Common 3-dimensional coordinate system for assessment of directional changes

Abstract

Introduction: The aims of this study were to evaluate how head orientation interferes with the amounts of directional change in 3-dimensional (3D) space and to propose a method to obtain a common coordinate system using 3D surface models.

Methods: Three-dimensional volumetric label maps were built for pretreatment (T1) and posttreatment (T2) from cone-beam computed tomography images of 30 growing subjects. Seven landmarks were labeled in all T1 and T2 volumetric label maps. Registrations of T1 and T2 images relative to the cranial base were performed, and 3D surface models were generated. All T1 surface models were moved by orienting the Frankfort horizontal, midsagittal, and transporionic planes to match the axial, sagittal, and coronal planes, respectively, at a common coordinate system in the Slicer software (open-source, version 4.3.1; http://www.slicer.org). The matrix generated for each T1 model was applied to each corresponding registered T2 surface model, obtaining a common head orientation. The 3D differences between the T1 and registered T2 models, and the amounts of directional change in each plane of the 3D space, were quantified for before and after head orientation. Two assessments were performed: (1) at 1 time point (mandibular width and length), and (2) for longitudinal changes (maxillary and mandibular differences). The differences between measurements before and after head orientation were quantified. Statistical analysis was performed by evaluating the means and standard deviations with paired t tests (mandibular width and length) and Wilcoxon tests (longitudinal changes). For 16 subjects, 2 observers working independently performed the head orientations twice with a 1-week interval between them. Intraclass correlation coefficients and the Bland-Altman method tested intraobserver and interobserver agreements of the x, y, and z coordinates for 7 landmarks.

Results: The 3D differences were not affected by the head orientation. The amounts of directional change in each plane of 3D space at 1 time point were strongly influenced by head orientation. The longitudinal changes in each plane of 3D space showed differences smaller than 0.5 mm. Excellent intraobserver and interobserver repeatability and reproducibility (>99%) were observed.

Conclusions: The amount of directional change in each plane of 3D space is strongly influenced by head orientation. The proposed method of head orientation to obtain a common 3D coordinate system is reproducible.

Fig 1

Images showing mandibular 3D volumetric model with 3 prelabeled landmarks (right and left condylions and pogonion) used to obtain reliable landmark identification for comparisons between before and after orientations and for testing the reproducibility of the method.

Fig 2

Representation of 3D measurements and changes in each component of the 3D space (x and y components). Distances between landmark coordinates (right and left condylions), representing the transversal (x-axis), anteroposterior (y-axis), and vertical (z-axis) differences. A, Before head orientation; B, after head orientation.

Fig 3

Representation of the 3D differences and changes in each component of the 3D space (y and z components) between 2 time points that were registered on the cranial base.

Fig 4

Figures illustrating the head orientation procedure: A, lateral view; B, frontal view; and C, superior view. The midsagittal plane of the 3D model was oriented vertically and coincident with the yellow (sagittal) plane, the Frankfort horizontal plane was oriented horizontally to coincide with the red (axial) plane, and the transporionic line was oriented to match with the intersection of the red (axial) and green (coronal) planes. The white box corresponds to the limits of the 3 cited planes, and it was not used as a reference for orientation.

Fig 5

A and B, Images with different head positions; C, simulation of coordinate generations of 4 landmarks from 2 head positions. Linear changes in each component of 3D space based on the x, y, and z coordinates could be affected because the same landmark (1, 2, 3, or 4) in the same 3D model with 2 head positions might have different x, y, and z coordinates.

Fig 6

Importance of head orientation for cross-sectional studies: A and B, anterior displacements do not mean displacement along the medial sagittal plane for both patients (represented by yellow and blue 3D models); C and D, images after head orientation. Anterior, vertical, and lateral displacements can be compared.