THREE DIMENSIONAL EYE MOVEMENTS OF … · to post rotatory horizontal nystagmus, ... of the angular...
Transcript of THREE DIMENSIONAL EYE MOVEMENTS OF … · to post rotatory horizontal nystagmus, ... of the angular...
Journal of Vestibular Research, Vol. 3, pp. 123-139, 1993 Printed in the USA. All rights reserved.
0957-4271/93 $6.00 + .00 Copyright © 1993 Pergamon Press Ltd.
THREE DIMENSIONAL EYE MOVEMENTS OF SQUIRREL MONKEYS FOLLOWING POSTROTATORY TILT
Daniel M. Merfeld, * Laurence R. Young, * Gary D. Paige,t and David L. Tomko:\:
*Man-Vehicle Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts; tDepartment of Neurology, University of Rochester, Rochester, New York;
tVestibular Research Facility, NASA Ames Research Center, Moffett Field, California Reprint address: Dr. D.M. Merfeld, Man-Vehicle Laboratory,
Massachusetts Institute of Technology, Cambridge, MA 02139
o Abstract - Three-dimensional squirrel monkey eye movements were recorded during and immediately following rotation around an earth-vertical yaw axis (1600/s steady state, l000/s2 acceleration and deceleration). To study interactions between the horizontal angular vestibulo-ocular reflex (VOR) and head orientation, postrotatory VOR alignment was changed relative to gravity by tilting the head out of the horizontal plane (pitch or roll tilt between 15° and 90°) immediately after cessation of motion. Results showed that in addition to post rotatory horizontal nystagmus, vertical nystagmus followed tilts to the left or right (roll), and torsional nystagmus followed forward or backward (pitch) tilts. When the time course and spatial orientation of eye velocity were considered in three dimensions, the axis of eye rotation always shifted toward alignment with gravity, and the postrotatory horizontal VOR decay was accelerated by the tilts. These phenomena may reflect a neural process that resolves the sensory conflict induced by this postrotatory tilt paradigm.
::J Ke~'worrls - vestibulo-oeula" reflex; eye movements; otolith organs: semicircular canals: monkey.
Introduction
When an upright subject is rotated at a constant velocity about an earth vertical axis and then rapidly decelerated, a postrotatory horizontal nystagmus occurs which then gradu-
ally decays. Studies have shown that the time course of the horizontal postrotatory response is dramatically affected by the orientation of the subject relative to gravity (1-3).
Recent studies in monkeys (4), humans (5), and cats (6) have also demonstrated the presence of a decaying vertical nystagmus as part of the postrotatory response following off vertical axis rotation (OVAR). In each of these studies, the vertical component of the eye movement shifted the plane of the response toward the earth-horizontal. Earlier studies (7,8), using low-velocity centrifuges, also reported the presence of a vertical nystagmus when the upright humans were facing the motion or had their backs to the motion. When these paradigms were repeated with monkeys, the axis of eye rotation clearly shifted toward alignment with gravitoinertial force (9,10).
Since a common neural element (11) has been hypothesized to explain the time course of optokinetic afternystagmus (OKAN) and :c yield horizontai pcstrot2,LOry nystagmu~ whi:!: outlas:, th~ enc o~g:ar. r~sp:mse: c: s:milar influence of gravity might be expected foilowing optokinetic stimulation. Research has confirmed this prediction in monkeys by showing that the axis of eye rotation during OKAN shifted toward alignment with gravity when the subject and optokinetic stimulus were tilted with respect to gravity (12), while human experiments have not confirmed this large axis shift (13).
RECEIVED 7 May 1992; REVISED MANUSCRIPT RECEIVED 16 September 1992; ACCEPTED 23 September 1992.
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While many of these studies have indicated the presence of a shift in the axis of eye rotation toward alignment with gravity, none have measured three dimensional (3-D) eye orientation, corrected for cross-talk between the eye position signals, quantified the extent of the axis shift, and quantified the time course of the angular VOR decay following constant velocity rotation. In this study, we quantified ~he effects of tilt on the angular 'lOR in an :u:empt :c :n'lestiga~e :he interac:ior.. 1)1' se!1-sory information from ~he semicircular canals and the otoliths. 3-D eye movements were recorded during and after reorientation of the monkey immediately following rapid deceleration from constant angular velocity around an earth-vertical axis. Postrotatory tilts were performed in both roll (left ear down/right ear down) and pitch (nose up/nose down), and the shift in the axis of eye rotation and the decay time constants were determined.
Methods
Experiment Design
Monkey preparation. Five adult male squirrel monkeys (Saimiri sciureus) weighing between 0.9 and 1.0 kg were the subjects. [These monkeys were also used in other studies (9,10,14).] A stainless steel bolt was used to stabilize the head of the monkey while allowing repeatable head positioning. The bolt was anchored to the skull using dental acrylic and miniature stainless steel screws which were inverted and secured in keyhole slots drilled in the skull. Right eye position was measured using a search coil technique (15). Prefabricated coils made of insulated stainless steel wire were implanted on the right eye. An 11-mm diameter 3-turn coil was sutured to the sclera concentric to the limbus in the eye's frontal plane, and an 8-mm diameter 4-turn coil was sutured to the globe laterally and posteriorly to the frontal coil in the eye's sagittal plane. The leads left the orbit such that they did not interfere with normal movements of the eye. See Paige and Tomko (14) for a complete description of all surgical procedures.
D. M. Merfeld et al
Experimental paradigm. The upright monkeys were accelerated (1000/S2) about an axis aligned with gravity and the monkey's spinal axis to a constant velocity (160 0/s) using a servo-controlled rotatory device at the NASA Vestibular Research Facility. The monkey's head was positioned such that the plane of the horizontal canals was perpendicular to the axis of rotation and such that the axis of rotation was directly between the ler't and iight -·/estibulcS. When [he :lorizomai :mgular 'lOR was nearly extinguished (>60 seconds), the monkey was quicklY decelerated (100 0/5 2) ro a stop. While the postrotatory ocular response was still strong (1 to 3 seconds after stopping), the monkey was manually tilted (1 to 2 seconds) 15, 32, 45 or 90 degrees in one of the four primary directions: nose up, nose down, left down, and right ear down. The lights were turned on between trials and extinguished just prior to the start of a trial. Three of the monkeys were tested on more than one occasion, with one monkey (B) tested five times. The order of the trials was randomized. To maintain monkey alertness, d-amphetamine (0.3 mg/ kg) was administered intramuscularly 15 minutes before the beginning of each test session.
Eye movement recording. The eye measurement system was calibrated using two orthogonal search coils similar to those implanted in the monkeys. The reference coils were mounted on a model eye secured to a nonmetallic three-axis calibration jig, which was used to set the measurement sensitivities. The accuracy of this calibration procedure has previously been verified (14,16).
Data Analysis
Eye kinematics. Using two search coils we can accurately estimate the 3-D orientation of the eye. For eye movements that do not deviate far from the primary eye position, the detector circuits accurately indicate yaw, pitch, and roll of the eye. However, as the eye position deviates from the primary gaze position a number of nonlinear errors become important (15). These errors are enhanced by any mis-
3-D Eye Movements Following Postrotatory Tilt
alignment of the search coils on the globe (17). An electronic correction scheme had been developed (14,16) to minimize these errors. As long as coil placement errors and eye displacements were limited to less than 10 degrees for each axis of eye rotation, the worst-case eye position measurement error was less than 100/0, and the mean error was less than 3%.
The electronic correction method proved inadequate for this study since eye displacements sometimes exceeded 20 degrees, leading to worst case errors of greater than 20%. To minimize these errors, we developed and applied here an exact solution algorithm that corrected for coil placement errors (9,18). With eye displacements of up to 20 degrees, this algorithm yields worst case measurement errors of less than 10% (18).
Coordinate system. Dynamic knowledge of the three-dimensional eye orientation allowed us to calculate a three dimensional representation of eye velocity (18). Eye velocity is a vector quantity and may be represented in a number of different coordinate frames. We chose to represent eye velocity in a head-fIxed Cartesian coordinate system to allow us to compare the eye responses directly to the motion stimuli. We defined the head-fixed, right-handed coordinate system such that the x-axis aligns with the naso-occipital axis, the y-axis aligns with the interaural axis, and the z-axis is perpendicular to the x- and y-axes. The positive direction is forward for the x-axis, leftward for the y-axis, and upward for the z-axis. In this Cartesian representation. eye veiocity 1:- repre<.::'mec by a ve·:tor wiIi'; components . I:. eacr: ~{' :~e ~hree· ·::i:-e:tian~ (x, y. and z). With the eye in the primary position, horizontal eye velocity is represented by a vector aligned with the head fixed z-axis (w z ). Similarly, vertical (Wy) and torsional (wx) eye velocities are presented by vectors aligned with the monkey's y-axis and x-axis, respectively (Figure 1). This representation is different from the commonly used Fick representation, where eye velocity is represented by three quantities, called Euler rates, which represent rates of ocular yaw, pitch, and roll. Euler rates are a reasonable approximation to
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eye velocity when eye movements are small «5 degrees) or when responses are limited to a single plane (yaw or pitch or roll), but are a poor choice during 3-D eye rotation because the Fick coordinate system moves with the eye, because the Euler rates are nonorthogonal (except in the primary position), and because the representation of eye velocity depends upon eye orientation.
Using the Cartesian representation, the primary post rotatory response following yaw rotation (around the z-axis) is a horizontal eye movement (wz ; also around the z-axis). To evaluate the extent to which postrotatory tilts caused the axis of eye rotation to shift away from the z-axis, we calculated the shift in the axis of eye rotation in both the roll (coronal) and pitch (sagittal) planes (Figure 1). The roll shift in the axis of eye rotation (Or) represents the angle by which the response shifts from the z-axis (8r = 0) toward the left or right ear (y-axis). This occurs when the response includes a head vertical component a well as the predominant head horizontal component. The pitch shift in the axis of eye rotation (Op) represents the angle by which the response shifts from the z-axis (Op = 0) toward or away from the nose (x-axis). This occurs when the response includes a torsional component as well as the predominant head horizontal component. To keep the axis of eye rotation aligned with gravity following postrotatory roll tilts of the head, the axis of eye rotation, measured relative to the head, must shift in roll (Or), with no change in pitch (Op)' Similarly, to keer the axis of eye rotation aligned with grav -
i:y foliowing DOS~iO:a:O:-y pitch tiltf of the je2.: th: c:.).:i~ .): e:': :-ota:io:: ::J.:..!S! shi:: ir:. pitch (Op), with no change in roll (Or)'
Fast phase removal. Since we were interested in the slow phase eye velocity as representative of the VOR, we used a computer algorithm to identify and remove the fast phases of the nystagmus. The algorithm used loworder digital filters to calculate three-dimensional eye velocity and eye acceleration. The movement was marked as a fast phase and removed if the acceleration of the eye exceeded a threshold set by the user. All edited data
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Figure 1. Post-rotatory tilt trillls for '311"jPct R. Left column shows data obtained for a 32-degree postrotatory tilt to the right. Right column shows data obtained for a 32-degree postrotatory tilt backwrord l)illgrams In the center column define the quantities plotted. The angular yaw stimulus as well as the horizontal ocular response are shown In the first row . 'hp vertical and torsional ocular responses are shown In the second and third rows, respectively. The roll shift (II.) and the pitch shift (lip) in the axis of ey .. rotlltion are shown In the fourth and fifth rows, respectively. Dashed vertical lines mark the postrotatory tilt. Discontinuities In the fourth and fifth rows result from l1llcp.rtainty In the calculation of the axis of eye rotation when the horizontal response nears zero.
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were manually reviewed and compared to the original data to verify the integrity of the algorithm and to remove any fast phases which were missed. This simple algorithm removed more than 95"70 of the fast phases; a limited number of fast phases were manually removed. All gaps were filled with a zero-order hold of the eye velocity preceding the saccade. [Data processing details including eye kinematics, coordinate systems, and fast phase removai are ;:>resemed ~lsew!1ere (9;~ 3) . :
Curve fits. Least squares regression l i 9) ':Vas used to perform linear fits to the data. To determine the dominant decay characteristics of the VOR responses, we estimated the decay time constant (1') of the responses by fitting the curve,
y = K + Ae-tlr, [1]
to the data (K, A, and l' are the parameters determined by the curve fit). This fit was obtained by minimizing the mean square error between the data and the curve [LevenbergMarquardt algorithm (20)]. K and A were necessary to obtain an acceptable curve fit, but were not analyzed further.
To minimize the effect of the axis shift on the estimated time constant we began the curve fit after the primary off-axis response (vertical for roll tilts; torsional for pitch tilts) had reached its maximum magnitude. This curve fit ignores the complex dynamics that occur during the build-up of the off-axis response and concentrates upon the decay of the response.
Large secondary responses (for example, horizontal and vertical VOR in the left column of Figure 1) were relatively rare, but to be sure that these responses were not systematically affecting our determination of the dominant time constant we also fit the curve,
to some of the data showing significant secondary responses. No large or systematic differences between the dominant time constant determined by the single exponential curve fit
D. M. Merfeld et al
(equation 1) and the double exponential curve fit (equation 2) were observed, so we chose to fit all the data with the single exponential.
Results
VOR Response
ReI! :,~;ds. A ::epresentative trial showing a 32-deg!"':!:: ;Jostfotatory roll Lilt co the right is shown in the plots in :he left I.:olumn of Figure 1. The -15°/s spike in the torsional VOR at approximately 70 seconds is a compensatory response to the roll rotation. The horizontal response decays immediately following the tilt, but then recovers slightly before decaying more gradually with a time constant of 7.3 seconds. Approximately 2.2 seconds after the tilt, a strong vertical ocular response appears and decays with a time constant of 6.4 seconds. In this trial, the vertical slow phase velocity reached a peak magnitude of approximately 500/s. Note that the horizontal and vertical responses reverse at nearly the same time (approximately 90 seconds), indicating that the responses may be loosely coupled.
The last two rows in Figure 1 show the time course of the shift in the axis of eye rotation. Since the primary horizontal and vertical responses are both negative, the roll shift of the axis of eye rotation is positive with a peak magnitude of approximately 45 degrees while the peak magnitude of the pitch shift is less than 10 degrees. The secondary horizontal and vertical responses following reversal are both positive, which again yield a positive shift in the axis of eye rotation. In this case the roll shift during the secondary response almost exactly equals the roll tilt of 32 degrees, while the secondary pitch shift is near zero. This response is characteristic of the roll tilt trials with the roll shift of the axis of eye rotation tending to align with gravity following the postrotatory tilt.
Pitch trials. A representative trial showing 32-degree nose up tilt following rotation is shown in the plots in the right column of Figure 1. The 400/s spike in the vertical response at ap-
3-D Eye Movements Following Post rotatory Tilt
proximately 70 seconds occurs as a compensatory response to the pitch rotation. Shortly after the tilt, a strong torsional ocular response appears and decays with a time constant of 2.4 seconds, while the horizontal ocular response decays with a time constant of 4.4 seconds. In this trial, the torsional slow phase velocity reached a peak of approximately 15°/s.
The last two graphs in the column show the shift in the axis of eye rotation. Since both the horizontal and torsional responses are negative, the pitch shift of the axis of eye rotation is positive with a magnitude of approximately 20 degrees, while the roll shift is near zero. This pitch shift tends to align the axis of eye rotation with gravity following the nose up postrotatory pitch tilt. Comparable results were obtained during nose down tilts, with the sign of the torsional response always opposite that obtained during nose up trials. The reversed sign of the torsional response led to a reversal in the calculated pitch of the axis of eye rotation, once again aligning the axis of eye rotation with gravity.
VOR Spatial Characteristics
The shift in the axis of eye rotation was determined for all trials for each monkey by calculating the average shift in the axis of eye rotation for one second after the peak verticalor torsional response was obtained.
We chose to average over a full second to minimize the affect 0; noise on the estimated angle. We chose the first second after the offaxis peak because the measurement becomes very sensitive to noise as the responses, particularly the horizontal, decay toward zero. The tilt angle measurement was relatively insensitive to alternate parameterizations, since both the horizontal and off-axis responses were simultaneously decaying. For example, we compared the chosen measure with onesecond averages, starting one second and two seconds after the peak. No consistent or significant differences (always < 10"70) existed in these three measures. As an example, once the torsional velocity in the right column of
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Figure 1 reaches a peak value and begins to decay, the pitch of the eye rotation axis remains relatively constant at approximately 20 degrees until the horizontal velocity decays to near zero. At this point, significant uncertainty in the calculated angle is evident in the increasing oscillations in the pitch of the eye rotation axis.
Roll trials. Figure 2 Panel A shows a plot of the roll shift (Or) of the axis of eye rotation for a single monkey (B). The slope of the least squares fit, shown as the thin line, is 0.96. The pitch shift (Op) of the axis of eye rotation is also plotted for these roll tilt trials. The slope of the least squares fit, shown as the thick line, is -0.03. Prior to head tilt, gravity and the axis of eye rotation are aligned. Following head roll tilt, the axis of eye rotation, relative to the head, shifts in a direction opposite the head roll. This axis shift with respect to the tilted head tends to maintain the orientation of the angular VOR response relative to gravity.
Perfect alignment of the axis of eye rotation with gravity would require that the response roll shift equal the head roll tilt (slope of plus one), while the pitch shift remains zero (slope of zero). More generally, a shift toward alignment with gravity requires that the roll shift (Or) demonstrate a positive correlation with roll tilt. These data show that the axis of eye rotation shifts toward alignment with gravity following roll tilts. The roll shift in the response shows a significant (P < 0.001) positive correiation (r = 0.984) with the head ro ll ~ilt, while ~he pi,.::h da~c. are no: significantl~
more, since the slope 0; th, iinear fit to the roll shift (0.96) is not significantly different from one, we can state that the axis of eye rotation closely aligned with gravity.
Pitch trials. Figure 2 Panel B shows a plot of the pitch shift (Op) of the axis of eye rotation as a function of head pitch for a single monkey (B). The slope of the least squares fit, shown as the thick line, is 0.46. The response roll shift (Or) is also plotted, and the slope of the least squares fit, shown as the thin line, is -0.030.
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D. M. Merfeld et al
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Figure 2. Shift in the axis of eye rotation. Panel A shows the calculated shift in the axis of eye rotation for monkey B during postrotatory tilts to the left and right. The roll of the axis of eye rotation (8, from Figure 1) for each trial (+) Is plotted versus the magnitude of the tilt. Thin line represents the least squares fit. The pitch of the axis of eye rotation (8p from Figure 1) for each trial (x) Is also plotted. The thick line represents the least squares fit. Panel B shows the calculated shift in the axis of eye rotation for monkey B during tilts forward and backward. As before, the roll of the axis of eye rotation (8,) for each trial (+) Is plotted versus the magnitude of the tilt. The pitch of the axis of eye rotation (8p) for each trial (x) Is also plotted. [Panel A after Merfeld and Young (18).]
3-D Eye Movements Following Postrotatory Tilt
Analogous to the above head roll tilt experiments, alignment of the axis of eye rotation following head pitch requires that the response pitch shift (Op) equal head pitch (slope of one), while the response roll shift (Or) show no correlation (slope of zero). More generally, a shift toward alignment with gravity requires that the pitch shift (Op) demonstrate a positive correlation with head pitch. Again, the data show that the axis of eye rotation shifted toward alignment with gravity. Statistically, the pitch response shows a significant (P < 0.001) positive correlation (r = 0.985), while the roll response is not significantly (P > 0.4) correlated (r = -0.124) with the pitch tilt. Unlike the roll experiment, the realignment of the ocular response axis with gravity following head pitch was incomplete and was roughly half (0.46) that required for alignment with gravity.
Comparison of pitch and roll responses. Table 1 shows a summary of the axis shift analysis for each monkey during roll tilts and pitch tilts. During roll tilt, data for each monkey clearly indicate that the axis of eye rotation shifted toward alignment with gravity, since
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the roll shift of the axis of eye rotation for each of the five monkeys has a high positive correlation (r> 0.96) with the roll tilt. Similarly, the pitch shift data from each monkey during pitch tilt show a high positive correlation (r > .98), again indicating that the axis of eye rotation shifted toward alignment with gravity.
Data from three of the five monkeys (B, E, F) tested with postrotatory roll tilts indicated that the axis of eye rotation closely aligned with gravity since the slopes of the linear fit to the roll shift were greater than 0.95. In contrast, none of the four monkeys (A, B, E, F) tested with postrotatory head pitch displayed a shift in the axis of eye rotation that fully aligned with gravity. The slope of the linear fit never exceeded 0.9. In fact, data from three of the four monkeys (B, E, F) during pitch tilts showed that the slope of the linear fit was less than 0.5. On the whole, the pitch shifts of the axis of eye rotation following pitch tilts were less than the roll shifts of the axis of eye rotation following comparable roll tilts. Only one monkey (A) had comparable response axis shifts for roll and pitch tilts of the head.
Table 1. Axis Shift Regression Analysis
8p versus angle of tilt 8r versus angle of tilt
Monkey n s r p s r
Roll Tilts (as in Figure 2A)
A 9 -0.007 -0.059 0.16 P> 0.400 0.823 0 .989 B 15 -0 .026 -0 .202 0.74 P > 0.400 0 .955 0 .984 0 12 -0.025 -0.975 13.84 p> 0.001 0 .773 0 .962 E 3 -0.105 -(.985 5.73 P> 0 400 0 .998 0.998 F 3 0.02:' C.796 1.31 p> (, .400 O.96L 0 .996
Pitch Tilts (as in Figure 2B)'
A 1 • 0 .870 0 .997 37.46 P < 0 .001 0 .133 0 .605 B 15 0.462 0.985 20.78 P < 0.001 -0 .030 -0.124 E 3 0 .399 0.988 6 .31 P < 0 .050 0 .090 0 .720 F 3 0.422 0.991 7.46 P < 0 .050 0 .060 0 .490
• Monkey 0 not included because torsion coil failed before forward/backward tilt trials were completed. Notation:
n is the number of trials. s is the slope of the linear regression. r is the sample regression coeffiCient. t is the calculated t-value representing the significance of the correlation. P represents the statistical significance of the correlation. . Op and Or represent the axis shift of the eye as shown in Figure 1 .
17.54 20.01 11.28 17.84 i -; .07
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P> 0 .05 P> 0.40 P> 0 .40 P > 0.40
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Time Course of the VOR Decay
Roll trials. The time course of the VOR decay was also affected by the postrotatory tilt. Figure 3 shows the effect that the postrotatory tilt has on the decay of the VOR. In Figure 3 Panel A, the horizontal time constants are plotted for varying head roll tilts. Despite a great deal of variability, the data indicate that the time constant decreases as the angle of head tilt increases. The dashed line shows the :east ,quares :inear :':r. Pus :iena 'NLlS ,llgruy
significant t? < 0.001). Since the mlsaiignmem of gravity :md [he POSt rotatory head aus (z-a'{is) will vary with the sine of the magnitude of the tilt angle (Ixl), we also used linear regression to fit the equation:
y = yeO) + A sine Ixl). [3]
The solid curve shows this fit. This simple nonlinear curve provides a better fit to the data as measured by a decreased mean square error and an increased regression coefficient (Table 2).
Figure 3 Panel C shows the vertical decay time constants versus the horizontal decay time constants during roll tilt. The time constants are positively correlated (r = 0.82) with high significance (P < 0.(01). The slope of the regression (s = 0.77) is somewhat less than one, indicating that, in general, the vertical response decayed a little more rapidly than the horizontal response.
Pitch trials. Figures 3 Panel B shows the horizontal VOR time constants for pitch tilts. Once again the data indicated that the horizontal time constant decreased as the angle of tilt increased to 90 degrees. Similar to the data for roll tilts, these data indicated that the nonlinear fit is better than the simple linear fit (Table 2) and that the downward trend was highly significant (P < 0.001).
Figure 3 Panel D shows the torsional decay time constants versus the horizontal decay time constants during pitch tilts. Again the time constants were positively correlated (r = 0.78) with high significance (P < 0.001), and the slope of the regression (s = 0.76) was,
D. M. Merfeld et al
again, somewhat less than one, indicating that, in general, the torsional response decayed a little more rapidly than the horizontal response.
Comparison oj pitch and roll responses. The similarity of the linear regression for roll tilts (Figure 3 Panel C) and pitch tilts (Figure 3 Panel D) and the similarity of the effects of tilt on the time course of [he horizontal angular VOR (Figure 3) suggest that the plane 0f r:he head tilt does not dramatically affect :he ~:me course of ~he response. This is m .:on[rast cO the spatial charQcteristics, which show that the magnitude of the shift in the axis or' eye rotation is less for pitch than for roll tilts.
Summary
These experiments quantified eye movement responses by determining the spatial and temporal characteristics of 3-D ocular responses following roll and pitch postrotatory tilt and showed that whole body tilts affect the postrotational angular VOR responses of monkeys. Most dramatically, the axis of eye rotation was shown to shift toward alignment with gravity following tilt. Quantitative analysis indicated that the axis shift was greater for roll than it was for pitch tilts (Figure 2 and Table 1). These results are similar to the previous quantitative findings showing that postrotatory eye movements following OVAR shifted toward an earth-horizontal plane (4-6).
The time course of the decay of the horizontal angular VOR was also affected by the postrotational tilt in both pitch and roll (Figure 3 and Table 2). Specifically, the decay time constant was shown to decrease as the angle of tilt increased, independent of the plane (pitch or roll) of the postrotatory tilt. This is consistent with previous research (2,3) that did not take the axis shift into account when determining the decay time constants. Furthermore, the decay time constant of the off-axis VOR response (vertical for roll tilt; torsional for pitch tilt) was correlated with the decay time constant of the horizontal VOR response with the slope of the correlation less than one. This indicates that the decay of the off-axis
w w
30, Horizontal Time ConSIllnt for Roll Tilts 20
1
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0' ~-~
00 0 10 20 30 ,10 50 60 70 80 90 5 10 15 20
Tilt rdr~rees] Horizontal Time Constant (seconds]
30 Horizontal Time Constant for Pitch Tilts
201
Time Constant Correlation for Pitch Tilts
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0 10 20 30 1n 50 60 70 80 90 0 5 10 15 20
Tilt fdf'grees] Horizontal Time Constant [seconds]
Figure 3. Effect of postrotatory tilt 011 von time constants. Panel A shows a plot of the decay time constant for the horizontal ocular response versus the postrotatory tilt angie for roll tilts, while Pnnel B shows a piot of the decay time constant for the horizontal ocular response versus the postrotatory tilt angle for pitch tilts. Dashed lines show the le~!;t c:q1HHPo; linear fits. Solid curves show the least squares fit to the equation, y = y(O) + A sin(lxl), where Ixl is the magnitude of the tilt angle. Panel C shows the clpr.ny time constant for the vertical ocular response plotted against the decay time constant for the horizontal ocular response for postrotatory roll tilts. Panel 0 show!; the decay time constant for the torsional ocular response plolted against the decay time constant for the horizontal ocular response for postrotatory pitch tilt!' I inp.s represent the least square linear fits to the data •
.,..
134 D. M. Merfeld et al
Table 2. Correlation of Horizontal VOR Time Constant with Tilt
Line fit [y = y(O) + s·x) Sine fit [y = y(O) + A·sin(\xl))
s y(O) MSE r P A y(O) MSE r P
Roll tilts -0.17 174.48 -0.696.50 P<0.001 -13.8 184.23 -0.737.308 P<0.001 Pitchtilts -0.19 17 4.37 -0.70 6.13 P<0.001 -14.4 17 4.10 -0.74 6.923 P<0.001
Notation: s is the siope of the linear regression. y(O) is the y·intercept. A is the amplitude of the sine correlation. ,'viSE is ihe mean souare error. : is ihe samole regression .:oeriiclem. : is the calculatec :'lJalue ,epresenting the significance of 'he ;orreiation. P represents the slaiistical significance oi the correlation.
response may be somewhat faster than the decay of the horizontal VOR.
Discussion
VOR Spatial Characteristics
While the time course of the horizontal VOR was not strongly dependent on the plane (pitch or roll) of the postrotatory tilt, the plane of rotation did significantly affect the direction of the eye movement responses, since large vertical responses followed roll tilt and large torsional responses followed pitch tilt. In all trials the off-axis responses shifted the axis of eye rotation toward alignment with gravity. Previous studies are consistent with this finding. For example, vertical responses were observed during eccentric yaw rotations of humans about an earth-vertical axis (7,8), When this paradigm was repeated with monkeys, the vertical component of the response was shown to always shift the axis of eye rotation toward alignment with gravitoinertial force (9,10). Studies have also shown that postrotatory eye movements shift toward an earth-horizontal plane immediately following OVAR stimulation (4-6). This is consistent with the 3-D measurements, showing that the axis of eye rotation aligns with gravity.
We propose that the shift in the axis of eye rotation indicates that the eNS resolves this sensory conflict by shifting a central estimate of rotation toward alignment with gravity
(Figure 4) (9,10,18). In order to discuss this hypothesis we must clearly and unambiguously define what we mean by "central estimate of rotation" and "sensory conflict".
We define the "central estimate of rotation" as a neural representation of angular velocity that is derived from the sensory afference. It has long been known that the time course of angular VOR responses differs significantly from the dynamics of the semicircular canals, and that visual stimuli can modify the VOR responses (11,23,24). For these reasons, Robinson explicitly hypothesized that the angular VOR reflects a central estimate of self-rotation (24), which is induced by a process of sensory integration that includes visual as well as semicircular canal signals. Since the neural processing required to transform retinal images to an estimate of self-motion exceeds the neural processing required to transform otolith afference, it is not difficult to believe that otolith cues could playa similar role in determining a central estimate of self-rotation. OVAR studies, which show that the rotation of gravity can induce a bias response component that partially compensates for the actual rotation (4-6,25,26), and postrotatory tilt studies reveal that otolith signals may influence the central estimate of rotation.
We, like Guedry (21,22), define "sensory conflict" to be an incongruity between at least two sensory systems. In this case, the sensory conflict occurs because the semi circular canals and the otoliths provide conflicting information regarding self motion. Immediately
3-D Eye Movements Following Post rotatory Tilt
following deceleration the otolith signal indicating gravity is aligned with the canal signal indicating rotation, but during the postrotatory tilt the semicircular canals tilt with the body and continue to indicate rotation about the body's z-axis, while the otoliths indicate the constant orientation of gravity which is now tilted with respect to the body. If, in fact, the tilted body were rotating about the body's z-axis (yaw) as indicated by the semicircular canals, then the otoliths would be expected to
135
measure the rotation of gravity about the yaw axis. Conversely, if gravity were truly fixed with respect to the body, then rotation could only occur about an axis aligned with gravity. Therefore, the sensory signals indicating the state of motion are incongruent and produce "sensory conflict."
We also define two ways to resolve the sensory conflict. Temporally, the conflict can be resolved by reducing the central estimate of rotation (Figure 4 Panel B). This resolution
Conflict Resolution
A
Central estimate of rotation (~) not aligned with gravity (g) , Sensory Conflict
B C
+~
~ " 19
No central estimate of rotation
~~ ~~} I ~' ... . ,,~ f "f
Central estimate of rotatior. (~) aligned with gravity (g)
t + Sensory Concurrence Sensory Concurrence
Figure 4. Sensory conflict resolution. Panel A demonstrates the sensory conflict created when the central estimate of rotation (~) doesn't align with the head-fixed orientation of gravity (g) following postrotatory tilt. Sensory conflict results since the central estimate of rotation should lead to a change In orientation of gravity with respect to the head, while the otoliths just as clearly indicate that the orientation of gravity with respect to the head is constant. One way to resolve the conflict is to eliminate the central estimate of rotation (Figure 4 panel B). Another way to resolve this conflict Is to align the central estimate of rotation with gravity (Figure 4 panel C), since the rotation no longer leads to a change in the orientation of gravity. The two resolution processes are not mutually exclusive.
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process may manifest itself as a weaker VOR response or as a more rapid decay of the response. Spatially, the conflict can be resolved by modifying the central estimate of rotation such that the axis of the central estimate aligns with gravity (Figure 4 Panel C). This resolution process may manifest itself by realigning the axis of the VOR with gravity.
We might expect that Ihe size of the eye response axis shi ft would jepend upon 'N.hether :he ·Jff-axis response ~s verricai or WfSlOnal, since the gain of the vertical and ~orsionai VORs are known to differ (27). By quantitatively analyzing the 3-D axis of eye rotation, we found that the shift in the axis of eye rotation was less for pitch than for roll tilts (Figure 2; Table 1). For roll tilts (left ear down/right ear down), where the off-axis response was primarily vertical, the axis of eye rotation aligned closely with gravity in the majority of the monkeys. For pitch tilts (forward/backward), where the off-axis response was primarily torsional, the axis of eye rotation never aligned with gravity. We hypothesize that this difference in the axis of eye rotation, with roll shift responses greater than pitch shift responses, might at least in part be due to the fact that the vertical angular VOR is 30070 to 100070 larger than the torsional angular VOR (27). Since the horizontal and vertical angular VOR gains are comparable (27), the measured axis of eye rotation might provide an accurate estimate of the axis of self rotation for roll tilts. On the other hand, since the torsional VOR gain is less than the horizontal VOR gain, the measured axis shift for pitch tilts may not quantitatively represent the shift in the central estimate of rotation.
While the magnitude of the axis shift may not always represent the magnitude of the shift in the central estimate of rotation, the time course of the axis shift might still represent the time course of the shift in the central estimate of rotation. In the absence of perceptual or other physiological measures of the apparent veltical, the time course of this axis shift may provide the best estimate for the time course of the shift in the central estimate of rotation and, in turn, of the time course of the shift in the central estimate of gravity (18).
D. M. Merfeld et al
Axis shifts similar to those measured following postrotatory tilt have also been measured following OVAR (2,4-6). The qualitative similarity of the responses following off vertical axis rotation (OVAR) and following postrotatory tilt (3,9,18) indicates that the exact paradigm used to reach a tilted postrotatory orientation might be less important than that such an orientation be obtained. In other words the rapid decay and axis shift depend onlY JPon the presence and magnitude of the competing otolith signal.
Axis shifts have also been noted following optokinetic stimulation when monkeys and the optokinetic stimulus were tilted with respect to gravity (12). Raphan and colleagues (23) hypothesized that optokinetic stimulation "charges" a velocity storage mechanism which is responsible for optokinetic nystagmus, optokinetic afternystagmus, and vestibular nystagmus. It has also been suggested that canal and visual cues might be merged to yield a single central estimate of head angular velocity (24). If we assume that the velocity storage mechanism is charged by both canal and visual cues and that a central estimate of head angular velocity results, then the response induced during tilted OKAN should be similar to that induced during postrotatory tilts and, therefore, should yield the observed shift in the axis of eye rotation.
Human studies have not confirmed the presence of a strong shift in the axis of eye rotation following optokinetic stimulation (13) or following postrotatory tilt (28). Other studies, using eccentric rotation stimuli, have shown that the axis shift is more gradual and weaker for humans (7,8) than it is for monkeys (9,10). Similarly, the axis shift following constant velocity OVAR stimulation has been shown to be weaker in humans (5) than in monkeys (4). This, along with that fact that OKAN is weaker in humans than in monkeys, may partially explain these species differences. Furthermore, some of the paradigms involve another difference. The monkey postrotatory tilts were passive, while the human postrotatory tilts were active. Perhaps the active process of tilt interferes with the axis shift due to information from either the neck receptors in-
3-D Eye Movements Following Post rotatory Tilt
dicating tilt of the head with respect to the torso or a copy of the efferent signals sent to the neck muscles.
Time Course of the VOR Decay
Horizontal VOR. Earlier studies, while not noting the shift in the axis of eye rotation, documented the effect of gravity on the horizontal postrotatory response by showing that the postrotatory nystagmus elicited by earthvertical and earth-horizontal rotation differed. Specifically, horizontal postrotatory nystagmus following a velocity trapezoid was shown to be weaker and to decay more rapidly when subjects were rotated around an earth-horizontal axis (1,2,25). Guedry (21,22) suggested that the difference was due to the sensory conflict induced following constantvelocity earth-horizontal rotation, since the otoliths correctly indicate the absence of orientation changes with respect to gravity while the postrotatory response of the semicircular canals indicates rotation after all motion has stopped (Figure 4 Panel A). Guedry proposed that the weaker response and more rapid decay were direct effects of the conflict, since the sensory conflict would be reduced or more rapidly eliminated by diminishing or eliminating the central estimate of rotation.
Benson (3) provided evidence supporting Guedry's hypothesis when he tilted his subjects immediately following constant velocity rotation about a vertical axis. He found that the horizontal postrotatory response decayed more rapidl~ foli owing tiit. and that the rate of horizontal VOR deca~ W2." ciependen~ or. the amount of tilt. However, the shift in me axis of eye rotation was not yet documented, so Benson could not take this shift into account while determining the decay time constant of the horizontal VOR. Our analysis (Figure 3) takes the axis shift into account by beginning the curve fit after the initial rapid decay (see Figure 1) and indicates that, in general, the time constant does decrease as tilt increases. It is important to note that the time constant did not always decrease with increased tilt, but the general trend is compel-
137
ling (Figure 3 Panels A and B). The data were similar for both roll tilts and pitch tilts, with the fastest decay occurring after tilts of 90°. These data are consistent with a process of sensory conflict resolution, since larger tilts, at least up to 90°, increase the sensory conflict induced by the graviceptor afference (29).
The data shown in Figure 1 provide examples which qualitatively support this interpretation of the results. Note that immediately following tilt the horizontal response begins to rapidly decay. This is consistent with Guedry's hypothesized process for resolving the sensory conflict. However, the horizontal response recovers and decays much more gradually once the off-axis response (vertical-left column; torsional-right column) is initiated. This might indicate that the sensory conflict that initiated the rapid decay of the response was reduced once the axis shift was underway. If we assume that the aXis shift represents a manifestation of sensory conflict resolution and that the rapid decay is another manifestation of the resolution process, then the data shown in Figure 1 are consistent with both conflict resolution hypotheses (Figure 4 Panels B and C).
Guedry's hypothesis provides one explanation for the effect of gravity on the decay time constant of the VOR, but other mechanisms have been proposed to explain this effect. For example, the velocity storage models (30,31) provide good phenomenological explanations for the observed gravitational effects by assuming that model parameters directly depend upon the orientation of gravity. In contrast to these models, another modeling approach (32) 2.ssume~ that :!1e signals frarr. tht- various sense organs are aynamicaiiy me;-geC: lC 17,; ;;
imize sensory conflict. This dynamic interaction of sensory signals appears more typical of our current knowledge of neural processing than is the idea of sensory signals dynamically and instantaneously changing the characteristics of the VOR neural network.
Off-axis VOR responses. The time constant of the off-axis response (vertical for roll tilts; torsional for pitch tilts) was highly correlated with the time constant of the horizontal re-
I i i
./
138
sponse (Figure 3), and the slope of the correlation (approximately 0.75) was similar for pitch and roll. A previous study, with tilted subjects rotated about an earth-vertical axis at constant velocity, showed a similar effect (33). Analysis showed that the vertical component of the response had a shorter time constant than the horizontal response. This was interpreted as indicating that the time constant ror vertical velocity storage is less than the :ime constanr :'or '1Corizo m a . c!CCW! 5IO r:J.ge even when both responses are m muimed simuitaneously. The same mechanism might explain the decay characteristics of the off-axis VOR responses following post rotatory roll tilt.
Summary
We measured three-dimensional eye movements and quantitatively showed that the axis of eye rotation always shifted toward alignment with gravity following postrotatory tilt. We also showed that the time constant of the
D. M. Merfeld et al
horizontal postrotatory response was reduced depending on the magnitude of the postrotatory tilt. These observations led us to hypothesize that the sensory conflict induced by postrotatory tilt might explain the VOR axis shift which has been observed in monkeys (4,9,10,12,18), humans (5), and cats (6). This process of conflict resolution may work in conjunction with the process described by Guedry (21 ,22) to reduce sensory conflict and :nay )r _ "we J. ,Jnyslc::-.i :xpianmion :'or :he effect or" !5ravity on '/eloc:ry storage.
Acknowledgments-This research was supported by NASA contracts NASW-3651, NAG2-445, NAS9-16523, the NASA Graduate Student Researchers Program, the GE Forgivable Loan Fund, and by NASA Space Medicine Tasks 199-16-12-01 and 199-16-12-03. We also wish to thank the staff at the NASA Ames Vestibular Research Facility for their support, Sherry Modestino for her assistance through all phases of this project, and Dr. Mark Shelhamer for reviewing a preliminary draft of the manuscript.
REFERENCES
1. Benson AJ, Bodin MA. Comparison of the effect of the direction of the gravitational acceleration on postrotational responses in yaw, pitch and roll. Aerospace Med. 1966;37:889-97.
2. Benson AJ, Bodin MA. Effect of orientation to the gravitational vertical on nystagmus following rotation about a horizontal axis. Acta Otol. 1966;61: 517-26.
3. Benson AJ. Modification of the per- and post-rotational responses by the concomitant linear acceleration. In: 2nd Symposium on the Role of the Vestibular System in Space Exploration. Washington, DC: US Government Printing Office; NASA SP-U5. 1966:199-213.
-+. Raphan T, Cohen B, Henn V. Effects of gravity on rotatory nystagmus in monkeys. Ann N Y Acad Sci. 1981;374:44-55 .
5. Harris LR, Barnes GR. Orientation of vestibular nystagmus is modified by head tilt. In: The vestibular system: neurophysiologic and clinical research, Graham, Kemink, (ed) . New York: Raven Press; 1987:539-48.
6. Harris LR. Vestibular and optokinetic eye movements evoked in the cat by rotation about a tilted axis. Exp Brain Res. 1987;66:522-32.
7. Lansberg MP, Guedry FE, Graybiel A. Effect of changing resultant linear acceleration relative to the subject on nystagmus generated by angular acceleration. Aerospace Med. 1965;36:456-60.
8. Crampton GH. Does linear acceleration modify cupular deflection? In: 2nd Symposium on the Role of the Vestibular System in Space Exploration. Washington, DC: US Government Printing Office; NASA SP-Il5. 1966: 169-84.
9. Merfeld OM. Spatial orientation in the squirrel monkey: an experimental and theoretical investigation [ph.D. thesis]. Cambridge, Massachusetts: Massachusetts Institute of Technology, 1990.
10. Merfeld OM, Young LR, Paige GO, Tomko DL. Spatial orientation of VOR to combined vestibular stimuli in squirrel monkeys. Acta Otol. 1991;481 (Suppl):287-92.
11. Cohen B, Henn V, Young LR. Visual-vestibular interaction in motion perception and the generation of nystagmus. 1980; Neurosciences Research Program Bulletin. Cambridge, Massachusetts: MIT Press; 18: 459-651.
12. Raphan T, Cohen B. Organizational principles of velocity storage in three dimensions; the effect of gravity on cross coupling of optokinetic after-nystagmus (OKAN) Ann N Y Acad Sci. 1988;545:74-92.
13. Lafortune SH, Ireland OJ, Jell RM. Suppression of optokinetic velocity storage in humans by static tilt in roll. J Vestibular Res. 1991;1:347-55.
14. Paige GO, Tomko DL. Eye movement responses to linear head motion in the squirrel monkey; 1: Basic characteristics. J Neurophys. 1991;65:1170-82.
15. Robinson DA. A method of measuring eye movement
3-D Eye Movements Following Post rotatory Tilt
using a scleral search coil in a magnetic field. IEEE Trans Biomed Electronics. 1963;BME-I0:137-45.
16. Haddad FB, Paige GO, Ooslak MJ, Tomko OL. Practical method, and errors, in 3-D coil eye movement measurements. Invest Ophthalmol Vis Sci. 1988;29{Suppl):342.
17. Ferman L, Collewijn H, Jansen TC, Van den Berg AV. Human gaze stability in the horizontal, vertical and torsional direction during voluntary head movements, evaluated with a three-dimensional scleral induction technique Vision Res. 1987;27:811-27.
18. Merfeld OM, Young LR. Three dimensional eye measurement following post-rotational tilts in monkeys. Ann N Y Acad Sci. 1992;656:783-94.
19. Larson RJ, and Marx ML. An introduction to mathematical statistics and its applications. Englewood Cliffs, New Jersey: Prentice-Hall. 1986.
20. Press W, Flannery B, Teukolsky S, Vetterling W. Numerical recipes: the art of scientific computing. Cambridge: Cambridge University Press. 1986.
21. Guedry FE. Orientation of the rotation-axis relative to gravity; its influence on nystagmus and the sensation of rotation. Acta Otolaryngol. 1965;60:30-49.
22. Guedry FE. Psychophysiological studies of vestibular function. In: Contributions to sensory physiology. New York: Academic Press; 1965:63-135.
23. Raphan T, Matsuo V, Cohen B. A velocity storage mechanism responsible for optokinetic nystagmus (OKN), optokinetic after-nystagmus (OKAN) and vestibular nystagmus. In: Baker R, Berthoz A, eds. Control of gaze by brain stem neurons, developments in neuroscience, vol 1. Amsterdam: Elsevier/North Holland Biomedical Press; 1977:37-47.
24. Robinson OA. Vestibular and optokinetic symbiosis: an example of explaining by modelling. In: Baker R, Berthoz, A, eds. Control of gaze by brain stem neu-
139
rons, developments in neuroscience, vol 1. Amsterdam: Elsevier/North-Holland Biomedical Press; 1977:49-58.
25. Correia NJ, Guedry FE. Modification of vestibular responses as a function of rate of rotation about an earth-horizontal axis. Acta Otol. 1966;62:297-308.
26. Benson AJ, Bodin MA. Interaction of linear and angular accelerations on vestibular receptors in man. Aerospace Med. 1966;37:144-54.
27. Bello S, Paige GO, Highstein SM. The squirrel monkey vestibulo-ocular reflex and adaptive plasticity in yaw, pitch, and roll. Exp Brain Res. 1991;87:57-66.
28. Fetter M, Tweed 0, Misslisch H, Hermann Vi, Koenig E. The influence of head reorientation on the axis of eye rotation and the vestibular time constant during postrotatory nystagmus. Ann NY Acad Sci. 1992; 656:838-40.
29. Udo de Haes HA, Schone H. Interaction between statolith organs and semi-circular canals on apparent vertical and nystagmus. Acta Otol. 1970;69: 25-31.
30. Hain TC. A model of the nystagmus induced by off vertical axis rotation. Bioi Cybern. 1986;54:337-50.
31. Raphan T, Cohen B. Multidimensional organization of the vestibulo-ocular reflex (VOR). In: Keller EL, Zee OS, eds. Adaptive processes in visual and oculomotor systems. New York: Pergamon Press. 1986: 285-92.
32. Merfeld OM, Young LR, Oman CM, Shelhamer MJ. A multidimensional model of the effect of gravity on the spatial orientation of the monkey. J Vestibular Res. 1993;3: 141-161.
33. Hain, TC, Buettner UW. Static roll and the vestibulo-ocular reflex (VOR). Exp Brain Res. 1990;82: 463-71.
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