Predicting Binocular Visual Field Sensitivity from Monocular Visual Field Results

Abstract

purpose. To compare methods of predicting binocular visual field sensitivity of patients with glaucoma from monocular visual field data.

methods. Monocular and binocular visual fields were obtained for 111 patients with varying degrees of glaucomatous damage in one or both eyes, using the Humphrey 30-2 full-threshold procedure. Four binocular sensitivity prediction models were evaluated: BEST EYE, predictions based on individual values for the most sensitive eye, defined by mean deviation (MD); AVERAGE EYE, predictions based on the average sensitivity between eyes at each visual field location; BEST LOCATION, predictions based on the highest sensitivity between eyes at each visual field location; and BINOCULAR SUMMATION, predictions based on binocular summation of sensitivity between eyes at each location. Differences between actual and predicted binocular sensitivities were calculated for each model.

results. The average difference between predicted and actual binocular sensitivities was close to zero for the BINOCULAR SUMMATION and BEST LOCATION models, with 95% of all predictions being within ±3 dB of actual binocular sensitivities. The best eye (MD) prediction had an average error of 1.5 dB (95% confidence limits [CL], ±3.7 dB). The average eye prediction was the poorest, with an average error of 3.7 dB (95% CL, ±4.6 dB).

conclusions. The BINOCULAR SUMMATION and BEST LOCATION models provided better predictions of binocular visual field sensitivity than the other two models, with a statistically significant difference in performance. The small difference in performance between the BINOCULAR SUMMATION and BEST LOCATION models was not statistically significant. For evaluations of functional visual field influences on task performance, daily activities, and related quality-of-life issues, either the BINOCULAR SUMMATION or BEST LOCATION model provides good estimates of binocular visual field sensitivity.

Although much is known about the binocular summation properties of the fovea for normal vision, ^{1 2 3 4 5} it is less clear how information from the two eyes is combined in the periphery or in patients with degraded visual function. Wood et al. ⁶ evaluated binocular characteristics of the peripheral visual field in a small sample of normal observers. They found that binocular visual field sensitivity was better than monocular visual field sensitivity. The amount of binocular summation varied from 10% to 50%, depending on stimulus size and visual field location. Crabb et al. ⁷ reported that binocular visual field detection of suprathreshold stimuli in patients with glaucoma is based on the eye with the better sensitivity at each visual field location. Because this investigation evaluated a screening procedure using suprathreshold stimuli, it is not known whether detection thresholds also display these characteristics. Esterman ⁸ developed a binocular visual field scoring system that is based on combining the most sensitive visual field locations from each eye, and Arditi ⁹ created a similar system to generate a binocular “volume visual field” from monocular visual field results. 

Several investigators have reported deficits in binocular visual threshold measures such as stereoacuity and spatial and temporal contrast sensitivity in glaucoma, ^{10 11} although these findings were obtained for central vision in patients with good visual acuity in both eyes (20/30 or better). 

For most patients with glaucoma, there are considerable differences in the location, shape, size, and severity of visual field sensitivity loss between eyes. Localized regions of visual field loss for each eye sometimes overlap and sometimes do not. It is difficult to predict how two disparate, inhomogeneous visual fields will be combined by higher visual centers to produce a single functional binocular visual field. To understand the relationship between glaucomatous visual field loss and quality-of-life factors, an accurate representation of the binocular visual field is needed. ¹² In particular, daily activities involving driving and mobility skills are dependent on the status of the binocular visual field. ^{9 10} There are also significant implications for binocular visual field characteristics and disability determinations. However, clinical perimetry is performed for each eye separately, and perimeters are not designed to perform binocular visual field testing. An accurate method of predicting binocular visual field sensitivity from monocular visual field test results would therefore be desirable. 

For many psychophysical tests, it has been shown that binocular sensitivity can be predicted from the monocular sensitivity of each eye according to a binocular summation model. ^{1 2 3 4 5} Depending on the specific model used for binocular summation, a 25% to 40% improvement in sensitivity is predicted for binocular viewing compared with monocular viewing, ^{1 2 3 4 5} assuming that the sensitivities of the two eyes are similar. One common form of the probability summation model is one that assumes that binocular sensitivity can be predicted by the square root of the summed squares of the two monocular sensitivities (quadratic summation)—i.e.,  

\[\mathrm{BINOCULAR\ SENSITIVITY}{=}\sqrt{(S_{\mathrm{L}})^{2}{+}(\mathit{S}_{\mathrm{R}})^{2}}\]

where S _L and S _R are the monocular sensitivities of the left and right eyes, respectively, for corresponding visual field locations. ⁵ We refer to this as the BINOCULAR SUMMATION model, and selected this particular form of binocular summation because it accurately predicts binocular contrast detection and other binocular visual tasks. ⁵  

This model predicts that binocular sensitivity is approximately 1.4 times (40%) better than individual monocular sensitivities, assuming that the monocular sensitivities are equal. The larger the difference in sensitivity between eyes, the more the predicted binocular sensitivity approximates the value of the most sensitive eye. The lower the sensitivity of the worst eye, the less it contributes to binocular sensitivity. The improvement in binocular sensitivity over the best monocular sensitivity can be as high as 40% if both eyes have equal sensitivity, or as low as 0% if one eye has no sensitivity. 

Based on foveal stereoacuity and binocular contrast sensitivity deficits reported for patients with glaucoma, ^{10 11} it could be alternatively proposed that binocular summation in patients with glaucoma does not occur, because at least one eye is impaired. Rather, it could be assumed that for corresponding visual field locations, the most sensitive of the two visual field locations between eyes would determine binocular sensitivity. The binocular visual field would therefore be a composite of the most sensitive of the two visual field locations for each eye. For suprathreshold testing, this model was adopted by Crabb et al. ⁷ We refer to this as the BEST LOCATION model. 

A third model has been used for investigating the relationship between visual field sensitivity and quality-of-life assessments. ¹² These studies assume that the eye with better overall visual field sensitivity, as determined by mean deviation (MD), determines the binocular visual field properties of patients with glaucoma. It was found that the MD of the better eye correlated better with quality-of-life measures than the MD of the worse eye. ¹² We refer to this as the BEST EYE model. MD was selected as the basis for the BEST EYE model, because it is generally used to characterize the overall severity of glaucomatous visual field loss. 

A final possibility is that the binocular visual field sensitivity represents an averaging of sensitivity of the two eyes at each visual field location. This would be similar in concept to the Levelt luminance-averaging model, except that he was applying it to binocular summation of suprathreshold stimuli (brightness). ¹ We refer to this as the AVERAGE EYE model. 

Our purpose was to evaluate these four models to determine the best method of predicting binocular visual field sensitivity from monocular visual field information in patients with glaucoma. 

Materials and Methods

Informed consent was obtained from all participants prior to testing, in accordance with the Declaration of Helsinki. We tested 111 patients with at least one abnormal visual field index (MD, corrected pattern standard deviation [CPSD], or glaucoma hemifield test[ GHT]) and characteristic glaucomatous visual field loss in one or both eyes. MD represents the patient’s average difference from age-corrected normal population values for the entire visual field. CPSD represents the patient’s departure from the slope of the visual field for age-corrected normal population values. The GHT examines the symmetry of sensitivity of the superior and inferior hemifields in comparison with age-corrected normal population values. These indices are visual field summary statistics commonly used to monitor patients with glaucoma. 

MD for both eyes of the patients with glaucoma ranged between +3.3 dB and −29.7 dB. Some patients had similar amounts of sensitivity loss between eyes, whereas others had large differences in sensitivity between eyes. The degree of overlap for regions of sensitivity loss between eyes varied considerably among patients, as did the magnitude of sensitivity loss for overlapping regions. By selecting a heterogeneous sample of patients with glaucoma, we were able to evaluate the performance of the four prediction models over the entire spectrum of glaucomatous damage. 

All visual field tests were conducted using a Humphrey Field Analyzer (San Leandro, CA) performing a 30-2 full-threshold test procedure. The 30-2 stimulus presentation pattern consists of 76 locations within the central 30° in a 6° grid bracketing the horizontal and vertical meridians. Monocular testing was performed according to standard procedures, with an optimal lens correction placed before the eye to be tested and a translucent eye patch placed over the nontested eye. The translucent eye patch attenuated the background luminance by approximately 0.3 log units (3 dB) for the nontested eye. Patients wore a modified pediatric trial frame (half frames) with the optimal lens correction placed before each eye for binocular testing. The modified trial frame minimized the likelihood that the trial frame and lenses obstructed the field of view of one or both eyes during testing. It was adjusted to account for differences in interpupillary distance so that the trial lenses were properly centered for each eye. The same visual field locations were examined for all tests. 

During binocular testing, patients were aligned to the perimeter by adjusting the vertical head position, alternately aligning the center of both pupils, and then adjusting the horizontal position to the bridge of the nose. This precluded the ability to monitor fixation during binocular visual field testing. However, all patients had undergone at least two previous visual field examinations, and patients with a history of poor fixation were excluded from the study. Both monocular and binocular visual field data were collected during the same visit, with rest periods of at least 15 minutes between tests. Periodic short rest breaks during a test procedure were provided to patients as needed. 

Four binocular visual field sensitivity prediction models were evaluated: BEST EYE, in which binocular visual field sensitivity was predicted by the eye with the best overall sensitivity, defined by MD; BEST LOCATION, in which binocular visual field sensitivity was predicted to be the most sensitive of the two visual field locations between eyes for corresponding visual field points; AVERAGE EYE, in which binocular visual field sensitivity was predicted to be the average sensitivity of the two eyes for corresponding visual field points; and BINOCULAR SUMMATION, in which binocular visual field sensitivity was predicted by probability summation of the sensitivities of the two eyes according to the following equation:  

\[\mathrm{Binocular\ sensitivity}{=}\sqrt{(S_{\mathrm{L}})^{2}{+}(S_{\mathrm{R}})^{2}}\]

as previously defined. We chose this particular form of binocular summation because it has previously been shown to accurately predict binocular contrast detection and other binocular visual tasks. ⁵ The probability summation calculation assumes that at threshold, the eyes function as two independent detectors. The probability of detecting a stimulus is thus a quadratic summation of sensitivity between the two eyes. If the sensitivities of the two eyes are equal, then probability summation predicts that the binocular sensitivity will be approximately 1.4 times better than the individual monocular sensitivities. If the sensitivities of the two eyes are different, then probability summation predicts that the binocular sensitivity will be better than the most sensitive monocular sensitivity, but by a factor smaller than 1.4. The greater the difference in sensitivity between eyes, the smaller the improvement in binocular sensitivity over the best monocular sensitivity. 

For each of the four models, the difference between predicted and actual binocular sensitivities was determined for corresponding visual field locations. The average difference between predicted and actual binocular sensitivities was then determined for each patient using the four prediction models. Foveal sensitivities and different visual field eccentricities were also examined individually. 

Results

The results are summarized in Table 1 . Both the BEST LOCATION and BINOCULAR SUMMATION models had average differences between actual and predicted binocular visual field sensitivities that were close to zero, with SDs that were approximately 1.5 dB and average maximum errors of approximately ±4.5 dB. The BINOCULAR SUMMATION model per formed slightly better, providing the best prediction in 45% of the cases compared with the 27% of cases in which the BEST LOCATION gave the best prediction. These two models produced similar predictions, and together they accounted for 72% of the best predictions. In addition, 95% of the patients had average binocular visual field predictions that were within 3 dB of the actual binocular thresholds for both models. There was no statistically significant difference for the correlation coefficients (predicted versus actual binocular sensitivities) of the two models. 

The BEST EYE model had poorer predictions, underestimating binocular visual field sensitivity by an average of approximately 1.5 dB. It also had more variable predictions, with an SD of approximately 1.85 dB, and average prediction errors ranging from approximately 7.6 dB of underestimation to approximately 2.3 dB of overestimation for individual patients. The worst predictions were produced by the AVERAGE model, which underestimated binocular visual field sensitivity by approximately 3.7 dB, with an SD of approximately 2.3 dB. Average prediction errors ranged from approximately 10.4 dB of underestimation to approximately 0.7 dB of overestimation. The correlation coefficients (predicted versus actual binocular sensitivity) for the BEST EYE and AVERAGE models were significantly worse (P < 0.001) than the BINOCULAR SUMMATION and BEST LOCATION models, but the difference between the two was not statistically significant. 

We individually evaluated the fovea and different visual field eccentricities to determine whether there were any differences in performance of the models for different locations and found that our results for the entire visual field also held true for individual visual field locations. We also evaluated whether there was evidence of binocular summation greater than the 1.4 probability summation value. The average summation value was 1.33 ± 0.59 (SD) for the fovea, 1.32 ± 0.66 for locations inside 10°, 1.42 ± 0.51 for locations between 10° and 20°, and 1.51 ± 0.61 for locations between 20° and 30°. These small differences were not statistically significant. 

Individual examples of good and poor predictions are shown in the results for the BINOCULAR SUMMATION model, because it produced the best and most consistent performance. Figure 1 shows a good binocular prediction for a patient with little or no visual field loss in each eye. The top graph presents the gray-scale representations and numeric dB values for monocular visual fields obtained for the left and right eyes. The binocular visual field results are presented in the center. The lower left graph is a scatterplot of predicted binocular sensitivity plotted as a function of actual binocular sensitivity for all 76 visual field locations. The diagonal line represents perfect correspondence between the two. The lower right graph is a histogram of the difference scores (actual minus predicted binocular sensitivity) for all 76 visual field locations. It can be observed that actual binocular sensitivities were close to the predicted values. 

Figure 2 presents the results of a good binocular prediction for a patient with more extensive visual field loss. The representation scheme is the same as that shown in Figure 1 . Again, there was good correspondence between the predicted and actual binocular sensitivity values over the entire visual field and the range of sensitivity values that are represented. 

Figure 3 presents the results for a patient in whom the binocular predictions were poor and highly variable, with large over- and underestimations. However, there did not appear to be any systematic tendency to over- or underestimate actual binocular sensitivity values. Instead, it appears that there was merely higher variability for all measures. This may therefore represent results from a relatively unreliable patient. 

Figure 4 presents the results for a patient in whom the predictions were good for locations with relatively normal sensitivity, but consistently overestimated binocular sensitivity for locations with sensitivity loss. Binocular sensitivity was lower than predicted in damaged visual field areas. 

Figure 5 shows an example of good predictions for locations with relatively normal sensitivity but consistent overestimation of binocular sensitivity at locations with visual field loss. Binocular sensitivity was higher than predicted in damaged visual field areas. 

Figure 6 presents an example in which the predicted binocular sensitivities consistently underestimated the actual binocular sensitivity at all locations. Similarly, Figure 7 presents an example of consistent underestimation of binocular visual field sensitivity at all visual field locations. 

A large majority of cases produced good predictions similar to those presented in Figures 1 and 2 . Only a small number of cases produced poor predictions such as those shown in Figures 3 4 5 6 7 . We performed additional correlational analyses to determine whether there were any factors that were associated with poor predictions of binocular visual field sensitivity. Poor binocular visual field sensitivity predictions were not related to the MD of either the better or worse eye, the difference in sensitivity between eyes, the reliability or short-term fluctuation of the better or worse eye, or the patient’s age. 

Discussion

Our findings indicate that it is possible to predict binocular visual field sensitivity from monocular visual field test results with good accuracy for most patients with glaucoma. The BINOCULAR SUMMATION model provided the best predictions. The BEST LOCATION model provided predictions that were nearly as good, and no statistically significant difference was found between the two models. In both instances, 95% of the cases had average predicted binocular visual field sensitivities that were within 3 dB of the actual binocular sensitivities. It is not surprising that these two models yielded similar results. The largest difference in predictions between the two models was 3 dB when sensitivity of a location was equal for both eyes, and identical predictions occurred when a location had 0 dB sensitivity in one eye. It is possible that our results would have been different if unbiased threshold determinations were performed, as is usual in conventional psychophysical experiments. However, we used the 4-2-2 staircase procedure of the field analyzer because we wanted our results to be applicable to conventional clinical perimetry. 

The present findings have significance for relationships among visual function measures, task performance, and quality-of-life measures in patients with glaucoma. Because visual field loss is the most prevalent and characteristic form of visual function loss associated with glaucoma, its relationship to quality-of-life measures ¹² and performance of everyday tasks ^{13 14} has been a topic of increasing interest. One difficulty in evaluating the influence of visual field loss on task performance and quality-of-life measures is selecting an appropriate visual field measure. Ideally, it would be best to measure binocular visual sensitivity in patients with glaucoma to provide the most accurate representation of the patient’s functional visual field that they normally use. However, clinical instruments for testing the visual field perform monocular testing and are not designed to perform binocular visual field testing. This means that either a custom device must be constructed or a clinical device must be used in a nonconventional manner. In either case, no standard protocols, normative databases, or analysis procedures are available. The present study shows that the BINOCULAR SUMMATION and BEST LOCATION models can accurately predict binocular visual field sensitivity from monocular visual field results. This means that the visual field information normally collected for disease management can be used. Because more than 95% of the cases are within 3 dB for each technique, either method should be more than adequate for assessing the role of the binocular functional visual field in relation to driving, activities of daily living, and other quality-of-life issues, as well as for determination of disability in glaucoma. 

Finally, we noted that in many instances, the appearance of the binocular visual field of patients with glaucoma was better than expected on the basis of observation of the monocular visual fields alone. This is in part because glaucomatous visual field loss only occasionally overlaps for corresponding locations in the two eyes, the degree of overlap is often partial, and the degree of sensitivity loss is often asymmetric between the two eyes. It is also partly because it is difficult to visually extract the best sensitivity locations from each eye and mentally combine them into a composite image. A method of generating an accurate representation of the binocular visual field from monocular visual field data may be useful for clinicians in assessing whether patients are likely to encounter difficulties with driving, mobility skills, and other everyday tasks. 

 Supported in part by National Eye Institute Research Grant EY-03424 (CAJ), a Research to Prevent Blindness Senior Scientific Investigator Award (CAJ), and an unrestricted Research Support Grant from Research to Prevent Blindness (University of California, Davis).

 Submitted for publication July 15, 1999; revised January 26, 2000; accepted February 10, 2000.

 Commercial relationships policy: N.

 

Table 1.

 

Mean Difference Between Actual and Predicted Binocular Visual Field Sensitivity for the Four Models

Model	MD (dB)	SD (dB)	Range (dB)	Percentage of Best Predictions
Best eye	1.49	1.85	7.58 to −2.27	24/111 (21)
Best location	0.05	1.53	4.73 to−4.34	33/111 (27)
Binocular summation	−0.40	1.51	4.37 to −4.67	50/111 (45)
Average eye	3.70	2.29	10.39 to −0.67	8/111 (7)

 The standard deviation and range of differences are also presented, along with the percentage of times each model produced the best prediction (best predictions/total predictions (%).

Figure 1.

 

An example in which the BINOCULAR SUMMATION model accurately predicted the binocular visual field sensitivity in a patient with minimal glaucomatous visual field loss. Top: Gray-scale representations and numeric dB values of the central visual fields of both eyes. Middle: Gray-scale representation and numeric dB values of the measured binocular visual field. Bottom left: Predicted binocular sensitivity as a function of measured sensitivity. Bottom right: Difference between measured and predicted binocular sensitivity values. This format applies to all figures.

Figure 2.

 

An example in which the BINOCULAR SUMMATION model accurately predicted the binocular visual field sensitivity in a patient with more extensive glaucomatous visual field loss.

Figure 3.

 

An example in which the BINOCULAR SUMMATION model produced a poor prediction of binocular visual field sensitivity in a patient with moderate glaucomatous visual field loss. Significant over- and underpredictions were present.

Figure 4.

 

An example in which the BINOCULAR SUMMATION model produced good predictions for normal visual field areas but consistently overestimated binocular sensitivity in areas of glaucomatous damage.

Figure 5.

 

An example in which the BINOCULAR SUMMATION model consistently overestimated the binocular sensitivity of all visual field locations.

Figure 6.

 

An example in which the BINOCULAR SUMMATION model produced good predictions for normal visual field locations but consistently underestimated binocular sensitivity for damaged visual field locations.

Figure 7.

 

An example in which the BINOCULAR SUMMATION model consistently underestimated binocular visual field sensitivity.