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Longitudinal Macular Structure-Function Relationships in Glaucoma and Their Sources of Variability

      Purpose

      To review central structure-function (SF) relationships in glaucoma; to compare contributions of within-session and between-session variability to total variability of macular optical coherence tomography (OCT) thickness measurements; and to test the hypothesis that longitudinal within-eye variability of central SF relationships is smaller than between-individual variability.

      Methods

      We reviewed the pertinent literature on central SF relationships in glaucoma. Thirty-eight eyes (20 normal or glaucoma subjects) had ×3 macular images per session over 3 sessions, and superpixels thickness measurements for ganglion cell layer (GCL), ganglion cell/inner plexiform layer (GCIPL), ganglion cell complex (GCC), and full macular thickness (FMT) were exported. Linear mixed models were used for estimating contributions of between- and within-session variability to total thickness variability. One hundred twenty eyes with ≥3 10° visual fields (VFs)/OCT images were enrolled for the longitudinal study. We investigated within-eye longitudinal SF relationships (GCIPL thickness vs VF total deviations) with a change-point regression model and compared within-eye to between-individual variabilities with components-of-variance models.

      Results

      In the cross-sectional study, the between-session component contributed 8%, 11%, 11%, and 36% of total variability for GCL, GCIPL, GCC, and FMT, respectively. In the longitudinal study, between-individual variability explained 78%, 77%, and 67% of total SF variability at 3.4°, 5.6°, and 6.8° eccentricities, respectively (P < .05). SF relationships remained stable over time within individual eyes.

      Conclusions

      Within-session variability accounts for most of macular thickness variability over time. Longitudinal within-eye SF variability is smaller than between-individual variability. Study of within-eye SF relationships could help clinicians better understand SF linking in glaucoma and help refine progression algorithms. NOTE: Publication of this article is sponsored by the American Ophthalmological Society.
      Glaucoma is a major cause of visual disability, diminished quality of life, and blindness worldwide.
      • Bourne R.R.
      • Taylor H.R.
      • Flaxman S.R.
      • et al.
      Number of people blind or visually impaired by glaucoma worldwide and in world regions 1990 - 2010: a meta-analysis.
      The hallmark of glaucoma is progressive loss of retinal ganglion cells (RGCs) and their axons projecting information to the visual cortex. Spectral-domain optical coherence tomography (SD-OCT) has provided us with an unprecedented opportunity to monitor the RGCs and their neural processes (i.e., axons and dendrites) by measuring the thickness of the peripapillary retinal nerve fiber layer (RNFL), the neuroretinal rim at the optic nerve head, or inner retinal layers in the macula.
      • Bogunović H.
      • Kwon Y.H.
      • Rashid A.
      • et al.
      Relationships of retinal structure and humphrey 24-2 visual field thresholds in patients with glaucoma.
      Damage to RGCs is expected to lead to loss of visual function. The subject of structure-function (SF) in glaucoma has elicited a great amount of interest in the glaucoma community.
      • Malik R.
      • Swanson W.H.
      • Garway-Heath D.F.
      ‘Structure-function relationship’ in glaucoma: past thinking and current concepts.
      Correlation of structure and function is helpful clinically to confirm and emphasize the topography and severity of glaucomatous damage at diagnosis. Simultaneous or sequential evidence of progressive RGC damage and corresponding visual field (VF) loss aid detection of disease deterioration and clinical decision making.
      There is some redundancy in the RGC complement of the human eye so that damage on standard achromatic perimetry (white-on-white target) may not appear before some loss of RGCs has occurred. Quigley et al found that VF sensitivity began to decline soon after the initial loss of RGCs in a sample of 6 cadaver eyes.
      • Quigley H.A.
      • Addicks E.M.
      • Green W.R.
      Optic nerve damage in human glaucoma. III. Quantitative correlation of nerve fiber loss and visual field defect in glaucoma, ischemic neuropathy, papilledema, and toxic neuropathy.
      Within the central 30° of the retina, 5-dB and 10-dB sensitivity losses corresponded to about 20% and 40% RGC loss, respectively. In addition, they reported that up to 40% of RGCs could be lost before evidence of field loss could be established on standard achromatic perimetry. On the other hand, signs of VF loss can also manifest before definitive signs of structural damage. Visual field loss was the most frequent earliest sign of conversion to glaucoma in the European Glaucoma Prevention Study.
      • Miglior S.
      • Zeyen T.
      • Pfeiffer N.
      • et al.
      Results of the European Glaucoma Prevention Study.
      There has been much discussion about the nature and strength of the relationship between RGC loss and functional deficits in glaucoma, commonly referred to as the SF relationship. Most studies have explored SF relationships in pooled cross-sectional samples of patients. Linear and nonlinear relationships have been described that are likely related to the type of structural and functional measurements used, the scale in which outcomes of interest are expressed (such as linear or logarithmic), and the amount of inter-individual variability for those outcome measures.
      • Malik R.
      • Swanson W.H.
      • Garway-Heath D.F.
      ‘Structure-function relationship’ in glaucoma: past thinking and current concepts.
      The advent of SD-OCTs ushered in a new era in glaucoma diagnostics and, for the first time, enabled us to accurately measure the thickness of retinal layers in the central macula. Although evidence for early macular RGC damage had been detected in animals with experimental glaucoma
      • Quigley H.A.
      • Addicks E.M.
      • Green W.R.
      Optic nerve damage in human glaucoma. III. Quantitative correlation of nerve fiber loss and visual field defect in glaucoma, ischemic neuropathy, papilledema, and toxic neuropathy.
      and was suspected based on functional measurements,
      • Stamper R.L.
      The effect of glaucoma on central visual function.
      Zeimer et al were the first investigators to demonstrate that evidence of retinal thinning could be detected clinically in the central macula in glaucoma.
      • Zeimer R.
      • Asrani S.
      • Zou S.
      • Quigley H.
      • Jampel H.
      Quantitative detection of glaucomatous damage at the posterior pole by retinal thickness mapping. A pilot study.
      About 30% of the RGC complement in the human eye is located within 16° of the foveal center.
      • Curcio C.A.
      • Allen K.A.
      Topography of ganglion cells in human retina.
      The macula is the only retinal region where the ganglion cell layer (GCL) is more than 1 cell thick, with the peak RGC density (about 6–7 layers of RGCs) occurring 750–1100 μm from the foveal center.
      • Wassle H.
      • Grunert U.
      • Rohrenbeck J.
      • Boycott B.B.
      Cortical magnification factor and the ganglion cell density of the primate retina.
      The RGCs in the central macula are affected early during the disease
      • Hood D.C.
      • Raza A.S.
      • de Moraes C.G.
      • Johnson C.A.
      • Liebmann J.M.
      • Ritch R.
      The nature of macular damage in glaucoma as revealed by averaging optical coherence tomography data.
      • Lisboa R.
      • Leite M.T.
      • Zangwill L.M.
      • Tafreshi A.
      • Weinreb R.N.
      • Medeiros F.A.
      Diagnosing preperimetric glaucoma with spectral domain optical coherence tomography.
      and, at the same time, are the last cells to be lost in glaucoma.
      • Asrani S.
      • Rosdahl J.A.
      • Allingham R.R.
      Novel software strategy for glaucoma diagnosis: asymmetry analysis of retinal thickness.
      • Belghith A.
      • Medeiros F.A.
      • Bowd C.
      • et al.
      Structural change can be detected in advanced-glaucoma eyes.
      Hence, imaging of the macula with SD-OCT could provide clinicians with valuable information regarding the course of the disease at all stages of glaucoma.
      There is evidence that measurement of the GCL or the GCIPL, the combined thickness of the GCL and inner plexiform layer (IPL), or the macular ganglion cell complex (GCC, the combined thickness of the RNFL, GCL, and IPL), can detect early glaucoma with a performance that approximates that of circumpapillary RNFL (cpRNFL) thickness measurements.
      • Tan O.
      • Chopra V.
      • Lu A.T.
      • et al.
      Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography.
      • Mwanza J.C.
      • Durbin M.K.
      • Budenz D.L.
      • et al.
      Glaucoma diagnostic accuracy of ganglion cell-inner plexiform layer thickness: comparison with nerve fiber layer and optic nerve head.
      • Nouri-Mahdavi K.
      • Nowroozizadeh S.
      • Nassiri N.
      • et al.
      Macular ganglion cell/inner plexiform layer measurements by spectral domain optical coherence tomography for detection of early glaucoma and comparison to retinal nerve fiber layer measurements.
      • Shin H.Y.
      • Park H.Y.
      • Jung K.I.
      • Choi J.A.
      • Park C.K.
      Glaucoma diagnostic ability of ganglion cell-inner plexiform layer thickness differs according to the location of visual field loss.
      Macular thickness measures demonstrate a strong correlation with VF sensitivities similar to that of cpRNFL thickness.
      • Shin H.Y.
      • Park H.Y.
      • Jung K.I.
      • Park C.K.
      Comparative study of macular ganglion cell-inner plexiform layer and peripapillary retinal nerve fiber layer measurement: structure-function analysis.
      Also, a strong correlation has been reported between the macular GCIPL layer thickness and estimates of RGC counts.
      • Zhang C.
      • Tatham A.J.
      • Weinreb R.N.
      • et al.
      Relationship between ganglion cell layer thickness and estimated retinal ganglion cell counts in the glaucomatous macula.
      • Raza A.S.
      • Hood D.C.
      Evaluation of the structure-function relationship in glaucoma using a novel method for estimating the number of retinal ganglion cells in the human retina.
      The role of macular imaging for detection of disease progression remains less well established and is the subject of ongoing investigations, although there is substantial evidence to support its utility. Of utmost importance with regard to detection of progression is the magnitude of variability for various macular outcomes of interest, both within a measurement session (i.e., within-session variability) and between sequential measurement sessions (i.e., between-session variability). Ideally, measurement variability should be minimized so that smaller amounts of change can be efficiently detected on follow-up testing. It is not clear, at this point, how much of the total variability seen on sequential imaging sessions is explained by within-session versus between-session variability. In case most of the longitudinal variability over time is explained by within-session variability, one could argue that within-session variability should be measured at baseline and used as a yardstick for gauging individual variability in a given eye and for defining limits of variability for individual eyes.
      Study of SF relationships in pooled cross-sectional samples of patients is of interest and has been the traditional approach used in the published literature. We propose that the study of SF relationships within individual eyes can provide researchers with important information regarding linking of RGC thickness to related functional measurements among different individuals and at various locations in the macula. The inner macular thickness measurements vary significantly as a function of distance from the foveal center; hence, this variability needs to be taken into account when SF relationships are studied in the macula.

      Study Aims

      The goals of the current study were: 1) to provide an overview of the SF relationships in the macula and propose a framework for studying central SF relationships within individual eyes; 2) to estimate and compare the relative contribution of within-session and between-session variability to total variability of macular superpixel thickness measurements; and 3) to test the hypothesis that within-eye variability of macular/central VF SF relationships is significantly smaller than between-individual variability, as within-eye variability mostly represents measurement noise. We will provide proof of concept in support of studying individual SF relationships to better understand the nature of RGC damage in the central macula. The radially symmetric structural and functional measurements around the fovea or the VF fixation point are expected to demonstrate the same underlying SF relationship within an individual eye. Therefore, between-individual variability in SF relationships is likely the most important contributing factor to the total variability observed in cross-sectional SF studies.

      Methods and Patients

      Both studies were approved by the Human Subject Protection Committee and the Institutional Review Board of the University of California, Los Angeles. Subjects were prospectively consented. The studies were carried out in accordance with the tenets of the Declaration of Helsinki and the Health Insurance Portability and Accountability Act.

       Summary of Evidence Regarding Central SF Relationships in Glaucoma

      We reviewed the pertinent literature regarding the utility of central SF relationships in glaucoma.

       Cross-sectional Study Sample

      Thirty-eight eyes of 20 normal subjects or patients with glaucoma were prospectively enrolled. The glaucoma eyes were diagnosed by 1 of the authors (K.N.M., J.C.) and had glaucomatous optic neuropathy and reproducible VF loss as detailed below.
      • Johnson C.A.
      • Sample P.A.
      • Cioffi G.A.
      • Liebmann J.R.
      • Weinreb R.N.
      Structure and function evaluation (SAFE): I. criteria for glaucomatous visual field loss using standard automated perimetry (SAP) and short wavelength automated perimetry (SWAP).
      Normal subjects had no history of ocular disease, and had open angles and normal optic nerve and retinal nerve fiber layer on dilated fundus exam. After a complete eye exam, the subjects underwent macular SD-OCT imaging as described below. Three macular images were acquired at each of 3 different sessions within 3 months by 1 operator with Spectralis OCT. The SD-OCT images were segmented with the Glaucoma Module Premium Edition (GMPE) software of Spectralis OCT, and the thickness of individual layers or combination of retinal layers (GCL, GCIPL, GCC, and FMT) was calculated for an 8 × 8 grid of 3˚ × 3˚ superpixels aligned horizontally (Figure 1). The central 36 (6 × 6) superpixels of the 8 × 8 grid were used for the cross-sectional part of the study, as we have previously shown that the most peripheral superpixels of the macular cube show the highest variability.
      • Miraftabi A.
      • Amini N.
      • Gornbein J.
      • et al.
      Local variability of macular thickness measurements with SD-OCT and influencing factors.
      Figure thumbnail gr1
      Figure 1An example of a macular image generated by the Spectralis spectral domain optical coherence tomography. The central 24° of the macular image is segmented, thickness measurements are calculated for individual retinal layers, and data are presented as an 8 × 8 grid of superpixels 3° × 3° in size. In this image, the top numbers in each superpixel represent ganglion cell layer thickness.

       Longitudinal Study Cohort

      One hundred twenty glaucoma eyes (from 120 patients) with 3 or more 10-2 standard achromatic VFs and macular SD-OCT images and ≥30 months of follow-up were enrolled from The Advanced Glaucoma Progression Study, which is a longitudinal prospective study underway in the Glaucoma Division of the Stein Eye Institute. The eligible eyes had good-quality macular SD-OCT images defined as quality factor >15 for all of the linear B-scans included in the central 24° × 24° grid and no major artifacts on these B-scans on review of the images. Glaucoma was defined as the presence of glaucomatous optic nerve damage and an associated reproducible VF defect on standard achromatic perimetry. Eligible eyes were also required to demonstrate a VF mean deviation worse than −6.0 dB or involvement of the central 10° on the standard achromatic 24-2 VFs defined as presence of 2 or more points with P < .05 on the pattern deviation plot. Other inclusion criteria included age 50–85 years, best corrected visual acuity ≥20/50, and no significant confounding retinal or neurological disease. Study eyes underwent a thorough eye exam at baseline, including biometry with IOLMaster, cpRNFL, and triplicate macular imaging with Spectralis SD-OCT (Heidelberg Engineering, Heidelberg, Germany), and SITA standard 24-2 and 10-2 VFs with Humphrey Field Analyzer (Carl Zeiss Meditec, San Leandro, California, USA).

       Imaging Procedures

      The macular imaging algorithm of the Spectralis OCT (Posterior Pole Algorithm) consists of 61 horizontal B-scans (repeated 9–11 times to improve image quality), each consisting of 768 A-scans spanning a 30° × 25°-wide area centered on the fovea. After segmentation of individual layers, the data are averaged, and an 8 × 8 grid of thickness measurements (64 superpixels within the central 24° × 24°, 3°-wide squares) for the layer of interest is created (Figure 1). The GMPE software is able to segment all the individual retinal layers. The main macular structural outcomes of interest were GCL, GCIPL, GCC, and FMT in the cross-sectional study and GCIPL thickness in the longitudinal study, as we have shown this parameter to have the highest correlation with pointwise central VF sensitivities.
      • Miraftabi A.
      • Amini N.
      • Morales E.
      • et al.
      Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range.
      The layer segmentation results were checked and manually corrected on the SD-OCT images as needed.
      For the longitudinal part of the study, GCIPL measurements at 64 superpixels from the Posterior Pole Algorithm and total deviation (TD) values for the 68 test locations from the 10-2 VFs were exported and matched topographically adjusting for ganglion cell displacement (Figure 2A). Although the macular images are acquired along the fovea-Bruch's membrane axis, the GMPE software allows for measurement of the superpixels in a horizontally aligned grid so that the superpixels represent the same locations across different eyes. Corresponding data from the central 18° of the macula and VF were included for further analyses, since beyond this eccentricity, the thickness of the inner macular layers rapidly decreases (Figure 2B). GCIPL thickness values were converted to log scale (logGCIPL = log10 GCIPL) so that they are expressed in the same scale as VF data.
      Figure thumbnail gr2
      Figure 2(A), an anatomically accurate overlay of the test locations from the central 10° visual field (10-2 strategy) onto the macular 8 × 8 grid after adjusting for retinal ganglion cell displacement.
      • Raza A.S.
      • Cho J.
      • de Moraes C.G.
      • et al.
      Retinal ganglion cell layer thickness and local visual field sensitivity in glaucoma.
      (B), circles demonstrate superpixels and visual field test locations at 3.4°, 5.6°, and 6.8° eccentricities where the macular inner layer thickness is adequate so that accurate measurements can be carried out and SF relationships may be explored. The central 36 superpixels were included for the cross-sectional study, whereas only the central 24 superpixels were included for the longitudinal study.

       Visual Field Examination

      The patients in the longitudinal part of the study underwent central 10° VF tests (10-2) performed every 6 months. The 10-2 strategy of the Humphrey Field Analyzer measures VF sensitivity at 68 test locations, 2° apart on vertical and horizontal axes, and within 10° of the fixation point. Since both SD-OCT and VF measurements are based on distance in degrees from the fovea or fixation point, such measurements can easily be overlaid (Figure 2). The VF test locations in Figure 2 were adjusted for displacement of RGCs in the central macula according to Raza et al, based on Drasdo et al's estimations of average displacements in normal subjects.
      • Drasdo N.
      • Millican C.L.
      • Katholi C.R.
      • Curcio C.A.
      The length of Henle fibers in the human retina and a model of ganglion receptive field density in the visual field.
      • Raza A.S.
      • Cho J.
      • de Moraes C.G.
      • et al.
      Retinal ganglion cell layer thickness and local visual field sensitivity in glaucoma.

       Statistical Methods

       Cross-sectional study

      The pairwise absolute differences between the 9 thickness measurements available for all the central 36 superpixels in each eye were calculated. The average absolute difference and the 95% confidence intervals (CIs) were plotted and compared for the 4 macular outcomes of interest with the Kruskal-Wallis test. The distribution of the limits of variability as a function of superpixel location was investigated qualitatively on scatter plots of absolute differences in thickness against superpixel location. Linear mixed models were used to estimate the relative contributions of between-session and within-session variability to total variability for macular outcomes of interest (i.e., GCL, GCIPL, GCC, and FMT). Diagnosis (glaucoma vs normal) and location of superpixel were used as fixed-effect variables; imaging session and patient identification were fitted as the variables with random effects in this model. The ratio of between-session variability to total variability was then calculated.

       Longitudinal study

      Bivariate plots of SF relationships for each individual eye were drawn at baseline with the logGCIPL thickness at superpixels on the Y-axis and the TD values at matching individual test locations on the X-axis. Total deviation values represent differences between measured sensitivity at a test location and the average age-corrected normal thresholds for the same test location. Fifty-three eyes in which the range of structural and functional measurements extended throughout most of the dynamic range for both measures were selected after a qualitative review of the plots by 1 of the investigators (K.N.M.). The SF plots were then separately studied in these 53 eyes as a function of distance from the fovea at 3 eccentricities of roughly 3.4° (4 superpixels), 5.6° (8 superpixels), and 6.8° (12 superpixels) (Figure 2B) so as to address the variability of thickness measurements with changing distance from the fovea.
      • Miraftabi A.
      • Amini N.
      • Morales E.
      • et al.
      Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range.
      From the 53 eyes, only those with at least 4 sessions for circle 1 (3.4° eccentricity) and at least 3 sessions for circles 2 and 3 (5.6° and 6.8° eccentricities) were included in the analyses to have a minimum of 16 points for regression analyses, as there are only 4 points available per eye per session at 3.4° eccentricity as opposed to 8 points at 5.6° eccentricity and 12 points for 6.8° eccentricity. The GCIPL measurements were transformed into logarithmic scale as the TD values are expressed in logarithmic scale (dB).
      A change-point mixed effects regression model (also known as the broken-stick model) was used to investigate the SF relationships within each individual eye. The broken-stick model assumes that within the dynamic range of OCT measurements (i.e., between the OCT measurement ceiling and measurement floor), there is a direct linear relationship between structure (OCT thickness at each superpixel) and function (TD at each corresponding 10-2 VF test location). After OCT measurements reach their floor, this relationship changes to a flat line with virtually no change in structure despite ongoing changes in function. This model can also investigate whether each eye displays a different SF relationship at different sessions or if the regression slope is constant over time.
      The change-point regression model of Y = log10GCIPL versus X = TD as a function of eccentricity or distance from the fovea is of the form
      Yij = ai + I (b0i + bi X + di * session + fi * X * session) + eij
      where
      I = 1 if X > Ci and I = 0 if X Ci;
      Ci is the break-point (change-point) for the ith eye;
      eij is within eye error;
      ai is the intercept for the ith eye;
      b0i is the change in the intercept if X > Ci for the ith eye
      bi is the slope for logGCIPL in units of log(μm)/dB for the ith eye;
      di is the change in Y per session for the ith eye; and
      fi is the change in the logGCIPL slope due to session (TD-session interaction) for the ith eye.
      If there is no upward or downward displacement of the SF relationship curve over multiple testing sessions, then its coefficient d would be equal or very close to 0, and f would be equal to 0 on average. If the GCIPL slope does not change over sessions, then the coefficient for the interaction of TD (X value) and session (f) would be 0 on average. An attempt to estimate the variances of ai, b0i, bi, ci, di, and fi assuming normal distribution and using a maximum likelihood approach was unsuccessful; in statistical terms, the model did not converge. Therefore, a broken-stick model was fit to each eye where the values were estimated for each eye. This method does not require any of the parameters to follow any known distribution such as the normal distribution. However, in this analysis, we required the change-point (Ci) to not be above –5 dB based on prior data.
      • Miraftabi A.
      • Amini N.
      • Morales E.
      • et al.
      Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range.
      If the minimum TD was >–5 TD units, we assumed that the TD data are all above (i.e., are beyond) the true break-point, and the break-point could not be estimated from the data. In this case, only the slope of logGCIPL against TD (but not the intercept) can be estimated. To measure the contributions of within-eye versus between-individual variation to the total variability observed in this sample, we defined the components of variance as follows.
      Total variance of Y = within-eye variance + between-eye variance
      The variance of the residual errors (eij) is the same as the within-eye (within-model) variance. If Ŷij is the predicted value for a given eye “i” and observation “j”, the variance of Ŷij represents the between-eye (between-model) variance. The intraclass correlation coefficient (ICC) is defined as the ratio of the between-eye variance to the total variance under the above change-point regression model. It varies between 0 and 1; a value closer to 1 indicates that between-subject variability explains a larger proportion of the total variability compared to within-eye variability.

      Results

       Cross-sectional Study

      Table 1 summarizes the demographic and clinical findings of the enrolled eyes in the cross-sectional study. Twenty-six eyes of 14 glaucoma patients and 12 eyes of 6 normal subjects were included in the cross-sectional study. The mean absolute difference in thickness at superpixels among the 9 set of SD-OCT images were 1.2 (±0.6), 1.6 (± 0.6), 1.8 (± 0.8), and 1.7 (± 0.7) μm for GCL, GCIPL, GCC, and FMT, respectively. Figure 3 displays boxplots comparing the mean and 95% CIs for the 4 macular parameters. The GCL demonstrated the lowest and GCC had the highest overall absolute thickness differences. All the pairwise differences between the macular outcome measures were statistically significant (P < .001; Kruskal-Wallis test). The ratio of variance to average thickness decreased with increasing thickness of the layer of interest (GCL > GCIPL > GCC > FMT; P < .05; Kruskal-Wallis test). The superpixel location across the macula did not seem to have a systematic effect on thickness variability (Figure 4). The contribution of between-session variability to total variability was lowest for GCL (8%) and increased to 11% for GCIPL and GCC and 36% for FMT, respectively (Figure 5). This means that most of the total observed variability over time could be explained by within-session variability.
      Table 1Demographic and Clinical Characteristics of the Cross-Sectional Study Sample
      Glaucoma (26 Eyes of 14 Patients)Normal (12 Eyes of 6 Subjects)
      Age (median/interquartile range, years)65.0 (56.2–72.3)49.2 (40.4–49.2)
      Gender (Female/Male)7/74/2
      Mean deviation (median/interquartile range, dB)−3.1 (−4.6 to −0.9)0.5 (−1.4 to 1.1)
      Visual acuity (median/interquartile range, logMAR)0.00 (−0.10 to 0.00)0.00 (0.00 to 0.00)
      Ethnicity
       White63
       Hispanic23
       Asian40
       African American20
      Figure thumbnail gr3
      Figure 3Box plot shows the mean absolute difference of 9 repeat optical coherence tomography images (3 images per session and 3 sessions) at each superpixel for the macular outcomes of interest. The pairwise mean differences were statistically different among all 4 parameters (P < .001; Kruskal-Wallis test). GCL = ganglion cell layer; GC/IPL = ganglion cell and inner plexiform layer; GCC = ganglion cell complex; FMT = full macular thickness.
      Figure thumbnail gr4
      Figure 4Scatter plots demonstrating the variability of macular thickness measurements, expressed as the absolute differences in thickness among the 9 optical coherence tomography images (3 images per session over 3 sessions) as a function of superpixel location (on the X axis).
      Figure thumbnail gr5
      Figure 5Bar graph shows the contribution of the between-session and within-session variability to total variability of macular superpixel thickness measurements on 9 different imaging sessions.

       Longitudinal Study

      One hundred twenty eyes with 3 or more sessions of macular SD-OCT imaging and 10-2 VF exams were eligible for the initial screening. Cross-sectional SF relationships were then plotted for individual eyes at baseline. Figure 6 depicts scatterplots demonstrating the relationship between the GCIPL thickness at superpixels and TD values at individual test locations on the central 10-2 VF for representative individual eyes. Three main patterns were observed depending on the severity of the glaucomatous damage at the level of macula and central field. The scatterplot on the top left displays a typical broken-stick pattern, since both GCIPL thickness and VF sensitivity values vary through most or all of their entire range of measurements. On the top right scatterplot, the GCIPL thickness measurements vary through most of their dynamic range, whereas there is limited variability in VF measurements, indicating that there was only mild corresponding VF damage. On the bottom image, the VF threshold values demonstrate a much wider range of variation in contrast to the GCIPL thickness, as the latter has reached its measurement floor.
      Figure thumbnail gr6
      Figure 6Three patterns were observed after examining bivariate plots of cross-sectional GCIPL and visual field (VF) total deviation measurements in individual eyes in the longitudinal study. (A), a typical broken-stick pattern is observed since both GCIPL thickness and VF sensitivity values vary through most or all of their entire range of measurements. (B), the GCIPL thickness measurements vary through most of their dynamic range, whereas there is limited variability in VF measurements, indicating only mild corresponding VF damage. (C), the VF threshold values demonstrate a much wider range of variation in contrast to the GCIPL thickness measurements as the latter have reached their measurement floor.
      Fifty-three eyes in which the bivariate plots demonstrated structural and functional measurements to vary through most of or the entire dynamic range were selected for further analyses (Table 2). The average (± standard deviation) mean deviation of the 10-2 VFs in this select group was –9.7 (±4.9) dB, and there was a median (interquartile range) of 4 (4–6) SD-OCT images and VF exams per eye over a median (interquartile range) follow-up time of 2.4 (2.2–2.9) years. The average GCIPL thickness was 56.0 ± 15.3, 63.4 ± 17.9, and 49.0 ± 11.2 μm for superpixels at 3.4°, 5.6°, and 6.8° eccentricities, respectively.
      Table 2Demographic and Clinical Characteristics of the Longitudinal Study Cohort
      Variables
      Age (median/interquartile range, years)56.6 (50.7–62.5)
      Gender (Female/Male)32/21
      Ethnicity
       White30
       Asian9
       African-American9
       Hispanic5
      24-2 visual field mean deviation (median/interquartile range, dB)–8.3 (±5.0)
      10-2 visual field mean deviation, average (± standard deviation) (dB)–9.7 (±4.9)
      No. of imaging/visual field sessions per eye, median (interquartile range)4 (4–6)
      Follow-up time (median/interquartile range, years)2.4 (2.2–2.9)
      Based on our previous work
      • Miraftabi A.
      • Amini N.
      • Morales E.
      • et al.
      Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range.
      and additional preliminary analyses, we limited the break-point to be equal to or lower than –5 dB, as mentioned above. The useful range of macular structural measures does not exceed 1 log unit of TD change (10 dB). This is consistent with findings by other investigators and our laboratory on other structural measures such as the cpRNFL and Bruch's membrane-based minimum rim width thickness.
      • Hood D.C.
      • Kardon R.H.
      A framework for comparing structural and functional measures of glaucomatous damage.
      • Mwanza J.C.
      • Kim H.Y.
      • Budenz D.L.
      • et al.
      Residual and dynamic range of retinal nerve fiber layer thickness in glaucoma: comparison of three OCT platforms.
      • Amini N.
      • Daneshvar R.
      • Sharifipour F.
      • et al.
      Structure-function relationships in perimetric glaucoma: comparison of minimum-rim width and retinal nerve fiber layer parameters.
      Table 3 summarizes the results of the 53 segmented (broken-stick) regression analyses in this group of patients as a function of eccentricity. Overall, our assumption of stability of SF relationships over time seemed to hold, as there were no significant interactions between the TD and session in any of the models, nor was the session effect significant for any eccentricity (P ≥ .057). A review of the broken-stick model fits revealed the following reasons some models could not be fit. In some eyes, the data below –10 dB of TD were limited, and, therefore, the change-point (C) confidence limits were large. Presence of outliers was another possible confounding factor, as we did not attempt to remove outliers in this study. Therefore, significant residual variability was observed in some eyes. Figure 7 demonstrates examples of longitudinal SF relationships in individual eyes.
      Table 3Results of Segmented Regression Analyses in 53 Eyes of Patients Who Had Macular Imaging (With Measurement of the Ganglion Cell/Inner Plexiform Layer Thickness) and Central 10-2 Visual Field Exams at 3 or More Sessions During Follow-up. The Column ‘Number of Eyes’ Represents the Number of Eyes Where the Model Could Be Fit
      3.4° Eccentricity (44 Eyes)
      Number of EyesQ1MedianQ3
      Intercept201.5261.5581.612
      Slope200.0060.0170.029
      Break point20−21.22−9.72−6.22
      5.6° Eccentricity (53 Eyes)
      Number of EyesQ1MedianQ3
      Intercept431.6271.6471.680
      Slope430.0150.0200.034
      Break point43−13.93−8.93−6.68
      6.8° Eccentricity (53 Eyes)
      Number of EyesQ1MedianQ3
      Intercept381.5881.6071.630
      Slope380.0100.0160.027
      Break point38−12.98−8.77−7.25
      P < .001 for all for comparison to zero; intercept = a+b0, slope=b.
      Figure thumbnail gr7
      Figure 7Examples of longitudinal structure-function relationships in individual eyes. (A), an eye with small variability in both macular thickness and 10-2 total deviation measurements over time. The change point was around –5 dB. (B), fairly consistent SF relationships over multiple sessions with moderate variability. The change point is around –10 dB. (C), longitudinal SF plot for an eye, in which the TD values do not fall below –15 dB. The change point was estimated around –9 dB in this eye.
      The estimated ICCs for comparison of longitudinal within-eye variability to between-individual variability in SF relationships were 0.780 (95% CI: 0.728–0.818), 0.766 (95% CI: 0.727–0.800), and 0.665 (95% CI: 0.607–0.723) at 3.4°, 5.6°, and 6.8° eccentricities, respectively. Since the ICCs for all eccentricities significantly exceeded 0.5, we can conclude that within-eye variability was significantly smaller than between-individual variability at all eccentricities, although the within-eye variability component was significantly lower for the 3.4° and 5.6° eccentricities compared to 6.8° eccentricity. Figure 8 depicts the median broken-stick or change-point model in this group of patients. Although the slopes for 5.6° and 6.8° eccentricities were parallel with a higher intercept for 5.6° eccentricity, the slope for the 3.4° eccentricity was less steep with the measurement floor (intercept) between the 2 farther eccentricities. A formal comparison with the Wilcoxon signed-rank test showed that the intercepts were different among the 3 eccentricities. The P value was < .001 for the pairwise comparison of 5.6° eccentricity against 3.4° and 6.8° eccentricities, whereas the P value for comparison of 3.4° eccentricity versus 6.8° eccentricity was .033. The P values for pairwise comparison of slopes at 3.4° versus 5.6°, 3.4° versus 6.8°, and 5.6° versus 6.8° eccentricities were .149, .701, and .136, respectively.
      Figure thumbnail gr8
      Figure 8Modeled relationship of the logGCIPL versus total deviation values at corresponding 10-2 visual field locations as a function of eccentricity.

      Discussion

       SF Relationships in Glaucoma

      The topic of SF relationships in glaucoma has been a subject of great interest since the development of automated imaging devices such as scanning laser ophthalmoscopy, scanning laser polarimetry, and, more recently, OCT. At the most basic level, one would expect that a reduction in the number of RGC axons would be consistent with visual functional loss measured with various devices on some scale. Perimetry has been the most commonly used technique for measuring visual function in SF studies in glaucoma.

       Lessons Learned from SF Relationships with SD-OCT cpRNFL Measures

      Many studies have investigated the relationship between global and sectoral cpRNFL thickness measurements derived from SD-OCT and corresponding parameters from standard achromatic perimetry. These studies showed that SF relationships do not show complete agreement, vary as a function of glaucoma severity, and can be improved if customized for individual eyes.
      • Miglior S.
      • Riva I.
      • Guareschi M.
      • et al.
      Retinal sensitivity and retinal nerve fiber layer thickness measured by optical coherence tomography in glaucoma.
      • Racette L.
      • Medeiros F.A.
      • Bowd C.
      • Zangwill L.M.
      • Weinreb R.N.
      • Sample P.A.
      The impact of the perimetric measurement scale, sample composition, and statistical method on the structure-function relationship in glaucoma.
      • Gonzalez-Hernandez M.
      • Pablo L.E.
      • Armas-Dominguez K.
      • de la Vega R.R.
      • Ferreras A.
      • de la Rosa M.G.
      Structure-function relationship depends on glaucoma severity.
      • Lee J.R.
      • Jeoung J.W.
      • Choi J.
      • Choi J.Y.
      • Park K.H.
      • Kim Y.D.
      Structure-function relationships in normal and glaucomatous eyes determined by time- and spectral-domain optical coherence tomography.
      • Rao H.L.
      • Zangwill L.M.
      • Weinreb R.N.
      • Leite M.T.
      • Sample P.A.
      • Medeiros F.A.
      Structure-function relationship in glaucoma using spectral-domain optical coherence tomography.
      • Nilforushan N.
      • Nassiri N.
      • Moghimi S.
      • et al.
      Structure-function relationships between spectral-domain OCT and standard achromatic perimetry.
      • Raza A.S.
      • Zhang X.
      • De Moraes C.G.
      • et al.
      Improving glaucoma detection using spatially correspondent clusters of damage and by combining standard automated perimetry and optical coherence tomography.
      • Pollet-Villard F.
      • Chiquet C.
      • Romanet J.P.
      • Noel C.
      • Aptel F.
      Structure-function relationships with spectral-domain optical coherence tomography retinal nerve fiber layer and optic nerve head measurements.
      • Ballae Ganeshrao S.
      • Turpin A.
      • Denniss J.
      • McKendrick A.M.
      Enhancing structure-function correlations in glaucoma with customized spatial mapping.
      • Danthurebandara V.M.
      • Sharpe G.P.
      • Hutchison D.M.
      • et al.
      Enhanced structure-function relationship in glaucoma with an anatomically and geometrically accurate neuroretinal rim measurement.
      Perfect correlation of structure and function is not expected nor desirable as this would mean that structural measures would not provide additional information beyond VF data or vice versa. Medeiros et al proposed an SF index incorporating both cpRNFL thickness and VF sensitivity data that could be used to estimate the number of RGCs in an individual eye.
      • Medeiros F.A.
      • Lisboa R.
      • Weinreb R.N.
      • Girkin C.A.
      • Liebmann J.M.
      • Zangwill L.M.
      A combined index of structure and function for staging glaucomatous damage.
      This index has been demonstrated to be able to stage glaucoma severity and estimate rates of change adequately compared to isolated measures of structure and function and possibly aid with detection of disease progression.
      • Medeiros F.A.
      • Zangwill L.M.
      • Anderson D.R.
      • et al.
      Estimating the rate of retinal ganglion cell loss in glaucoma.
      • Meira-Freitas D.
      • Lisboa R.
      • Tatham A.
      • et al.
      Predicting progression in glaucoma suspects with longitudinal estimates of retinal ganglion cell counts.
      • Tatham A.J.
      • Weinreb R.N.
      • Medeiros F.A.
      Strategies for improving early detection of glaucoma: the combined structure-function index.
      • Zhang C.
      • Tatham A.J.
      • Daga F.B.
      • Jammal A.A.
      • Medeiros F.A.
      Event-based analysis of visual field change can miss fast glaucoma progression detected by a combined structure and function index.
      Although different approaches have been used to study SF relationships in glaucoma,
      • Garway-Heath D.F.
      • Caprioli J.
      • Fitzke F.W.
      • Hitchings R.A.
      Scaling the hill of vision: the physiological relationship between light sensitivity and ganglion cell numbers.
      • Garway-Heath D.F.
      • Holder G.E.
      • Fitzke F.W.
      • Hitchings R.A.
      Relationship between electrophysiological, psychophysical, and anatomical measurements in glaucoma.
      • Swanson W.H.
      • Felius J.
      • Pan F.
      Perimetric defects and ganglion cell damage: interpreting linear relations using a two-stage neural model.
      • Pan F.
      • Swanson W.H.
      A cortical pooling model of spatial summation for perimetric stimuli.
      • Drasdo N.
      • Mortlock K.E.
      • North R.V.
      Ganglion cell loss and dysfunction: relationship to perimetric sensitivity.
      • Harwerth R.S.
      • Wheat J.L.
      • Fredette M.J.
      • Anderson D.R.
      Linking structure and function in glaucoma.
      the most widely adopted model is the one called the simple linear model by Hood and Kardon.
      • Hood D.C.
      • Kardon R.H.
      A framework for comparing structural and functional measures of glaucomatous damage.
      This models posits that structural measurements, such as cpRNFL, consist of a neural component (i.e., RGC axons) and a non-neural component, which consists of glial tissues, blood vessels, and other connective tissue components. With progressing damage in glaucoma, the neural component thins out, whereas there is no significant change to the non-neural component, or it could actually increase in thickness, as proposed by Harwerth et al.
      • Harwerth R.S.
      • Carter-Dawson L.
      • Shen F.
      • Smith 3rd, E.L.
      • Crawford M.L.
      Ganglion cell losses underlying visual field defects from experimental glaucoma.
      Therefore, the thickness of any OCT outcome measure, such as cpRNFL, never reaches zero, and there is a measurement floor that varies according to the outcome of interest, the topography of damage, and the characteristics of an individual eye. Many studies reported that the cpRNFL thickness reaches its measurement floor after about a 10-dB decrease in threshold (i.e., an average sectoral mean deviation of –10 dB).
      • Hood D.C.
      • Kardon R.H.
      A framework for comparing structural and functional measures of glaucomatous damage.
      • Mwanza J.C.
      • Kim H.Y.
      • Budenz D.L.
      • et al.
      Residual and dynamic range of retinal nerve fiber layer thickness in glaucoma: comparison of three OCT platforms.
      • Amini N.
      • Daneshvar R.
      • Sharifipour F.
      • et al.
      Structure-function relationships in perimetric glaucoma: comparison of minimum-rim width and retinal nerve fiber layer parameters.
      Circumpapillary RNFL thickness reaches a plateau at around this level of damage beyond which the amount of change is very small to none. The magnitude of the correlation between cpRNFL thickness measurements and VF threshold sensitivity or global or sectoral mean deviation values has been quite variable in the reported studies, with a peak correlation of 0.70–0.80.
      • Miglior S.
      • Riva I.
      • Guareschi M.
      • et al.
      Retinal sensitivity and retinal nerve fiber layer thickness measured by optical coherence tomography in glaucoma.
      • Racette L.
      • Medeiros F.A.
      • Bowd C.
      • Zangwill L.M.
      • Weinreb R.N.
      • Sample P.A.
      The impact of the perimetric measurement scale, sample composition, and statistical method on the structure-function relationship in glaucoma.
      • Gonzalez-Hernandez M.
      • Pablo L.E.
      • Armas-Dominguez K.
      • de la Vega R.R.
      • Ferreras A.
      • de la Rosa M.G.
      Structure-function relationship depends on glaucoma severity.
      • Lee J.R.
      • Jeoung J.W.
      • Choi J.
      • Choi J.Y.
      • Park K.H.
      • Kim Y.D.
      Structure-function relationships in normal and glaucomatous eyes determined by time- and spectral-domain optical coherence tomography.
      • Rao H.L.
      • Zangwill L.M.
      • Weinreb R.N.
      • Leite M.T.
      • Sample P.A.
      • Medeiros F.A.
      Structure-function relationship in glaucoma using spectral-domain optical coherence tomography.
      • Nilforushan N.
      • Nassiri N.
      • Moghimi S.
      • et al.
      Structure-function relationships between spectral-domain OCT and standard achromatic perimetry.
      • Raza A.S.
      • Zhang X.
      • De Moraes C.G.
      • et al.
      Improving glaucoma detection using spatially correspondent clusters of damage and by combining standard automated perimetry and optical coherence tomography.
      • Pollet-Villard F.
      • Chiquet C.
      • Romanet J.P.
      • Noel C.
      • Aptel F.
      Structure-function relationships with spectral-domain optical coherence tomography retinal nerve fiber layer and optic nerve head measurements.
      • Ballae Ganeshrao S.
      • Turpin A.
      • Denniss J.
      • McKendrick A.M.
      Enhancing structure-function correlations in glaucoma with customized spatial mapping.
      • Danthurebandara V.M.
      • Sharpe G.P.
      • Hutchison D.M.
      • et al.
      Enhanced structure-function relationship in glaucoma with an anatomically and geometrically accurate neuroretinal rim measurement.

       SF Relationships in the Macula

      All SD-OCT devices are able to measure the macular layers, with slightly different algorithms providing clinicians with thickness measurements for GCL, GCIPL, GCC, or FMT, depending on the imaging and segmentation strategy used by the device. Macular SD-OCT outcome measures demonstrate high correlations with threshold sensitivity in the central VF similar to cpRNFL.
      • Shin H.Y.
      • Park H.Y.
      • Jung K.I.
      • Park C.K.
      Comparative study of macular ganglion cell-inner plexiform layer and peripapillary retinal nerve fiber layer measurement: structure-function analysis.
      • Miraftabi A.
      • Amini N.
      • Morales E.
      • et al.
      Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range.
      • Ohkubo S.
      • Higashide T.
      • Udagawa S.
      • et al.
      Focal relationship between structure and function within the central 10 degrees in glaucoma.
      • Rao H.L.
      • Januwada M.
      • Hussain R.S.
      • et al.
      Comparing the structure-function relationship at the macula with standard automated perimetry and microperimetry.
      Central test locations of the 24-2 VF or 10-2 VF test locations measuring the sensitivity at 68 test locations within 10° from the fixation point have been used for this purpose. Overall, the strength of SF relationships in the macula seems similar to those for cpRNFL thickness. Multiple studies, including those from our research laboratory (see below), have confirmed this finding, with correlation coefficients for global or local SF relationships reported as high as 0.6–0.75.
      • Ohkubo S.
      • Higashide T.
      • Udagawa S.
      • et al.
      Focal relationship between structure and function within the central 10 degrees in glaucoma.
      • Sato S.
      • Hirooka K.
      • Baba T.
      • Tenkumo K.
      • Nitta E.
      • Shiraga F.
      Correlation between the ganglion cell-inner plexiform layer thickness measured with cirrus HD-OCT and macular visual field sensitivity measured with microperimetry.
      • Le P.V.
      • Tan O.
      • Chopra V.
      • et al.
      Regional correlation among ganglion cell complex, nerve fiber layer, and visual field loss in glaucoma.
      • Kim S.
      • Lee J.Y.
      • Kim S.O.
      • Kook M.S.
      Macular structure-function relationship at various spatial locations in glaucoma.
      • Lee J.W.
      • Morales E.
      • Sharifipour F.
      • et al.
      The relationship between central visual field sensitivity and macular ganglion cell/inner plexiform layer thickness in glaucoma.
      There is a one-to-one relationship in the macula between the local thickness measurements (or superpixels) and the threshold sensitivity or TD values at individual VF test locations (Figure 2). Thicker GCIPL or GCC measurements have been associated with higher threshold sensitivity in normal eyes.
      • Araie M.
      • Saito H.
      • Tomidokoro A.
      • Murata H.
      • Iwase A.
      Relationship between macular inner retinal layer thickness and corresponding retinal sensitivity in normal eyes.
      Regional or local SF relationships for individual macular superpixels, sectors, or circular areas around corresponding VF test locations have been investigated.
      • Miraftabi A.
      • Amini N.
      • Morales E.
      • et al.
      Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range.
      • Raza A.S.
      • Cho J.
      • de Moraes C.G.
      • et al.
      Retinal ganglion cell layer thickness and local visual field sensitivity in glaucoma.
      • Ohkubo S.
      • Higashide T.
      • Udagawa S.
      • et al.
      Focal relationship between structure and function within the central 10 degrees in glaucoma.
      The inferotemporal macular sector discriminates best between glaucoma and normal eyes.
      • Mwanza J.C.
      • Durbin M.K.
      • Budenz D.L.
      • et al.
      Glaucoma diagnostic accuracy of ganglion cell-inner plexiform layer thickness: comparison with nerve fiber layer and optic nerve head.
      • Nouri-Mahdavi K.
      • Nowroozizadeh S.
      • Nassiri N.
      • et al.
      Macular ganglion cell/inner plexiform layer measurements by spectral domain optical coherence tomography for detection of early glaucoma and comparison to retinal nerve fiber layer measurements.
      The inferotemporal sector or inferior hemi-macula has been found to demonstrate the strongest association with VF thresholds.
      • Mwanza J.C.
      • Durbin M.K.
      • Budenz D.L.
      • et al.
      Glaucoma diagnostic accuracy of ganglion cell-inner plexiform layer thickness: comparison with nerve fiber layer and optic nerve head.
      • Nouri-Mahdavi K.
      • Nowroozizadeh S.
      • Nassiri N.
      • et al.
      Macular ganglion cell/inner plexiform layer measurements by spectral domain optical coherence tomography for detection of early glaucoma and comparison to retinal nerve fiber layer measurements.
      Evidence of retinal thinning could also be detected in the hemi-macular region corresponding to the normal hemifield in eyes that showed VF loss only in 1 hemifield.
      • Takagi S.T.
      • Kita Y.
      • Yagi F.
      • Tomita G.
      Macular retinal ganglion cell complex damage in the apparently normal visual field of glaucomatous eyes with hemifield defects.
      • Inuzuka H.
      • Kawase K.
      • Sawada A.
      • Aoyama Y.
      • Yamamoto T.
      Macular retinal thickness in glaucoma with superior or inferior visual hemifield defects.
      As with cpRNFL thickness, macular outcome measures reach their floor of measurements by the time 10-dB loss is registered at the corresponding test location. The advantage of macular SD-OCT measures over cpRNFL outcomes is that the macular RGC axonal complex persists until later stages of the disease and therefore could be potentially used for detection of change over time.
      We explored correlations between TD measurements at 10-2 VF test locations and GCIPL thickness on a 100 × 100 array of superpixels derived from Cirrus high-definition OCT in 137 eyes of 125 glaucoma patients.
      • Lee J.W.
      • Morales E.
      • Sharifipour F.
      • et al.
      The relationship between central visual field sensitivity and macular ganglion cell/inner plexiform layer thickness in glaucoma.
      We reported that the macular GCIPL loss demonstrated an arcuate pattern, the topography of which depended on the corresponding location in the central field. We recently tested the hypothesis that measuring the GCL, where the RGC somas are located, would improve SF relationships and extend the range of utility of macular thickness measurements.
      • Miraftabi A.
      • Amini N.
      • Morales E.
      • et al.
      Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range.
      We enrolled a cohort of glaucoma eyes from the Advanced Glaucoma Progression Study to compare the SF relationships and measurement floor among various macular outcomes of interest. We estimated localized SF relationships between macular thickness at superpixels and the VF TD values at corresponding individual test locations on 10-2 VFs in 96 glaucoma and 10 normal eyes and measured the dynamic range of structural measurements.
      • Miraftabi A.
      • Amini N.
      • Morales E.
      • et al.
      Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range.
      We analyzed the central 24 superpixels located in the central 18° of the macula and the corresponding VF test locations after correcting for RGC displacement. Beyond the central 18° from the fovea, the thickness of many inner retinal layers significantly decreases to very low levels.
      • Curcio C.A.
      • Messinger J.D.
      • Sloan K.R.
      • Mitra A.
      • McGwin G.
      • Spaide R.F.
      Human chorioretinal layer thicknesses measured in macula-wide, high-resolution histologic sections.
      SF plots were constructed as bivariate plots with the TD values at individual test locations on the X-axis and various macular thickness measures (in μm) on the Y-axis. Based on nonparametric correlation analysis between macular measures and VF TD values, SF relationships were strongest for GCIPL, GCL, and GCC in that order (Spearman's ρ =0.669, 0.654, and 0.638, respectively); however, the differences were not clinically meaningful. We then used a broken-stick model to fit the SF data.
      • Hood D.C.
      • Kardon R.H.
      A framework for comparing structural and functional measures of glaucomatous damage.
      • Hood D.C.
      • Anderson S.C.
      • Wall M.
      • Kardon R.H.
      Structure versus function in glaucoma: an application of a linear model.
      A broken-stick model in the form of Y = a if X < C, Y = a + b (X−C) if X ≥ C was fit to the cross-sectional SF data where a is the intercept (an estimate of the measurement floor for macular outcome measures) in μm, b represents the slope beyond the change-point in μm/dB, and C denotes the VF threshold at the change-point (Figure 9). The model posits that beyond the change-point, the macular thickness is linearly correlated with the corresponding TD values. The dynamic range was considered to be the difference between the intercept for the broken-stick model (i.e., the bottom of measurements), and the 90th percentile normal thickness as the measurement ceiling.
      • Mwanza J.C.
      • Kim H.Y.
      • Budenz D.L.
      • et al.
      Residual and dynamic range of retinal nerve fiber layer thickness in glaucoma: comparison of three OCT platforms.
      Figure 9 demonstrates a plot of predicted macular IPL, GCL, GCIPL, GCC, and FMT (i.e., predicted y's) at superpixels against VF TD at corresponding individual 10-2 test locations.
      Figure thumbnail gr9
      Figure 9The plots demonstrate the modeled relationship between macular thickness at 3°×3° superpixels and visual field total deviation based on a broken-stick model. The thickness of the ganglion cell layer, ganglion cell/inner plexiform layers, ganglion cell complex, or full macular thickness within central 24 superpixels is represented on the Y axis; the total deviation at individual test locations of the 10-2 visual field is displayed on the X axis. The red arrows point to the change-point for various macular outcome measures based on the broken-stick model. The numbers represent the absolute dynamic range at 5.6° eccentricity. Note that the absolute range increases as a function of the average thickness of the layers of interest in normal subjects. IPL = inner plexiform layer; GCL = ganglion cell layer; GCIPL = ganglion cell and inner plexiform layers; GCC = ganglion cell complex; FMT = full macular thickness.
      (From Miraftabi A, Amini N, Morales E, et al. Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range. Invest Ophthalmol Vis Sci 2016;57(11):4815–4823.)
      The variability of any given macular parameter needs to be considered compared to its dynamic range and not in comparison to the total measurement range. As mentioned above, with both macular and cpRNFL measurements, there is a lower plateau or measurement floor below which the measurements almost never drop.
      • Mwanza J.C.
      • Kim H.Y.
      • Budenz D.L.
      • et al.
      Residual and dynamic range of retinal nerve fiber layer thickness in glaucoma: comparison of three OCT platforms.
      • Hood D.C.
      • Anderson S.C.
      • Wall M.
      • Kardon R.H.
      Structure versus function in glaucoma: an application of a linear model.
      • Bowd C.
      • Zangwill L.M.
      • Weinreb R.N.
      • Medeiros F.A.
      • Belghith A.
      Estimating optical coherence tomography structural measurement floors to improve detection of progression in advanced glaucoma.
      The absolute dynamic range of measurements in the above study was a function of the average layer thickness in normal subjects and was highest for FMT, followed by GCC, GCIPL, and GCL, in that order (Table 4). However, inner macular outcome measures had the highest relative dynamic range (GCL > GCIPL > GCC, in that order). The change-points were similar for all outcome measures ranging between −7.8 and −8.9 dB. Since the variability of all macular outcome measures is uniform across the macula with current technology,
      • Miraftabi A.
      • Amini N.
      • Gornbein J.
      • et al.
      Local variability of macular thickness measurements with SD-OCT and influencing factors.
      GCL measurements may not provide added value compared to GCC or GCIPL at this point. However, given the higher relative dynamic range for GCL, this issue deserves further exploration with longitudinal data.
      Table 4The Absolute and Relative Dynamic Range (DR) for Various Macular Outcomes of Interest at 5.6° Eccentricity. The Ganglion Cell Layer Demonstrated the Largest Relative Dynamic Range
      ParameterAbsolute DR (μm)Average Thickness (μm)Relative DR
      Ganglion cell layer35.243.481%
      Ganglion cell and inner plexiform layers54.980.468%
      Ganglion cell complex65.7105.562%
      Full macular thickness81.1321.325%
      A shortcoming of available SF studies is that the associations observed are highly dependent on the level of structural and functional damage, the number of eyes recruited, and inclusion of normal and glaucoma suspect subjects in addition to glaucoma patients. From a statistical point of view, a significant amount of the association observed is driven by points at the 2 ends of the data cloud (i.e., those with lowest and highest X values). In addition, in studies that use a change from average normal values, these average values for thickness or sensitivity measurements have large 95% prediction intervals and do not necessarily represent the true amount of change from baseline for any individual eye at any given point in time. The above factors highly affect the strength and the pattern of correlation observed in a study, and, therefore, comparison across studies can be very challenging. A more meaningful type of correlation analysis would be to compare a change from baseline in structure to a change from baseline in function. This type of comparison obviates some of the shortcomings mentioned above and can provide a better insight into the relationship between structure and function. Our research laboratory is actively investigating this topic at the time of this writing.

       Detection of Disease Progression with Macular SD-OCT Imaging

      Given that SD-OCTs have been in clinical use for a relatively short time, only preliminary data are available regarding the performance of macular SD-OCT measurements for detection of glaucoma worsening.
      • Sung K.R.
      • Sun J.H.
      • Na J.H.
      • Lee J.Y.
      • Lee Y.
      Progression detection capability of macular thickness in advanced glaucomatous eyes.
      • Na J.H.
      • Sung K.R.
      • Baek S.
      • et al.
      Detection of glaucoma progression by assessment of segmented macular thickness data obtained using spectral domain optical coherence tomography.
      • Lee K.S.
      • Lee J.R.
      • Na J.H.
      • Kook M.S.
      Usefulness of macular thickness derived from spectral-domain optical coherence tomography in the detection of glaucoma progression.
      • Suda K.
      • Hangai M.
      • Akagi T.
      • et al.
      Comparison of longitudinal changes in functional and structural measures for evaluating progression of glaucomatous optic neuropathy.
      Sung et al showed that rates of progression for macular full thickness measurements were significantly higher than cpRNFL rates of changes in eyes progressing based on VF or optic disc criteria.
      • Sung K.R.
      • Sun J.H.
      • Na J.H.
      • Lee J.Y.
      • Lee Y.
      Progression detection capability of macular thickness in advanced glaucomatous eyes.
      The average baseline VF mean deviation was −14 dB in that study. None of the cpRNFL rates was significantly different from zero. Lee and associates reported similar findings using event analyses in a group of glaucoma eyes mostly (90%) composed of normal tension glaucoma patients.
      • Lee K.S.
      • Lee J.R.
      • Na J.H.
      • Kook M.S.
      Usefulness of macular thickness derived from spectral-domain optical coherence tomography in the detection of glaucoma progression.
      Na and colleagues found that the optic nerve head, cpRNFL, and macular parameters all showed a faster rate of progression in deteriorating glaucoma eyes compared to stable eyes.
      • Na J.H.
      • Sung K.R.
      • Baek S.
      • et al.
      Detection of glaucoma progression by assessment of segmented macular thickness data obtained using spectral domain optical coherence tomography.
      Suda et al demonstrated that the longitudinal noise of GCC measurements was similar to cpRNFL measurements in a group of eyes with moderate glaucoma (average mean deviation =−6.2 dB)
      • Suda K.
      • Hangai M.
      • Akagi T.
      • et al.
      Comparison of longitudinal changes in functional and structural measures for evaluating progression of glaucomatous optic neuropathy.
      ; however, the correlation of structural rates of progression with perimetric rates of change was weak. Hammel and co-investigators reported that, in a subset of eyes with severe glaucoma (20 eyes), the average normalized GCIPL rates of change were higher (–1.8%, 95% CI: –3.6%, –0.01%) than average cpRNFL rate of change (–1.1%, 95% CI: –2.4%, 0.3%).
      • Hammel N.
      • Belghith A.
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      • Medeiros F.A.
      • Mendoza N.
      • Zangwill L.M.
      Comparing the rates of retinal nerve fiber layer and ganglion cell-inner plexiform layer loss in healthy Eyes and in glaucoma eyes.
      Lee et al found that the average GCIPL thickness in the hemimacular area corresponding to the affected hemifield showed significantly faster rates of thinning in eyes progressing according to VFs and optic nerve head/RNFL photographs compared to stable eyes.
      • Lee W.J.
      • Kim Y.K.
      • Park K.H.
      • Jeoung J.W.
      Trend-based analysis of ganglion cell-inner plexiform layer thickness changes on optical coherence tomography in glaucoma progression.

       Measurement Variability of Macular Thickness Measures

      Within-session and inter-session reproducibility of SD-OCT parameters are important as far as detection of change over time is concerned. The reproducibility of various macular thickness parameters has been shown to be excellent.
      • Tan O.
      • Chopra V.
      • Lu A.T.
      • et al.
      Detection of macular ganglion cell loss in glaucoma by Fourier-domain optical coherence tomography.
      • Miraftabi A.
      • Amini N.
      • Gornbein J.
      • et al.
      Local variability of macular thickness measurements with SD-OCT and influencing factors.
      • Mwanza J.C.
      • Oakley J.D.
      • Budenz D.L.
      • Chang R.T.
      • Knight O.J.
      • Feuer W.J.
      Macular ganglion cell-inner plexiform layer: automated detection and thickness reproducibility with spectral domain-optical coherence tomography in glaucoma.
      • Hirasawa H.
      • Araie M.
      • Tomidokoro A.
      • et al.
      Reproducibility of thickness measurements of macular inner retinal layers using SD-OCT with or without correction of ocular rotation.
      Although the magnitude of within- and between-session variability has been reported for larger regions of the macula, the relative contribution of these 2 components of variability has not been previously reported for macular outcomes. In a study by Tan et al, both GCC and macular full thickness measurements were highly reproducible with ICC ≥0.98 for all measures.
      • Tan O.
      • Li G.
      • Lu A.T.
      • Varma R.
      • Huang D.
      Mapping of macular substructures with optical coherence tomography for glaucoma diagnosis.
      In another study, ICCs for repeated measurements within the same session were 0.995, 0.994, and 0.989 for the average, superior hemiretinal, and inferior hemiretinal GCC thickness, respectively.
      • Kim N.R.
      • Kim J.H.
      • Lee J.
      • Lee E.S.
      • Seong G.J.
      • Kim C.Y.
      Determinants of perimacular inner retinal layer thickness in normal eyes measured by Fourier-domain optical coherence tomography.
      Within-session test-retest variability values, defined as the 95% boundaries for variability, were 3.6, 5.0, and 4.1 μm for the same parameters. The corresponding coefficients of variation (CoV) were also very low (2.1%, 2.9%, and 2.4%, respectively). Mwanza et al found that GCIPL measurements showed excellent reproducibility and suggested that this parameter could be used for detection of structural progression.
      • Mwanza J.C.
      • Oakley J.D.
      • Budenz D.L.
      • Chang R.T.
      • Knight O.J.
      • Feuer W.J.
      Macular ganglion cell-inner plexiform layer: automated detection and thickness reproducibility with spectral domain-optical coherence tomography in glaucoma.
      Hirasawa et al reported high reproducibility for GCC and GCIPL layers with 3D OCT-1000 with CoVs that were <1% for all regional and global measures.
      • Hirasawa H.
      • Araie M.
      • Tomidokoro A.
      • et al.
      Reproducibility of thickness measurements of macular inner retinal layers using SD-OCT with or without correction of ocular rotation.
      Kim et al investigated macular thickness variability over time in 109 glaucoma eyes that were considered to be clinically stable.
      • Kim K.E.
      • Yoo B.W.
      • Jeoung J.W.
      • Park K.H.
      Long-term reproducibility of macular ganglion cell analysis in clinically stable glaucoma patients.
      They confirmed that variability was very low for all GCIPL-derived parameters. They also found that worsening glaucoma severity (i.e., thinner baseline GCIPL) did not affect between-session variability. Francoz et al reported that between-session variability was very low in seemingly stable glaucoma eyes over wider sectors of the macula.
      • Francoz M.
      • Fenolland J.R.
      • Giraud J.M.
      • et al.
      Reproducibility of macular ganglion cell-inner plexiform layer thickness measurement with cirrus HD-OCT in normal, hypertensive and glaucomatous eyes.
      Measurement variability is expected to vary across the macular region depending on its topography and to be higher in smaller areas of the macula. In a recent study, we used the Posterior Pole Algorithm of the Spectralis OCT to estimate within-session thickness measurement variability in 123 glaucoma and normal eyes at the level of 3° × 3° superpixels.
      • Miraftabi A.
      • Amini N.
      • Gornbein J.
      • et al.
      Local variability of macular thickness measurements with SD-OCT and influencing factors.
      We found that the local within-session variability was excellent and did not exceed 3 μm for all macular parameters (IPL, GCL, macular RNFL, GCIPL, GCC, and FMT) after excluding a small percentage of outliers. This excellent repeatability (lower than the 4-μm nominal axial resolution of Spectralis OCT) is explained by averaging of data and the fact that the software uses all available 3-dimensional information when segmenting the inner retinal layers.
      • Sohn E.H.
      • Chen J.J.
      • Lee K.
      • Niemeijer M.
      • Sonka M.
      • Abràmoff M.D.
      Reproducibility of diabetic macular edema estimates from SD-OCT is affected by the choice of image analysis algorithm.
      • Liu X.
      • Shen M.
      • Huang S.
      • Leng L.
      • Zhu D.
      • Lu F.
      Repeatability and reproducibility of eight macular intra-retinal layer thicknesses determined by an automated segmentation algorithm using two SD-OCT instruments.
      Any change beyond the cutoff point for within-session variability as defined in this study (about 3 μm) would be of potential clinical significance, assuming that between-session variability does not exceed within-session variability significantly, which was an issue investigated in this thesis. We found that variability was highest on the nasal and superior columns/rows of superpixels on the macular images. The size of superpixels on the Posterior Pole Algorithm was empirically chosen to be 3° × 3° degrees by the manufacturer. Our unpublished data previously showed that variability increased as the size of the area of interest decreased. However, this relationship may not be linear, and there may be a plateau representing the optimal superpixel size at which point the best compromise of variability and size occurs. Figure 10 demonstrates the percentage of outliers at individual superpixels, as a proxy for variability, in the above study.
      • Miraftabi A.
      • Amini N.
      • Gornbein J.
      • et al.
      Local variability of macular thickness measurements with SD-OCT and influencing factors.
      The GCIPL's variability increased only when the thickness approached the measurement floor (Figure 11). Variability was slightly higher for GCC as compared to GCIPL in this study.
      Figure thumbnail gr10
      Figure 10The percentage of outliers at individual superpixels in a group of glaucoma and normal eyes, which had ×3 macular measurements within the same session, as a proxy for variability, for various macular outcome measures. Darker shades represent higher proportion of outliers. IPL = inner plexiform layer; GCL = ganglion cell layer; mRNFL = macular retinal nerve fiber layer; GC/IPL = ganglion cell and inner plexiform layer; GCC = ganglion cell complex; Full = full macular thickness.
      (From Miraftabi A, Amini N, Gornbein J, et al. Local variability of macular thickness measurements with SD-OCT and influencing factors. Transl Vis Sci Technol 2016;5(4):5.)
      Figure thumbnail gr11
      Figure 11Scatter plot displays the proportion of outliers (a proxy for within-session variability) for ganglion cell/inner plexiform layer (GCIPL) thickness at 3° × 3° superpixels as a function of GCIPL thickness. GCIPL variability increased only when the thickness approached the measurement floor.
      (From Miraftabi A, Amini N, Gornbein J, et al. Local variability of macular thickness measurements with SD-OCT and influencing factors. Transl Vis Sci Technol 2016;5(4):5.)

       Discussion of Our Findings and Their Relevance and Implications

       Within-session versus between-session variability

      As mentioned above, we have demonstrated that within-session variability is very small when measured across 3° × 3° macular superpixels and does not exceed 3 μm after exclusion of a small percentage of outliers.
      • Miraftabi A.
      • Amini N.
      • Gornbein J.
      • et al.
      Local variability of macular thickness measurements with SD-OCT and influencing factors.
      However, variability of thickness measurements does vary among different patients, and, hence, estimating measurement variability in individual eyes is of potential clinical interest. We herein report that most of the total variability of macular thickness measurements observed on multiple imaging sessions over a period of 3 months or less could be explained by within-session variability. We chose an upper limit of 3 months for carrying out the 3 sessions of imaging, as glaucoma would be expected to remain stable in treated patients during such a short period of time. The between-session variability component was highest for the FMT (36%) compared to other parameters and was lowest for GCL (8%). It is not quite clear why FMT thickness measurements demonstrated a higher between-session component, as full thickness measurements are expected to be less prone to segmentation errors. Presence of blood vessels could potentially increase variability, but blood vessels are included in both GCC and FMT measurements. After removal of the outer rim of superpixels that are known to be more variable, the magnitude of variability was uniform across the macula (Figure 10). From a clinical point of view, these findings suggest that repeat baseline macular SD-OCT images can be performed in a single session to gauge the magnitude of variability in individual eyes, and there is no need to acquire repeat images on multiple sessions. Since the measurement variability is uniform in the central region of the macula consisting of the central 36 superpixels, one can obtain pooled eye-specific variability estimates based on repeat macular images at baseline and use those for optimizing detection of progression in individual eyes. The sum of within-session and between-session variability also tended to correlate with the average superpixels thickness and was highest for GCC and lowest for GCL. Although the difference in variability between various thickness parameters was statistically significant due to the high number of superpixels involved, the absolute average difference was very small and given the resolution of current SD-OCT devices is of uncertain clinical significance.
      The comparative utility of various macular measures for detection of progression especially in advanced glaucoma is yet to be fully established. With worsening glaucoma, inner retinal layers thin out, tissue density and density gradients diminish, and measurement accuracy decreases as segmentation algorithms are more likely to fail; hence, in more severe stages of glaucoma, FMT or GCC outcome measures may be more useful for detection of changes in thickness over time. Understandably, when the disease approaches the end stage, all structural data will lose their utility, and detection of progression will have to rely only on functional approaches.

       Longitudinal SF relationships and their variability

      Most previous studies pooled cross-sectional data from glaucoma (and normal) subjects to estimate the strength of SF relationships. As such, it is not clear how much of the total variability in this setting can be attributed to within-eye as opposed to between-individual components. A recent study found that variability was similar in glaucoma patients and normal subjects, suggesting that inter-individual variability constitutes a large fraction of total variability seen in cross-sectional SF studies.
      • Ashimatey B.S.
      • Swanson W.H.
      Between-subject variability in healthy eyes as a primary source of structural-functional discordance in patients with glaucoma.
      Macular thickness measurements provide us with an opportunity to directly explore such SF relationships in individual eyes, as the macular SD-OCT measurement cube and the central 10° VFs produce numerous measurements around the fovea or the fixation point. The SF relationships at equidistance regions of the macula and visual fields are expected to display similar patterns.
      Studying SF relationships in individual glaucoma patients has been challenging for the following reasons: a) the limited amount of data available from each eye cross-sectionally; b) the significant variability of neuroretinal rim and cpRNFL measurements in and around the optic nerve head reaching peaks and troughs that do not have corresponding variations in VF sensitivity measurements; and c) issues related to exact topographic matching of cpRNFL or neuroretinal rim measures and functional data in individual eyes.
      • Lamparter J.
      • Russell R.A.
      • Zhu H.
      • et al.
      The influence of intersubject variability in ocular anatomical variables on the mapping of retinal locations to the retinal nerve fiber layer and optic nerve head.
      • Garway-Heath D.F.
      • Poinoosawmy D.
      • Fitzke F.W.
      • Hitchings R.A.
      Mapping the visual field to the optic disc in normal tension glaucoma eyes.
      Studying longitudinal SF relationships between macular thickness and central VF sensitivities addresses most of these limitations: there are multiple SF measurements at similar eccentricities in relation to the fovea; also, the relationship of macular superpixels and central VF threshold sensitivity measurements is, for the most part, one-to-one after adjusting for the RGC displacement around the fovea, although such corrections are done for the average eye.
      • Turpin A.
      • Chen S.
      • Sepulveda J.A.
      • McKendrick A.M.
      Customizing structure-function displacements in the macula for individual differences.
      We used multiple measurements taken over time in each individual eye to plot SF relationships as a function of distance from the fovea. We assumed that the “true” relationship between macular GCIPL thickness derived from SD-OCT and corresponding VF sensitivities in individual eyes did not change over time regardless of disease stability or progression. We hypothesized that by combining multiple structural and functional measurements taken over time from the same eye, the “true” relationship could be modeled more accurately given the larger number of data points available. Since there were only 4 corresponding superpixel/TD values available at each exam at 3.4° eccentricity, we required at least 4 exams to be available in contrast to the 3 required exams for data at 5.6° and 6.8° eccentricities.
      Our findings can be summarized as follows: 1) Within-eye variability in SF relationships is significantly less than between-patient variability regardless of distance from the fovea/fixation point; therefore, our approach should be able to more accurately estimate the SF parameters in individual eyes. 2) The broken-stick model could be fit for most eyes at 5.6° and 6.8° eccentricities, whereas it could be fit in fewer than half of the superpixels/test locations at 3.4°, which is likely related to the small sample size per eye. 3) Differences were found in structural measurement floor as a function of eccentricity and may exist in SF slopes. 4) SF relationships seem to remain stable over time within individual eyes (i.e., no session-slope interaction was evident).
      We used GCIPL thickness as the structural parameter of choice, since it is one of the best performing macular parameters for detection of early glaucoma and demonstrates the highest local correlation with VF TD values.
      • Miraftabi A.
      • Amini N.
      • Morales E.
      • et al.
      Macular SD-OCT outcome measures: comparison of local structure-function relationships and dynamic range.
      We used the logarithm of GCIPL, as studying SF relationship on the same scale as VFs could result in stronger correlations than log-linear correlations.
      • Garway-Heath D.F.
      • Caprioli J.
      • Fitzke F.W.
      • Hitchings R.A.
      Scaling the hill of vision: the physiological relationship between light sensitivity and ganglion cell numbers.
      As expected, the relationship between logGCIPL thickness and TD measurements was linear beyond the change point.
      A question of interest is whether the SF relationships (including the slopes, intercepts, and break points) follow a Gaussian distribution, i.e., whether there is evidence that the joint SF parameters in these eyes belong to a bigger family of normally distributed parameters and variations seen in individual eyes merely represent measurement noise. We found that some of the aforementioned joint SF parameters at various eccentricities were not typically distributed in a Gaussian fashion (data not shown). Although our study was not powered or tailored to address this question, the lack of a normal distribution for some parameters suggests the possibility that, in contrast to what one would have expected, true differences in SF relationships may exist between individuals. This is a topic of significant interest, and we plan to carry out future studies to better clarify this issue.
      Both the neuroretinal rim and cpRNFL measurements reach their measurement floor in moderately advanced glaucoma, and their clinical utility significantly diminishes in the later stages of glaucoma.
      • Sung K.R.
      • Sun J.H.
      • Na J.H.
      • Lee J.Y.
      • Lee Y.
      Progression detection capability of macular thickness in advanced glaucomatous eyes.
      On the other hand, macular structural measurements demonstrate residual thickness at later stages of the disease and therefore, are of potential interest for detection of progression in all stages of the disease, including advanced glaucoma. Studying individual-eye macular SF relationships will facilitate better understanding and modeling of the inherent variability in these relationships across the spectrum of disease severity. We hypothesize that the longitudinal study of within-eye SF relationships can potentially be helpful for monitoring disease progression by combining, in a simple way, changes in the structural and functional data gleaned over time. Combining structure and function is a topic of significant interest in glaucoma.
      • Medeiros F.A.
      • Leite M.T.
      • Zangwill L.M.
      • Weinreb R.N.
      Combining structural and functional measurements to improve detection of glaucoma progression using Bayesian hierarchical models.
      • Russell R.A.
      • Malik R.
      • Chauhan B.C.
      • Crabb D.P.
      • Garway-Heath D.F.
      Improved estimates of visual field progression using bayesian linear regression to integrate structural information in patients with ocular hypertension.
      Although various approaches, such as Bayesian methods, have been explored, our proposed technique provides a simple method for simultaneous consideration of both structural and functional changes in a model that can be implemented in real time in the clinic and updated at each visit in an automated fashion. We hypothesize that downward and/or leftward movement of points along the modeled SF curve would represent disease deterioration, if confirmed over time and if consistent along both structural and functional axes. Figure 12 shows a scatter plot of superpixel thickness against VF TD values for a study eye at baseline and after 3 years of follow-up. A large number of data points moved downward and leftward after 3 years of follow-up; this highly suggests that this eye was deteriorating in both structural and functional domains during the follow-up period.
      Figure thumbnail gr12
      Figure 12Scatter plot of ganglion cell/inner plexiform layer (GCIPL) thickness (in microns) at macular 3° × 3° superpixels versus visual field total deviation values at corresponding test locations at baseline (blue full circles) and after 36 months of follow-up (maroon hollow circles) in an individual eye. A large number of points moved left and down, which is an indication of worsening in both structural and functional domains. Arrows showcase a few examples of worsening macular superpixels and corresponding visual field test locations.
      The results of the current study need to be interpreted in the light of its limitations. This approach requires a large number of corresponding structural and functional measurements for a given eye over time. A formal power calculation was elusive as there are differences in the magnitude of SF variability in individual eyes. The fact that we were able to fit the broken-stick model in fewer than half of eyes at 3.4° eccentricity probably reflects the lower sample size at this eccentricity, as there were only 4 superpixels/test locations available per session. A broken-stick model can be fit only if SF measurements in an individual eye extend through most of the dynamic range of both structural and functional measurements. Only a median of 4 VF/OCT images per eye were available for this study. This may have limited the power of some of our analyses. We are planning a follow-up study that would address this topic after all study eyes have had 5 years of follow-up. From a diagnostic point of view, at some point during the course of the disease, all structural data will lose their utility, and detection of progression will have to rely only on perimetric or other functional approaches.

      Conclusion

      The published literature provides strong evidence in favor of the utility of measuring central SF relationships in glaucoma. We demonstrate that acquiring repeat macular SD-OCT measurements within a single (baseline) session is adequate to estimate longitudinal variability in an individual eye over time. This finding has important implications with regard to designing algorithms to optimize macular OCT imaging for monitoring glaucoma.
      Our study also demonstrates that longitudinal within-eye SF relationships have lower variability than those derived from pooled eyes and introduces the study of longitudinal within-eye SF relationships as a new concept for better understanding the relationship between macular RGC axonal complex and the corresponding functional measurements of the visual pathways. The proposed approach would potentially improve our understanding of the linking of SF in glaucoma and help refine progression algorithms based on macular and central VF measurements. More sensitive and reliable detection of glaucoma progression would allow for better monitoring of the effectiveness of treatment and guide clinicians as to when more aggressive treatment may be required.
      Funding/Support: This study was supported by an unrestricted Departmental Grant from Research to Prevent Blindness , an unrestricted grant from Heidelberg Engineering , and a National Institutes of Health K23 grant ( K23EY022659 , KNM). Financial Disclosures: Heidelberg Engineering (KNM, software and hardware support, unrestricted grant, honorarium). Contributions of Authors: Kouros Nouri-Mahdavi, MD, MS: study design, data analyses, manuscript preparation. Nima Fatehi, MD: data collection, analyses, manuscript review. Joseph Caprioli, MD: review of results and manuscript.
      Other Acknowledgments: Jeff Gornbein, DrPH, statistical consultant, SBCC Director, UCLA Department of Biomathematics, provided statistical expertise.

      Supplemental Data

      • Kouros Nouri-Mahdavi was born in Isfahan, Iran. He obtained his MD and finished his first residency in Ophthalmology at Isfahan University of Medical Sciences. He then did a medical retina fellowship followed by a glaucoma fellowship in Paris, France and a research fellowship in glaucoma at Yale Eye Center. After his return to Iran, he was in academic Ophthalmology for 6 years before his return to UCLA as an International Glaucoma Fellow at Stein Eye Institute. He also obtained an MS degree in Clinical Research at UCLA’s David Geffen School of Medicine during his fellowship. After his second residency at UCSD’s Shiley Eye Center, he joined the faculty at Stein Eye Institute, UCLA.

        Dr. Nouri-Mahdavi is an Associate Professor in Residence at UCLA. His clinical practice is focused on management of complex adult glaucoma and cataract surgery. He is the Director of the Glaucoma Advanced Imaging Laboratory. His main research interests are structure and function in glaucoma with an emphasis on OCT imaging, use of artificial intelligence in glaucoma, and studying glaucoma surgical outcomes.

        Dr. Nouri-Mahdavi received AAO’s Achievement Award in 2014 and is a recipient of the 2019 AAO’s Secretariat Award. He has been a member of the American Glaucoma Society’s Research and International Committees and is currently a member of the AGS’ Annual Meeting Committee. He served as the Methodologist for Ophthalmology Technology Assessment Committee’s Glaucoma Panel from 2015 to 2018. He has been a member of the Association for Research in Vision and Ophthalmology since 1994 and is on the Editorial boards of Journal of Glaucoma, International Glaucoma Review, and Journal of Vision and Eye Research. He has published more than 100 peer-reviewed manuscripts and is a reviewer for all top-tiered American journals. Dr. Nouri-Mahdavi is a co-editor of a reference book on glaucoma OCT imaging (Optical Coherence Tomography in Glaucoma: A Practical Guide) and another book on clinical glaucoma (Pearls of Glaucoma Management). He received the Alcon Senior Investigator Award in 2019 for his innovative collaboration on development of a chip-base OCT device and has been a recipient of UCLA Innovation Awards in 2018 and 2019.

        He is married to Maryam Navab, DDS, who practices dentistry in Encino, CA. They have two daughters; Ava is a junior at UC Berkeley and Tina is a high school sophomore in Calabasas where they live. He has been actively involved in free clinic events in Los Angeles area to donate his time. In his spare time, Kouros is an avid reader in multiple languages, continues to learn and play classical guitar and likes to explore food and wines from around the world.

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