An evaluation of clusters in the glaucomatous visual field

Efficacy of Smoothing Algorithms to Enhance Detection of Visual Field Progression in Glaucoma

Purpose

To evaluate and compare the effectiveness of nearest neighbor (NN)- and variational autoencoder (VAE)-smoothing algorithms to reduce variability and enhance the performance of glaucoma visual field (VF) progression models.

Design

Longitudinal cohort study.

Subjects

7150 eyes (4232 patients), with ≥ 5 years of follow-up and ≥ 6 visits.

Methods

Vsual field thresholds were smoothed with the NN and VAE algorithms. The mean total deviation (mTD) and VF index rates, pointwise linear regression (PLR), permutation of PLR (PoPLR), and the glaucoma rate index were applied to the unsmoothed and smoothed data.

Main Outcome Measures

The proportion of progressing eyes and the conversion to progression were compared between the smoothed and unsmoothed data. A simulation series of noiseless VFs with various patterns of glaucoma damage was used to evaluate the specificity of the smoothing models.

Results

The mean values of age and follow-up time were 62.8 (standard deviation: 12.6) years and 10.4 (standard deviation: 4.7) years, respectively. The proportion of progression was significantly higher for the NN and VAE smoothed data compared with the unsmoothed data. VF progression occurred significantly earlier with both smoothed data compared with unsmoothed data based on mTD rates, PLR, and PoPLR methods. The ability to detect the progressing eyes was similar for the unsmoothed and smoothed data in the simulation data.

Conclusions

Smoothing VF data with NN and VAE algorithms improves the signal-to-noise ratio for detection of change, results in earlier detection of VF progression, and could help monitor glaucoma progression more effectively in the clinical setting.

Financial Disclosures

Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Prediction of visual field progression in glaucoma: existing methods and artificial intelligence

Timely treatment is essential in the management of glaucoma. However, subjective assessment of visual field (VF) progression is not recommended, because it can be unreliable. There are two types of artificial intelligence (AI) strong and weak (machine learning). Weak AIs can perform specific tasks. Linear regression is a method of weak AI. Using linear regression in the real-world clinic has enabled analyzing and predicting VF progression. However, caution is still required when interpreting the results, because whenever the number of VF data sets investigated is small, the predictions can be inaccurate. Several other non-ordinal, or modern AI methods have been constructed to improve prediction accuracy, such as clustering and more modern AI methods of Analysis with Non-Stationary Weibull Error Regression and Spatial Enhancement (ANSWERS), Variational Bayes Linear Regression (VBLR), Kalman Filter and sparse modeling (The least absolute shrinkage and selection operator regression: Lasso). It is also possible to improve the prediction performance using retinal thickness measured with optical coherence tomography by using machine learning methods, such as multitask learning.

[Optical coherence tomography and optical coherence tomography angiography for detecting glaucoma progression. Part 2. Clinical and functional correlations, monitoring of advanced glaucoma and limitations of the method]

The purpose of this study is to analyze the literature on the role of optical coherence tomography (OCT) and optical coherence tomography angiography (OCTA) in the diagnosis of glaucoma. This review considers the structural and functional correlations observed during the progression of glaucomatous optic neuropathy, as well as the capabilities of the method in late glaucoma, describes the strengths and weaknesses of OCT and OCTA, and pays particular attention to the role of OCT in assessing the effectiveness of treatment. Optical coherence tomography is the main method for determining the progression of glaucoma, which plays a key role in the choice of treatment algorithm. However, the use of OCT in far advanced glaucoma has certain particularities and limitations. OCTA can be helpful in overcoming this problem.

[Static automated perimetry in the diagnosis of glaucoma. Part 2: Research protocol, glaucoma classifications, perimetric defects through the prism of structural-functional correlation]

Examination of the central visual field is currently required for glaucoma diagnosis. Modern computer perimeters make it possible to qualitatively and quantitatively evaluate defects of light sensitivity. Perimetric indices are calculated showing the severity of the defects. This allows the use of perimetric results to create universal classifications of glaucoma. Recently, new perimeter programs based on optical coherence tomography data have appeared. The possibility of personalizing perimeter programs are being tested. This review attempts to systematize data on the capabilities of computer perimeters in assessing functional defects, presents the widely used glaucoma classifications, and describes ways of developing static perimetry programs for earlier diagnosis of glaucoma with respect to structural and functional correlations.

Cluster analysis of computerized visual field and optical coherence tomography–ganglion cell complex defects in high intraocular pressure patients or early stage glaucoma

Purpose:

The aim of the study is to evaluate the relationship between functional defects shown by cluster analysis of computerized visual field and anatomic defects from optical coherence tomography–ganglion cell complex examination in ocular hypertension or eyes affected by glaucoma.

Methods:

205 eyes affected by ocular hypertension (intraocular pressure > 22 mmHg) or early stage glaucoma were enrolled. The age of the patients ranged from 26 to 87 years (average: 61.83 ± 1.54 years). Computerized 30° visual field (Octopus G1x Dynamic strategy) and optical coherence tomography–ganglion cell complex (I-Vue Optovue) analyses were performed for each eye selected; 68 eyes were tested and retested from two to seven times for a total of 320 visual fields and 320 optical coherence tomography–ganglion cell complex examinations. The visual field was considered abnormal with a mean defect < –2 and loss variance > 6. The optical coherence tomography–ganglion cell complex was considered abnormal with a significant focal loss volume (p < 5%) and/or a significant thinning of total, superior, or inferior thickness (p < 5%). Four different groups of examinations were created according to the results of visual field and ganglion cell complex: normal visual field and normal ganglion cell complex (group 1), abnormal visual field and abnormal ganglion cell complex (group 2), normal visual field and abnormal ganglion cell complex (group 3), and abnormal visual field and normal ganglion cell complex (group 4). The cluster analysis of visual fields (EyeSuite software Interzeag CH) was performed only in the visual field of group 3, and the correlation between cluster values and topographical changes at optical coherence tomography–ganglion cell complex was analyzed.

Results:

The results of the ganglion cell complex and visual field examinations matched 247 (77.19%) times. In 143 cases, the examinations belonged to group 1, in 104 to group 2, in 23 to group 3, and, finally, in 50 to group 4. The visual field cluster analysis performed on group 3 showed that the correlation between optical coherence tomography–ganglion cell complex and visual field cluster analysis defects was 100% (both the exams altered). In 72% of them, there was also a topographical correspondence between the visual field and optical coherence tomography–ganglion cell complex defects.

Conclusion:

In the early stages of glaucoma, the visual field cluster analysis seems to be useful to detect some focal defects that can be otherwise underestimated when globally considering the visual field. In group 3, where the conventional analysis of visual field was normal while the optical coherence tomography–ganglion cell complex exam was abnormal, the visual field cluster analysis showed a topographical correlation with optical coherence tomography–ganglion cell complex defects in more than 70% of the examinations performed. In addition, the patients with abnormal visual field and normal optical coherence tomography–ganglion cell complex were older than those with normal visual field and abnormal optical coherence tomography–ganglion cell complex (66.44 ± 3.51 vs 57.04 ± 5.96 years, p < 0.001 (0.0002)). These results confirm that the reliability of a visual field examination is subjective and decreases with age because of its difficulty and the personal compliance of the patient toward this examination.

Machine learning models based on the dimensionality reduction of standard automated perimetry data for glaucoma diagnosis

INTRODUCTION

Visual field testing via standard automated perimetry (SAP) is a commonly used glaucoma diagnosis method. Applying machine learning techniques to the visual field test results, a valid clinical diagnosis of glaucoma solely based on the SAP data is provided. In order to reflect structural-functional patterns of glaucoma on the automated diagnostic models, we propose composite variables derived from anatomically grouped visual field clusters to improve the prediction performance. A set of machine learning-based diagnostic models are designed that implement different input data manipulation, dimensionality reduction, and classification methods.

METHODS

Visual field testing data of 375 healthy and 257 glaucomatous eyes were used to build the diagnostic models. Three kinds of composite variables derived from the Garway-Heath map and the glaucoma hemifield test (GHT) sector map were included in the input variables in addition to the 52 SAP visual filed locations. Dimensionality reduction was conducted to select important variables so as to alleviate high-dimensionality problems. To validate the proposed methods, we applied four classifiers-linear discriminant analysis, naïve Bayes classifier, support vector machines, and artificial neural networks-and four dimensionality reduction methods-Pearson correlation coefficient-based variable selection, Markov blanket variable selection, the minimum redundancy maximum relevance algorithm, and principal component analysis- and compared their classification performances.

RESULTS

For all tested combinations, the classification performance improved when the proposed composite variables and dimensionality reduction techniques were implemented. The combination of total deviation values, the GHT sector map, support vector machines, and Markov blanket variable selection obtains the best performance: an area under the receiver operating characteristic curve (AUC) of 0.912.

CONCLUSION

A glaucoma diagnosis model giving an AUC of 0.912 was constructed by applying machine learning techniques to SAP data. The results show that dimensionality reduction not only reduces dimensions of the input space but also enhances the classification performance. The variable selection results show that the proposed composite variables from visual field clustering play a key role in the diagnosis model.

Application of Pattern Recognition Analysis to Optimize Hemifield Asymmetry Patterns for Early Detection of Glaucoma

Purpose

To assess the diagnostic utility of a new hemifield asymmetry analysis derived using pattern recognition contrast sensitivity isocontours (CSIs) within the Humphrey Field Analyzer (HFA) 24-2 visual field (VF) test grid. The performance of an optimal CSI-derived map was compared against a commercially available clustering method (Glaucoma Hemifield Test, GHT).

Methods

Five hundred VF results of 116 healthy subjects were used to determine normative distribution limits for comparisons. Pattern recognition analysis was applied to HFA 24-2 sensitivity data to determine CSI theme maps delineating clusters for hemifield comparisons. Then, 1019 VF results from 228 glaucoma patients were assessed using different clustering methods to determine the true-positive rate. We also assessed additional 354 VF results of 145 healthy subjects to determine the false-positive rate.

Results

The optimum clustering method was the CSI-derived seven-theme class map, which identified more glaucomatous VFs compared with the GHT map. The seven-class theme map also identified more cases compared with the five-, six-, and eight-class maps, suggesting no effect of number of clusters. Integrating information regarding the location of glaucomatous defects to the CSI clusters did not improve detection rate.

Conclusions

A clustering map derived using CSIs improved detection of glaucomatous VFs compared with the currently available GHT. An optimized CSI-derived map may serve as an additional means to aid earlier detection of glaucoma.

Translational Relevance

Pattern recognition–derived theme maps provide a means for guiding test point selection for asymmetry analysis in glaucoma assessment.

MRI Study of the Posterior Visual Pathways in Primary Open Angle Glaucoma

PURPOSE OF THE STUDY

The purpose of the study was to evaluate neurodegeneration along brain visual pathways in primary open angle glaucoma (POAG) using improved analysis methods of volumetric and diffusion tensor magnetic resonance imaging (MRI) data.

METHODS

Eleven POAG patients (60.0±9.2 y) with primarily mild to moderate POAG and 11 age-matched controls (55.9±7.5 y) were studied using structural and diffusion tensor MRI. Surface-based segmentation was applied to structural MRI to obtain visual cortical area and volume. Fiber tracking was applied to diffusion tensor data to obtain diffusion parameters along the optic tract and optic radiation. MRI parameters in glaucoma patients were compared with the corresponding left and right visual fields and retinal nerve fiber layer thicknesses, instead of with the left and right eye.

RESULTS

Area and volume of the primary visual cortex were significantly reduced in POAG patients compared with controls (P<0.05) but did not correlate with visual field loss. Fractional anisotropy was reduced at multiple locations along the optic tracts and optic radiations in POAG patients compared with controls. Axial and radial diffusivity along the fiber tracts showed trends but were not significantly different between POAG patients and controls when averaged over the whole structures. Only fractional anisotropy (P<0.05) of the optic radiations was significantly correlated with visual field loss. No MRI parameters were correlated with retinal nerve fiber layer thickness.

CONCLUSIONS

Improved analysis techniques of MRI data improves delineation of degeneration in the brain visual pathways and further supports the notion that neurodegeneration is involved with glaucoma pathogenesis.

Enhancement of Visual Field Predictions with Pointwise Exponential Regression (PER) and Pointwise Linear Regression (PLR)

Purpose

The study was conducted to evaluate threshold smoothing algorithms to enhance prediction of the rates of visual field (VF) worsening in glaucoma.

Methods

We studied 798 patients with primary open-angle glaucoma and 6 or more years of follow-up who underwent 8 or more VF examinations. Thresholds at each VF location for the first 4 years or first half of the follow-up time (whichever was greater) were smoothed with clusters defined by the nearest neighbor (NN), Garway-Heath, Glaucoma Hemifield Test (GHT), and weighting by the correlation of rates at all other VF locations. Thresholds were regressed with a pointwise exponential regression (PER) model and a pointwise linear regression (PLR) model. Smaller root mean square error (RMSE) values of the differences between the observed and the predicted thresholds at last two follow-ups indicated better model predictions.

Results

The mean (SD) follow-up times for the smoothing and prediction phase were 5.3 (1.5) and 10.5 (3.9) years. The mean RMSE values for the PER and PLR models were unsmoothed data, 6.09 and 6.55; NN, 3.40 and 3.42; Garway-Heath, 3.47 and 3.48; GHT, 3.57 and 3.74; and correlation of rates, 3.59 and 3.64.

Conclusions

Smoothed VF data predicted better than unsmoothed data. Nearest neighbor provided the best predictions; PER also predicted consistently more accurately than PLR. Smoothing algorithms should be used when forecasting VF results with PER or PLR.

Translational Relevance

The application of smoothing algorithms on VF data can improve forecasting in VF points to assist in treatment decisions.

Mapping glaucoma patients' 30-2 and 10-2 visual fields reveals clusters of test points damaged in the 10-2 grid that are not sampled in the sparse 30-2 grid

Purpose

To cluster test points in glaucoma patients' 30-2 and 10-2 visual field (VF) (Humphrey Field Analyzer: HFA, Carl Zeiss Meditec, Dublin, CA) in order to map the different regions damaged by the disease.

Method

This retrospective study included 128 eyes from 128 patients. 142 total deviation (TD) values (74 from the 30-2 VF and 68 from the 10-2 VF) were clustered using the ‘Hierarchical Ordered Partitioning And Collapsing Hybrid – Partitioning Around Medoids’ algorithm. The stability of the identified clusters was evaluated using bootstrapping.

Results

65 sectors were identified in total: 38 sectors were located outside the 10-2 VF whereas 29 sectors were located inside the 10-2 VF (two sectors overlap in both grids). The mapping of many sectors appeared to follow the distribution of retinal nerve fiber bundles. The results of bootstrapping suggested clusters were stable whether they were outside or inside the 10-2 VF.

Conclusion

A considerable number of sectors were identified in the 10-2 VF area, despite the fact that clustering was carried out on all points in both the 30-2 VF and 10-2 VF simultaneously. These findings suggest that glaucomatous central VF deterioration cannot be picked up by the 30-2 test grid alone, because of poor spatial sampling; denser estimation of the central ten degrees, than offered by the 30-2 test grid alone, is needed. It may be beneficial to develop a new VF test grid that combines test points from 30-2 and 10-2 VFs – the results of this study could help to devise this test grid.

[Visual field progression in glaucoma: cluster analysis]

BACKGROUND

Visual field progression analysis is one of the key points in glaucoma monitoring, but distinction between true progression and random fluctuation is sometimes difficult. There are several different algorithms but no real consensus for detecting visual field progression. The trend analysis of global indices (MD, sLV) may miss localized deficits or be affected by media opacities. Conversely, point-by-point analysis makes progression difficult to differentiate from physiological variability, particularly when the sensitivity of a point is already low. The goal of our study was to analyse visual field progression with the EyeSuite™ Octopus Perimetry Clusters algorithm in patients with no significant changes in global indices or worsening of the analysis of pointwise linear regression.

PATIENT AND METHOD

We analyzed the visual fields of 162 eyes (100 patients - 58 women, 42 men, average age 66.8 ± 10.91) with ocular hypertension or glaucoma. For inclusion, at least six reliable visual fields per eye were required, and the trend analysis (EyeSuite™ Perimetry) of visual field global indices (MD and SLV), could show no significant progression. The analysis of changes in cluster mode was then performed. In a second step, eyes with statistically significant worsening of at least one of their clusters were analyzed point-by-point with the Octopus Field Analysis (OFA).

RESULTS

Fifty four eyes (33.33%) had a significant worsening in some clusters, while their global indices remained stable over time. In this group of patients, more advanced glaucoma was present than in stable group (MD 6.41 dB vs. 2.87); 64.82% (35/54) of those eyes in which the clusters progressed, however, had no statistically significant change in the trend analysis by pointwise linear regression.

CONCLUSION

Most software algorithms for analyzing visual field progression are essentially trend analyses of global indices, or point-by-point linear regression. This study shows the potential role of analysis by clusters trend. However, for best results, it is preferable to compare the analyses of several tests in combination with morphologic exam.

Assessing visual field clustering schemes using machine learning classifiers in standard perimetry

PURPOSE

To compare machine learning classifiers trained on three clustering schemes to determine whether distinguishing healthy eyes from those with glaucomatous optic neuropathy (GON) can be optimized by training with clustered data.

METHODS

Two machine learning classifiers-quadratic discriminant analysis (QDA) and support vector machines with Gaussian kernel (SVMg)-were trained separately using standard perimetry data from the Diagnostic Innovations in Glaucoma Study (DIGS), clustered using three clustering schemes on a training data set (123 eyes/123 glaucoma patients with GON; 135 eyes/135 normal control subjects). Trained classifiers were then applied to an independent data set containing 69 eyes of 69 glaucoma patients with early visual field loss and 83 eyes of 83 normal control subjects. Two control conditions were included: unclustered data and a random assignment of locations to clusters.

RESULTS

Areas under the receiver operating characteristic (ROC) curve ranged from 0.85 (SVMg, thresholds clustered by Glaucoma Hemifield Test sectors) to 0.92 (QDA, thresholds clustered by Garway-Heath mapping) for the training data set. Use of clustered data showed no significant optimization of sensitivity over use of unclustered data, and no single clustering method resulted in significantly higher performance in the independent data set. Sensitivities tended to be higher with QDA than with SVMg, regardless of specificity cutoff and clustering

METHOD

CONCLUSIONS

QDA performed better with the early glaucoma data set than did the SVMg. Clustering may be advantageous when data-dimension reduction is needed-for example, when combining field results with other high-dimensional data (e.g., structural imaging data)-but it is not necessary for visual field data alone.

Repeatability of Normal Multifocal VEP: Implications for Detecting Progression

PURPOSE

To assess the repeatability of the multifocal visual evoked potential (mfVEP) and to compare it with the repeatability of standard automated perimetry (SAP) in the same group of 50 normal controls retested after 1 year. Our second aim was to assess the repeatability of false alarm rates determined previously for the mfVEP using various cluster criteria.

METHODS

Fifty individuals with normal vision participated in this study (33 females and 17 males). The age range was 26.7 to 77.9 years and the group average age (+/- SD) was 51.4 (+/- 12.1) years. Pattern-reversal mfVEPs were obtained using a dartboard stimulus pattern in VERIS and two 8-minute runs per eye were averaged. The average number of days between the first and second mfVEP tests was 378 (+/- 58). SAP visual fields were obtained within 17.4 (+/- 20.3) days of the mfVEP using the SITA-standard threshold algorithm. Repeatability of mfVEPs and SAP total deviation values were evaluated by calculating point-wise limits of agreement (LOA). Specificity (1-false alarm rate) was evaluated for a range of cluster criteria, whereby the number and probability level of the points defining a cluster were varied.

RESULTS

Point-wise LOA for the mfVEP signal-to-noise ratio (SNR) ranged from 2.0 to 4.3 dB, with an average of 2.9 dB across all 60 locations. For SAP, LOA ranged from 2.4 to 8.9 dB, with an average of 4.0 dB (excluding the points immediately above and below the blind spot). Clusters of abnormal points were not likely to repeat on either mfVEP or SAP. When an mfVEP abnormality was defined as the repeat presence (confirmation) of a 3-point (P < 0.05) cluster anywhere within a single hemifield, only 1 (of 200) monocular hemifield was deemed abnormal. Although the LOA of the mfVEP were similar throughout the field, the limited dynamic range of SNR at superior field locations will limit the ability to follow progression in "depth" at those locations.

CONCLUSIONS

Repeatability of the mfVEP was slightly better than SAP visual fields in this group of controls with a 1-year retest interval. This suggests that progression in early stages should be more easily detectable by mfVEP. However, in certain field locations (eg, superior periphery), the relatively more narrow dynamic range of the SNR of the mfVEP may limit detection of progression to just 1 event. Confirmation of a 3-point cluster abnormality is highly suggestive of a true defect on the mfVEP.

Determining abnormal interocular latencies of multifocal visual evoked potentials

PURPOSE

To describe methods for measuring interocular latency differences of multifocal visual evoked potentials (mfVEP) and for determining regions with abnormal interocular latencies in patients.

METHODS

The mfVEPs from 100 individuals with normal visual fields and normal fundus examinations were analyzed. Individuals ranged in age from 21.6 to 92.4 years. The stimulus was a 60 sector, pattern-reversing dartboard display. Each sector had 16 checks, 8 white (200 cd/m2) and 8 black (< 1 cd/m2). Interocular latency was measured as the temporal shift producing the best cross-correlation value between the corresponding responses of each eye. The 'corrected interocular latency' was defined as the difference between this shift and the mean interocular latency (shift) for a particular sector and recording channel.

RESULTS

The variability of the corrected interocular latency decreased as the signal-to-noise ratio (SNR) of the mfVEP responses increased. For example, the 95% confidence intervals decreased from over 16 ms to under 4 ms as SNR increased. Grouping and summing the responses also lead to an increase in SNR and a decrease in the confidence interval. The results of various cluster criteria were also derived. A cluster criterion (e.g. two or more contiguous points within a hemisphere exceeding a given confidence interval), can serve to increase the specificity for detection of eyes or individuals with abnormal interocular latencies. For example, while 21% of the eyes had 3 or more points exceeding the 5% confidence interval, only 1.8% of the eyes had a cluster of 3 or more of these points. Finally, interocular latency was only weakly correlated with age (r = 0.26).

CONCLUSION

In testing for abnormalities in interocular latencies, the confidence interval should be based upon the SNR of the response. Grouping and summing responses to increase SNR or employing a cluster test may also prove useful.

Normative ranges and specificity of the multifocal VEP

PURPOSE

To describe a normative database for the multifocal VEP (mfVEP) and to evaluate specificity for a range of cluster criteria.

METHODS

One hundred persons (62 females and 38 males) with normal visual fields and ranging in age from 21.6 to 92.4 years participated in this study. Self-reported race in 80 of these 100 persons was 'White or Caucasian,' eight were 'Black or African-American,' eight were 'Asian,' and four were 'Hispanic or Latino.' Pattern-reversal mfVEPs were obtained using a dartboard stimulus pattern in VERIS and two 8-min runs per eye were averaged. A bootstrap technique was used to estimate the normal range of mfVEP response signal-to-noise ratio (SNR) and inter-ocular amplitude ratio at each location. Specificity (1 - false alarm rate) was evaluated for a range of cluster criteria, whereby the number and probability level of the points defining a cluster were varied.

RESULTS

There was no overall effect of age on SNR (r2 = 0.16, p = 0.22) nor was the interaction between age and location significant (F = 0.83, p = 0.82, ANOVA). The location with the largest age effect had an r2 of only 0.13. There was a small but significant effect of sex (t = 2.1, p = 0.04) such that SNR was slightly (11%) larger in females than males, but there was no significant interaction between sex and age (t = 0.82, p = 0.41). There was a slight trend toward higher SNR in the Asian group and lower SNR in the African-American group, but the overall effect of race was not significant (F = 1.99, p = 0.12). Specificity depended on the number and probability level of the points defining a cluster. Specificity did not vary by age group in a simple monotonic manner. False positive rates were slightly higher in females than males, and slightly higher in the African-American group as compared with the Asian group.

CONCLUSIONS

Excellent specificity can be achieved for the mfVEP by using particular cluster criteria for monocular and inter-ocular tests. The effects of age, sex, and race were all very small and only the effect of sex was statistically significant. This normative database can be used for analyses of mfVEP results from individual patients with little risk that demographic factors such as age and sex will confound diagnostic accuracy.

Localised changes in glaucomatous visual fields after trabeculectomy

BACKGROUND AND OBJECTIVE

Modern techniques of automated perimetry have shown that surgical reduction of intraocular pressure (IOP) may have a beneficial effect on the glaucomatous visual field. The purpose of the present study was to analyse and quantify the changes in the visual fields of glaucoma patients after trabeculectomy.

MATERIALS AND METHODS

Octopus visual fields of twenty-seven glaucoma patients were analysed. Change in visual field mean sensitivity (MS) was calculated to detect total field changes. A clinical and a statistical analysis of small clusters of test points were used to define whether local changes had occurred.

RESULTS

MS in the operated eyes improved significantly from 16.4+/-5.6 to 18.2+/-5.5 dB. The patients had on average 3.9+/-6.2 clusters where the retinal sensitivity had improved at least 5 dB and only 0.4+/-0.9 clusters where sensitivity had deteriorated at least 5 dB after trabeculectomy. 17 patients had more improved than deteriorated clusters postoperatively.

CONCLUSION

Statistically significant improvement was seen in the MS, but improvement was also found in small local areas of the visual fields after trabeculectomy.

Mathematical and optimal clustering of test points of the central 30-degree visual field of glaucoma

PURPOSE

To determine a mathematically optimal sector pattern of the central 30 degree visual field for the follow-up of glaucomatous visual field change based on a large number of actual visual field test data of patients with glaucoma.

METHODS

Visual field test data obtained from 1,039 eyes of 1,039 patients with open-angle glaucoma (OAG) using the 30-2 program of the Humphrey Field Analyzer were used for sectorization of the central 30 degree visual field. Of the 1,039 visual field data, 698 (modeling data) were used for determining the sector pattern and 341 (testing data) for checking the sector pattern. The modeling data were further divided into three groups according to the mean deviation (MD) (MD > or = -10 dB, -20 < or = MD < -10 dB, and MD < -20 dB), and the sector pattern was constructed from visual field data of each group using a clustering procedure called VARCLUS. The testing data were used for determining the optimal sector pattern. In a separate set of repeated visual field data of 303 patients with OAG, the fluctuation of MD, sector values of each sector determined, and total deviation of each test point were calculated and compared.

RESULTS

The sector pattern constructed from visual field data of MD > or = -10 dB summarized the visual field performance most effectively. The fluctuation of the sector value of each sector was roughly 1.5 times smaller than the total deviation of each test point.

CONCLUSION

The sector pattern determined may be useful in analyses of the visual field data of patients with glaucoma.

Mapping the visual field to the optic disc in normal tension glaucoma eyes

PURPOSE

To establish the anatomical relationship between visual field test points in the Humphrey 24-2 test pattern and regions of the optic nerve head (ONH) DESIGN: Cross-sectional study.

PARTICIPANTS

Glaucoma patients and suspects from the Normal Tension Glaucoma Clinic at Moorfields Eye Hospital.

METHODS

Sixty-nine retinal nerve fiber layer (RNFL) photographs with well-defined RNFL defects and/or prominent bundles were digitized. An appropriately scaled Humphrey 24-2 visual field grid and an ONH reference circle, divided into 30 degrees sectors, were generated digitally. These were superimposed onto the RNFL images. The relationship of visual field test points to the circumference of the ONH was estimated by noting the proximity of test points to RNFL defects and/or prominent bundles. The position of the ONH in relation to the fovea was also noted.

MAIN OUTCOME MEASURES

The sector at the ONH corresponding to each visual field test point, the position of the ONH in relation to the fovea, and the effect of the latter on the former.

RESULTS

A median 22 (range, 4-58), of a possible 69, ONH positions were assigned to each visual field test point. The standard deviation of estimations was 7.2 degrees. The position of the ONH was 15.5 degrees (standard deviation 0.9 degrees ) nasal and 1.9 degrees (standard deviation 1.0 degrees ) above the fovea. The location of the ONH had a significant effect on the corresponding position at the ONH for 28 of 52 visual field test points.

CONCLUSIONS

A clinically useful map that relates visual field test points to regions of the ONH has been produced. The map will aid clinical evaluation of glaucoma patients and suspects, as well as form the basis for investigations of the relationship between retinal light sensitivity and ONH structure.

Comparison of methods to detect visual field progression in glaucoma

OBJECTIVE

The purpose of the study is to develop alternative statistical approaches for evaluating the trend of visual field series over time and to compare the results to human observers.

DESIGN

Retrospective analysis of visual field results.

PARTICIPANTS

Eighty-three eyes of 83 patients (phakic or pseudophakic) with open-angle glaucoma and 5 or more eligible fields were included in the study.

INTERVENTION

Three experienced observers independently reviewed the field series to determine stability or progression.

MAIN OUTCOME MEASURES

The following additional methods to determine progression of visual field loss were used: (1) pointwise univariate regression analysis and a glaucoma change analysis; (2) univariate regression analysis on visual field indices mean deviation, corrected loss variance, and glaucoma pattern index; (3) pointwise multivariate regression analysis with fixed effects on panel data; and (4) clusterwise multivariate regression analysis with fixed effects on panel data. The results of different statistical methods were compared by determining the pairwise agreement (Cohen's weighted kappa) between each technique and three experienced observers.

RESULTS

Patients were observed for a mean (+/-standard deviation) of 5.6 (+/-1.4) years. The visual fields of 27 (33%) and 56 (67%) eyes were considered to have progressed or remained stable, respectively, based on agreement of at least 2 of 3 observers. Univariate regression analysis on visual field indices was not useful for detection of visual field progression. Pointwise and clusterwise regression analyses with fixed effects on panel data performed as well as pointwise univariate regression analysis compared with human observers (kappa = 0.52, 0.53, and 0.55, respectively). Both methods showed better agreement with human observers than with glaucoma change analysis (kappa = 0.41).

CONCLUSIONS

A new statistical model, multivariate regression analyses with fixed effects on panel data, is an appropriate method to evaluate the course of visual field series over time and shows reasonable agreement with experienced observers and pointwise univariate regression analysis.

Improving the prediction of visual field progression in glaucoma using spatial processing

PURPOSE

The authors show how the predictive performance of a method for determining glaucomatous progression in a series of visual fields can be improved by first subjecting the data to a spatial processing technique.

METHOD

Thirty patients with normal-tension glaucoma, each with at least ten Humphrey fields and 3.5 years of follow-up, were included. A linear regression model of sensitivity against time of follow-up determined rates of change at individual test locations over the first five fields (mean follow-up 1.46 years; standard deviation = 0.08) in each field series. Predictions of sensitivity at each location of the field nearest to 1 and 2 years after the fifth field were generated using these rates of change. Predictive performance was evaluated by the difference between the predicted and measured sensitivity values. The analysis was repeated using the same field data subjected to a spatial filtering technique used in image processing.

RESULTS

Using linear modeling of the unprocessed field series, at 1 year after the fifth field, 72% of all predicted values were within +/- 5 dB of the corresponding measured threshold. This prediction precision improved to 83% using the processed data. At the 2-year follow-up field, the predictive performance improved from 56% to 73% with respect to the +/- 5 dB criterion.

CONCLUSIONS

Predictions of visual field progression using a pointwise linear model can be improved by spatial processing without increased cost or patient time. These methods have clinical potential for accurately detecting and forecasting visual field deterioration in the follow-up of glaucoma.

A cluster and scotoma analysis based on empiric criteria

From a collection of 288 visual fields of glaucomatous or glaucoma suspects, 30 were selected at random and were analyzed by one expert interpreter. Visual field damage varied from nonexistent to severe. The interpreter defined clusters or scotomas subjectively according to adjacency criteria: adjacent test locations which exceeded a critical loss value were grouped as clusters or scotomas. A computer algorithm has been devised which simulates such evaluation methods. In general, a standard setting of several parameters produced a cluster display containing the same number of clusters as determined by the expert interpreter. Another display mode grouped clusters according to polygonal areas of a predetermined size (Voronoi diagram). Due to the broad selection of visual field defects, the specificity of the program with regard to various field decay patterns was small and it should thus be applicable to a broad spectrum of glaucomatous field damage.