A two-stage neural spiking model of visual contrast detection in perimetry

The Role of Retinal Ganglion Cell Structure and Function in Glaucoma

Glaucoma, a leading cause of irreversible blindness globally, primarily affects retinal ganglion cells (RGCs). This review dives into the anatomy of RGC subtypes, covering the different underlying theoretical mechanisms that lead to RGC susceptibility in glaucoma, including mechanical, vascular, excitotoxicity, and neurotrophic factor deficiency, as well as oxidative stress and inflammation. Furthermore, we examined numerous imaging methods and functional assessments to gain insight into RGC health. Finally, we investigated the current possible neuroprotective targets for RGCs that could help with future glaucoma research and management.

Detectability of Visual Field Defects in Glaucoma Using Moving Versus Static Stimuli for Perimetry

Purpose

We have previously shown that using moving, instead of static, stimuli extends the effective dynamic range of automated perimetry in glaucoma. In this study, we further investigate the effect of using moving stimuli on the detectability of functional loss.

Methods

We used two experimental perimetry paradigms to test 155 subjects with a diagnosis of glaucoma or glaucoma suspect, and 34 healthy control subjects. One test used stimuli moving parallel to the average nerve fiber bundle orientation at each location; the other used static stimuli. Algorithms were otherwise identical. Sensitivities to moving stimuli were transformed to the equivalent values for static stimuli based on a Bland-Altman plot. The proportions of locations outside age-corrected normative limits were compared, and test-retest variability was compared against defect depth for each stimulus type.

Results

More tested locations were below the fifth percentile of the normative range for that location using static stimuli. However, among locations abnormal according to standard clinical perimetry on the same day, 19.2% were abnormal using static stimuli, versus 20.5% using moving stimuli (P = 0.372). Test-retest variability was 44% lower for moving stimuli across the range of defect depths.

Conclusions

When compared with static automated perimetry and expressed on a common scale, moving stimuli extend the effective dynamic range and decrease variability, without decreasing the detectability of known functional defects.

Translational Relevance

Moving stimuli provide a method to improve known problems of current clinical perimetry.

Moving Stimulus Perimetry: A New Functional Test for Glaucoma

Purpose

Static pointwise perimetric sensitivities of less than approximately 19 dB are unreliable in glaucoma owing to excessive variability. We propose using moving stimuli to increase detectability, decrease variability, and hence increase this dynamic range.

Methods

A moving stimulus was designed to travel parallel to the average nerve fiber bundle orientation at each location, and compared against an otherwise identical static stimulus. To assess dynamic range, psychometric functions were measured at 4 locations of each of 10 subjects. To assess clinically realistic test-retest variability, 34 locations of 94 subjects with glaucoma and glaucoma suspects were tested twice, 6 months apart. Pointwise sensitivity estimates were compared using generalized estimating equation regression models. The test-retest limits of agreement for each stimulus were assessed, adjusted for within-eye clustering.

Results

Using static stimuli, 9 of the 40 psychometric functions had less than a 90% maximum response probability, suggesting being beyond the dynamic range. Eight of those locations had asymptotic maximum of more than 90% with moving stimuli. Sensitivities were higher for moving stimuli (P < 0.001); the difference increased as sensitivity decreased (P < 0.001). Test-retest limits of agreement were narrower for moving stimuli (-6.35 to +6.48 dB) than static stimuli (-12.7 to +7.81 dB). Sixty-two percent of subjects preferred using moving stimuli versus 19% who preferred static stimuli.

Conclusions

Using a moving stimulus increases perimetric sensitivities in regions of glaucomatous loss. This extends the effective dynamic range, allowing reliable testing later into the disease. Results are more repeatable, and the test is preferred by most subjects.

Translational Relevance

Moving stimuli allow reliable testing in patients with more severe glaucoma than currently possible.

Long- and Short-Term Variability of Perimetry in Glaucoma

Purpose

Test–retest variability in perimetry consists of short-term and long-term components, both of which impede assessment of progression. By minimizing and quantifying the algorithm-dependent short-term variability, we can quantify the algorithm-independent long-term variability that reflects true fluctuations in sensitivity between visits. We do this at locations with sensitivity both < 28 dB (when the stimulus is smaller than Ricco's area and complete spatial summation can be assumed) and > 28 dB (when partial summation occurs).

Methods

Frequency-of-seeing curves were measured at four locations of 35 participants with glaucoma. The standard deviation of cumulative Gaussian fits to those curves was modeled for a given sensitivity and used to simulate the expected short-term variability of a 30-presentation algorithm. A separate group of 137 participants was tested twice with that algorithm, 6 months apart. Long-term variance at different sensitivities was calculated as the LOESS fit of observed test–retest variance minus the LOESS fit of simulated short-term variance.

Results

Below 28 dB, short-term variability increased approximately linearly with increasing loss. Long-term variability also increased with damage below this point, attaining a maximum standard deviation of 2.4 dB at sensitivity 21 dB, before decreasing due to the floor effect of the algorithm. Above 30 dB, the observed test–retest variance was slightly smaller than the simulated short-term variance.

Conclusions

Long-term and short-term variability both increase with damage for perimetric stimuli smaller than Ricco's area. Above 28 dB, long-term variability constitutes a negligible proportion of test–retest variability.

Translational Relevance

Fluctuations in true sensitivity increase in glaucoma, even after accounting for increased short-term variability. This long-term variability cannot be reduced by altering testing algorithms alone.

Differences in the Relation Between Perimetric Sensitivity and Variability Between Locations Across the Visual Field

Purpose

Perimetric sensitivities become more variable with glaucomatous functional loss. This study examines the extent to which this relation varies between locations, and whether this can be predicted by eccentricity-related differences in spatial summation.

Methods

Longitudinal series of visual fields from standard automated perimetry were obtained from participants with suspected or extant glaucoma. For each location in the 24-2 visual field, heterogeneous fixed-effects models were fit to the data, assuming that variability increased exponentially as sensitivity decreased. The predicted variability at each location was calculated when sensitivity was either 30 dB or 25 dB.

Results

Variability significantly increased with damage at all 52 locations. When sensitivity was 30 dB, variability increased with eccentricity, with P = 0.0003. The average SD was 1.54 dB at the four most central locations, versus 1.74 dB at the most peripheral locations. When sensitivity was 25 dB, variability did not vary predictably with eccentricity, with P = 0.340. The average SD was 2.36 dB at the four central locations, versus 2.24 dB at the most peripheral locations.

Conclusions

The relation between sensitivity and variability differed by eccentricity. Among healthy locations, variability was lower centrally, where the stimulus size is larger than Ricco's area, than peripherally. Among damaged locations, variability did not systematically vary with eccentricity. This could be because Ricco's area expands in glaucoma, such that stimuli were now smaller than this area at all locations.

Individual differences in the shape of the nasal visual field

Between-subject differences in the shape of the nasal visual field were assessed for 103 volunteers 21-85years of age and free of visual disorder. Perimetry was conducted with a stimulus for which contrast sensitivity is minimally affected by peripheral defocus and decreased retinal illumination. One eye each was tested for 103 volunteers free of eye disease in a multi-center prospective longitudinal study. A peripheral deviation index was computed as the difference in log contrast sensitivity at outer (25-29° nasal) and inner (8° from fixation) locations. Values for this index ranged from 0.01 (outer sensitivity slightly greater than inner sensitivity) to -0.7 log unit (outer sensitivity much lower than inner sensitivity). Mean sensitivity for the inner locations was independent of the deviation index (R²<1%), while mean sensitivity for the outer locations was not (R²=38%, p<0.0005). Age was only modestly related to the index, with a decline by 0.017 log unit per decade (R²=10%). Test-retest data for 21 volunteers who completed 7-10 visits yielded standard deviations for the index from 0.04 to 0.17 log unit, with a mean of 0.09 log unit. Between-subject differences in peripheral deviation persisted over two years of longitudinal testing. Peripheral deviation indices were correlated with indices for three other perimetric stimuli used in a subset of 24 volunteers (R² from 20% to 49%). Between-subject variability in shape of the visual field raises concerns about current clinical visual field indices, and further studies are needed to develop improved indices.

The Effect of Limiting the Range of Perimetric Sensitivities on Pointwise Assessment of Visual Field Progression in Glaucoma

PURPOSE

Automated perimetry does not produce reliable estimates of true psychophysical threshold in glaucomatous visual fields when the perimetric threshold falls below 15 to 19 dB. It may be possible to truncate testing at such locations and not use stimuli with very high contrast. However, this can only be recommended if it does not harm the ability to monitor change. This study examined the effect of applying such a cutoff by censoring sensitivities in two existing longitudinal datasets.

METHODS

Series of six visual fields were taken from participants with glaucoma or high-risk ocular hypertension in the Portland Progression Project (P3) and Rotterdam Eye Study (RES). Pointwise linear regression was used to find "progressing" locations, defined as a slope ≤ -1 dB/y with P < 1%. An eye was labeled progressing if ≥3 locations were progressing. This was repeated after setting any sensitivities below the cutoff value C (CdB) to instead equal that value for different integer values of CdB.

RESULTS

In the P3 cohort tested using Swedish Interactive Testing Algorithm (SITA) Standard, censoring below 15 to 19 dB did not reduce the number of eyes flagged as progressing. For the RES cohort tested using the Full Threshold algorithm, censoring below 10 dB did not reduce the number of eyes flagged as progressing, but a modest reduction was seen for CdB between 10 dB and 15 to 19 dB.

CONCLUSIONS

The proportion of eyes flagged as progressing was not decreased by censoring unreliable sensitivities. Restricting the range of contrast used in clinical perimetry may be possible without hampering the ability to monitor glaucomatous visual field progression.

Contrast sensitivity perimetry and clinical measures of glaucomatous damage

Purpose

To compare conventional structural and functional measures of glaucomatous damage with a new functional measure—contrast sensitivity perimetry (CSP-2).

Methods

One eye each was tested for 51 patients with glaucoma and 62 age-similar control subjects using CSP-2, size III 24-2 conventional automated perimetry (CAP), 24-2 frequency-doubling perimetry (FDP), and retinal nerve fiber layer (RNFL) thickness. For superior temporal (ST) and inferior temporal (IT) optic disc sectors, defect depth was computed as amount below mean normal, in log units. Bland-Altman analysis was used to assess agreement on defect depth, using limits of agreement and three indices: intercept, slope, and mean difference. A criterion of p < 0.0014 for significance used Bonferroni correction.

Results

Contrast sensitivity perimetry-2 and FDP were in agreement for both sectors. Normal variability was lower for CSP-2 than for CAP and FDP (F > 1.69, p < 0.02), and Bland-Altman limits of agreement for patient data were consistent with variability of control subjects (mean difference, −0.01 log units; SD, 0.11 log units). Intercepts for IT indicated that CSP-2 and FDP were below mean normal when CAP was at mean normal (t > 4, p < 0.0005). Slopes indicated that, as sector damage became more severe, CAP defects for IT and ST deepened more rapidly than CSP-2 defects (t > 4.3, p < 0.0005) and RNFL defects for ST deepened more slowly than for CSP, FDP, and CAP. Mean differences indicated that FDP defects for ST and IT were on average deeper than RNFL defects, as were CSP-2 defects for ST (t > 4.9, p < 0.0001).

Conclusions

Contrast sensitivity perimetry-2 and FDP defects were deeper than CAP defects in optic disc sectors with mild damage and revealed greater residual function in sectors with severe damage. The discordance between different measures of glaucomatous damage can be accounted for by variability in people free of disease.

Choice of Stimulus Range and Size Can Reduce Test-Retest Variability in Glaucomatous Visual Field Defects

PURPOSE

To develop guidelines for engineering perimetric stimuli to reduce test-retest variability in glaucomatous defects.

METHODS

Perimetric testing was performed on one eye for 62 patients with glaucoma and 41 age-similar controls on size III and frequency-doubling perimetry and three custom tests with Gaussian blob and Gabor sinusoid stimuli. Stimulus range was controlled by values for ceiling (maximum sensitivity) and floor (minimum sensitivity). Bland-Altman analysis was used to derive 95% limits of agreement on test and retest, and bootstrap analysis was used to test the hypotheses about peak variability.

RESULTS

Limits of agreement for the three custom stimuli were similar in width (0.72 to 0.79 log units) and peak variability (0.22 to 0.29 log units) for a stimulus range of 1.7 log units. The width of the limits of agreement for size III decreased from 1.78 to 1.37 to 0.99 log units for stimulus ranges of 3.9, 2.7, and 1.7 log units, respectively (F = 3.23, P < 0.001); peak variability was 0.99, 0.54, and 0.34 log units, respectively (P < 0.01). For a stimulus range of 1.3 log units, limits of agreement were narrowest with Gabor and widest with size III stimuli, and peak variability was lower (P < 0.01) with Gabor (0.18 log units) and frequency-doubling perimetry (0.24 log units) than with size III stimuli (0.38 log units).

CONCLUSIONS

Test-retest variability in glaucomatous visual field defects was substantially reduced by engineering the stimuli.

TRANSLATIONAL RELEVANCE

The guidelines should allow developers to choose from a wide range of stimuli.

Assessment of the reliability of standard automated perimetry in regions of glaucomatous damage

PURPOSE

Visual field testing uses high-contrast stimuli in areas of severe visual field loss. However, retinal ganglion cells saturate with high-contrast stimuli, suggesting that the probability of detecting perimetric stimuli may not increase indefinitely as contrast increases. Driven by this concept, this study examines the lower limit of perimetric sensitivity for reliable testing by standard automated perimetry.

DESIGN

Evaluation of a diagnostic test.

PARTICIPANTS

A total of 34 participants with moderate to severe glaucoma; mean deviation at their last clinic visit averaged -10.90 dB (range, -20.94 to -3.38 dB). A total of 75 of the 136 locations tested had a perimetric sensitivity of ≤ 19 dB.

METHODS

Frequency-of-seeing curves were constructed at 4 nonadjacent visual field locations by the Method of Constant Stimuli (MOCS), using 35 stimulus presentations at each of 7 contrasts. Locations were chosen a priori and included at least 2 with glaucomatous damage but a sensitivity of ≥ 6 dB. Cumulative Gaussian curves were fit to the data, first assuming a 5% false-negative rate and subsequently allowing the asymptotic maximum response probability to be a free parameter.

MAIN OUTCOME MEASURES

The strength of the relation (R(2)) between perimetric sensitivity (mean of last 2 clinic visits) and MOCS sensitivity (from the experiment) for all locations with perimetric sensitivity within ± 4 dB of each selected value, at 0.5 dB intervals.

RESULTS

Bins centered at sensitivities ≥ 19 dB always had R(2) >0.1. All bins centered at sensitivities ≤ 15 dB had R(2) <0.1, an indication that sensitivities are unreliable. No consistent conclusions could be drawn between 15 and 19 dB. At 57 of the 81 locations with perimetric sensitivity <19 dB, including 49 of the 63 locations ≤ 15 dB, the fitted asymptotic maximum response probability was <80%, consistent with the hypothesis of response saturation. At 29 of these locations the asymptotic maximum was <50%, and so contrast sensitivity (50% response rate) is undefined.

CONCLUSIONS

Clinical visual field testing may be unreliable when visual field locations have sensitivity below approximately 15 to 19 dB because of a reduction in the asymptotic maximum response probability. Researchers and clinicians may have difficulty detecting worsening sensitivity in these visual field locations, and this difficulty may occur commonly in patients with glaucoma with moderate to severe glaucomatous visual field loss.

The effect of test variability on the structure-function relationship in early glaucoma

PURPOSE

To determine whether the weakness of the structure-function relationship could be produced by test variability alone, without implying underlying dissociation between the true rates of structural and functional change.

METHODS

Perimetric mean deviation (MD), and rim area (RA) and cup volume (CV) from confocal scanning laser ophthalmoscopy, over six visits, were taken from 166 eyes of 92 participants with high-risk ocular hypertension or suspected/early glaucoma in the Portland Progression Project. Models were created of each measure's variability. A further model predicted the rate of functional change from the rate of structural change. These were used to generate realistic simulated sequences of both functional and structural data with different standard deviations σ between the underlying rates of change. 'Observed' structure-function relationships were calculated. An empirical p-value was derived, equaling the proportion of simulated series for which the 'observed' structure-function dissociation was greater than that seen in patient data.

RESULTS

The correlation between the rates of structural (RA) and functional (MD) change was 0.171, consistent with σ < 0.02 dB/yr. Using CV, the correlation was -0.091, consistent with σ < 0.01 dB/yr. By comparison, the models predicted that the standard deviation of the rate of functional change for a healthy eye due to test variability would be 0.18 dB/yr.

CONCLUSION

Test variability is sufficiently large that realistic patient data can be simulated without requiring a large variability between the underlying rates of structural and functional change. This absence of implied dissociation is a necessary condition for it to be valid to combine structural and functional measures to improve estimates of functional change and/or to reduce perimetric variability.

'Structure-function relationship' in glaucoma: past thinking and current concepts

An understanding of the relationship between functional and structural measures in primary open-angle glaucoma is necessary for both grading the severity of disease and for understanding the natural history of the condition. This article outlines the current evidence for the nature of this relationship and highlights the current mathematical models linking structure and function. Large clinical trials demonstrate that both structural and functional change are apparent in advanced stages of disease, and at an individual level, detectable structural abnormality may precede functional abnormality in some patients, whereas the converse is true in other patients. Although the exact nature of the 'structure-function' relationship in primary open-angle glaucoma is still the topic of scientific debate and the subject of continuing research, this article aims to provide the clinician with an understanding of the past concepts and contemporary thinking in relation to the structure-function relationship in primary open-angle glaucoma.

Determining mechanisms of visual loss in glaucoma using Rarebit perimetry

PURPOSE

Evidence for ganglion cell visual dysfunction in human glaucoma is often indirect, being either measured at the cellular level in animal models or being inferred from the pooled responses of a large number of ganglion cells in human observers. Rarebit perimetry (RBP) uses repeated, intense (150 cd/m2) stimuli-whose size is close to the spatial scale of a ganglion cell-to search for small retinal areas with zero sensitivity. Decreasing the stimulus luminance to 64 cd/m2 in normal observers does not alter the percentage of RBP stimuli detected [the mean hit rate (MHR)], and so we hypothesized that a similar response robustness should occur in glaucoma if the elements detecting the RBP target show no signs of visual dysfunction.

METHODS

Nineteen glaucoma subjects and 19 age-matched controls were tested with a customized RBP test at 13 stimulus luminances (10 to 150 cd/m2, 0.14 log unit intervals). A four-parameter (threshold, spread, false positive proportion, and miss rate) cumulative Gaussian psychometric function was fitted to the response rate data from a glaucoma-affected region (glaucoma subjects; MHR >50% and <80%) and from the corresponding region in an age-matched normal control. Our hypothesis would predict that only the miss rates should differ between groups.

RESULTS

Glaucoma subjects showed significantly higher miss rates (0.18 vs. 0.04, p < 0.001), lower false positive proportions (0.009 vs. 0.025, p = 0.004), greater spreads (0.30 vs. 0.19, p = 0.002), and elevated thresholds [1.57 log(cd/m2) vs. 1.13 log(cd/m2), p < 0.001].

CONCLUSIONS

Responses to RBP stimuli are not robust to decreasing luminances in glaucoma. Our results more directly imply the presence of ganglion cell visual dysfunction in human glaucoma than studies using larger targets where contrast sensitivity losses could result through ganglion cell death alone. Such dysfunction may not be detected by Rarebit's MHR given that dysfunctional elements may still respond to the very intense RBP stimulus.

Modeling the patterns of visual field loss in glaucoma

PURPOSE

A computer model was developed to test the assumption that diffuse neural loss can result in the field loss pattern characteristic of glaucoma.

METHODS

The anterior visual pathways comprised the retinal ganglion cells, and their axons up to the optic nerve head (ONH) were modeled in a computer program. Axon resistance to stress was accounted for depending on the location on the ONH, taking into consideration the presence or absence of vessels in the area. Damage patterns were applied to the axons at the ONH, and the corresponding dendritic fields were removed accordingly. A visual field was extracted and represented on a gray scale after a predetermined stage of damage was reached. Two patterns of damage were considered, a diffuse damage produced by randomly removing fibers and an ordered anteroposterior elimination.

RESULTS

Random damage never rendered a pattern loss. Ordered centrifugal fiber loss may produce a radial pattern more conspicuous when the vessels are endowed with a protective role. In both cases, scotomas tend to be detectable earlier in more peripheral locations, attributable to the increasing size of the receptive fields with eccentricity.

CONCLUSIONS

The model shows that pattern loss typical of glaucoma cannot be solely the result of a random loss of fibers. Anteroposterior damage of the ONH can explain radial progression of scotomas if a protective role is introduced for the central vessels.