**Purpose.**:
To determine whether a second-degree polynomial equation can fit the retinal nerve fiber (RNF) and retinal artery (RA) trajectories in the posterior pole of eyes and whether the RNF and RA trajectories are correlated with the axial length of the eye.

**Methods.**:
This was a prospective observational cross-sectional study of 109 right eyes of 109 healthy participants. All participants underwent axial length measurements, optical coherence tomography (OCT) to determine the peripapillary retinal nerve fiber layer (RNFL) thickness, and red-free fundus photography. The supratemporal and infratemporal peaks of the RNFL thickness were determined in the OCT RNFL circle scan images. The trajectories of the RNF passing through the peaks of the RNFL thickness were plotted in the red-free fundus photographs and were fitted to a second-degree polynomial equation (*ax* ^{2}/100 + *bx* + *c*) by ImageJ. The coefficient *a* represented the steepness of the trajectories. Intraclass correlation coefficient was used to measure the reliability between the raters. The relationships between the RNF or RA trajectories and the axial length were investigated using linear regression analyses.

**Results.**:
The mean axial length was 25.5 ± 1.4 mm, and the mean RNF trajectory and the mean RA trajectory, *a*, were 0.472 ± 0.123 and 0.442 ± 0.109, respectively. The intrarater and interrater correlation coefficients of the RNF trajectories were 0.954 and 0.881, respectively. The RNF and RA trajectories were significantly and positively correlated with the axial length (*R* = 0.28, 0.33, *P* < 0.01).

**Conclusions.**:
A longer axial length is associated with narrower RNF and RA trajectories. (www.umin.ac.jp/ctr number, UMIN000006040.)

^{ 1,2 }Thus, an assessment of the RNF defects in eyes suspected of having glaucoma is important before functional defects develop.

^{ 3,4 }This is important because the prevalence of myopia is increasing worldwide.

^{ 5–7 }In the early stage of glaucoma in myopic eyes, the retinal nerve fiber layer (RNFL) defects and corresponding visual field defects are more likely to be detected in the paracentral area.

^{ 8–10 }The paracentral RNFL defects and corresponding paracentral visual field defects in myopic glaucoma patients can lead to severe visual impairments.

^{ 11–16 }Earlier studies demonstrated that these two peaks shifted temporally as the axial length increased.

^{ 17–19 }This shift may explain the paracentral RNFL defects in eyes at the early stage of myopic glaucoma. However, the shift in the RNFL peaks in myopic eyes has been investigated only in circumferential scans.

^{ 20,21 }We have investigated whether a mathematical model of the RNFL trajectories can help in understanding how the RNFL defects develop in myopic eyes.

**Figure 1**

**Figure 1**

^{ 17,22,23 }Since myopia is a risk factor for glaucoma and myopic eyes tend to have longer axial lengths, we also determined whether there was a significant correlation between the RNF and RA trajectories and the axial lengths of the eyes.

^{ 17 }

**Figure 2**

**Figure 2**

*x*and

*y*coordinates in the red-free fundus photograph were converted to a new set of data (

*x*and

*y*) with the center of the disc as the origin. Finally, the converted coordinate data were fitted to a second-degree polynomial (

*ax*

^{2}/100 +

*bx*+

*c*) equation with the curve-fitting program of ImageJ. The

*a*,

*b*, and

*c*are constants calculated by the curve-fitting program of ImageJ. The curve-fitting program automatically determined the best-fit second-degree polynomial (

*ax*

^{2}/100 +

*bx*+

*c*) equation by the least squares method. Under these conditions, a larger

*a*will make the curve steeper and narrower and will bring the arms of the curve closer to the fovea. Thus, the

*a*constant was used as the degree of the RNF trajectory. The pixel coordinates and curve fittings of the RA trajectories were calculated using the same method as for the RNF trajectories. In eyes in which the RA branched, the plotting was made with the following rules. If a branch artery was smaller than the main artery, the main artery was used to determine the RA trajectory. If the branch artery was as large as the main artery, the plotting was not done after the branching point. Even so, the plotting was done with more than 20 points. Additionally, to eliminate the effect of ocular torsion of individual eyes, we also evaluated the images in which the fovea–disc axis was rotated vertically (model 2).

**Figure 3**

**Figure 3**

*R*= −0.83,

*P*< 0.001; Fig. 4A).

**Figure 4**

**Figure 4**

**Table**

*P*< 0.001). The interrater correlation coefficient of the RNFL trajectories was 0.881 (95%CI 0.831–0.917,

*P*< 0.001). The intrarater and the interrater repeatabilities of the RNF trajectories were excellent.

*P*< 0.001). The interrater repeatability of the RA trajectories was also excellent. Therefore, the mean values of the RNF or RA trajectories of the two raters were used for the analyses. The means and standard deviations of the RNF and RA trajectories were 0.472 ± 0.123 and 0.442 ± 0.109, respectively.

*R*= 0.28,

*P*= 0.003), and the RNF trajectories, expressed as the

*a*constant of second degree polynomial, increased by 0.03 per millimeter increase of the axial length (Fig. 4B). The RA trajectories were significantly and positively correlated with the axial length (

*R*= 0.33,

*P*< 0.001), and the RA trajectories, expressed as the

*a*constant of second degree polynomial, increased by 0.03 per millimeter increase of the axial length (Fig. 4C). The RNF trajectories were significantly correlated with the RA trajectories (

*R*= 0.82,

*P*< 0.001; Fig. 4D).

*R*= 0.98,

*P*< 0.001). The correlation coefficient between the original RNF trajectories and the RA trajectories of model 2 was also high (

*R*= 0.94,

*P*< 0.001). The RNF trajectories of model 2 were significantly and positively correlated with the axial length (

*R*= 0.32,

*P*= 0.001). The RA trajectories of model 2 were significantly and positively correlated with the axial length (

*R*= 0.29,

*P*= 0.002). The RNF trajectories of model 2 were significantly correlated with the RA trajectories of model 2 (

*R*= 0.87,

*P*< 0.001). The results of the RNF and RA trajectories of model 2 were very similar to the original RNF and RA trajectories. Thus, it is possible that the width of trajectories of RNF or RA can be evaluated by either model because the approximation formula was used for the comparison (see Supplementary Fig. S1).

^{ 20,21 }Although these methods also described the RNF bundle trajectories well, their complexities prevented their general use for research and clinical evaluations. In comparison, our mathematical model is relatively simple and easy to use and requires only a fundus photograph and the easily accessible free public software, ImageJ, provided by the National Institutes of Health.

^{ 9,10,24 }In nonmyopic eyes, such changes usually occur in the intermediate to late stages of glaucoma. The present findings may explain the reason for the location of the defect. Eyes with longer axial lengths are usually myopic and have RNFL bundles running closer to the fovea than those with normal axial lengths, that is, nonmyopic eyes. Because the RNFL bundle defects in glaucomatous eyes generally begin in the supra- or infratemporal sectors (thicker RNFL bundles), the visual field damage would develop closer to the fovea from the earlier stages in myopic eyes than in nonmyopic eyes. Nonetheless, a direct comparison of RNFL defects and RNF trajectories will be still necessary to validate this interpretation.

^{ 25 }If the RA is located closer to the fovea in myopic eyes, it would be advisable to examine patients with the HFA 10-2 so as not to overlook early glaucomatous damage.

^{ 26 }Thus, a long axial length does not necessarily mean that the axial length will be longer after attainment of full growth. More specifically, even though two eyes have the same axial length in adulthood, if the axial length differed at birth, the degree of elongation must have been different between these eyes during the growth period. This may affect the trajectories of the RNF and the arcade arteries. The present model may help in determining the mechanism for the formation of these eyes and obtaining a correct diagnosis. Furthermore, if a modification of the present formula fits the empiric data better than the original formula, the modified factor might prove to be an important factor for determining the trajectories.

**Figure 5**

**Figure 5**

*x*-axis and

*y*-axis change proportionately to the axial length. There is another reason why the correction method for the magnification effect was not suitable for this study. Bennett's formula is supposedly the most suitable method to adjust the deviated results from the magnification effect, and this formula contains the axial length variable.

^{ 27,28 }However, this was not applicable to the present data to determine the correlation between the fovea–RNF distance and the axial length because each variable contains the common variable of axial length. Thus, using the present analysis, the trajectories were found to be narrower with an elongation of the axial length. However, these results did not fully support the idea that the fovea–RNF distance is smaller in eyes with narrow trajectories than with wide trajectories because we could not measure the distance directly. This issue needs further investigation.

^{ 6 }and the individuals studied were university students, who are known to be myopic. Thus, our results describe the characteristics of young myopic eyes and might not hold for older and nonmyopic populations. On the other hand, the reliability of the examination was very high because no pathological factors such as cataract or vitreal opacities were present in young healthy individuals, and understanding of the examination was high. In addition, the narrow range of age prevented interference of cohort effects and age effects. There are many factors that affect the trajectories of the RNF or RA, for example, the size and shape and torsion of the eye.

^{ 29,30 }None of these were considered in our analyses. Only the effect of the eye torsion could be minimized by use of the second-degree polynomial approach (model 2). There will always be limitations in mathematical models. The present model cannot consider the various and complex factors that could affect the structures of the posterior pole of the eye, especially in those with glaucoma. Study of glaucomatous eyes will be mandatory. In comparison to previous reports, in which the RNFL shift was depicted on the circle of optic disc,

^{ 17–19 }the present approach plotted the RNF trajectories on a much broader area. However, it still covered only the area from the optic disc to the foveal area. Therefore, we do not know about the area temporal to the fovea even from the present model. Finally, it is known that the shadow of an artery affects the identification of the RNFL peak, and this is a limitation of the present analysis of the OCT images.

^{ 22,23 }In B-scans of the Spectralis OCT, we could not draw an accurate borderline of the RNFL (Fig. 2) because the blood vessel shadow masked the borderline of the RNFL in most of the images. Thus, we adopted the method commonly used in earlier studies, using the RNFL thickness peak position in the OCT images

^{ 17–19 }for analysis of the trajectories. These limitations should be remembered in interpretation of the results.

**T. Yamashita**, None;

**T. Sakamoto**, None;

**H. Terasaki**, None;

**M. Tanaka**, None;

**Y. Kii**, None;

**K. Nakao**, None

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