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Year: 2009

Modulation of saccade curvature by ocular counterroll

Weber, K P; Bockisch, C J; Olasagasti, M I; Straumann, D

Weber, K P; Bockisch, C J; Olasagasti, M I; Straumann, D (2009). Modulation of saccade curvature by ocularcounterroll. Investigative Ophthalmology and Visual Science, 50(3):1158-1167.Postprint available at:http://www.zora.uzh.ch

Posted at the Zurich Open Repository and Archive, University of Zurich.http://www.zora.uzh.ch

Originally published at:Investigative Ophthalmology and Visual Science 2009, 50(3):1158-1167.

Weber, K P; Bockisch, C J; Olasagasti, M I; Straumann, D (2009). Modulation of saccade curvature by ocularcounterroll. Investigative Ophthalmology and Visual Science, 50(3):1158-1167.Postprint available at:http://www.zora.uzh.ch

Posted at the Zurich Open Repository and Archive, University of Zurich.http://www.zora.uzh.ch

Originally published at:Investigative Ophthalmology and Visual Science 2009, 50(3):1158-1167.

Modulation of saccade curvature by ocular counterroll

Abstract

PURPOSE: On close inspection, most saccadic trajectories are not straight, but curve slightly, i.e. theyare not single-axis ocular rotations. We asked whether saccade curvatures are systematically influencedby static ocular counterroll (OCR). METHODS: OCR was elicited by static whole-body roll position.Eight healthy human subjects performed horizontal and vertical saccades (amplitude: 10 degrees ;eccentricity: 0 degrees and 10 degrees ; head-fixed coordinate system) in upright and ear-downwhole-body roll positions (45 degrees right, 45 degrees left). Three-dimensional eye movements wererecorded with modified dual search coils at 1000Hz. RESULTS: Saccade curvature was systematicallymodulated by OCR depending on saccade direction. In the horizontal-vertical plane, primarily verticalsaccades were modulated with downward saccades curving towards the upper ear and upward saccadescurving towards the lower ear. Modulation of saccade curvature in the torsional direction only correlatedsignificantly with OCR in abducting saccades. CONCLUSIONS: No universal mechanism likevisual-motor coordinate transformation or kinematical characteristics of the saccadic burst generatoralone could explain the complex modulation pattern of saccade curvature. OCR-induced changes of theocular motor plant, including transient force imbalances between agonist eye muscles (vertical rectusand oblique muscles) and shifting eye muscle pulleys, are suitable to explain the founddirection-dependent modulation pattern.

Weber et al.

MODULATION OF SACCADE CURVATURE BY OCULAR COUNTERROLL

Revised manuscript IOVS-08-2453

Konrad P. Weber1, Christopher J. Bockisch1,2,3, Itsaso Olasagasti1, Dominik Straumann1

1Department of Neurology, Zurich University Hospital, Switzerland 2Department of Ophthalmology, Zurich University Hospital, Switzerland

3Department of Otorhinolaryngology, Zurich University Hospital, Switzerland

Word count: 4266

Corresponding author:

Dominik Straumann, MD

Neurology Department

Zurich University Hospital

Frauenklinikstrasse 26

CH-8091 Zurich

Switzerland

Phone: +41-44-255-55-64

Fax: +41-44-255-45-07

Email: dominik@neurol.unizh.ch

Grant information:

Supported by Swiss National Science Foundation (#3200B0-105434) and

Betty and David Koetser Foundation for Brain Research, Zurich, Switzerland.

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Weber et al.

ABSTRACT

PURPOSE: On close inspection, most saccadic trajectories are not straight, but curve slightly,

i.e. they are not single-axis ocular rotations. We asked whether saccade curvatures are

systematically influenced by static ocular counterroll (OCR).

METHODS: OCR was elicited by static whole-body roll position. Eight healthy human

subjects performed horizontal and vertical saccades (amplitude: 10°; eccentricity: 0° and 10°;

head-fixed coordinate system) in upright and ear-down whole-body roll positions (45° right,

45° left). Three-dimensional eye movements were recorded with modified dual search coils at

1000Hz.

RESULTS: Saccade curvature was systematically modulated by OCR depending on saccade

direction. In the horizontal-vertical plane, primarily vertical saccades were modulated with

downward saccades curving towards the upper ear and upward saccades curving towards the

lower ear. Modulation of saccade curvature in the torsional direction only correlated

significantly with OCR in abducting saccades.

CONCLUSIONS: No universal mechanism like visual-motor coordinate transformation or

kinematical characteristics of the saccadic burst generator alone could explain the complex

modulation pattern of saccade curvature. OCR-induced changes of the ocular motor plant,

including transient force imbalances between agonist eye muscles (vertical rectus and oblique

muscles) and shifting eye muscle pulleys, are suitable to explain the found direction-

dependent modulation pattern.

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Weber et al.

INTRODUCTION

Commonly it is assumed that a saccade between two visual targets consists of a single-axis

rotation of the ocular globe about a head-fixed axis. Mathematically, a single-axis rotation

implies that the positional trajectory between movement onset and offset is straight when

expressed as quaternion or rotation vectors.1-3 Listing’s law states that, with the head not

moving, these rotation vectors lie in a plane, called Listing’s plane.4 Tweed and Vilis have

shown that visually guided saccades, at least to a first approximation, are single-axis rotations

and obey Listing’s law.5

If the orientation of the ocular rotation axis changes during a saccade, its trajectory

becomes curved. Saccades with curvatures in the horizontal-vertical plane can be elicited by

displacing the visual target shortly after its appearance in a so-called double-step paradigm.6

Clearly, such curved saccades cannot result from a single-axis rotation. However, single-axis

rotations are not a necessary condition for saccades to obey Listing’s law. In fact, Minken

and coworkers showed that even strongly curved double-step saccades lie in Listing's plane,

although their rotation axes change during the displacement.7

On close examination, even normal saccades are slightly curved.8 A systematic analysis of

saccadic transients in the horizontal-vertical plane demonstrated curved trajectories

predominantly during oblique saccades.9 Three-dimensional measurements of saccades also

revealed transient curvatures in the torsional direction, called blips.10 Blips evoked by

horizontal saccades systematically depend on direction and gaze elevation; blips evoked by

vertical saccades are idiosyncratic, but consistent upon repetition.11 In contrast to deviations

in the horizontal-vertical plane, torsional transients by definition violate Listing’s law.

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Weber et al.

In the present study, we asked whether saccade curvature depends on torsional eye

position. A torsional offset that is added to eye positions before, during and after saccades

can be introduced by tilting the subject’s head in the roll plane.12 Since this ocular counterroll

(OCR), which leads to a shift of Listing’s plane along the naso-occipital axis12,13, modifies

the configuration of the extra-ocular muscles and their pulleys14, we expected increasing

saccadic curvatures, if they were the result of altered ocular motor plant characteristics.

Alternatively, central mechanisms of signal transformation from retinal input to ocular motor

output could also lead to predictable saccadic curvatures depending on OCR.15

The study of saccade curvature requires high-resolution and artifact-free measurements of

ocular trajectories in three dimensions. The dual search coil technique is considered the gold

standard due to its high temporal and spatial resolution.16,17 Nonetheless, time and again, the

validity of the torsional signal with standard search coils in humans has been questioned.18

Therefore, we opted to base our analysis on measurements with search coils with a modified

exiting wire19 to ensure maximal torsional accuracy and validated the main findings with 3D

video-oculography.

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METHODS

Subjects

Eight healthy subjects (29-45 years, 3 female) volunteered for the experiment. Informed

consent was obtained from all subjects after the experimental procedure was explained. The

protocol was approved by a local ethics committee and was in accordance with the ethical

standards laid down in the Declaration of Helsinki for research involving human subjects.

Setup

Subjects were seated on a turntable with three servo-controlled motor-driven axes

(Acutronic, Jona, Switzerland). Pillows and safety belts minimized movements of the body.

The head was restrained with an individually molded thermoplastic mask (Sinmed, Reeuwijk,

The Netherlands).

Three-dimensional movements of the viewing eye were recorded with dual search coils

manufactured by Skalar (Delft, The Netherlands). The coils were mounted on the eye after

topical anesthesia with oxybuprocaine hydrochloride 0.4% eye drops (Novartis Ophthalmics,

Hettlingen, Switzerland). Dual search coils were calibrated in vitro on a gimbal system before

each experiment.11 A chair-fixed coil frame (side length 0.5m) that produced three orthogonal

magnetic fields with frequencies of 80, 96, and 120kHz surrounded the subject's head. A

digital signal processor computed a Fast Fourier Transform in real-time on the digitized

search coil signal to determine the voltage induced in the coil by each magnetic field (system

manufactured by Primelec, Regensdorf, Switzerland). Eye position signals were sampled at

1000Hz and digitized with 12-bit precision. Coil orientation could be determined with a

precision of about 0.05° and an error of < 7% over a range of ±30°. Typical noise levels were

below <0.05° (root mean square deviation).

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Weber et al.

Experimental procedure

Recordings were done in dim light. Subjects monocularly tracked a jumping laser target

projected on a spherical screen at a distance of 1.4m. Either eye alternately was the viewing

eye, while the fellow eye was covered. For each eye, horizontal and vertical saccades with

amplitudes of 10° were recorded at -10°, 0° and 10° eccentricity. The laser dot jumped every

3 seconds to and fro without randomization. After every 10 saccades a break of 10 seconds

was provided for blinking. In total, 10 saccades for each direction and eccentricity were

recorded. Saccades were recorded in upright, 45° left-ear-down, and 45° right-ear-down

whole-body roll positions in a fixed order (6×10 minutes). Targets for horizontal and vertical

saccades were presented in a head-fixed coordinate system, i.e. the position of the targets

rotated with the subject. OCR at gaze straight ahead was determined for each eye in 45° left-

ear-down and 45° right-ear-down whole-body roll positions and referenced to zero eye

torsion defined in upright position. Since ocular torsion gradually adapts to roll tilt, torsional

eye positions were determined at least 10 seconds after change of body position.20

Data analysis

Ocular traces were analyzed with MatLab software (Version 7.0.1, The MathWorks,

Natick, MA). Three-dimensional eye positions were low-pass filtered with a Savitzky-Golay

filter21 (quadratic polynomial, window size 11ms) and expressed as rotation vectors1,22 in a

head-fixed coordinate system that rotated with the subject. A rotation vector describes the

instantaneous orientation of the eye as a single rotation from the reference position looking

straight ahead. The rotation vector r is oriented parallel to the axis of this rotation, and its

length is defined by , where

r

tan( )ρ/2 ρ is the angle of rotation. Note that a single-axis

rotation is represented by a straight line in rotation vector space. The components of the

rotation vector represent torsional, vertical and horizontal eye rotations. The signs of the t,v,hr

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Weber et al.

rotation vector components are determined by the right-hand rule, that is, clockwise,

downward, and leftward rotations, as seen from the subject, are positive. In the figures, the

signs of axes are defined accordingly and rotation vector components are expressed in

degrees by 1tan ( ) 360 /deg π−= ∗r r . From rotation vectors, angular velocity vectors t,v,hω were

derived.23 Angular velocity vectors point along the instantaneous rotation axis and their

length is proportional to the rotational speed.

Saccades were sorted according to gaze direction. Each saccade, including 1 second of

pre-saccadic and three seconds post-saccadic fixation, was processed by a computer program

and interactively selected. Selection criteria included start and end positions in proximity of

the visual targets, maintained pre- and post-saccadic fixation, and absence of blinks. On

average, 79% ±6SD of a total of 720 saccades per subject were accepted for further analysis.

Horizontal, vertical, and torsional traces were aligned to the median eye position during the

250msec fixation period preceding the saccade. Individual traces were shifted along the time

axis such that they aligned at the instant when saccades passed a level of 3º.

Video setup for complementary eye movement recordings

Three-dimensional eye movements were binocularly recorded at 200Hz with three-

dimensional video-oculography24 (Eye Tracker Version 1C/2003, Chronos Vision, Berlin,

Germany) mounted on the thermoplastic mask. For every experimental condition, the system

was calibrated at 0° and ±10° horizontal and vertical position.25 To optimize pupil tracking

and torsion analysis, pupils were constricted with pilocarpine 0.5% eye drops. Raw video

data was processed with the iris tracker software (Version 2.1.6.1., Chronos Vision): pupil

tracking to obtain horizontal and vertical eye position was performed using an algorithm

based on the Hough transform and ellipse fitting.24 Ocular torsion was determined by iris

segment cross-correlation.26

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Weber et al.

RESULTS

To analyze the three-dimensional kinematical properties of saccades, horizontal, vertical, and

torsional components of rotation vectors are plotted against each other in different planes,

corresponding to different views of the trajectories. Figure 1 depicts horizontal and torsional

curvatures during 10° downward saccades in upright, 45° left-ear-down, and 45° right-ear-

down whole-body roll positions for a typical subject (C.B.). In the vertical-horizontal plane

(Fig. 1ABC), which represents the view from the subject's perspective, downward saccades

of the viewing left eye were somewhat curved to the right in upright position (Fig. 1B). The

horizontal curvature became larger in left-ear-down position (Fig. 1A) and even reversed in

right-ear-down position (Fig. 1C). The curvature slightly increased with 10° adduction (right

gaze) and decreased with 10° abduction (Fig. 1B, compare between overlays of left and right

gaze). In the vertical-torsional plane (Fig. 1DEF) there was little curvature compared to the

trajectories in the vertical-horizontal plane (Fig. 1ABC). In this example, intorsional

curvature increased slightly in left-ear-down position (Fig. 1D). Upward saccades of the same

left eye (data not shown) deviated to the right as well with the subject in upright position.

Contrary to downward saccades, rightward curvature of upward saccades increased in right-

ear-down position and decreased in left-ear-down position.

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−10 right−505left 10

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Figure 1: Modulation of horizontal (A-C) and torsional (D-F) curvature during vertical

saccades at different whole-body roll positions. Example of 10° downward saccades of a left

eye at -10°, 0°, and 10° horizontal eccentricities in upright, left-ear-down, and right-ear-

down positions (subject C. B.). A-C: Eye position in the vertical-horizontal plane (projection

from the subject's perspective). Starting positions are aligned for clarity. D-F: vertical-

torsional plane. Separate saccade trajectories represent different horizontal eccentricities

corresponding to panels A-C. AD: 45° left-ear-down whole-body roll position (LED). BE:

Upright position (up). CF: 45° right-ear-down whole-body roll position (RED).

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Weber et al.

Figure 2 shows horizontal saccades of the same subject as in figure 1. Adducting

rightward 10° saccades of the viewing left eye were almost straight in the horizontal-vertical

plane in upright position (Fig. 2B). In contrast to the vertical saccades, the trajectories were

only slightly modulated by roll position, with increasing upward curvature in right-ear-down

position (Fig. 2AC). Likewise, compared to vertical saccades the effect of gaze eccentricity

was less pronounced during horizontal saccades: trajectories tended to bend downward at 10°

downgaze (Fig. 2B). In the horizontal-torsional plane, adducting saccades made along the

horizontal meridian showed a small extorsional curvature (Fig. 2E). These torsional

deviations were similar in both ear-down positions (Fig. 2DF). Abducting saccades showed a

reversed pattern with a small downward curvature that increased in right-ear-down position

(data not shown). In abducting saccades intorsional curvature slightly increased at

contralateral ear-down position.

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Weber et al.

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Figure 2: Modulation of vertical (A-C) and torsional (D-F) curvature during horizontal

saccades at different whole-body roll positions. 10° adducting rightward saccades of a

viewing left eye at -10°, 0° and 10° vertical eccentricity in upright, left-ear-down and right-

ear-down position (subject C. B.). A-C: Eye position in the horizontal-vertical plane

(projection from the subject’s perspective). Starting positions are aligned for clarity. D-F:

horizontal-torsional plane. Separate saccade trajectories represent different vertical

eccentricities corresponding to panels A-C. AD: 45° left-ear-down whole-body roll position

(LED). BE: Upright position (up). CF: 45° right-ear-down whole-body roll position (RED).

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Weber et al.

Figure 3 illustrates how horizontal curvature of a typical downward saccade of a left eye was

analyzed (subject C. B.). Saccade onset was defined 4msec before angular velocity crossed

the threshold of 30°/sec.27 Saccade offset was defined 4msec after velocity declined below

this level (Fig. 3C, dashed vertical lines). This criterion excludes post-saccadic drift and

possible catch-up saccades from the analysis. The moment of peak acceleration was

determined by the maximum of the derivative of angular velocity vector length (Fig. 3D,

solid vertical line). Typically, peak acceleration was reached very early during the course of

the saccade (Fig. 3A, arrow). A negative transient in the horizontal eye position represents

the rightward curvature of the saccade (Fig. 3B, dark-gray trace). As a result of the horizontal

transient, the velocity trace of the horizontal component appears biphasic (Fig. 3C, dark-gray

trace).

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Figure 3: Analysis of the curvature of a typical 10° downward saccade in a left eye (subject

C. B.). A: vertical-horizontal plane (projection from the subject’s perspective). Bold trace:

trajectory from saccade onset to saccade offset. Thin trace: subsequent catch-up saccade.

Dashed line: straight connection between onset and offset. Arrow: eye position at peak

acceleration. B: Traces of torsional (light-gray), vertical (black) and horizontal (dark-gray)

rotation vector components (converted to degrees). Dashed vertical lines: saccade onset and

offset. Solid vertical line: peak acceleration. C: Traces of angular velocity vector

components. D: Trace of the derivative of angular velocity vector length.

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Weber et al.

To analyze the behavior of the ocular rotation axis during saccades, we used angular velocity

vectors.23 Note that angular velocity vectors are oriented horizontally during vertical

displacements and vertically during horizontal displacements; directions of vectors follow the

right-hand rule. For example, the angular velocity vector of a downward saccade points to the

left along the (positive) vω -axis.

Figure 4 shows angular velocity vectors of three typical downward saccades in a left eye

(again subject C.B.). In upright position, angular velocity vectors formed a loop with an early

negative and later positive vertical component added to the main positive horizontal

component (Fig. 4B, same saccade as in Fig. 3). This loop reflects the rightward curvature of

the downward saccade. The non-linear trajectory implies that the orientation of the ocular

rotation axis was not stable during the saccade but rotated clockwise (from the subject’s

view) in the vertical-horizontal plane. The mean angular velocity vector (bold arrow) of the

saccade, however, pointed horizontally to the left, as expected if the eye finally reaches the

vertically displaced target. The initial angular velocity vector from saccade onset to peak

acceleration (empty arrow) pointed down and to the left, indicating a rightward deviation at

the beginning of the saccade. In the torsional direction (Fig. 4E) angular velocity vectors

were closely aligned during the entire saccade indicating no torsional curvature in upright

position.

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Weber et al.

0100200300

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Figure 4: Example of downward saccades in different whole-body roll positions (subject

C.B.). Trajectories of angular velocity vectors represent ocular rotation axes. Bold arrow:

mean angular velocity vector of the entire saccade. Empty arrow: initial angular velocity

vector from saccade onset to peak acceleration. Lengths of arrows are multiplied by 1.5 for

clarity. A-C: vertical-horizontal plane. D-F: vertical-torsional plane. AD: 45° left-ear-down

whole-body roll position (LED). BE: Upright position (up). CF: 45° right-ear-down whole-

body roll position (RED).

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Weber et al.

Roll tilt towards the left ear (Fig. 4AD) increased the loop of angular velocity vectors in

the vertical-horizontal plane, which corresponds to an increase of horizontal curvature of the

downward saccade. Roll tilt towards right ear (Fig. 4CF) decreased the loop of angular

velocity vectors in the vertical-horizontal plane. In the torsional direction, however, angular

velocity vectors remained almost aligned in both ear-down positions.

Saccade curvature was quantified by the angle between the initial angular velocity vector

and the mean angular velocity vector in the respective plane. The sign of the angle was

determined by the sign of the direction of the saccade multiplied by the sign of the direction

of the deviation according to the right-hand rule. For example, a downward saccade (positive)

with a rightward curvature (negative) resulted in a negative deviation angle.

Figure 5 summarizes the modulation of horizontal curvature of saccades made along the

vertical meridian by different roll positions for all subjects. Except for one extreme value,

mean horizontal curvature in downward saccades of viewing left eyes scattered around zero

in upright position (Fig. 5A, up). In right-ear-down position, curvature systematically

increased towards the left (upper) ear and vice versa. Upward saccades of viewing left eyes

showed a similar pattern: Curvature scattered around zero in upright position (Fig. 5C, up)

but systematically increased towards the lower ear in ear-down position. The right eye, when

viewing (Fig. 5BD) followed the same rule: Downward saccades curved towards the upper

ear and upward saccades towards the lower ear in ear-down position.

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Weber et al.

LED up RED

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Figure 5: Modulation of horizontal curvature of saccades made along the vertical meridian

as a function of whole-body roll position. Connected symbols: mean saccade curvature in the

horizontal direction of individual subjects. AB: 10° downward saccades. CD: 10° upward

saccades. AC: viewing left eye. BD: viewing right eye. Ordinate: horizontal saccade

curvature (direction indicated by the respective curved arrows). Dashed line: level of straight

saccade. Abscissa: 45° left-ear-down (LED), upright (up), and 45° right-ear-down whole-

body roll position (RED).

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Weber et al.

Figure 6 depicts torsional curvature of vertical saccades of all subjects using the same

definition as in figure 5. Downward saccades of viewing left eyes predominantly showed a

small extorsional curvature when subjects were in upright position (Fig. 6A). In contrast to

saccade curvature in the vertical-horizontal plane (Fig. 5A), there was no consistent

modulation pattern by roll position in the torsional direction. Viewing right eyes showed a

mirrored pattern with extorsional saccade curvature in upright position (Fig. 6 B). Upward

saccades exhibited a small extorsional curvature in upright position (Fig. 6CD). In contrast to

downward saccades, upward saccades showed a small, but systematic modulation by roll

position with intorsion of the lower eye.

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Weber et al.

LED up REDextor

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A B

C D

downward saccades

upward saccades

Figure 6: Modulation of torsional curvature in saccades made along the vertical meridian as

a function of whole-body roll position. Connected symbols: mean saccade curvature in the

torsional direction of individual subjects. AB: 10° downward saccades. CD: 10° upward

saccades. AC: viewing left eye. BD: viewing right eye. Ordinate: torsional saccade curvature

(intor, extor: torsion of the respective eye). Dashed line: level of straight saccade. Abscissa:

45° left-ear-down (LED), upright (up) and 45° right-ear-down whole-body roll position

(RED).

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Weber et al.

For statistical analysis, right eyes were mirrored as left eyes, and all eyes were pooled

(n=16 of 8 subjects). To quantify the modulation of saccade curvature by roll position, linear

regression was performed for each eye through curvature of every saccade in left-ear-down,

upright and right-ear-down position. Figure 7 summarizes the results for saccades made along

the vertical meridian. The positive slope for downward saccades denotes a modulation of

horizontal curvature by roll position towards the upper ear (Fig. 7A, first column). In the t-

test, slopes were significantly different from zero (p<0.01, indicated by an asterisk on the

abscissa label). The mean offset (Fig. 7C, first column, open square), however, was close to

zero, which indicates no directional preponderance of horizontal curvature in upright

position. The slope of torsional curvature scattered mostly around zero suggesting no

systematic modulation of torsional curvature of downward saccades by roll position (Fig. 7A,

second column). The offset of torsional curvature was significantly different from zero,

indicating an extorsional curvature in downward saccades (Fig. 7C, second column). Upward

saccades exhibited a similar pattern of horizontal curvature as downward saccades: On

average, downward saccades were straight in upright position (Fig. 7D, first column) and

significantly curved towards the lower ear in ear-down position (Fig. 7B, first column).

Torsional curvature of upward saccades showed a small, but significant modulation by roll

position with intorsion of the lower eye, but no significant predominance of torsional

curvature in upright position (Fig. 7BD, second column).

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Weber et al.

A B

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right extor

Fi

gure 7: Horizontal and torsional curvatures during vertical saccades as a function of whole-

body roll position. AC: downward saccades. BD: upward saccades. AB: slopes indicating

modulation of horizontal curvature (first column) and torsional curvature (second column) as

a function of roll position. CD: offsets in horizontal curvature (first column) and torsional

curvature (second column) in upright position. Open circles: average values of each eye

(n=16 of 8 subjects). Open squares with error bar: mean ±1SD. Asterisk in abscissa label:

mean is significantly different from zero (t-test: p<0.01).

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Weber et al.

In analogy to the previous figure for vertical saccades, Figure 8 summarizes the analysis of

saccades along the horizontal meridian. In abducting saccades, both vertical and torsional

curvature was modulated by whole-body roll position (Fig. 8A). Adducting saccades showed

only a small modulation of vertical curvature and no consistent modulation of torsional

curvature (Fig. 8B). In ear-down positions, saccadic trajectories of both eyes towards the

lower ear tended to bend upwards, whereas trajectories towards the upper ear bended

downwards (Fig. 8AB, first column). Torsional curvature was only modulated in abducting

saccades with increasing intorsion at contralateral ear-down position (Fig. 8A, second

column). In upright position, abducting saccades showed a significant downward and

intorsional deviation (Fig. 8C). Adducting saccades exhibited an extorsional curvature (Fig.

8D, second column) in the same direction as the intorsional curvature of the abducting fellow

eye.

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Weber et al.

A B

vertical* torsional*

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

curvature ofabducting saccades

slop

e

vertical* torsional

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

curvature ofadducting saccades

vertical* torsional*

−20

−10

0

10

20

offs

et[°]

vertical torsional*

−20

−10

0

10

20

C Ddown

down

up

up

intor

extor

extor

intor

Figure 8: Vertical and torsional curvatures during horizontal saccades as a function of

whole-body roll position. AC: abducting saccades. BD: adducting saccades. AB: slopes

indicating modulation of vertical curvature (first column) and torsional curvature (second

column) as a function of roll position. CD: offsets in vertical curvature (first column) and

torsional curvature (second column) in upright position. Open circles: average values of

each eye (n=16 of 8 subjects). Open squares with error bar: mean ±1SD. Asterisk in abscissa

label: mean is significantly different from zero (t-test: p<0.01).

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Weber et al.

In a next step, we asked whether the magnitude of saccade curvature was related to the

amount of OCR. If so, subjects with higher OCR amplitudes should show greater modulation

of saccade curvature as a function of whole-body roll. OCR amplitudes from 45° left-ear-

down to 45° right-ear-down position (mean 12.0° ±4.2SD, both eyes pooled) were correlated

against the slopes from figure 7 and 8 (panels AB) as a measure of modulation of saccade

curvature. Vertical saccades showed significant correlation between horizontal curvature and

OCR (Pearson’s correlation coefficient for downward saccades: r=0.73, p=0.0012; for

upward saccades: r=0.51, p=0.043). In contrast, the correlation between vertical curvatures of

horizontal saccades and OCR was not significant. Torsional curvatures of horizontal and

vertical saccades did not significantly correlate with OCR, except for abducting saccades

(r=0.62, p=0.01).

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Weber et al.

For a visual validation of our results, we compared the dual search coil recordings with 3D

video-oculography. Figure 9A-F shows 3D video-oculographic data collected from the same

subject (C.B.) and during the same paradigm as in Figure 1. Downward saccades showed the

same modulation pattern of horizontal curvature with a small offset between both recording

methods (Fig. 9G). Torsional curvature of downward saccades was comparable and showed a

predominantly extorsional offset and only little modulation compared to the horizontal

curvature with both methods (Fig. 9H). The same correspondence between dual search coil

recordings and 3D video-oculography was found in all four subjects that were tested with

both recording methods.

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Weber et al.

D E−10 right−505left 10

−5

0

5

LED

horizontal [°]

verti

cal [

°]

−10−50510

−5

0

5

up

horizontal [°]−10−50510

−5

0

5

RED

horizontal [°]

ccw 0 −5 0 5 0 cw

−5

0

5

torsional [°]

verti

cal [

°]

0 −5 0 5 0

−5

0

5

torsional [°]0 −5 0 5 0

−5

0

5

torsional [°]

A B C

F

-20

-10

0

10

20

horiz

onta

l sac

cade

cur

vatu

re [°

]

LED up RED

dual search coil(Fig. 1 A,B, C)

3D video oculography(Fig. 10 A,B, C)

horizontal curvatureof downward saccades

G

LED up REDextor

-20

-10

0

10

20

intor

torsional curvatureof downward saccades

tors

iona

l sac

cade

cur

vatu

re[°

] dual search coil(Fig. 1 D,E, F)

3D video oculography(Fig. 10 D,E, F)

H

3D video oculography

up

down

up

down

Figure 9: Comparison of 3D video-oculography (A-F) with dual search coil recordings

(same paradigm and same subject, C.B. as in Fig. 1). (A-F) 3D video-oculography of the left

eye during downward saccades. (G) Horizontal curvature during downward saccades

recorded with 3D video-oculography (empty triangles, data from Fig. 9 ABC) compared to

dual search coils (filled triangles, data from Fig. 1ABC). (H) Torsional curvature in

downward saccades recorded with 3D video-oculography (empty triangles, data from Fig.

9DEF) compared to dual search coils (filled triangles, data from Fig. 1DEF).

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Weber et al.

DISCUSSION

The purpose of this study was to explore the influence of ocular counterroll (OCR) on the

kinematics of saccades. We found a specific modulation pattern of saccade curvature by OCR

depending on saccade direction (qualitative summary figure 10): OCR predominantly

influenced horizontal curvatures of vertical saccades: Downward saccades curved to the

upper ear, whereas upward saccades curved to the lower ear in roll positions. Vertical

curvature of horizontal saccades was slightly modulated by ear-down positions as well (Fig.

8AB), but the direct correlation with OCR did not reach significance. Modulation of saccade

curvature by OCR was also found in the torsional direction, but this effect was only

significant in abducting horizontal saccades.

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Weber et al.

LED upright RED

horizontal and verticalsaccade curvature

ad

ab

up

dow

n

Figure 10: Modulation of saccade curvature by whole-body roll position in a left eye

(qualitative summary plot). Horizontal and vertical saccade curvature as seen from the

subject's perspective. Grey shade: significant correlation between modulation of saccade

curvature and OCR amplitude. Abduction=ab, adduction=ad, left-ear-down position=LED,

right-ear-down position=RED.

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Weber et al.

To explain the complex modulation patterns of saccade curvatures by OCR, we considered

different mechanisms along the path of signal transformation from retinal input to ocular

motor output. Saccade curvatures could arise as a result of (1) a mismatch between retinal

and ocular motor coordinates; (2) an imperfection of the saccadic burst generator to observe

the non-commutative properties of three-dimensional eye rotations; and (3) characteristics of

the ocular motor plant including transient force imbalances between agonist eye muscles

(vertical rectus and oblique muscles) and eye muscle pulley shifts during vertical saccades.

Mechanism 1: mismatch between retinal and ocular motor coordinates

A mismatch between the sensed oculo-centric target directions and head-fixed ocular

motor commands during OCR could explain the horizontal curvatures of vertical saccades in

ear-down positions.15 Similar as in Schworm et al.20, 45° head-roll induced about 6° OCR in

our subjects. Hence head-fixed targets appear rotated clockwise by 6° in right-ear-down

position. Therefore, the target for a downward saccade appears down and shifted to the left,

the target for an upward saccade up and shifted to the right. The initial motor command

would aim towards the perceived, not the actual target location, if OCR was not considered

by the visual-motor transformation mechanism. To prevent a directional mismatch between

the endpoint of the saccade and the target, an adaptation-driven mechanism ensures that,

during the later part of the saccade, the initial directional error is corrected and the saccade

trajectory curves towards the actual target. This mechanism would hold not only for vertical,

but also for horizontal saccades. The horizontal curvature of vertical saccades is compatible

with this hypothesis, but the pattern of vertical curvature during horizontal saccades is not.

Although OCR reduces the roll-tilt of the visual input in ear-down positions, perceptional

studies demonstrated that subjects tend to overestimate the angle of the perceived earth

vertical in body roll positions <60°.28 This observation, called e-effect, was also found if

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Weber et al.

subjects had to indicate earth vertical (not body vertical) directly with saccadic eye

movements.29 Contrary to the coordinate transformation hypothesis above, such a perceptual

hypothesis would only explain the results for vertical curvature of horizontal saccades, but

not for horizontal curvature of vertical saccades.

Mechanism 2: Kinematic imperfections of the saccadic burst generator

There has been a long debate whether the explicit implementation of Listing's law for

saccades occurs at the level of premotor neurons, the ocular plant, or both. Tweed and Vilis

described a model of a neural controller that takes into account the non-commutativity of

rotations to encode a three-dimensional eye position signal in Listing's plane.2 The existence

of a saccadic burst generator that takes into account current eye position has been questioned

by several authors, although a commutative controller invariably produces torsional

deviations during and after saccades.30 The amplitudes of those so-called blips, however, is

considerably smaller than predicted in the computer model.11 This observation led to the idea

that Listing's law is implemented at the level of eye muscle pulleys.31 These structures,

consisting of connective tissue and smooth muscles, change extra-ocular muscle pulling

directions as a function of eye position. Such a mechanical implementation of Listing's law is

suitable to simplify the neural control of saccades. Recent experiments in monkeys confirmed

that horizontal eye movements still obey Listing’s law, when they are elicited by micro

electric stimulation of the abducens nerve.32 The preservation of Listing’s law during such a

non-physiological activation of the lateral rectus muscle further supports the notion that this

law is implemented at the level of the ocular motor plant.

Indeed, our data shows no universal modulation pattern as predicted by a kinematical

mechanism, but a pattern that is different depending on saccade direction. In addition, there is

a striking disparity between the modulation of saccade curvature in the horizontal-vertical

plane compared to the torsional direction. For example, clear horizontal modulation of

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Weber et al.

vertical saccades is scarcely reflected in ocular torsion (Figure 7A). This dissociation further

argues against an explicit three-dimensional saccadic burst generator and in favor of a

mechanical implementation of Listing’s law.

Mechanism 3: Characteristics of the ocular motor plant

The dynamics and kinematics of saccades are determined by force changes in agonist eye

muscles. While agonist activity during horizontal eye movements is restricted to one muscle,

agonist activity during vertical eye movements involves two muscles.33 Unless their

secondary actions in the torsional and horizontal directions cancel, the eyes will deviate from

a straight vertical trajectory.34,35 For example, both the superior oblique and inferior rectus

muscle contract during downward saccades. The secondary actions of these muscles in the

torsional (superior oblique: intorsion; inferior rectus: extorsion) and horizontal (superior

oblique: abduction; inferior rectus: adduction) direction must cancel each other for a saccade

to be perfectly downward.

OCR leads to an imbalance between the two co-agonist eye muscles for downward saccades:

During intorsion the superior oblique muscle contracts and stretches the inferior rectus

muscle.36 Considering the length-tension curve of eye muscles37-40, the shorter (pre-

contracted) superior oblique muscle will develop less traction than the longer (stretched)

inferior rectus muscle. Hence, OCR reciprocally changes the dynamic characteristics of the

two co-agonist eye muscles. This transient force imbalance between the two vertically pulling

co-agonist muscles can lead to a curved saccade trajectory. During the initial part of a

downward saccade, the eye would deviate towards the pulling direction of the inferior rectus

muscle, i.e. medially and extorsionally, similar to the pattern found in patients with trochlear

nerve palsy.41,42 During the final part of the saccade, the eye would deviate towards the

pulling direction of the superior oblique muscle, i.e. intorsionally and laterally. In our data,

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Weber et al.

the observed horizontal curvatures of vertical saccades are consistent with such transient

force imbalances during saccades with two co-agonist muscles.

Transient force imbalances between agonist muscles during vertical saccades should not only

cause horizontal but also torsional curvatures that are modulated by OCR. Such a modulation

of torsional curvature, however, was not evident in our data. Possibly, the configuration of

rectus muscle pulleys, which shift in the presence of OCR, cancels torsional curvature in

order to preserve Listing's law even in roll positions.14

Likewise, shifts of eye muscle pulleys could also provide an explanation for direction-

dependent saccade curvature in the horizontal-vertical plane. Clark and colleagues have

shown that lateral rectus muscle pulleys shift with vertical gaze, while there is no

commensurate pulley shift with horizontal gaze.43,44 Such distinct characteristics of individual

eye muscle pulleys would help to explain different curvature patterns depending on saccade

direction.

Conclusion

Neither of the proposed universal mechanisms, visual-motor coordinate transformations or

kinematical characteristics of the saccadic burst generator, can explain the entire modulation

pattern of saccade curvature by OCR that we found. Consideration of characteristics of the

ocular motor plant allows for individual deviation patterns depending on saccade direction.

Dynamic interactions of agonist eye muscles in vertical saccades and shifting eye muscle

pulleys are both suitable to explain such a direction-dependent modulation pattern by OCR.

Additional insights can be expected from studies of saccade curvature in patients with

individual eye muscle palsies.42

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Weber et al.

ACKNOWLEDGEMENTS

The authors thank Oliver Bergamin, Sarah Marti, Antonella Palla, Alexander Tarnutzer,

and Albert Züger for assistance and the reviewers for their helpful comments.

DISCLOSURES

The authors have reported no conflicts of interest.

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Weber et al.

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