Material and methods

In this retrospective study, we evaluated 54 pretreatment records (photos and CBCT volumes) of patients from the Department of Orthodontics of Case Western Reserve University in Cleveland, Ohio. Initial pretreatment photographs of 300 Angle Class II malocclusion patients were examined to search for Class II subdivision malocclusions that met the following criteria: (1) erupted permanent dentition from first molar to first molar in both arches; (2) no missing teeth, excluding third molars; (3) no craniofacial syndromes that would cause severe skeletal asymmetries; (4) one side of the arch with an Angle Class I molar relationship and the other side with at least a half-step Angle Class II molar relationship or greater; and (5) clear pretreatment photographs and CBCT volumes.

Once the patients were identified, the amounts of crowding per quadrant were estimated by the principal investigator (C.M.M.) and recorded so that the role of dental crowding could also be evaluated in the Class II subdivision malocclusions. Two groups were created: a noncrowded group (no crowding or ≤2 mm of crowding in any quadrant), and a crowded group (≥3 mm of crowding in any quadrant). Patients with excess spacing were not included in either group.

The scans were made by using the CBCT unit (Hitachi, Tokyo, Japan) at Case Western Reserve University’s Craniofacial Imaging Center. All images were taken at settings of 2 mA, 120 kV, and 12-in field of view. The CBCT volumes were analyzed and measured by using Dolphin 3D software (version 11.0 premium software; Dolphin Imaging & Management Solutions, Chatsworth, Calif).

Establishing a consistent method of orientation ensured that the coordinate systems would be the same for each image so that the measurements for each subject could be reliably compared. This was done in the Dolphin 3D software by setting the x-, y-, and z-axes on reproducible anatomic landmarks that could be easily identified.

From the right lateral view, the z-axis was set to the Frankfort horizontal, a line passing through the right porion and right orbitale. Then the y-axis was set perpendicular to the z-axis through the middle of the sella turcica by clipping the image from the sagittal view to obtain a clear view of the sella.

From the frontal view, the x-axis was defined by a line passing through the right and left orbitales. From the superior view, the z-axis was constructed by drawing a line from the crista galli through the middle of the sella and perpendicular to the x-axis through the middle of the sella.

By establishing the x-, y-, and z-axes, 3 planes in space were created that intersected at the origin. The origin (0, 0, 0) was located along the midsagittal plane, just below the sella, and at the level of Frankfort horizontal. After the reconstructed model was oriented and the axes and planes were defined, landmarks could be plotted in precise anatomic locations by using sagittal, coronal, and axial slices of the CBCT volume.

Twenty-one digital landmarks, skeletal and dental, were selected based on ease of identification and reproducibility ( Fig , Table I ). Three midline landmarks—origin, incisive foramen, and genial tubercles—were chosen to represent the middle of the cranial base, the maxilla, and the mandible, respectively. The other 18 landmarks were located on the right and left halves of the skull and dental arches.

Skeletal landmarks.

Each landmark was assigned unique coordinates (x, y, z) when it was plotted in the Dolphin 3D software. These coordinates could then be copied and pasted into Excel (Microsoft, Redmond, Wash), with a spreadsheet designed so that the direct measurements in millimeters could be calculated between any 2 landmarks by using the distance formula. In 3-dimensional space, the distance between points (x ₁ , y ₁ , z ₁ and x ₂ , y ₂ , z ₂ ) is determined with this equation:

Measurements were also made in the Class II side of the maxilla and the mandible that were compared with the measurements in the Class I side of the maxilla and the mandible ( Table II ). These measurements were evaluated to determine whether there were any Class II side vs Class I side differences in the following.

• 1.

  The positions of the maxilla or the mandible in relation to the cranial base (rotation of the maxilla or the mandible, when one side is ahead of or behind the other side).

• 2.

  The positions of the maxilla and the mandible in relation to each other (intermaxillary measurement).

• 3.

  Intramaxillary dimensions (one side larger or smaller than the other).

• 4.

  Intramandibular dimensions.

• 5.

  The intra-arch positions of the molars and canines relative to the maxilla (mesial or distal position of the teeth in the arch on 1 side).

• 6.

  The intra-arch positions of the molars and canines relative to the mandible.

Each measurement was a straight-line distance between the 2 points.

Fifteen of the 54 subjects were randomly selected, and the CBCT orientations, landmark identifications, and measurements were repeated by the same examiner (C.M.M.) to test for reliability.

The method error ( ME ), or casual error, was calculated by using Dahlberg’s formula : ME=√(∑d2/2n),
ME = √ ( ∑ d 2 / 2 n ) ,
with d as the difference between the original and repeated measurements and n as 15 for the sample size that was repeated.

The method error tests for the reproducibility of each measurement and provides an estimate of the standard deviation around the mean of each measurement.