A Novel Three-Dimensional Vector Analysis of Axial Globe Position in Thyroid Eye Disease

Abstract

Purpose. To define a three-dimensional (3D) vector method to describe the axial globe position in thyroid eye disease (TED). Methods. CT data from 59 patients with TED were collected and 3D images were reconstructed. A reference coordinate system was established, and the coordinates of the corneal apex and the eyeball center were calculated to obtain the globe vector [Formula: see text]. The measurement reliability was evaluated. The parameters of [Formula: see text] were analyzed and compared with the results of two-dimensional (2D) CT measurement, Hertel exophthalmometry, and strabismus tests. Results. The reliability of [Formula: see text] measurement was excellent. The difference between [Formula: see text] and 2D CT measurement was significant (p = 0.003), and [Formula: see text] was more consistent with Hertel exophthalmometry than with 2D CT measurement (p < 0.001). There was no significant difference between [Formula: see text] and Hirschberg test, and a strong correlation was found between [Formula: see text] and synoptophore test. When one eye had a larger deviation angle than its fellow, its corneal apex shifted in the corresponding direction, but the shift of the eyeball center was not significant. The parameters of [Formula: see text] were almost perfectly consistent with the geometrical equation. Conclusions. The establishment of a 3D globe vector is feasible and reliable, and it could provide more information in the axial globe position.

Figure 1

The landmarks and reference coordinate system. PoR = right porion; PoL = left porion; OrR = right orbitale; OrL = left orbitale; N = nasion; S = sella; LoR = right lateral orbital point; LoL = left lateral orbital point. The positive x, y, and z coordinate values indicated the front, left, and superior orientation, respectively.

Figure 2

The eyeball vector diagram. The arrowhead represents point C, and the other point of the arrow represents point E. The red and blue arrows represent $\overrightarrow{\mathrm{E}\mathrm{C}}$ of the right and left eye, respectively, and it could be viewed and compared in the 3D coordinate system from different directions.

Figure 3

Bland-Altman plots compared the results of Hertel exophthalmometer and CT measurement. The left one showed the difference between the Hertel results and the coordinate x_E of $\overrightarrow{\mathrm{E}\mathrm{C}}$, and the right one showed the difference between the Hertel results and 2D CT exophthalmos. It could be found that the difference between the Hertel results and 2D CT exophthalmos was more dispersed than that between the Hertel results and x_E and had much fewer plots within −1~1 mm.

Figure 4

The geometrical relationship between the corneal apex and the eyeball center. Theoretically, $x_{\mathrm{C}}=\cos \left(\arg X\right)\times \left|\overrightarrow{\mathrm{E}\mathrm{C}}\right|+x_{\mathrm{E}}$. Similarly, the calculation equation could be acquired for y_C and z_C.

Figure 5

The scatterplots about the theoretical and actual coordinates of the corneal apex. The dotted line represents the equation y = x, and we could find that the theoretical values were consistent with the actual values near perfect.