A comparison of Goldmann III, V and spatially equated test stimuli in visual field testing: the importance of complete and partial spatial summation

Abstract

Purpose: Goldmann size V (GV) test stimuli are less variable with a greater dynamic range and have been proposed for measuring contrast sensitivity instead of size III (GIII). Since GIII and GV operate within partial summation, we hypothesise that actual GV (aGV) thresholds could predict GIII (pGIII) thresholds, facilitating comparisons between actual GIII (aGIII) thresholds with pGIII thresholds derived from smaller GV variances. We test the suitability of GV for detecting visual field (VF) loss in patients with early glaucoma, and examine eccentricity-dependent effects of number and depth of defects. We also hypothesise that stimuli operating within complete spatial summation ('spatially equated stimuli') would detect more and deeper defects.

Methods: Sixty normal subjects and 20 glaucoma patients underwent VF testing on the Humphrey Field Analyzer using GI-V sized stimuli on the 30-2 test grid in full threshold mode. Point-wise partial summation slope values were generated from GI-V thresholds, and we subsequently derived pGIII thresholds using aGV. Difference plots between actual GIII (aGIII) and pGIII thresholds were used to compare the amount of discordance. In glaucoma patients, the number of 'events' (points below the 95% lower limit of normal), defect depth and global indices were compared between stimuli.

Results: 90.5% of pGIII and aGIII points were within ±3 dB of each other in normal subjects. In the glaucoma cohort, there was less concordance (63.2% within ±3 dB), decreasing with increasing eccentricity. GIII found more defects compared to GV-derived thresholds, but only at outermost test locations. Greater defect depth was found using aGIII compared to aGV and pGIII, which increased with eccentricity. Global indices revealed more severe loss when using GIII compared to GV. Spatially equated stimuli detected the greatest number of 'events' and largest defect depth.

Conclusions: Whilst GV may be used to reliably predict GIII values in normal subjects, there was less concordance in glaucoma patients. Similarities in 'event' detection and defect depth in the central VF were consistent with the fact that GIII and GV operate within partial summation in this region. Eccentricity-dependent effects in 'events' and defect depth were congruent with changes in spatial summation across the VF and the increase in critical area with disease. The spatially equated test stimuli showed the greatest number of defective locations and larger sensitivity loss.

Keywords: Humphrey Visual Field Analyzer; Ricco's area; glaucoma; partial summation; perimetry; spatial summation.

Figure 1

Representative schematic of spatial summation functions for central (a) and peripheral (b) locations, adapted from Redmond et al., Kalloniatis and Khuu, and a subset of data from the present study. Error bars have been excluded from (a) and (b) for clarity. A representative normal subject is shown in black and a hypothetical patient with glaucoma is shown in red. The position of Ac is estimated by the point of inflection; the left slope of −1 indicates the region in which the stimulus is within complete spatial summation; and the right slope is the slope of partial summation, n2. Blue lines indicate the threshold elevation in glaucoma when using a stimulus within (dotted) and outside (solid) of the normal subject's Ac. At a central testing location (a), GIII and GV are outside of Ac for normal and disease subjects, and so threshold elevation is approximately equal, i.e. no discordance in detection of visual loss. In the periphery (b), GV is outside of Ac and GIII is at the border of Ac, which therefore allows the use of GV to predict GIII in normal subjects. However, GIII is within Ac in the patient with disease, and so threshold elevation using a GIII is larger than when using a GV stimulus, i.e. discordance in detection of visual loss. The predicted GIII value using GV and n2 also shows discordance with the actual GIII threshold elevation (dotted red line and asterisk). In (c), a representative spatial summation function for peripheral test location for normal subjects, similar to that presented in (b), with error bars is shown. The error bars delineate the 5th and 95th percentile of the normal distribution for each Goldmann size. The range of the 5th and 95th percentiles is largest with GI, and decreases with increasing stimulus size. In the present study, an ‘event’ is defined as an output threshold that lies outside the upper error bar (as the y-axis has been reversed), i.e. below the 95% lower threshold limit.

Figure 2

(a) A schematic of the rings within the 30-2 test pattern (right eye orientation) utilised for analysis, denoted by colour. The fovea is shown in the middle of the figure in black, and the two crossed out points indicate the blind spot locations. Here, the thicker black line denotes the limit of the 24-2 test pattern. (b) Difference between pGIII and aGIII (in dB) as a function of position on the spatial map for normal subjects. Each open circle represents a datum point from a subject at that spatial location. The two interruptions in the blue group of dots indicate the two blind spot test locations. A positive difference indicates a relatively higher pGIII, whilst a negative difference indicates a relatively higher aGIII. The black dotted lines indicate the limits of ±2 dB, and the grey solid lines indicate the limits of ±3 dB.

Figure 3

(a) Difference between pGIII and aGIII (in dB) as a function of position on the spatial map (as per Figure 2a) for glaucoma patients. Each open circle represents the result of an individual patient at that spatial location. For clarity in displaying the eccentricity effect, the spatial locations for the 30-2 have been separated into rings, denoted by different colours. A positive difference indicates a relatively higher pGIII, whilst a negative difference indicates a relatively higher aGIII. The black dotted lines indicate the limits of ±2 dB, and the grey solid lines indicate the limits of ±3 dB. In (b), the mean and 95% confidence intervals (error bars) of the magnitude of difference (dB) between aGIII and pGIII for points outside of ±3 dB only are plotted for normal subjects and glaucoma. The foveal point and innermost results, which had only three and five points outside of ±3 dB for normal subjects, are not shown for clarity. Asterisks indicate level of significance [p < 0.0001 (****)].

Figure 4

The magnitude of difference between pGIII and aGIII (in dB) for individual points at each eccentric location, divided by whether there was matching (both pGIII and aGIII flagging the point below the 95% lower limit of the normal cohort, i.e. ‘co-local’, black circles) or mismatching (either pGIII (‘missed’, red circles) or aGIII (‘extra points’, cyan circles) flagging the point). A positive difference indicates that pGIII had a higher sensitivity at that location, whilst a negative difference indicates that aGIII had a higher sensitivity. The black solid line indicates no difference (i.e. 0 dB), and the black dashed lines indicate ±3 dB. Solid lines represent the mean of the magnitude of difference within each group. As the direction has an effect on the comparative analysis between matched and mismatched groups, the absolute magnitude of the difference was used for comparison. Asterisks indicate the level of significance of the tests of multiple comparisons of the absolute differences [p < 0.05 (*), p < 0.001 (***), p < 0.0001 (****)].

Figure 5

The average proportion of points within glaucoma patients with a dB value below that of the lower limit of the 95% distribution of the normal cohort (‘events’) found using aGIII (black), aGV (red) and spatially equated (as per the test pattern of figure 1C in Kalloniatis & Khuu9) (grey) thresholds at each eccentric location. The numbers of events are expressed as proportion of the total number of test locations within each eccentricity as shown in the inset coloured schematic. The fovea proportions are not shown for clarity (p > 0.05). Asterisks indicate the level of significance of the tests of multiple comparisons [p < 0.05 (*), p < 0.001 (***) and p < 0.0001 (****)]. Error bars indicate 1 SEM.

Figure 6

(a) The magnitude of difference of aGIII (black), aGV (red) and spatially equated stimuli (blue) thresholds from the 95% lower limits of their respective normal cohort values (in dB) for individual points at each eccentric location. A negative difference indicates worse sensitivity. The black solid line indicates no difference (i.e. 0 dB), and the black dashed line indicates −3 dB. Solid lines represent the mean of the magnitude of difference within each group. (b) The mean difference in dB for aGIII, aGV and spatially equated stimuli from the lower limits of 95% distribution of their respective cohort values (in dB) at each location (fovea not shown for clarity). Asterisks indicate the level of significance [p < 0.05 (*), p < 0.01 (**), p < 0.001 (***), p < 0.0001 (****)]. The symbols indicate significant pairwise comparisons between the groups (†: significant difference between aGIII and spatially equated stimuli; ‡: significant difference between aGV and spatially equated stimuli; §: significant difference between aGIII and aGV). Error bars indicate the 95% confidence interval.

Figure 7

Relative frequency distributions of normal subjects (number of subjects, normalised within each test size) as a function of threshold (dB) for test sizes within a representative eccentric location (peripheral: yellow; and paracentral: red, in the inset graph). The ranges of threshold values along the x-axis for (a)–(b) and (c)–(e) have been equated to allow for better visual comparison of the width of the normative distributions. Frequency distributions have been fitted with Gaussian functions (all passed D'Agostino & Pearson normality test p > 0.05). The black dotted line in the middle of the function denotes the mean threshold, and the dotted line to the left indicates a threshold level 1.645 S.D. less than the mean (numerical value shown in brackets; for example: in (a), 4.48 dB indicates 1.645 times the S.D. (2.723 dB) away from the mean). For each stimulus location (a)–(b) for peripheral, and (c)–(e) for paracentral), coloured dashed lines and the above subject (S) number show the threshold values of representative glaucoma patients. Thus, coloured lines that are situated to the left of the 1.645 S.D. black dotted line indicate thresholds that are outside the approximate 95% normative distribution, i.e. detected as an ‘event’.