**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/mm^{2}, *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.

^{ 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.

^{ 2 }For glaucoma evaluation, OCT provides reproducible quantitative measurements of RNFL around the optic nerve head (ONH)

^{ 3 }and in the macular region.

^{ 4–8 }Retinal nerve fiber layer assessment is important because structural damage to the ONH and RNFL often precede functional changes detected by perimetry.

^{ 9–18 }

^{ 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.

^{ 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.

*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.

^{ 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.

^{ 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).

*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).

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 (mm^{2}) | 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 |

*P*= 0.164). Our sample size was sufficient to detect a slope of 5 μm/mm

^{2}(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).

*P*= 0.04) between RNFL thickness and both disc diameter and area.

Parameter | Slope (μm/x) | SE | 95% CI | R 2 | P Value |

Disc area (mm^{2}) | 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 |

*L*/

_{a}*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.

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 (mm^{2}) | 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 |

^{ 4,24–33 }race, and ethnicity

^{ 24,32–34 }; (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 }

^{2}.

^{ 40–44 }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.

- 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).
- Image magnification is inversely proportional to eye axial length (equation 6).
- The true millimeter diameter of the OCT scan circle is inversely proportional to image magnification (equation 9).
- The apparent disc diameter on an OCT image is inversely proportional to image magnification (equation 7).

- Given a fixed nominal scan radius
*r*(fixed in degrees of visual angle), the measured RNFL thickness is proportional to image magnification (equation 10)._{a} - The overall RNFL thickness over a circular scan is inverse proportional to the scan radius
*r*(in millimeters, equation 5). - An artifactual correlation between RNFL thickness and disc diameter (or area) could be caused by magnification variation that is not corrected.

^{ 37–39,47 }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.

^{ 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.

^{ 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.

*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.

^{ 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.

*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.

^{ 26–28 }and measured by scanning laser polarimetry,

^{ 29–31 }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.

^{ 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.

*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.

*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.

*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*.

^{ 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

*L*is the axial length of the average eye.

_{a}*D*is the measured disc diameter and

_{m}*D*is the actual disc diameter.

*r*is the actual OCT scan radius and

*r*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.

_{a}*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

*T*is the average RNFL thickness of the average eye.

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