Three-dimensional Neuroretinal Rim Thickness and Visual Fields in Glaucoma: A Broken-stick Model

Abstract

Precis: In open-angle glaucoma, when neuroretinal rim tissue measured by volumetric optical coherence tomography (OCT) scans is below a third of the normal value, visual field (VF) damage becomes detectable.

Purpose: To determine the amount of neuroretinal rim tissue thickness below which VF damage becomes detectable.

Methods: In a retrospective cross-sectional study, 1 eye per subject (of 57 healthy and 100 open-angle glaucoma patients) at an academic institution had eye examinations, VF testing, spectral-domain OCT retinal nerve fiber layer (RNFL) thickness measurements, and optic nerve volumetric scans. Using custom algorithms, the minimum distance band (MDB) neuroretinal rim thickness was calculated from optic nerve scans. "Broken-stick" regression was performed for estimating both the MDB and RNFL thickness tipping-point thresholds, below which were associated with initial VF defects in the decibel scale. The slopes for the structure-function relationship above and below the thresholds were computed. Smoothing curves of the MDB and RNFL thickness covariates were evaluated to examine the consistency of the independently identified tipping-point pairs.

Results: Plots of VF total deviation against MDB thickness revealed plateaus of VF total deviation unrelated to MDB thickness. Below the thresholds, VF total deviation decreased with MDB thickness, with the associated slopes significantly greater than those above the thresholds (P<0.014). Below 31% of global MDB thickness, and 36.8% and 43.6% of superior and inferior MDB thickness, VF damage becomes detectable. The MDB and RNFL tipping points were in good accordance with the correlation of the MDB and RNFL thickness covariates.

Conclusions: When neuroretinal rim tissue, characterized by MDB thickness in OCT, is below a third of the normal value, VF damage in the decibel scale becomes detectable.

FIGURE 1

Neuroretinal rim broken-stick model for global values: determining the tipping point at which global neuroretinal rim thinning is first associated with visual field (VF) damage. This graph correlates minimum distance band (MDB) neuroretinal rim values (x-axis) with corresponding VF total deviation values (y-axis) for 157 healthy and glaucomatous eyes, where each of the 52 total deviation points were unlogged, averaged, then log-transformed back to decibel scale. Broken-stick model is represented by the dashed diagonal black line with the lowess smoothing fit in pink. Red squares represent healthy eyes. Blue stars represent glaucoma eyes. The yellow open circle represents the tipping point of global MDB thickness, with the 95% confidence interval indicated by vertical dashed lines.

FIGURE 2

Neuroretinal rim broken-stick model for quadrant values: determining the tipping point at which quadrant neuroretinal rim thinning is first associated with visual field (VF) damage. This graph correlates minimum distance band (MDB) neuroretinal rim values (x-axis) with corresponding VF total deviation (TD) values (y-axis) for 157 healthy and glaucomatous eyes for each of the 4 quadrants. Broken-stick models are represented by the dashed diagonal black lines with the lowess smoothing fit in pink. Red squares represent healthy eyes. Blue stars represent glaucoma eyes. The yellow open circles represent the tipping points, with the 95% confidence interval indicated by vertical dashed lines.

FIGURE 3

Neuroretinal rim broken-stick model for sector values: determining the tipping point at which sector neuroretinal rim thinning is first associated with visual field (VF) damage. This graph correlates minimum distance band (MDB) neuroretinal rim values (x-axis) with corresponding VF total deviation (TD) values (y-axis) for healthy and glaucomatous eyes for each of the 4 sectors. Graphs are presented for average VF TD for each of the 4 sector values versus the corresponding MDB values. Broken-stick model is represented by the dashed black line with the lowess smoothing fit in pink. Red squares represent healthy eyes. Blue stars represent glaucoma eyes. The yellow open circles represent the tipping points, with the 95% confidence interval indicated by vertical dashed lines.

FIGURE 4

Retinal nerve fiber layer (RNFL) broken-stick model for global values: determining the tipping point at which global RNFL thinning is first associated with visual field (VF) damage. This graph correlates RNFL values (x-axis) with corresponding VF total deviation values (y-axis) for healthy and glaucomatous eyes, where each of the 52 testing points were unlogged, averaged, then log-transformed back to decibel scale. Graphs are presented for average VF total deviation values versus the global RNFL values. Broken-stick model is represented by the dashed black line with the lowess smoothing fit in pink. Red squares represent healthy eyes. Blue stars represent glaucoma eyes. The yellow open circle represents the tipping point, with the 95% confidence interval indicated by vertical dashed lines.

FIGURE 5

Retinal nerve fiber layer (RNFL) broken-stick model for quadrant values: determining the tipping point at which quadrant RNFL thinning is first associated with visual field (VF) damage. This graph correlates RNFL values (x-axis) with corresponding VF total deviation (TD) values (y-axis) for healthy and glaucomatous eyes, where each of the 52 testing points were unlogged, averaged, then log-transformed back to decibel scale. Graphs are presented for average VF TD values versus the quadrant RNFL values. Broken-stick model is represented by the dashed black line with the lowess smoothing fit in pink. Red squares represent healthy eyes. Blue stars represent glaucoma eyes. The yellow open circles represent the tipping points, with the 95% confidence interval indicated by vertical dashed lines.

FIGURE 6

Retinal nerve fiber layer (RNFL) broken-stick model for sector values: determining the tipping point at which sector RNFL thinning is first associated with visual field (VF) damage. This graph correlates RNFL values (x-axis) with corresponding VF total deviation (TD) values (y-axis) for healthy and glaucomatous eyes, where each of the 52 testing points were unlogged, averaged, then log-transformed back to decibel scale. Graphs are presented for average VF TD values versus the sectoral RNFL values. Broken-stick model is represented by the dashed black line with the lowess smoothing fit in pink. Red squares represent healthy eyes. Blue stars represent glaucoma eyes. The yellow open circles represent the tipping point, with the 95% confidence interval indicated by vertical dashed lines.

FIGURE 7

Correspondence of the independently determined tipping points for minimum distance band (MDB) neuroretinal rim thickness and retinal nerve fiber layer (RNFL) thickness for the global, quadrant, and sector values. The graph shows the correlation of the RNFL thickness (y-axis) with the MDB thickness (x-axis) for the global average, the 4 quadrants, and the 4 sectors. A point with coordinates given by the independently determined MDB tipping point and the RNFL tipping point is plotted on the scatter plot (indicated by the green star). The corresponding 95% confidence intervals for both tipping points are plotted (horizontal and vertical dashed lines). The red squares represent the normal subjects; the blue stars represent the glaucomatous subjects. A lowess smoothing fit (bold black line) to the RNFL-MDB data and its bootstrapped 95% confidence bounds were included to delineate the RNFL-MDB correlation for comparing the consistency of the tipping points. The confidence bounds falling within the 95% confidence regions (central dotted rectangle) defined by the tipping point indicates good one-to-one correspondence of the tipping points.