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1 Department of Neurology, The Johns Hopkins University, Baltimore, Maryland 21287; 2 Department of Otolaryngology—Head and Neck Surgery, The Johns Hopkins University, Baltimore, Maryland 21287; 3 Department of Neuroscience, The Johns Hopkins University, Baltimore, Maryland 21287; 4 Department of Ophthalmology, The Johns Hopkins University, Baltimore, Maryland 21287; 5 Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, Maryland 21287; 6 Department of Biomedical Engineering, The Catholic University of America, Washington, DC 20064
Submitted 29 July 2002; accepted in final form 4 November 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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). This same requirement holds during head movements. To maintain fixation on an object that is stationary in space, the vestibular system must produce eye movements that perform 2 functions: 1) match the amplitude and direction of the head movement (more specifically the rotation and the translation of the orbit) to maintain zero gaze velocity, and 2) take into account the need to keep the fovea of both eyes aimed at the point of regard to maintain a constant gaze position. Under normal conditions, this function is fulfilled by the equal and opposite slow-phase eye response to head rotation [the rotational vestibulo-ocular reflex (VOR)], with necessary adjustments for translation of the head (orbits), viewing distance, and target eccentricity. The limits within which the vestibular slow-phases operate are adequate, however, they are set by the nominal operating parameters of the vestibular system of each individual. The system is considered "challenged" when the properties of the head stimulus (velocity, acceleration, frequency content) exceed these limits. The system can be challenged with labyrinthine hypofunction (when the operating range and sensitivity are reduced), or with unaccustomed head motion at the limits of normal operation, or with both hypofunction and unusual motion of the head. In the last condition, locomotion would certainly present a natural challenge to the system. Under these conditions during head motion, not only is there unwanted motion of images on the retina (gaze-velocity error) or oscillopsia (the illusory motion of the visual environment), but also the image of the object of interest moves away from the fovea (gaze-position error) leading to a decline in visual acuity. Persons with vestibular loss often complain of problems with vision while walking in the environment, such as the case of "J.C." (1952). Accordingly, adaptive mechanisms are triggered to restore the amplitude and direction of the slow-phase response, although there are probably enduring limitations to the degree to which normal vestibular slow phases can be recalibrated (Pulaski et al. 1981; Takahashi et al. 1989). The degree to which pathological vestibular slow phases can be recalibrated is not known.
Brief transient head rotations have long been used (e.g., Gauthier and Robinson 1975) to quantify the human VOR. A position "step," which results from these head rotations, is a complex signal composed ideally of an infinite number of frequencies. The amplitude and duration of the step determine the range of dominant frequencies, velocities, and accelerations. By varying these step parameters one can examine the response of a control system across a large range of stimulus properties, easily placing the vestibular system in a "challenged" state when the velocities and accelerations are high enough. The "step" displacement of the head also closely resembles natural head movements (Zangemeister et al. 1981). Moreover, because the function of the VOR varies with mental set (effort of spatial localization), the brevity of the step stimulus (<500 ms) allows a constant mental set to be assumed while the head is moving. Recently, many studies have applied high acceleration steps to replicate the clinical "head-impulse test" (Halmagyi et al. 1988, 1990) or "head thrust." Experimental accelerations of the head range from 700 to 2,800°/s2 (electromechanical rotational devices of Tabak et al. 1997a; Tian et al. 2000) to 1,500–4,000°/s2 (manual perturbations of Aw et al. 1996a; Halmagyi et al. 1990) to 1,900–7,100°/s2 (head taps of Maas et al. 1989) to approximately 10,000°/s2 (manual perturbations of Schmid-Priscoveanu et al. 1999), with stimulus durations of 100–200 ms. The ranges of accelerations in these head thrusts are comparable to those accelerations imposed on the system during natural locomotion (Grossman et al. 1988).
Studies using transient head rotations have assessed the vestibular slow-phase response in normal and challenged vestibular systems. Studies have shown that when slow-phase responses are inadequate (in a challenged state), other mechanisms are triggered to help stabilize images on the fovea after the head begins to move. They include the substitution and enhancement of other sensory reflexes, such as the cervico-ocular reflex; the substitution of mechanisms to satisfy a function, such as preprogramming of slow phases in anticipation of head motion; and the substitution of other behaviors, such as the use of saccades to generate rapid eye movements in the direction of the deficient slow-phase response (e.g., Kasai and Zee 1978). Quantitatively, the vestibular (position) step response has been used to estimate the gain (eye motion/head motion) of inadequate slow phases (Allison et al. 1997; Aw et al. 1996b; Cremer et al. 1998; Foster et al. 1997; Halmagyi et al. 1990; Schmid-Priscoveanu et al. 1999; Tabak et al. 1997b) and to estimate the contributions of compensatory saccades to gaze stabilization (Bloomberg et al. 1991; Segal and Katsarkas 1988a,b; Tian et al. 2000). The latter studies showed that when compensatory saccades are observed in the step response, they interact synergistically with the slow-phase components to augment gaze stabilization, such that smaller slow-phase components during the step were matched with larger saccadic components and vice versa. In these studies, compensatory saccades were observed in unilateral vestibular-deficient (UVD) subjects during ipsilesional rotations and in bilateral vestibular-deficient (BVD) subjects. With the exception of one study (Tian et al. 2000), compensatory saccades were also observed in normal subjects and in UVD subjects during contralesional rotations.
Quantitative measures of gain provide an assessment of vestibular function limited by the specific conditions in each study. For example, in the studies using steplike inputs, the stimulus characteristics and the method of gain calculation have varied widely. The method for calculating slow-phase gain is usually determined at a set interval of time after the onset of the transient head motion, averaged across 35–45 ms for slow-phase gain (Tian et al. 2000), 40- to 50-ms acceleration gain (Collewijn and Smeets 2000), and 30- and 100-ms velocity gain (Aw et al. 1996a,b). Carey and colleagues (2002) used the largest velocity gain value within the 30-ms interval before the onset of peak head velocity during each head thrust. The properties of each stimulus therefore tested a different portion of the operating range, and the resulting characteristics of the responses reflected these differences in terms of gain. To achieve an overall assessment of gain, studies used their own averaging, threshold, and fitting methods on selected time intervals or point(s) in time. In this manner, contributions from vestibular slow-phase components and saccadic components were reduced to 2 numbers. It is also understood that the nominal operating parameters for each system will vary, especially among the patients. Factors such as degree of deficit, age, duration of symptoms, and rate at which deficits were acquired may be critical in setting the nominal operating range for each subject. Therefore it is not surprising that the gains differed among studies. The gains in effect provide "static snapshots" of the approximate vestibular and saccadic components for a given set of calculation constraints. They do not relate the dynamic response characteristics over the time period of the stimulus. Gain ratios have meaning when there is a causal relationship between the input and the output. In a challenged vestibular system a single input (head motion) may trigger multiple outputs (e.g., from the vestibular and saccadic systems) and these outputs in turn may be more causally related to other inputs (e.g., neck afferents). The slow-phase gain therefore describes an overall performance level composed of slow-phase responses from multiple sources, rather than just being of vestibular origin. Finally, because the function of the vestibular system is to optimize gaze velocity and gaze position simultaneously, it is unclear from previous studies how gaze velocity is minimized in relation to gaze position. Dell'Osso and colleagues (1992a,b,c) studied the effects of congenital nystagmus, another condition that disturbs steady foveal fixation, grappling with similar issues of analysis. Among their many methods, they used phase planes, which provided a means to analyze the intricate dynamics of "foveation" and allowed them to follow the interactions between "foveating- and braking-saccades" and the slow phases of congenital nystagmus.
We undertook this study to characterize the dynamic function of the vestibular system over the duration of a steplike stimulus. Many studies over the past 30 years have analyzed the VOR in subjects with normal vestibular function or with unilateral or bilateral vestibular hypofunction. These studies, however, have not examined how the vestibular system acts to simultaneously minimize gaze position and gaze velocity—the 2 fundamental functions of the system. Here, we devised a phase plane method for systematically presenting the gaze dynamics of the head thrust response. In this study, we describe a method that offers 3 fundamental advantages in the analysis of these responses in comparison to techniques that have been used previously. First, the method provides a robust depiction of responses over different periods of time during the stimulus. Second, variability in responses between subjects and between stimulus repetitions in a single subject can be readily visualized and interpreted. Third, the method allows eye-movement responses to be analyzed in terms of the simultaneous contributions to minimization of gaze-velocity and gaze-position error. We tested the system across a large range of accelerations: 1,400–20,000°/s2, applying the stimulus in unpredictable directions and amplitudes, with the following questions and hypotheses in mind: How do the gaze-position and gaze-velocity errors that are produced in vestibular systems challenged by pathology compare with those in normal vestibular systems challenged by unnatural stimuli? We hypothesized that gaze errors are produced along a continuum depending on the challenge. How do patients and normal subjects compensate for gaze-position and gaze-velocity errors? We hypothesized that phase-plane analysis will more easily show whether strategies from recovery of vestibular challenge will preferentially reduce gaze-position or gaze-velocity errors. We hypothesized that patients with more residual function would exhibit better compensation for gaze-position errors than those with less residual function. We hypothesized that patients with bilateral loss rely more on gaze-position correction mechanisms, such as saccades. Preliminary analyses of these data were presented elsewhere (Peng et al. 1997, 1998, 2000).
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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We present data from 8 patients with unilateral vestibular deficits (UVD), ages 30 to 67 yr, who had undergone surgical resection of the superior and inferior vestibular nerves, for removal of an acoustic neuroma (6) or for Ménière's disease (2). The UVD patients were tested 10 days to 37 mo after their surgeries. We also present data from 8 patients with bilateral vestibular deficits (BVD), ages 20 to 85 yr. The etiology of the loss of function in the BVD patients was gentamicin toxicity (3), presumed bilateral vestibular neuritis (1), and of unknown origin (4). One BVD patient (LO) was tested twice, 9 and 21 mo after developing symptoms. Eleven normal subjects, ages 23 to 54 yr, were also tested. These normal subjects had no clinical symptoms of a vestibular disorder and had a normal neuro-otological examination. All experimental protocols were approved by the Joint Committee on Clinical Investigation of The Johns Hopkins University School of Medicine. Each subject gave informed consent for participation in this study.
Subjects were seated in a chair, with their heads free to move inside a triaxial magnetic field search coil system. Subjects wore search coils that allowed for measurement of eye motion around all 3 axes of rotation. The coils were embedded in an annulus that adhered to the sclera of the eye (Skalar, Delft, Netherlands). All patients wore one eye coil, except for BVD patients MI, LO2, RO, and GR who wore coils on both eyes. Two of 10 normal subjects wore coils on both eyes. Each eye coil was placed on the eye after applying a topical anesthetic (Ferman et al. 1987). Each subject used a dental bite plate to hold a triaxial, handmade search coil, which transduced the motion of the head. In each search coil, a current was induced by the oscillating magnetic fields, composed of a superposition of the 3 frequencies of each magnetic field. Movement of each search coil thereby modulated the amplitude of the 3 frequencies (on the coil) with respect to the 3-dimensional orientation of the coil in space. Synchronous detection of each frequency component produced voltages proportional to the amplitude of coil rotation relative to each field (linear across all the fields). These voltages were low-pass filtered with a single-pole, Butterworth antialiasing filter at 90 Hz, and sampled at 500 Hz through a 12-bit A/D converter. The resolution of the eye coil was 0.1° for eye rotations in the horizontal and vertical planes and 0.2° in the torsional plane. More details about the coil system are described in Bergamin et al. (2001).
Before each head thrust, the experimenter centered the head (within 1.5°) in the yaw, pitch, and roll planes using a video feedback screen. The experimenter stood behind the subject and applied head thrusts: the experimenter held the subject's head and imposed an abrupt, "position-step" stimulus, rotating the subject's head at a high acceleration to bring the head 10–25° from center. Head thrusts were produced in the horizontal plane (yaw head thrusts), over a range of accelerations in random rightward and leftward directions, with 10 to 20 head thrusts toward each side. The experimenter observed the video screen to ensure that components of pitch and roll head movements were close to zero during each yaw head thrust. The subject was asked to maintain fixation on an LED at a distance of 124 cm from the eyes, in an otherwise dark room.
Peak head velocities of head thrusts ranged from 70 to 410°/s. The head reached peak velocity between 30 to 140 ms after it began rotating. The peak head accelerations ranged from 1,400 to 10,600°/s2. In normal subjects, the kinematics of head motion during the high acceleration (HA) head thrusts were in the same ranges of those of the patients. For the very high acceleration (VHA) head thrusts (only for normal subjects), the peak velocities ranged from 230 to 550°/s, the head reached peak velocity between 35 and 70 ms after it began rotating, and the peak head accelerations ranged from 5,000 to 20,000°/s2.
Data analysis
The search coils were calibrated relative to the maximum field strength values detected by the coil from the 3 orthogonal magnetic fields. The calibration values were then used postrecording to process the data into rotation matrices, which were then transformed into rotation vector coordinates (see Bergamin et al. 2001 for a detailed description of the calibration procedure and rotation vector calculations). The angular positions of each eye coil (relative to spatial coordinates) were then calculated from the rotation vectors. To calculate the angular velocity trajectories, a 5th-order 100-Hz low-pass FIR filter was first applied to the rotation matrices (resulting in M). The resulting data were differentiated using a 5th-order REMEZ (Matlab) FIR filter, designed to differentiate 
100 Hz and low-pass filter the data above 100 Hz. The differentiated data were then used with the undifferentiated, filtered rotation matrices (M), to calculate angular velocity (Hepp 1990). The SD of the velocity noise after filtering was ±2°/s. To calculate the angular acceleration trajectories, the angular velocity data were differentiated with the same 5th-order REMEZ combination differentiator and low-pass filter.
We compare mean error values listed in Table 1, using a 2-tailed, unpaired t-test. Because we made only a few selected comparisons between the 15 groups of data, it was unnecessary to adjust the significance level with multivariate analysis methods. Five comparisons (detailed in the RESULTS, Static analysis of gaze stabilization errors) were made to determine the significance of means that were dissimilar. The resulting P values (0.006, 0.003, 0.002, 0.0009, 0.037), if added together, still remained significant to 5% (0.0489). Before performing the t-test, we calculated the F-test statistic to compare the variance of the means of the 2 groups. The F-values showed that those comparisons with normal subjects tested at HA and VHA had variances of the mean that were significantly different from the variances of the mean from the patient groups. For these comparisons, we used the t-test assuming unequal variances. In the other comparisons between patient groups, we used the t-test assuming equal variances.
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We used a wavelet transform technique to determine the onsets and offsets of head and eye movements, and the transient eye movements within the head thrusts. We chose this technique over other approaches because its ease of use. Particularly with the variability in these data (both in the stimulus and response), this technique can be applied systematically to the data with minimal adjustment of parameters. Other methods, of course, can be used to achieve the same results, but likely with additional processing and parameter adjustments.
The time-varying properties of wavelet analysis allow detection of the smallest change in the unfiltered position signal, without compromising the time resolution around the transitions (Daubechies 1992). We applied the continuous "Morlet" wavelet transform (Matlab, Natick, MA; Torrence and Compo 1998) on the angular position data (without prior digital filtering), independently on each position trajectory [head-in-space (head), eye-in-space (gaze), and eye-in-head (eye)]. The transform generated the corresponding real wavelet coefficients relative to both scale (which is inversely related to frequency) and time. For the head trajectories, Morlet waveforms with scales corresponding to 1–10 Hz were used. For the eye and gaze trajectories, Morlet waveforms with scales corresponding to 5–50 Hz were used. The absolute values of the coefficients were summed across the scales and plotted over time. Each peak in the wavelet power plots marked a transition in the original position trajectory. The width of each peak defined the duration of the transition. The latter parameter established the onset and offset times used throughout the data analysis.
Gaze plane methodology
To assess the gaze strategies in each subject, we found it fruitful to focus on the behavior of the gaze components relative to its derivatives, rather than relative to time. We devised "gaze planes" so that the position and velocity components of large quantities of multiparametric gaze data can be characterized simultaneously. Note that our "gaze planes" differ from "gaze planes" first presented by Zangemeister and Stark (1982), which depict the eye and head components of gaze on separate axes. Our gaze planes are based on classical phase-plane methods for analysis of signals. Phase-plane plots of dependent variables and their derivatives are often used to display behavior without explicit time dependency. We found that these plots provided the clearest and most efficient means for comparing single time trajectories. As described below, large amounts of data from multiple head thrusts could be presented in a compressed format using the phase-plane plots.
The time trajectories of head, eye, and gaze, in position and velocity, during 2 example head thrusts, are presented in Fig. 1. Figure 1A displays a response from a normal subject and Fig. 1B displays a response from a UVD patient (during a head thrust toward his lesioned side). When 2 time trajectories are plotted against each other, phase-plane plots are formed. We created a phase plane in which the gaze-velocity trajectories are plotted against the gaze-position trajectories (thick solid lines in the time trajectories shown in the top panels). The corresponding phase planes of the time trajectories are shown in the bottom panels in Fig. 1. These "gaze planes" of the head thrust responses characterize the dynamics of the error of the eye response. To represent the time behavior in the gaze plane, we formed 50-ms time epochs in each head thrust response between 0 and 200 ms, delineated by the vertical gray bars and corresponding color bars in the top panels, and coded each gaze-plane trajectory with respect to the color bar. The gaze plane was divided into quadrants to facilitate description of the responses. For the gaze plane of an undercompensatory VOR, each gaze trajectory began at the origin (circles, time = 0 ms, blue epoch) and proceeded toward the right halves of the plots for rightward yaw thrusts and toward the left halves of the plots for leftward yaw thrusts, ending at 200 ms (asterisk, pink epoch).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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In this section, we first describe the measurements of maximal gaze-velocity and maximal gaze-position errors that are made at static points along the eye and head movement trajectories. Then we describe the gaze errors at the end of the head thrust in terms of position. In the subsequent sections, we will compare these results with the dynamic phase-plane results. Figure 1 shows the points (A–F) along the time trajectories that are used to calculate the gaze errors. Four selected measures are determined from each head thrust response in UVD, BVD, and normal subjects and presented in Table 1. The "normalized peak gaze velocity error" (NVE) defines an estimate of maximum gaze-velocity error during the head thrust normalized to peak head velocity (the maximum error that is found only in the direction of the head thrust). In Fig. 1, NVE = E/F. A NVE of 1.0 indicates no gaze-velocity compensation, or 100% velocity error.
As shown in the table in the UVD subjects, the NVEs were <1.0, indicating that some residual gaze-velocity compensation existed during head thrust toward the side of the lesion (73% mean error). The velocity compensation on the intact side was much better, but still lower (44 ± 16%, mean ± SD) than that observed in both sides of normal (HA) subjects (21 ± 8%; P = 0.006). In the BVD subjects, the NVE indicated that there was little or no velocity compensation (91% mean error). In the normal subjects, the NVEs were not zero, indicating that the normal VOR is not perfect in these conditions.
The "normalized peak gaze position error" (NPE) defines an estimate of maximum gaze-position error accumulation when normalized to peak head position (the maximum change in head position during the head thrust). In Fig. 1, NPE = A/B. An NPE value of 1.0 indicates 100% position error (i.e., there is no eye in head position movement). In UVD patients, NPE reflected the asymmetry in the responses toward the lesion side and the intact side. As shown in the table, the NPE toward the lesion side in UVD patients were lower (56 ± 14%) than the NPE from either side in the BVD subjects (76 ± 12%; P = 0.003). The NPE values toward the intact side in UVD patients were higher (29 ± 10%) than the NPE from both sides in the normal (HA) subjects (9 ± 4%; P = 0.002). The group mean of peak gaze position (absolute error) in UVD patients was 8.9 ± 2.7° during head thrusts toward the lesion side and 4.4 ± 1.5° during head thrusts toward the intact side. In BVD patients the group mean of peak gaze position for head thrusts toward both sides was 10.3 ± 1.6°. In normal subjects the group mean of peak gaze position for head thrusts toward both sides was 1.5 ± 0.9°, during high acceleration (HA) head thrusts.
We have provided 2 measures for estimating the amount of correction for gaze-position error at the end of the head thrust: "normalized end gaze position error" (NEE) and "end gaze position." (Gaze velocity was always minimized by the end of the head thrust because reduction of head motion reduces gaze-velocity errors.) As we describe in Range of UVD responses, these measures of end gaze position depend on the variability in timing of the corrections. The NEE provided a normalized estimate of gaze-position error at 200 ms or at the end of any corrective movement that is still ongoing at 200 ms after the start of the head thrust. In Fig. 1, NEE = D/C. A zero NEE corresponds to perfect compensation (0% error) with the image of the target being on the fovea at the end of the head rotation. As shown in Table 1, the negative NEE values indicate that the gaze position had moved to the other side of the zero target, on the side opposite the direction of the head thrust (overcompensation). In UVD subjects, NEE values toward the lesioned side were larger (32 ± 11%) than those toward the intact side (10 ± 8%; P = 0.0009). The reduction in position error (NPE minus NEE) was comparable on the lesion side (24 ± 16%) as well as on the intact side (19 ± 9%; P = 0.48). The NEE values on the intact side (10 ± 8%) were never reduced to the level observed in the normal subjects (1 ± 4%; P = 0.037). In the BVD subjects, the reduction in position error was nearly equal for head thrusts to both sides (42 ± 22%).
The "end gaze position" defines the accuracy of the response to the head thrust at 200 ms or at the end of any position correction that is still ongoing at 200 ms. This parameter provided an absolute measure of gaze-position error toward the end of the head thrust (point D in Fig. 1). In general the end gaze positions indicated that both UVD and BVD populations were able to reduce their gaze-position errors by the end of the head thrust, but were not able to achieve the accuracy of normal subjects. In the table, the mean values of end gaze position that were negative indicated that the eye had gone beyond the target position. In summary, we calculated values representing the maximal gaze-position (NPE) and gaze-velocity (NVE) errors during each head thrust, to determine the worst-case performance of each subject. For each head thrust, the maximal errors may have occurred at different times after the onset of head motion. These values provide an absolute measure of overall performance independent of time, whereas traditional measures of gain are highly dependent on time as described in the INTRODUCTION. In the table we also present measures of NEE and end gaze position.
In Fig. 2A, we show the relationship between the maximum gaze-velocity error and the maximum gaze-position error by plotting NVE versus NPE for all subjects, with mean responses from each side plotted with separate symbols. This figure shows that each subject exhibited maximum error values that were clustered according to which population they belonged. When all the populations were observed together, a gradient was formed in which gaze-velocity and gaze-position error increased linearly from normal subjects to normal subjects tested at VHA (very high acceleration), to UVD patients tested on the intact side, to UVD patients tested on the side of the lesion, to BVD patients. This linear relationship between NVE and NPE was biased, with 15% more NVE than NPE in all populations (solid line). A plot of equal errors (dotted line) is shown for comparison. The 4 asterisks in Fig. 2 depict the data from the normal subjects tested at VHA (see Table 1). In Fig. 2A, these data overlap with the UVD data from the intact side, indicating that the errors in these normal subjects were elevated above those normally observed in the normal population at HA (high acceleration). The NVE values of the normal subjects at VHA (34 ± 3%) were comparable to those in the UVD data on the intact side (44 ± 1 6%; P = 0.11). Similarly the NPE values of the normal subjects at VHA (27 ± 4%) were comparable to those in the UVD data on the intact side (29 ± 10%; P = 0.65). Only 2 UVD subjects [CR (solid arrows) and WI] had errors from the intact side (open triangles), which overlapped with the normal population at HA. One UVD subject (HE) had errors on the lesioned side (closed triangle), which fit within the BVD error cluster. There was very little correlation between the NVE values (R2 = 0.2) to the side of the lesion versus those on the intact side, or between NPE values (R2 = 0.1) to each side in UVD patients. In summary, these data support our hypothesis that gaze-position and gaze-velocity errors produced by challenged vestibular systems do indeed fall along the same continuum for normal subject and patient populations.
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50%. All normal subjects during VHA exhibited 50% or more error, with one subject (MA: VHA, in Table 1) having no observable reduction in gaze-position error on the right side (asterisk on dotted line). The amount of error reduction varied among UVD and BVD populations. Six of 7 UVD patients during head thrusts toward their intact side (open triangles) were able to diminish their gaze-position error by 50% or more. Only UVD patient CO remained above the 50% level. Only 3 of 7 UVD patients during head thrusts toward their lesioned side (closed triangles) were able to diminish their gaze-position error by 50% or more. As NPE increased, the amount of error reduction required to reduce gaze-position error below the 50% level also increased. BVD subjects [MI (x) and RO (+)] were able to reduce their gaze position by almost 70%. In summary, these results appear to reject our hypothesis that patients with more residual function (e.g., UVD) would exhibit better compensation for gaze-position errors compared with those with less residual function (e.g., BVD). Within the UVD population, some patients with less residual function (i.e., larger NVE) actually have better compensation than those with more residual function. As well, there are BVD patients who have better compensation than several UVD patients. Range of UVD responses
The information presented so far shows a static summary of selected results in all the subjects tested. From these results, it is difficult to ascertain what is actually happening during the head thrust responses in each subject. These static values provide us height and width measures in the phase plane, giving a basis from which error minimization begins in each subject. Now we will show how these results were achieved, using phase-plane analysis. We explained how the phase plane plots are related to the time response trajectories in the METHODS, Gaze plane methodology.
In this section we focus on 2 UVD patients. One UVD patient [CR (Fig. 2 solid arrows)] who compensated for more than 50% of his gaze-position errors on his lesioned side, and one UVD patient [BR (Fig. 2 dotted arrows)] who compensated <50% of her gaze-position errors on her lesioned side. The responses from the intact and lesioned side of these 2 UVD patients also represent a large portion of the range of NPE values for all UVD patients (see Fig. 2).
BETTER-COMPENSATED UVD RESPONSES. Figure 3A shows an example of the time trajectories from a single yaw head thrust toward the intact (left) side of patient CR (a 39-yr-old man tested 25 mo after resection of an acoustic neuroma on the right side with associated loss of vestibular function in the right labyrinth). Figure 3B exhibits the same time trajectories from a single yaw head thrust toward the paretic (right) side in the same patient. Note in each response, a corrective movement is produced (highlighted in yellow) that minimizes gaze-position errors. The individual gaze trajectories from all head thrusts were superimposed (and presented in Fig. 3C), so the variability within the data could be easily observed across 40–60 responses. Simply averaging the responses from multiple trials might provide an inaccurate representation of the subject's general behavior, given that head input kinematics varied between head thrusts, and the response patterns varied widely from 50 ms after the onset of head motion. The response from the intact side (Fig. 3A) is therefore contained within the trajectories in the left half-plane, whereas the response from the paretic side (Fig. 3B) is contained within the trajectories in the right half-plane. The mean head dynamics (velocity vs. position) are superimposed (thick color-coded trajectories) to show how gaze dynamics differed from head dynamics. In this patient, the individual responses are highly repeatable, showing similar patterns of behavior among head thrusts. Later (in Fig. 5) we will discuss some particular dynamics within this set of data. The asymmetry in gaze error in this UVD patient was clear, with less error in the responses on the intact side (quadrant 3) compared with the lesioned side (quadrant 1). In this patient, the minimization of gaze-position error (black arrows in Fig. 3C) involves significant velocity components (loops in quadrants 4 and 2). This corresponded to the large accelerations during the highlighted transients in Fig. 3, A and B. The corrections on the intact side actually occurred later than those on the impaired side, after a long "pause" in gaze velocity (seen in the purple highlight in the time trajectory and the green epoch in the gaze plane). Notice the onsets of the corrections (pluses) are lined up on the abscissa (zero gaze velocity), where many of the responses were reaching peak head position (triangles). The corrections on the lesioned side were, however, triggered well before the head reached peak position. No pauses were observed on the lesioned side. In summary, the relevance of the gaze planes is enhanced when individual responses are viewed simultaneously in one gaze plane and the colors and symbols are assessed together. The superimposed responses reflect the consistency of the responses in this better-compensated UVD patient. Furthermore, quadrants 4 and 2 are particularly important for identifying the distinguishing characteristics of the compensatory response. In this patient, the corrections that appear in these quadrants are very effective in reducing gaze-position error. The patterns within these quadrants will thereby aid in the evaluation of our hypotheses.
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LESS-COMPENSATED UVD RESPONSES. Figure 4 displays data from the paretic side of UVD patient BR (a 49-yr-old woman tested 10 days after resection of an acoustic neuroma with associated loss of vestibular function from the right labyrinth). This patient showed multiple corrections within 200 ms of the response. In all the head thrust responses the first corrective eye movement (single arrowhead) resulted only in the reduction of the slope of gaze-position error. In the gaze plane this response corresponded to gaze-position error continuing to increase along the positive x-axis. In this patient, a second corrective eye movement (double arrowhead) was usually produced within 50 ms of the first. In Fig. 4A the second correction was triggered as the head velocity was decreasing; thus less eye velocity was required to surpass head velocity, facilitating the reduction of gaze-position error (in the gaze plane the response was brought closer to the origin in the negative x-direction). In Fig. 4B the second correction was generated while the head velocity was increasing, and thus was able to reduce only the slope of gaze-position error. In this patient, a third correction (triple arrowhead) was usually generated after a "pause" in gaze-velocity activity (when gaze velocity remains at zero for a period of time, marked by the purple highlights). Because this third correction was generated when the head velocity was close to zero, the eye velocity of this correction was able to reduce gaze-position error, similar to that of a head-fixed saccade. In summary, in this less-compensated UVD patient, multiple GVCs were observed, whereas GPCs were less prevalent. For those corrections in which eye speed did not exceed head speed, the end effect was a reduction of gaze velocity only, which can be defined as gaze-velocity corrections (GVC). In the gaze plane, the trajectory remains in the originating quadrant (1 or 3). For those corrections in which eye velocity exceeded head velocity, the end effect was a reduction of gaze-position error, which can be defined as gaze-position corrections (GPC). In the gaze plane, these position corrections cause the trajectory to cross into the next quadrant (4 or 2). The gaze plane therefore facilitates our ability to distinguish between GVC and GPC, and thus evaluate preferential reduction of gaze-position and gaze-velocity errors.
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Figure 5 gives an example of how 2 GPC from 2 successive head thrusts can have the same gaze velocity, but different effective speeds (gaze velocity from abscissa to peak) and therefore show differences in quadrant 4. This figure demonstrates the normal variability in behavior within the 200-ms window of the head thrust. Two individual responses to head thrusts directed toward the side of the lesion are shown in the left (Fig. 5A) and right (Fig. 5B) panels, from the same UVD patient CR whose results were also shown in Fig. 3. In Fig. 5, the head thrust dynamics were nearly identical (dotted lines in gaze planes; head reaches peak position at the triangles) and the NVE values were very similar (0.67 and 0.74), yet the response patterns were different. In both responses, the first correction (single arrowhead) was triggered around the same time after head onset and was a GVC. The second correction, however, was triggered nearly 40 ms earlier in Fig. 5B (double arrowhead). In both responses, the second correction became a GPC (once it crossed the abscissa). The GPC generated soon after the onset of peak head velocity (in Fig. 5B) was less accurate (end gaze position at 200 ms = 6°) than that generated later (in Fig. 5A) (end gaze position at 200 ms = 2°), even though the GPC triggered later had to produce a larger position correction. In the phase plane, the differences in latency are marked by the onset of the GPC (+ sign and double arrowhead) in the green epoch close to zero gaze velocity (Fig. 5A), and in the red epoch just after peak gaze velocity was reached (Fig. 5B). Thus gaze-velocity error was nearly minimized in Fig. 5A before the GPC was triggered. Both GPC in Fig. 5, A and B had similar speeds (approximately 350°/s onset to peak), but because the GPC in Fig. 5A had a larger (150°/s more) effective speed (abscissa to peak in quadrant 4), the resulting gaze-position correction was larger and closer to zero by the end of the GPC (squares in quadrant 4). In Fig. 5B a late third correction (triple arrowhead) was necessary to adequately minimize gaze position. In this case, this was the second GPC that was produced in this response. There was no third correction in Fig. 5A because the GPC formed by the second correction was adequate for minimizing gaze-position error. Notice in Fig. 5B that the second GPC began after a 50-ms pause (purple highlight), and was incomplete at end of the pink epoch (the trajectory is moving downward and away from the abscissa in the gaze plane). Thus because of the 200-ms window, the end gaze position of 6° and end gaze velocity of 100°/s (at 200 ms, asterisk) can present a misleading evaluation of performance, if one considers only these end-point values.
In summary, the responses in the time domain (Fig. 5, top panels) show temporal variability in generating the second correction, the pause, and the third correction. In the gaze plane, we are able to focus on the effectiveness of the corrections and the dynamic relationships between position and velocity error. From the examples in Figs. 4 and 5, we found that later GPCs allowed GVCs to complete minimization of gaze-velocity error, and later GPCs were usually more accurate in minimizing gaze-position error. Early GPCs (generated in quadrant 1 or 3) did not allow GVCs to be complete, and usually required additional GPCs to completely minimize gaze position.
Range of BVD responses
In Fig. 6, we present 4 examples of BVD responses. The top row displays patients whose GVC and GPC were unable to achieve 50% compensation, and the bottom row displays patients who were able to compensate for 50% of the gaze-position error. Data in Fig. 6A are from BVD patient RI (56-yr-old woman tested 4 mo after experiencing symptoms from gentamicin toxicity). Data in Fig. 6B are from BVD patient WU (65-yr-old man tested 23 yr after experiencing symptoms of bilateral deficit from unknown etiology). Patient WU had larger NPE and NVE values (NPE: 78–79%, NVE: 84–87%) than those of patient RI (NPE: 60–61%, NVE: 73–80%). The gaze planes in Fig. 6A show that RI had very slow (rounded) responses that contained several GVCs, but did not generate any high-velocity GPCs during leftward head thrusts. During rightward head thrusts, a few higher-velocity GPCs were generated. The final responses of all the trajectories therefore did not end close to the origin. The gaze planes in Fig. 6B show that WU triggered several GVCs in the initial quadrants, and waited until the head reached peak position (zero head velocity, triangles) and then triggered a few GPCs during leftward head thrusts. The trajectories ended far from the origin. Neither patient was able to achieve significant gaze position compensation before 200 ms.
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Although (in Fig. 2) the NPE, NVE, and NEE values for RO (+ signs) were very close to those in MI (x signs), it is the gaze planes that help distinguish these 2 BVD patients. The GPCs of MI (Fig. 6C) were triggered before the head reached peak position, in the red epoch, exhibiting a sharp drop in gaze velocity in the green epoch. Nearly all of his responses were composed of just one high-velocity GPC. The dynamics of RO's responses were delayed, with GPCs generated after the head stopped moving. In summary, the gaze planes provide clear dynamic information that differentiates between responses that may appear similar when only static error values are compared. In less-compensated BVD patients, gaze-velocity errors rather than gaze-position errors are reduced. In better-compensated BVD patients, the ability to effectively reduce gaze-position error is reflected in the generation of high-velocity GPCs.
Range of normal responses
We now consider the gaze-plane dynamics of the data within NPE from 0 to 20% accounting for the normal subject responses at HA (high acceleration), and NPE from 20 to 30% (see asterisks in Fig. 2) for the normal subject responses at VHA (very high acceleration). On a small scale, normal subjects at HA exhibited various types of idiosyncratic behavior, with the gaze plane readily showing asymmetries in head thrust directions as well as various combinations of corrective eye movements. Figure 7, A and C show 2 examples of normal responses at HA. In Fig. 2 we see that because NPE is small, little compensation is required. Some subjects did not show any gaze-position error reduction in the time frames examined.
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In the gaze plane for subject GG (Fig. 7D), VHA head thrusts triggered a similar correction (to that observed in MA) immediately after head onset. After gaze-velocity error was minimized, a second correction was generated as a small GPC in the green epoch (100–150 ms). Then in the final epoch (pink, 150–200 ms), large GPCs were triggered to minimize gaze-position errors to levels observed at HA. This subject triggered high-velocity GPCs to reduce the gaze-position error by 200 ms. The timing pattern in GG resembled that in UVD patient CR during head thrusts toward his intact side. Those responses consistently produced a pause between 100 and 150 ms (see Fig. 3, A and C). High-velocity GPCs were triggered in the last (pink, 150–200 ms) epoch and in many instances after the head had stopped moving (triangles), later than those triggered on the lesioned side. Nevertheless, the end gaze positions on the intact side were more accurate (0.3 ± 1.8°) at the end of the 200-ms trajectories than those on the lesioned side (5.8 ± 2.9°) (see Table 1). The data in Fig. 2 indicate that of all the VHA responses, only the rightward head thrusts in GG (Fig. 7D) were able to compensate 50% of the gaze-position error.
In summary, the data from normal subjects show that the gaze errors increase as the amount of challenge is increased. The gaze errors exhibited by normal subjects at VHA are contained within the same range as those produced by UVD patients during head thrusts to their intact side. The gaze planes indicate that the strategy for compensation is also comparable to those observed in all patients. As in UVD and BVD patients, in "less-compensated" normal subjects, gaze-velocity error is preferentially reduced, whereas "better-compensated" normal subjects develop higher-velocity GPCs that reduce gaze-position error. On the other hand, in patients we did not find that residual vestibular function is the primary contributor to overall compensation when the challenge is high. Both normal subjects at VHA and patients (UVD and BVD) rely on GPC once compensation is achieved.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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In this study we developed a framework of analysis to characterize the dynamic properties of gaze stabilization during head thrusts over a large range of accelerations, in various subject populations. Through our gaze-plane analysis we were able to delineate distinguishing patterns of performance that persisted despite variation in the stimulus from trial to trial. The gaze planes provide critical dynamic information that differentiates between responses that may otherwise appear similar when only static error values are compared. In the gaze plane, we are able to focus on the effectiveness of the corrections and the dynamic relationships between position and velocity error, despite temporal variability. Our goal to characterize the dynamic function of the vestibular system over the duration of a step stimulus resulted in a multilevel (corrections, GVC and GPC outcomes, compensatory patterns), multivariable analysis of gaze. Through this process we found the main factors to be: the number of corrective eye movements, the outcomes of the corrections [gaze-velocity correction (GVC) and gaze-position correction (GPC)], the amplitude and timing of the corrections, and the pause behavior within the corrective sequence.
Gaze error continuum
We found that gaze-position and gaze-velocity errors are linearly related, and this linear relationship increased along a continuum from normal subjects to normal subjects challenged by unnatural stimuli to patients challenged by various degrees of physiological deficit. Gaze position and gaze velocity first increased from normal response levels when a novel head stimulus not experienced naturally was introduced to normal subjects. These VHA responses in normal subjects overlapped with those from the contralesional side of patients with UVD. Progressing along the continuum, gaze-position error and gaze-velocity errors increased to levels observed from the lesioned side of patients with UVD, then to the maximal levels observed from both sides of patients with BVD. The amplitude of error (the dynamics in the initial quadrants) increased in a linear manner in both gaze position and gaze velocity.
The similarity in errors between the contralesional responses in UVD and in normal responses at VHA suggests that the head stimuli had exceeded the limits in which the contralateral labyrinth normally functions. In the UVD patients, no vestibular contribution is expected from the contralateral labyrinth during contralesional rotations. In the normal subjects at VHA, the contralateral labyrinth is experiencing ampullofugal (inhibitory) stimulation. We know from Ewald's second law that ampullopetal (excitatory) stimulation of the lateral canal has a larger firing range than that during ampullofugal (inhibitory) stimulation (Ewald 1892). It is likely that at VHA stimuli, the inhibitory afferents and/or central vestibular neurons have reached both velocity and acceleration cutoff, therefore contributing very little to the compensatory response.
In Fig. 2, we find that maximal gaze-velocity error is consistently larger (approximately 15%) than maximal gaze-position error in all subjects when normalized to the respective head kinematics. In other words, the percentage of gaze error relative to head velocity is always higher than the percentage of gaze error relative to head position. If one considers gaze error minimization as a control problem, it would be more difficult to control gaze velocity than it would be to control gaze position. Gaze position can be controlled by current gaze-position and gaze-velocity values. Using gaze velocity, or the slope of gaze position, the brain will be able to anticipate the direction of the gaze position and minimize it. Future values for gaze velocity, however, could be predicted with gaze acceleration, although this parameter, being inherently more noisy and variable, may be more difficult for the brain to process with fidelity. Therefore minimizing gaze velocity relies mainly on current values of gaze velocity and the functioning of the VOR.
Contralesional responses on average were 20% higher in both maximal gaze-velocity and gaze-position errors, compared with normal subjects. This relative increase in gaze-velocity error was comparable to the decrease in velocity gain found previously during yaw head thrusts in normal subjects to patients with UVD (contralesional side), 24% at 100 ms after head onset (Aw et al. 1996a,b). Tabak and colleagues (1997a,b) found smaller decreases, 12–13% with manual head thrusts and 3–4% with helmet head thrusts, whereas Tian and colleagues (2000
