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1 From the Departments of Neurology and 3 Ophthalmology, Zürich University Hospital, Switzerland; and 2 Department of Neurology, Johns Hopkins Hospital, Baltimore, Maryland.
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Abstract |
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 Top Abstract IntroductionMethodsResultsDiscussionAppendix IAppendix IIAppendix IIIReferences |
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METHODS. In orthotropic and strabismic human subjects, both eyes were recorded with dual scleral search coils in a three-field magnetic system. Before mounting the search coil annuli on the eyes, the voltage offsets of each channel and the relative magnitudes of the three magnetic fields were determined. For calibration, subjects were only required to fix monocularly on a single reference target. During fixation of targets on the Hess screen by the uncovered eye, the three-dimensional eye position of both the occluded and the viewing eye was simultaneously measured.
RESULTS. For clinical interpretation, an easy to understand graphical description of the three-dimensional Hess screen test was developed. Positions of orthotropic and strabismic eyes tended to follow Listing’s law, which in both eyes allowed the determination of the primary position, that is, the position of gaze from which pure horizontal and pure vertical movements do not lead to an ocular rotation about the line-of-sight. To a first approximation, the location of primary position is a result of the summation of the individual rotation axes of the six extraocular muscles and thus can be used to infer which muscle is paretic.
CONCLUSIONS. The three-dimensional Hess screen test with binocular dual search coils in a three-field magnetic system is an objective method to assess the ocular alignment in three dimensions with high precision. From these recordings, the clinician can relate deviations of primary position to specific eye muscle palsies.
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix IAppendix IIAppendix IIIReferences |
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The two-dimensional Hess screen test is not an objective method, because the patient has to indicate the position of the green light. Another disadvantage is that the torsional degree of freedom of eye rotation cannot be measured easily. This makes it impossible to test whether the ocular motor laws for three-dimensional eye position3 4 5 are valid in strabismic eyes.
Objective measures of torsional eye position are based on ophthalmoscopy6 and fundus photography.7 Here, the lines between the centers of the optic disc and the fovea are determined. In orthotropic subjects, this line is not horizontal, because the optic disc is higher than the fovea, a configuration that is named excyclorotation. Perimetry of the blind spot (scotometry) also allows one to quantify the cyclorotation of the fundus, but this procedure requires excellent cooperation by the patient. Both fundus photography and scotometry are usually restricted to an eye position with the line-of-sight pointing straight ahead. If the clinician wants to determine ocular torsion at different horizontal, vertical, and oblique directions of gaze, no objective measures of ocular torsion are available.
Methods that allow the description of relative torsion between both eyes with the line-of-sight pointing straight ahead include the Maddox double-rod test and the Bagolini striated lenses.8 Using the synoptophore,9 the Harms tangent scale,10 or the Lancaster test with horizontal or vertical bars,11 one can measure the torsional deviation between both eyes at different gaze directions. Afterimages can be used to describe the relative rotation of the eyeball about the visual axis at different directions of gaze with respect to the ocular position where the vertical or horizontal light bar was flashed.12
An ideal Hess screen test should not only give the difference in torsion between the two eyes, but also the torsion of each eye separately and simultaneously at any direction of gaze. Furthermore, this test should be objective, that is, not rely on a subjective alignment of visual bars. The dual search coil technique meets all these requirements. This method, developed by D. A. Robinson in the early 1960s, was the first that could objectively measure all three rotatory components of ocular movements.13 In the mid-1980s, H. Collewjin14 15 16 modified the scleral annulus, such that three-dimensional search-coil measurements could be applied in humans routinely.
The aim of this article is to provide an algorithm for the neuro-ophthalmologist and strabismologist on how to combine the conventional Hess screen test with binocular three-dimensional search coil measurements and analyze the data for clinical purposes.
The advantage of the method will be demonstrated with examples of an orthotropic and a strabismic subject, as well as in four patients with trochlear nerve palsy before and after eye muscle surgery.
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix IAppendix IIAppendix IIIReferences |
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300 US$ and can be reused with proper
disinfection up to 10 times. The field system consisted of a cubic coil frame of welded aluminum that produces three orthogonal magnetic fields with frequencies of 55.5, 83.3, and 41.6 kHz and intensities of 0.088 Gauss. Amplitude-modulated signals were extracted by synchronous detection (modified Remmel system).17 The bandwidth of the system was 0 to 90 Hz. Peak-to-peak noise signals in all three principal directions after calibration, as measured by a dual search coil placed in the center of the magnetic frame, were about 0.1°.
Calibration Procedure
The major part of the calibration was done in vitro, that is,
with no subject participation required. This property of the procedure
is especially useful for eye movement recordings of patients in whom in
vivo calibrations by a fixation task are difficult or impossible. The
voltage offsets of the system were zeroed with the dual search coils in
the center of a soft iron tube that shielded the coils from the
magnetic fields.18
Thereafter, the relative gains of the
three-magnetic fields were determined with the search coils on a gimbal
system placed in the center of the coil frame. The details of the
calibration procedure are given in Appendix I.
The three-dimensional eye position in the magnetic coil frame was
expressed in rotation vectors. A rotation vector
r = (rx,
ry, rz) describes
the instantaneous orientation of a body as a single rotation from the
reference position; the vector is oriented parallel to the axis of this
rotation, and its length is defined by tan (
/2), where is the
rotation angle. The three head-fixed orthogonal axes of the coil frame
define the coordinate system of rotation vectors, with the
x-axis pointing forward, the y-axis leftward, and
the z-axis upward. The signs of rotations about these cardinal axes are
determined by the right-hand rule, that is, clockwise, leftward, and
downward rotations, as seen from the subject’s view, were positive.
The algorithm for converting the raw data into rotation vectors is
described in Appendix II. The transformation of rotation vectors, which
express ocular positions in a head coordinate frame, to gaze angles for
the interpretation by the clinician is elaborated on in Results.
Hess Screen Test
Subjects were seated inside the magnetic field coil (side
length, 1.4 m) so that the center of the interpupillary line
coincided with the center of the frame. The head of the subject was
immobilized with a bite bar that was oriented along earth-horizontal.
Dual search coils were mounted on both eyes, after anesthetizing the
conjunctiva and cornea with proparacaine HCl 0.5% (Ophthetic;
Allergan, Irvine, CA).
During measurements, subjects monocularly fixed on dots on a tangent screen at a distance of 1.24 m at its center, while the other eye was covered. The dots were located straight-ahead and at eight eccentric positions (horizontal and vertical coordinates in degrees: [0, 20]; [20, 20]; [20, 0]; [20, -20]; [0, -20]; [-20, -20]; [-20, 0]; [-20, 20]). The dots were arranged as a square with straight sides 20° from the center fixation point, that is, a "Harms" type projection. The entire procedure lasted about 20 minutes. Voltages related to the orientation of the eye coils in the magnetic coil frame were digitized with a 16-bit A/D converter at 1000 Hz and written to a hard disc. The data were analyzed off-line in MATLAB Version 5.4.
Torsional Coil Slippage
During search coil recordings, one frequently observes a
long-term drift of torsional coil signals, which is due to a gradual
slippage of the silicon annulus on the conjunctiva about the
line-of-sight.19
20
To minimize this problem off-line, the
torsional position was reset to the value measured at the beginning of
a trial during each straight-ahead fixation. Thus, the values of
torsion at eccentric positions were always relative to the value of
torsion at the reference (0,0) fixation position. The absolute value of
torsion cannot be measured with the search coil technique.
Subjects
In the Results section of this article, typical data of an
orthotropic subject, three patients with acquired trochlear nerve palsy
and two patients with congenital trochlear nerve palsy are presented.
Experimental protocols adhered to the Declaration of Helsinki for
research involving human subjects (adopted by the 18th World Medical
Assembly, Helsinki, Finland, 1964, and as revised last in Hong Kong in
1989) and approved by the local Ethical committee.
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Results |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix IAppendix IIAppendix IIIReferences |
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The nine data clouds of rotation vectors associated with target fixations were selected with an interactive computer program. Then, the median of the three-dimensional rotation vector was computed for each target point. Figure 2 depicts examples of binocular recordings from an orthotropic subject and a strabismic patient. For better visualization, the eccentric values are connected with the central value. The left column (Figs. 2Aa Ab, Ac ) is based on the same right eye data as the previous figure, with the covered right eye in blue and the viewing left eye in red. The right column (Figs. 2Ba Bb, Bc ) shows the data of a patient with an acquired trochlear nerve palsy of the right eye. Again, the covered right eye (paretic) is in blue and the viewing left eye (healthy) is in red. The panels of each row illustrate the front (Figs. 2Aa Ba ), side (Figs. 2Ab Bb ), and top (Figs. 2Ac Bc ) views of median three-dimensional eye rotation vectors. To make the front view (horizontal–vertical projection) comparable with a standard two-dimensional Hess test, both the y- and z-components were multiplied by (-1). Hence, in the two panels on the top row, rightward and upward movements are positive. The three-dimensional orientation of the axes about which the eyes rotated with respect to the head (see inserted heads) can easily be identified in the views from the right side (Figs. 2Ab Bb ) and from the top (Figs. 2Ac Bc ).
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The following procedures (formulae given in Appendix III) were applied to the nine median rotation vectors21 : (1) the vertical–horizontal gaze direction in degrees was computed. (2) The gaze direction was inverted both in the horizontal and vertical directions, such that upward and rightward became positive. This convention is equivalent to the one used for the standard two-dimensional Hess screen test, in which the coordinates are plotted from the subject’s perspective, that is, from behind ("right is right, up is up"). (3) The torsional component of the rotation vectors was converted to degrees.
Figure 3 contains the same data as in the previous figure, but here we attempted to help the clinician to grasp immediately the three-dimensional eye position of the viewing eye and, at the same time, the three-dimensional alignment between the viewing and the covered eye, in a single panel.
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Two sectors are depicted at each fixation dot of the viewing eye. The sectors with the smaller radius (thinner stroke) describe the torsional rotation vector components of the fixing eye. The following scale was adopted: 1 hour corresponds to 1° of torsion, with zero torsion at 12 o’clock; the direction of torsion is defined from the perspective of the subject. For example, 3 hours of counterclockwise rotation of left fixing eye corresponds to an excyclorotation by 3°. If the right eye is fixing, the same sector corresponds to an incyclorotation by 3°. The sectors with the larger radius (thicker stroke) give the amount of cyclovergence. The same scale was adopted as for the torsional component of the fixing eye. For example, with the left eye viewing, 2 hours of counterclockwise rotation means a relative 2° incyclorotation of the covered right eye with respect to the viewing left eye, that is, a 2° incyclovergence. If the right eye is viewing, 2 hours of clockwise rotation means a relative 2° incyclorotation of the covered left eye with respect to the viewing right eye, and again, a 2° incyclovergence.
The large filled circle and the large filled triangle show the primary
positions of the fixating eye and the covered eye, respectively.
Primary position was determined by fitting a plane through the data
cloud of the nine median rotation vectors:
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The horizontal (ph) and vertical
(pv) components of primary position in
degrees are directly computed from the slopes of the
regression21
:
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In the orthotropic subject, there was a small exophoria of less than 2°, independent of whether the left (Fig. 3Aa ) or the right (Fig. 3Ab ) eye was viewing. There was a slight right hyperphoria in left gaze and a left hyperphoria during fixations along the vertical meridian and in left gaze. The vertical phoria was always less than 2°. The torsional phoria never exceeded 3°. This value for torsional phoria is a relative quantity because the torsion measured in each eye at a given position was always referenced to the torsion in the straight-ahead viewing position (= reference position). The horizontal–vertical directions of the line-of-sight of both eyes were all close to the fixation targets. Independent of which eye was fixing, the primary viewing positions of both the viewing (filled circle) and the covered (filled triangle) eyes were located above the horizontal meridian and slightly shifted to the left.
In the patient (Figs. 3Ba Bb ), the eye with the acquired trochlear nerve palsy (right eye) was deviated upwards; the right eye over left eye position was maximal in adduction and downward gaze. Compared with the measurement with the left eye viewing (Fig. 3Ba ), the vertical deviation was larger during fixation with the palsied right eye (Fig. 3Bb ), that is, the secondary deviation exceeded the primary deviation. There was a striking gradient of increasing horizontal and vertical misalignment from right-upward to left-downward gaze. The gradient of excyclovergence pointed in the same direction. The left eye showed a gradient of increasing excyclorotation from right-down to left-up gaze. This gradient was parallel to the gradient of increasing incyclorotation of the right eye. The primary position of the paretic right eye was shifted to the right, that is, temporally, by almost 30°; the primary position of the left eye was displaced in the same direction, that is, nasally, by about half the amount. The locations of the primary positions were similar during fixation with the left (L; healthy) or right (R; paretic) eye, thus relatively independent of which eye was fixing.
Figure 4 provides a summary of the alignment values in the orthotropic subject (Fig. 4A) , and in the patient with the right-sided acquired trochlear nerve palsy (Fig. 4B) , from the subject’s viewpoint. The numbers are based on the same fixation trial as shown in the previous figure with the left eye viewing. For each direction of gaze, horizontal (Exo or Eso), vertical (right eye position higher than left eye position [R/L] or L/R), and the torsional (Excyc or Incyc) vergence are quantified. The horizontal and vertical numbers specify the direction of gaze, whereas the torsional numbers correspond to the torsional component of the rotation vector. The inset above the main table gives the horizontal (adduction [Add] or abduction [Abd]) and vertical (elevation[Ele] or depression[Dep]) direction of the primary position (PP) for both eyes.
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Discussion |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix IAppendix IIAppendix IIIReferences |
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The term "primary position" was originally introduced by Helmholtz5 : "Among the different eye positions, one can be found from which a movement, up or down, right or left, does not introduce rotation about the line-of-sight. This position is called primary gaze direction." Clearly, in Helmholtz’ definition, primary (gaze) position does not necessarily coincide with gaze straight ahead. If, for instance, an eye intorts when looking up and extorts when looking down from the straight-ahead position, primary position lies to the temporal side from the straight-ahead position.
Primary position is directly related to Listing’s law: If primary position is chosen as the reference position, all other eye positions can be reached from this position by a rotation about an axis that is perpendicular to the direction of gaze in primary position.5 In this case, rotation vectors lie in the frontal plane of the coordinate system. If primary position deviates from the reference position, the plane of these rotation axes—so called Listing’s plane—is rotated in the direction of primary position by half the angle.21 22 In orthotropic subjects, in the presence of convergence, the primary positions of both eyes move temporally,23 24 but not by the whole amount that is required to strictly preserve the sensory requirement of retinal correspondence.25 Only if the primary positions of both eyes coincide is there no torsional disparity for targets at infinite distance. Normally, however, the primary positions of the two eyes are not exactly aligned, which leads to different torsional disparities at different gaze directions. Because torsional disparity can be fused centrally to a certain degree,26 the amount of torsional vergence in different gaze directions cannot be directly related to the magnitude of torsional diplopia.
Perhaps the main significance of primary position for the clinician is its relationship to the pulling directions of the different extraocular muscles. To a first approximation, the axes about which the eye rotates are determined by the vectorial summation of the forces of the six extraocular muscles. The contraction of each muscle in isolation leads to a rotation of the eye about an axis that is perpendicular to the pulling direction of this muscle. For instance, the activation of the superior oblique muscle rotates the ocular globe from the straight-ahead position about an axis that nearly lies in the horizontal plane (x-y plane) and forms an angle of approximately 35° with the sagittal axis (x-axis).27 If eye movements were accomplished by contraction and relaxation of this muscle only, the horizontal component of primary position would be located in the nasal direction (recall the definition of primary position). In the case of an eye muscle palsy, we propose that the primary position produced by the remaining five muscles can be predicted by vectorially subtracting the primary position of the palsied muscle from the primary position measured with all eye muscles intact. On the basis of this hypothesis, we speculate that the change of primary position is largest in palsies that affect eye muscles with major torsional components of their pulling direction, that is, especially the oblique and vertical recti muscles. On the other hand, we expect that palsies of the horizontal recti would not lead to major changes of primary position, unless there is compensation by other muscles with torsional pulling directions. In our example of isolated acquired right trochlear nerve palsy, the primary position of the paretic eye moved temporally, as one would predict (Fig. 3B) . Changes of the location of extraocular muscle pulleys could also play a role in modifying primary position28 : In patients with a superior oblique muscle palsy, the pulley of the medial rectus muscle showed an upward displacement, probably as a consequence of the atrophy of the adjacent superior oblique muscle belly.29
Interestingly, in our example of a right-sided trochlear nerve palsy (Fig. 3B) , the primary position of the healthy eye is located in the nasal hemifield by more than 10°, thus minimizing the "horizontal deviation" of both primary positions. This phenomenon could be explained by a compensatory decreased activity of the inferior rectus muscle of the healthy left eye (yoke muscle), which would lead to an increased intorsion as the eye moves down. Also, changes in the neural control of extraocular muscle pulleys could lead to modifications of Listing’s plane and, hence, of primary position of the healthy eye.30 The horizontal and vertical difference between the primary positions of the two eyes is directly related to the gradients of cyclovergence as a function of gaze direction. In the example of the patient with a right acquired trochlear nerve palsy (Fig. 3B) , there is a gradient of increasing incyclovergence from downward to upward gaze. This gradient means that the rotation axes for vertical movements of the two eyes are not parallel but form an angle that points forward.
Figure 5
schematically explains the relation between the vertical gradient of
torsional vergence and the horizontal component of primary position. In
Figure 5A
, both eyes are depicted from above (top view). The horizontal
axis about which the left eye rotates to move upward is in the frontal
plane; thus, primary position coincides with the straight-ahead
position. On the other hand, the horizontal axis of the right eye with
the acquired trochlear nerve palsy is tilted outward by 
/2 =
15°, and the primary position of this eye is rotated = 30°
to the right. For mathematical reasons, the shift of primary position
is always twice the angle of the rotation axis.21
Because
of the outward tilt of the rotation axis, an upward movement of the
right eye is associated with an intorsional movement of the ocular
globe with respect to the head (In this context, "torsion" is
defined as a rotation about the x-axis in the head-fixed
coordinate system and not a rotation about the line-of-sight). This
leads to a gradient of increasing incyclovergence when the patient is
changing his eye position from downward to upward.
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= 20° upward gaze (solid). Clearly, in the
left eye, both crosses coincide, whereas in the right eye, there is an
intorsion of the retina in upgaze by 
= 5.1°. In fact, the
retinal torsion during vertical eye movements () is a function of
the horizontal component of primary position () and the elevation of
gaze ():
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To date, little is known about the location of primary position in the presence of a concomitant strabismus. Melis et al.31 reported on a subject with a concomitant alternating strabismus, in which the Listing’s planes of the two eyes varied depending on whether the right or the left eye was viewing.
To what extent Listing’s law is still obeyed in the presence of extraocular muscle palsy before and after surgery is presently being investigated with the three-dimensional Hess screen test. So far, no statistical data are available, but there are clear indications that muscle surgery on one eye changes the primary position of both eyes: Figure 6 demonstrates how both eyes’ primary positions are affected by a contralateral inferior rectus recession in typical patients with a left-sided trochlear nerve palsy. In all four patients the primary position of the healthy eye moved downward as a result of the operation. There was, however, a differential effect of the surgery on the primary position of the paretic eye, depending on whether the palsy was acquired or congenital. In the patients with the acquired palsy (Fig. 6A) , the temporally displaced primary position moved closer to the vertical meridian, but in the patients with the congenital palsy (Fig. 6B) , the primary position moved in the temporal direction. Whether this finding can be generalized remains to be explored, but this example demonstrates that eye muscle surgery has a direct effect on the primary position, and, hence, the three-dimensional orientation of ocular rotation axes.
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Appendix I |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix IAppendix IIAppendix IIIReferences |
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Constant offset voltages (undesirable pickup, internal amplifier biases) are compensated by placing the annulus in a soft iron tube, which isolates the search coils from the magnetic fields, and setting the offset knobs of the amplifier to zero. Then, after the annulus is removed from its shield, all signals at the output of the detector are due to the search coils alone.
After the offsets are nulled, the annulus is placed on a gimbal system and rotated in six positions, each of which picks up the maximum voltage induced by one magnetic field in one search coil (two coils times three directions for each eye). The alignment of the two search coil sensitivity vectors with the magnetic field must follow the right-hand rule to obtain the maximal amplitudes with the correct signs, that is, the coil sensitivity vectors must be aligned in sequence with the x-axis (pointing forward), the y-axis (pointing leftward), and the z-axis (pointing upward).
Once the offsets are eliminated and the measurement of the magnetic fields completed, the raw signals can be used to compute the orientation of the dual search coil in the space-fixed magnetic frame. For each moment in time, the computer calculates the rotation necessary to move the dual search coil from a defined reference position to the instantaneous position (algorithm see Appendix II). The reference position is usually defined as the position when the line-of-sight is directed to a specified straight-ahead target that is far enough away so the vergence angle is negligible.
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Appendix II |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix IAppendix IIAppendix IIIReferences |
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Each sample now consists of two vectors that are nonorthogonal, because
the effective surfaces of the search coils in the annulus usually do
not form a perfect 90° angle. Thus, the next step is to orthogonalize
the sensitivity vector of the torsion coil (t) to the
sensitivity vector of the direction coil (d). First, we
normalize the vector of the direction coil:
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Appendix III |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix IAppendix IIAppendix IIIReferences |
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Acknowledgements |
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Footnotes |
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Submitted for publication June 28, 2000; revised November 3, 2000; accepted November 22, 2000.
Commercial relationships policy: N.
Corresponding author: Dominik Straumann, Neurology Department, Zürich University Hospital, Frauenklinikstrasse 26, CH-8091 Zürich, Switzerland. dominik{at}neurol.unizh.ch
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References |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix IAppendix IIAppendix IIIReferences |
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, •: primary position of the right eye before
surgery; 
, 
: primary position of the left eye before surgery.
: primary position after surgery. (A) Two patients
(circles, triangles) with acquired trochlear nerve palsy;
(B) two patients (circles, triangles) with
congenital trochlear nerve palsy.