May 2014
Volume 55, Issue 5
Free
Glaucoma  |   May 2014
Customized, Automated Stimulus Location Choice for Assessment of Visual Field Defects
Author Affiliations & Notes
  • Luke X. Chong
    Department of Optometry and Vision Sciences, The University of Melbourne, Australia
  • Allison M. McKendrick
    Department of Optometry and Vision Sciences, The University of Melbourne, Australia
  • Shonraj B. Ganeshrao
    Department of Optometry and Vision Sciences, The University of Melbourne, Australia
    Department of Computing and Information Systems, The University of Melbourne, Australia
  • Andrew Turpin
    Department of Computing and Information Systems, The University of Melbourne, Australia
  • Correspondence: Andrew Turpin, Department of Computing and Information Systems, The University of Melbourne, Melbourne, Victoria, Australia; aturpin@unimelb.edu.au
Investigative Ophthalmology & Visual Science May 2014, Vol.55, 3265-3274. doi:10.1167/iovs.13-13761
  • Views
  • PDF
  • Share
  • Tools
    • Alerts
      ×
      This feature is available to authenticated users only.
      Sign In or Create an Account ×
    • Get Citation

      Luke X. Chong, Allison M. McKendrick, Shonraj B. Ganeshrao, Andrew Turpin; Customized, Automated Stimulus Location Choice for Assessment of Visual Field Defects. Invest. Ophthalmol. Vis. Sci. 2014;55(5):3265-3274. doi: 10.1167/iovs.13-13761.

      Download citation file:


      © ARVO (1962-2015); The Authors (2016-present)

      ×
  • Supplements
Abstract

Purpose.: To introduce a perimetric algorithm (gradient-oriented automated natural neighbor approach [GOANNA]) that automatically chooses spatial test locations to improve characterization of visual field (VF) loss without increasing test times.

Methods.: Computer simulations were undertaken to assess the performance of GOANNA. GOANNA was run on a 3° grid of 150 locations, and was compared with a zippy estimation by sequential testing (ZEST) thresholding strategy for locations in the 24-2 test pattern, with the remaining 98 locations being interpolated. Simulations were seeded using empirical data from 23 eyes with glaucoma that were measured at all 150 locations. The performance of the procedures was assessed by comparing the output thresholds to the input thresholds (accuracy and precision) and by evaluating the number of presentations required for the procedure to terminate (efficiency).

Results.: When collated across whole-fields, there was no significant difference in accuracy, precision, or efficiency between GOANNA and ZEST. However, GOANNA targeted presentations on scotoma borders; hence it was more precise and accurate at locations where the sensitivity gradient within the VF was high.

Conclusions.: Compared with ZEST, GOANNA was marginally less precise in areas of the VF that had spatially uniform sensitivity, but improved accuracy and precision in regions surrounding scotoma edges. GOANNA provides a principled framework for automatic placement of additional test locations to provide spatially denser testing around the borders of VF loss.

Introduction
The spatial resolution in the commonly used 24-2 and 30-2 programs of the Humphrey field analyzer (HFA; Zeiss Humphrey Systems, Dublin, CA, USA) is restricted to an equally spaced 6° × 6° rectangular grid. However, previous research has demonstrated that a 6° × 6° rectangular grid is too coarse to detect subtle defects and has limited ability to detect small spatial changes in subsequent tests. 15 Condensed grids with higher spatial resolution are able to identify scotomata beyond the resolution of conventional perimetry. 19 These discoveries suggest that the spatial resolution of conventional perimetry is not high enough to detect early glaucomatous change. 
Approaches to increase the spatial resolution of visual field (VF) tests have been examined in the past, 35,816 but have not been suitable for clinical application. Haeberlin and colleagues 15 reported a procedure called the Spatially Adaptive Program (SAPRO), which tested locations at resolutions of 3.2°, 1.6°, and 0.8°. 14,17,18 It was recognized that the long test duration of SAPRO was a major limitation of this procedure, where 236 presentations were required to examine a 15° field with a 3.2° grid. 14 More recently, scotoma-oriented perimetry (SCOPE) 5,11 and fundus-oriented perimetry (FOP) 4,16,19,20 have been reported, which involve a clinician selecting more points to test within a region of interest. A procedure that automatically adds a fixed number of locations for further testing to a completed 24-2 pattern by computing the gradient between previously tested locations has also been proposed recently (Aoyama K, et al. IOVS 2013;54:ARVO Abstract 3914). 
The aim of this study was to develop an automated approach to choose spatial test locations in order to improve characterization of VF loss without increasing test times. The resulting approach is a novel perimetric procedure, the gradient-oriented automated natural neighbor approach (GOANNA). GOANNA begins with a pool of possible test locations, and autonomously selects stimulus locations during a VF test. The locations are chosen so regions surrounding scotoma borders receive increased spatial resolution, without increasing test times over those procedures that use a fixed pattern of locations like the zippy estimation by sequential testing (ZEST). 2123  
ZEST was chosen as our baseline as it has been shown to perform better than Swedish interactive threshold algorithms (SITA) and full threshold in terms of accuracy and precision of sensitivity estimates. 23 It displays reduced test–retest variability compared with full threshold, particularly when the initial estimates used by the procedures are remote from the true threshold for the location (e.g., at scotomata edges). 23,24 Furthermore, the mechanics of SITA are not available in the public domain, making comparisons using simulation impossible. 
The aim of GOANNA is to improve precision (degree of test–retest variability) and accuracy (true threshold less measured threshold) of threshold estimates, while maintaining efficiency (number of presentations) compared with current approaches. These procedures were tested through computer simulations seeded with fields prospectively collected on a 3° grid covering the central 21° of vision with exception to the nasal region, which extended out to 27°; twice the resolution of conventional perimetry. 
Methods
Computer Simulation Overview
Simulation allows thousands of threshold estimates to be obtained rapidly and has been used previously to evaluate clinical test algorithms prior to clinical application. 21,2528 A key advantage of simulation over clinical studies is that the true threshold is known, and sources of measurement error can be introduced at a desired rate, hence their effects on individual test procedures can be studied. 
Test procedures are run with a simulated patient responding as if the input thresholds were the patient's true threshold, incorporating responses based on the modelled patient's frequency of seeing (FOS) curve and predetermined rate of false-negative (FN) and false-positive (FP) responses. A typical FP response error profile (15% FP, 3% FN) was investigated, which has been used previously. 29 Reliable (0% FP, FN), typical false negative (3% FP, 15% FN) and unreliable (20% FP, 20% FN) conditions were also fully explored, and are included in a supplementary section. The slope of the FOS curve for a given threshold was modelled as the SD of a cumulative Gaussian distribution determined in accordance to published variability formulae, 30 capped to a maximum of 6 dB. This was achieved using the “SimHenson” mode of the open perimetry interface (OPI). 31  
The performance of procedures was assessed by the differences between output and input thresholds (median for accuracy, interquartile range for precision) and by comparing the number of presentations required for the procedure to terminate (efficiency). Simulations were run 50 times on each of the 23 fields, resulting in 1150 trials. 
Input Visual Fields
In order to test algorithm performance on fields with dense spatial locations, empirical data was collected on a 3° grid of 150 locations on an Octopus 900 (Haag Streit AG, Koeniz, Switzerland) perimeter. The Octopus dB scale is defined as Display FormulaImage not available , where Display FormulaImage not available is the maximum stimulus luminance and Display FormulaImage not available is the stimulus luminance. We set the background intensity at 10 cd/m2 (31.4 apostilbs [asb]) with the maximum stimulus intensity being 1273 cd/m2 (4000 asb). A Goldmann Size III target was used. The ZEST test strategy with uniform prior probability mass functions (PMFs) was used to measure sensitivity at each location (Refer to Test Procedures section for a detailed description of ZEST). In order to get a relatively unbiased estimate of the spatial characteristics of the VFs, uniform priors were used (where each possible threshold is initially considered equally probable for the location being tested). Nonuniform priors used in clinical procedures speed up tests, but show bias toward the most-likely thresholds in the assumed threshold distribution.32 Because testing with uniform priors requires more presentations than typical clinical procedures (but results in better accuracy), testing was split into eight separate tests, with each partial test completing around 20 locations across the whole field in approximately 6 minutes. Short breaks were provided between each partial test. The OPI31 was used to run the procedure.  
Twenty-three clinically diagnosed glaucoma participants were tested. A histogram of the input sensitivities from these 23 fields (3450 locations in total) can be seen in Figure 1. Participants with visual acuity less than 6/9, refractive error greater than ±6 diopters (D; spherical equivalent), migraine, diabetes, tilted optic discs, or any other optic disc abnormalities or ocular diseases other than glaucoma were excluded. For each participant, a single eye was tested; if both eyes satisfied the criteria then one eye was chosen at random. 
Figure 1
 
Histogram of input sensitivities of the 23 input fields used in the simulations.
Figure 1
 
Histogram of input sensitivities of the 23 input fields used in the simulations.
Twenty-one participants had their VF measured twice on separate days, and two participants were measured once. The fields used as input for the simulation were the average of the two fields taken, all converted to right eye format. 
The Ocular Hypertension Treatment Study scotoma classification system 33 was used to classify the scotoma patterns observed in our sample: three altitudinal, two partial peripheral rim, six widespread loss, two superior depression, five arcuate, one inferior depression, and four nasal step defects. 
The data collection followed the tenets of the Declaration of Helsinki and written informed consent was obtained from the subjects after explanation of the nature and possible consequences of the study. Human research ethics approval for the study was obtained from the University of Melbourne Human Research Ethics Committee. 
Test Procedures
ZEST Algorithm.
The ZEST implementation used for the simulations was performed using the OPI. 31 The ZEST procedure is based on a maximum-likelihood determination described previously in the literature. 21,34 At each tested location, a PMF over the domain −5 to 40 dB is chosen as a prior, and the mean of the prior PMF is presented. Depending upon the patient's response, a likelihood function (which represents the likelihood of patient seeing a stimulus) is multiplied with the prior PMF to generate a new PMF. The likelihood function used in these simulations is the same as in previous studies. 23 The mean of the new PMF is then presented for the next response. This process continues until the SD of the PMF is less than 1.5 dB. The mean of final PMF upon termination is taken as the output threshold. 
In this study, the prior PMF at each location was either uniform, where all probabilities are the same, or bimodal, with one peak at 0 dB modelling thresholds of damaged locations, and a second peak at M dB, where M varies for each location. 22,23,34 We adopted the approach of the Humphrey Field Analyzer 24-2 “growth pattern” for choosing M. 35 With this approach, four primary locations (±9°, ±9°) have M set to 26 dB. Once the final thresholds are determined for these locations, the immediate neighbors set their M value to the value of the primary location. After these 24 locations terminate, their immediate neighbors take their M values as the mean of their neighbors, and so on. 
GOANNA Algorithm.
Unlike conventional test patterns and our ZEST implementation, GOANNA contains a pool of potential test locations, some of which will be used for stimulus presentations, and some that may not; the points tested are chosen dynamically during the test. Like other Bayesian procedures, 21,36 each location maintains a discrete PMF over all possible threshold values for that location. As per ZEST, we use a domain of −5, −4, ..., 40 dB. 
Some locations are deemed “seed locations,” and these are given a prior PMF before the test begins. We report results for both uniform priors, and bimodal priors with M equaling 26 dB. 
At any point during the test, a location can be “active,” if it has had at least one presentation; “inactive,” if it has never had a presentation; or “finished” if its PMF has reached some predetermined termination criteria. 
The general structure of GOANNA is as follows: 
  1.  
    Decide on a set of locations that covers the desired VF. Choose a subset of these locations as seed points, assign them a prior PMF and mark them as active;
  2.  
    While the termination criteria is not met:
     
    •  
      a. Choose any active or inactive location for presentation;
    •  
      b. If the location is inactive, make a PMF for that location using natural neighbor interpolation of neighboring active or finished points (see later for details); and
    •  
      c. Present at the mean of that PMF and update PMF as in ZEST.
  3.  
    Create PMFs for inactive locations upon termination criteria being met.
We now elaborate on each step. 
Step 1 – Locations and Seeds
Figure 2 shows the locations used for the 3° grid. There are 150 possible test locations and 36 seed locations. Presentations are first given at the seed locations until the SD of their PMFs falls below 6 dB. 
Figure 2
 
Seed pattern implemented in GOANNA. Seed locations are denoted by the black squares and nonseed locations by the grey squares.
Figure 2
 
Seed pattern implemented in GOANNA. Seed locations are denoted by the black squares and nonseed locations by the grey squares.
Step 2a – Location for Presentation
If there is an active location that has a PMF with SD greater than 6 dB, it is chosen. Otherwise, the gradient between all pairs of active and finished locations are calculated. The gradient is given as the difference in the expectation (mean) of the PMFs divided by the distance in degrees between two points. The location closest to the midpoint of the pair of locations with the greatest gradient is chosen, with ties broken at random. If the locations that form the pair are neighbors and do not have any locations in between, then one of the two locations will be selected at random to be tested if they are both active. If one location of that pair is finished, then the unfinished, active location will be tested. If both locations are finished, then the location pair with the second largest gradient is used to find a location to test, and so on. 
Step 2b – Making a PMF for an Inactive Location
When an inactive location is chosen to be tested, its PMF is determined by natural neighbor interpolation 37,38 on active and finished points (Fig. 3). This form of interpolation forms a Voronoi tessellation 37,38 of the field using polygons around each active or finished point. Each polygon encloses the area that is closest to its location compared with the other locations. After this, a second Voronoi tessellation is created but that includes the new, inactive location. The polygon of the inactive location (outlined in red in Fig. 3) is then superimposed on top of the initial tessellation. 
Figure 3
 
A Voronoi tessellation used in natural neighbor interpolation (A). The location in red is the location to be interpolated. The decibel value for the red dot is the weighted sum of the five colored dots, with the weights being proportional to their areas of overlap with the red polygon. Filled dots denote active locations and unfilled dots denote inactive locations. (B) The resultant PMF of the interpolated location from ([A]; shown in red). The locations marked ‘A' and ‘B' are the location pair with the steepest gradient. Vertical green lines denote true threshold. The locations shaded in grey are the locations that have already terminated. Np = number of presentations; ex = expected mean.
Figure 3
 
A Voronoi tessellation used in natural neighbor interpolation (A). The location in red is the location to be interpolated. The decibel value for the red dot is the weighted sum of the five colored dots, with the weights being proportional to their areas of overlap with the red polygon. Filled dots denote active locations and unfilled dots denote inactive locations. (B) The resultant PMF of the interpolated location from ([A]; shown in red). The locations marked ‘A' and ‘B' are the location pair with the steepest gradient. Vertical green lines denote true threshold. The locations shaded in grey are the locations that have already terminated. Np = number of presentations; ex = expected mean.
To create the new PMF for this location, a weighted average of the PMFs over the neighbors of this point is then calculated, with the weights proportional to the amount of overlap the inactive location polygon has with the polygons of its neighbors. After the interpolation, the PMF is scaled such that the minimum probability is no less than 0.002. An example of a PMF creation is shown in Figure 3B. 
Step 2c – Updating the PMF
The prior PMF is updated based on the response given. It is multiplied by either a “yes” or “no” likelihood function, depending on whether the stimulus was seen or unseen, respectively. The likelihood functions used for GOANNA were the same as described for ZEST. 
Step 3 – Termination Criteria and Creating PMFs for Inactive Locations After Termination
GOANNA repeats steps 2a, b and c until a predefined minimum number of presentations have been used, or until all individual locations terminate: whichever is first. The minimum is imposed to ensure that for uniform fields the procedure does not terminate with many locations untested. In the simulations, this predefined number was matched to the median number of presentations of ZEST run on the same data set. Once the limit is reached, if the largest gradient between all pairs of active and finished locations is greater than 6 dB/deg, GOANNA will continue to run until either the maximum gradient among active and finished pairs is less than 6 dB/deg or all locations have completely terminated. If there are inactive locations upon termination, these locations are assigned a PMF by natural neighbor interpolation, in the same way a prior is created in Step 2b. 
GOANNA Compared With ZEST With Interpolation on a 3° Grid
The performance of GOANNA on a dense grid of 150 locations was compared with Bimodal ZEST with a growth pattern on a standard 24-2 grid of 52 locations, obtaining thresholds for the other unmeasured locations through natural neighbor interpolation. Locations in the blind spot (15° ± 3°, 0° ± 3°) were not tested. Absolute error (absolute difference between true and measured thresholds) was examined for three location groups: (1) all locations, (2) non 24-2 locations, and (3) 24-2 locations. Results from all locations of the 23 fields were pooled for analysis of absolute error and total number of presentations. A Wilcoxon rank sum test was performed to compare the median absolute error (MAE) of GOANNA and ZEST. 
In order to examine the spatial behavior of GOANNA, locations were grouped by their Max_d value, where Max_d is the greatest difference in sensitivity (dB) between a location and any eight of its adjacent locations (ignoring the omitted locations at the blind spot). Hence, a location with a high Max_d value would be at the edge of a scotoma. Conversely, a location with a low Max_d would be in an area of uniform sensitivity. Boxplots and difference plots of locations by proximity to scotoma edges (Max_d) were plotted. 
Results
Although a number of variations on the ZEST and GOANNA procedures were investigated (varying type of prior PMFs, termination criteria, seed location pattern, and growth pattern versus no growth pattern), only the ZEST and GOANNA procedures that performed the best in each simulation are reported here. 
While the MAE of bimodal GOANNA was statistically higher than ZEST (2.00 vs. 1.91 dB, Wilcoxon P < 0.001; interquartile range [IQR] 3.30 vs. 2.94 dB) across all locations (Fig. 4), the magnitude of difference is almost certainly not clinically significant. The median number of presentations was equal for both procedures but the IQR was significantly lower in bimodal GOANNA (8 vs. 61). Over the non 24-2 locations, bimodal GOANNA had an equal MAE to ZEST (2.0 dB). As expected, ZEST performed better than bimodal GOANNA in terms of both MAE (1.99 vs. 1.75 dB, Wilcoxon P < 0.001) and IQR (3.25 vs. 2.42 dB) over the 24-2 locations. This is because GOANNA does not use as many presentations at these locations as ZEST. It is also apparent in Figure 4 that GOANNA with a bimodal prior is slightly superior to GOANNA with a uniform prior, and so we use a bimodal prior from now on. 
Figure 4
 
Boxplots of GOANNA and ZEST for the typical FP responder. Left column: absolute error and total presentations at all locations. Middle column: absolute error and total presentations at non 24-2 locations. Right column: absolute error and total presentations at 24-2 locations.
Figure 4
 
Boxplots of GOANNA and ZEST for the typical FP responder. Left column: absolute error and total presentations at all locations. Middle column: absolute error and total presentations at non 24-2 locations. Right column: absolute error and total presentations at 24-2 locations.
Figure 4 illustrates that GOANNA performs approximately the same as ZEST on average over whole fields. However, GOANNA is designed to target regions of high gradient in the field. Therefore, it would be expected that it should have lower MAE in areas around the edges of scotomata compared with ZEST. Figure 5 separates locations in the field by their proximity to a scotoma border (Max_d). 
Figure 5
 
Top: Boxplots of absolute error for ZEST and GOANNA in terms of Max_d in the typical FP responder. Bottom: difference plots of ZEST less GOANNA in terms of Max_d. Values in the positive range indicate where GOANNA performs better than ZEST.
Figure 5
 
Top: Boxplots of absolute error for ZEST and GOANNA in terms of Max_d in the typical FP responder. Bottom: difference plots of ZEST less GOANNA in terms of Max_d. Values in the positive range indicate where GOANNA performs better than ZEST.
The boxplots in Figure 5 illustrate that the absolute error of ZEST increases as Max_d increases. However, GOANNA does not exhibit this trend, as absolute error is lowest at both high and low Max_d. The difference plots in the bottom two rows of the figure reveal that GOANNA performs better than ZEST when the Max_d is between 12 and 29 dB across all locations (Fig. 5, left column). Similarly, GOANNA exhibits lower IQR within a similar region (17–29 dB). ZEST exhibits lower MAE at 0 to 11 dB (with the exception at 1 dB), and lower IQR at 2 to 11 dB compared with GOANNA. Furthermore, it can be seen that ZEST performs better over the 24-2 locations (Fig. 5, right column). The real gains for GOANNA are in the locations that are at the edges of scotomata (high Max_d). 
In Figure 6, it is evident that GOANNA spends more presentations at locations near a scotoma edge (high Max_d), and less presentations at locations in the middle of a scotoma or normal region (low Max_d). Furthermore, ZEST expends more presentations on the 24-2 locations than GOANNA (right column in Fig. 6). 
Figure 6
 
Top: Boxplots of presentations for bimodal ZEST and bimodal GOANNA for Max_d between adjacent locations in the typical FP responder. Locations on the edge of a scotoma will have a high maximum difference in sensitivity. Bottom: difference plots of median number of presentations (ZEST less GOANNA) for Max_d.
Figure 6
 
Top: Boxplots of presentations for bimodal ZEST and bimodal GOANNA for Max_d between adjacent locations in the typical FP responder. Locations on the edge of a scotoma will have a high maximum difference in sensitivity. Bottom: difference plots of median number of presentations (ZEST less GOANNA) for Max_d.
Figure 7 provides a comparison of a global measure, mean deviation (MD), and the variability of this measure between GOANNA and ZEST. Of the 23 input fields, GOANNA displayed lower MD variability than ZEST in 16 fields and higher variability in nine fields. 
Figure 7
 
Boxplots of MD for ZEST (top) and GOANNA (middle) for each of the 23 fields for the typical FP responder. The bottom panel illustrates the difference in interquartile range of MD between ZEST and GOANNA. Positive differences indicate that GOANNA displays lower variability, whereas negative differences indicate that ZEST displays lower variability.
Figure 7
 
Boxplots of MD for ZEST (top) and GOANNA (middle) for each of the 23 fields for the typical FP responder. The bottom panel illustrates the difference in interquartile range of MD between ZEST and GOANNA. Positive differences indicate that GOANNA displays lower variability, whereas negative differences indicate that ZEST displays lower variability.
A typical result of GOANNA's performance is shown in Figure 8. The input field shows a deep circumscribed arcuate defect that affects the immediate superior paracentral region (Fig. 8A). The locations in bold denote the 24-2 locations. It can be seen that the majority of presentations lie within the area that corresponds to that arcuate defect (Fig. 8C). The numbers shown at each location represent the median over the 50 repeats for these fields. In fields that are normal (Figs. 8D–F), it can be seen that GOANNA does not find a VF region to test more densely as there is no detected localized loss. 
Figure 8
 
Bubble plots of input threshold (A), mean absolute error (B) and mean number of presentations (C) from 50 trials on a field with a superior arcuate defect. The right column shows input threshold (D), mean absolute error (E) and mean number of presentations (F) from 50 trials on a normal field. Numbers highlighted in bold denote 24-2 locations. The sizes of the circles are proportional to the number within those circles. Thresholds of −1 dB indicate that the stimulus was not seen when 0 dB was presented.
Figure 8
 
Bubble plots of input threshold (A), mean absolute error (B) and mean number of presentations (C) from 50 trials on a field with a superior arcuate defect. The right column shows input threshold (D), mean absolute error (E) and mean number of presentations (F) from 50 trials on a normal field. Numbers highlighted in bold denote 24-2 locations. The sizes of the circles are proportional to the number within those circles. Thresholds of −1 dB indicate that the stimulus was not seen when 0 dB was presented.
Discussion
Earlier studies looking at spatially high resolution stimulus arrangements possess one or more of the following limitations: (1) test duration is too high to be applied within a clinical setting, (2) additional locations need to be manually added by a trained operator, (3) total area covered by the test is reduced to limit the number of presentations, or (4) the output of perimetric data obtained is not in a standard format, thus making it difficult to interpret the results for nonexperts. GOANNA was designed to overcome all four shortcomings. 
The results have shown that on average over the whole field, bimodal GOANNA performs similarly to bimodal ZEST with a growth pattern (Fig. 4). But if the field is separated into areas of uniform sensitivity (low Max_d) and nonuniform sensitivity (high Max_d), differences between the procedures emerge (bottom two rows of Fig. 5). GOANNA spends more presentations at locations bordering scotomata. Sensitivities obtained in areas of the field surrounding scotomata are more precise and accurate with GOANNA. These results suggest that GOANNA would be more sensitive to spatial changes of a scotoma, but not subtle deepening of the center of a large defect. Therefore, we predict that GOANNA would be able to detect progression of a scotoma earlier than ZEST when progression involves spatial spread more so than defect deepening. 
As illustrated in Figure 8, GOANNA is able to identify scotomata and test more locations within those regions of visual deficit. The nature of the dynamic stopping criteria that is implemented in GOANNA allows for early identification and termination if a field is normal, but also allows for more presentations to be spent if there is a localized scotoma identified. The tradeoff is that GOANNA does not sample as densely in normal regions of VF compared with ZEST, and thus is neither as accurate nor precise as ZEST in these areas. 
There may also be benefits in the spatial pattern of GOANNA's stimulus location choices. After sampling coarsely over the hill of vision, GOANNA first targets regions of localized loss, which are typically highly variable. On the contrary, the Humphrey growth pattern implemented in ZEST and SITA tests central locations first, and peripheral locations last. 35 Hence, areas of loss in the periphery do not receive presentations until well into the test. By testing these areas first, GOANNA may minimize fatigue effects 39 at these locations, and hence may reduce the variability caused by fatigue in these regions. 
Naturally, there are still limitations on the spatial resolution of GOANNA. Here we have experimented with a grid pattern spaced at 3°, rather than the more conventional 6° grid. Thus, scotomata smaller than 3° can still remain undiscovered. There are two input parameters to GOANNA that control the likelihood of detecting small scotomata. The first is the set of possible locations, which can be made as large as one desires, but, with a limited number of presentations, in large sets many locations will never receive presentations. The second is the location of the seed points. If an isolated scotoma falls between seed points that have normal sensitivity, then they are unlikely to be detected unless the total number of locations is small. There is a tradeoff between the number of locations tested, and the location of seed points. Exploring this tradeoff is work in progress in our lab. Also, if GOANNA were to be applied clinically, it may be important to consider distinguishing for the clinician between those locations where threshold was estimated following direct participant response, and those which were estimated by interpolation. 
It has recently been argued that the coarse sampling of most current VF patterns with size III targets, when combined with microsaccadic fixational eye movements, contributes significantly to perimetric test–retest variability in areas of VF loss. 1 The author formalizes the concept that the spatial pattern of measured VF defects will depend on the sampling grid, in part due to spatial aliasing, and illustrates the contribution of such undersampling to measured variability. If true VF defects are patchy and include high spatial frequency detail, they cannot be accurately represented by coarsely sampled VF tests due to spatial aliasing. 1 Because GOANNA will more densely sample in some regions than others, the ability to truthfully represent the spatial pattern of the underlying VF loss will vary across the field. In this study we present simulation results that are based on empirical data from size III white-on-white targets, however, GOANNA is a thresholding algorithm that could be applied to other stimuli. The effect of sampling errors on test–retest variability should be reduced by using larger, smooth edged stimuli. 1 In such a case, a base stimulus grid for GOANNA could involve continuous tiling of the central 30° of VF. 
Another factor that might feed into the selection of seed locations is the idea of giving importance to regions that are more likely to progress or would have greater implications on quality of life. For example, more seed points could be placed at the paracentral inferior region, which has more of a bearing on quality of life compared with the peripheral superior region. 4042 Assuming asymmetries within the VF, GOANNA will always test some areas more superficially than others. Heuristics to limit the permitted extent of this superficially could be incorporated depending on the clinical context of the VF assessment. 
Currently, GOANNA is not disease specific. For example, the gradient calculations are not constrained by midlines; all active/finished locations are calculated, regardless of where they lie with respect to the horizontal and vertical midline. However, if required, GOANNA could be made more disease specific by customizing the position of the seed locations. For example, if testing for a cortical lesion, the majority of the seed locations could be placed on either side of the vertical midline to explore for hemianopia. Alternatively, extra heuristics could be added to GOANNA such that gradients in areas of importance in the VF (based on the disease of interest) are given higher weightings. 
A side effect of the GOANNA logic is that blind areas of the field will be discovered and not tested extensively during the field examination. Reduced testing in areas already known to be blind has been proposed as a retest heuristic. 43 The authors suggested that locations that were blind (<0 dB) on three consecutive tests tended to remain blind, hence omitting these locations on future tests will not influence the ability to determine VF progression and will save time. 43 GOANNA differs from that approach, in that GOANNA has the potential to undersample blind areas of the VF at the initial test, because the gradient of the VF is uniform in such areas. The ability of GOANNA to determine VF progression falls outside the scope of this study, however, undersampling of blind areas with a commensurate increase in sampling in areas on scotoma borders may confer some benefits. 
In this study, although four different response error profiles were investigated, only the typical FP responder case was reported. In the other conditions, differences between procedures were similar to the FP case, with minimal differences in absolute error when locations were pooled, and GOANNA displaying lower absolute error when Max_d is high. In practice it is highly unlikely that a given patient would respond as an “unreliable responder” (20% FP, 20% FN), as they would have to give both FP and FN responses in equal proportions. This situation is best avoided by adequate patient training and instruction. False negative responses are difficult to interpret as it is hard to discern whether it is a true false response or due to pathology. Higher rates of FN responses have been reported among glaucoma patients compared with healthy subjects. 4448 The more likely chance that an observer would give a FN response would be in regions within a scotoma due to a flatter frequency of seeing slope, in which case it would not be deemed a FN response but their true response. 4448  
To conclude, we have introduced a novel algorithmic approach to selecting test locations on a fine grid autonomously during the test. GOANNA was shown to improve the characterization of scotomata in regions surrounding scotomata edges. Although a 3° grid was investigated, the general principles of GOANNA hold for any grid resolution or test pattern. Further testing is required to see if this improvement in the characterization of scotoma borders leads to earlier detection of VF progression. 
Acknowledgments
Supported by Victorian Life Sciences Computation Initiative (VLSCI) Grant number VR0052 on its Peak Computing Facility at the University of Melbourne, an initiative of the Victorian Government, Australia, the Australian Research Council FT0990930 (AMM), FT0991326 (AT), LP100100250 (SBG), and a Melbourne Research Scholarship (LXC). 
Disclosure: L.X. Chong, None; A.M. McKendrick, Heidelberg Engineering (F, R), Haag-Streit (R); S.B. Ganeshrao, Heidelberg Engineering (F, R); A. Turpin, Heidelberg Engineering (F, R), Haag-Streit (R) 
References
Maddess T. The influence of sampling errors on test-retest variability in perimetry. Invest Ophthalmol Vis Sci . 2011; 52: 1014–1022. [CrossRef] [PubMed]
Westcott MC Garway-Heath DF Fitzke FW Kamal D Hitchings RA. Use of high spatial resolution perimetry to identify scotomata not apparent with conventional perimetry in the nasal field of glaucomatous subjects. Br J Ophthalmol . 2002; 86: 761–766. [CrossRef] [PubMed]
Westcott MC McNaught AI Crabb DP Fitzke FW Hitchings RA. High spatial resolution automated perimetry in glaucoma. Br J Ophthalmol . 1997; 81: 452–459. [CrossRef] [PubMed]
Schiefer U Flad M Stumpp F Increased detection rate of glaucomatous visual field damage with locally condensed grids: a comparison between fundus-oriented perimetry and conventional visual field examination. Arch Ophthalmol . 2003; 121: 458–465. [CrossRef] [PubMed]
Nevalainen J Paetzold J Papageorgiou E Specification of progression in glaucomatous visual field loss, applying locally condensed stimulus arrangements. Graefes Arch Clin Exp Ophthalmol . 2009; 247: 1659–1669. [CrossRef] [PubMed]
Tuulonen A Lehtola J Airaksinen PJ. Nerve fiber layer defects with normal visual fields. Do normal optic disc and normal visual field indicate absence of glaucomatous abnormality? Ophthalmology. 1993; 100: 587–597, discussion 597–588.
Airaksinen PJ Heijl A. Visual field and retinal nerve fibre layer in early glaucoma after optic disc haemorrhage. Acta Ophthalmol (Copenh) . 1983; 61: 186–194. [CrossRef] [PubMed]
Weber J Dobek K. What is the most suitable grid for computer perimetry in glaucoma patients? Ophthalmologica . 1986; 192: 88–96. [CrossRef] [PubMed]
Westcott MC Fitzke FW Hitchings RA. Abnormal motion displacement thresholds are associated with fine scale luminance sensitivity loss in glaucoma. Vision Res . 1998; 38: 3171–3180. [CrossRef] [PubMed]
Kaiser HJ Flammer J Bucher PJ De Natale R Stumpfig D Hendrickson P. High-resolution perimetry of the central visual field. Ophthalmologica . 1994; 208: 10–14. [CrossRef] [PubMed]
Schiefer U Papageorgiou E Sample PA Spatial pattern of glaucomatous visual field loss obtained with regionally condensed stimulus arrangements. Invest Ophthalmol Vis Sci . 2010; 51: 5685–5689. [CrossRef] [PubMed]
Schiefer U Pascual JP Edmunds B Comparison of the new perimetric GATE strategy with conventional full-threshold and SITA standard strategies. Invest Ophthalmol Vis Sci . 2009; 50: 488–494. [CrossRef] [PubMed]
Nevalainen J Krapp E Paetzold J Visual field defects in acute optic neuritis–distribution of different types of defect pattern, assessed with threshold-related supraliminal perimetry, ensuring high spatial resolution. Graefes Arch Clin Exp Ophthalmol . 2008; 246: 599–607. [CrossRef] [PubMed]
Fankhauser F Funkhouser A Kwasniewska S. Advantages and limitations of the spatially adaptive program SAPRO in clinical perimetry. Int Ophthalmol . 1986; 9: 179–189. [CrossRef] [PubMed]
Haeberlin H Fankhauser F. Adaptive programs for analysis of the visual field by automatic perimetry–basic problems and solutions. Efforts oriented towards the realisation of the generalised spatially adaptive Octopus program SAPRO. Doc Ophthalmol . 1980; 50: 123–141. [CrossRef] [PubMed]
Schiefer U Malsam A Flad M Evaluation of glaucomatous visual field loss with locally condensed grids using fundus-oriented perimetry (FOP). Eur J Ophthalmol . 2001; 11 (suppl 2): S57–S62. [PubMed]
Fankhauser F Funkhouser A Kwasniewska S. Evaluating the applications of the spatially adaptive program (SAPRO) in clinical perimetry: part I. Ophthalmic Surg . 1986; 17: 338–342, contd. [PubMed]
Fankhauser F Funkhouser A Kwasniewska S. Evaluating the applications of the spatially adaptive program (SAPRO) in clinical perimetry: part II. Ophthalmic Surg . 1986; 17: 415–428. [PubMed]
Schiefer U Benda N Dietrich TJ Selig B Hofmann C Schiller J. Angioscotoma detection with fundus-oriented perimetry. A study with dark and bright stimuli of different sizes. Vision Res . 1999; 39: 1897–1909. [CrossRef] [PubMed]
Nakatani Y Ohkubo S Higashide T Iwase A Kani K Sugiyama K. Detection of visual field defects in pre-perimetric glaucoma using fundus-oriented small-target perimetry. Jpn J Ophthalmol . 2012; 56: 330–338. [CrossRef] [PubMed]
King-Smith PE Grigsby SS Vingrys AJ Benes SC Supowit A. Efficient and unbiased modifications of the QUEST threshold method: theory, simulations, experimental evaluation and practical implementation. Vision Res . 1994; 34: 885–912. [CrossRef] [PubMed]
McKendrick AM Turpin A. Advantages of terminating Zippy Estimation by Sequential Testing (ZEST) with dynamic criteria for white-on-white perimetry. Optom Vis Sci . 2005; 82: 981–987. [CrossRef] [PubMed]
Turpin A McKendrick AM Johnson CA Vingrys AJ. Properties of perimetric threshold estimates from full threshold, ZEST, and SITA-like strategies, as determined by computer simulation. Invest Ophthalmol Vis Sci . 2003; 44: 4787–4795. [CrossRef] [PubMed]
McKendrick AM. Recent developments in perimetry: test stimuli and procedures. Clin Exp Optom . 2005; 88: 73–80. [CrossRef] [PubMed]
Turpin A McKendrick AM Johnson CA Vingrys AJ. Development of efficient threshold strategies for frequency doubling technology perimetry using computer simulation. Invest Ophthalmol Vis Sci . 2002; 43: 322–331. [PubMed]
Bengtsson B Olsson J Heijl A Rootzen H. A new generation of algorithms for computerized threshold perimetry, SITA. Acta Ophthalmol Scand . 1997; 75: 368–375. [CrossRef] [PubMed]
Johnson CA Chauhan BC Shapiro LR. Properties of staircase procedures for estimating thresholds in automated perimetry. Invest Ophthalmol Vis Sci . 1992; 33: 2966–2974. [PubMed]
Spenceley SE Henson DB. Visual field test simulation and error in threshold estimation. Br J Ophthalmol . 1996; 80: 304–308. [CrossRef] [PubMed]
Turpin A Jankovic D McKendrick AM. Retesting visual fields: utilizing prior information to decrease test-retest variability in glaucoma. Invest Ophthalmol Vis Sci . 2007; 48: 1627–1634. [CrossRef] [PubMed]
Henson DB Chaudry S Artes PH Faragher EB Ansons A. Response variability in the visual field: comparison of optic neuritis, glaucoma, ocular hypertension, and normal eyes. Invest Ophthalmol Vis Sci . 2000; 41: 417–421. [PubMed]
Turpin A Artes PH McKendrick AM. The Open Perimetry Interface: an enabling tool for clinical visual psychophysics. J Vis . 2012; 12( 11). pii: 22. [CrossRef] [PubMed]
McKendrick AM Turpin A. Combining perimetric suprathreshold and threshold procedures to reduce measurement variability in areas of visual field loss. Optom Vis Sci . 2005; 82: 43–51. [CrossRef] [PubMed]
Keltner JL Johnson CA Cello KE Classification of visual field abnormalities in the ocular hypertension treatment study. Arch Ophthalmol . 2003; 121: 643–650. [CrossRef] [PubMed]
Vingrys AJ Pianta MJ. A new look at threshold estimation algorithms for automated static perimetry. Optom Vis Sci . 1999; 76: 588–595. [CrossRef] [PubMed]
Anderson DR Patella VM. Automated Static Perimetry. 2nd ed. Philadelphia: Mosby; 1999.
Watson AB Pelli DG. QUEST: a Bayesian adaptive psychometric method. Percept Psychophys . 1983; 33: 113–120. [CrossRef] [PubMed]
Sambridge M Braun J McQueen H. Geophysical parameterization and interpolation of irregular data using natural neighbours. Geophysical Journal International . 1995; 122: 837–857. [CrossRef]
Braun J Sambridge M. A numerical method for solving partial differential equations on highly irregular evolving grids. Nature . 1995; 376: 655–660. [CrossRef]
Hudson C Wild JM O'Neill EC. Fatigue effects during a single session of automated static threshold perimetry. Invest Ophthalmol Vis Sci . 1994; 35: 268–280. [PubMed]
Black AA Wood JM Lovie-Kitchin JE. Inferior visual field reductions are associated with poorer functional status among older adults with glaucoma. Ophthalmic Physiol Opt . 2011; 31: 283–291. [CrossRef] [PubMed]
Marigold DS Patla AE. Visual information from the lower visual field is important for walking across multi-surface terrain. Exp Brain Res . 2008; 188: 23–31. [CrossRef] [PubMed]
Turano KA Broman AT Bandeen-Roche K Munoz B Rubin GS West S. Association of visual field loss and mobility performance in older adults: Salisbury Eye Evaluation Study. Optom Vis Sci . 2004; 81: 298–307. [CrossRef] [PubMed]
Junoy Montolio FG, Wesselink C, Jansonius NM. Persistence, spatial distribution and implications for progression detection of blind parts of the visual field in glaucoma: a clinical cohort study. PLoS One . 2012; 7: e41211. [CrossRef] [PubMed]
Bengtsson B. Reliability of computerized perimetric threshold tests as assessed by reliability indices and threshold reproducibility in patients with suspect and manifest glaucoma. Acta Ophthalmol Scand . 2000; 78: 519–522. [CrossRef] [PubMed]
Birt CM Shin DH Samudrala V Hughes BA Kim C Lee D. Analysis of reliability indices from Humphrey visual field tests in an urban glaucoma population. Ophthalmology . 1997; 104: 1126–1130. [CrossRef] [PubMed]
Katz J Sommer A. Reliability indexes of automated perimetric tests. Arch Ophthalmol . 1988; 106: 1252–1254. [CrossRef] [PubMed]
Katz J Sommer A. Reliability of automated perimetric tests. Arch Ophthalmol . 1990; 108: 777–778. [CrossRef] [PubMed]
Katz J Sommer A. Screening for glaucomatous visual field loss. The effect of patient reliability. Ophthalmology . 1990; 97: 1032–1037. [CrossRef] [PubMed]
Figure 1
 
Histogram of input sensitivities of the 23 input fields used in the simulations.
Figure 1
 
Histogram of input sensitivities of the 23 input fields used in the simulations.
Figure 2
 
Seed pattern implemented in GOANNA. Seed locations are denoted by the black squares and nonseed locations by the grey squares.
Figure 2
 
Seed pattern implemented in GOANNA. Seed locations are denoted by the black squares and nonseed locations by the grey squares.
Figure 3
 
A Voronoi tessellation used in natural neighbor interpolation (A). The location in red is the location to be interpolated. The decibel value for the red dot is the weighted sum of the five colored dots, with the weights being proportional to their areas of overlap with the red polygon. Filled dots denote active locations and unfilled dots denote inactive locations. (B) The resultant PMF of the interpolated location from ([A]; shown in red). The locations marked ‘A' and ‘B' are the location pair with the steepest gradient. Vertical green lines denote true threshold. The locations shaded in grey are the locations that have already terminated. Np = number of presentations; ex = expected mean.
Figure 3
 
A Voronoi tessellation used in natural neighbor interpolation (A). The location in red is the location to be interpolated. The decibel value for the red dot is the weighted sum of the five colored dots, with the weights being proportional to their areas of overlap with the red polygon. Filled dots denote active locations and unfilled dots denote inactive locations. (B) The resultant PMF of the interpolated location from ([A]; shown in red). The locations marked ‘A' and ‘B' are the location pair with the steepest gradient. Vertical green lines denote true threshold. The locations shaded in grey are the locations that have already terminated. Np = number of presentations; ex = expected mean.
Figure 4
 
Boxplots of GOANNA and ZEST for the typical FP responder. Left column: absolute error and total presentations at all locations. Middle column: absolute error and total presentations at non 24-2 locations. Right column: absolute error and total presentations at 24-2 locations.
Figure 4
 
Boxplots of GOANNA and ZEST for the typical FP responder. Left column: absolute error and total presentations at all locations. Middle column: absolute error and total presentations at non 24-2 locations. Right column: absolute error and total presentations at 24-2 locations.
Figure 5
 
Top: Boxplots of absolute error for ZEST and GOANNA in terms of Max_d in the typical FP responder. Bottom: difference plots of ZEST less GOANNA in terms of Max_d. Values in the positive range indicate where GOANNA performs better than ZEST.
Figure 5
 
Top: Boxplots of absolute error for ZEST and GOANNA in terms of Max_d in the typical FP responder. Bottom: difference plots of ZEST less GOANNA in terms of Max_d. Values in the positive range indicate where GOANNA performs better than ZEST.
Figure 6
 
Top: Boxplots of presentations for bimodal ZEST and bimodal GOANNA for Max_d between adjacent locations in the typical FP responder. Locations on the edge of a scotoma will have a high maximum difference in sensitivity. Bottom: difference plots of median number of presentations (ZEST less GOANNA) for Max_d.
Figure 6
 
Top: Boxplots of presentations for bimodal ZEST and bimodal GOANNA for Max_d between adjacent locations in the typical FP responder. Locations on the edge of a scotoma will have a high maximum difference in sensitivity. Bottom: difference plots of median number of presentations (ZEST less GOANNA) for Max_d.
Figure 7
 
Boxplots of MD for ZEST (top) and GOANNA (middle) for each of the 23 fields for the typical FP responder. The bottom panel illustrates the difference in interquartile range of MD between ZEST and GOANNA. Positive differences indicate that GOANNA displays lower variability, whereas negative differences indicate that ZEST displays lower variability.
Figure 7
 
Boxplots of MD for ZEST (top) and GOANNA (middle) for each of the 23 fields for the typical FP responder. The bottom panel illustrates the difference in interquartile range of MD between ZEST and GOANNA. Positive differences indicate that GOANNA displays lower variability, whereas negative differences indicate that ZEST displays lower variability.
Figure 8
 
Bubble plots of input threshold (A), mean absolute error (B) and mean number of presentations (C) from 50 trials on a field with a superior arcuate defect. The right column shows input threshold (D), mean absolute error (E) and mean number of presentations (F) from 50 trials on a normal field. Numbers highlighted in bold denote 24-2 locations. The sizes of the circles are proportional to the number within those circles. Thresholds of −1 dB indicate that the stimulus was not seen when 0 dB was presented.
Figure 8
 
Bubble plots of input threshold (A), mean absolute error (B) and mean number of presentations (C) from 50 trials on a field with a superior arcuate defect. The right column shows input threshold (D), mean absolute error (E) and mean number of presentations (F) from 50 trials on a normal field. Numbers highlighted in bold denote 24-2 locations. The sizes of the circles are proportional to the number within those circles. Thresholds of −1 dB indicate that the stimulus was not seen when 0 dB was presented.
×
×

This PDF is available to Subscribers Only

Sign in or purchase a subscription to access this content. ×

You must be signed into an individual account to use this feature.

×