A Novel Distribution of Visual Field Test Points to Improve the Correlation between Structure–Function Measurements

Abstract

Purpose.: To create a new visual field (VF) test grid centered at the optic disc (disc-centered field [DCF]) and to infer the combination of VF test points (structure–function field [SFF]), taken from the DCF and the conventional fovea-centered 24-2 grid (24-2) of standard automated perimetry, which yields the strongest sectorial correlation between structure–function measurements of retinal nerve fiber layer (RNFL) thickness and VF sensitivity.

Methods.: In 50 eyes with ocular hypertension or open angle glaucoma, the DCF and 24-2 VF were measured with a Humphrey Field Analyzer II (Full Threshold strategy) and RNFL thickness was measured with Stratus optical coherence tomography. Test points from the DCF and 24-2 VF were combined and divided into 12 sectors according to the spatial distribution of the RNFL. A novel VF for structure–function studies was established using the following criteria: each sector must contain at least one or two test points (depending on the sector's location), and the combination of test points which yields the strongest structure–function correlation is selected.

Results.: The SFF consisted of 40 test points. The structure–function correlation for the SFF was compared with the standard 24-2 VF; a multiple-comparison test for dependent groups was carried out using a percentile bootstrap method, which indicated that the sector correlation coefficients in the SFF were significantly higher than those in the 24-2 VF.

Conclusions.: The SFF, with fewer test locations, has a stronger structure–function correlation than the 24-2 VF. This improved correlation may help clinicians to better interpret functional measurements in relation to structural measurements.

Introduction

Since the mid-1970s, static automated perimetry has been the foremost method of assessing visual function in patients with disorders of the retina, optic nerve, and brain. In particular, standard automated perimetry has become the gold standard method of visual field (VF) testing for the diagnosis and management of glaucoma. 

Garway-Heath et al. reported a retinotopic map (Garway-Heath map) in 2000. ¹ When the Garway-Heath map is considered, it is immediately apparent that, in relation to the retinal nerve fiber layer (RNFL) distribution, more sensitivity measurements are made in some retinal areas than others. In the fovea-centered 24-2 grid of standard automated perimetry (24-2 VF), test points are located at regular intervals of 6°, irrespective of the direction of the RNFL or the proportion of axons within an RNFL cross-section in each sector. As a result, there is an uneven test point distribution across 30° peripapillary RNFL sectors. To date, alternative test locations, other than those used in standard automated perimetry, have attracted limited study. ^2,3 Disproportionately sparse sampling of the VF may reduce the strength of the structure–function correlation in some sectors compared to its strength in others and distort summary estimates of damage. The latter arises because, when summary (average) structure and function measurements are used, the sectors with more VF test locations effectively result in a greater weight for that sector than for others. The first purpose of this study is to create a disc-centered-field (DCF) test grid which has an equal number of test points in all 30° RNFL sectors and investigate how this affects the structure–function relationship in each sector. 

The precise effects of the arrangement of test points on the structure–function correlation are yet to be established, although previous reports have shown that the detection rate of a glaucomatous VF defect is affected by the arrangement ⁴ and number ^3,5,6 of test points. The second purpose of this study is to determine the optimum number and arrangement of VF test locations, taken from the DCF and 24-2 VF, to provide the highest structure–function correlation at each sector. 

Methods

Participants and Tests

Fifty patients with glaucoma or ocular hypertension were recruited from the General Glaucoma Clinic, the Glaucoma Phenotyping Clinic, and the Ocular Hypertension Clinic at Moorfields Eye Hospital, London, United Kingdom, regardless of VF status on conventional perimetry. Both glaucomatous and ocular hypertensive patients were chosen in order to maximize the range of RNFL thickness (RNFLT) values. The inclusion criteria for ocular hypertension were as follows: at least 18 years of age, IOP of >22 millimeters of mercury (mm Hg) on two or more occasions, <30 mm Hg at time of imaging, and two previous documented, reliable VFs (see below). The inclusion criteria for glaucomatous eyes were IOP of <30 mm Hg at time of imaging and two previous documented, reliable VFs with glaucomatous VF defects. A glaucomatous VF defect was defined as three or more contiguous points at a P value of <0.05, 2 or more contiguous points at a P value of <0.01, a 10-decibel (dB) difference across the nasal horizontal midline at 2 or more adjacent points, or mean deviation (MD) worse than −5 dB. ⁷ The exclusion criteria were a history of diabetes, dementia, multiple sclerosis, or active ocular disease other than glaucoma, visual acuity of worse than 6/12, refractive error of more than ±6 diopters, and astigmatism of more than ±2 diopters. One eye of each of the fifty subjects was tested. This study was approved by the regional Ethics Committee, and all subjects were treated in accordance with the Declaration of Helsinki. 

Only one eye per subject was included in the study. When only one eye qualified for inclusion, that eye was used for the study. If both eyes qualified, one eye was randomly selected to be included in the study, using the “rand()” function in Microsoft Excel 2007 (Microsoft Corporation, Redmond, WA). 

A detailed medical and surgical history was taken. Slit-lamp biomicroscopy was performed, which included an evaluation of the cornea, anterior chamber, lens, and the anterior vitreous. In addition, gonioscopy was performed. Indirect fundus biomicroscopy was also carried out under mydriasis (tropicamide hydrochloride 1.0%) in order to check for signs of conditions, other than glaucoma, of the peripheral retina, macula, and optic nerve head. IOP measurements were obtained with a Goldmann applanation tonometer (Haag-Streit, Harlow, UK). 

Optical Coherence Tomography (OCT) Measurement

OCT scans were performed using a Stratus OCT (version 5.1; Carl Zeiss Meditec, Inc., Dublin, CA), employing the Peripapillary Scan and the RNFL Thickness 3.4 protocols. Three scans with a signal strength of equal to or better than 6 were taken. All scans included in our analysis were well centered on the optic nerve head. The RNFLT data, 1536 test points in total, were exported, and the mean RNFLTs for the three scans were calculated. 

VF Tests

Both tests were undertaken using the same device (Humphrey Field Analyzer [HFA] II 750, software version Rev.A10.2; Carl Zeiss Meditec, Inc.), with the Goldmann size III stimulus under standard perimetric conditions (background, 10 candela [cd]/m²) with the full-threshold strategy. Only the test locations were different for these two tests. 

24-2 VF Locations

24-2 VF measurements were recorded using an HFA II with the standard 24-2 test grid, with adjacent locations 6° apart. ⁸ A reliable VF was defined as a <15% false-positive (FP) rate and <25% fixation losses. ⁹  

DCF Measurement

The DCF was developed on the conventional HFA (HFA II 750, Custom mode). Briefly, from the system setup menu, we selected Additional Setup, then Custom Test, and then Create Threshold Test, and finally, the locations of the test points (x- and y-axis coordinates) were programmed. The DCF test is a full-threshold test similar to the 24-2 VF test except that the test locations differ between the two strategies. The number of test points across the DCF was chosen to distribute evenly over 12 optic disc sectors (30° in each sector; sector 1 corresponds to the area just above the papillomacular line, and subsequent sectors proceed superiorly, nasally, inferiorly, and then temporally), with four test points in each sector of the DCF. The coverage of the HFA's Custom mode is only 30° {calculated as the square root of [(x-axis eccentricity)² + (y-axis eccentricity)²]}. Within this area, the locations of the DCF points were chosen based upon the direction of the corresponding RNFL bundle (Fig. 1), using the results of a previous study which described the path of the main RNFL bundles in relation to the optic nerve head. ¹ An even spread of points across each sector was achieved according to the distance of each point from the blind spot and the magnitude of the angle of the RNFL branching from the optic disc. 

Figure 1. 

 

Mapping between the optic disc and VF. The optic disc was divided into twelve 30° sectors. A novel VF test grid was developed such that each of these 12 sectors contained four test points. This new VF is denoted as DCF. White dots: test points using 24-2 VF. Numbers in red: test points in the nasal area. Numbers in yellow: temporal area (DCF). Reprinted with permission from Garway-Heath DF, Poinoosawmy D, Fitzke FW, Hitchings RA. Mapping the visual field to the optic disc in normal tension glaucoma eyes. Ophthalmology. 2000;107:1809–1815. Copyright 2000 Elsevier.

The HFA Custom mode measurement does not measure fixation losses, FPs, or false negatives (FNs), and hence, fixation was monitored by the examiner (RA) throughout the test and was acceptable for all tests. Both the 24-2 VF and DCF tests were performed on the same visit with a rest period of at least 15 minutes between each test. The order of the two tests was randomized. Periodic short rest breaks during a test procedure were provided to patients as required. If a subject's left eye was tested, the recorded data were mapped to a right-eye format for analysis. 

In order to obtain an arithmetic average sensitivity for the sectorial and entire VF, sensitivity values at each test point were first converted from decibels to linear units (1/Lamberts) ¹¹ and then averaged in the linear domain before being converted back to a decibel value. 

Derivation of Test Points for the New Structure–Function Field (SFF)

The SFF was derived by first merging test points from the DCF and 24-2 VF test grid (48 points from the DCF and 52 points from the 24-2 VF, with three identical/overlapping test locations, to give a total of 97 unique test points) at each sector and then identifying the points which had the highest structure–function correlation, as outlined below. 

Sensitivity values from the 24-2 and the DCF were transformed to estimate underlying retinal ganglion cell (RGC) density (RGC/mm²), following the two-phase model described by Swanson et al., ¹⁰ since the structure–function relationship is nonlinear. ¹¹ For VF sensitivity of <31.25 dB, log RGC = (observed VF sensitivity [dB] − 16), and for VF sensitivity >31.25 (dB), log RGC = (observed VF sensitivity [dB] − 27.44) × 4. This transformation ensures that functional change is represented evenly from early- to advanced-stage disease. 

For each sector, Spearman's correlation coefficient between RNFLT measurements and the average RGC density was calculated for each of all possible “n choose k” (denoted ${(}_k^n)$) combinations of test points. In combinatorics, ${(}_k^n)$ is defined as the number of k-element subsets of an n-element set, that is, the number of different ways of choosing k elements from a set of n elements. For instance, in sector 5, there is a total of five test points (n = 5) in the combined VF and, therefore, a total of 31 different combinations, since there are (1 + 5 + 10 + 10 + 5) different combinations for “n choose k,” where k is equal to 5, 4, 3, 2, and 1, respectively. The distribution of test points for the SFF was selected to obtain the strongest structure–function correlation using the following criteria: each sector must contain at least one or two test points (depending on the location of the sector), and the combination of test points which yields the strongest structure–function correlation is selected. In the temporal sectors (sectors 1–4, 9, and 12), a minimum of two test points per sector was required. However, in the nasal sectors (sectors 5–8), only one test point per sector was required (as in the 24-2 VF). 

Comparison of Correlations for the SFF and 24-2 VF with RNFLT

Bootstrapping (10,000 samples) was carried out in order to calculate a 95% confidence interval (CI) for Spearman's r correlation coefficient for each sector of the 24-2 VF and SFF with RNFLT measurements. Bootstrapping offers a straightforward means to approximate a sampling distribution using only the observed data sample. Bootstrapping repeatedly samples with replacement from the original sample (until each resample is of equal size to the original observed sample). Hence, the original sample is used to approximate the population from which it was drawn. Furthermore, Spearman's correlation coefficients of the 24-2 VF and SFF with RNFLT measurements were compared using a paired test over all 11 sectors present in both the 24-2 VF and SFF. Specifically, the marginal distributions were compared with an M-estimator using a percentile bootstrap method (taking 10,000 bootstrap samples from the 50 patients); the method employs a bias adjustment to account for the dependent groups. ¹² The R function “rmmcppb” from the R package “WRS” was used to carry out this statistical test. ¹²  

For comparison, we also calculated the structure–function correlation for the combination of test points having the weakest structure–function correlation. We followed the same approach to finding the SFF but instead sought the selection of test points which had the lowest correlation with RNFLT measurements. 

Statistical analyses were performed with Medcalc version 9.3.8.0 for Windows (MedCalc Statistical Software, Mariakerke, Belgium) and the statistical programming language R (version 2.15.1; The R Foundation for Statistical Computing, Vienna, Austria). 

Results

Subject characteristics are given in Table 1. 

Table 1. 

 

Subject Demographics

Parameter	Value
Age, y [mean ± standard deviation (range)]	66.9 ± 11.9 (88–38)
Mean deviation, dB [mean ± standard deviation (range)]	−9.4 ± 7.0 (−25.6–1.6)
Male/female	36:14
Ratio of right/left eyes	1.26
No. of eyes with glaucoma	42
No. with primary open angle glaucoma	35
No. with normal tension glaucoma	4
No. with pseudoexfoliation glaucoma	3
No. of eyes with ocular hypertension	8
RNFLT, μm [mean ± standard deviation (range)]	61.4 ± 16.0 (18.4–104.7)

 Age, mean deviation, and RNFLT are described as mean ± standard deviation, with range shown in parentheses.

The test locations for the DCF are shown in Figure 1. Table 2 gives the number of VF test locations for each RNFL sector for the 24-2 field and the DCF and the test location coordinates for the DCF. The 24-2 field contains more test points than the DCF in RNFL sectors 3, 4, 9, and 10 and fewer points in sectors 1, 5, 6, 7, 8, 11, and 12. Both the 24-2 field and the DCF contain four test points in sector 4. Notably, the 24-2 field includes no test points corresponding to sector 12. 

Table 2. 

 

Comparison of Number of Test Points in Each Sector between 24-2 and DCF and the Coordinates of Test Points Using DCF

Sector	No. of Test Points in:		Coordinates Using DCF
	24-2 VF	DCF
1	2	4	(5, −1), (6, −3), (10, −1), (11, −3)
2	4	4	(10, −7), (1, −9), (−1, −5), (−9, −3)
3	11	4	(6, −12), (−2, −16), (−11, −12), (−15, −6)
4	7	4	(11, −15), (14, −10), (15, −15), (16, −10)
5	1	4	(19, −9), (21, −8), (20, −14), (23, −13)
6	1	4	(21, −4), (22, −2), (27, −9), (29, −4)
7	1	4	(22, 2), (21, 4), (27, 9), (29, 4)
8	1	4	(21, 8), (19, 9), (23, 13), (20, 14)
9	8	4	(14, 10), (16, 10), (14, 15), (16, 15)
10	13	4	(5, 12), (−4, 13), (−7, 6), (−14, 10)
11	3	4	(−1, 4), (3, 5), (6, 4), (9, 3)
12	0	4	(0, 1), (4, 1), (8, 1), (11, 1)
Total	52	48

 The coordinates are written as (x-axis coordinate, y-axis coordinate) as used in the 24-2 VF.

A comparison of sector and global sensitivity values for the 24-2 field and the DCF is given in Table 3. The average global sensitivity values for the 24-2 field and the DCF were similar. No significant difference was observed in mean sensitivity between the 24-2 field and the DCF at any sector or whole field (P < 0.05, Mann-Whitney test). 

Table 3. 

 

Comparison of Average Sensitivity (Arithmetic Mean) between 24-2 VF and DCF in Each Sector and Whole Field (Paired t-Test)

Sector	24-2 VF (dB)	DCF (dB)	P Value
1	28.0 ± 5.5 (0.0–33.1)	27.7 ± 5.5 (4.4–33.5)	0.16
2	24.9 ± 8.6 (0.0–33.1)	24.1 ± 9.2 (0.0–33.5)	0.60
3	22.4 ± 8.0 (0.0–31.4)	21.6 ± 9.4 (0.0–31.8)	0.91
4	23.0 ± 7.6 (0.0–31.1)	24.1 ± 7.6 (0.0–31.0)	0.11
5	23.3 ± 8.6 (0.0–31.0)	23.5 ± 7.5 (0.0–31.0)	0.64
6	24.9 ± 6.8 (0.0–31.0)	24.7 ± 6.2 (0.0–31.7)	0.55
7	23.5 ± 7.2 (0.0–31.0)	23.3 ± 7.2 (0.0–30.4)	0.79
8	21.1 ± 8.7 (0.0–32.0)	21.1 ± 8.6 (0.0–29.2)	0.93
9	18.0 ± 8.6 (0.0–30.0)	19.3 ± 8.7 (0.0–29.9)	0.33
10	18.3 ± 1.0 (0.0–30.6)	17.1 ± 1.1 (0.0–30.2)	0.65
11	23.9 ± 9.1 (0.0–33.1)	22.4 ± 9.7 (0.0–33.3)	0.29
12	NA	27.9 ± 3.3 (20.1–30.4)	NA
Total	25.5 ± 3.9 (11.2–30.9)	25.8 ± 3.3 (16.5–31.4)	0.98

 Data are described as the mean value ± standard deviation, with range shown in parentheses. NA, not applicable.

Table 4 shows Spearman's r values between RNFLT and arithmetic mean sensitivity. The correlation coefficients were significant (P < 0.05) at all sectors and the whole field with both the 24-2 field and the DCF. In general, the correlation coefficients were similar between the 24-2 VF and DCF, as indicated by overlapping 95% CIs of the correlation coefficients for the 24-2 VF and the DCF. There was no relationship between the strength of the structure–function correlation and the number of VF test locations in each sector. 

Table 4. 

 

Spearman's Correlation Coefficient Values between RNFLT (Measured by OCT) and Arithmetic Mean of the Visual Field Sensitivity in the 24-2 Visual Field and the DCF

Sector	24-2 VF			DCF
	r	P Value	CI	r	P Value	CI
1	0.42	<0.01	0.16 to 0.62	0.29	0.044	0.01 to 0.52
2	0.57	<0.01	0.35 to 0.73	0.56	<0.01	0.33 to 0.73
3	0.58	<0.01	0.36 to 0.74	0.61	<0.01	0.39 to 0.76
4	0.56	<0.01	0.33 to 0.72	0.44	<0.01	0.18 to 0.64
5	0.33	0.018	0.06 to 0.56	0.50	<0.01	0.26 to 0.69
6	0.44	<0.01	0.19 to 0.64	0.45	<0.01	0.19 to 0.64
7	0.33	0.019	0.06 to 0.56	0.34	0.016	0.07 to 0.56
8	0.49	<0.01	0.24 to 0.67	0.53	<0.01	0.29 to 0.70
9	0.66	<0.01	0.46 to 0.79	0.63	<0.01	0.43 to 0.77
10	0.86	<0.01	0.76 to 0.92	0.85	<0.01	0.75 to 0.91
11	0.79	<0.01	0.65 to 0.87	0.73	<0.01	0.57 to 0.84
12	NA			0.52	<0.01	0.29 to 0.70
Whole field	0.67	<0.01	0.49 to 0.80	0.70	<0.01	0.53 to 0.88

 Data are described as the r value and P value of Spearman's correlation coefficient and the 95% CI of the r value.

The locations of test points in the SFF (totaling 40) are illustrated in Figure 2. The SFF grid was markedly different from the 24-2 VF grid, with a less regular spacing, and the numbers of test points within the temporal sectors (sectors 1–4 and 9–12) of the SFF tended to be considerably fewer than the numbers in the 24-2 VF. Bootstrap analysis suggested that there was a significant structure–function correlation for each of the 12 sectors, since no CI spanned zero (Fig. 3). The correlation coefficients for the SFF and 24-2 VF are presented in Table 5. 

Figure 2. 

 

Locations of the 40 test points in the SFF. Blue circles: 24-2 VF test points. Red circles: DCF test points. Coordinates (x-axis coordinate, y-axis coordinate) of SFF test points: sector 1, (3, −3), (9, −3); sector 2, (3, −9), (−1, −5); sector 3, (3, −15), (−3, −15), (9, −9), (−9, −15); sector 4, (9, −21), (3, −21), (−3, −21); sector 5, (19, −9), (21, −8); sector 6, (21, −3), (22, −2), (29, −4); sector 7, (21, 3), (22, 2), (21, 4), (27, 9); sector 8, (19, 9), (23, 13), (20, 14); sector 9, (3, 21), (9, 15), (−9, 21), (15, 15), (14, 10), (16, 15); sector 10, (9, 9), (3, 9), (−3, 9), (−3, 15), (−21, 3); sector 11, (3, 3), (−3, 3), (3, 5), (−1, 4); sector 12, (4, 1), (8, 1).

Figure 3. 

 

Means and 95% CIs, derived from bootstrapping, of sectorial correlation coefficients in the SFF.

Table 5. 

 

Spearman's Correlation Coefficient and P Value between RNFLT Measurements and the Estimated RGC Density in the SFF and 24-2 VF

Sector	SFF			24-2 VF
	r	P Value	CI	r	P Value	CI
1	0.40	<0.01	0.14 to 0.63	0.40	<0.01	0.14 to 0.61
2	0.66	<0.01	0.45 to 0.81	0.52	<0.01	0.28 to 0.69
3	0.67	<0.01	0.49 to 0.79	0.57	<0.01	0.35 to 0.74
4	0.59	<0.01	0.39 to 0.73	0.56	<0.01	0.33 to 0.72
5	0.53	<0.01	0.31 to 0.69	0.33	0.018	0.06 to 0.56
6	0.49	<0.01	0.21 to 0.70	0.44	<0.01	0.19 to 0.64
7	0.39	<0.01	0.11 to 0.62	0.33	0.019	0.06 to 0.56
8	0.54	<0.01	0.34 to 0.69	0.49	<0.01	0.24 to 0.67
9	0.70	<0.01	0.53 to 0.80	0.66	<0.01	0.46 to 0.79
10	0.88	<0.01	0.77 to 0.93	0.86	<0.01	0.76 to 0.92
11	0.80	<0.01	0.68 to 0.87	0.78	<0.01	0.65 to 0.87
12	0.61	<0.01	0.41 to 0.76	NA
Whole field	0.67	<0.01	0.51 to 0.81	0.64	<0.01	0.49 to 0.80

The test points with the weakest structure–function correlation (totaling 39 points) are shown in Figure 4. The test points tend to be more in the periphery and upper hemifield and adjacent to the optic nerve head than in the 24-2 VF and SFF. Furthermore, as shown in Figure 5, there is a tendency for test points that contribute less to the structure–function correlation to lie on the same retinal nerve fiber bundle as other points, in contrast to those in the SFF. 

Figure 4. 

 

Locations of the 39 test points with the weakest structure–function relationship. Blue circles: 24-2 VF test points. Red circles: DCF test points. Coordinates (x-axis coordinate, y-axis coordinate [as used in 24-2 field]) of test points: sector 1, (11, −3), (10, −1); sector 2, (−3, −3), (−3, −9); sector 3, (−15, −3), (−21, −3), (−21, −9), (−27, −3); sector 4, (15, −9), (11, −15), (14, −10); sector 5, (21, −9), (23, −13); sector 6, (21, −3), (21, −4), (22, −2); sector 7, (22, 2), (21, 4), (27, 9), (29, 4); sector 8, (21, 9), (21, 8), (23, 13); sector 9, (9, 21), (3, 21), (−3, 21), (−15, 15), (16, 10), (14, 15); sector 10, (9, 9), (3, 15), (−3, 15), (5, 12), (−4, 13); sector 11, (3, 3), (9, 3), (6, 4); sector 12, (11, 1), (0, 1). Spearman's correlation coefficients between the fraction of observed-to-normal RGC density and the RNFLT were as follows: sector 1, 0.17 (P = 0.24); sector 2, 0.46 (P < 0.01); sector 3, 0.40 (P < 0.01); sector 4, 0.46 (P < 0.01); sector 5, 0.36 (P < 0.01); sector 6, 0.40 (P < 0.01); sector 7, 0.35 (P = 0.014); sector 8, 0.48 (P < 0.01); sector 9, 0.62 (P < 0.01); sector 10, 0.82 (P < 0.01); sector 11, 0.65 (P < 0.01); sector 12, 0.39 (P < 0.01), whole field, 0.56 (P < 0.01).

Figure 5. 

 

The relationship between the test points with the weakest structure–function test grid and the RNFL. Test points were superimposed on a retinal photograph; test points of the same color (except black) lie on the same or closely adjacent retinal nerve fiber bundles. The retinal photograph is reprinted with permission from Garway-Heath DF, Poinoosawmy D, Fitzke FW, Hitchings RA. Mapping the visual field to the optic disc in normal tension glaucoma eyes. Ophthalmology. 2000;107:1809–1815. Copyright 2000 Elsevier.

The bias-adjusted percentile bootstrap method detailed in Methods suggested that the sector correlation coefficients with the SFF were significantly higher than those for the 24-2 field for all sectors (P < 0.005). 

Discussion

In the first part of this study, the correlation between structure (RNFLT) and function was evaluated for the conventional 24-2 VF and a newly developed DCF, with four test points in each 30° disc sector. Test points of the 24-2 VF cover the VF at regular intervals of 6°. However, there is little correspondence between the distribution of test points in the 24-2 VF and the distribution of the retinal nerve fibers. The streams of nerve fibers are arcuate and dense in the central area of the retina, while in the retina nasal to the optic disc, nerve fibers are straighter and less dense. The DCF was created so that there was a more even distribution of VF test locations across 30° RNFL sectors. In the second part of this study, a novel VF test grid was established, referred to as the SFF, which has a stronger structure–function correlation at each sector than the conventional 24-2 VF or DCF. Bootstrapping was carried out to evaluate the reliability of the structure–function correlation in samples from the same population as the test sample, and this analysis suggested that all correlation values were significant. 

For both the 24-2 VF and the DCF, the strongest correlation between structure and function was found in the inferotemporal sector (sector 10), with r values of 0.86 (24-2 field, 13 VF locations) and 0.85 (DCF, 4 VF locations). Previous studies have reported strong relationships in the superotemporal and inferotemporal sectors, with r values between 0.61 and 0.72, ^13–16 which may be sites for early glaucomatous damage. A possible explanation for the increased correlation in these regions is a wide range of threshold values, from healthy to damaged, which influences the size of the correlation coefficients. ^13,17,18 Furthermore, in the central VF, the structure–function slope is shallower than in the periphery, when function is measured in decibels of light sensitivity. ¹⁰ Lower structure–function correlation values may be due to the low precision of VF sensitivity estimates (used to predict RGC number) in the central VF; this is because the same perimetric staircase step size is used across the VF and is likely to result in less precise estimation of RGC numbers where the structure–function slope is shallow (central) than where it is steep (peripherally). These studies support the finding that the structure–function correlation varies according to the region of the retina being tested. ^13,17,18  

Importantly, the current study highlights the fact that the number of test points across 24-2 VF regions that relate equal-sized RNFL sectors at the optic nerve head varies greatly. Notably, the 24-2 VF contains more than 10 points in the superotemporal and inferotemporal sectors (sectors 3 and 10). In the DCF, these sectors contain only four test points, and yet, the structure–function correlation coefficients are similar (the same in sector 10 and slightly higher for the DCF in sector 3). In the 24-2 VF, the four nasal sectors (sectors 5–8) are represented by only one test location in each sector, whereas the DCF has four test locations in each sector. Surprisingly, the R values for these nasal sectors are similar for the 24-2 VF and the DCF, despite the sampling difference. These findings suggest that increasing the number of test points in any given sector does not necessarily improve the strength of the structure–function correlation. Notably, it seems that fewer test locations than are present in the 24-2 VF may be needed to achieve an equivalent strength of structure–function association; this is supported by the findings for the SFF. Fewer locations tested would result in a shorter test and less fatigue and, consequently, more reliable performance. ^19–21  

The test points in the VF with the weakest structure–function correlation tended to be located around the blind spot or in the periphery and upper hemifield. We hypothesize that this result is due to higher measurement variability in these areas; it has been reported that test-to-test reproducibility decreases with increasing eccentricity, ²² and short-term fluctuation also increases around the blind spot. ²³  

Few studies have analyzed where the test points should be and how many should be present in a VF. Krakau et al. reported that reducing the number of test points in a computerized VF analysis did not necessarily impair the detectability of an early glaucomatous VF defect. ⁵ Also, Zeyen et al. evaluated the relationship between the number of test points in Octopus perimetry and diagnostic precision; they reported that there is a steep ascending portion of the curve in which diagnostic precision increases rapidly with the number of points tested (between 1 and 16 test points). ⁶ The study showed that a diagnostic precision of 82% was achieved if a set of 16 specific points was tested, and the precision increased by only 8% (to 90%) if a further 16 points were tested. In fact, they also estimated that diagnostic precision was reduced by just 3% to 4% by reducing the number of test points from 52 (as in the conventional 24-2 field) to 36. A similar result was shown in another report. ³ The present study goes further and identifies the best location for the test points. 

Comparing the SFF and 24-2 VF, it is apparent that correlation values tended to be higher in the SFF in all sectors (Table 5). It is important to note that the particular combination of test points is crucial to obtain a strong structure–function correlation; if new test points were added in random locations there might be no benefit to the structure–function correlation. For example, in sectors 3 and 10 of the 24-2 field, many test points are set in the Bjerum area and possibly correspond to the same or nearby nerve fiber bundles. In the nasal area of the VF (sectors 2–4 and 9–11), it is clear that the density of test points is higher when using the 24-2 VF than the SFF; these locations, although anatomically the same distance apart as elsewhere in the VF, tend to be closer functionally. ²⁴ Conversely, in the SFF, the points tend to be further from neighbors with a high functional correlation (although adjacent points exist in sectors 7 and 9). Supporting this, the test points in the VF with the weakest structure–function correlation appear to lie in the same or on adjacent nerve fiber bundles. This may be important for the diagnostic performance of the SFF, since Zeyen et al. showed that the removal of neighboring VF points, particularly points on the same retinal nerve fiber stream, did not reduce the detectability of a glaucomatous VF defect. ⁶  

In the SFF, test points are fairly evenly distributed across all sectors (between two and five points per sector). However, the numbers of test points in the 24-2 VF vary dramatically between sectors (between 0 and 13 points per sector). A number of previous reports have suggested that the entire VF should be sampled more completely, since the temporal area of the VF can be preferentially damaged by glaucoma in some eyes, ^25–30 particularly in patients with myopia. ^30–32 The 24-2 VF largely ignores the temporal field and concentrates almost entirely on the region nasal to the optic disc. However, it has been reported that in early disease, deformation of the optic nerve head occurs in all four quadrants, ³³ suggesting that corresponding functional damage may be missed if temporal regions of the VF are not tested. In addition, the VF region corresponding to sector 12 is not measured in the 24-2 VF. However, the newly created DCF enabled the measurement of sensitivity in this region. 

The SFF was derived from the results of the 24-2 VF and DCF, and hence, an actual measurement using the SFF grid was not carried out in the current study; this is a future work to be performed. However, the test time is expected to be comparable to or less than (which is more likely) that of the 24-2 VF, since the most important factor in full-threshold testing is the number of test points. 

A weakness of our study was that the FP and FN rates were not monitored in the DCF test, as the “custom” test mode does not allow FP/FN presentations. Fixation, though, was monitored using the eye tracker. As all participants were reliable VF takers, having performed at least two tests with low FP (<15%) and FN (<25%) rates before taking part in the study, this is not expected to have much effect on the results of our study. Furthermore, there is a report which showed that mean deviation is the most important factor explaining test–retest variability and that the reliability indices added remarkably little. ³⁴ In addition, as the order of the 24-2 and DCF tests was randomized, we expect overall FP and FN rates to be balanced across the two tests being evaluated. 

The correlation between structure and functional measures has been used as an endpoint for this study for consistency with other previous studies. ^35–37 However, an improved correlation for the DCF does not necessarily translate to an improved ability to detect glaucomatous loss compared to the use of the 24-2 grid, and this latter outcome will be the subject of future comparison between the two tests. 

An alternative approach to using the path of RNFL bundles to estimate test locations would be to distribute locations within the test grid based on estimates of RGC density within the retina, with sparser sampling of regions of low RGC density. Recently, with the development of Fourier domain OCT, it has become possible to measure the RGC layer thickness in the macula. Future research investigating a structure–function map based on RGC thickness, with the adjustment for the displacement between RGC and photoreceptor rather than RNFL bundle directions, would be very interesting. ^38,39 The advantage of using bundle distribution is that glaucoma damage follows the distribution of the RNFL and, in considering bundle distribution, some anatomical redundancy in the number of test locations may be addressed. The advantage of using the RGC thickness would be to better match the sampling density of the VF test to the RGC density. A way of combining these two concepts would be to adjust the number of VF test points in each sector according to the number of RGC axons in the sector and adjust the retinal location of the test points according to local RGC density. 

Another potential weakness of the methods is that an average path of RNFL bundles has been used to derive the test locations for this study. The exact path of RNFL bundles in each eye is expected to vary with factors such as axial length, optic nerve tilt, and the distance between the optic disc and fovea. A set of customized locations for a given eye based on such factors may further improve the structure–function correlation. 

In conclusion, the SFF has a stronger structure–function correlation than the 24-2 VF and achieves this with considerably fewer test points. 

Footnotes

 Supported by the Japan Society for the Promotion of Science (RA) and by the Department of Health's National Institute for Health Research (NIHR) Biomedical Research Centre at Moorfields Eye Hospital National Health Service (NHS) Foundation Trust and the University College London (UCL) Institute of Ophthalmology (RAR, RM, and DFG-H). The views expressed in this publication are those of the authors and not necessarily those of the Department of Health. DFG-H's chair at UCL is supported by funding from the International Glaucoma Association.

Footnotes

 Disclosure: R. Asaoka, None; R.A. Russell, None; R. Malik, None; D.P. Crabb, None; D.F. Garway-Heath, None