distributions indicate proportional relationships
between the eyes’ movements, producing the high MIOri
of 1.59 for velocity and 1.12 for position. In the right
panels the relationships were removed by a randomiza-
tion of the paired samples, which dramatically decreased
the MIRan. However, MIRandid not vanish completely,
demonstrating the overestimation due to the limited
sample size (330 pairs). In contrast, since CR analysis
does not give an overestimation, the CR of randomised
samples (CRRan) became nearly zero.
Figure 6C left panel shows a probability distribution of
position in the period between 90 and 100 ms. The
probabilities were concentrated on particular eye posi-
tions, which is a reflection of stable fixation during the
analysis time window (11 ms) in each trial after the end
of the saccade. The variance for the specific point of
fixation of the eye positions is reflected in a trial var-
iance when the eye is at the fixating position. The pro-
portional relationship of the variance produced the high
MIOriof 2.51. However, its high MIRanof 1.24 (Fig. 6C,
right panel) indicates a large overestimation of the MIOri
and the need for a correction method, i.e., a subtraction
of MIRan. While the eyes’ positions exhibited a strong
proportional relationship, the probability distribution for
velocity showed little relationship (Fig. 6D, left panel;
MIOri= 0.02), and thus was not very different from the
distribution of the randomized samples (Fig. 6D, right
panel) as the probability densities for both had a normal
distribution.
Mutual information
The time courses of MI are shown for eye velocities in
Fig. 7A and for positions in 7B. Averages among all sub-
jects are shown for each experimental condition. MI was
computed without the delay between the eyes. The velo-
city MI started to increase at 5 ms before the saccade
initiation and exhibited its primary peak at 5 ms after
the initiation, and then decreased. The velocity MI
increased again at the latencies between 20 and 35 ms
depending on the experimental conditions, and exhib-
ited its secondary peak before the end of the saccade.
On the other hand, the time courses for positional MI
lagged behind the velocity MI. They increased at 0 ms
and showed a peak at 10 ms. After a decrease, the posi-
tional MI started to increase again at the latencies
between 35 and 50 ms depending on the conditions.
These results suggested that positional yoking was a
result of the velocity yoking.
An ANOVA using each time slice found that the velo-
city MI was significantly higher for the leftward saccades
(Fig. 7A, red lines) than the rightward ones (blue lines)
in periods between 15 and 30 ms and between 50 and
70 ms (red square brackets). The positional MI was also
higher for the leftward saccades than the rightward ones
in periods between 20 and 45 ms and between 70 and
90 ms (Fig. 7B, red lines). When Japanease read a text
written in their traditional style, the eyes move down-
ward and return in an upward direction, while the eyes
of Caucasians move rightward and return with a quick
saccade to the left. Thus, we added one factor of race
(Japanese and Caucasian) and applied a five-way
ANOVA (direction × session type × day × race × sub-
ject), but no significant main effect or interaction of
race was obtained (p > 0.1). The positional MI before
the saccade initiation was significantly higher in the
Go/NoGo sessions (dashed lines) than the Go-Only ses-
sions (solid lines) except for the leftward saccades on
the 2ndday, and on the 2ndday (right panel) than the
1stday (left panel) except for the leftward saccades in
the Go-Only sessions.
The onsets of significant effects for saccadic direction
are linked between the velocity and positional MIs by
red arrows in Fig. 7C. The direction effect on the velo-
city MI led with respect to that on the positional MI,
which suggests that the velocity yoking was “causing”
positional yoking.
The CR analysis found the two peaks for velocity yoking
after the initiation and before the end of saccades (Supple-
mentary Fig. 5A in Additional file 3), as did the MI analy-
sis. However, for position (Supplementary Fig. 5B in
Additional file 3), the CR analysis showed only the peak
yoking after saccade initiation and failed to detect the
increase in yoking following the peak velocity. The CR
analysis for position also failed to detect the cognitive load
effect before saccade initiation (Supplementary Fig. 5B in
Additional file 3). The failure of CR analysis to detect
changes in yoking strength identified by the MI analysis is
evidence for nonlinear contributions in positional yoking.
The results therefore highlight an advantage for MI analy-
sis compared to CR analysis in general and for studying
yoking in particular.
Discussion
Source of statistical interocular relationship
The variance of each eye’s velocity was large during the
saccades (Fig. 5A and 5B). In each experimental condi-
tion the variance peaked soon after saccade initiation. In
some conditions a second peak in variance was identified
just before saccade end. Similarly the MI (computed for
zero interocular delay) was high during the saccade and
peaked after the initiation and before the end (Fig. 7A).
The two results show that velocity variances of the eyes
were statistically linked to each other even when no
interocular delay was allowed for. Thus the variances of
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A Velocity yoking
1.5
B Positional yoking
1.5
050100
Latency from saccade initiation (ms)
0
0.5
1.0
050100
Latency from saccade initiation (ms)
Positional yoking Positional yoking
0 ms
Initiation
21 ms
Peak velocity
57 ms
End
Leftward > Rightward
Go/NoGo > Go-Only
Velocity yokingVelocity yoking
C Transfer between velocity and position
Mutual information
1 day
st
2 day
nd
Leftward, Go-Only
Rightward, Go-Only
Leftward, Go/NoGo
Rightward, Go/NoGo
0 50100
Latency from saccade initiation (ms)
0
0.5
1.0
050100
Latency from saccade initiation (ms)
Mutual information
12 day
st nd
day >
Figure 7 Time courses of MI:A. Between the left and right eyes’ velocities; B. Between the left and right eyes’ pzositions. The samples were
paired between the eyes without delay relative to each other. The overestimation of MI was corrected by the difference between the MIOriand
the mean MI obtained from 100 sample randomizations (MIRan): MI
Cor
toward the left (red lines) and right (blue lines) in the sessions of Go-Only (solid lines) and Go/NoGo (dashed lines), on the 1stday (left panels)
and 2ndday (right panels). Horizontal axes are the latency from the saccade initiation. The latencies of significantly stronger relationship are
denoted by red square brackets for the leftward saccade relative to the rightward, by green square brackets for the saccades in the Go/NoGo
sessions than the Go-Only except for the leftward saccade on the 2ndday, and by cyan square brackets for the saccades on the 1stday than the
2ndday except for the leftward saccade in the Go-Only session. The significant differences were revealed by ANOVA factoring the saccade
direction, the session type, the experiment day and the subject (p < 0.05 for 10 ms or more). C. Time courses comparisons between the velocity
MICorand the positional MICor. The red arrows that link the red horizontal bars suggest causal relationship between the velocity MICorand
positional MICorwith respect to the significant difference between the leftward and rightward saccades. The green horizontal bar indicates the
latency of significant cognitive load effect, and the cyan one indicates that of significant day effect, obtained only for the positional MICor.
MIMI
Ori
Ran
=−
. MICoris averaged among all subjects for the saccade
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the eyes could be partially explained by neural activity in
control structures of the oculomotor pathway with bilat-
eral rather than monocular influence. This confirmed a
previous study in which the size of the correlation coeffi-
cient between the eyes was more than 0.75 for peak velo-
city, saccade duration and saccade curvature [4].
However, it can not be the sole explanation for velocity
variance. In the current study, while the cognitive load
increased the eyes’ velocity variance (Go/NoGo vs. Go-
Only in Fig. 5A and 5B), it did not increase the velocity
MI (Fig. 7A). This result suggests that the changes in
cognitive load may alter neural processes in areas where
oculomotor influence is either monocular, or at least
weakly binocular. There could be several responsible
structures in the neural control pathway. A previous
study from our group using identical saccade task sug-
gested that neural activity in the brainstem and the floc-
culus might be responsible. An increase in linkage
between these areas just before and in the early part of
the saccade was identified for the task with higher cogni-
tive load in this previous MEG study [7].
The increase of velocity MI, after initiation and before
the end of the saccade, led those of positional MI (Fig. 7A
and 7B). Also the significant influence of saccade direction
was identified for velocity MI before positional MI
(Fig. 7C). These results suggested that positional yoking
was caused by velocity yoking. This could be a conse-
quence of the analysis method used since position was
simply a temporal integration of velocity, the saccades
being in the horizontal direction [6]. However CR analysis
failed to associate the increase of velocity yoking before
the saccadic end with that of positional yoking (Supple-
mentary Fig. 5 in Additional file 3). These results therefore
highlight the advantages of MI analysis over CR analysis.
Before the initiation of saccades, the positional MI was
significantly higher in the Go/NoGo sessions relative to
the Go-Only sessions, and on the 1stday compared to
the 2ndday (Fig. 7). Similarly, the positional fluctuations
of the eyes were significantly large for the Go/NoGo
sessions on the 1stday (Supplementary Fig. 3C and D
and Supplementary Fig. 4 in Additional file 3). Taken
together, the larger variance of eye position could be a
reflection of binocular neural control processes rather
than at a monocular level, exerting an influence on the
oculomotor system even before saccade initiation. The
larger variance of position could possibly reflect a longer
latency of saccade initiation for the Go/NoGo sessions
on the 1stday (Fig. 3A), rather than the cognitive load
or a practice effect. Alternatively it may be a conse-
quence of a more complex preparation sequence that
reaches the ocular muscles and even prepares their state
before the final command for saccade execution. Evi-
dence for such a mechanism is presented in another
paper from our group in this volume.
Laterality
The effects of saccade direction and practice on the
average velocity were identified in the left eye before
those of the right eye (Fig. 4C). The large variance in
velocity in the abducting saccades in Go/NoGo sessions
was also found in the left eye prior to the right eye
(Fig. 5C). Recalling the dominant eye was the right in all
subjects, it is not likely that the left eye guided the right
eye. A more plausible explanation is that the left eye
movements were easily modulated by the different
experimental conditions, and thus the right eye move-
ments compensated so that the two eyes exactly
foveated the same object.
Consistent laterality differences in timing across sub-
jects have not been found for horizontal saccades [10,13].
In the current study, both eyes showed longer latencies
to peak velocity for leftward than for rightward saccades
(Fig. 3B). We also found a higher velocity for leftward
saccades relative to rightward ones (Fig. 4). There were
also differences in MI for the binocular control of left-
ward saccades, i.e., stronger leftward yoking than for
rightward saccades (Fig. 7). In the previous MEG study
[7], Fig. 3, also carried out with right handed subjects and
the same tasks, coherency of neural activation across
trials in the frontal eye field (FEF) of the right hemisphere
clearly increased after the initiation of leftward saccades,
whereas both sides of the FEF showed only a small
increase for rightward saccades. Further, in another MEG
study from this laboratory on saccades in both waking
and sleeping, it was found that the interaction between
cortical and sub-cortical areas were more complicated
for leftward relative to rightward saccades in the waking
condition [14], [Fig. 10]. These different neural processes
for left and right saccades might be a reflection of the dif-
ferences we found in this study from the behavioral data
between left and right saccadic movements. The laterality
of saccade direction was not significantly different for the
reading groups, suggesting that a cultural bias would not
account for the difference between saccades to the left
and right, also many Japanese now read books written in
Japanese with a standard western left right format.
A recent study [15] has shown that the left and right par-
ietal regions exert different control on saccade direction
a further point for the asymmetry of saccade genesis.
Outlook
Failures in basic mechanisms integrating information
from the two eyes lead to pathological conditions, for
example small lesions in the brainstem, cerebellum, cor-
tex or in the thalamus can all lead to disorders of eye
movements. More recently eye movement disorders
have been described in schizophrenia, depression [16]
and dementia [17]. It is not yet known if these move-
ment changes can have predictions for treatment
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response. Our long term goal is to develop new clinical
methods for the detection of early oculomotor deficits
that could be widely available and cheap. This goal is
pursued by two research strands. The first research
effort continues the work of our earlier studies using
detailed tomographic analysis of MEG data to describe
activity in the oculomotor system under different condi-
tions [7,14]. As part of the same work we also study in
detail how key parts of oculomotor system are activated
in specific tasks, e.g. the frontal eye field [18]. We are
using the MEG to relate activity in specific brain areas
in the cortex, cerebellum and brainstem, to specific eye-
movement tasks. In the second research strand we are
using the knowledge about spatiotemporal brain activity
patterns to develop biomarkers for normal and patholo-
gical activity. These biomarkers could rely on the detec-
tion of spatiotemporal patterns with EEG or values of
parameters extracted from eye tracking measurements.
Successful implementation of our research goals could
then lead to widely available and relatively cheap clinical
tools that can be part of routine screening. The clinical
utility for early diagnosis could include problems not
only in the oculomotor areas, but also in areas in the
frontal lobe, cerebellum and brainstem where any gen-
eral disturbances will also affect key structures of the
oculomotor system.
Conclusions
We have shown that mutual information analysis is suc-
cessful in determining the detailed relational structure
of eye movements, and this analysis has given informa-
tion about the saccade that was not apparent in the
individual velocity and position measurements. This new
method could have clinical utility for the detection of
early ocular muscular imbalance in a number of patho-
logical conditions where failures occur in basic mechan-
isms integrating information from the two eyes.
Additional file 1: Details of analytical methods on detection of
saccade latencies, optimization of Gaussian kernel and simulation
of MI analysis.
Additional file 2: Supplementary Figure 1. Simulation results of MI
analysis using computer-generated samples.
Additional file 3: Supplementary Fig 2. Dependency of averaged
eye positions on experimental conditions.Supplementary Fig 3.
Trial- by-trial variance of eyes velocities and positions, showing
effects of abducting-adducting and cognitive load.Supplementary
Fig 4. Time courses of dependency of positional variances on
experimental conditions.Supplementary Figure 5. Time courses of
correlation coefficient between left and right eye velocities and
between left and right eye positions.
Acknowledgements
The authors thank Shinya Kuriki for lending the eye tracker. The experiment
and data analysis was performed at the MEG laboratory, BSI RIKEN. Following
the closing of the laboratory in September 2009 the contribution from AAI
and PCBF was supported by Cyprus Research Promotion Foundation (grant
no 0308/09).
This article has been published as part of Nonlinear Biomedical Physics
Volume 4 Supplement 1, 2010: Consciousness and its Measures: Joint
Workshop for COST Actions Neuromath and Consciousness. The full
contents of the supplement are available online at
http://www.nonlinearbiomedphys.com/supplements/4/S1.
Author details
1Laboratory for Human Brain Dynamics, RIKEN Brain Science Institute, 2-1
Hirosawa, Wakoshi, Saitama 351-0198, Japan .2Present address: CEA/DSV/
I2BM / NeuroSpin, INSERM U992 - Cognitive Neuroimaging Unit, Bât 145 -
Point Courrier 156, Gif sur Yvette F-91191, France .3Laboratory for Human
Brain Dynamics. AAI Scientific Cultural Services Ltd., 33, Arch. Makarios III
Avenue, Nicosia, 1065, Cyprus.
Authors’ contributions
MM performed the experiment, developed the mutual information analysis
with the contribution of AAI, and carried out all analyses. MM and AAI
designed the experiment together guided by an earlier MEG design used in
a separate MEG experiment. AAI conceived the usage of mutual information
analysis to measure eyes’ yoking, and organized whole of the study. PBCF
and AAI formulated the physiological and cognitive discussion of the results
with the contribution of MM. The manuscript was written initially by MM
and revised by PBCF and AAI. All authors read and approved the final
manuscript.
Competing interests
The authors declare that they have no competing interests.
Published: 3 June 2010
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doi:10.1186/1753-4631-4-S1-S10
Cite this article as: Maruyama et al.: Interocular yoking in human
saccades examined by mutual information analysis. Nonlinear Biomedical
Physics 2010 4(Suppl 1):S10.
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Maruyama et al. Nonlinear Biomedical Physics 2010, 4(Suppl 1):S10
http://www.nonlinearbiomedphys.com/content/4/S1/S10
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