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After their introduction by Robinson (IEEE Trans Biomed Eng 10:137-145, 1963), magnetic scleral search coils quickly became an accepted standard for precise eye movement recordings. While other techniques such as video-oculography or electro-oculography may be more suitable for routine applications, search coils still provide the best low-noise and low-drift characteristics paired with the highest temporal and spatial resolution. The problem with search coils is that many research laboratories still have their large and expensive coil systems installed and are acquiring eye movement data with old, analog technology. Typically, the number of recording channels is limited and modifications to an existing search coil system can be difficult. We propose a system that allows to retro-fit an existing analog search coil system to become a digital recording system. The system includes digital data acquisition boards and a reference coil as the hardware part, receiver software, and a new calibration method. The circuit design has been kept simple and robust, and the proposed software calibration allows the calibration of a single coil within a few seconds.

We propose a new method to measure torsional eye movements from videos taken of the eye. In this method, we track iris features that have been identified as Maximally Stable Volumes. These features, which are stable over time, are dark regions with bright borders that are steep in intensity. The advantage of Maximally Stable Volumes is that they are robust to nonuniform illumination and to large changes in eye and camera position. The method performs well even when the iris is partially occluded by reflections or eyelids, and is faster than cross-correlation. In addition, it is possible to use the method on videos of macaque eyes taken in the infrared, where the iris appears almost featureless., (Copyright © 2010 Elsevier B.V. All rights reserved.)

The orientation of Listing's Plane (LP) was examined under one-g and zero-g conditions during parabolic flight. Ten healthy subjects participated in the experiment. In zero-g the orientation of LP was consistently altered. LP elevation was tilted backwards by approx. 10 degrees (p=0.003). The azimuth angles of the left and right eyes also diverged in zero-g, with a statistically significant change (p=0.04) in the vergence angle between 6.1 degrees and 11.8 degrees . A discernible dissociation in torsional eye position was also observed, which proved to be statistically significant (p=0.03). The thickness of LP was found to be of the order of 1 degrees , and was not significantly altered by the transitions between one-g and zero-g. Additional control experiments involving repeated measurements of LP under normal laboratory conditions demonstrated that the parameters of LP remain stable in the individual. The parabolic flight results demonstrate that in contrast to re-orientation in the one-g gravitational field, the elimination of gravity represents a qualitative change for the vestibular and oculomotor systems. It appears that given the lack of voluntary control of ocular torsion, the tonic otolith afferences are instrumental in the stabilisation of torsional eye position and consequently of Listing's Plane. The observed torsional divergence also provides support for the so-called otolith asymmetry hypothesis.

The consequences of changes in the oculomotor system on the three-dimensional eye movements are difficult to grasp. Although changes to the rectus muscles can still be approximately understood with simplified geometric models, this approach no longer works with the oblique muscles. It is shown how SEE++, a biomechanical model of the oculomotor plant that was built on the ideas of Miller and Robinson (1984) can improve the understanding of the effects of changes to the oblique eye muscles. By displaying only selected muscles, and by illustrating the relative contribution of these muscles through color-coding the bulb surface, the functional properties of the oblique muscles can be presented in a much clearer way. Investigating the effects of a hyperactive inferior oblique muscle shows that this type of model can help to clarify the functional cause of a pathology, which can otherwise be unclear, even for common pathologies.

Eye movement recordings with video-based techniques have become very popular, as long as they are restricted to the horizontal and vertical movements of the eye. Reliable measurement of the torsional component of eye movements, which is especially important in the diagnosis and investigation of pathologies, has remained a coveted goal. One of the main reasons is unresolved technical difficulties in the analysis of video-based images of the eye. Based on simulations, we present solutions to two of the primary problems: a robust and reliable calibration of horizontal and vertical eye movement recordings, and the extraction of suitable iris patterns for the determination of the torsional eye position component.

Purpose: To explain the positive Bielschowsky head-tilt (BHT) sign in unilateral trochlear nerve palsy (uTNP) by the kinematics of three-dimensional eye rotations., Methods: Twelve patients with uTNP monocularly fixed on targets on a Hess screen were oscillated (+/- 35 degrees, 0.3 Hz) about the roll axis on a motorized turntable (dynamic BHT). Three-dimensional eye movements were recorded with dual search coils. Normal data were collected from 11 healthy subjects., Results: The rotation axis of the viewing paretic or unaffected eye was nearly parallel to the line of sight. The rotation axis of the covered fellow eye, however, was tilted inward relative to the other axis. This convergence of axes increased with gaze toward the unaffected side. Over entire cycles of head roll, the rotation axis of either eye remained relatively stable in both the viewing and covered conditions., Conclusions: In patients with uTNP, circular gaze trajectories of the covered paretic or unaffected eye during dynamic BHT are a direct consequence of the nasal deviation of the rotation axis from the line of sight. This, in turn, is a geometrical result of decreased force by the superior oblique muscle (SO) of the covered paretic eye or, according to Hering's law, increased force parallel to the paretic SO in the covered unaffected eye. The horizontal incomitance of rotation axes along horizontal eye positions can be explained by the same mechanism.

Strabismus due to palsy of a single muscle in one eye is always incomitant, which is a consequence of Hering's law of equal innervation. We asked whether this law had similar consequences on the orientation of ocular rotation axes. Patients with unilateral trochlear nerve palsy were oscillated about the nasooccipital (= roll) axis (+/-35 degrees, 0.3 Hz), and monocularly fixed on targets on a head-fixed Hess screen. Both the covered and uncovered eyes were measured with dual search coils. The rotation axis of the covered eye (paretic or healthy) tilted more nasally from the line of sight when gaze was directed toward the side of the healthy eye. The rotation axis of the viewing eye (paretic or healthy), however, remained roughly aligned with the line of sight. We conclude that incomitance due to eye muscle palsy extends to ocular rotation axes during vestibular stimulation.

The semi-circular canals and the otolith organs both contribute to gaze stabilization during head movement. We investigated how these sensory signals interact when they provide conflicting information about head orientation in space. Human subjects were reoriented 90 degrees in pitch or roll during long-duration, constant-velocity rotation about the earth-vertical axis while we measured three-dimensional eye movements. After the reorientation, the otoliths correctly indicated the static orientation of the subject with respect to gravity, while the semicircular canals provided a strong signal of rotation. This rotation signal from the canals could only be consistent with a static orientation with respect to gravity if the rotation-axis indicated by the canals was exactly parallel to gravity. This was not true, so a cue-conflict existed. These conflicting stimuli elicited motion sickness and a complex tumbling sensation. Strong horizontal, vertical, and/or torsional eye movements were also induced, allowing us to study the influence of the conflict between the otoliths and the canals on all three eye-movement components. We found a shortening of the horizontal and vertical time constants of the decay of nystagmus and a trend for an increase in peak velocity following reorientation. The dumping of the velocity storage occurred regardless of whether eye velocity along that axis was compensatory to the head rotation or not. We found a trend for the axis of eye velocity to reorient to make the head-velocity signal from the canals consistent with the head-orientation signal from the otoliths, but this reorientation was small and only observed when subjects were tilted to upright. Previous models of canal-otolith interaction could not fully account for our data, particularly the decreased time constant of the decay of nystagmus. We present a model with a mechanism that reduces the velocity-storage component in the presence of a strong cue-conflict. Our study, supported by other experiments, also indicates that static otolith signals exhibit considerably smaller effects on eye movements in humans than in monkeys.

Our understanding of the functional structure of extraocular muscles has undergone a profound change: while these muscles used to be represented by strings running straight from their origin in the posterior orbita to their insertion on the globe, we now know that their paths and pulling directions are dominated by fibromuscular pulley structures, keeping them close to the orbital wall for most of their path. An overview is presented of recent models that have been developed to understand the implications of muscle pulleys for the neural control of eye movements and the applications of such models to the interpretation of experimental data.

We investigated how three-dimensional (3D) eye position is influenced by static head position relative to gravity, a reflex probably mediated by the otolith organs. In monkeys, the torsional component of eye position is modulated by gravity, but little data is available in humans. Subjects were held in different head/body tilts in roll and pitch for 35 s while we measured 3D eye position with scleral coils, and we used methods that reduced torsion artifacts produced by the eyelids pressing on the contact lens and exit wire. 3D eye positions were described by planar fits to the data (Listing's plane), and changes in these planes showed how torsion varied with head position. Similar to findings in monkeys, the eyes counterrolled during roll tilts independent of horizontal and vertical eye position, reaching a maximum torsion of 4.9 degrees. Counterroll was not proportional to the shear force on the macula of the utricles: gain (torsion/sine of the head roll angle) decreased by 50% from near upright to ear down. During pitch forward, torsion increased when subjects looked right, and decreased when they looked left. However, the maximum change of torsion was only -0.06 degrees per degree of horizontal eye position, which is less than reported in monkey. Also in contrast to monkey, we found little change in torsion when subjects were pitched backwards.

We recorded three-dimensional eye movements elicited by velocity steps about axes that were tilted with respect to the earth-vertical. Subjects were accelerated in 1 s from zero to 100 degrees/s, and the axis of rotation was tilted by 15 degrees, 30 degrees, 60 degrees, or 90 degrees. This stimulus induced a constant horizontal velocity component that was directed opposite to the direction of rotation, as well as a modulation of the horizontal, vertical and torsional components with the frequency of the rotation. The maximum steady-state response in the horizontal constant-velocity component was much smaller than in other species (about 6 degrees/s), reaching a maximum at a tilt angle of about 60 degrees. While the amplitude of the horizontal modulation component increased up to a tilt angle of 90 degrees (8.4 degrees/s), the vertical and torsional modulation amplitudes saturated around 60 degrees (ca. 2.5 degrees/s). At small tilt angles, the horizontal modulation component showed a small phase lag with respect to the chair position, which turned into a small phase lead at large tilt angles. The torsional component showed a phase lead that increased with increasing tilt angle. The vertical and torsional velocity modulation at large tilt angles was not predicted by a recent model of otolith-canal interaction by Merfeld. Agreement between model and experimental data could be achieved, however, by introducing a constant force along the body's z-axis to compensate for the gravitational pull on the otoliths in the head-upright position. This approach had been suggested previously to explain the direction of the perceived subjective vertical during roll under different g-levels, and produced in our model the observed vertical and torsional modulation components at large tilt angles.

Purpose: To determine whether volitional effort on the part of the subject can influence the results of the Bielschowsky Head Tilt Test., Patients and Methods: Bielschowsky Head Tilt testing was performed in five normal subjects. Vertical amplitudes were measured with prism alternate cover testing when the head tilt was voluntary (volitionally maintained in a tilted position by the subject), forced (restrained in the tilted position by the examiner while the patient actively resisted) and active (restrained in a tilted position by the examiner with the subject actively trying to increase the tilt). Three-dimensional scleral search coil recordings were performed in three additional normal subjects using the same paradigm to determine the effect of volition on the torsional positions of the eyes., Results: No vertical deviation of the eyes was detectable with prism alternate cover testing in any position of tilt, regardless of whether the tilt was voluntary, forced, or active. Volitional attempts to tilt the head were preceded by a transient ipsiversive torsional movement of the measured eye, which was quickly followed by a normal ocular counterroll. Following completion of the counterroll, the position of the eyes was constant for any position of head tilt, regardless of whether the tilt was forced, active, or voluntary., Conclusion: Anticipatory torsional movements of the eyes are evoked by an attempted volitional head movement in the roll plane and its associated innervation to the cervical musculature. However, these volitional movements do not alter the final torsional position of the eyes, which is a function of the degree of head tilt and the normal ocular counterroll. These anticipatory torsional movements do not influence the results of the Bielschowsky Head Tilt Test clinically by prism alternate cover testing.

The semicircular canals selectively transduce angular velocity and are normally insensitive to gravity and linear acceleration. In acute alcohol intoxication, however, the cupula becomes lighter than the endolymph, rendering it sensitive to gravity (buoyancy hypothesis). This results in positional alcohol nystagmus (PAN) and rotatory vertigo. We evaluated PAN in 8 normal subjects by means of three-dimensional eye-movement analysis in an attempt to clarify if the buoyancy mechanism is sufficient to explain PAN. Forty minutes after intake of 0.8 g of alcohol/kg of body weight, the subjects were positioned such that the lateral canals were earth vertical. They were then rotated in the plane of the lateral canals about an earth-horizontal axis to either 45 degrees or 90 degrees , right or left ear down, and eye movements were recorded for 40 seconds in each position. The spatial analysis of the responses showed that in addition to the nystagmus induced by the buoyancy of all six cupulae, alcohol intoxication also causes a vertical velocity offset (in all subjects, slow phase down) that is independent of the orientation of the subject in space. The offset may represent a toxic effect on central vestibular pathways, producing a tone imbalance of the vertical vestibulo-ocular reflex.

The eye muscles in humans are arranged such that they allow rotations of the globe about any axis in three-dimensional space. Only 3D analysis techniques will suffice to describe the sometimes complex dependencies between the elicited eye movements and the stimulation conditions. With the recent availability of modern 3D eye movement measurement techniques and the further development of appropriate mathematical descriptions, we are now able to study eye movements in all three degrees of freedom. This article describes the basic mathematical tools for 3D eye movement analysis like rotation vectors, reference frames, coordinate systems, and the concept of Listing's law. In a second part some clinical applications are presented. The close coupling between the vestibular and the oculomotor system suggests that by observing spontaneous and elicited eye movements in the case of an acute unilateral vestibular pathology we might be able to find out which parts of the vestibular system (that is, which of the semicircular canals or which of the otoliths) are affected. The rationale of such an analysis is based on the observation that electrical stimulation of single semicircular canal afferents in animals induces eye movements that lie roughly in the plane of the canal. It is, therefore, possible to deduce which canals cause the eye movements observed when only some parts of the vestibular system are defective. Thus, the analysis of 3D movements not only provides an improved understanding of how the brain organizes movement in 3D space, but also has the potential to significantly improve our diagnostic capabilities.

Horizontal and vertical movements of the human eye bring new objects to the center of the visual field, but torsional movements rotate the visual world about its center. Ocular torsion stays near zero during head-fixed gaze shifts, and eye movements to visual targets are thought to be driven by purely horizontal and vertical commands. Here, analysis of eye-head gaze shifts revealed that gaze commands were three-dimensional, with a separate neural control system for torsion. Active torsion optimized gaze control as no two-dimensional system could have, stabilizing the retinal image as quickly as possible when it would otherwise have spun around the fixation point.

Hypothesis and Background: Quantitative caloric testing is considered to be one of the most sensitive parameters in the diagnosis of peripheral vestibular disorders. In the past, because of limitations in the methods, the evaluation of the caloric response was restricted to mainly lateral semicircular canal functions. In this study, the authors tried to extend caloric testing to the function of all semicircular canals by using three-dimensional (3-D) analysis techniques., Methods: The authors studied in seven normal subjects 3-D eye movement responses to air caloric of the right ear with the subjects positioned in standard caloric position (lateral semicircular canal vertical) or such that one of the three semicircular canals of the right side was horizontal. Movement of the left eye was measured in 3-D with a dual-magnetic search coil. During stimulation, 10 seconds of maximum response were selected and desaccaded to yield the slow-phase velocity profile. From this profile, the average magnitude and direction of the eye rotation axis (velocity vector) were calculated in head coordinates., Results: In all subjects, in standard caloric position, warm caloric produced eye velocity vectors that clustered closely along the direction expected from an excitation of the right lateral semicircular canal. When the subjects were positioned with one of the vertical semicircular canals horizontal, the orientation of the velocity vectors shifted toward a direction expected from the combined excitation of the lateral and the other vertical semicircular canal and vice versa., Conclusions: The 3-D eye movement recordings during caloric stimulation in different head positions allow the evaluation of the function of all semicircular canals.

1. The kinematics of the human angular vestibuloocular reflex (VOR) in three dimensions was investigated in 12 normal subjects during high-acceleration head rotations (head "impulses"). A head impulse is a passive, unpredictable, high-acceleration (3,000-4,000 degrees/s2) head rotation of approximately 10-20 degrees in roll, pitch, or yaw, delivered with the subject in the upright position and focusing on a fixation target. Head and eye rotations were measured with dual search coils and expressed as rotation vectors. The first of these two papers describes a vector analysis of the three-dimensional input-output kinematics of the VOR as two indexes in the time domain: magnitude and direction. 2. Magnitude is expressed as speed gain (G) and direction as misalignment angle (delta). G is defined as the ratio of eye velocity magnitude (eye speed) to head velocity magnitude (head speed). delta is defined as the instantaneous angle by which the eye rotation axis deviates from perfect alignment with the head rotation axis in three dimensions. When the eye rotation axis aligns perfectly with the head rotation axis and when eye velocity is in a direction opposite to head velocity, delta = 0. The orientation of misalignment between the head and the eye rotation axes is characterized by two spatial misalignment angles, which are the projections of delta onto two orthogonal coordinate planes that intersect at the head rotation axis. 3. Time series of G were calculated for head impulses in roll, pitch, and yaw. At 80 ms after the onset of an impulse (i.e., near peak head velocity), values of G were 0.72 +/- 0.07 (counterclockwise) and 0.75 +/- 0.07 (clockwise) for roll impulses, 0.97 +/- 0.05 (up) and 1.10 +/- 0.09 (down) for pitch impulses, and 0.95 +/- 0.06 (right) and 1.01 +/- 0.07 (left) for yaw impulses (mean +/- 95% confidence intervals). 4. The eye rotation axis was well aligned with head rotation axis during roll, pitch, and yaw impulses: delta remained almost constant at approximately 5-10 degrees, so that the spatial misalignment angles were < or = 5 degrees. delta was 9.6 +/- 3.1 (counterclockwise) and 9.0 +/- 2.6 (clockwise) for roll impulses, 5.7 +/- 1.6 (up) and 6.1 +/- 1.9 (down) for pitch impulses, and 6.2 +/- 2.2 (right) and 7.9 +/- 1.5 (left) for yaw impulses (mean +/- 95% confidence intervals). 5. VOR gain (gamma) is the product of G and cos(delta). Because delta is small in normal subjects, gamma is not significantly different from G. At 80 ms after the onset of an impulse, gamma was 0.70 +/- 0.08 (counterclockwise) and 0.74 +/- 0.07 (clockwise) for roll impulses, 0.97 +/- 0.05 (up) and 1.09 +/- 0.09 (down) for pitch impulses, and 0.94 +/- 0.06 (right) and 1.00 +/- 0.07 (left) for yaw impulses (mean +/- 95% confidence intervals). 6. VOR latencies, estimated with a latency shift method, were 10.3 +/- 1.9 (SD) ms for roll impulses, 7.6 +/- 2.8 (SD) ms for pitch impulses, and 7.5 +/- 2.9 (SD) ms for yaw impulses. 7. We conclude that the normal VOR produces eye rotations that are almost perfectly compensatory in direction as well as in speed, but only during yaw and pitch impulses. During roll impulses, eye rotations are well aligned in direction, but are approximately 30% slower in speed.

We recorded three-dimensional eye movements during angular acceleration steps from 0 to 250 degrees/s at 20 degrees/s2 about an earth-vertical axis. Experiments were performed on 27 normal subjects and on 19 patients who had recovered well from unilateral vestibular deafferentation on the right or left side. In addition to compensatory horizontal eye movements, significant vertical and torsional eye movement components were elicited. These vertical and torsional eye velocity traces led to a shift of the axis of eye velocity away from the axis of head velocity. Horizontal, vertical, and torsional velocity components showed clear differences between normals and patients with unilateral vestibular deafferentation. In normals, the axis of eye velocity tilted backward and slightly away from the axis of head velocity. Patients showed similar, but more pronounced, shifts during rotations toward the intact ear and shifts in the opposite direction for rotations toward the operated ear. Eye velocity traces were analyzed with special consideration given to the orientation of the axis of eye velocity. We speculate that the vertical and torsional velocity components may be due to the effects of Listing's plane, as well as the contributions of the otolith signals.

Polar cross correlation is commonly used for determination of ocular torsion from video images, but breaks down at eccentric positions if the spherical geometry of the eye is not considered. We have extended this method to allow three-dimensional eye position measurement over a range of +/- 20 deg by determining the correct projection of the eye onto the image plane of the camera. We also determine the orientation of the camera with respect to the eye, allowing eye position to be represented in appropriate head-fixed coordinates. These algorithms have been validated using both in vitro and in vivo measures of eye position.

Polar cross-correlation is a commonly used technique for determination of torsional eye position from video images. At eccentric eye positions, the projection of the sampling window onto the image plane of the camera is translated and deformed due to the spherical shape of the eyeball. In this paper, we extend the polar cross-correlation technique by developing the formulas required to determine the correct location and shape of the sampling window at all eye positions. These formulas also allow the representation of three-dimensional eye position in Fick-angles, which are commonly used in oculomotor research. A numerical simulation shows the size of the errors in ocular torsion if the spherical geometry of the eye is not considered. Other effects which can affect the accuracy of video-based eye position measurements are also discussed.

The recording of three-dimensional eye position has become the accepted standard in oculomotor research. In this paper we review the mathematics underlying the representation of three-dimensional eye movements. Rotation matrices, rotation vectors and quaternions are presented, and their relations described. The connection between search coils and rotation matrices is explained, as well as the connection between eye position and eye velocity. While examples of applications of the formulas to vestibulo-ocular research are given, the methods and mathematical analyses are also useful for studying other motor systems.

Using dual torsion scleral search coils we have recorded 3-dimensional eye position during yaw angular accelerations of 20 degrees/s2 about an earth vertical axis in healthy subjects and in patients with unilateral vestibular deafferentation (UVD). These experiments produced two interesting results: i) even in healthy subjects, the axis of eye velocity did not coincide with the (earth vertical) stimulus axis during centred rotation; ii) Patients with UVD had torsional eye velocity components that were systematically different from those in normal subjects. While in normals the direction of the torsional component of the eye velocity depended on the direction of rotation and was on average approximately symmetric for CW and CCW yaw rotation, there was a clear asymmetry in patients, which was distinctly different for left and right UVD.

The parameters characterizing Listing's plane have been determined in a group of normal subjects, and in patients who have had unilateral vestibular deafferentation on the right or left side. All patients were well compensated. There was no statistically significant difference in the orientation of Listing's plane between either of these groups: Listing's plane was approximately perpendicular to the horizontal stereotaxic plane and showed a systematic temporal tilt, i.e., it tilted right for the right eye, and left for the left eye. We also found a considerable intersubject variability in the orientation of Listing's plane. The effect of this variability on the interpretation of three-dimensional eye position and velocity data is discussed.

In three rhesus monkeys three-dimensional eye positions were measured with the dual search coil technique. Recordings of spontaneous eye movements were made in the light and in the dark, with the monkeys in different static roll or pitch positions. Eye positions were expressed as rotation vectors. In all static positions eye rotation vectors were confined to a plane, i.e. Listing's plane was conserved. Tilt about the roll axis shifted the plane along this axis, i.e. a constant torsional component was added to all eye positions. Tilt about the pitch axis changed the pitch angle of Listing's plane.

We have recorded eye, head, and upper arm rotations in five healthy human subjects using the three-dimensional search coil technique. Our measurements show that the coordination of eye and head movements during gaze shifts within +/- 25 deg relative to the forward direction is organized by restricting the rotatory trajectories of the two systems to almost parallel planes. These so-called "Listing planes" for eye-in-space and head-in-space rotations are workspace-oriented, not body-fixed. Eye and head trajectories in their respective planes are closely related in direction and amplitude. For pointing or grasping, the rotatory trajectories of the arm are also restricted to a workspace-oriented Listing plane. During visually guided movements, arm follows gaze, and the nine-dimensional rotatory configuration space for eye-head-arm-synergies (three degrees of freedom for each system) is reduced to a two-dimensional plane in the space of quaternion vectors.

We have tested Listing's law in the monkey using the dual search coil technique to record 3-dimensional eye positions during smooth pursuit and during spontaneous eye movements in the light. Our results indicate that during smooth pursuit the eye positions obey Listing's law with a least the same accuracy as during spontaneous eye movements or during periods of fixations.