Each rectus EOM location was determined by its area centroid, equivalent to the center of gravity of a shape of uniform density and thickness.
7 Quantitative analysis of MRIs requires the following consideration of individual subject variation in orbital size, and angular and linear head orientation in the scanner. Initially, data for each of the rectus EOMs was collected in Cartesian scanner coordinates from the original MRIs. Data were transformed by a sequence of rotations into a standard coordinate system as previously described,
7 and only a brief summary follows. Approximating the globe as spherical, its 3-D center was determined to subpixel resolution in scanner coordinates, using curve-fitting to three cross-sectional images of the globe, as previously described.
5 14 This operation permits determination of the globe center at subpixel resolution, because the center is not determined from any one pixel, but from combined data representing all the pixels in three complete globe cross sections. This method is not significantly compromised by asphericity of the globe in pathologic cases. Analytical simulations with globes distorted from sphericity by up to 25% result in a maximal error in globe center determination of only approximately 0.15 mm. All rectus EOM positions were then translated to place the 3-D coordinate origin at the computed center of the globe. After translation, the data were rotated about the globe center using extraorbital landmarks (no suitable global referents exist).
7 First, a horizontal rotation (yaw) was performed to align the interhemispheric fissure of the brain, which direction was taken as true anteroposterior. A vertical rotation (pitch) was then performed to bring the junction of the superior ethmoid air sinus and the orbit to the standard angle of 10° elevation from true horizontal. An illustration of this consistent landmark has been published.
7 This vertical rotation was selected to be 10°, because it was the mean angle required to bring the MR to true horizontal in the first 20 orbits analyzed. Finally, a torsional rotation (roll) was performed to bring the interhemispheric fissure of the brain to true vertical. The skull and globe were assumed to be rigid bodies. Consequently, points on either could be shifted by both rotation and translation relative to the coordinate system. The geometric center of the globe was used as the origin of the transformed coordinate system in which EOM area centroids were represented, but this analysis makes no assumptions about actual center of rotation of the eye. After transformation, scanner coordinates were scaled to millimeters, and were further scaled to normalize each globe to the measured average diameter of 24.3 mm.
7 Displacement of the globe–optic nerve junction from its position in central gaze was used to estimate ocular rotation, as previously described.
7 In interpreting such data, it is helpful to recognize that earlier studies have shown rectus EOM paths near the orbital apex to be highly stable over the range of gaze,
7 consistent with histologic evidence of the rigid EOM origins and other connective tissue constraints in that region.
15 Therefore, apparent parallel shifts in EOM paths near the orbital apex must represent globe translation, and any apparent changes in the angles of posterior EOM paths must represent residual angular deviations of the head.