Ординатура / Офтальмология / Английские материалы / Advances in Understanding Mechanisms and Treatment of Infantile Forms of Nystagmus_Leigh, Devereaux_2008

ABSTRACT

We studied the ability to hold the eyes in eccentric horizontal or vertical gaze angles in 33 normal humans, age range 22 to 37 years (mean 29.3). Subjects attempted to sustain visual fixation of a briefly flashed (750 milliseconds) target located

±30° in the horizontal plane and ±15° in the vertical plane in a dark environment. Conventionally, the ability to hold eccentric gaze is estimated by fitting centripetal eye drifts with exponential curves and calculating the time constant (τc) of these slow phases of “gaze-evoked nystagmus.” Although the distribution of time-constant measurements (τc) in our normal subjects was particularly skewed due to occasional gaze-holding that was almost perfectly stable (large τc values), we found that log10(τc) was approximately normally distributed within classes of target direction. Therefore, statistical estimation and inference on the effect of target direction was performed on values of z ≡ log10τc. Subjects showed considerable variation in their eye-drift performance over repeated trials; nonetheless, statistically significant differences emerged: values of τc were significantly higher for gaze elicited to targets in the horizontal plane than for the vertical plane (p < 10–5), suggesting eccentric gaze-holding is more stable in the horizontal than in the vertical plane. Furthermore, centrifugal eye drifts were observed in 12.0%, 8.5%, 4.3%, and 65.7% of cases for rightward, leftward, upward, and downward gaze tests, respectively.

Fifth-percentile values of the time constant were estimated to be 10.8 seconds, 13.0 seconds, 3.3 seconds, and 3.7 seconds for rightward, leftward, upward, and downward gaze, respectively. Our statistical method for representing the range of normal eccentric gaze stability can be readily applied in the clinical setting of patients with neurological disease and normal subjects exposed to environments that may affect the properties of their ocular motor integrator. Patients with gaze-evoked nystagmus can be identified by referring to the above-mentioned normative criteria.

During natural activities, human subjects often direct their line of sight at an object of interest located off to one side and maintain the eyes at eccentric positions in the orbits while the object is watched. In order to program such “eccentric gaze-holding,” the brain must take into account the mechanical properties imposed by the orbital tissues. Specifically, a sustained contraction of the extraocular muscles is necessary to oppose the elastic forces that continually pull the eye back to the central position.1,2 To achieve this sustained muscle contraction, the ocular motoneurons must generate commands with an eye position component.

Electrophysiological studies confirm that the ocular motoneurons modulate their discharge rate with eye position (and also with velocity during movements),3 although the demonstration of orbital pulleys has indicated that the mechanism may be complex.4 Premotor neurons that send vestibular,5 saccadic,6 and smoothpursuit signals7 to the ocular motoneurons modulate

their discharge with eye velocity, not position. Thus an integration of velocity-coded premotor signals to position-coded motoneuron commands is achieved by the nervous system. Important components for carrying out this integration are (a) for horizontal gaze holding, the nucleus prepositus hypoglossi/medial vestibular nuclei complex (NPH/MVN)8,9; and (b) for vertical gaze holding, the interstitial nucleus of Cajal (INC).10 In addition, the cerebellum, especially the flocculus, makes an important contribution to the integration.2,11,12 Lesions in any of these structures may impair the ability to hold the eyes in eccentric gaze, allowing the eyes to drift back toward the center of the orbits, causing corrective quick phases, known as “gazeevoked nystagmus.” Normal subjects also show some centripetal drifts, indicating that the neural integrator for eye movements is not perfect but rather has a “leak” defined by the time constant of the centripetal drift (τc).

Most prior reports of gaze-holding ability in normals have studied only a few subjects and have not measured performance in both the horizontal and vertical planes. Thus the main goal of this study was to establish a normative model of eccentric gaze-holding performance, in both planes, in a healthy subject population free from vestibular or visual defects. Because of the reported variability of gaze-holding ability between different subjects,13-16 we attempted to use a simple methodology that can be easily repeated in both clinical and laboratory settings. Preliminary studies indicated that the distribution of time-constant measurements (τc) in normal subjects is particularly skewed due to cases that approached perfect stability (τc = ∞). As a result, statistical estimation and inference on the effect of target direction was performed on values of z ≡ log10τc, which we found to be well modeled by a normal distribution. Lower percentiles of the estimated normal distributions of z for each target direction can be used as standards of comparison for patients when gaze-holding ability is evaluated.

METHODS

Subjects

Horizontal and vertical gaze-holding for eccentric targets were examined in 33 normal subjects (31 males, 2 females, ages 22 to 37 years, mean 29.3 years). Testing was performed only after each subject signed a consent form approved by the Johnson Space Center’s Institutional Review Board. All subjects were screened medically prior to testing, and none presented with vestibular or neurological symptoms or were any taking medication with effects on the central nervous system. Subjects were either emmetropes or wore their corrective contact lenses during testing.

Equipment

The subjects’ eye movements were recorded using a SensoMotoric Instruments (SMI) three-dimensional binocular infrared video eye tracker (VET) (linear range of ±30° horizontal and ±30° vertical; sampling rate of 60 Hz; system noise assessed at <0.5° root mean square [RMS]). The camera system was integrated with an in-house pupil-tracking algorithm as described elsewhere.17 The sampling rate of 60 Hz was determined to be sufficient for this experimental protocol because it encompassed the bandwidth of slow-phase velocity waveforms. The visual stimuli consisted of an array of five light-emitting diodes (LEDs), located at center, right and left 30°, and up and down 15°, mounted on a cruciform-shaped target positioned 0.5 m from the subject’s outer canthus and parallel to the coronal plane. The cruciform target was solidly mounted to a restraint chair in which the subject was seated. The restraint chair was lightly padded and included a head and neck restraint that prevented unwanted head movements and assisted the subjects in maintaining straight-ahead head and gaze position.

Procedure

All eye movements were obtained in a completely dark environment. Eye movements were calibrated by requiring the subjects to visually acquire a series of LEDs that were displayed in both the horizontal and vertical planes. Following calibration, each trial began with the subject fixating on the center (0°) LED, and then subsequently cued to acquire one of the four eccentric LED targets located at right 30°, left 30°, up 15°, or down 15°. The cue was a 750-millisecond-duration flash of the new target LED. Coincident with the flash of the eccentric target, the center LED was extinguished. After 20 seconds, the subject was cued with an audio tone to return gaze to the remembered position of the center LED. Gaze was maintained on the remembered central LED position for an additional 20 seconds, whereupon the center LED was again illuminated and the subject made any necessary correction in gaze to the central target. The sequence described above was then repeated for a new eccentric target location until all four eccentric targets were displayed.

Data Analysis

The gaze-holding protocol was designed to measure the subject’s ability to maintain gaze on a remembered target (first 2 seconds of data after acquiring the eccentric target) and to charge the neural integrator for an investigation of rebound nystagmus following a return to center (the remainder of the 20-second period).

The decision to use only the first 2 seconds of data for gaze holding is further justified by the observation that beyond the first 2 to 3 seconds, either gaze had stabilized or gaze-holding could be interrupted by random saccadic eye movements. Using programs written in MATLAB (The MathWorks, Natick, MA), the VET signals were filtered using a median and sliding window filter to remove digitization noise associated with video-oculography.18 The data were then calibrated using the initial calibration targets contained at the beginning of each file. To obtain the time constant of centripetal eye drift, each target file was loaded, and the first saccade was identified interactively. The operator then selected all slow-phase drifts within the first 2 seconds after the initial saccade (Fig. 15.1A). We assumed that each drift followed resetting of the neural integrator by the prior quick phase; therefore, the onset time for each drift was set to zero, allowing the fitting algorithm to treat each as the beginning of an exponential curve instead of as a continuation of a previous one. Each drift was then fitted using a natural log transformation, after taking the absolute values. After applying the natural log transformation to each drift, we performed a linear regression and used the resultant slope to calculate the time constant (τc = 1/| slope |), as shown in Figure 15.1B. We excluded individual slow phases with τc < 1.1 seconds, since these were more likely due to saccadic pulse-step mismatch than a near-absence of integrator function. All linear regressions with R2 values below 0.8 were discarded as poor fits. In 20% of drifts, the slow-phase drifts moved away from the central position (centrifugally). In these situations, we assumed the drift was moving toward an asymptote located away from center, and we calculated exponential time constants accordingly. For purposes of assessing gaze-holding ability, we assumed time constants were comparable, regardless of the direction of drift. In other words, a drift in the direction away from center was considered to be as detrimental to clear vision as a similar drift toward center.

Statistical Analysis

The objective of the statistical analysis was, for each target direction, to estimate the fifth percentile of the distribution of time constants one would see for random normal individuals taking the test one time as in a clinical setting. However, because the data for this experiment comprised multiple trials in a highly unbalanced design (Table 15.1), merely using the sample fifth percentile as the estimate is influenced too much by the small set of subjects that had many trials. As an alternative, after removal of outliers (τc < 1.1, one point dropped), we assumed a “normal distribution with random effects” model for log (τc) and used

Time (s)

Horizontal eye position Vertical eye position

Horizontal target position

B

Time (s)

Figure 15.1 (A) Representative gaze-holding trial. The subject begins by fixating the center LED and then makes a saccade to a left 30° target. The subject maintains the approximate gaze angle for 20 seconds before being cued to return to center by an audio tone. After 20 seconds at center, the center LED is re-illuminated. Insert: During analysis, the drifts from the first 2 seconds after the first saccade are selected interactively.

(B) Natural log transformation and linear regression. Using the same data as in (A), each drift was inverted and reset to a start time of zero. The natural log was applied, and then a linear regression was used to fit the data. The time constants were calculated to be 17.9, 14.6, 19.5, and 29.0 seconds, respectively. Note the variability within one subject’s trial.

Table 15.1 Test Frequency by Subject and Direction

estimates of the betweenand within-subject variance components to calculate the percentiles of interest. This model, while not perfect (Fig. 15.2), gives a reasonable approximation of the distribution of time constants after removal of outliers (τc < 1.1).

The random-effects model is of the form

where zijk = log10(τc) for the jth observation on the ith subject for target direction k, µk is the mean value of

log10(τc) for target direction k, ai is a between-subject random effect normally distributed as N(0, σ a2 ), and eijk is a within-subject error term normally distributed as N(0, σ2). All random effects and error terms are assumed statistically independent from one another; however, we considered the possibility that values of

Figure 15.2 Residual plot. Shown is the histogram of the residuals after fitting the mixed model for all target directions (N = 529). Note that the residuals are normally distributed, indicating a reasonable approximation to the distribution of time-constants.

the variance parameters σ a2 and σ2 might depend on the target direction. From Equation 1, it can be seen that the distribution of log10(τc) for a random individual performing the test one time in target direction k would

of target direction was performed by restricted maxi- mum-likelihood estimation of the statistical parameters in Equation 1 using Stata Version 9 statistical software (STATA Corporation, College Station, TX) and testing the effect of target direction on the parameters. Because of the monotone log transformation, any significant differences (p < 0.05) in the distribution of z correspond directly to significant differences in the distribution of τc. Similar statistical inference could be applied to data from clinical studies comparing normal subjects with a group of subjects for whom gazeholding ability is expected to be abnormal.

To obtain a measure of uncertainty in estimates of Z05 induced by sampling, we could have used asymptotic standard errors of the model parameter estimates and applied the “delta method.”19 Instead, we chose to estimate Z05 directly, with Bayesian methods using WinBUGS software (Imperial College and Medical Research Council, Cambridge, UK). The posterior distribution of Z05 given the data was then used to construct a “Bayesian credibility interval,” analogous to a confidence interval. The endpoints of this confidence interval were then exponentially transformed to obtain a confidence interval for τ05.

RESULTS

Distribution of Time Constants

Total sample sizes of 141, 141, 139, and 108 (from 33 subjects) were obtained for the rightward, leftward, upward, and downward target conditions, respectively; however, the number of observations per subject varied considerably—from 0 to 21, depending on the target direction (Table 15.1). Because of this imbalance, fitting the multilevel model (Eq. 1) gives a more accurate estimate of population means for each target direction than would simple averaging of the data. For a similar reason, estimates of fifth percentiles obtained from the multilevel model parameters are more accurate than empirical fifth percentiles of the data.

After experimentation, we found that the model (Eq. 1) fit best by allowing the mean (µk) of z and the variance component σ a2 to vary with target direction (k). Resulting estimates are shown in Table 15.2. An examination of this table shows significant differences in the estimates of the parameter µ between the right and left directions (difference = 0.081, SE = 0.026; p = 0.002). The most salient feature of Table 15.2 is the indication of a substantial decrease in the mean of z (and hence median of τc) for vertical relative to horizontal targets (decrease = 0.412, SE = 0.035; p < 10–5), suggesting eccentric gazeholding is more stable in the horizontal than in the vertical plane. Furthermore, we observed that 66% of drifts elicited to downward targets were away from center (centrifugal), compared to only 4% of drifts associated with upward targets. Therefore, we feel there is, at a minimum, a functional difference between upward and downward vertical gaze, and we suggest using distinct fifth-percentile values for these cases. Table 15.2 also shows the estimates of the median (τ50) and fifth percentile (τ05) of the time-constant distribution, as well as the lower and upper confidence limits for the fifth percentile (τ05).

Applying the Model

In a clinical setting, one would simply apply the appropriate fifth percentile from Table 15.2 as a threshold to detect potentially abnormal gaze-holding performance,

since these values would lie outside the 95% prediction interval. The probability of being able to detect a particular pathology by this method would depend on how much the time-constant distribution is shifted (presumably downward) for the patient. To illustrate this point, Figure 15.3 indicates how well these thresholds would be able to successfully detect abnormalities (up and down results were averaged for this plot because their difference was relatively small). The figure depicts the probability that the time-constant distribution of a patient from a degraded population would fall below the fifth-percentile threshold value shown in Table 15.2 as a function of a percent difference between the median time constant for the degraded

Figure 15.3 Detection probability plot. Shown is the probability of a single drift being identified as abnormal (below the normative fifth percentile) based on the percent difference between the median time constant for the degraded population and the median for a clinically normal population. Note that for a 0% drop in time constant (no change), the probability is 5%, meaning that any particular drift would have a 0.05 probability of 0.05 being identified as abnormal. If the median time constant for a subject were shifted by 50% from normal, we would expect a single drift to have a probability of 0.33 of being identified as being abnormal for horizontal targets and of 0.24 for vertical targets.

population and the median for a clinically normal population. For a zero-percent change in median time constant (no shift in the subject’s distribution relative to the distribution of normal subjects), the probability of a single observed-drift time constant falling below the threshold would be 0.05, as expected. On the other hand, if the patient’s median time constant were 50% lower than that of normal subjects, the probability of a single drift having a time constant falling below the threshold would now be 0.33 for horizontal gaze-holding and 0.24 for vertical gaze-holding.

DISCUSSION

We set out to compare the ability to hold steady eccentric gaze in the horizontal versus vertical planes in a large group of healthy human subjects. There are two main findings of this study. First, using a lognormal distribution to model the time constant of drift is a reasonable approach to dealing with extremely skewed time-constant data. This approach provides a means to summarize the normal range and define abnormal gaze-holding ability. Second, using this statistical model, we have been able to show that normal subjects show better eccentric gaze-holding ability in the horizontal than the vertical plane.

Development of a New Statistic for

Measurement of Gaze-Holding

It should be noted that our estimates of the time constant are based on eye drifts when subjects attempted to view a remembered target located at ±30° in the horizontal plane and ±15° in the vertical plane. Although it is convenient to assume a linear model for the ocular motor plant and a neural integrator with a single time constant, in practice this is not observed. Thus it is known that with greater eccentricity, different time constants are observed,20 for which a neural network mechanism has been proposed.21 Application of our statistical results depends on similar target locations being used during testing. How well the lognormal distributions estimated here could fit data generated during attempts to fixate targets at the extremes of gaze requires further study. Nonetheless, the eccentricities that we have chosen challenge gazeholding ability but are within the linear range of most eye movement monitors.

Possible Physiological and Anatomical Basis for Current Findings

A number of prior studies have reported that normal subjects show a range of ability (measured by

time constant of centripetal eye drift) to hold steady, horizontal, eccentric gaze in darkness.13,14,16,22 Indeed, some normal subjects show “endpoint nystagmus” when viewing a target.22 In the present study of normal subjects, we show that the range of normal gaze-hold- ing ability in the horizontal plane is less stable than previously reported and, for the first time, demonstrate that eccentric vertical gaze-holding is also less stable than horizontal gaze-holding. One possible explanation for the difference in horizontal and vertical gaze-holding relates to the observation that different structures of the brainstem, and perhaps the cerebellum, contribute to horizontal or vertical gaze-holding. For example, in monkeys, chemical lesions of NPH/ MVN in the medulla abolish horizontal gaze-holding ability but leave some gaze-holding ability intact.23 On the other hand, pharmacological inactivation of INC in the midbrain mainly impairs vertical gaze-holding ability.24 Another contributing factor concerns the mechanical properties of the orbital tissues. The discovery of pulleys that guide the extraocular muscles might provide an explanation based on orbital mechanics.4 Thus, each extraocular muscle comprises an outer orbital layer that attaches to a pulley (and moves it) and an inner global layer that passes through the pulley and attaches to the eyeball. For example, Demer4 has suggested that the restricted range of upward gaze movement encountered in normal elderly subjects may be due to changes in the attachment of the orbital layer of the inferior oblique muscle to other connective tissues in the orbit. The subjects that we studied were predominantly young and showed no limitation of upward gaze. Although there was no asymmetry of upward versus downward time constant, we did note a larger percentage of drifts away from center when looking to the downward target. Future studies of older, healthy populations might show significant differences.

In clinical practice, impaired ability to hold eccentric gaze—manifested as gaze-evoked nystagmus—is a common finding; frequent causes are drug intoxications (e.g., alcohol) and cerebellar disease.2 In some individuals, there is doubt as to whether gaze-evoked nystagmus is indicative of underlying disease or represents the range of normal behavior (such as physiological “endpoint nystagmus”). In such patients, clinicians traditionally look for other clues of cerebellar disease, but comparison of patients’ values of τc with a large data base, such as is presented here, may aid diagnosis. In preliminary studies we were able to apply part of the data presented in this paper to identify abnormal gazeholding in a group of patients with cerebellar disease.25 However, larger numbers of patients require study to validate these predictions. Finally, rare patients may show an unstable rather than a leaky integrator.12,26 It is therefore of interest that some normals may also show

centrifugal eye drifts but, unlike reported patients with cerebellar disease, only do so while in darkness, when visual fixation is prevented.

ACKNOWLEDGMENTS This work was supported by the National Space Biomedical Research Institute through the National Aeronautics and Space Administration NCC 9-58 (grant NA00208), National Institute of Health grant EY06717, the Department of Veterans Affairs, and the Evenor Armington Fund.

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