Photographic Analysis

In the interest of drawing the corneal contour in 2-dimensional photographs, the corneal margin was captured using Adobe Illustrator CS version 12.0.0 (Adobe Systems, San Jose, California, USA). The curved line of the corneal margin that was visible from the original photograph was separated ( Figure 1 ). A full ellipse was extrapolated from the remaining part of the corneal margin so the corneal contour could be drawn. This had to be done because the elliptical corneal contour was not fully visible in the photographs to eyelid covering.

Extrapolation of the corneal contour of both eyes in 2-dimensional photographs to measure ocular oblique muscle dysfunction objectively. (Top) Photograph of a patient with inferior oblique muscle overaction in the right eye looking at the upper leftward direction. (Bottom) The curved line of the corneal margin that is visible from the original photograph was transcribed (dashed line) and a full ellipse is extrapolated so the corneal contour can be drawn. The full ellipse drawing (continuous line) was separated from the picture for photographic analysis.

A simulating program presenting a rotating circle based on the intended longitude (angle of horizontal deviation) and latitude (angle of vertical deviation) was developed using the polar coordinate system. The center of the inner circle representing the cornea was expressed as polar coordinates. The ratio of this circle’s horizontal diameter and vertical diameter was based on the general corneal contour of 11.5:10. If the circle rotated α degrees around the x-axis and −β degrees around the y-axis, and then the circle was projected onto the x-y plane, an ellipse was presented that coincided with the 2-dimensional photographic image of the cornea ( Figures 2 and 3 ). This was implemented using Microsoft Excel Visual Basic Editor (Microsoft Corporation, Redmond, Washington, USA).

Schematic model of the simulating program of an eyeball presenting as a rotating circle using the polar coordinate system. (Left) Schematic model of the eyeball in the primary position. The outer circle represents the eyeball and the inner circle represents the cornea. (Right) Figure of the eyeball that rotated horizontally (−β degrees) around the y-axis and vertically (α degrees) around the x-axis. The cornea is then projected onto the x-y plane presenting as an ellipse, which coincides with the 2-dimensional photographic image of the cornea.

Examples of measuring the rotated angle of the eyeball in both eyes by applying the extrapolated ellipse of the cornea to the simulating program of the eyeball. The thin dark-colored lines are the extrapolated ellipse of the cornea from the 2-dimensional photograph of the patient in Figure 1 . The serrated thick light-colored lines are the projected 2-dimensional image of the corneal contour made by the simulating program that were operated to coincide with the thin dark-colored lines. The degree of elevation or depression (α) and abduction or adduction (β) represent the vertical and horizontal rotated angles of the eyeball by the simulating program, respectively, that matched with the corneal contour of the photographs. (Left) Photographic analysis applied to the right eye of the patient in Figure 1 . The right eye has rotated 12 degrees vertically and 32 degrees horizontally. (Right) Photographic analysis applied to the left eye of the patient in Figure 1 . The left eye has rotated 0 degrees vertically and 35 degrees horizontally.

Using the newly designed program simulating the projected image of the cornea rotating in 3 dimensions, the degree of elevation or depression (α) in both eyes could be calculated when the ellipse matched with the corneal contour of the photographs. The α difference between the 2 eyes (adducting eye − abducting eye) then was calculated, defined as the simple angular difference method. A positive value of α difference of the adducting eye was determined as overaction, and a negative value was determined as underaction. The simple angular method was applied readily on photographs obtained during adduction in the primary position without vertical rotation of the abducting eye. In contrast, if the eye looked upward or downward during adduction, the abducting eye theoretically should rotate exactly the same amount as the target. However, this is not, in fact, what happens, and the amount of vertical deviation of the abducting eye may be less or more than the intended fixation point of the target. Considering the fact that the degree of ocular oblique muscle dysfunction maximizes in the direction of muscle action, and based on Hering’s law of equal innervation to both eyes, the degree of ocular oblique muscle dysfunction may be affected by the amount of vertical rotation of the abducting eye. Therefore, we set a standardized position of vertical deviation at 20 degrees and adjusted the results of simple angular difference according to the actual vertical deviation of the abducting eye, defined as the adjusted angular difference method. For example ( Figure 4 ), if the abducting right eye is elevated 10 degrees and the adducting left eye is elevated 15 degrees during adduction, the simple angular difference in elevation is: 15 degrees − 10 degrees = 5 degrees of left inferior oblique overaction. If the vertical position of the abducting right eye is adjusted to 20 degrees, the adjusted angular difference is: simple angular difference (5 degrees) × 20 degrees / vertical angle of the abducting eye (10 degrees) = 10 degrees ( Figure 4 ). Ocular oblique muscle dysfunction was measured using these 2 methods simultaneously when applicable.

The simple and adjusted methods of measuring ocular oblique muscle dysfunction by calculating the degree of elevation or depression (α) in both eyes using photographic analysis. Each drawing is the sagittal view of the eyeball. (Top) The simple angular difference method is measured by the α difference of both eyes (adducting eye − abducting eye). A positive value was determined as overaction and a negative value as underaction. The adjusted angular difference method was calculated according to the actual vertical deviation of the abducting eye in reference to the standardized position of vertical deviation set at 20 degrees. For example, if the abducting right eye is elevated 10 degrees and the adducting left eye is elevated 15 degrees, the simple angular difference is: 15 degrees − 10 degrees = 5 degrees of left inferior oblique overaction. If the vertical position of the right eye is adjusted to the standard 20 degrees, the adjusted angular difference is: simple angular difference (5) degrees × 20 degrees/vertical angle of the abducting eye (10 degrees) = 10 degrees.

Comparison Between Photographic Analysis and the Model Eye

We applied photographic analysis to a model eye to evaluate the accuracy of photographic analysis. A model eye was made that freely rotated and displayed goniometric readings of the center of the cornea in longitude (angle of horizontal deviation along the x-axis) and latitude (angle of vertical deviation along the y-axis). To generate standard photographs for analysis, the model eye was rotated in a stepwise manner by 5-degree intervals from 0 to 30 degrees along the horizontal and vertical axis. All possible combinations of horizontal and vertical vectors were applied, and 36 photographs were generated in each quadrant. Finally, a total of 144 photographs were presented in random order for analysis. A masked observer (H.K.Y.) measured the longitude (horizontal deviation) and latitude (vertical deviation) on each photograph using photographic analysis. The goniometric readings of the model eye were compared with the angles obtained by photographic analysis.

Comparison Between Photographic Analysis and the Scleral Search Coil

Twelve healthy volunteers recorded 2-dimensional scleral search coils in both eyes simultaneously. The camera was placed at 1 m in front of each subject. A frame with a target at 4 fixation points (20 degrees right/20 degrees up, 20 degrees right/20 degrees down, 20 degrees left/20 degrees up, 20 degrees left/20 degrees down) was used. Photographs were obtained while the subject viewed the 4 fixation points. During the test, 2 subjects could not record the magnetic scleral search coil because of discomfort and 1 subject’s data was discarded because of sudden coil breakage. Finally, 9 volunteers (4 men and 5 women; age range, 23 to 48 years; mean age, 28.3 years) completed the test and a total of 36 photographs were gathered from 9 volunteers. At each fixation point, the horizontal and vertical angles of the scleral search coil were compared with the angles obtained by photographic analysis. The level of agreement between the scleral search coil and photographic analysis was assessed using Bland-Altman analysis.

Comparison Between Photographic Analysis and Clinical Evaluation

Photographic analysis of ocular oblique muscle overaction or underaction and the clinical gradings from medical records were compared in patients. Nine-gaze photographs were obtained on the same day the patients were examined. All gradings of oblique muscle dysfunction were made by 1 examiner (J.-M.H.). A total of 27 patients (17 men and 10 women; age range, 3 to 27 years; mean age, 9.1 years) were included in the study. For photographic analysis, inferior oblique overaction was measured from photographs during ipsilateral adduction in the primary position, inferior oblique underaction was measured during ipsilateral adduction in upward gaze with the simple and adjusted angular difference methods, and superior oblique overaction and underaction were measured during ipsilateral adduction in downward gaze with the simple and angular difference methods. A total of 162 photographs were obtained for analysis (6 photographs in each of 27 patients). An angular difference of 5 degrees was defined as 1 unit of overaction or underaction. Spearman correlation coefficients were determined between the clinical gradings and photographic analysis. Nonparametric analysis of clustered receiver operating characteristic curves was used to determine the diagnostic accuracy of the test.

Statistical Analysis

SPSS for Windows software version 18.0 (SPSS, Inc, Chicago, Illinois, USA) and SAS software version 9.1 (SAS Institute, Inc, Cary, North Carolina, USA) were used for statistical analysis. Measurements of photographic analysis were compared with goniometric readings of the model eye by paired t test. The level of agreement between the scleral search coil and photographic analysis was assessed using Bland-Altman analysis. Spearman correlation coefficients were determined between photographic analysis and clinical gradings. Nonparametric analysis of clustered receiver operating characteristic curves and the area under the receiver operating characteristic curve (AUC) were analyzed to determine the diagnostic accuracy of the photographic analysis compared with clinical gradings.