Estimating Ganglion Cell Complex Rates of Change With Bayesian Hierarchical Models

Detection of glaucoma progression on longitudinal series of en-face macular optical coherence tomography angiography images with a deep learning model

BACKGROUND/AIMS

To design a deep learning (DL) model for the detection of glaucoma progression with a longitudinal series of macular optical coherence tomography angiography (OCTA) images.

METHODS

202 eyes of 134 patients with open-angle glaucoma with ≥4 OCTA visits were followed for an average of 3.5 years. Glaucoma progression was defined as having a statistically significant negative 24-2 visual field (VF) mean deviation (MD) rate. The baseline and final macular OCTA images were aligned according to centre of fovea avascular zone automatically, by checking the highest value of correlation between the two images. A customised convolutional neural network (CNN) was designed for classification. A comparison of the CNN to logistic regression model for whole image vessel density (wiVD) loss on detection of glaucoma progression was performed. The performance of the model was defined based on the confusion matrix of the validation dataset and the area under receiver operating characteristics (AUC).

RESULTS

The average (95% CI) baseline VF MD was -3.4 (-4.1 to -2.7) dB. 28 (14%) eyes demonstrated glaucoma progression. The AUC (95% CI) of the DL model for the detection of glaucoma progression was 0.81 (0.59 to 0.93). The sensitivity, specificity and accuracy (95% CI) of DL model were 67% (34% to 78%), 83% (42% to 97%) and 80% (52% to 95%), respectively. The AUC (95% CI) for the detection of glaucoma progression based on the logistic regression model was lower than the DL model (0.69 (0.50 to 0.88)).

CONCLUSION

The optimised DL model detected glaucoma progression based on longitudinal macular OCTA images showed good performance. With external validation, it could enhance detection of glaucoma progression.

TRIAL REGISTRATION NUMBER

NCT00221897.

Comparison of Retinal Nerve Fiber Layer and Ganglion Cell Complex Rates of Change in Patients With Moderate to Advanced Glaucoma

PURPOSE

To compare ganglion cell complex (GCC) and retinal nerve fiber layer (RNFL) rates of change (RoC) in eyes with central or moderate to advanced glaucoma.

DESIGN

Prospective cohort study.

PARTICIPANTS

A total of 918 matched macular and RNFL OCT scan pairs from 109 eyes (109 patients) enrolled in the Advanced Glaucoma Progression Study with ≥2 years of follow-up and ≥4 OCT scans.

METHODS

We exported GCC and RNFL thickness measurements in 49 central macular superpixels and 12 RNFL clock-hour sectors, respectively. We applied our latest Bayesian hierarchical longitudinal model to estimate population and subject-specific baseline thickness (intercepts) and rates of change (RoC) in macular superpixels and RNFL sectors. Global RNFL and GCC RoC were analyzed in a single bivariate longitudinal model to properly compare them accounting for the correlation between their RoC.

MAIN OUTCOME MEASURES

Proportion of significant negative (deteriorating) and positive (improving) RoC expressed in μm/year. Standardized RoC were calculated by dividing RoC by the corresponding population SD. Analyses were repeated in eyes with visual field mean deviation (MD) ≤-6 and > -6 dB.

RESULTS

Average (SD) 24-2 visual field MD and follow-up length were -8.6 (6.3) dB and 4.2 (0.5) years, respectively. Global RNFL RoC (-0.70 µm/year) were faster than GCC (-0.44 µm/year) (P < .001); corresponding normalized RoC were not significantly different (P = .052). In bivariate analysis, patients with a significant negative global RNFL RoC (n = 63, 57%) or GCC (n = 56, 51%) frequently did so for both outcomes (n = 49, 45%). The average proportion of significantly decreasing RNFL sectors within an eye was 30.7% in eyes with MD > -6 dB compared to 20.5% in those with MD ≤ -6 dB (P = .014); the proportions for GCC superpixels were 21.1% versus 18.7%, respectively (P = .63).

CONCLUSIONS

Both GCC and RNFL measures can detect structural progression in glaucoma patients with central damage or moderate to advanced glaucoma. The clinical utility of RNFL imaging decreases with worsening severity of glaucoma.

Detecting Fast Progressors: Comparing a Bayesian Longitudinal Model to Linear Regression for Detecting Structural Changes in Glaucoma

PURPOSE

Demonstrate that a novel Bayesian hierarchical spatial longitudinal (HSL) model identifies macular superpixels with rapidly deteriorating ganglion cell complex (GCC) thickness more efficiently than simple linear regression (SLR).

DESIGN

Prospective cohort study.

SETTING

Tertiary Glaucoma Center.

SUBJECTS

One hundred eleven eyes (111 patients) with moderate to severe glaucoma at baseline and ≥4 macular optical coherence tomography scans and ≥2 years of follow-up.

OBSERVATION PROCEDURE

Superpixel-patient-specific GCC slopes and their posterior variances in 49 superpixels were derived from our latest Bayesian HSL model and Bayesian SLR. A simulation cohort was created with known intercepts, slopes, and residual variances in individual superpixels.

MAIN OUTCOME MEASURES

We compared HSL and SLR in the fastest progressing deciles on (1) proportion of superpixels identified as significantly progressing in the simulation study and compared to SLR slopes in cohort data; (2) root mean square error (RMSE), and SLR/HSL RMSE ratios.

RESULTS

Cohort- In the fastest decile of slopes per SLR, 77% and 80% of superpixels progressed significantly according to SLR and HSL, respectively. The SLR/HSL posterior SD ratio had a median of 1.83, with 90% of ratios favoring HSL. Simulation- HSL identified 89% significant negative slopes in the fastest progressing decile vs 64% for SLR. SLR/HSL RMSE ratio was 1.36 for the fastest decile of slopes, with 83% of RMSE ratios favoring HSL.

CONCLUSION

The Bayesian HSL model improves the estimation efficiency of local GCC rates of change regardless of underlying true rates of change, particularly in fast progressors.

A Bayesian Hierarchical Spatial Longitudinal Model Improves Estimation of Local Macular Rates of Change in Glaucomatous Eyes

Purpose

Demonstrate that a novel Bayesian hierarchical spatial longitudinal (HSL) model improves estimation of local macular ganglion cell complex (GCC) rates of change compared to simple linear regression (SLR) and a conditional autoregressive (CAR) model.

Methods

We analyzed GCC thickness measurements within 49 macular superpixels in 111 eyes (111 patients) with four or more macular optical coherence tomography scans and two or more years of follow-up. We compared superpixel-patient-specific estimates and their posterior variances derived from the latest version of a recently developed Bayesian HSL model, CAR, and SLR. We performed a simulation study to compare the accuracy of intercept and slope estimates in individual superpixels.

Results

HSL identified a significantly higher proportion of significant negative slopes in 13/49 superpixels and a significantly lower proportion of significant positive slopes in 21/49 superpixels than SLR. In the simulation study, the median (tenth, ninetieth percentile) ratio of mean squared error of SLR [CAR] over HSL for intercepts and slopes were 1.91 (1.23, 2.75) [1.51 (1.05, 2.20)] and 3.25 (1.40, 10.14) [2.36 (1.17, 5.56)], respectively.

Conclusions

A novel Bayesian HSL model improves estimation accuracy of patient-specific local GCC rates of change. The proposed model is more than twice as efficient as SLR for estimating superpixel-patient slopes and identifies a higher proportion of deteriorating superpixels than SLR while minimizing false-positive detection rates.

Translational Relevance

The proposed HSL model can be used to model macular structural measurements to detect individual glaucoma progression earlier and more efficiently in clinical and research settings.

Mesenchymal stem cells differentiate to retinal ganglion-like cells in rat glaucoma model induced by polystyrene microspheres

AIM

The study aimed to evaluate the differentiation ability of intravitreally injected rat bone marrow-derived mesenchymal stem cells (rBM-MSCs) to retinal ganglion-like cells in a polystyrene microsphere induced rat glaucoma model.

MATERIALS AND METHODS

The glaucoma rat model was generated via intracameral injection of 7 microliter polystyrene microspheres. Green fluorescence protein-labeled (GFP) rBM-MSCs were transplanted intravitreally at or after induction of ocular hypertension (OHT), depending on the groups. By the end of the fourth week, flat-mount retinal dissection was performed, and labeled against Brn3a, CD90, GFAP, CD11b, Vimentin, and localization of GFP positive rBM-MSCs was used for evaluation through immunofluorescence staining and to count differentiated retinal cells by flow cytometry. From 34 male Wistar albino rats, 56 eyes were investigated.

RESULTS

Flow cytometry revealed significantly increased CD90 and Brn3a positive cells in glaucoma induced and with rBM-MSC injected groups compared to control(P = 0.006 and P = 0.003 respectively), sham-operated (P = 0.007 and P < 0.001 respectively), and only rBM-MSCs injected groups (P = 0.002 and P = 0.009 respectively). Immunofluorescence microscopy revealed differentiation of GFP labeled stem cells to various retinal cells, including ganglion-like cells. rBM-MSCs were observable in ganglion cells, inner and outer nuclear retinal layers in rBM-MSCs injected eyes.

CONCLUSION

Intravitreally transplanted rBM-MSCs differentiated into retinal cells, including ganglion-like cells, which successfully created a glaucoma model damaged with polystyrene microspheres. Promisingly, MSCs may have a role in neuro-protection and neuro-regeneration treatment of glaucoma in the future.

Association of Blood Pressure With Rates of Macular Ganglion Cell Complex Thinning in Patients With Glaucoma

Importance

There are scarce data on the association of blood pressure measures with subsequent macular structural rates of change in patients with glaucoma.

Objective

To investigate the association of baseline blood pressure measures with rates of change of the macular ganglion cell complex in patients with central or moderate to advanced glaucoma damage at baseline.

Design, Setting, and Participants

This prospective cohort study, conducted from August 2021 to August 2022, used data from patients in the Advanced Glaucoma Progression Study at the University of California, Los Angeles. Participants were between 39 and 80 years of age and had more than 4 macular imaging tests and 2 or more years of follow-up.

Exposures

A diagnosis of glaucoma with either central damage or a visual field mean deviation worse than -6 dB.

Main Outcomes and Measures

The main outcome was the association of blood pressure measures with ganglion cell complex rates of change. Macular ganglion cell complex thickness rates of change were estimated with a bayesian hierarchical model. This model included relevant demographic and clinical factors. Blood pressure measures, intraocular pressure, and their interactions were added to the model to assess the association of baseline blood pressure measures with global ganglion cell complex rates of change.

Results

The cohort included 105 eyes from 105 participants. The mean (SD) age, 10-2 visual field mean deviation, and follow-up time were 66.9 (8.5) years, -8.3 (5.3) dB, and 3.6 (0.4) years, respectively, and 67 patients (63.8%) were female. The racial and ethnic makeup of the cohort was 15 African American (14.3%), 23 Asian (21.9%), 12 Hispanic (11.4%), and 55 White (52.4%) individuals based on patient self-report. In multivariable analyses, female sex, history of taking blood pressure medications, higher intraocular pressure, thicker central corneal thickness, shorter axial length, higher contrast sensitivity at 12 cycles per degree, and higher baseline 10-2 visual field mean deviation were associated with faster ganglion cell complex thinning. Lower diastolic blood pressure was associated with faster rates of ganglion cell complex thinning at higher intraocular pressures. For intraocular pressures of 8 and of 16 mm Hg (10% and 90% quantiles, respectively), every 10 mm Hg-lower increment of diastolic blood pressure was associated with 0.011 μm/y slower and -0.130 μm/y faster rates of ganglion cell complex thinning, respectively.

Conclusions and Relevance

In this cohort study, a combination of lower diastolic blood pressure and higher intraocular pressure at baseline was associated with faster rates of ganglion cell complex thinning. These findings support consideration of evaluating and addressing diastolic blood pressure as a therapeutic measure in patients with glaucoma if supported by appropriate clinical trials.

Comparison of Ganglion Cell Layer and Inner Plexiform Layer Rates of Change in Suspected and Established Glaucoma

PURPOSE

We compared ganglion cell layer (GCL) and inner plexiform layer (IPL) rates of change (RoC) in patients with glaucoma suspect (GS) and established glaucoma (EG) to test the hypothesis that IPL thickness changes would occur earlier than GCL changes in eyes with early damage.

DESIGN

Prospective, cohort study.

METHODS

A total of 64 GS eyes (46 patients) and 112 EG eyes (112 patients) with ≥2 years of follow-up and ≥3 macular optical coherence tomography scans were included. GCL and IPL superpixel thickness measurements were exported. A Bayesian hierarchical model with random intercepts/slopes and random residual variances was fitted to estimate RoC in individual superpixels. Normalized RoC and proportions of superpixels with significantly negative and positive GCL and IPL RoC were compared within the groups.

RESULTS

The average (SD) follow-up time and number of scans were 3.5 (0.7) years and 4.2 (1.0), respectively, in the GS group and 3.6 (0.4) years and 7.3 (1.1) in the EG group. Mean (SD) normalized RoC was faster for GCL than IPL (-0.69 [0.05] vs -0.33 [0.04]) in the GS group, whereas it was faster for IPL (-0.47 [0.03] vs -0.28 [0.02]) in EG eyes. GCL RoC were significantly negative in 24 of 36 superpixels compared with 8 of 36 for IPL (P < .001) in GS eyes. In the EG group, 23 of 36 superpixels had significant negative IPL RoC compared with 13 of 36 superpixels for GCL (P = .006).

CONCLUSIONS

GCL thickness is more likely to demonstrate change over time compared with IPL in glaucoma suspects. There is no evidence of preferential IPL thinning in eyes with suspected early glaucoma damage.

Artificial Intelligence to Aid Glaucoma Diagnosis and Monitoring: State of the Art and New Directions

Recent developments in the use of artificial intelligence in the diagnosis and monitoring of glaucoma are discussed. To set the context and fix terminology, a brief historic overview of artificial intelligence is provided, along with some fundamentals of statistical modeling. Next, recent applications of artificial intelligence techniques in glaucoma diagnosis and the monitoring of glaucoma progression are reviewed, including the classification of visual field images and the detection of glaucomatous change in retinal nerve fiber layer thickness. Current challenges in the direct application of artificial intelligence to further our understating of this disease are also outlined. The article also discusses how the combined use of mathematical modeling and artificial intelligence may help to address these challenges, along with stronger communication between data scientists and clinicians.

Multivariate Longitudinal Modeling of Macular Ganglion Cell Complex: Spatiotemporal Correlations and Patterns of Longitudinal Change

Purpose

To investigate spatiotemporal correlations among ganglion cell complex (GCC) superpixel thickness measurements and explore underlying patterns of longitudinal change across the macular region.

Design

Longitudinal cohort study.

Subjects

One hundred eleven eyes from 111 subjects from the Advanced Glaucoma Progression Study with ≥ 4 visits and ≥ 2 years of follow-up.

Methods

We further developed our proposed Bayesian hierarchical model for studying longitudinal GCC thickness changes across macular superpixels in a cohort of glaucoma patients. Global priors were introduced for macular superpixel parameters to combine data across superpixels and better estimate population slopes and intercepts.

Main Outcome Measures

Bayesian residual analysis to inspect cross-superpixel correlations for subject random effects and residuals. Principal component analysis (PCA) to explore underlying patterns of longitudinal macular change.

Results

Average (standard deviation [SD]) follow-up and baseline 10-2 visual field mean deviation were 3.6 (0.4) years and -8.9 (5.9) dB, respectively. Superpixel-level random effects and residuals had the greatest correlations with nearest neighbors; correlations were higher in the superior than in the inferior region and strongest among random intercepts, followed by random slopes, residuals, and residual SDs. PCA of random intercepts showed a first large principal component (PC) across superpixels that approximated a global intercept, a second PC that contrasted the superior and inferior macula, and a third PC, contrasting inner and nasal superpixels with temporal and peripheral superpixels. PCs for slopes, residual SDs, and residuals were remarkably similar to those of random intercepts.

Conclusions

Introduction of cross-superpixel random intercepts and slopes is expected to improve estimation of population and subject parameters. Further model enhancement may be possible by including cross-superpixel random effects and correlations to address spatiotemporal relationships in longitudinal data sets.

Ganglion Cell Complex: The Optimal Measure for Detection of Structural Progression in the Macula

PURPOSE

To test the hypothesis that macular ganglion cell complex (GCC) thickness from optical coherence tomography (OCT) provides a stronger change signal regardless of glaucoma severity compared with other macular measures.

DESIGN

Prospective cohort study.

METHODS

Eyes were from 112 patients with moderate to severe glaucoma at baseline from a tertiary glaucoma center. In each 3° × 3° macular superpixel, a hierarchical Bayesian random intercept and slope model with random residual variance was fit to longitudinal full macular thickness (FMT), outer retina layers, GCC, ganglion cell-inner plexiform layer (GCIPL), and ganglion cell layer (GCL) measurements. We estimated population- and individual-level slopes and intercepts. Proportions of substantial worsening and improving superpixel slopes were compared between layers and in superpixels with mild to moderate vs severe damage (total deviation of corresponding visual field location ≥ -8 vs < -8 dB).

RESULTS

Mean (SD) follow-up time and baseline 10-2 visual field mean deviation were 3.6 (0.4) years and -8.9 (5.9) dB, respectively. FMT displayed the highest proportion of significant negative slopes (1932/3519 [54.9%]), followed by GCC (1286/3519 [36.5%]), outer retina layers (1254/3519 [35.6%]), (GCIPL) (1075/3518 [30.6%]), and (GCL) (698/3518 [19.8%]). Inner macular measures detected less worsening in the severe glaucoma group; yet GCC (223/985 [22.6%]) identified the highest proportion (GCIPL: 183/985 [18.6%]; GCL: 106/985 [10.8%]). Proportions of positive rates were small and comparable among all measures.

CONCLUSIONS

GCC is the optimal macular measure for detection of structural change in eyes with moderate to severe glaucoma. Although a higher proportion of worsening superpixels was observed for FMT, a large portion of FMT change could be attributed to changes in outer retina layers.