Abstract
Purpose.:
To make an initial assessment of the feasibility of using records of eye movements during perimetry to improve the estimate of scotoma edge location.
Methods.:
The nasal edge of the blind spot was mapped in seven normal subjects with a 2° grid of test locations, using a custom test station, while gaze direction was monitored with an eye tracker. Records were analyzed to determine whether the combined sensitivity and eye movement data could be used to estimate the nature of the blind spot edge.
Results.:
Analysis was conducted for 15 high-variability test locations. For 11 locations the blind spot edge estimates fit plausibly with the general form of the blind spot (edge orientation within 90° of expected); for four locations the agreement was poor. One consequence of interpreting the test results using the edge estimates was an average reduction of test–retest variability by 58%.
Conclusions.:
Recordings of eye movements during perimetry can be used to generate an improved estimate of scotoma boundaries. A byproduct of the new estimate is a substantial reduction of test–retest variability.
Visual fields of patients are most frequently assessed by means of computerized perimetry or standard automated perimetry (SAP). Although in the normal visual field, test–retest variability is relatively low, on the order of 1 to 2 dB,
1,2 in damaged visual fields it can become much higher.
3 –8 This makes it difficult to determine whether a patient's condition is stable or progressing.
Small fixational eye movements during testing may contribute to increased test–retest variability in damaged fields.
2,9 –12
Assessing damaged visual fields often involves assessing size and location of scotomas, and one difficulty in static perimetry is determining where scotoma edges are located. To date, in experimental work studying sensitivity near edges of scotomas or the edge of the blind spot (using it as a physiological scotoma), the location of the edge relative to the test locations has generally been unknown. To clarify this, in a commonly encountered situation, a row of three test locations gives the after results: At the first location, sensitivity is repeatedly found to be near normal, while at the third location sensitivity is repeatedly found to be essentially absent. At the second (middle) test location, results may be like those of the first location, or like those of the third location, or highly variable from test to test. In the case of high variability at the middle location, all that can be said about the boundary between healthy and damaged fields is that it lies between the first and third locations, which—in the case of the usual 6° or 2° grids—locates the boundary to within 12° or 4°, respectively. Examples of such situations are commonplace findings in repeated visual fields near edges (e.g.,
Fig. 2 of Ref.
2); upper subject:
x = 5°,
y = 1°, 3°, 5° deg; lower subject:
x = –1°, 1°, 3°,
y = 3°).
One reason why scotoma edge location is an important issue is that sensitivity can change rapidly as one crosses such an edge. If a visual field test location lies near an edge, a small eye movement can potentially cause a large difference in sensitivity at the location to which a test stimulus is delivered. A number of researchers have considered the possibility that fixational eye movements could be involved in test–retest variability. There have been reports that variability increases near the edges of scotomas
9,13,14 and that the number of steep scotoma boundaries in a field is correlated with the variability.
10 Pan et al.,
15 modeling the retina-plus-cortex, looked at the effect of randomly damaging the retinal ganglion cell array together with random fixation shifts. As might be expected, in the presence of damage this created variability in sensitivity in an otherwise noise-free model, at least for smaller stimuli (Goldmann size III). In visual fields of patients with glaucoma, Wyatt et al.
2 found a strong spatial correlation between the gradient of sensitivity in the visual field and test–retest variability, and argued that it was most easily explained by small eye movements causing variability where the gradient was steep. However, findings in this area have been mixed: Haefliger and Flammer
14 concluded that the gradient of sensitivity has less effect on variability for glaucomatous defects than for the physiological blind spot, and Henson et al.
12 concluded that fixation errors may have only a minor influence on perimetric variability.
If fixational eye movements contribute to test–retest variability, studying eye movements during visual field testing might illuminate the issue. (This need not necessarily be the case; random or patchy damage on a fine scale could make it difficult to see any relationship.) However, there have been no studies of sensitivity near scotoma edges in which the time course of eye movements has been related to the time course of the test results—that is, the time course of the staircase of test presentations used to arrive at the test results.
If the gaze direction (fixation error) were known for each test flash in a perimetric determination, it would mean that the actual retinal location of each test flash would be known. It seemed possible that in such a situation the spatial distribution of test flash contrasts and subject responses could be used to determine the most likely boundary between healthy and damaged fields. If the spatial pattern of damage is relatively simple, with substantial areas of healthy and damaged fields separated by simple boundaries, then a manageable number of repeat tests might provide enough data to estimate the retinal location of the boundary. In the present work, visual sensitivity near the blind spot was measured in normal subjects and gaze direction was measured concurrently. A post hoc analysis indicated that a substantial part of the test–retest variability could be accounted for by the eye movements measured for each subject.
Apparatus.
Visual Stimuli.
Subjects.
Experimental Protocol.
After subjects were positioned in the apparatus, the eye tracker was calibrated by having subjects sequentially fixate steady stimuli at an array of five locations: the central fixation target, ±3° horizontal, and ±3° vertical, for 1.5 seconds each while the eye tracker recorded “raw” gaze direction data. (Gaze direction data consisted of horizontal and vertical coordinates of the location of the pupil center and of the reflection of the eye tracker infrared source in the first corneal surface.)
In addition to the x–y calibrations, subjects also participated in a “light–dark” trial, in which they fixated the central calibration target while a large, bright (54 cd/m2) stimulus was turned on and off with a 4-second period (2 seconds on, 2 seconds off, etc.), and pupil and gaze direction data were recorded for 16 seconds. This produced substantial pupil responses, and the data were used in analysis of experimental eye tracker data (see below).
The visual field testing, using the test array of
Figure 1, used a 2 dB/1 dB, two-reversal staircase. Initial stimulus luminance was randomly set at either 8.09 or 6.23 cd/m
2. For test locations presented within the average location of the blind spot, initial stimulus luminance was set at 20.50 cd/m
2. Subjects pressed a button connected to the Macintosh computer to indicate that they had seen a given test flash. Blank trials were presented at a rate of 1 in 6. For each test flash (including blanks), the computer recorded the time, location, and luminance of the flash and the subject's response.
Gaze Direction Data Analysis.
Gaze direction data were converted from raw data into an estimate of gaze direction by (1) removing blinks using a blink detection algorithm based on rate of change of pupil diameter, (2) calculating the horizontal and vertical distances between pupil center and corneal reflex, (3) correcting the calculated distances according to pupil diameter (see below), and (4) using the calibration values to calculate gaze direction relative to the fixation target. The resulting records of gaze direction as a function of time during the trial were smoothed using 7-bin (7/60 seconds = 0.117 second) “boxcar” smoothing (running average of 7 bins). Under the conditions of these experiments, five of the seven subjects had pupils large enough and palpebral fissures small enough so that vertical pupil diameter measures were contaminated. Therefore, vertical eye position measurements were unreliable for these subjects and only horizontal eye position data were used in subsequent analyses.
Correction of Gaze Direction for Pupil Diameter.
For the post hoc analysis, test locations were selected where test–retest variability was high. A “look-up” of data for the staircase information for that location was conducted: For each session, the staircase for the selected test location was extracted from the complete record of the session, and the time, luminance, and subject response were noted for each test flash presented at the location. The time was then used to look up gaze direction at the time of each flash. Pooling data for all sessions for the particular subject created a data set of actual retinal test locations, test luminances, and subject responses for the selected test location.
The data were then fitted with a spatial function, consisting of two spatial regions of differing sensitivities, separated by a sharp edge. For both regions comprising the spatial function, the probability distribution for seeing a stimulus of contrast
z was taken to be Quick's version of a Weibull function
17 :
where α is threshold contrast (
P = 0.5) and β determines the steepness, with larger β giving a steeper curve corresponding to less variability. For two-dimensional (2-D) gaze-direction data, there were five parameters: angle and placement of the edge, two values of sensitivity α (one value on each side of the edge), and the steepness parameter β. For one-dimensional (1-D) gaze-direction data, the edge was assumed to be vertical, leaving four parameters.
The functions were fitted using maximum likelihood estimation (MLE), in which each test delivered is assigned probability P(z) if seen and (1 – P(z)) if not seen, the probabilities being evaluated for the current set of parameters. The MLE approach maximizes the product of these probabilities for the entire set of test presentations. The fitting was carried out using a Monte Carlo technique in a data analysis program written (IGOR; WaveMetrics, Inc., Lake Oswego, OR). Some constraints were placed on parameters; in particular, β was allowed to vary from 0.5 to 6, covering a reasonably broad range of steepness. 106 trials were performed for an initial fit and 105 trials were performed to refine the parameters in smaller ranges near the best values from the initial fit.
For each subject, the blind spot contour map of sensitivity generated from the basic test data were fitted by eye with an ellipse, and tangents to that ellipse were used to estimate the orientation (and polarity) of the blind spot edge for each test location studied in the post hoc analysis.
To permit a comparison between test–retest variability with and without consideration of gaze direction, a fit was performed as above, but with the assumption that the eye did not move; the single “fit” value was determined by fitting all the test contrasts and responses with a single probability function of the type above.
In a clinical setting, stabilizing test targets on the retina, as proposed in a 1975 patent by Lynn and Tate, might seem preferable to post hoc correction. However, the technology for stabilization is still somewhat limited; microperimeters stabilize by registering selected retinal landmarks; they currently operate at approximately 20 updates per second and are not invulnerable to eye movements. Heidelberg Engineering (FRG) employs a similar registration system to provide some degree of stabilization for their ophthalmic scanning systems and their edge perimeter. All video eye trackers, even the fastest models available, are subject to imprecision in using pupil center and corneal reflex to estimate gaze direction,
21 though some improvement through corrections such as those used here is possible. Microperimeters are also expensive at present, compared to standard automated perimeters. Other high-precision devices for evaluating gaze direction, such as Purkinje image-based eye trackers, are even less practicable. Less elaborate video-based eye trackers could be used in stabilization, but there are still issues such as lid intrusion as well as the shift with pupil size change. In many less industrialized parts of the world, stabilized perimetry is probably not practicable at present.
From a different perspective, if perfect stabilization were possible, would standard test arrays such as 24 to 2 or 10 to 2 provide the greatest amount of information? The chance of test locations falling on very steep scotoma boundaries may be fairly small because steep boundaries have little spatial extent. Thus, with a perfectly stabilized array, especially a 24 to 2 array with 6° spacing, boundaries would probably fall between test locations and real but modest changes in those boundaries might escape detection. Manual selection of test locations would be a possible approach, but that is demanding in a clinical setting. The presence of small eye movements, which vary the actual test location, might arguably be considered an advantage, if devices were capable of acquiring and using information about those eye movements.
The post hoc correction approach does have drawbacks; a substantial amount of data (and therefore time) is required to perform successful fits. In the present study, subjects participated in at least three sessions. On the other hand, because the uncorrected data comprise standard perimetric findings, or would do so if a standard test array were used, conventional perimetric results would be available until there were enough repeats for a post hoc analysis. In current clinical practice, repeat fields are the basis for determining whether a patient with glaucoma is progressing; thus, acquiring the data to perform later post hoc corrections would take no extra time. The addition of post hoc corrections might then clarify the question of progression. In fact, if there were enough repeats for, say, the first and second half-sets to provide independent edge estimates, it is possible that movement of the edge might be observable for a case of progression.
Supported by NEI Grant R03EY014549.
Disclosure:
H.J. Wyatt (P)
The author thanks William H. Swanson for many helpful comments and much discussion.