Fig 1.
Calculation of the center of eye rotation in a two-dimensional image plane.
(A) Pupil ellipses and the minor axis of the pupil ellipse obtained during circular eye movement induced by swirling the mouse around manually. (B) Point of intersection of multiple minor axes of a pupil ellipse. Ideally, multiple minor axes of a pupil ellipse would intersect at a single point, but they did not. The point of intersection of multiple minor axes of a pupil ellipse were determined as a point of the sum of the squares of the minimum distances between the point and the minor axes (black lines). (C) Center of eye rotation in the image calculated from the six minor axes shown in (A). The six minor axes shown in (A) are drawn here. The white small circle was the point where the sum of the squares of the distance between the point and the minor axis was minimum. After calculating the coordinates of the center of eye rotation in the image plane, a three-dimensional coordinate frame of XYZ was determined, as shown in the Inset.
Fig 2.
Schema for analyzing three-dimensional rotation vectors of eye movements during rotation in mice and the image-processing procedure for analyzing movement of the turntable.
(A) Movements of the turntable and the eyes of the mice were recorded by two high-speed infrared CCD cameras. Images obtained by the two cameras were synchronized. (B) Original image of the markers on the turntable. (C) Same as that in (B) but in a contrast-enhanced image. (D) The center of gravity of the two markers was detected. (E) The movement of the line connecting the two centers of gravity of the markers was calculated to be equivalent to the movement of the turntable.
Fig 3.
Image-processing procedure for detecting the center of the pupil ellipse and the center of gravity of an iris freckle in mouse A.
(A) Original image of the left eye of mouse A. (B) Same eye as in (A) but in a contrast-enhanced image. (C) White areas are where the gray scale was less than the threshold value. Black rectangle shows the region of interest (ROI) for detecting the left edge of the pupil. (D) Left edge of the pupil was detected. (E) White areas are where the gray scale was less than the threshold value. Black rectangle shows the ROI for detecting the right edge of the pupil. (F) Right edge of the pupil was detected. (G) The edge of the pupil was approximated by the pupil ellipse and calculated at the center of the ellipse. (H) ROI for detecting an iris freckle was determined after calculating the pupil ellipse. The region was some distance from the center of the ellipse and had the same curvature as the ellipse. (I) In the region shown in (H), an iris freckle was detected with the gray scale less than the threshold value. (J) Coordinates of the iris freckle were calculated as the center of gravity of the white areas shown in (I).
Fig 4.
Calculation of the length of the radius of rotation of the center of the pupil and the radius of rotation of an iris freckle.
(A) Calculation of the length of the radius of rotation of the pupil center, R. Eqs 1–3 apply when the eye rotates θ from the eye position during frontal vision in the plane P, which includes the center of eye rotation and the diameter that corresponds to the minor axis of the pupil ellipse of the image plane (gray line, left figure), where r is the length between o and the center of the pupil ellipse p. (B) Next, we calculate the length of the radius of rotation of an iris freckle. When an iris freckle is on the same plane as the pupil edge, the radius of rotation, R’, is calculated by Eq 4, in which a is the distance between the center of the pupil ellipse and the center of gravity of an iris freckle in the image, b is the distance between the center of the pupil ellipse and point c in the image, point c is the point of intersection of the edge of the pupil ellipse and the line connecting of the center of the pupil ellipse and the center of gravity of an iris freckle in the image.
Fig 5.
Vestibulo-ocular reflex (VOR) data for mouse A.
(A) Data for the position of the turntable during rotation. (B) X component of the rotation vector of eye position during rotation. (C) Y component of the rotation vector of eye position during rotation. (D) Z component of the rotation vector of eye position during rotation. The Z component was in phase with the X and Y components, but it was 180° out of phase with the turntable shown in (A). (E) Changes in the length of the minor and major axes of the pupil ellipse during rotation. The length of the major axis of the pupil ellipse was almost constant during rotation. The length of the minor axis of pupil ellipse changed in phase with the Z component phase, as shown in (D). (F) Velocity data of the turntable during rotation. (G) X component of the rotation vector of eye velocity during rotation. The length of the minor axis of the pupil ellipse changed in phase with the Z component change, as shown in (D). (F) Velocity data for the turntable during rotation. (G) X component of rotation vectors of eye velocity during rotation. (H) Y component of rotation vectors of eye velocity during rotation. (I) Z component was the main component of the rotation vectors of eye movement. X and Y component values were low. Z component was 180° and was out of phase with the turntable, as shown in (F). (J) Angular velocity of eye rotation around the axis of rotation. As the value of the rotation vectors of eye velocity were always positive, we let the sign of angular velocity of eye rotation around the axis of rotation coincide with the Z component of the rotation vector of eye velocity. We calculated the gain and phase of VOR using these data.
Fig 6.
A, X component of the rotation vector of eye position during rotation in mouse B. B, Y component of the rotation vector of eye position during rotation in mouse B. C, Z component of the rotation vector of eye position during rotation in mouse B. D, Angular velocity of eye rotation around the axis of rotation in mouse B and velocity data of the turntable during rotation. The gain of VOR was 0.74 [(65.7°/sec) / (88.5°/sec)] and the phase of VOR was 4.88°. E, Changes in the length of the minor and major axes of the pupil ellipse during rotation in mouse B. The length of the major axis of the pupil ellipse was almost constant during rotation. The length of the minor axis of pupil ellipse changed in phase with the Z component phase, as shown in (C). F, Contrast-enhanced image of the eye of mouse B. G, Contrast-enhanced image of the eye of mouse C. H, Data for the position of the turntable during mouse C was rotated. I, The movement of the coordinate of center of pupil of mouse C in two-dimensional images. The unit of this graph was “dots,” not “degrees” because the iris freckle could not be detected, and the rotational angle could not be analyzed.