We retrospectively examined 1173 eyes from 730 consecutive patients whose eyes with axial length of ≥26 mm underwent 9-mm cross scans of spectral-domain OCT (RS-3000; Nidek, Gamagori, Japan) with the fovea at the center, at least two times with interval of at least 1 year at the Department of Ophthalmology in Kyoto University Hospital (Kyoto, Japan) from April 2010 through November 2016. Only patients aged ≥20 years were included. Among the 1173 eyes, 79 were excluded because of insufficient quality of OCT images to precisely plot the Bruch's membrane line and a total of 1094 eyes from 698 patients were used for the analysis. For each eye, scans acquired at two time points with maximum interval were selected for the analysis. The axial length was measured using partial coherence interferometry or ultrasound. The axial length at the closest day from the time point of the first scan and age of the patient at the first scan were used for the analysis. The Ethics Committee at Kyoto University Graduate School of Medicine approved this study, which was conducted in accordance with the tenets of the Declaration of Helsinki.
The local curvature of the Bruch's membrane on the OCT image was evaluated at intervals of 1 μm using custom software RetinaView (Canon, Tokyo, Japan), as our previously established work.
16–18 The mean absolute curvature and variance of absolute curvature were calculated for each eye to evaluate the protruding shape change and undulating shape change, respectively (
Fig. 1). The speed of the mean curvature change was calculated as the difference between the mean curvatures at the last and the first examinations, divided by the examination interval. The speed of the curvature variance change was calculated as the difference between variances of curvature at the last and the first examinations, divided by the examination interval.
Examples of the Bruch's membrane lines in OCT images are shown as curved lines in
Figure 2. The curvature at each point is represented by the length of arrows in order to explain the concept of curvature analysis. The longer arrow indicates steeper curvature compared with the shorter arrow, and dotted lines were drawn to help readers easily comprehend the curvature. (A) A representative eye with continuously weak curvature. The mean curvature of this eye is calculated by averaging the curvatures measured at 1-μm intervals. Because the curvature severity represented by the length of the arrow at several points is the same for all arrows in this eye, the mean curvature is calculated as the length of a single arrow. The curvature variance of this eye is calculated using the curvatures measured at 1-μm intervals. The curvature is represented by the arrow length at several points, and the length is the same in all arrows in this eye; hence, the curvature variance is calculated as 0. (B) A representative eye with constant curvature. Because the curvature is greater, the drawing shows longer arrows. In this eye, the mean curvature is calculated by averaging the curvatures measured at 1-μm intervals. Because the curvature is represented by a greater length of the arrows at several points, and the length is the same in all arrows in this eye, the mean curvature is calculated based on the length of the longer arrows. Because the length of all arrows is the same in this eye, the curvature variance is calculated as 0. (C) A representative eye with steeper curvature at the bottom around the fovea. According to the curvature, the drawing shows arrows of greater length at the bottom and those of shorter length around the edge. The mean curvature of this eye is represented by the average length of all the arrows. The curvature variance calculated using all the arrows is greater than that of the eye with constant curvature. (D) A representative eye with steeper curvature at the bottom around the fovea, with undulated surface. The mean curvature calculated through using all the arrows is greater since there are many long arrows indicating steep curvature, and the curvature variance calculated through using all the arrows is greater because this eye has both short arrows and long arrows.
In the OCT image of the eye, the change between the curved line drawn in (A) and the curved line in (B) in 500 days, represents the amount of change of the mean curvature calculated as the difference between the length of the short arrow in (A) and the length of the longer arrow in (B). The speed of the mean curvature change per day is calculated by dividing the change amount by 500, and that of the change per year is calculated by multiplying the speed per day by 365. Because the variance of absolute curvature is 0 in both eyes, the speed of the curvature variance change is calculated as 0.
In the OCT image of the eye, the change between the curved line drawn in (C) and the curved line in (D) in 500 days, represents the amount of change of the mean curvature calculated as the difference between the average length of the arrow in (C) and the average length of the arrow in (D). The speed of the mean curvature change per day is calculated by dividing the change amount by 500, and that of the change per year can be calculated by multiplying the change speed per day by 365. The change amount of the curvature variance is represented by the difference between the variance of the arrow length in (C) and the variance of the arrow length in (D). The speed of the curvature variance change per day is calculated by dividing the change amount by 500, and that of the change per year can be calculated by multiplying the speed per day by 365.
The speed of change of the mean curvature and curvature variance were compared between males and females using the unpaired t-test. Moreover, the speed was compared among six age groups: age of <40 years, -(40); ≥40 and <50, 40-(50); ≥50 and <60, 50-(60); ≥60 and <70, 60-(70); ≥70 and <80, 70-(80); and ≥80, 80-; and five axial length groups: eyes with axial length of ≥26 mm and <27 mm, 26-(27); ≥27 mm and <28 mm, 27-(28); ≥28 mm and <29 mm, 28-(29); ≥29 mm and <30 mm, 29-(30); and ≥30 mm, 30-, using ANOVA and Tukey's test. In addition, the speed was compared among five groups of mean curvature at the first examination: <7.5 × 10−5 μm−1 (-[7.5]), ≥7.5 × 10−5 μm−1 and <10.0 × 10−5 μm−1 (7.5-[10]), ≥10.0 × 10−5 μm−1 and <12.5 × 10−5 μm−1 (10-[12.5]), ≥12.5 × 10−5 μm−1 and <15.0 × 10−5 μm−1 (12.5-[15]), and ≥15.0 × 10−5 μm−1 (15-); and five groups of curvature variance at the first examination: <2.5 × 10−9 μm−2 (-[2.5]), ≥2.5 × 10−9 μm−2 and <5.0 × 10−9 μm−2 (2.5-[5]), ≥5.0 × 10−9 μm−2 and <7.5 × 10−9 μm−2 (5-[7.5]), ≥7.5 × 10−9 μm−2 and <10.0 × 10−9 μm−2 (7.5-[10]), and ≥10.0 × 10−9 μm−2 (10-), using ANOVA and Tukey's test. All statistical analyses were performed using Statistical Package for the Social Sciences (SPSS, version 24.0; IBM, New York, NY, USA). A P value of <0.05 was considered as statistically significant.