Material and methods

The project was approved by the research ethics committee of the Institute of Collective Health Studies from the Federal University of Rio de Janeiro. A sample calculation, based on previous studies, showed that at least 17 subjects would be necessary in each group to detect differences of 65 mm ² in the minimal cross-sectional area and 2500 mm ³ in the PA volume, with a power of 0.8 and a significance level of 0.05.

All the patients were selected from the archives of Hospital da Face (São Paulo, SP, Brazil) from a pool of 338 operated patients. None had a documented diagnosis of obstructive sleep apnea. The selection process was carried out in 2 phases. In the first phase, these inclusion criteria were applied: (1) patients from 18 to 30 years of age, (2) preoperative and postoperative CBCT scans taken with the same machine, (3) the postoperative scan taken from 5 to 8 months after surgery (immediately after bracket debonding), and (4) craniocervical inclination between 90° and 110°. Exclusion criteria applied were (1) important maxillary and mandibular transverse asymmetry, (2) chin augmentation, (3) syndromic patients, and (4) evident airway pathology. The second phase comprised 2 specific steps: preoperative (T1) and postoperative (T2) scans of the eligible patients were loaded into Dolphin Imaging software (version 11.5; Dolphin Imaging & Management Solutions, Chatsworth, Calif). The head orientation was performed by an experienced operator (D.P.B.): the horizontal reference was the Frankfort horizontal plane (FHP), defined bilaterally by porion and right orbitale landmarks, parallel to the floor; the midsagittal plane (MSP), vertically oriented and defined by nasion, anterior nasal spine, and basion; and the transporionic plane, defined by bilateral porion landmarks and oriented perpendicular to the FHP and the MSP.

On step 1 of the second phase, 5 points were used on the MSP: S point, posterior nasal spine (PNS), A-point, B-point, and menton. S point served as a reference for the delineation of the horizontal reference line (parallel to the FHP) and the vertical reference line (perpendicular to the FHP). A vertical analysis ( Fig 1 , A ) and a horizontal analysis ( Fig 1 , B ) were performed on the T1 and T2 scans. The purpose of the vertical analysis was to exclude patients with substantial vertical variations (greater than 2 mm for any point between T1 and T2) from the sample. The horizontal analysis excluded patients with anteroposterior variations of less than 3 mm for either A-point or B-point, to ensure that only patients with significant anteroposterior jaw displacement would be selected.

Images showing the measurements used in step 1 of the second phase of the sample selection process: A, the 4 vertical measurements (perpendicular distance of PNS, and A, B, and Me points to the horizontal reference line); B, the 4 horizontal measurements (perpendicular distance of PNS, and A, B, and Me points to the vertical reference line).

In the second step, 2 customary cephalometric measurements were performed on the T1 and T2 scans as well. If the palatal plane or the occlusal plane had a variation greater than 5° (either clockwise or counterclockwise), the patient was eliminated from the study. This criterion was applied to better visualize the PA modifications after isolated anteroposterior jaw movements.

At the end of the selection, 42 subjects were selected, of which 22 (10 male, 12 female) had undergone maxillary advancement associated with mandibular setback and were allocated to group 1. The other 20 (8 male, 12 female) had undergone maxillomandibular advancement and constituted group 2 ( Table I ).

All CBCT scans were taken with an i-CAT machine (Imaging Sciences International, Hatfield, Pa) by the same radiology technician. The scanning protocol was 120 kV, 5 mA, 13 × 17 cm field of view, 0.4 mm voxel, and scanning time of 20 seconds. The patients had been told to maintain natural head position, to keep the teeth in occlusion, to not swallow, and to breathe smoothly during the examination. All scans were requested as a part of the initial or final records of the orthodontic treatment. The same oral surgeon (L.V.) was responsible for all the surgical procedures, performing a LeFort 1 osteotomy for the maxilla and a bilateral sagittal split osteotomy for the mandible. Titanium plates were used for rigid fixation of the jaws.

For the volume assessment, the PA was divided into 2 segments using the “sinus/airway” tool of the Dolphin3D software. The superior segment (VolA) had the following limits (on the MSP): superior limit, line parallel to the FHP through the most superior point of the PA ; anterior limit, line perpendicular to the FHP through the most anterior and inferior point of the sphenoidal sinus; inferior limit, line parallel to the FHP through the most concave point of the anterior and inferior wall of the second cervical vertebra; posterior limit, line perpendicular to the FHP through the most posterior point of the pharynx (posterior wall) ( Fig 2 , A ). The lower segment (VolB) had the same anterior and posterior limits as VolA. Its superior limit was the same as VolA’s inferior limit, and its inferior limit was a line parallel to the FHP through the most inferior and anterior point of the fourth cervical vertebra ( Fig 2 , B ). The total volume (VolTo) was obtained by the sum of both segments’ volumes. The division limit of the 2 segments was measured (perpendicular distance from the limit line to S point) at T1 and reproduced on the T2 scan, with the aid of the reference line. The minimal cross-sectional area (min CSA) was assessed by the “sinus/airway” tool as well. The upper and lower limits and the threshold (sensitivity) used were the same as the ones determined for the volumetric measurements; once they were set, the software indicated the most constricted point of the PA. All measurements were performed on the T1 and T2 scans, and their variations were assessed through percentage (T2/T1−1) and absolute (T2−T1) values.

Demonstrative images of the boundaries used to measure the 2 volume segments that constituted the PA (on the midsagittal plane). The reference line (perpendicular distance to S point) depicted was built on the T1 scan and reproduced on the T2 scan to increase the reliability of the volumetric measurements. A, Boundaries used to measure the upper segment volume (VolA); B, boundaries on the lower segment (VolB).

To obtain the jaw displacement, a method of CBCT scan superimposition that has already been described and tested in the literature was used. In summary, the cranial base and both jaws were segmented from the T1 and T2 scans using the ITK-SNAP open-source software. With the software IMAGINE (developed by the National Institutes of Health, Bethesda, Md, and modified at the University of North Carolina, Chapel Hill), a voxel-wise method for cranial base superimposition was performed using T1 as the reference and moving T2 with 6 degrees of freedom. Then, 3D surface models were imported to CMF software (Maurice Muller Institute, Bern, Switzerland) that allows quantifying the distance between 2 surfaces at any location. Details of this methodology of superimposition can be found in the study of Carvalho et al. Two tools of the CMF—color map and isoline—were used to assess the distance of A-point and B-point between the T1 and T2 scans ( Fig 3 ). The A-point distance represented maxillary 3D displacement and B-point the mandibular 3D displacement.

Lateral and frontal views (CMF software) of the superimposed preoperative and postoperative models of a patient who had undergone maxillomandibular advancement. The color map tool depicts in different colors what occurred to the respective structures after the surgery: green , no movement; red , forward movement; and blue , backward movement. The isoline shows Point B displacement after surgery.

The volume variation of each segment and the min CSA area were correlated (Pearson correlation) with the jaw displacement, and a linear regression model was proposed. At first, the groups were analyzed separately, and then the data were combined and the tests redone just for the volume variations. All measurements of the 20 patients were repeated after a 2-week interval for the calibration test. A t test for independent samples was performed to detect differences between the groups concerning baseline volumetric measurements and the amount of displacement of the jaws. All statistical tests were performed using SPSS software (version 17.0; SPSS, Chicago, Ill).

Results

All the measurements showed excellent intraclass correlation coefficients, higher than 0.9 ( Table II ). The baseline measurements had no statistical differences between sexes or groups.

VolA variation percentages for groups 1 and 2 were 14.90% ± 6.51% and 31.11% ± 12.48%, respectively, and VolB’s were −2.05% ± 2.57% and 26.49% ± 9.34%, respectively. The maxilla had similar displacements in the 2 groups ( P = 0.098), whereas the mandible had evident differences ( Table III ).

The majority of the correlations—13 of 16—showed greater strengths when made with the percentage value and so were used to describe the results ( Table IV ). Stronger correlations were found between the jaw and the volume segment that was closer to it in both groups ( Fig 4 ). In contrast, jaws seem to have little influence on the more distant segments. The strongest correlation and best goodness of fit to the linear regression model (expressed by R ² ) were observed between the maxillary displacement and VolA percentage variation (VolA%) in group 2 (r = 0.898, R ² = 0.888; P ≤0.001). “R ² = 0.888” means that 88.80% of the variation in VolA% could be explained by the respective maxillary displacement, showing that the latter is a good predictor of VolA’s percentage variation. When total volume correlations were analyzed (Max-VolTo% and Mand-VolTo%), the maxilla showed a higher influence than did the mandible. When the volumetric data of both groups were analyzed together (n = 42), the variables Max-VolA% showed a bad adjustment to the regression model (r = 0.587, R ² = 0.345; P ≤0.01). There was a statistical difference on the VolA% variation in the groups ( P ≤0.001), despite their similar maxillary displacements ( P ≤0.001) ( Fig 5 ). Regarding the correlation Mand-VolB% with the combined data, the strongest correlation and the best adjustment to the regression model (r = 0.921, R ² = 0.914; P ≤0.001) of the entire study were found ( Fig 5 ).

Linear regression models of the variables “jaw displacement” and “percentage of volume variation” of their closer volume segment: A, variables maxillary displacement and percentage variation of the upper segment volume—Max-VolA(%)—in group 1 (r = 0.841, R ² = 0.812; P ≤0.001); B, variables Mand-VolB(%) in group 1 (r = 0.879, R ² = 0.769; P ≤0.001); C, variables Max-VolA(%) in group 2 (r = 0.898, R ² = 0.888; P ≤0.001); D, variables Mand-VolB(%) in group 2 (r = 0.861, R ² = 0.846; P ≤0.001).

Linear regression models, controlled for kind of surgery, of the combined data of both groups: A, the variables Max-VolA(%) showed a bad adjustment to the regression model (r = 0.587, R ² = 0.345; P ≤0.01), represented as the black line ; B, variables Mand-VolB(%) showed the strongest correlation and the best adjustment of the entire study (r = 0.921, R ² = 0.914; P ≤0.001).

The min CSA percentage variation presented a linear variation just when correlated with the maxillary displacement (r = 0.710, R ² = 0.604; P ≤0.01) on the maxillomandibular advancement surgery ( Fig 6 ). In group 1, neither the maxillary nor the mandibular displacement could be considered a good predictor for the min CSA% variation ( Table V ).

Linear regression models, controlled for kind of surgery, correlating the degree of jaw displacement with the percentage variation of the minimal cross-sectional area of the PA: A, variables Max-min CSA(%) in group 1 (r = 0.486, R ² = 0.312; P ≥0.05) and group 2 (r = 0.710, R ² = 0.604; P ≤0.01); B, variables Mand-min CSA(%) in group 1 (r = 0.084, R ² = 0.051; P ≥0.05) and group 2 (r = 0.215, R ² = 0.088; P ≥0.05).

Table V

Measurement variations times jaw displacements

Group	Absolute (T2−T1)		Percentage (T2/T1−1)
	r	R 2	r	R 2
1
Max-VolA	0.677 †	0.612 †	0.841 ‡	0.812 ‡
Max-VolB	0.056	0.003	0.106	0.011
Max-VolTo	0.656 †	0.402 †	0.783 ‡	0.611 ‡
Mand-VolA	0.053	0.003	0.159	0.025
Mand-VolB	0.702 †	0.503 †	0.879 ‡	0.769 ‡
Mand-VolTo	0.494 ∗	0.244 ∗	0.411 ∗	0.169
Max-min CSA	0.212	0.045	0.486 ∗	0.312
Mand-min CSA	0.81	0.038	0.084	0.051
2
Max-VolA	0.810 ‡	0.668 ‡	0.898 ‡	0.888 ‡
Max-VolB	0.280	0.078	0.205	0.093
Max-VolTo	0.708 †	0.573 †	0.804 ‡	0.647 ‡
Mand-VolA	0.146	0.021	0.160	0.026
Mand-VolB	0.794 †	0.679 †	0.861 ‡	0.846 ‡
Mand-VolTo	0.559 ∗	0.311 ∗	0.644 †	0.414 ∗
Max-min CSA	0.485 ∗	0.258 ∗	0.710 †	0.604 †
Mand-min CSA	0.308	0.172	0.215	0.088

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