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Multidisciplinary Ophthalmic Imaging  |   July 2012
Does Optic Nerve Head Size Variation Affect Circumpapillary Retinal Nerve Fiber Layer Thickness Measurement by Optical Coherence Tomography?
Author Affiliations & Notes
  • David Huang
    From the Oregon Health & Science University, Casey Eye Institute, Portland, Oregon; and the
  • Vikas Chopra
    Doheny Eye Institute and Department of Ophthalmology, Keck School of Medicine, University of Southern California, Los Angeles, California.
  • Ake Tzu-Hui Lu
    Doheny Eye Institute and Department of Ophthalmology, Keck School of Medicine, University of Southern California, Los Angeles, California.
  • Ou Tan
    From the Oregon Health & Science University, Casey Eye Institute, Portland, Oregon; and the
  • Brian Francis
    Doheny Eye Institute and Department of Ophthalmology, Keck School of Medicine, University of Southern California, Los Angeles, California.
  • Rohit Varma
    Doheny Eye Institute and Department of Ophthalmology, Keck School of Medicine, University of Southern California, Los Angeles, California.
  • Corresponding author: David Huang, Casey Eye Institute, Oregon Health & Science University, 3375 S.W. Terwilliger Boulevard, Portland, OR 97239‐4197; davidhuang@alum.mit.edu
Investigative Ophthalmology & Visual Science July 2012, Vol.53, 4990-4997. doi:10.1167/iovs.11-8214
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      David Huang, Vikas Chopra, Ake Tzu-Hui Lu, Ou Tan, Brian Francis, Rohit Varma, Advanced Imaging for Glaucoma Study (AIGS) Group; Does Optic Nerve Head Size Variation Affect Circumpapillary Retinal Nerve Fiber Layer Thickness Measurement by Optical Coherence Tomography?. Invest. Ophthalmol. Vis. Sci. 2012;53(8):4990-4997. doi: 10.1167/iovs.11-8214.

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      © 2015 Association for Research in Vision and Ophthalmology.

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Abstract

Purpose.: To determine the relationship between retinal nerve fiber layer (RNFL) thickness, optic disc size, and image magnification.

Methods.: The cohort consisted of 196 normal eyes of 101 participants in the Advanced Imaging for Glaucoma Study (AIGS), a multicenter, prospective, longitudinal study to develop advanced imaging technologies for glaucoma diagnosis. Scanning laser tomography was used to measure disc size. Optical coherence tomography (OCT) was used to perform circumpapillary RNFL thickness measurements using the standard fixed 3.46-mm nominal scan diameter. A theoretical model of magnification effects was developed to relate RNFL thickness (overall average) with axial length and magnification.

Results.: Multivariate regression showed no significant correlation between RNFL thickness and optic disc area (95% confidence interval [CI] = −0.9 to 4.1 μm/mm2, P = 0.21). Linear regression showed that RNFL thickness depended significantly on axial length (slope = −3.1 μm/mm, 95% CI = −4.9 to −1.3, P = 0.001) and age (slope = −0.3 μm/y, 95% CI = −0.5 to −0.2, P = 0.0002). The slope values agreed closely with the values predicted by the magnification model.

Conclusions.: There is no significant association between RNFL thickness and optic disc area. Previous publications that showed such an association may have been biased by the effect of axial length on fundus image magnification and, therefore, both measured RNFL thickness and apparent disc area. The true diameter of the circumpapillary OCT scan is larger for a longer eye (more myopic eye), leading to a thinner RNFL measurement. Adjustment of measured RNFL thickness by axial length, in addition to age, may lead to a tighter normative range and improve the detection of RNFL thinning due to glaucoma.

Introduction
Optical coherence tomography (OCT) 1 is widely used in the evaluation and management in retinal and optic nerve disorders. It uses low-coherence interferometry to measure time-of-flight delay of backscattering light and determines the depth of reflections from retinal layers. This principle produces cross-sectional images with higher resolution than is possible with other noninvasive imaging modalities. 
Glaucomatous optic neuropathy is characterized by a progressive loss of retinal ganglion cells and their respective axons, which comprise the retinal nerve fiber layer (RNFL). 2 For glaucoma evaluation, OCT provides reproducible quantitative measurements of RNFL around the optic nerve head (ONH) 3 and in the macular region. 48 Retinal nerve fiber layer assessment is important because structural damage to the ONH and RNFL often precede functional changes detected by perimetry. 918  
OCT systems are widely used for RNFL imaging. Commercial OCT systems generally provide an age-stratified normative database of circumpapillary RNFL thickness. Circular RNFL scans around the ONH are commonly used. Previously, Schuman et al. 5 demonstrated that the 3.4-mm fixed-diameter scan was more accurate and reproducible when compared with smaller or larger diameter scans. Thus, the 3.4-mm scan has been adopted as the standard circular scan in clinical practice and research studies. 
The strategy of using a fixed-scan diameter has been contested. Several studies have found that RNFL thickness measured at fixed diameter was positively correlated with optic disc area. 19,20 The implication was that the number of nerve fibers in the RNFL depends on the disc area, and it might be possible to reduce the variation in the measured RNFL thickness if the scan diameter was adjusted according to disc diameter. 
We offer an alternative hypothesis in that the number of nerve fibers in the RNFL is not dependent, to any significant degree, on the disc area in human eyes, and that the RNFL thickness, measured at a fixed OCT scan diameter, is not related to the true disc area. The correlation between the RNFL thickness and apparent disc area could be explained by the image magnification variation due to the variation of the axial length of the eye. We test our hypotheses by studying the relationships between OCT RNFL thickness, ONH area (by Heidelberg Retinal Tomograph II), and eye axial length. 
Materials and Methods
The cohort included all eligible normal participants in the Advanced Imaging for Glaucoma Study (AIGS), which is a multicenter, prospective, longitudinal study to develop advanced imaging technologies to improve the detection and management of glaucoma. The Institutional Review Board at each participating center (University of Southern California Keck School of Medicine, University of Miami Miller School of Medicine, University of Pittsburgh School of Medicine) approved the study protocol, and all study procedures conformed to Health Insurance Portability and Accountability regulations and the Declaration of Helsinki for research involving human subjects. 
Clinical Procedures and Definitions
After informed consent was obtained, participants underwent a complete ophthalmic examination by a glaucoma specialist including visual acuity, refraction, and slit-lamp evaluation. Two measurements of intraocular pressure (IOP) were obtained using the Goldmann applanation tonometry (Haag–Streit, Bern, Switzerland), which were then averaged to yield a single value for each eye. Visual field testing was performed using a field analyzer (Humphrey Automated; Carl Zeiss Meditec, Dublin, CA [Swedish interactive threshold algorithm Standard 24‐2]). Following dilation, a detailed posterior-segment examination and stereo optic disc photography were performed. Axial length measurements were determined using the intraocular lens (IOL) optical biometer (IOL Master; Carl Zeiss Meditec, Dublin, CA) by an experienced ophthalmic technician. 
Inclusion Criteria.
Inclusion criteria included participants between the age of 40 and 79 years, the absence of ocular pathology on a detailed eye exam, IOP < 21 mm Hg, and normal visual field. The refractive errors were between +3.0 diopters (D) and −7.0 D spherical equivalent. Although the AIGS allowed enrollment of participants with previous uncomplicated cataract surgery, this subset was excluded from the current analysis because cataract surgery and IOL implantation removes the natural connection between axial eye length and refractive error. In addition, scans with signal strength score < 6 were excluded to avoid artifactually low RNFL thickness measurements due to inadequate signals. The complete inclusion and exclusion criteria are listed in the AIGS Manual of Procedures posted on www.AIGStudy.net
Optic Disc Size Determination with Scanning Laser Ophthalmoscopy.
A confocal scanning laser ophthalmoscope has been shown (The Heidelberg Retinal Tomograph II [HRT II]; Heidelberg Engineering GmbH, Dossenheim, Germany) to provide reproducible measurements of the optic disc, 21 and was used to measure disc area in this study. Using reflectance and height maps (HRT II), the disc boundaries were traced by an experienced, AIGS-certified ophthalmic photographer according to the procedure recommended by the manufacturer. Values from two high-quality scans were averaged. The focus setting, which provides information on the eye's refractive error, and the keratometry were recorded (HRT II). Based on this information, the software (HRT II) corrects the effect of magnification on the disc measurements. The HRT method had been found to correct for most magnification errors, to within a mean residual error of −1.3 to 2.0%, compared with an axial length derived standard. 22 Thus, HRT-determined disc area should be much closer to the true value than the OCT-derived disc area, which was not corrected for magnification variation between eyes. The HRT-determined disc area measurement was used to calculate a disc diameter assuming a circular shape. 
RNFL Thickness Measurements.
Circumpapillary RNFL measurements were obtained using the standard “Fast RNFL” scan pattern. The scan records three consecutive circles around the optic disc, for a total of 768 axial scans recorded in 1.9 seconds. The circles have a nominal diameter of 3.46 mm (equivalent to 12°). Experienced photographers who were certified by the AIGS performed two separate, good quality scans (well-centered scans with signal strength ≥ 7). The overall average RNFL thickness measurements from the two scans were averaged to yield a single RNFL thickness value for each eye. 
Statistical Analysis
Both eyes of each subject were used for the analysis. To adjust for the correlation between the right and left eyes of each participant, the linear mixed models 23 was used in the statistical tests. Univariate and multivariate regression analyses were performed to identify independent associations between RNFL thickness measurements and other parameters. All analyses were conducted at a <0.05 significance level and used statistical analysis system programs (SAS System 8 programs; SAS Institute Inc., Cary, NC). 
Results
Demographics and Measurement Statistics
From the normal group of the AIGS, 196 eyes of 101 participants were found to satisfy the inclusion criteria for this study. The statistics on their demographics and eye measurements are listed in Table 1. The sex was 65.4% female and the ethnicity was 90.1% Caucasian. 
Table 1. 
 
Demographics and Measurement Statistics of Normal Participants
Table 1. 
 
Demographics and Measurement Statistics of Normal Participants
Parameter Mean SD Minimum Maximum
Age (y) 54.0 9.7 40.2 76.1
Axial length (mm) 23.7 0.8 21.9 25.5
Spherical equivalent (D) −0.5 1.5 −5.5 3.6
Disc area (mm2) 1.9 0.5 0.8 3.9
Disc diameter (mm) 1.5 0.2 1.0 2.2
RNFL (μm) 99.8 9.3 74.6 120.7
Univariate Regression on RNFL Thickness
Univariate regression was performed between overall average RNFL thickness and several independent variables: age, axial length, spherical equivalent refractive error, disc area, sex, and ethnicity (Table 2). Age and axial length were found to have significant correlations with RNFL thickness, whereas sex almost reached statistical significance with RNFL thickness (P = 0.054). The linear regression slope of RNFL thickness versus axial length was −3.3 μm/mm, with a 95% confidence interval of −5.2 to −1.3 (Fig. 1). This result agrees with the calculated value of −4.2 μm/mm for the slope as predicted by our theoretical model of magnification effects (see Appendix, equation 12). 
Figure 1. 
 
Plot of RNFL thickness versus axial length. The solid line represents the linear regression fit.
Figure 1. 
 
Plot of RNFL thickness versus axial length. The solid line represents the linear regression fit.
Table 2. 
 
Univariate Regression of RNFL Thickness against Other Parameters
Table 2. 
 
Univariate Regression of RNFL Thickness against Other Parameters
Parameter Slope (μm/x) SE of
Slope
95% CI
of Slope
R 2 P Value
Age (y) −0.3 0.1 −0.5, −0.2 0.13 <0.0001
Axial length (mm) −3.3 1.0 −5.2, −1.3 0.09 0.001
Spherical equivalent (D) 0.8 0.5 −0.2, 1.8 <0.01 0.109
Disc area (mm2) 1.9 1.3 −0.8, 4.6 0.03 0.164
Disc diameter (mm) 4.7 3.3 −1.9, 11.3 0.03 0.164
Sex (female) 3.6 1.9 −0.1, 7.3 0.03 0.054
Ethnicity (Caucasian) −2.9 3.0 −8.8, 3.1 0.008 0.337
No correlation was found between RNFL thickness and disc area (P = 0.164). Our sample size was sufficient to detect a slope of 5 μm/mm2 (20% of the predicted magnification effect) at P = 0.05 significance level with more than 80% power. Furthermore, there was no significant correlation between disc area and axial length (P = 0.8). 
Multivariate Regression Results
Multivariate regression analysis (Table 3) confirmed the results of the univariate regression. Age and axial length were again found to be significantly correlated with RNFL thickness, and the slopes were similar. The lack of association between RNFL and disc area was also confirmed. 
Table 3. 
 
Multivariate Regression of RNFL Thickness against Other Parameters*
Table 3. 
 
Multivariate Regression of RNFL Thickness against Other Parameters*
Parameter Slope
(μm/x)
SE 95% CI P Value
Disc area (mm2) 1.7 1.3 −0.9, 4.1 0.21
Age (y) −0.3 0.1 −0.5, −0.2 0.0002
Sex (female) 2.8 1.6 −0.4, 6.1 0.08
Axial length (mm) −3.1 0.9 −4.9, −1.3 0.001
Univariate Regression after Introducing Magnification Error on Disc Measurements
Since our disc size measurements have been corrected for magnification effects (HRT II software), we did not expect a correlation with RNFL thickness. However, reports of studies in previous literature have found such a correlation using disc size measurements that were not corrected for magnification variation. To re-create this artifactual correlation, we performed univariate regression of RNFL thickness on disc diameter and area, after reintroducing the magnification variation according to axial length variation (see Appendix, equations 7 and 8). The results (Table 4) showed a significant correlation (P = 0.04) between RNFL thickness and both disc diameter and area. 
Table 4. 
 
Univariate Regression of RNFL Thickness against Disc Parameters, after Reintroducing Magnification Variation into Disc Measurements
Table 4. 
 
Univariate Regression of RNFL Thickness against Disc Parameters, after Reintroducing Magnification Variation into Disc Measurements
Parameter Slope (μm/x) SE 95% CI R 2 P Value
Disc area (mm2) 2.7 1.3 0.1, 5.3 0.06 0.04
Disc diameter (mm) 6.7 3.2 0.3, 13.1 0.06 0.04
Nerve Fiber Layer Thickness after Magnification Correction
We corrected for the effect of magnification by dividing the measured RNFL thickness by the magnification factor La /L (see Appendix, equations 6 and 10). The corrected RNFL thickness is equivalent to the RNFL thickness measured at a true scan diameter of 3.46 mm rather than a nominal scan diameter of 3.46 mm. The corrected RNFL thickness has a significant correlation with age, but not with other variables (Table 5). The corrected RNFL thickness no longer has a significant correlation with axial length. This again supports the argument that the correlation between RNFL thickness and axial length was due to the magnification effect, not a true anatomic correlation. 
Table 5. 
 
Univariate Regression of Magnification-Corrected RNFL Thickness against Other Parameters
Table 5. 
 
Univariate Regression of Magnification-Corrected RNFL Thickness against Other Parameters
Parameter Slope (μm/x) SE 95% CI R 2 P Value
Age (y) −0.3 0.1 −0.5, −0.2 0.13 <0.0001
Axial length (mm) 0.8 1.0 −1.1, 2.8 <0.01 0.40
Spherical equivalent (D) −0.2 0.5 −1.2, 0.7 <0.01 0.62
Disc area (mm2) 1.7 1.3 −0.9, 4.3 0.03 0.19
Disc diameter (mm) 4.3 3.2 −2.2, 10.7 0.04 0.19
Sex (female) 3.1 1.8 −0.5, 6.6 0.03 0.09
Ethnicity (Caucasian) −3.8 2.9 −9.5, 1.8 0.02 0.18
Discussion
To optimize the detection of glaucomatous RNFL thinning, it is important to account for factors that can affect the measured RNFL thickness and allow for them by adjusting the RNFL thickness value or diagnostic threshold. So far, the following factors have been identified: (1) demographic factors such as age, 4,2433 race, and ethnicity 24,3234 ; (2) larger optic disc size (diameter or area) was associated with thicker RNFL 19,20,35 ; (3) RNFL thickness decreases further away from optic disc margin 36,37 ; and (4) longer axial eye length and myopia were associated with thinner RNFL. 38,39  
Demographic factors such as age and race could be dealt with separately from the other two, by the use of a diverse normative database that provides reference over a wide range of age and representative diversity of race and ethnicity. Factor (2) is an important consideration because the ONH size shows considerable variability between individuals, ranging between 0.8 and 6.00 mm2. 4044 It is not clear how to eliminate RNFL thickness variations related to ONH size, however. Different investigators have proposed performing OCT scans at either factor (1), fixed distance from the optic disc margin, 37,45 or factor (2), fixed multiples of optic disc diameter. 20,46 Another alternative would be to perform OCT scanning at a fixed diameter, and then perform adjustment for optic disc size using a mathematical formula. Because factors (2), (3), and (4) are all affected by optical magnification of OCT scanning, it is difficult to know which scanning approach is best and which method of post-measurement adjustment to use. A quantitative theoretical framework that ties these factors together is needed. 
To clarify the intertwined relationship between axial length, RNFL thickness, and disc size, we developed a mathematical model (Appendix) that started from simple reasonable assumptions. This model was used to resolve the question on whether the apparent relationship between RNFL thickness and disc size could be an artifact due to magnification (axial length) variation between eyes. 
  1.  
    The cross-sectional area of each retinal nerve fiber and its associated glial tissue are approximately constant; therefore, the total RNFL cross-sectional area is approximately constant over scan circles near the ONH (see Appendix, equations 3 and 4).
  2.  
    Image magnification is inversely proportional to eye axial length (equation 6).
  3.  
    The true millimeter diameter of the OCT scan circle is inversely proportional to image magnification (equation 9).
  4.  
    The apparent disc diameter on an OCT image is inversely proportional to image magnification (equation 7).
Our model produced the following prediction that could be tested against results from our clinical study and other clinical studies: 
  1.  
    Given a fixed nominal scan radius ra (fixed in degrees of visual angle), the measured RNFL thickness is proportional to image magnification (equation 10).
  2.  
    The overall RNFL thickness over a circular scan is inverse proportional to the scan radius r (in millimeters, equation 5).
  3.  
    An artifactual correlation between RNFL thickness and disc diameter (or area) could be caused by magnification variation that is not corrected.
Several other groups of investigators had found that RNFL thickness was correlated with axial length and refractive error. 3739,47 The magnification effect was one possible explanation for this correlation. Our results showed that the slope of this correlation was close to the value predicted by the magnification effect (equation 12). Our model also provided a way to compensation for the effect of magnification (axial length) on RNFL thickness (equation 10). After accounting for the effect of magnification, RNFL thickness no longer depended on axial length or refractive error (Table 5). Patel et al., 37 Kang et al., 39 and Savini et al. 47 all found that mathematical magnification compensation removed the dependence of RNFL thickness on refractive error and axial length, in agreement with our results and reasoning. Rauscher et al. 38 thought that lower RNFL measurements recorded in myope could be due to differences in reflectivity in longer eyes or a predisposition to develop glaucoma in myopes. This explanation does not appear necessary since the magnification effect can entirely explain the lower RNFL measurement in myopes. 
The true relationship between RNFL thickness and optic disc size is another issue that is confounded by magnification variation. 
Our results support the hypothesis that the number of nerve fibers in the nerve fiber layer is not dependent on the optic disc size. The RNFL thickness measured by OCT was not correlated with the HRT-determined optic disc area, which is magnification corrected. Previously, histologic studies have found that there are more nerve fibers in monkey eyes with larger optic disc heads. 48 Human histologic studies were equivocal. Two studies found no correlation between axon count and disc size or scleral canal area. 36,49 Another study found a small correlation between nerve fiber count and optic disc area, but the correlation (R 2 = 0.14 ) was much smaller than the correlation between nerve fiber count with retrobulbar optic nerve cross-sectional area (R 2 = 0.67 ). 50 Overall, the evidence supports that, in humans, the optic disc area is only weakly associated with the number of nerve fibers that pass through it. A recent study by Mansoori et al. 51 found no correlation between spectral domain OCT-derived RNFL thickness and optic disc size, and the authors suggested that the number and distribution of optic nerve fibers within the RNFL is somewhat independent of optic disc size. 
If the total RNFL cross-sectional area is not dependent on optic disc size, then what accounts for the apparent relationship between the average RNFL thickness and disc size found by a number of investigators? 19,20,35 Our results suggest that this was due to magnification variation related to axial length variation within the human population. When the disc area was corrected for magnification variation, there was no correlation with RNFL thickness noted. When the magnification variation was reintroduced, a significant correlation was found between RNFL thickness and apparent disc area. These evidences support magnification as the link between RNFL thickness and apparent disc area (or diameter). Previous investigators did not take the magnification variation into account. Savini et al. 19 used the OCT to measure optic disc size without making correction for axial length or magnification. Budenz et al. 35 corrected the magnification differences between fundus cameras, but did not account for the magnification variation due to axial length variation. Thus, the link between RNFL thickness and apparent disc size that was found by Savini and colleagues and Budenz and colleagues was probably due to the magnification artifact rather than a true anatomic correlation. 
Our derivation of the 1/r dependence of RNLF thickness (equation 5) using Gauss's flux theorem (equations 1 and 2) is valid only for the overall average thickness, but not for quadrant or other sector averages (see Appendix). Because the course of nerve fibers shifts temporally as they radiate out from the optic disc, the temporal quadrant gains at the expense of the nasal quadrant at greater scan radii. Thus the temporal quadrant RNFL thickness can be expected to decrease more slowly than 1/r, whereas the nasal quadrant decreases more quickly. This deviation also affects the associated magnification correction formula (equation 10). Kang and colleagues found that the effect of axial length variation on RNFL thickness differs across quadrants. This is to be expected from the asymmetric divergence of the retinal nerve fibers. An important corollary of Gauss's flux theorem when applied to the RNFL is that the integral of RNFL thickness over a complete scan circle is the total RNFL cross-sectional area, a conserved quantity. This not only provides a simple 1/r dependence but also means that the overall average RNFL thickness is not affected by decentration of the scan circle due to eye motion or variation in disc morphology or RNFL distribution. Thus, the overall average RNFL thickness has a special advantage relative to quadrant and sector averages for the purpose of detecting glaucoma by comparison with a normative database or comparison of multiple measurements made over time. 
Because of the apparent correlation between RNFL thickness and apparent disc size, some investigators 20,46 have advocated that the scan circle diameter should be a fixed multiple of the disc diameter or the disc diameter plus a constant. Our results do not support varying the diameter of the scan circle. According to equation 5, the measured RNFL thickness is inversely related to the radius (or diameter) of the scan circle. Therefore increasing the scan diameter for a larger disc would artifactually decrease the measured RNFL thickness. Indeed, this effect was found by Savini et al. 46 and Carpineto et al. 20 when they tried to vary the scan diameter. Although it is possible to compensate for the use of differing scan diameters in different eyes by the use of a mathematical model, this adds an additional level of complexity; moreover, the compensation is strictly valid only for overall RNFL thickness, not sector or quadrant RNFL thickness. 
A more accurate way of minimizing RNFL thickness variation in the normal reference population would be to scale the nominal scan radii by the magnification factor. This way, the actual millimeter scan radius can be made constant. However, this still requires the use of a second instrument to provide the necessary axial length data prior to the OCT scan. A simpler and more flexible method would be to scan at a constant nominal radius (what is being done now) and correct for the magnification effect of axial length variation afterward. This correction is small for most people but more important for high myopes or hyperopes. 
A limitation of this study is that we did not directly show the 1/r dependence of overall RNFL thickness in individual eyes. Skaf et al. 45 and Patel et al. 37 analyzed RNFL thickness at various distances from the disc margin. They both found that RNFL became thinner with greater distance from the disc margin, but this relationship was clearly not linear when plotted over a 1.2- or 1.4-mm distance. By examining the appearance of their plots, this nonlinear relationship could be consistent with 1/r, but unfortunately they did not perform any fit with 1/r. With higher speed Fourier-domain (also known as spectral or spectral-domain) OCT, it is now possible to map RNFL thickness over a wide area and make measurements over a range of analytic circles or ellipses in postanalysis. 37,39 We plan to analyze the Fourier-domain OCT results in the AIG study database and report the results in a later publication. 
In addition to the correlation between axial length and RNFL thickness, we also found age to be correlated with RNFL thickness in our study. Thinner RNFL thickness measurements were found in the eyes of older participants. Our results confirm data from previous histology and clinical cross-sectional studies. Increasing age is associated with decreasing RNFL thickness, as shown by histology, 2628 and measured by scanning laser polarimetry, 2931 as well as OCT. 4,24,52 Contrary results showing the lack of difference in RNFL thickness between young and old individuals has also been demonstrated previously by histology. 53 However, the great preponderance of data supports an age-related attenuation of RNFL thickness. 
To summarize, we found that overall RNFL thickness, as measured by OCT scans of constant diameter, does not depend on the true disc size. Therefore, there is no need to vary the scan diameter between eyes according to disc size. To minimize the variation in measured RNFL thickness in normal eyes, one may wish to correct for the effects of axial length variation and age-related attenuation. 
Figure A1. 
 
Electric field analogy of RNFL. Ganglion cell bodies are represented by unit positive charges, the nerve fibers by electric field lines, and the ONH by an aggregate negative charge equal to the sum of all the positive charges. The circular tomographic scan line L transects all of the nerve fibers because it encloses the ONH, just as the integral of electric field lines passing through an enclosing surface is equal to the enclosed electric charges according to Gauss's equation.
Figure A1. 
 
Electric field analogy of RNFL. Ganglion cell bodies are represented by unit positive charges, the nerve fibers by electric field lines, and the ONH by an aggregate negative charge equal to the sum of all the positive charges. The circular tomographic scan line L transects all of the nerve fibers because it encloses the ONH, just as the integral of electric field lines passing through an enclosing surface is equal to the enclosed electric charges according to Gauss's equation.
Appendix. Mathematical Model of Magnification Effect on RNFL Thickness
Relationship between RNFL Thickness and Scan Radius
Retinal nerve fibers originate from cell bodies in the ganglion cell layer, traverse the RNFL, and exit the eye at the ONH. 54,55 This source-and-sink system is a two-dimensional analogy to the charge-and-flux system of electric field theory. The ganglion cells are analogous to unit positive charges, the nerve fibers are analogous to electric field flux lines, and the ONH is analogous to a large aggregate of negative charges (Fig. A1). We can borrow from Gauss's law concerning the electric field, which in its integral form states the surface integral of electric field flux is equal to the electric charge enclosed by the surface. 56  where Q is the sum electric charge enclosed in surface S, ε is the electric constant, E is the electric field, and ds is the differential surface area. 
Gauss's law of electric field is one physical application of Gauss's flux theorem. The same mathematical theorem can be applied to the retinal nerve fiber layer. The equivalent equation for nerve fibers is written by reducing Gauss's equation from three dimensions to two dimensions. where N is the total number of retinal nerve fibers enclosed in line L (Fig. A1), n is the nerve fiber number density per length, and dl is the differential line length. 
To convert from nerve fibers number to RNFL thickness, we multiply equation 2 by cross-sectional area a to obtain equation 3. The area a is the average cross-section of a nerve fiber plus its associated glial tissue. where A = Na is the total cross-sectional area of the RNFL in an eye and t = a is the RNFL thickness. 
In a circular scan of the RNFL, the integral of equation 3 can be simply evaluated: where r is the radius of the scan circle and T is the RNFL thickness averaged over the scan circle. We rewrite equation 4 to show how the average RNFL thickness depends on scan radius.   
The theoretical result shows that the average RNFL thickness should be inversely proportional to the radius of the scan circle in an OCT circumpapillary scan. The number of nerve fibers transected by the scan circle is diminished by the number of ganglion cells enclosed inside the circle (in Fig. A1 this equivalent to having some positive charges inside the enclosing circle would partially cancel the negative charge of the ONH). However, if the scan circle is close to the optic disc edge, then the number of ganglion cells enclosed can be considered to be negligibly small. 
Note that equation 4 is true for only total RNFL cross-sectional area and, therefore, equation 5 is true only for the overall average RNFL thickness. If one measures the cross-sectional area of RNFL over a quadratic arc, there is no guarantee that the result would be ¼ of the total RFNL cross-sectional area, and the average RNFL thickness over a quadrant is not guaranteed to obey the 1/r trend. In the eye, the RNFL distribution is known to be nonuniform: as nerve fibers radiate out from the disc, they shift away from the nasal quadrant toward the temporal quadrant because the macula is temporal to the disc. This asymmetric divergence should make temporal RNFL thickness decrease more slowly than 1/r and nasal RNFL thickness decrease more rapidly than 1/r
Fundus Image Magnification and Axial Length
It has been shown that the magnification of fundus imaging is inversely proportional to the axial length of the eye being imaged. 57 The transverse dimension of a fundus feature measured by a fundus imaging system (fundus camera, OCT scanner, or scanning laser ophthalmoscope) is proportional to the angle θ subtended by rays from the edges of the object. The angle θ is equal to the physical dimension x of the object divided by the distance from the fundus to the nodal point of the eye. Thus the longer the eye is, the smaller θ is by proportion. Thus for the “Fast RNFL” scan pattern, it would be more accurate to say that the scan diameter is 12° rather than 3.46 mm, because the angular specification is not dependent on axial length variation. A simple equation to describe this is: where M is the relative magnification factor (its value being 1 for the average eye), L is the axial length, and La is the axial length of the average eye. 
Magnification and Apparent Disc Size
If a fundus imaging system does not adjust for axial length variation, then the measured optic disc diameter will be proportional to the magnification factor. 
where Dm is the measured disc diameter and D is the actual disc diameter. 
The disc area is proportional to the square of the disc diameter, so the magnification effect is squared as well. where Am is the measured disc area and A is the actual disc area. 
Magnification and Average RNFL Thickness
Scan patterns for OCT are specified in terms of angles and displayed as lengths, assuming an average axial length. Thus the Fast RNFL scan pattern has a fixed angular diameter, and the millimeter diameter depends on the axial length of the eye, having the nominal value of 3.46 mm only for an eye of exact average dimensions. The same scan pattern would project to a larger physical dimension on the fundus for a longer eye. The relationship between the actual radius of the fast RNFL scan pattern, relative to the nominal value, is expressed by the following equation: where r is the actual OCT scan radius and ra is the nominal OCT scan radius, which for the Fast RNFL scan is 1.73 mm. The nominal scan radius was specified for the average eye. 
Combining equations 5 and 9, we obtain: A linear regression analysis of RNFL thickness against axial length should find correlation due to magnification having a slope that can be found by differentiating T against L. where d is the differential operator. Evaluation of this expression near the average axial length of a normal population gives the following approximate value: where Ta is the average RNFL thickness of the average eye. 
We expect a positive correlation between the average RNFL thickness and apparent disc size because both are proportional to the magnification factor and inversely related to the axial length (equations 6–12). This correlation should disappear if axial length variation is taken into account in multivariate analysis. 
AIG Study Group List, 2012
Oregon Health & Science University, Casey Eye Institute, Portland, OR: John Morrison, MD, Peter Francis, MD, Beth Edmunds, MD, Mansi Parikh, MD, Devin Gattey, MD, Rebecca Armour, MD, Lorinna Lombardi, MD, Ou Tan, PhD, Yimin Wang, PhD, Xinbo Zhang, PhD. 
University of Pittsburgh Medical Center University of Pittsburgh School of Medicine, Pittsburgh, PA: Joel S. Schuman, MD, Gadi Wollstein, MD, Hiroshi Ishikawa, MD, Richard Bilonick, PhD, Eiyass Albeiruti, MD. 
University of Miami, Bascom Palmer Eye Institute, Palm Beach, FL: David S. Greenfield, MD, Mitra Sehi, PhD. 
University of Southern California, Keck School of Medicine, Doheny Eye Institute, Los Angeles, CA: Rohit Varma, MD, MPH, Vikas Chopra, MD, Brian Francis, MD. 
Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science and Research Lab of Electronics, Cambridge, MA: James G. Fujimoto, PhD, Benjamin Potsaid, PhD, Bernhard Baumann, PhD, Martin F. Kraus, MS. 
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Footnotes
 Supported in part by National Eye Institute/National Institutes of Health Grant R01 EY013516, Doheny Core Grant P30 EY03040, and Research to Prevent Blindness (New York, New York).
Footnotes
 Disclosure: D. Huang, Carl Zeiss Meditec, Inc. (F), Optovue, Inc. (F, I, C, P); V. Chopra, None; A.T.-H. Lu, None; O. Tan, Optovue, Inc. (F, P); B. Francis, None; R. Varma, None
Figure 1. 
 
Plot of RNFL thickness versus axial length. The solid line represents the linear regression fit.
Figure 1. 
 
Plot of RNFL thickness versus axial length. The solid line represents the linear regression fit.
Figure A1. 
 
Electric field analogy of RNFL. Ganglion cell bodies are represented by unit positive charges, the nerve fibers by electric field lines, and the ONH by an aggregate negative charge equal to the sum of all the positive charges. The circular tomographic scan line L transects all of the nerve fibers because it encloses the ONH, just as the integral of electric field lines passing through an enclosing surface is equal to the enclosed electric charges according to Gauss's equation.
Figure A1. 
 
Electric field analogy of RNFL. Ganglion cell bodies are represented by unit positive charges, the nerve fibers by electric field lines, and the ONH by an aggregate negative charge equal to the sum of all the positive charges. The circular tomographic scan line L transects all of the nerve fibers because it encloses the ONH, just as the integral of electric field lines passing through an enclosing surface is equal to the enclosed electric charges according to Gauss's equation.
Table 1. 
 
Demographics and Measurement Statistics of Normal Participants
Table 1. 
 
Demographics and Measurement Statistics of Normal Participants
Parameter Mean SD Minimum Maximum
Age (y) 54.0 9.7 40.2 76.1
Axial length (mm) 23.7 0.8 21.9 25.5
Spherical equivalent (D) −0.5 1.5 −5.5 3.6
Disc area (mm2) 1.9 0.5 0.8 3.9
Disc diameter (mm) 1.5 0.2 1.0 2.2
RNFL (μm) 99.8 9.3 74.6 120.7
Table 2. 
 
Univariate Regression of RNFL Thickness against Other Parameters
Table 2. 
 
Univariate Regression of RNFL Thickness against Other Parameters
Parameter Slope (μm/x) SE of
Slope
95% CI
of Slope
R 2 P Value
Age (y) −0.3 0.1 −0.5, −0.2 0.13 <0.0001
Axial length (mm) −3.3 1.0 −5.2, −1.3 0.09 0.001
Spherical equivalent (D) 0.8 0.5 −0.2, 1.8 <0.01 0.109
Disc area (mm2) 1.9 1.3 −0.8, 4.6 0.03 0.164
Disc diameter (mm) 4.7 3.3 −1.9, 11.3 0.03 0.164
Sex (female) 3.6 1.9 −0.1, 7.3 0.03 0.054
Ethnicity (Caucasian) −2.9 3.0 −8.8, 3.1 0.008 0.337
Table 3. 
 
Multivariate Regression of RNFL Thickness against Other Parameters*
Table 3. 
 
Multivariate Regression of RNFL Thickness against Other Parameters*
Parameter Slope
(μm/x)
SE 95% CI P Value
Disc area (mm2) 1.7 1.3 −0.9, 4.1 0.21
Age (y) −0.3 0.1 −0.5, −0.2 0.0002
Sex (female) 2.8 1.6 −0.4, 6.1 0.08
Axial length (mm) −3.1 0.9 −4.9, −1.3 0.001
Table 4. 
 
Univariate Regression of RNFL Thickness against Disc Parameters, after Reintroducing Magnification Variation into Disc Measurements
Table 4. 
 
Univariate Regression of RNFL Thickness against Disc Parameters, after Reintroducing Magnification Variation into Disc Measurements
Parameter Slope (μm/x) SE 95% CI R 2 P Value
Disc area (mm2) 2.7 1.3 0.1, 5.3 0.06 0.04
Disc diameter (mm) 6.7 3.2 0.3, 13.1 0.06 0.04
Table 5. 
 
Univariate Regression of Magnification-Corrected RNFL Thickness against Other Parameters
Table 5. 
 
Univariate Regression of Magnification-Corrected RNFL Thickness against Other Parameters
Parameter Slope (μm/x) SE 95% CI R 2 P Value
Age (y) −0.3 0.1 −0.5, −0.2 0.13 <0.0001
Axial length (mm) 0.8 1.0 −1.1, 2.8 <0.01 0.40
Spherical equivalent (D) −0.2 0.5 −1.2, 0.7 <0.01 0.62
Disc area (mm2) 1.7 1.3 −0.9, 4.3 0.03 0.19
Disc diameter (mm) 4.3 3.2 −2.2, 10.7 0.04 0.19
Sex (female) 3.1 1.8 −0.5, 6.6 0.03 0.09
Ethnicity (Caucasian) −3.8 2.9 −9.5, 1.8 0.02 0.18
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