title: Quantification of retinal nerve fiber and retinal artery trajectories using second-order polynomial equation and its association with axial length.
abstract: OBJECTIVE
  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.).
authors: Department of Ophthalmology, Kagoshima University Graduate School of Medical and Dental Sciences, Kagoshima, Japan.
authors: Takehiro
authors: T
authors: Yamashita
authors: Department of Ophthalmology, Kagoshima University Graduate School of Medical and Dental Sciences, Kagoshima, Japan.
authors: Taiji
authors: T
authors: Sakamoto
authors: Department of Ophthalmology, Kagoshima University Graduate School of Medical and Dental Sciences, Kagoshima, Japan.
authors: Hiroto
authors: H
authors: Terasaki
authors: Department of Ophthalmology, Kagoshima University Graduate School of Medical and Dental Sciences, Kagoshima, Japan.
authors: Minoru
authors: M
authors: Tanaka
authors: Department of Ophthalmology, Kagoshima University Graduate School of Medical and Dental Sciences, Kagoshima, Japan.
authors: Yuya
authors: Y
authors: Kii
authors: Department of Ophthalmology, Kagoshima University Graduate School of Medical and Dental Sciences, Kagoshima, Japan.
authors: Kumiko
authors: K
authors: Nakao
mesh_terms: D000328:Adult; D058452:Axial Length, Eye; D003430:Cross-Sectional Studies; D005260:Female; D005654:Fundus Oculi; D006801:Humans; D008297:Male; D015233:Models, Statistical; D009412:Nerve Fibers; D011446:Prospective Studies; D012161:Retinal Artery / Q000033:anatomy & histology*; D012165:Retinal Ganglion Cells / Q000166:cytology*; D041623:Tomography, Optical Coherence; D055815:Young Adult
keywords: image analysis; myopia; optical coherence tomography; retinal nerve fiber