May 2012
Volume 53, Issue 6
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Glaucoma  |   May 2012
Structure–Function Relationships between Spectral-Domain OCT and Standard Achromatic Perimetry
Author Affiliations & Notes
  • Naveed Nilforushan
    From the Glaucoma Division, Jules Stein Eye Institute, UCLA, Los Angeles, California; the
    Eye Research Center, Rassoul Akram Hospital, Tehran University of Medical Sciences, Tehran, Iran; and the
  • Nariman Nassiri
    From the Glaucoma Division, Jules Stein Eye Institute, UCLA, Los Angeles, California; the
  • Sasan Moghimi
    From the Glaucoma Division, Jules Stein Eye Institute, UCLA, Los Angeles, California; the
    Farabi Eye Hospital, Tehran University of Medical Sciences, Tehran, Iran.
  • Simon K. Law
    From the Glaucoma Division, Jules Stein Eye Institute, UCLA, Los Angeles, California; the
  • JoAnn Giaconi
    From the Glaucoma Division, Jules Stein Eye Institute, UCLA, Los Angeles, California; the
  • Anne L. Coleman
    From the Glaucoma Division, Jules Stein Eye Institute, UCLA, Los Angeles, California; the
  • Joseph Caprioli
    From the Glaucoma Division, Jules Stein Eye Institute, UCLA, Los Angeles, California; the
  • Kouros Nouri-Mahdavi
    From the Glaucoma Division, Jules Stein Eye Institute, UCLA, Los Angeles, California; the
  • Corresponding author: Kouros Nouri-Mahdavi, Jules Stein Eye Institute, UCLA, 100 Stein Plaza, Los Angeles, CA 90095; nouri-mahdavi@jsei.ucla.edu
Investigative Ophthalmology & Visual Science May 2012, Vol.53, 2740-2748. doi:10.1167/iovs.11-8320
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      Naveed Nilforushan, Nariman Nassiri, Sasan Moghimi, Simon K. Law, JoAnn Giaconi, Anne L. Coleman, Joseph Caprioli, Kouros Nouri-Mahdavi; Structure–Function Relationships between Spectral-Domain OCT and Standard Achromatic Perimetry. Invest. Ophthalmol. Vis. Sci. 2012;53(6):2740-2748. doi: 10.1167/iovs.11-8320.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: To explore structure–function relationships in early glaucoma with spectral-domain optical coherence tomography (SD-OCT) and standard achromatic perimetry.

Methods.: One hundred thirty-six eyes of 97 patients with suspected or early glaucoma were enrolled from the clinical database at UCLA's Glaucoma Division. All patients had good-quality peripapillary retinal nerve fiber layer (RNFL)/optic disc measurements and a reliable 24-2 SITA-Standard Humphrey visual field (VF) within a 6-month period. Correlations of global and sectoral RNFL thickness and rim area (RA) measurements, with corresponding global and regional VF sensitivities (both in logarithmic [dB] and 1/Lambert scales [1/L]), were investigated with components of variance models.

Results.: The average RNFL thickness, RA, and mean deviation (MD) were 85.6 ± 5.7 μ, 1.0 ± 0.3 mm2, and −1.3 ± 1.9 dB, respectively. Global RA demonstrated a stronger correlation with MD compared to average RNFL thickness (P = 0.002). The highest correlations were observed between superonasal VF cluster (in dB scale) and inferotemporal RA (R 2 = 0.26, 95% CI: 0.15–0.40) or inferotemporal RNFL thickness (R 2 = 0.24, 95% CI: 0.13–0.37). In glaucoma suspects, the highest correlations were seen between superonasal VF cluster and inferotemporal RA (R 2 = 0.16) in dB scale or RNFL thickness (R 2 = 0.10) in 1/L scale. Correlations were slightly greater with dB scale than 1/L scale and tended to be linear with both scales.

Conclusions.: Structure–function relationships can be detected in early glaucoma with SD-OCT. Correlations of RA with VF thresholds tended to be higher compared to those of RNFL. Structure–function relationships were well described with a linear model.

Introduction
Glaucoma is a progressive optic neuropathy in which structural changes to the optic nerve head (ONH) and peripapillary retinal nerve fiber layer (RNFL) are associated with characteristic visual field (VF) defects. 1,2 It is widely thought that structural damage can frequently precede functional loss in glaucoma and that imaging devices measuring the retinal nerve fiber layer thickness or neuroretinal rim area (RA) are more sensitive for early detection of glaucoma than visual field testing. 37 The relationship between structural and functional measures in glaucoma is important from a clinical point of view, because it is assumed that the two provide related and likely complementary information on the extent of damage in any given eye. But the relationship between the functional loss (as measured with standard achromatic perimetry, or SAP) and structural loss (as detected with RNFL thickness and RA measurements) has been found to be modest at best. 810 The magnitude of this correlation depends on the stage of glaucoma and the variables of interest as well as the technique used to measure them. As more precise and reproducible techniques of measuring optic disc and nerve fiber layer anatomy are introduced and improved functional tests are developed, this relationship may eventually redefine clinical definitions of the glaucomatous process. Spectral–domain optical coherence tomography (SD-OCT) helps clinicians obtain automated measurements of the optic nerve head and surrounding RNFL with higher speed and resolution in comparison to time-domain OCT devices. 11,12  
The purpose of the present study was to investigate the structure–function associations between RNFL thickness and RA measurements from an SD-OCT machine with threshold sensitivity values derived from SAP in a group of patients with early or suspected glaucoma. In addition, the authors investigated whether using visual field sensitivity in 1/ Lambert (1/L) scale (in contrast to logarithmic or decibel scale) improves structure–function relationships. 
Methods
Study Subjects
In this cross-sectional study, 136 eyes of 97 patients with a diagnosis of early or suspected glaucoma were retrospectively enrolled from the clinical database at the Glaucoma Division, Jules Stein Eye Institute (Los Angeles, CA). This study was conducted in accordance with the ethical standards stated in the Declaration of Helsinki and with the approval of the Institutional Review Board of University of California Los Angeles. Patients meeting the following criteria in either eye were included: mean deviation (MD) better than −5 dB on SAP, best corrected visual acuity 20/80 or better, age >30 years, spherical equivalent >−8 D, astigmatism <3 D, and visual field and OCT exams within 6 months of each other. Exclusion criteria were presence of other intraocular or neurological diseases affecting the RNFL, optic disc, or visual field, secondary causes of increased intraocular pressure (IOP) or glaucoma, abnormal appearance of the disc such as tilted disc, non-glaucomatous disc damage or extensive peripapillary atrophy, and prior incisional glaucoma surgery. Patients with a history of uncomplicated cataract surgery were not excluded. 
Glaucoma Definition
Study eyes were classified as having perimetric glaucoma, preperimetric glaucoma, or being glaucoma suspects. Perimetric glaucoma was defined as presence of at least two consecutive abnormal SAP exams regardless of the appearance of the optic disc or RNFL. Eyes with preperimetric glaucoma had glaucomatous optic disc changes (neuroretinal rim thinning or notching, localized or diffuse RNFL defects indicative of glaucoma, or an asymmetry of the vertical cup-to-disc ratio of more than 0.2) by masked stereoscopic disc photograph assessment. The stereoscopic disc photographs were independently reviewed by two experienced clinicians (K.N.M., S.K.L.). In case of disagreement, the two clinicians reviewed the photographs to reach an agreement. Suspected glaucoma was defined as presence of a history of ocular hypertension (IOP >21 mm Hg) or suspicious appearance of the optic disc. All subjects in the suspected or preperimetric glaucoma groups had normal or borderline VF results. 
Visual Field Examination
Standard achromatic perimetry was performed with 24-2 Swedish Interactive Thresholding Algorithm (SITA) strategy (Humphrey Field Analyzer, HFA II; Carl Zeiss Meditec, Inc., Dublin, CA). The visual field was defined as reliable when fixation losses were <33%, and false-positive and false-negative error rates were <20%. All patients were experienced with perimetry before the visual field included in the study was performed. Visual field threshold values for all the 54 test locations across the 24-2 field were exported to a personal computer with PeriData software (PeriData software GmbH, Hurth, Nordrehein-Westfalen, Germany). The 2 test locations at the blind spot were excluded. Cluster threshold sensitivities were calculated by averaging thresholds measured at each point within the 6 visual field regions according to Garway-Heath et al. (Fig. 1). 13 Superior and inferior hemifield sensitivities were also calculated. For evaluation of structure–function correlation, threshold sensitivities were also converted to linear scale (1/L). For this purpose, the authors first converted the threshold sensitivity at each of 52 visual field test locations to 1/L scale and then averaged the sensitivity within each cluster or hemifield. An abnormal visual field was defined as presence of Glaucoma Hemifield Test flagged as “Outside Normal Limits” or 4 abnormal (P < .05) test locations on the pattern deviation probability plot. These criteria have been shown to have good specificity for detection of glaucoma. 14  
Figure 1.
 
Six corresponding regions of neuroretinal rim area (A), peripapillary retinal nerve fiber layer (B), and visual field (C), used to measure the structure–function relationship (based on structure–function map introduced by Garway-Heath et al. 13 ).
Figure 1.
 
Six corresponding regions of neuroretinal rim area (A), peripapillary retinal nerve fiber layer (B), and visual field (C), used to measure the structure–function relationship (based on structure–function map introduced by Garway-Heath et al. 13 ).
Optical Coherence Tomography Imaging
Spectral-domain OCT imaging was performed with Cirrus HD-OCT software version 5.1 (Carl Zeiss Meditec, Inc.). The principles of SD-OCT have been described in detail elsewhere. 11,15 The “Optic Disc Cube 200 × 200” scan protocol was used to measure the RNFL thickness and optic disc RA in a 6 × 6 mm area, consisting of 200 × 200 axial scans (40,000 points) centered on the optic disc. The Cirrus HD-OCT's algorithm automatically places the circumpapillary measurement circle (3.46 mm diameter) around the center of the optic disc (automatically detected by the device) and measures the RNFL thickness at 256 points on this circle. Only good-quality scans, defined as scans with signal strength >6, without RNFL discontinuity, misalignment, involuntary saccade, or blinking artifacts were used for analysis. Blinking is indicated by a straight horizontal black line across the fundus OCT image, whereas involuntary saccade artifacts manifests as breaks in the vessels within a 1.73-mm radius around the optic nerve head (ONH) or breaks or shifts at the ONH. Retinal nerve fiber layer thickness measurements were exported to a personal computer. Sectoral RNFL thickness measurements were calculated by averaging RNFL thickness within 6 regions based on the structure–function map described by Garway-Heath et al. (Fig. 1). The average RA in the same 6 sectors was also calculated as follows. The Cirrus research browser (version 5.0.0.326) allows exporting of the rim width or thickness at 2-degree intervals starting at 9 o'clock (0 degrees, right eye format). Each adjacent pair of the 2-degree RA width measurements was taken as the longer parallel sides of a trapezoid and the trapezoid's base was assumed to be equal to the disc circumference divided by 180. The disc circumference was estimated from the disc area assuming that the disc was a circle. 
Statistical Analyses
Distribution of numerical data was evaluated with the Wilk–Shapiro test. The bivariate correlations were evaluated both for the entire group and in the subgroup of the subjects with preperimetric glaucoma/suspected glaucoma. Average threshold sensitivity in 6 clusters of visual field, and average RNFL thickness and RA in the corresponding SD-OCT sectors, along with global structural and functional measures, were the main outcomes used for evaluating structure–function relationships (Fig. 1). In addition, for decreasing the possible effect of mismatching of the 6 RA/RNFL sectors and visual field clusters, the two corresponding superior and inferior regions of visual field (excluding central and temporal clusters) and OCT (excluding temporal and nasal sectors) were also correlated. 
Retinal nerve fiber layer thickness and RA measurements were expressed in microns or mm2, and visual field measurements were expressed in decibels (logarithmic scale) and 1/Lambert (linear) scales. The following formula was used to convert the dB values to 1/L scale:    
Bivariate correlations were investigated using a generalization of Pearson's correlation coefficient. Since the correlations of the 2 eyes needed to be taken into account, correlations were estimated using a components of variance model (MIXED and NLMIXED procedure in SAS ) of the form:  where X is a fixed effect and the person effect and error are random effects. Under this model,     
Thus, the squared correlation is the proportion of the total variation in Y (visual field sensitivity) that is accounted for by X (RNFL thickness or rim area), controlling for both between- and within-person variation rather than just between person variation. 
The authors also explored for the possibility of nonlinear relationships between visual field (dependent variable) and structural measures (independent variables = X). The null hypothesis was linearity versus an alternative hypothesis of nonlinearity. The authors used the following model to determine how significantly a nonlinear component explained the variation in the dependent variable:  where f(x) is the spline function of x. The null hypothesis here is that c = 0, that is, no spline needed. A small P value (based on the F statistic) rejects linearity in this setting. With the inclusion of the spline regression, there are 4 components explaining the total variation of Y:    
The first component is given by the R 2 and any potential contribution of the nonlinear component is in addition to the R 2. A modification of the Hotelling–Williams test was used to compute P values for comparing the paired correlations (i.e., RNFL or RA vs. visual field). Analyses were performed using SAS version 9.2 (SAS Inc., Cary, NC) and Stata version 11.2 (Stata Corp., College Station, TX) statistical software. 
Results
A total of 136 eyes from 97 patients were enrolled. Forty-eight eyes (of 33 patients) had glaucoma and 88 eyes (of 64 patients) were diagnosed as preperimetric (30 eyes of 23 patients) or suspected glaucoma (58 eyes of 43 patients). Table 1 shows the demographic and ocular characteristics of the study participants. The mean (± SD) age of the study subjects was 66.5 (± 12.1) years. The average (± SD) MD, RNFL thickness, and RA were −1.3 (± 1.9) dB, 85.6 (± 10.2) μ, and 1.0 (± 0.3) mm2, respectively. 
Table 1.
 
Demographic and Ocular Characteristics of the Study Sample
Table 1.
 
Demographic and Ocular Characteristics of the Study Sample
All Subjects Glaucoma Preperimetric/ Suspected Glaucoma
No. of patients (no. of eyes) 97 (136) 33 (48) 64 (88)
Age, years (median and interquartile range) 68.4 (59.4–73.9) 70.9 (56.1–89.1) 64.8 (57.3–72.3)
P < 0.001*
Sex (male/female) 53 / 83 19 / 29 34 / 54
P = 0.914
RNFL thickness, μm, average ± SD (range) 85.6 ± 10.2 (52.5–101.9) 79.8 ± 13.6 (52.5–101.9) 88.7 ± 5.9 (69.5–99.6)
P < 0.001
RA area, mm2, average ± SD (range) 1.0 ± 0.3 (0.3–1.8) 0.8 ± 0.2 (0.3–1.3) 1.1 ± 0.3 (0.7–1.8)
P < 0.001
MD, dB, average ± SD (range) −1.3 ± 1.9 (−5.0–2.6) –2.7 ± 1.7 (−5.0–2.0) –0.5 ± 1.6 (−4.7–2.6)
P < 0.001
PSD, dB, average ± SD (range) 2.3 ± 1.2 (0.5–7.8) 3.3 ± 1.5 (1.8–7.8) 1.8 ± 0.6 (0.5–5)
P < 0.001
Refractive error (diopter, median, and interquartile range) 0 (−1.00–0.25) −0.38 (−1.75–0) 0 (−0.5–0.5)
P < 0.001
IOP, mm Hg (median and interquartile range) 14 (12–17) 14 (12–16) 15 (13–17)
P = 0.330
Bivariate correlation analyses of global structural and functional measures showed better correlation of rim area with the mean deviation compared to RNFL (R 2 = 0.19, vs. R 2 = 0.05, P = 0.002; Fig. 2 and Tables 2, 3). The relationship between average RNFL and RA was mostly linear in the glaucoma and preperimetric/suspected glaucoma groups but the rim area varied within a fairly wide range in eyes with suspected glaucoma (Fig. 3). In bivariate regional correlation analyses derived from the components of variance model, the associations of structural measures with visual field in logarithmic and 1/L scales were strongest between the inferotemporal sectors of RNFL or RA and the superonasal visual field cluster (R 2 = 0.24 and 0.26, respectively; P < 0.001 for both) in dB scale, and tended to be higher compared to the 1/L scale (R 2 = 0.19 and 0.20, respectively; P < 0.001 for both) (Tables 2, 3 and Fig. 4). Similarly, in eyes with normal visual fields (suspected or preperimetric glaucoma group), the inferotemporal RNFL thickness and RA showed the highest correlation with the superonasal visual field in both dB (R 2 = 0.08 and 0.16; P = 0.004 and <0.001, respectively) and 1/L scales (R 2 = 0.10 and 0.09; P < 0.001 and = 0.005, respectively). The other significant correlations in glaucoma suspects were observed between the inferior RA and superior hemifield in both dB and 1/L scales (P = 0.003 vs. 0.019, respectively, Tables 4, 5) and between global RA and MD (P = 0.010). In the entire study sample (136 eyes), the following correlations were higher for RA compared to RNFL in dB scale: global RA vs. MD (R 2 difference = 0.14, P = 0.002) and inferonasal sector vs. superotemporal cluster (R 2 difference = 0.09; P = 0.002) and temporal sector vs. central field (R 2 difference = 0.07; P = 0.01). The only significant difference between correlations of RNFL or RA with visual field in 1/L scale was in the correlation of inferonasal sector versus superotemporal cluster (R 2 difference = 0.05; P = 0.05) in favor of rim area. In preperimetric/suspected glaucoma group (88 eyes), there were no significant differences between correlations of RNFL thickness or RA with the corresponding VF clusters (in dB or 1/L scale) except for the correlation between the temporal sector and central VF cluster in 1/L scale (R 2 difference = 0.05, P = 0.03). 
Figure 2.
 
Scatter plots showing the correlation between visual field mean deviation (in dB), against the average retinal nerve fiber layer thickness (A) and the average rim area (B).
Figure 2.
 
Scatter plots showing the correlation between visual field mean deviation (in dB), against the average retinal nerve fiber layer thickness (A) and the average rim area (B).
Table 2.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Retinal Nerve Fiber Layer Thickness Measurements in 136 Eyes of 97 Patients
Table 2.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Retinal Nerve Fiber Layer Thickness Measurements in 136 Eyes of 97 Patients
Correlated Variables R 2 for dB (vs. 1/L) Scales 95% CI for dB (vs. Linear) Scales P Value dB vs. 1/L
Average RNFL vs. average MD 0.051 / NA 0.004–0.150 / NA 0.007 / NA
Temporal RNFL vs. central VF 0.000 (0.030) 0.021–0.028 (0.000–0.137) 0.878 / 0.03
Superotemporal RNFL vs. inferonasal VF 0.055 (0.045) 0.008–0.144 (0.006–0.123) 0.002 / 0.003
Superonasal RNFL vs. inferotemporal VF 0.016 (0.005) 0.002–0.089 (0.009–0.058) 0.144 / 0.391
Nasal RNFL vs. temporal VF 0.002 (0.000) 0.013–0.042 (0.022–0.026) 0.572 / 0.939
Inferonasal RNFL vs. superotemporal VF 0.000 (0.001) 0.021–0.035 (0.019–0.042) 0.800 / 0.703
Inferotemporal RNFL vs. superonasal VF 0.237 (0.187) 0.133–0.369 (0.094–0.311) <0.001 / <0.001
Superior RNFL vs. inferior VF 0.068 (0.041) 0.050–0.356 (0.002–0.127) <0.001 / 0.01
Inferior RNFL vs. superior VF 0.107 (0.068) 0.031–0.229 (0.010–0.177) <0.001 / 0.002
Table 3.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Rim Area in 136 Eyes of 97 Patients
Table 3.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Rim Area in 136 Eyes of 97 Patients
Correlated Variables R 2 for dB (vs. 1/L) Scales CI 95% for dB (vs. Linear) Scales P Value dB vs. 1/L
Global RA vs. average MD 0.194 / NA (0.091–0.336) / NA <0.001 / NA
Temporal RA vs. central VF 0.066 (0.057) 0.011–0.168 (0.005–0.163) 0.001 / 0.005
Superotemporal RA vs. inferonasal VF 0.097 (0.081) 0.024–0.217 (0.021–0.181) <0.001 / <0.001
Superonasal RA vs. inferotemporal VF 0.051 (0.040) 0.003–0.156 (0.001–0.133) 0.009 / 0.016
Nasal RA vs. temporal VF 0.027 (0.018) 0.000–0.117 (0.003–0.104) 0.066 / 0.151
Inferonasal RA vs. superotemporal 0.091 (0.047) 0.020–0.216 (0.000–0.170) <0.001 / 0.030
Inferotemporal RA vs. superonasal VF 0.258 (0.201) 0.148–0.398 (0.101–0.336) <0.001 / <0.001
Superior RA vs. inferior VF 0.074 (0.060) 0.012–0.188 (0.007–0.161) 0.001 / 0.003
Inferior RA vs. superior VF 0.213 (0.134) 0.107–0.355 (0.044–0.274) <0.001 / <0.001
Figure 3.
 
Scatter plot with spline fits demonstrating the association between the average retinal nerve fiber layer thickness and average rim area in glaucoma suspects/preperimetric glaucoma and perimetric glaucoma patients. As can be seen, the relationship between the average RNFL and rim area is significantly different between glaucoma suspects and perimetric glaucoma patients, although both follow a linear or almost linear pattern. The pattern indicates high variability in rim area as compared to RNFL thickness in glaucoma suspects leading to a bilinear relationship between the 2 structural measures.
Figure 3.
 
Scatter plot with spline fits demonstrating the association between the average retinal nerve fiber layer thickness and average rim area in glaucoma suspects/preperimetric glaucoma and perimetric glaucoma patients. As can be seen, the relationship between the average RNFL and rim area is significantly different between glaucoma suspects and perimetric glaucoma patients, although both follow a linear or almost linear pattern. The pattern indicates high variability in rim area as compared to RNFL thickness in glaucoma suspects leading to a bilinear relationship between the 2 structural measures.
Table 4.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Retinal Nerve Fiber Layer Thickness Measurements in 88 Eyes of 64 Patients with Preperimetric or Suspected Glaucoma
Table 4.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Retinal Nerve Fiber Layer Thickness Measurements in 88 Eyes of 64 Patients with Preperimetric or Suspected Glaucoma
Correlated Variables R 2 for dB (vs. 1/L) Scales CI 95% for dB (vs. Linear) Scales P Value dB vs. 1/L
Average RNFL vs. average MD 0.022 / NA 0.003–0.125 / NA 0.156 / NA
Temporal RNFL vs. central VF 0.001 (0.056)* 0.017–0.043 (0.004–0.165) 0.651 / 0.007*
Superotemporal RNFL vs. inferonasal VF 0.004 (0.007) 0.016–0.067 (0.008–0.069) 0.497 / 0.334
Superonasal RNFL vs. inferotemporal VF 0.000 (0.006) 0.034–0.047 (0.017–0.080) 0.876 / 0.462
Nasal RNFL vs. temporal VF 0.001 (0.001) 0.025–0.043 (0.022–0.049) 0.791 / 0.688
Inferonasal RNFL vs. superotemporal VF 0.002 (0.010) 0.022–0.060 (0.011–0.096) 0.616 / 0.333
Inferotemporal RNFL vs. superonasal VF 0.080 (0.103) 0.009–0.220 (0.024–0.238) 0.004 / <0.001
Superior RNFL vs. inferior VF 0.000 (0.000) 0.036–0.047 (0.036–0.046) 0.895 / 0.903
Inferior RNFL vs. superior VF 0.020 (0.017) 0.004–0.120 (0.005–0.106) 0.170 / 0.196
Table 5.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Rim Area in 88 Eyes of 64 Patients with Preperimetric or Suspected Glaucoma
Table 5.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Rim Area in 88 Eyes of 64 Patients with Preperimetric or Suspected Glaucoma
Correlated Variables R 2 for dB (vs. 1/L) Scales CI 95% for dB (vs. Linear) Scales P Value dB vs.1/L
Average RA vs. average MD 0.076 / NA 0.005–0.233 / NA 0.010 / NA
Temporal RA vs. central VF 0.001 (0.005) 0.028–0.058 (0.024–0.087) 0.716 / 0.532
Superotemporal RA vs. inferonasal VF 0.013 (0.016) 0.005–0.088 (0.001–0.087) 0.230 / 0.130
Superonasal RA vs. inferotemporal VF 0.000 (0.001) 0.032–0.039 (0.030–0.050) 0.917 / 0.800
Nasal RA vs. temporal VF 0.010 (0.007) 0.013–0.102 (0.021–0.101) 0.354 / 0.462
Inferonasal RA vs. superotemporal VF 0.035 (0.032) 0.001–0.163 (0.002–0.160) 0.091 / 0.107
Inferotemporal RA vs. superonasal VF 0.156 (0.09) 0.045–0.334 (0.008–0.249) <0.001 / 0.005
Superior RA vs. inferior VF 0.003 (0.007) 0.018–0.059 (0.011–0.073) 0.567 / 0.383
Inferior RA vs. superior VF 0.095 (0.063) 0.012–0.257 (0.002–0.211) 0.003 / 0.019
Use of 1/L scale for visual field sensitivity did not significantly improve the linearity of structure–function relationships. A linear model could explain most correlations (data not shown). At its highest, nonlinearity accounted for only 7% of the variation in y (for correlation of MD vs. average RNFL thickness in dB scale) in addition to the linear component, although most frequently it was in the 3% or less range. The authors also investigated whether adjusting for the disc size would improve the bivariate correlations. However, the correlation coefficients did not significantly change when the analyses were adjusted for the potential confounding effect of disc size and the effect of disc size was not statistically significant in any of the analyses (data not shown). 
Of the 48 eyes with perimetric glaucoma, 14 eyes (29%) had no evidence of an RNFL defect on the OCT printouts (defined as presence of RNFL thickness at 5th percentile or less in ≥1 clock hour sector or quadrant). Of these eyes, 12 eyes had definitive evidence of glaucoma on stereoscopic disc photographs and 2 eyes were suspected to have signs of glaucomatous damage. Among eyes with normal visual field (88 eyes with preperimetric glaucoma or glaucoma suspects), only 10 out of 30 eyes (34%) with preperimetric glaucoma and 14 of 58 suspected glaucoma eyes (24%) had evidence of RNFL loss on the SD-OCT reports according to the criteria described above. 
Discussion
The authors investigated the correlation of SD-OCT structural measures (RNFL thickness and RA) with functional measures derived from SAP in a group of eyes with early or suspected glaucoma. To identify the best descriptors of structure–function associations, the authors used both logarithmic (dB) and 1/L scales for visual field thresholds. The strongest correlation was found between the inferotemporal sectors of RNFL or RA and the superonasal visual field cluster in decibel scale. All RA sector measurements (as opposed to some of the RNFL sectors) were significantly correlated with the visual field sensitivity in the corresponding clusters. The location of the RNFL or RA sectors showing the most significant correlations with visual field was consistent with prior studies and clinical findings. 9,10,16 Also, correlation coefficients tended to be larger when RA was used as the structural outcome compared with the RNFL thickness measurements. When eyes with perimetric glaucoma were excluded from analyses, the only significant correlation was observed between the inferotemporal sector (both RNFL thickness and RA measurements) and the superonasal visual field cluster. The strength of structure–function relationships did not generally improve when visual field sensitivity was expressed in 1/L scale and tended to be linear in most cases when either the dB or 1/L scale was used. 
The relationship between global and regional visual field sensitivity and structural measurements from various imaging devices such as confocal scanning laser ophthalmoscopy (Heidelberg Retina Tomograph, HRT), OCT, and scanning laser polarimetry (SLP) has been evaluated by many investigators. 9,10,1722 Most studies comparing OCT, HRT, and SLP concluded that these imaging instruments have similar diagnostic performance for glaucoma detection. 19,2327 On the other hand, some studies have reported a higher diagnostic sensitivity with OCT RNFL measurements. 9,21,2831  
Optical coherence tomography was originally used to evaluate retinal nerve fiber layer thickness in glaucoma, but recent software enhancements also permit ONH analysis. The vast majority of the studies evaluating the structure–function relationships used the HRT for measurements of ONH parameters and OCT or SLP for measurement of peripapillary RNFL thickness. In the present study, the authors used the Cirrus HD-OCT for measurement of both RA and peripapillary RNFL thickness. The ability of SD-OCT ONH measurements to differentiate glaucomatous from healthy subjects and the strength of structure–function relationships has not been widely studied yet. Rao et al. investigated the association between visual field loss (in dB and 1/L scales) and peripapillary RNFL thickness, ONH rim area, and macular retinal thickness with SD-OCT (RTVue-100; Optovue Inc., Fremont, CA).10 In glaucomatous eyes (average MD = −2.7 dB), the highest associations were reported between the inferotemporal RNFL thickness (R 2 = 0.26) and inner inferior average macular thickness (R 2 = 0.30) with the corresponding visual field regions in 1/L scale. The association between ONH sectors and visual field loss was weaker with the best correlation (R 2 = 0.08) observed between the inferior RA and superior visual field. This is in contrast to a similar study reported by the same team of investigators with Stratus OCT. 32 The authors found stronger correlations between sectoral and global RA measurements and visual field thresholds compared to RNFL thickness measurements. Strouthidis and colleagues investigated longitudinal changes of the ONH with Spectralis SD-OCT (Heidelberg Engineering, GmbH, Dossenheim, Germany) in experimental glaucoma in rhesus monkeys. 33 They found that structural changes in the ONH, such as decreased RA and deepening of anterior laminar cribrosa surface occurred earlier than RNFL thinning. The relationship between these structural changes to subsequent functional changes needs further cross-sectional and longitudinal studies in human subjects. The authors' finding of a better correlation of RA with visual field thresholds is consistent with the fact that a fairly large minority of glaucomatous eyes (29%) with visual field damage or evidence of glaucomatous damage at the level of the ONH (preperimetric glaucoma, 66%) did not have obvious evidence of RNFL loss on the SD-OCT report as determined by abnormalities on the peripapillary measurement circle. 
The strength of structure–function relationship is related to the individual anatomy and its variation in the study patients, stage of glaucoma in the study sample, visual field scale, and the regression model used. Based on a linear model, both structural and functional changes occur at the same time and RNFL thickness and RA are linearly related to visual field loss. It is reasonable to believe that the relation between structure and function is linear when both are changing and the lag between one and the other is short. A possible apparent non-linearity can arise because of lags between a change in structure and a subsequent change in function as well as possible floor and/or ceiling effects where either the change in structure or function has reached its limit. 
In early glaucoma, evidence of RNFL damage or RA loss can precede evidence of field loss potentially resulting in a non-linear relationship between structural and functional measures. 34 Interestingly, evidence of nonlinearity was infrequent for structure–function associations with dB scale and was obvious only in the MD versus average RNFL thickness scatter plots and in the inferotemporal or superotemporal rim area versus corresponding regions of the field. Importantly, when structure–function relationships were explored in eyes without definitive visual field loss, weak correlations could still be shown for the inferotemporal RNFL or RA sectors versus the corresponding visual field cluster, providing evidence that early visual field loss was already present but clinically undetectable in these eyes, likely a result of high variability in threshold sensitivity in normal eyes. This correlation again tended to be stronger for RA than RNFL thickness. In addition, a scatter plot of average RNFL thickness versus global RA showed a bilinear pattern with evidence of significant variability in RA compared to average RNFL thickness in eyes with suspected or preperimetric glaucoma. This finding could be explained by the anatomical changes in the shape and position of the neuroretinal rim before RNFL loss in early stages of glaucoma along with the high variability of RNFL thickness measurements in normal subjects. Changes in the rim may not be always accompanied by RNFL loss, since changes in rim height may only represent a change in topography and may not reflect loss of axons, leading to a less consistent relationship of the rim area with RNFL loss. This is corroborated by recent findings from Strouthidis et al. 33 Also, horizontal (en face) rim area measurements may not correlate as well as expected with the RNFL thickness in early glaucoma because of the variable configuration of the neuroretinal rim. 35 This would be expected to be most prominent in eyes with larger rim area. In addition, the authors speculate that the observed bilinear relationship could also be partially caused by the variations in rim area and RNFL thickness measurements as a function of disc size. It is possible that the RNFL thickness measurements and the rim area are affected in different ways by the disc size. 
The strength of global structure–function associations tends to diminish across studies as the severity of glaucoma decreases. For example, such relationships were much larger in the study by Leung et al. (R 2 = 0.59–0.68; average MD = −11.1 dB) than those reported by Cho et al. (best R 2 = 0.30; average MD = −7.0 dB), which was in turn higher than that reported by Bowd et al. (R 2 = 0.14–0.25; average MD = −3.0 dB). 9,18,22 In the present study, the average MD of the study sample was −1.3 dB and the R 2 values were more consistent with the study by Bowd et al., likely a result of a similar severity of glaucoma in the enrolled eyes. 
There is a lack of agreement among studies regarding differences between linear and nonlinear estimates of structure–function associations. In the present study, the differences in structure–function correlations for dB versus 1/L scales were very small with the dB scales showing mostly stronger (and mostly linear) correlations. This was true regardless of whether the entire sample or only the suspected glaucoma eyes were included in the analyses. Bowd et al. found no significant differences in most cases between linear and nonlinear regression when the visual field threshold was expressed in dB. 9 Garway-Heath et al. reported stronger nonlinear fits in dB scale and stronger linear fits in 1/L scale. 36 In a study by Leung et al., reporting the correlation between MD and RNFL thickness with Stratus OCT and SLP-VCC, the linear regression attained the best correlation only when VF sensitivity was expressed in 1/L scale after exclusion of normal subjects. 18 In another study, Schlottmann et al. showed small but significant improvements in structure–function associations with logarithmic regression analysis in dB scale and linear regression in 1/L scale in a group of patients with average MD of −6.9 dB. 37 The authors did not explore logarithmic regression models. The scatter plot for structure–function relationships is normally s-shaped when glaucomatous eyes with a wide range of damage are included. The lower plateau is due to the limited dynamic range of measurements and the fact that because of residual glial and vascular tissues the RNFL thickness never reaches zero microns. 38,39 The upper plateau is due to the variability of structural measurements in glaucoma suspects or normal subjects who have minimal or no evidence of glaucomatous field damage. In normal subjects, the correlation between structural and functional measures has been observed to be nonexistent or very weak. 10,40 The authors speculate that one reason for the linear relationships seen with the dB scale in this study is the very early nature of glaucoma in the enrolled patients. Since no advanced glaucoma patients were included in this study (MD was required to be better than −5.0 dB, and average MD was −1.3 dB), an obvious change in the slope of bivariate correlations was less likely to be observed, although the authors observed evidence of this pattern in some of the analyses. 
The results of this study should be interpreted with its limitations in mind. One issue is that MD measurements are corrected for age by the HFA while the structural measurements were not. In a recent study, the regression coefficient for change of rim area with age was very small (β = −0.004, 95% CI: −0.008 to −0.001) and was about 2 microns per decade for the average RNFL. 41 Given the significant variability of neuroretinal rim area and RNFL among healthy individuals, the authors believe this issue is unlikely to have introduced a significant bias. The sectoral neuroretinal rim area was calculated by assuming the optic disc to be circular and the sides of the trapezoid forming the 2-degree rim sectors to be parallel. This assumption may not be true especially in eyes with small cups or oval disc shape. The authors found that the calculated global RA, based on the sum of all 180 two-degree sectors, was larger than automated SD-OCT measurements especially in eyes with larger global rim area. Also, the average difference between the calculated and automated global rim area was somewhat smaller in glaucoma eyes (0.15 mm2) versus the entire sample (0.27 mm2). After excluding eyes with anomalous disc or those with incorrect identification of the disc border by the automated algorithm of Cirrus HD-OCT (9 eyes), the difference in global rim area decreased to 0.2 mm2. However, global structure–function relationships (based on automated rim area data provided by the Cirrus HD-OCT) were still stronger for RA as opposed to average RNFL thickness measurements and the location of RA sectors showing significant correlation with the visual field was consistent with those found with RNFL sectors. Therefore, there is no indirect evidence that the correlations of calculated sectoral rim areas with visual field clusters were significantly biased as a result of the authors' approach. 
In summary, the authors' results demonstrate that global and regional structure–function relationships tended to be linear in this study sample with very early glaucomatous damage. Correlations of RA measurements with visual field sensitivities were stronger than those of RNFL thickness. Weak regional correlations were still detectable in eyes with no definitive visual field loss. 
Figure 4.
 
Scatter plots showing the correlation between average visual field threshold in superonasal cluster (dB and 1/Lambert) and the average rim area (A, B) and average retinal nerve fiber layer thickness (C, D) in the inferotemporal sector.
Figure 4.
 
Scatter plots showing the correlation between average visual field threshold in superonasal cluster (dB and 1/Lambert) and the average rim area (A, B) and average retinal nerve fiber layer thickness (C, D) in the inferotemporal sector.
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Footnotes
 Supported in part by Research to Prevent Blindness.
Footnotes
 Disclosure: N. Nilforushan, None; N. Nassiri, None; S. Moghimi, None; S.K. Law, None; J. Giaconi, None; A.L. Coleman, None; J. Caprioli, None; K. Nouri-Mahdavi, None
Footnotes
 Presented in part as a poster at the annual meeting of the Association for Research in Vision and Ophthalmology, Fort Lauderdale, Florida, May 2011.
Figure 1.
 
Six corresponding regions of neuroretinal rim area (A), peripapillary retinal nerve fiber layer (B), and visual field (C), used to measure the structure–function relationship (based on structure–function map introduced by Garway-Heath et al. 13 ).
Figure 1.
 
Six corresponding regions of neuroretinal rim area (A), peripapillary retinal nerve fiber layer (B), and visual field (C), used to measure the structure–function relationship (based on structure–function map introduced by Garway-Heath et al. 13 ).
Figure 2.
 
Scatter plots showing the correlation between visual field mean deviation (in dB), against the average retinal nerve fiber layer thickness (A) and the average rim area (B).
Figure 2.
 
Scatter plots showing the correlation between visual field mean deviation (in dB), against the average retinal nerve fiber layer thickness (A) and the average rim area (B).
Figure 3.
 
Scatter plot with spline fits demonstrating the association between the average retinal nerve fiber layer thickness and average rim area in glaucoma suspects/preperimetric glaucoma and perimetric glaucoma patients. As can be seen, the relationship between the average RNFL and rim area is significantly different between glaucoma suspects and perimetric glaucoma patients, although both follow a linear or almost linear pattern. The pattern indicates high variability in rim area as compared to RNFL thickness in glaucoma suspects leading to a bilinear relationship between the 2 structural measures.
Figure 3.
 
Scatter plot with spline fits demonstrating the association between the average retinal nerve fiber layer thickness and average rim area in glaucoma suspects/preperimetric glaucoma and perimetric glaucoma patients. As can be seen, the relationship between the average RNFL and rim area is significantly different between glaucoma suspects and perimetric glaucoma patients, although both follow a linear or almost linear pattern. The pattern indicates high variability in rim area as compared to RNFL thickness in glaucoma suspects leading to a bilinear relationship between the 2 structural measures.
Figure 4.
 
Scatter plots showing the correlation between average visual field threshold in superonasal cluster (dB and 1/Lambert) and the average rim area (A, B) and average retinal nerve fiber layer thickness (C, D) in the inferotemporal sector.
Figure 4.
 
Scatter plots showing the correlation between average visual field threshold in superonasal cluster (dB and 1/Lambert) and the average rim area (A, B) and average retinal nerve fiber layer thickness (C, D) in the inferotemporal sector.
Table 1.
 
Demographic and Ocular Characteristics of the Study Sample
Table 1.
 
Demographic and Ocular Characteristics of the Study Sample
All Subjects Glaucoma Preperimetric/ Suspected Glaucoma
No. of patients (no. of eyes) 97 (136) 33 (48) 64 (88)
Age, years (median and interquartile range) 68.4 (59.4–73.9) 70.9 (56.1–89.1) 64.8 (57.3–72.3)
P < 0.001*
Sex (male/female) 53 / 83 19 / 29 34 / 54
P = 0.914
RNFL thickness, μm, average ± SD (range) 85.6 ± 10.2 (52.5–101.9) 79.8 ± 13.6 (52.5–101.9) 88.7 ± 5.9 (69.5–99.6)
P < 0.001
RA area, mm2, average ± SD (range) 1.0 ± 0.3 (0.3–1.8) 0.8 ± 0.2 (0.3–1.3) 1.1 ± 0.3 (0.7–1.8)
P < 0.001
MD, dB, average ± SD (range) −1.3 ± 1.9 (−5.0–2.6) –2.7 ± 1.7 (−5.0–2.0) –0.5 ± 1.6 (−4.7–2.6)
P < 0.001
PSD, dB, average ± SD (range) 2.3 ± 1.2 (0.5–7.8) 3.3 ± 1.5 (1.8–7.8) 1.8 ± 0.6 (0.5–5)
P < 0.001
Refractive error (diopter, median, and interquartile range) 0 (−1.00–0.25) −0.38 (−1.75–0) 0 (−0.5–0.5)
P < 0.001
IOP, mm Hg (median and interquartile range) 14 (12–17) 14 (12–16) 15 (13–17)
P = 0.330
Table 2.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Retinal Nerve Fiber Layer Thickness Measurements in 136 Eyes of 97 Patients
Table 2.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Retinal Nerve Fiber Layer Thickness Measurements in 136 Eyes of 97 Patients
Correlated Variables R 2 for dB (vs. 1/L) Scales 95% CI for dB (vs. Linear) Scales P Value dB vs. 1/L
Average RNFL vs. average MD 0.051 / NA 0.004–0.150 / NA 0.007 / NA
Temporal RNFL vs. central VF 0.000 (0.030) 0.021–0.028 (0.000–0.137) 0.878 / 0.03
Superotemporal RNFL vs. inferonasal VF 0.055 (0.045) 0.008–0.144 (0.006–0.123) 0.002 / 0.003
Superonasal RNFL vs. inferotemporal VF 0.016 (0.005) 0.002–0.089 (0.009–0.058) 0.144 / 0.391
Nasal RNFL vs. temporal VF 0.002 (0.000) 0.013–0.042 (0.022–0.026) 0.572 / 0.939
Inferonasal RNFL vs. superotemporal VF 0.000 (0.001) 0.021–0.035 (0.019–0.042) 0.800 / 0.703
Inferotemporal RNFL vs. superonasal VF 0.237 (0.187) 0.133–0.369 (0.094–0.311) <0.001 / <0.001
Superior RNFL vs. inferior VF 0.068 (0.041) 0.050–0.356 (0.002–0.127) <0.001 / 0.01
Inferior RNFL vs. superior VF 0.107 (0.068) 0.031–0.229 (0.010–0.177) <0.001 / 0.002
Table 3.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Rim Area in 136 Eyes of 97 Patients
Table 3.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Rim Area in 136 Eyes of 97 Patients
Correlated Variables R 2 for dB (vs. 1/L) Scales CI 95% for dB (vs. Linear) Scales P Value dB vs. 1/L
Global RA vs. average MD 0.194 / NA (0.091–0.336) / NA <0.001 / NA
Temporal RA vs. central VF 0.066 (0.057) 0.011–0.168 (0.005–0.163) 0.001 / 0.005
Superotemporal RA vs. inferonasal VF 0.097 (0.081) 0.024–0.217 (0.021–0.181) <0.001 / <0.001
Superonasal RA vs. inferotemporal VF 0.051 (0.040) 0.003–0.156 (0.001–0.133) 0.009 / 0.016
Nasal RA vs. temporal VF 0.027 (0.018) 0.000–0.117 (0.003–0.104) 0.066 / 0.151
Inferonasal RA vs. superotemporal 0.091 (0.047) 0.020–0.216 (0.000–0.170) <0.001 / 0.030
Inferotemporal RA vs. superonasal VF 0.258 (0.201) 0.148–0.398 (0.101–0.336) <0.001 / <0.001
Superior RA vs. inferior VF 0.074 (0.060) 0.012–0.188 (0.007–0.161) 0.001 / 0.003
Inferior RA vs. superior VF 0.213 (0.134) 0.107–0.355 (0.044–0.274) <0.001 / <0.001
Table 4.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Retinal Nerve Fiber Layer Thickness Measurements in 88 Eyes of 64 Patients with Preperimetric or Suspected Glaucoma
Table 4.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Retinal Nerve Fiber Layer Thickness Measurements in 88 Eyes of 64 Patients with Preperimetric or Suspected Glaucoma
Correlated Variables R 2 for dB (vs. 1/L) Scales CI 95% for dB (vs. Linear) Scales P Value dB vs. 1/L
Average RNFL vs. average MD 0.022 / NA 0.003–0.125 / NA 0.156 / NA
Temporal RNFL vs. central VF 0.001 (0.056)* 0.017–0.043 (0.004–0.165) 0.651 / 0.007*
Superotemporal RNFL vs. inferonasal VF 0.004 (0.007) 0.016–0.067 (0.008–0.069) 0.497 / 0.334
Superonasal RNFL vs. inferotemporal VF 0.000 (0.006) 0.034–0.047 (0.017–0.080) 0.876 / 0.462
Nasal RNFL vs. temporal VF 0.001 (0.001) 0.025–0.043 (0.022–0.049) 0.791 / 0.688
Inferonasal RNFL vs. superotemporal VF 0.002 (0.010) 0.022–0.060 (0.011–0.096) 0.616 / 0.333
Inferotemporal RNFL vs. superonasal VF 0.080 (0.103) 0.009–0.220 (0.024–0.238) 0.004 / <0.001
Superior RNFL vs. inferior VF 0.000 (0.000) 0.036–0.047 (0.036–0.046) 0.895 / 0.903
Inferior RNFL vs. superior VF 0.020 (0.017) 0.004–0.120 (0.005–0.106) 0.170 / 0.196
Table 5.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Rim Area in 88 Eyes of 64 Patients with Preperimetric or Suspected Glaucoma
Table 5.
 
Correlation of Global or Sectoral Visual Field Threshold Sensitivity (in both decibel and 1/L scales) versus Global or Sectoral Rim Area in 88 Eyes of 64 Patients with Preperimetric or Suspected Glaucoma
Correlated Variables R 2 for dB (vs. 1/L) Scales CI 95% for dB (vs. Linear) Scales P Value dB vs.1/L
Average RA vs. average MD 0.076 / NA 0.005–0.233 / NA 0.010 / NA
Temporal RA vs. central VF 0.001 (0.005) 0.028–0.058 (0.024–0.087) 0.716 / 0.532
Superotemporal RA vs. inferonasal VF 0.013 (0.016) 0.005–0.088 (0.001–0.087) 0.230 / 0.130
Superonasal RA vs. inferotemporal VF 0.000 (0.001) 0.032–0.039 (0.030–0.050) 0.917 / 0.800
Nasal RA vs. temporal VF 0.010 (0.007) 0.013–0.102 (0.021–0.101) 0.354 / 0.462
Inferonasal RA vs. superotemporal VF 0.035 (0.032) 0.001–0.163 (0.002–0.160) 0.091 / 0.107
Inferotemporal RA vs. superonasal VF 0.156 (0.09) 0.045–0.334 (0.008–0.249) <0.001 / 0.005
Superior RA vs. inferior VF 0.003 (0.007) 0.018–0.059 (0.011–0.073) 0.567 / 0.383
Inferior RA vs. superior VF 0.095 (0.063) 0.012–0.257 (0.002–0.211) 0.003 / 0.019
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