Various types of eye movements are involved in performing tasks such as reading, finding objects in crowded places, or searching facial features for face recognition, but most of the visual information is acquired during fixations. People with normal vision use their fovea—where resolution is best—to fixate, whereas patients with central vision loss involving the fovea use preferred retinal loci (PRLs) from the nonfoveal retina.1–3 Fixation stability with a PRL is generally poor, and this deficit may be related to impaired visual performance.4–10
The location of the PRL on the retina along with fixation stability is identified with imaging instruments among which the most modern ones have eye-tracking capabilities to record eye positions when the patient fixates on a stationary target. In the past 10 years, our laboratory has used the MP-1 microperimeter (Nidek Technologies Srl., Vigonza, PD, Italy) and, following the manual’s recommendations, recorded fixation stability for periods between 15 and 30 s. However, these recommendations are arbitrary and atypically long. Lengthy fixations are required only occasionally in laboratory or clinical settings (i.e. for microperimetry examinations, visual field tests, MRI tests), and an evaluation of fixation stability during a few minute periods of fixation would be of interest in these unique situations. However, for normal observers in naturalistic situations, visual tasks require brief fixations whereas prolonged ones are rarely or never needed. The average fixation duration during silent reading is 200 to 250 ms, during visual search is 275 ms, and during scene perception is 330 ms.11 In addition, the long fixation examinations recommended by the MP-1 manual are tiring and this may affect the patient’s ability to keep steady fixation during examination.
The purpose of this study was to examine how fixation stability changes over 15 s of data acquisition in patients with central vision loss. Specifically, we asked two questions: (1) Does fixation stability change with increasing the duration of fixation recording? For this, we examined fixation stability for the first 5 s, the first 10 s, and the first 15 s of the same fixation examination. (2) Does fixation stability change over time? For this, we examined fixation stability over three consecutive 5-s intervals of the same fixation examination. The answers to these questions were also verified with shorter sampling intervals.
Fixation stability examinations recorded with the MP-1 microperimeter were reviewed for patients with bilateral central vision loss from our research database. All these participants consented to be part of various research studies in the Ocular Motor Laboratory at the Toronto Western Hospital for which ethics approval had been obtained from the institutional research ethics board. All research was conducted in adherence to the declaration of Helsinki.
Only one fixation examination per participant was included. Eyes with central fixation (i.e. with foveal sparing, relative scotoma) were excluded. A fixation examination was included if (1) it was at least 15 s in length; (2) was recorded only during a fixation examination test, and not during microperimetry; (3) a red-cross fixation stimulus with a size of 3 to 6 deg was used; (4) based on visual inspection, only one PRL was used during 15 s of examination; and (5) if fixation examinations existed for both eyes, only that from the right eye was used. Based on these criteria, data from 76 patients with central vision loss (mean age = 80 ± 9.6 yrs; median age = 82 yrs, range 35–94 yrs) were included. All data were recorded only by one of the authors (LTN).
The MP-1 records horizontal and vertical eye positions during fixation at a rate of 25 Hz. The fixation stability examination output is presented immediately using a quasi-quantitative measure based on Fuji’s classification12,13 and a quantitative measure with bivariate contour ellipse area (BCEA).14 Fuji’s classification shows the percentage of fixation points that fall within a 2-deg- and a 4-deg-diameter area, whereas BCEA is a bivariate area that encompasses a given proportion of fixation points (i.e. 68%, 95%, or 99%). The BCEA calculation assumes that the data are normally distributed on the horizontal and vertical axes. Although this assumption is often violated,6,8,15 the BCEA has become one of the most common metric for quantifying fixation stability.
The BCEA can also be calculated offline from the raw data exported from the MP-1 following the guidelines described elsewhere,8 and this was the method used in the present study. The formula is
where σ x and σ y are standard deviations of the horizontal and vertical eye positions, ρ is the correlation coefficient of the horizontal and vertical eye positions, and χ 2 represents the chi-squared value with 2 degrees of freedom associated with the probability area chosen. In our case, the probability is P = .95 and the χ 2 value associated with it is 5.99.
Each fixation examination was analyzed as follows: (1) raw data from the MP-1 were exported, (2) data beyond 15 s were deleted, and (3) far outliers (±3SD) were removed. Far outliers represent about 1% of the data but can have a large influence on the BCEA values8; (4) data were separated into three intervals (0–5 s, 0–10 s, and 0–15 s) and for three consecutive 5-s intervals (0–5 s, 5–10 s, and 10–15 s); (5) bivariate ellipses were computed for all intervals. BCEAs, ellipse’s centroid coordinates (i.e. means of the horizontal and the vertical eye positions), the length of the ellipse’s axes (i.e. major and minor axes), and ellipse’s tilt (i.e. the angle between ellipse’s major axis and horizontal axis) were calculated for data of each of these intervals. The formulae for the length of the major and minor axes calculation, and for ellipse’s tilt were taken from Timberlake et al.6 The formula for tilt angle is
In order to answer the question of whether fixation stability changes with recording duration, the of the bivariate ellipse (i.e. area, centroid coordinates, axes, tilt angle) for three fixation recording intervals (i.e. 0–5 s, 0–10 s, and 0–15 s) were analyzed with Friedman’s nonparametric test for three related samples because some data overlap. Post hoc analysis was performed with Wilcoxon signed-rank test. To answer the question of whether fixation stability changes over time, the parameters of the bivariate ellipse (i.e. area, centroid coordinates, axes, tilt angle) for the three consecutive 5-s intervals (i.e., 0–5 s, 5–10 s, and 10–15 s) were analyzed with repeated-measures analyses of variance (ANOVAs) using a Geisser-Greenhouse conservative F statistic. These three consecutive 5-s intervals had the same number of data points (25 Hz × 5 s = 125 points) and data did not overlap. All post hoc analyses were performed with Bonferroni correction. An alpha level was set at 0.05 for all statistical tests. The same statistical analyses were performed on the log10 transformations of the BCEAs producing identical results. We therefore only discuss the untransformed values to simplify the discussion of the centroid coordinates, axes, and tilts of the ellipses.
Q1: Does Fixation Stability Change with the Length of Fixation Recording?
In order to answer this question, Friedman’s test for three related samples were conducted for BCEA, centroid coordinates, the length of the major and minor axes, and tilt angle for recording intervals 0 to 5 s, 0 to 10 s, and 0 to 15 s. The analysis showed that the BCEA got significantly worse with increasing the length of fixation recording, χ 2(2) = 48.0, P < .001. Post hoc analysis with Wilcoxon signed-rank test revealed that all comparisons were significant (largest P < .001). Compared to the BCEA during the first 5 s of examination recording, median BCEA increased (i.e. fixation stability deteriorated) by a factor of 1.4 for the first 10 s and a factor of 1.6 for the first 15 s of recording.
The bivariate ellipse’s centroid corresponds to the location of the PRL. The horizontal and vertical coordinates of the ellipse’s centroid (i.e. means of the horizontal and the vertical eye positions) did not change significantly with duration of the fixation recordings, χ 2(2)x = 6.1, P = .05 and χ 2(2)y = 1.5, P = .5, respectively.
The major and minor axes indicate the extent of the bivariate ellipse. The major axis did not change significantly with increasing the duration of fixation recording, χ 2(2) = 4.5, P = .1, but the minor axis got significantly larger, χ 2(2) = 28.9, P < .001. Post hoc analysis showed that all comparisons for the minor axis were significant (largest P < .001).
The angle between the ellipse’s major axis with a horizontal axis is the ellipse’s tilt. The tilt angle changed significantly with increasing the duration of fixation recording, χ 2(2) = 5.2, P = .07. All these results are summarized in Table 1.
Q2: Does Fixation Stability Change Over Time? The Relevant Variable Is the Duration of the Sampling Interval, Regardless of When after Trial Initiation It Begins
In order to answer this question, one-way repeated-measures ANOVAs were conducted for BCEAs, centroid coordinates, the length of the major and minor axes, and tilt angle for the three consecutive recording intervals 0 to 5 s, 5 to 10 s, and 10 to 15 s. The analysis showed that the BCEAs for the three consecutive 5-s intervals did not change over time, F(2, 150) = 0.4, P = .7, partial η2 = 0.005. These results are illustrated in Fig. 1A.
In addition, no significant differences in the horizontal, F(1.8, 137.6) = 1.0, P = .4, partial η2 = 0.01, or vertical, F(1.7, 125.2) = 0.09, P = .9, partial η2 = 0.001, coordinates of the ellipse’s centroid were found. Likewise, the ellipses’ major axis, F(2, 150) = 0.5, P = .6, partial η2 = 0.006, and minor axis, F(2, 150) = 0.3, P = .7, partial η2 = 0.01, did not differ. However, the ellipse’s tilt angle changed significantly over time, F(2, 150) = 4.9, P = .01, partial η2 = 0.6. Follow-up analysis showed a significant difference only between the ellipse’s tilt angle of the first (0–5 s) and last (10–15 s) 5-s intervals of fixation recordings (P = .005). The results are summarized in Table 2. An example of eye position traces during fixation and the scatter plots of the horizontal and vertical eye positions for different time intervals are shown in Fig. 2. Data shown here were collected from the left eye of an 88-year-old patient with AMD and a dense central scotoma and the PRL located at the border of scotoma, nasally on the retina.
Do These Results Hold True for Other Sampling Intervals?
We chose 5-s intervals because it provides a reasonable number of data points for calculating the BCEA (i.e. 125 data points). In this section, we re-examined whether the results reported above hold true for other sampling intervals. Because the MP-1 has a sampling rate of 25 Hz, we decided that any recording lasting less than 1 s would produce too few data points for stable analysis. We therefore did not test samples less than 1 s.
To examine whether fixation stability changes with the length of fixation recording, we tested samples lasting 1, 2, 3, 4, 5, 10, and 15 s and subjected them to Friedman’s nonparametric analysis of variance. The analysis yielded highly significant results, χ 2(6) = 205.4, P < .0001. Fig. 3 shows fixation stability gets significantly worse (i.e. the BCEA increases) as the length of the fixation recording increases.
We also tested 1-s samples starting at 0, 1, 2, 3, and 4 s and computed BCEAs for each one. As an additional test, and instead of testing each and every 1-s duration sample for the whole 15 s, we computed the last second of recording (14–15 s). The first thing to notice is the remarkable consistency in the values of the BCEA for each of the six 1-s sample durations (Fig. 1B). Analysis of variance showed no significant differences in BCEA among these 1-s samples, F(3.2, 237.8) = 1.2, P = .3, partial η2 = 0.02.
Fixation stability examination with the MP-1 for patients with central vision loss is important because it determines the location of the PRL on the retina and provides information about the precision of the ocular motor control when keeping the gaze steady on a target. The MP-1 manual recommends fixation stability recording for periods of 15 to 30 s, which is tiring and atypically long. This paper quantified fixation stability recorded over different intervals for a large sample of patients and found that, whereas the BCEA deteriorates with increasing recording time, it is constant over fixed recording intervals. These results suggest that the current recommendations for fixation stability recording with the MP-1 can be shortened to a less demanding duration (i.e. 5 s).
This study was designed to answer two questions. The first one asked whether fixation stability changes with increasing the duration of fixation. We compared the bivariate ellipses recorded for the first 5 s with that for the first 10 s and the first 15 s of fixation examination and found that BCEA deteriorates with increasing test duration by a factor of 1.4 and 1.6, respectively. These changes were driven by a rise in the ellipse’s minor axis length with increasing the duration of recording. Interestingly, the ellipse’s centroid (i.e. means of the horizontal and the vertical eye positions)—which determines the center location of the PRL—did not change for these intervals. When we examined fixation stability over more intervals, we found the same pattern of results: fixation stability worsens with increasing the length of fixation recording (see Fig. 2).
The second question of this study asked whether fixation stability changes over time. The relevant variable is the duration of the sampling interval, regardless of when after trial initiation it begins. For this, we examined the bivariate ellipses for three consecutive 5-s periods of the same fixation recording. We chose a 5-s—rather than, for example, 1-s—intervals because of the greater stability of measurement provided by the larger number of data points. We found that the bivariate ellipses for these equal periods were the same in terms of area, centroid location, and the length of the axes, but differed significantly in tilt angle. These findings are important for at least two reasons. First, these results show that fixation stability (quantified with BCEA) and the PRL location do not change over three consecutive 5-s periods, suggesting that no critical information will be lost if fixation examination is shortened to a 5-s interval. Second, these findings provide insight into why BCEA increases with the length of the recording. The possible explanations for this were (1) worsening of fixation stability over time (i.e. BCEAs for the three consecutive 5-s intervals get larger as shown schematically in Fig. 4A), (2) a shift in PRL location over time (i.e. the centroid of the bivariate ellipses for the fixed consecutive intervals are different as shown in Fig. 4B), (3) variation in the length of the ellipses’ axes for these fixed consecutive intervals (Fig. 4C), or (4) changes in ellipses’ tilt for these shorter intervals (Fig. 4D). Our results support the latter explanation. The result that fixation stability does not change for equal periods is also supported by our analysis for shorter (1-s) intervals. When we analyzed the bivariate ellipses for the first five consecutive 1-s intervals, and the last 1-s interval, we found no differences.
Changes in the angle of the ellipse reflect changes in eye position over time that maintain the sample’s average accuracy (i.e. the ellipse’s centroid stays the same). What determines the change in the angle of the ellipse? An explanation of these findings would probably require an analysis of the direction and amplitude of drifts and microsaccades, which the low sampling rate of the MP-1 does not permit. The short-term fatiguing of the oblique extraocular muscles could also manifest as a tilt of the fixation distributions, but this can only be evaluated using equipment with the capability for measuring torsional eye movements. The underlying mechanisms for these results remain an open question, but nevertheless, the findings reported here are in agreement with reports of the fixation stability of older observers with healthy vision. For example, Kosnik et al. recorded eye movements during fixation using an eye tracker and showed no change in BCEA over 15 trials of fixed duration16 but an increase in BCEA with increasing fixation duration.17
The data presented in this study were collected using one type of fixation target at the primary position of gaze, and conclusions are limited to fixation stability recorded under these conditions. Further data would need to be collected to determine whether using different fixation targets or moving the fixation target to secondary positions of gaze produce similar results.2 In addition, the conclusions of this study are pertinent to data recorded with the MP-1 at 25 Hz. Instruments such as eye trackers can record eye movements at higher sampling rates, and further studies will be required to examine changes in fixation stability over shorter intervals using such instruments.
In summary, this study shows that the BCEA deteriorates with increasing the duration of fixation recording, but when fixation is evaluated over shorter, 5-s intervals, only a difference in the ellipse’s tilt angle is found. Fixation stability recorded over periods of 5 s with the MP-1 is both comfortable for the patients and at the same time generates a reasonable number of data points so that the BCEA can be computed with confidence. We conclude that the information gained from longer fixation tests is probably not relevant to typical fixation stability conditions.
Esther G. González
Vision Science Research Program
Toronto Western Research Institute
399 Bathurst Street
FP 6-212 Toronto, ON
M5T 2S8 Canada
Received November 15, 2016; accepted September 30, 2016.
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Keywords:© 2017 American Academy of Optometry
central vision loss; fixation stability; fixation duration; PRL location; MP-1 microperimeter