## Introduction

This study aimed to evaluate maxillary skeletal and dental yaw in patients with skeletal Class III facial asymmetry and investigate its correlation with menton deviation.

## Methods

Initial cone-beam computed tomography data from 60 patients with skeletal Class III malocclusion were used. There were 30 patients in both the symmetrical group (menton deviation <2 mm) and the asymmetrical group (menton deviation >4 mm). After reconstruction of 3-dimensional (3D) cone-beam computed tomography data, maxillary yaw and 3D positions of skeletal and dental landmarks were measured and compared between the groups. After that, correlations between menton deviation and the other variables were assessed.

## Results

No significant difference was noted in maxillary skeletal and dental yaw between the 2 groups. In the assessment of 3D positions, translation of the maxillary bone and maxillary dentition toward the menton deviation was observed ( *P* <0.01). Maxillary skeletal and dental yaw was not significantly correlated with menton deviation in the asymmetrical group.

## Conclusions

Maxillary skeletal and dental yaw was not evident in either group. Therefore, when planning maxillary surgery for patients with skeletal Class III facial asymmetry malocclusion, it may be appropriate to shift the focus of decompensation from maxillary yaw to maxillary translation.

## Highlights

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We evaluated maxillary skeletal and dental yaw in patients with skeletal Class III facial asymmetry.

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No significant difference was noted in yaw between symmetrical and asymmetrical groups.

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No significant correlation was observed between maxillary yaw and menton deviation.

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Translation of the maxillary bone and dentition toward the menton deviation was observed.

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When planning surgery, decompensation needs to be focused on maxillary translation instead of yaw.

Approximately 40%-80% of patients with skeletal Class III malocclusion exhibit facial asymmetry. Orthognathic surgery is essential for such patients to restore both masticatory function and appearance. ^{,} Orthognathic surgery is the process of positioning the maxilla and mandible to their proper positions according to the 6 degrees of freedom. Therefore, to establish an appropriate surgical plan, it is crucial to preoperatively assess the deviation of each skeletal unit, considering the 6 degrees of freedom.

Among the 6 degrees of freedom, yaw is defined as the rotation of a skeletal unit around the vertical axis. Yaw can affect both the maxilla and mandible, and it causes asymmetry of the affected skeletal unit. For instance, maxillary yaw has been considered a possible cause of midline deviation and asymmetrical Angle classification of the molars. ^{,}

To address such maxillary asymmetry, maxillary yaw correction has been suggested. The purposes of maxillary yaw correction are to resolve midline deviation and position the maxillary molars symmetrically with respect to the midsagittal plane to reposition the mandible appropriately. ^{,} ^{,} Although the approach mainly focuses on resolving maxillary dental asymmetry, this is a currently accepted protocol for maxillary bone surgery.

However, asymmetry of the bone and dentition, while related, are separate issues in terms of management strategies. Although asymmetry of the bone is treated by orthognathic surgery, asymmetry of the dentition must be resolved by orthodontic treatment. Because these management approaches are different, it is mandatory to clearly distinguish these 2 problems before treatment. Nevertheless, most reports on maxillary yaw to date have generally measured maxillary dental yaw and have described it simply as maxillary yaw without a strict differentiation between dental and skeletal yaw. ^{,} ^{,} ^{,}

In addition, Proffit et al suggested that, while yaw of the maxillary dentition may be present in compensation for the rotated mandible, skeletal yaw of the maxilla is rare. This became the basis for rotational decompensation of the maxillary dentition, being one of the main focuses during presurgical orthodontics. However, most studies on dental compensation have mainly addressed axial and vertical aspects of the compensation. To date, few studies have provided meaningful statistics on rotational compensation of the skeletal maxilla and the dentition, respectively.

This cone-beam computed tomography (CBCT) study aimed to compare maxillary skeletal and dental yaw between patients classified with either asymmetrical or symmetrical skeletal Class III and analyze the correlation between menton deviation and skeletal and dental yaw. The null hypothesis was that there is no significant difference in maxillary skeletal and dental yaws between the 2 groups.

## Material and methods

A power analysis using G∗Power software (version 3.1.9.4; Franz Faul, Christan-Albrechts-University, Kiel, Germany) was performed to determine the sample size. The effect size was 0.83 with a mean difference of 1.0 and standard deviation of 1.2, which were based on previous reports with similar measures. ^{,} With a 2-sided significance level of 0.05, a test power of 0.85, and a sample allocation ratio between groups of 1:1, the minimum sample size was calculated to 27 for each group. Considering the central limit theorem in statistics and the result of the power analysis, the sample size of 30 patients for each group, was justified.

The samples for this study were collected from South Korean patients with skeletal Class III facial asymmetry who visited the Department of Orthodontics at Kyungpook National University Dental Hospital for surgical-orthodontic treatment between 2012 and 2017. The inclusion criteria were: ANB ≤0.0, no malformed teeth, no supernumerary or missing teeth, no prosthetic crowns, no congenital systemic disease, no history of previous orthodontic treatment, and symmetrically distributed crowding or spacing <3 mm. These patients were assigned to the symmetrical group if they had menton deviation <2 mm from the skeletal midline and the asymmetrical group if they had menton deviation >4 mm. Patients who had a menton deviation of 2-4 mm were excluded from the study. Data from 60 patients (30 patients in each group) were used in the final analysis. The sample characteristics and distributions are summarized in Tables I and II . This study was approved by the Kyungpook National University Dental Hospital Institutional Review Board (KNUDH-2018-08-014).

Group | Symmetrical | Asymmetrical | P value |
---|---|---|---|

n | 30 | 30 | – |

Age (y) | 20.40 ± 2.01 | 20.73 ± 2.79 | 0.598 |

MP-SN (°) | 35.38 ± 5.74 | 35.15 ± 6.51 | 0.887 |

SNA (°) | 81.55 ± 3.62 | 82.45 ± 2.86 | 0.290 |

SNB (°) | 85.29 ± 4.24 | 86.25 ± 3.39 | 0.340 |

ANB (°) | −3.74 ± 2.36 | −3.79 ± 2.28 | 0.848 |

Wits appraisal (mm) | −12.57 ± 4.16 | −12.17 ± 3.97 | 0.473 |

Menton deviation (mm) | 0.97 ± 0.53 | 7.59 ± 3.09 | <0.001 ^{∗ } |

Groups | Symmetry | Asymmetry | P value |
---|---|---|---|

Gender | 0.017 ^{∗ } |
||

Male | 23 | 14 | |

Female | 7 | 16 | |

AP | 0.282 | ||

Maxillary deficiency | 3 | 1 | |

Mandibular prognathism | 21 | 26 | |

Combination type | 6 | 3 | |

Vertical | 0.962 | ||

Normal angle | 12 | 11 | |

High angle | 14 | 15 | |

Low angle | 4 | 4 |

We used CBCT data taken in habitual occlusion for diagnostic purposes at the initial consultation. The CBCT scanner (CB MercuRay; Hitachi, Osaka, Japan) had the following settings: 15 mA, 120 kV, exposure time of 9.6 seconds, voxel size of 0.2 mm, axial slice thickness of 0.38 mm, and scanning area of 19.3 × 19.3 cm, and the imaging results were converted to the digital imaging and communication in medicine (DICOM) format. These DICOM files were reconstructed in 3-dimensions using InVivo Dental software (version 5.2; Anatomage, San Jose, Calif) before the data were analyzed.

The 3-dimensional (3D) analysis land marks are defined in Table III ( Fig 1 ). To reduce errors from the head position, the 3D models were reoriented by defining reference planes ( Fig 2 ; Table IV ). ^{,} The origin of the coordinate system was set to the nasion. The x-axis, y-axis, and z-axis were defined as the axes orthogonal to the midsagittal plane, frontal plane, and Frankfort Horizontal (FH) plane, respectively. The positive values of each axis were set, respectively, as the left, posterior, and superior sides of the patient.

Landmark | Definition |
---|---|

N | The most superior point of the frontonasal suture |

Or_R | The most inferior point of the bony orbit |

Po_R | The most superior point of the external auditory meatus |

FZP_R, L | The intersection point of the frontozygomatic suture and the margin of the bony orbit |

Mx_R, L | The most concave point on the contour of maxilla around molars and lower contour of zygomaticomaxillary process |

Mx_mid | The midpoint of Mx_R and Mx_L |

ANS | The tip of the anterior nasal spine |

Me | The most inferior point of the symphysis of the mandible |

Go_R, L | The midpoint of the bony border of the mandibular angle |

Go_mid | The midpoint of Go_R and Go_L |

UR1 | The midpoint of the incisor edge of the maxillary right incisor |

UL1 | The midpoint of the incisor edge of the maxillary left incisor |

U1_mid | The midpoint between UR1 and UL1 |

UR3 | The cusp tip of the maxillary right canine |

UL3 | The cusp tip of the maxillary left canine |

U3_mid | The midpoint between UR3 and UL3 |

UR6 | The mesiobuccal cusp tip of the maxillary right first molar |

UL6 | The mesiobuccal cusp tip of the maxillary left first molar |

U6_mid | The midpoint between UR6 and UL6 |

LR1 | The midpoint of the incisor edge of the mandibular right incisor |

LL1 | The midpoint of the incisor edge of the mandibular left incisor |

L1_mid | The midpoint between LR1 and LL1 |

LR3 | The cusp tip of the mandibular right canine |

LL3 | The cusp tip of the mandibular left canine |

L3_mid | The midpoint of LR3 and LL3 |

LR6 | The mesiobuccal cusp tip of the mandibular right first molar |

LL6 | The mesiobuccal cusp tip of the mandibular left first molar |

L6_mid | The midpoint between LR6 and LL6 |

Reference planes | Definition |
---|---|

Midsagittal plane | The plane passing through N, perpendicular to the line between FZP_R and FZP_L |

FH plane | The plane perpendicular to the midsagittal plane, containing both Po_R and Or_R |

Frontal plane | The plane passing through N, perpendicular to both midsagittal and FH plane |

The variables used in the analysis are defined in Table V . To measure yaw, we referred to a previous study. ^{,} The yaw of the bone and dentition of the maxilla and mandible were measured separately ( Fig 3 ). In addition, the dental yaw was measured separately for the anterior and posterior teeth. The yaw was assigned a positive sign when it was observed in the same direction as the menton deviation. To assess the 3D position of the maxillary bone and dentition, the anteroposterior (AP), transverse, and vertical positions were measured ( Fig 4 ). The AP position was measured as the distance of the landmark from the frontal plane. The position was assigned a positive sign if it was located posteriorly to the frontal plane. The transverse and vertical positions were measured as the distances of the landmarks from the midsagittal plane and FH plane, respectively. However, the transverse positions of the maxillary incisor and ANS were assigned a positive value if they were deviated in the same direction as the menton. Angular measurements were taken to the nearest 0.01°, and linear measurements to the nearest 0.01 mm. All measurements were taken by a single operator (H.K.N).

Variables | Definition |
---|---|

Yaw | |

Maxillary skeletal yaw | The angle between the midsagittal plane and a line, projected onto the FH plane, connecting ANS and Mx_mid |

Maxillary dental anterior yaw | The angle between the midsagittal plane and a line, projected onto the FH plane, connecting U1_mid and U3_mid |

Maxillary dental posterior yaw | The angle between the midsagittal plane and a line, projected onto the FH plane, connecting U1_mid and U6_mid |

Mandibular skeletal yaw | The angle between the midsagittal plane and a line, projected onto the FH plane, connecting Me and Go_mid |

Mandibular dental anterior yaw | The angle between the midsagittal plane and a line, projected onto the FH plane, connecting L1_mid and L3_mid |

Mandibular dental posterior yaw | The angle between the midsagittal plane and a line, projected onto the FH plane, connecting L1_mid and L6_mid |

AP position | |

ANS | The distance from frontal plane to ANS |

Mx DEV | The distance from frontal plane to Mx point on the deviated side |

Mx NDEV | The distance from frontal plane to Mx point on the nondeviated side |

Mx DEV-NDEV | The value obtained by subtracting the AP position of Mx on the nondeviated side from that on the deviated side |

U1 | The distance from frontal plane to U1_mid |

U3 DEV | The distance from frontal plane to the cusp tip of the maxillary canine on the deviated side |

U3 NDEV | The distance from frontal plane to the cusp tip of the maxillary canine on the nondeviated side |

U3 DEV-NDEV | The value obtained by subtracting the AP position of the cusp tip of the maxillary canine on the nondeviated side from that on the deviated side |

U6 DEV | The distance from frontal plane to the mesiobuccal cusp tip of the maxillary first molar on the deviated side |

U6 NDEV | The distance from frontal plane to the mesiobuccal cusp tip of the maxillary first molar on the nondeviated side |

U6 DEV-NDEV | The value obtained by subtracting the AP position of the mesiobuccal cusp tip of the maxillary first molar on the nondeviated side from that on the deviated side |

Transverse position | |

ANS | The distance from midsagittal plane to ANS |

Mx DEV | The distance from midsagittal plane to Mx point on the deviated side |

Mx NDEV | The distance from midsagittal plane to Mx point on the nondeviated side |

Mx DEV-NDEV | The value obtained by subtracting the transverse position of Mx point on the nondeviated side from that on the deviated side |

U1 | The distance from midsagittal plane to U1_mid |

U3 DEV | The distance from midsagittal plane to the cusp tip of the maxillary canine on the deviated side |

U3 NDEV | The distance from midsagittal plane to the cusp tip of the maxillary canine on the nondeviated side |

U3 DEV-NDEV | The value obtained by subtracting the transverse position of the cusp tip of the maxillary canine on the nondeviated side from that on the deviated side |

U6 DEV | The distance from midsagittal plane to the mesiobuccal cusp tip of the maxillary first molar on the deviated side |

U6 NDEV | The distance from midsagittal plane to the mesiobuccal cusp tip of the maxillary first molar on the nondeviated side |

U6 DEV-NDEV | The value obtained by subtracting the transverse position of the mesiobuccal cusp tip of the maxillary first molar on the nondeviated side from that on the deviated side |

Vertical position | |

ANS | The distance from FH plane to ANS |

Mx DEV | The distance from FH plane to Mx point on the deviated side |

Mx NDEV | The distance from FH plane to Mx point on the nondeviated side |

Mx NDEV-DEV | The value obtained by subtracting the vertical position of Mx point on the deviated side from that on the nondeviated side |

U1 | The distance from FH plane to U1_mid |

U3 DEV | The distance from FH plane to the cusp tip of the maxillary canine on the deviated side |

U3 NDEV | The distance from FH plane to the cusp tip of the maxillary canine on the nondeviated side |

U3 NDEV-DEV | The value obtained by subtracting the vertical position of the cusp tip of the maxillary canine on the deviated side from that on the nondeviated side |

U6 DEV | The distance from FH plane to the mesiobuccal cusp tip of the maxillary first molar on the deviated side |

U6 NDEV | The distance from FH plane to the mesiobuccal cusp tip of the maxillary first molar on the nondeviated side |

U6 NDEV-DEV | The value obtained by subtracting the vertical position of the mesiobuccal cusp tip of the maxillary first molar on the deviated side from that on the nondeviated side |

## Statistical analysis

A chi-square test was used to analyze gender distribution between the groups. To test normality, the Shapiro-Wilk test was used. For normally distributed variables, independent *t* tests and paired *t* tests were used for between-group and within-group comparisons. Similarly, Mann-Whitney U tests and Wilcoxon signed rank sum tests were used for nonnormally distributed variables. The Pearson correlation coefficient was calculated to evaluate the correlation between menton deviation and the other variables in each group. The bias-corrected and accelerated bootstrap 95% confidence intervals were also presented along with the *P* values for correlation.

To test reliability, 30 of the 60 patients were randomly selected for repeat measurements by the same operator at a 4-week interval. The original and repeat measurements were compared using intraclass correlation coefficients. The method error was calculated using Dahlberg’s formula.

All statistical tests were evaluated at a significance level of 5% and performed using SPSS software (version 20.0; IBM Corp, Armonk, NY).

## Results

The mean intraclass correlation coefficient was 0.966 (minimum, 0.875; maximum, 0.996), indicating a high correlation. The mean method error for angular measurements was 0.91° (minimum, 0.31°; maximum, 1.98°) and 0.66 mm for linear measurements (minimum, 0.21 mm; maximum, 1.24 mm). The repeated measurements showed high reproducibility, and the original data were used for all subsequent statistical analyses.

The comparison of mean yaw in the maxilla and mandible between the symmetrical and asymmetrical groups is summarized in Table VI . No statistical differences were noted between the groups for maxillary skeletal yaw, maxillary dental anterior yaw, and maxillary dental posterior yaw. However, the mandibular skeletal yaw ( *P* <0.001), mandibular dental anterior yaw ( *P* <0.01), and mandibular dental posterior yaw ( *P* <0.001) all had significant differences between the 2 groups.