**Purpose.**:
To verify the effect of the scan angle of the optic nerve head (ONH) on measurements of peripapillary retinal nerve fiber layer (RNFL) thickness by using spectral-domain optical coherence tomography (OCT).

**Methods.**:
Both eyes of 64 healthy volunteers were scanned by the optic disc cube 200 × 200 scan of a spectral-domain OCT system. Ultra-high resolution OCT images of the ONH were used to determine the horizontal, vertical, and three-dimensional scan angles of the ONH. The adjusted clock-hour RNFL thicknesses generated by the three-dimensional scan angle of the ONH were then compared with the original clock-hour RNFL thicknesses.

**Results.**:
The mean horizontal, vertical, and three-dimensional scan angles of the ONH were 12.62 ± 5.17°, 4.17 ± 3.30°, and 13.62 ± 5.13°, respectively. In 125 (97.66%) eyes, the scanned ONH image was tilted temporally; in 89 (69.53%) eyes it was tilted inferiorly. The adjusted clock-hour RNFL thicknesses generated by the three-dimensional scan angle of the ONH were significantly different from the original values (*P* = 0.009); the mean difference was 13.26 ± 14.95 μm, and the overall correlation and agreement were not excellent, especially in the inferior quadrant.

**Conclusions.**:
Current intraretinal imaging devices such as OCT assume that the ONH is positioned exactly in front of the scanning beam; however, this assumption appears to be inaccurate. Because the scan angle of the ONH varies and also influences RNFL thickness measurements, it may be better to consider using the ONH scan angle as an adjustment factor when peripapillary RNFL thicknesses are calculated by OCT.

^{ 1,2 }measurements of peripapillary retinal nerve fiber layer (RNFL) thickness have contributed to glaucoma detection.

^{ 3,4 }The progressive thinning of the RNFL is an important predictor of disease progression.

^{ 5 }

^{ 6 }

*x*

_{0}is the position of the vertical axis at the deepest point of the ONH;

*z*

_{1}is the position of a nasal intersection point of the RPE fit line and the cube margin on the en face axis;

*z*

_{2}is the position of an intersection point of the RPE fit line and the

*x*

_{0}axis on the en face axis; and

*z*

_{3}is the position of a temporal intersection point of the RPE fit line and the cube margin on the en face axis. Regarding the vertical OCT image, the

*z*

_{4},

*z*

_{5},

*z*

_{6}, and

*y*

_{0}values correspond to the

*z*

_{1},

*z*

_{2},

*z*

_{3}, and

*x*

_{0}values, respectively, on the horizontal OCT image. The

*x*

_{0}and

*y*

_{0}values are between 0 and 200; the

*z*

_{1},

*z*

_{2},

*z*

_{3},

*z*

_{4},

*z*

_{5}, and

*z*

_{6}values are between 0 and 1024.

*X–Y*Cartesian coordinate system (Fig. 3). Using the equation of a circle passing through three given points, we computed the horizontal scan angle (α) of the ONH: Similarly, the vertical scan angle (β) of the ONH was determined:

*X–Y–Z*Cartesian coordinate system was then applied to the ONH (Fig. 4). Because the ONH is tilted along the horizontal and vertical axes, it has a three-dimensional scan angle (δ). The cross product (

*V*

_{2}×

*V*

_{1}) of two vectors representing tangents from the RPE fit line for the horizontal and vertical images was found. Using the dot product of the

*Y*-axis and this cross product (

*V*

_{2}×

*V*

_{1}), we calculated the three-dimensional scan angle (δ) of the ONH:

*X–Y*Cartesian coordinate system (Fig. 5), if the equation for a circle passing through three given points and the equation for points at fixed distances from a line are used, the real point positions (

*d*

_{1}and

*d*

_{2}) for the RNFL thickness measurement can be determined:

*X–Y*coordinate system can then be expanded to a three-dimensional

*X–Y–Z*Cartesian coordinate system. Theoretically, if a spatial rotation of a unit vector representing the

*Y*-axis ([0, 1, 0]) to another

*V*

_{2}×

*V*

_{1}vector ([

*ad*,

*bd*,

*bc*]) is understood (Fig. 4), the same rotation of the entire space about a vector is intuitive. Using the quaternion and its 3 × 3 rotation matrix,

^{ 7,8 }any point (

*x*, 0,

*z*) on the 3.46-mm-diameter circle with the ideal ONH can be moved to a new position (

*x*′,

*y*′,

*z*′) in a scanned cubic space:

*t*-tests and linear regression analyses and calculated Pearson's correlation coefficients. Bland-Altman plots were constructed in one program (MedCalc, ver. 9.5.0.0; MedCalc Software, Mariakerke, Belgium) and all other statistical analyses were performed with another program (SPSS, ver. 12.0.1; SPSS Inc., Chicago, IL).

*P*<0.05 were considered significant.

Scanned Angle (deg) | |
---|---|

Horizontal, α | 12.62 ± 5.17 (range, 0.98–24.84) |

Vertical, β | 4.17 ± 3.30 (range, 0.04–15.40) |

Three-dimensional, δ | 13.62 ± 5.13 (range, 2.28–24.88) |

*P*= 0.009); the mean difference was 13.26 ± 14.95 μm (range, 0–103).

Quadrant | Scanned Sector | Distance of Adjustment (mm) |
---|---|---|

Nasal | Clock-hour 4, RE/8, LE | 0.049 ± 0.038 (range, 0.000–0.182) |

Clock-hour 3, RE/9, LE | 0.051 ± 0.036 (range, 0.001–0.160) | |

Clock-hour 2, RE/10, LE | 0.049 ± 0.039 (range, 0.001–0.169) | |

Superior | Clock-hour 1, RE/11, LE | 0.049 ± 0.039 (range, 0.001–0.169) |

Clock-hour 12, RE/12, LE | 0.051 ± 0.036 (range, 0.001–0.160) | |

Clock-hour 11, RE/1, LE | 0.049 ± 0.038 (range, 0.000–0.182) | |

Temporal | Clock-hour 10, RE/2, LE | 0.049 ± 0.038 (range, 0.000–0.182) |

Clock-hour 9, RE/3, LE | 0.051 ± 0.036 (range, 0.001–0.160) | |

Clock-hour 8, RE/4, LE | 0.049 ± 0.039 (range, 0.001–0.169) | |

Inferior | Clock-hour 7, RE/5, LE | 0.049 ± 0.039 (range, 0.001–0.169) |

Clock-hour 6, RE/6, LE | 0.051 ± 0.036 (range, 0.001–0.160) | |

Clock-hour 5, RE/7, LE | 0.049 ± 0.038 (range, 0.000–0.182) | |

Total | 0.050 ± 0.038 (range, 0.000–0.182) |

Quadrant | Scanned Sector | Original RNFL Thickness (μm) | Adjusted RNFL Thickness (μm) | Difference (μm) | P * |
---|---|---|---|---|---|

Nasal | Clock-hour 4, RE/8, LE | 64.40 ± 11.27 (range, 43–110) | 65.73 ± 15.44 (range, 37–117) | 12.20 ± 9.19 (range, 0–44) | 0.324 |

Clock-hour 3, RE/9, LE | 58.14 ± 11.26 (range, 38–104) | 56.20 ± 12.52 (range, 34–104) | 3.62 ± 2.69 (range, 0–12) | <0.001 | |

Clock-hour 2, RE/10, LE | 85.11 ± 15.89 (range, 53–137) | 84.57 ± 20.03 (range, 51–149) | 5.85 ± 4.98 (range, 0–30) | 0.429 | |

Superior | Clock-hour 1, RE/11, LE | 121.89 ± 21.57 (range, 78–187) | 126.90 ± 26.29 (range, 72–215) | 8.41 ± 7.67 (range, 0–32) | <0.001 |

Clock-hour 12, RE/12, LE | 136.32 ± 26.86 (range, 81–234) | 144.36 ± 30.78 (range, 75–251) | 9.88 ± 7.53 (range, 0–36) | <0.001 | |

Clock-hour 11, RE/1, LE | 127.68 ± 20.41 (range, 66–201) | 134.50 ± 24.20 (range, 60–205) | 9.13 ± 6.42 (range, 0–32) | <0.001 | |

Temporal | Clock-hour 10, RE/2, LE | 80.03 ± 14.45 (range, 52–125) | 77.94 ± 15.43 (range, 45–122) | 7.63 ± 5.37 (range, 0–24) | 0.010 |

Clock-hour 9, RE/3, LE | 56.02 ± 8.77 (range, 39–81) | 57.55 ± 11.27 (range, 38–103) | 6.43 ± 6.43 (range, 0–35) | 0.055 | |

Clock-hour 8, RE/4, LE | 68.20 ± 12.54 (range, 43–117) | 71.57 ± 19.57 (range, 34–134) | 12.48 ± 11.61 (range, 0–47) | 0.025 | |

Inferior | Clock-hour 7, RE/5, LE | 127.74 ± 29.07 (range, 71–198) | 129.70 ± 29.00 (range, 70–219) | 34.28 ± 23.11 (range, 1–103) | 0.595 |

Clock-hour 6, RE/6, LE | 143.69 ± 22.81 (range, 94–202) | 140.66 ± 30.05 (range, 79–232) | 20.70 ± 19.07 (range, 0–88) | 0.224 | |

Clock-hour 5, RE/7, LE | 122.63 ± 25.81 (range, 74–204) | 118.18 ± 22.17 (range, 59–184) | 28.57 ± 17.48 (range, 0–98) | 0.133 | |

Total | 99.32 ± 37.52 (range, 38–234) | 100.65 ± 39.94 (range, 34–251) | 13.26 ± 14.95 (range, 0–103) | 0.009 |

_{O}) and adjusted (RNFL

_{A}) peripapillary RNFL thicknesses were determined by linear regression analyses and Pearson's correlation coefficients (Table 4). Overall, correlations were not excellent. In a superonasal half sector (the 10- to 3-clock-hour area of the right eye) they showed relatively good correlations (Pearson's correlation coefficients, 0.816–0.955), but in another half sector (the 4- to 9-clock-hour area of the right eye), they showed poor correlations (no correlation coefficients >0.624). The agreements between the original and adjusted peripapillary RNFL thicknesses were also assessed by using Bland-Altman plots (Fig. 6). Overall agreement in this analysis was also not good; the mean difference was −1.3 μm (+1.96 SD, 37.8; −1.96 SD, −40.4), indicating that the adjusted RNFL thicknesses were slightly thicker than the original RNFL thicknesses. With regard to quadrants, the mean differences were +0.4 μm (+1.96 SD, 20.4; −1.96 SD, −19.6), −6.6 μm (+1.96 SD, 12.2; −1.96 SD, −25.4), −0.9 μm (+1.96 SD, 23.3; −1.96 SD, −25.1), and +1.8 μm (+1.96 SD, 69.9; −1.96 SD, −66.2) for the nasal, superior, temporal, and inferior quadrants, respectively. The agreement was therefore poor, especially in the inferior quadrant.

Quadrant | Scanned Sector | Linear Regression Equation* | P † | P ‡ | Correlation Coefficient§ | P ‖ |
---|---|---|---|---|---|---|

Nasal | Clock-hour 4, RE/8, LE | RNFL_{A} = 0.523 × RNFL_{O} + 32.030 | <0.001 | <0.001 | 0.382 | <0.001 |

Clock-hour 3, RE/9, LE | RNFL_{A} = 1.053 × RNFL_{O} −5.023 | <0.001 | 0.009 | 0.947 | <0.001 | |

Clock-hour 2, RE/10, LE | RNFL_{A} = 1.177 × RNFL_{O} −15.585 | <0.001 | <0.001 | 0.934 | <0.001 | |

Superior | Clock-hour 1, RE/11, LE | RNFL_{A} = 1.130 × RNFL_{O} −10.810 | <0.001 | 0.034 | 0.927 | <0.001 |

Clock-hour 12, RE/12, LE | RNFL_{A} = 1.094 × RNFL_{O} −4.843 | <0.001 | 0.253 | 0.955 | <0.001 | |

Clock-hour 11, RE/1, LE | RNFL_{A} = 1.109 × RNFL_{O} −7.105 | <0.001 | 0.144 | 0.935 | <0.001 | |

Temporal | Clock-hour 10, RE/2, LE | RNFL_{A} = 0.872 × RNFL_{O} + 8.154 | <0.001 | 0.071 | 0.816 | <0.001 |

Clock-hour 9, RE/3, LE | RNFL_{A} = 0.803 × RNFL_{O} + 12.584 | <0.001 | 0.014 | 0.624 | <0.001 | |

Clock-hour 8, RE/4, LE | RNFL_{A} = 0.826 × RNFL_{O} + 15.207 | <0.001 | 0.065 | 0.529 | <0.001 | |

Inferior | Clock-hour 7, RE/5, LE | RNFL_{A} = −0.017 × RNFL_{O} + 131.829 | 0.851 | <0.001 | −0.017 | 0.851 |

Clock-hour 6, RE/6, LE | RNFL_{A} = 0.612 × RNFL_{O} + 52.710 | <0.001 | 0.001 | 0.456 | <0.001 | |

Clock-hour 5, RE/7, LE | RNFL_{A} = 0.037 × RNFL_{O} + 113.661 | 0.631 | <0.001 | 0.043 | 0.631 | |

Total | RNFL_{A} = 0.925 × RNFL_{O} + 8.765 | <0.001 | <0.001 | 0.869 | <0.001 |

^{ 9–11 }The position of the scan circle is very important, and a small displacement can cause a ripple effect that affects the entire RNFL thickness analysis.

^{ 12–14 }Similarly, the size of the scan circle is important for peripapillary RNFL thickness measurements.

^{ 15,16 }Because a circle diameter of 3.4 mm is large enough to avoid overlap with the ONH in normal eyes and is placed on the area with an almost radially oriented nerve bundle, it permits one to assume a direct relation between the accumulated nerve bundle cross section and the RNFL thickness measurement. Thus, the most widely used time-domain OCT scanner, the Stratus OCT (Carl Zeiss Meditec, Inc.), uses a scan circle 3.46 mm in diameter that is centered on the ONH; it provides 256 RNFL thickness measurements along this circle. The new spectral-domain Cirrus HD OCT scanner (Carl Zeiss Meditec, Inc.) also selects the same-sized calculation circle. For peripapillary RNFL thickness analysis, the Stratus OCT scanner directly obtains OCT images only along the scan circle and provides 256 measurements over 360°. At the time of scanning, the operator should manually adjust the ocular alignment and centering of the scanning circle. The Cirrus HD OCT scanner, however, first obtains OCT images as a whole cube through a 6-mm

^{2}grid and automatically places a calculation circle 3.46 mm in diameter on the center of ONH.

^{ 6 }Even after the scanning is finished, the location of this calculation circle can be freely adjusted at the discretion of the operator.

^{ 6 }; this automatic adjustment has made it increasingly possible for operators to forego manual ocular alignment. However, although the Cirrus HD OCT scanner successfully finds the ONH center and places the calculation circle at the proper position, the ONH may have a large ONH scan angle, totally distorting the RNFL thickness analysis.

^{ 7,8 }The quaternion is a somewhat complicated concept, but it provides a convenient mathematical rotation of objects in three dimensions and is a good linear approximation of the real situation. In this study, the quaternion was used for spatial rotation of the entire sphere about the ideal ONH. In the imaginary three-dimensional

*X–Y–Z*Cartesian coordinate system (Fig. 4), the original 12-clock-hour points on the ideal calculation circle with a 3.46-mm diameter were moved to new positions. Then, for each clock-hour point, the calculation circle was manually moved to pass through its new position to record the adjusted RNFL thickness.

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