Classification and characterization of facial asymmetry in adult patients with skeletal Class III malocclusion using cluster analysis

Introduction

This study aimed to analyze the comprehensive maxillofacial features of patients with skeletal Class III malocclusion and facial asymmetry to develop a classification system for diagnosis and surgical planning.

Methods

A total of 161 adult patients were included, with 121 patients in the asymmetry group (menton deviation >2 mm) and 40 patients in the symmetry group (menton deviation ≤2 mm). Twenty-eight variables were determined, including transverse translation, roll and yaw of each facial unit, transverse width, mandibular morphology, and transverse dental compensation. Principal component (PC) analysis was conducted to extract PCs, and cluster analysis was performed using these components to classify the asymmetry group. A decision tree was constructed on the basis of the clustering results.

Results

Six PCs were extracted, explaining 80.622% of the data variability. The asymmetry group was classified into 4 subgroups: (1) atypical type (15.7%) showed an opposite roll direction of maxillary dentition than of menton deviation; (2) compound type (34.71%) demonstrated significant ramus height differences, maxillary roll, and mandibular roll and yaw; (3) mandibular yaw type (44.63%) showed slight mandibular yaw without mandibular morphology asymmetry; and (4) maxillary-shift type (4.96%) shared similarities with the compound type but showed significant maxillary translation. The classification and regression tree model achieved a prediction accuracy of up to 85.11%.

Conclusions

This study identified 4 distinct phenotypes using cluster analysis and proposed tailored treatment recommendations on the basis of their specific characteristics. The classification results emphasized the importance of spatial displacement features, especially mandibular yaw, in diagnosing facial asymmetry. The established classification and regression tree model enables clinicians to identify patients conveniently.

Highlights

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We proposed a new classification based on comprehensive features of facial asymmetry.
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The clustering-based decision tree model could accurately predict classification.
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Mandibular yaw played a significant role in the diagnosis of facial asymmetry.
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Personalized treatment strategies were proposed based on the classification outcomes.

Facial asymmetry is characterized by a discordant relationship among the size, shape, and arrangement of facial features on either side of the median sagittal plane. There is a significant association between the sagittal skeletal pattern and the incidence of facial asymmetry. According to previous reports, approximately 48% of Asian patients with skeletal Class III malocclusion exhibit facial asymmetry.

Several facial asymmetry classifications have been proposed. Obwegeser and Makek categorized mandibular hemiplegia into hemimandibular elongation and hemimandibular hyperplasia. Hwang et al divided orthodontic patients into 5 groups on the basis of 3 variables of frontal cephalograms. Maeda et al divided patients into 3 groups by calculating the asymmetry indexes of the maxilla, mandibular ramus, and mandibular body. However, most studies were based on 2-dimensional images or focused solely on the asymmetry pattern of the mandible, and some studies only described the degree of asymmetry without addressing the direction, thus overlooking patients in which facial units move in opposite directions. Consequently, they did not provide the necessary information for surgical planning.

Baek et al proposed that objective classification of facial asymmetry on the basis of recognizable patient-specific features is necessary for diagnosis and surgical planning. They employed cone-beam computed tomography (CBCT) to capture patients’ skeletal features and conducted a cluster analysis, which led to the division of patients with facial asymmetry into 4 distinct groups. However, 1 limitation of their study was the omission of considering the spatial rotational features of facial units. In 2007, Ackerman et al expanded the spatial characteristics of commonly used clinical planar terms (anteroposterior, transverse, and vertical) by introducing 3 eronautic rotational descriptors: roll, yaw, and pitch. Kim et al used this description method to establish a classification system. They divided facial asymmetry into 4 types: rolling-dominant, translation-dominant, yawing-dominant, and atypical. However, the classification by Kim et al did not provide statistical evidence or criteria. Chen et al divided patients with facial asymmetry into 3 groups on the basis of menton deviation direction and magnitude relative to ramus asymmetry; however, their classification did not provide statistical evidence. Ha et al conducted a study analyzing the skeletal features using CBCT. They used mandibular yaw, maxillary cant, and menton deviation as indicators to perform cluster analysis in patients with facial asymmetry; however, the indicators were relatively limited.

Asymmetry is a complex condition that affects various aspects of the maxillofacial units. In terms of hard tissue, facial asymmetry is primarily characterized by the morphologic asymmetry of maxillofacial units, positional asymmetry of maxillofacial units, ^, ^, and transverse dentition compensation. Positional asymmetry typically manifests in the forms of transverse translation, roll rotation, and yaw rotation. ^, Currently, a few studies have classified asymmetry on the basis of comprehensive maxillofacial characteristics. Principal component analysis (PCA) is a mathematical algorithm commonly used in data analysis to reduce the dimensionality of data while retaining most of its variability. When combined with cluster analysis, PCA can reduce the correlation between variables and yield new independent components, which helps to reduce the impact of noisy variables on the cluster structure. Previous studies have demonstrated the effectiveness of incorporating PCA as a preprocessing step in cluster analysis. ^,

Thus, this study aimed to analyze the maxillofacial features of patients with skeletal Class III malocclusion and facial asymmetry using CBCT, apply PCA for feature extraction, and use the resulting components for cluster analysis to develop a classification system for diagnosis and surgical planning guidance.

Material and methods

We focused on patients with skeletal Class III malocclusion to exclude the influence of different sagittal skeletal patterns on maxillofacial characteristics. Patients with skeletal Class III malocclusion who were treated in the Orthodontic Department of Shandong University between 2017-2022 were selected for this study. The inclusion criteria were as follows: (1) cervical bone age at cervical stage 5 or 6, (2) ANB angle <0°, (3) availability of complete CBCT data before treatment, (4) no supernumerary or missing teeth, (5) no history of congenital or acquired diseases affecting facial symmetry, and (6) no history of orthodontic treatment. Patients with a menton deviation >2 mm were included in the asymmetry group, whereas those with a menton deviation <2 mm were included in the symmetry group, in which the face was mostly symmetrical. A total of 161 patients were included in this study, with 121 patients in the asymmetry group (47 males and 74 females, aged 21.21 ± 3.84 years) and 40 in the symmetry group (15 males and 25 females, aged 20.90 ± 3.59 years). This study was approved by the Shandong University School of Stomatology Ethics Association (no. 20230373) and was conducted in accordance with the Declaration of Helsinki. Informed consent was obtained from all the patients.

All patients underwent CBCT (NewTom 5G, Verona, Italy; settings: 5 mA, 110 kV; voxel size: 0.3 mm; axial slice thickness: 0.3 mm; exposure time: 9.6 seconds) before orthodontic treatment. The same experienced physician performed a CBCT machine. The patients were instructed to remain calm and maintain maximum occlusal contact without swallowing throughout the scanning process. The CBCT data of the patients were exported in digital imaging and communications in medicine format and imported into the Mimics software (version 17.0; Materialise, Leuven, Belgium) for 3-dimensional (3D) reconstruction.

Table I lists the landmarks used to obtain the measurements. In this study, we established a reference plane to reorient the 3D model ( Fig 1 , A ; Table Ⅰ ). The sagittal plane based on 3 midline landmarks of the cranial base may underestimate the degree of menton deviation when there is facial asymmetry. However, the midsagittal plane based on the nasion and sella, perpendicular to the Frankfurt horizontal plane, has been found to have less error in evaluating menton deviation and yaw displacement. Therefore, we used the latter as the reference plane. Distinguishing between skeletal and dental asymmetries is essential because they require different treatment approaches. Therefore, we defined separate reference planes for the maxilla, maxillary dentition, mandible, and mandibular dentition, according to previous studies ( Fig 1 , B-D ; Table Ⅰ ). ^,

Table I

Definition of landmarks and reference planes

Variables	Abbreviation	Definition
Landmarks
Nasion	N	Most superior point of the frontonasal suture
Basion	Ba	Midpoint of the anterior edge of foramen magnum
Porion (R, L)	Po	Most superior point of the external auditory meatus
Orbitale (R, L)	Or	Most inferior point of the lower margin of the orbit
Maxillary point (R, L)	Mx	Most concave point on the intersection of the alveolar process and lower contour of the zygomatic process
Midpoint of maxillary point	Mx-mid	Midpoint of bilateral maxillary point
Upper width point of Penn’s analysis (R, L)	Uw	The buccal cortex at the level of the buccal root apex of U6
Anterior nasal spine	ANS	Tip of the anterior nasal spine
Maxillary incisor (R, L)	U1	Midpoint of the incisor edge of maxillary incisors
Midpoint of maxillary incisor	U1-mid	Midpoint of bilateral U1
Maxillary canine (R, L)	U3	The cusp tip of the maxillary canine
Maxillary canine apex (R, L)	U3A	The root apex of maxillary canine
Maxillary molar (R, L)	U6	The central fossa on maxillary first molar occlusal surface
Root furcation of maxillary molar (R, L)	U6F	The centers of the root furcation point of the maxillary first molar
Midpoint of maxillary molar	U6-mid	Midpoint of bilateral U1
Gonion (R, L)	Go	The midpoint of the outline of the angle of the mandible
Midpoint of gonion	Go-mid	Midpoint of bilateral Go
Sigmoid notch (R, L)	SN	The most concave point of the sigmoid notch
Ramus points (R, L)	Rmp	The point of intersection between the plane parallel to the FH plane and passing through the SN point and the outermost edge of the ascending ramus contour
Menton	Me	The most inferior point of symphysis of the mandible
Condylion (R, L)	Co	The most superior point of the condyle
Lower width point of Penn’s analysis (R, L)	Lw	Buccal cortex at the level of the center of resistance of mandibular first molar
Mental foramen (R, L)	MtF	Most inferior point of the mental foramen
Mandibular foramen (R, L)	MdF	Most inferior point of mandibular foramen
Mandibular incisor (R, L)	L1	Midpoint of the incisor edge of mandibular incisors
Midpoint of mandibular incisor	L1-mid	Midpoint of bilateral L1
Mandibular canine (R, L)	L3	The cusp tip of mandibular canine
Mandibular canine apex (R, L)	L3	The root apex of mandibular canine
Mandibular molar (R,L)	L6	The central fossa on mandibular first molar occlusal surface
Midpoint of mandibular molar	L6-mid	Midpoint of bilateral L6
Root furcation of mandibular molar (R, L)	L6	The center of root furcation points of mandibular first molar
Planes
Midsagittal plane	MSP	A plane passing through the Ba and N, perpendicular to the FHP
Frankfort horizontal plane	FHP	A plane passing through bilateral Or and right Po
Coronal plane	CP	A plane passing through Ba, perpendicular to the FHP and MSP
Maxillary sagittal plane	MxSP	A plane passing through Mx-mid and ANS, perpendicular to the MxHP
Maxillary horizontal plane	MxHP	A plane passing through bilateral Mx and ANS
Maxillary coronal plane	MxCP	A plane passing through Mx-mid, perpendicular to Mx-SP and MxHP
Maxillary dentition sagittal plane	MxdSP	A plane passing through U1-mid and U6-mid, perpendicular to the MxdHP
Maxillary dentition horizontal plane	MxdHP	A plane passing through U1-mid and bilateral U6
Maxillary dentition coronal plane	MxdCP	A plane passing through U6-mid, perpendicular to MxdSP and MxdHP
Mandibular sagittal plane	MnSP	A plane passing through Go-mid and Me, perpendicular to the MnHP
Mandibular horizontal plane	MnHP	A plane passing through Me and bilateral Go
Mandibular coronal plane	MnCP	A plane passing through Go-mid, perpendicular to MnHP and MnSP
Mandibular dentition sagittal plane	MndSP	A plane passing through L1-mid and L6-mid, perpendicular to MndHP
Mandibular dentition horizontal plane	MndHP	A plane passing through L1-mid and bilateral L6
Mandibular dentition coronal plane	MndCP	A plane passing through L6-mid, perpendicular to MndSP and MndHP

R , right; L , left.

Table II shows the variables analyzed, including transverse translation, roll, and yaw of the facial units; mandibular ramus height and body length; frontal ramus inclination; compensatory inclinations of the maxillary and mandibular molars and canines; and the difference in transverse width between the maxilla and mandible ( Fig 2 ). The craniofacial sagittal plane previously used for measuring transverse dental compensation is no longer applicable because of changes in the position of the jaw during surgery. Instead, the dental inclination should be assessed relative to the basal bone. In this study, the transverse dental inclination was determined on the basis of the maxillary horizontal plane and mandibular horizontal plane ( Fig 2 , D ). The transverse width differences were measured and evaluated using Yonsei transverse analysis and the University of Pennsylvania CBCT analysis ( Fig 2 , F-G ). All measurements were performed by the same operator who was familiar with the Mimics software.

Table II

Description of variables

Variables	Abbreviation	Description
Yaw
Maxillary yaw	Mx-yaw	The angle between the projection lines of MSP and Mx-SP on FHP
Maxillary dentition yaw	Mxd-yaw	The angle between the projection lines of MSP and MxdSP on FHP
Mandibular yaw	Mn-yaw	The angle between the projection lines of MSP and MnSP on FHP
Mandibular dentition yaw	Mnd-yaw	The angle between the projection lines of MSP and MndSP on FHP
Roll
Angulation
Maxillary roll	Mx-roll	The angle between the projection lines of FH and Mx-SP on CP
Maxillary dentition roll	Mxd-roll	The angle between the projection lines of FH and MxdSP on CP
Mandibular roll	Mn-roll	The angle between the projection lines of FH and MnSP on CP
Mandibular dentition roll	Mnd-roll	The angle between the projection lines of FH and MndSP on CP
Distance
Maxillary roll	Mx-FH D-ND	The value calculated by subtracting the distance from Mx to FHP on D from that on ND
Maxillary dentition roll	U6F-FH D-ND	The value calculated by subtracting the distance from U6F to FHP on D from that on ND
Mandibular anterior roll	MtF-FH D-ND	The value calculated by subtracting the distance from MtF to FHP on D from that on ND
Mandibular roll	MdF-FH D-ND	The value calculated by subtracting the distance from MdF to FHP on D from that on ND
Mandibular dentition roll	L6F-FH D-ND	The value calculated by subtracting the distance from L6F to FHP on D from that on ND
Transverse translation
Maxillary translation	Mx-MSP D-ND	The value calculated by subtracting the distance from Mx to MSP on D from that on ND
Maxillary dentition translation	U6F-MSP D-ND	The value calculated by subtracting the distance from U6 to MSP on D from that on ND
Menton deviation	Me-SP	The distance between Me and MSP
Mandibular anterior translation	MtF-MSP D-ND	The value calculated by subtracting the distance from MtF to MSP on D from that on ND
Mandibular translation	MdF-MSP D-ND	The value calculated by subtracting the distance from MdF to MSP on D from that on ND
Mandibular dentition translation	L6F-MSP D-ND	The value calculated by subtracting the distance from L6 to MSP on D from that on ND
Dental compensation
Mandibular canine transverse compensation	L3-MnSP D-ND	The line connecting L3 and L3A represents the long axis of the mandibular canines. The difference value between the bilateral acute angle formed by the MnSP and the projection of canine long axes onto MnCP is calculated
Mandibular molar transverse compensation	L6-MnSP D-ND	The line connecting L6 and L6F represents the long axis of the mandibular molars. The difference value between the bilateral acute angle formed by the MnSP and the projection of molar long axes onto MnCP is calculated
Maxillary canine transverse compensation	U3-Mx-SP D-ND	The line connecting U3 and U3A represents the long axis of the maxillary canines. The difference value between the bilateral acute angle formed by the Mx-SP and the projection of canine long axes onto MxCP is calculated
Maxillary molar transverse compensation	U6-Mx-SP D-ND	The line connecting U6 and U6F represents the long axis of the maxillary molars. The difference value between the bilateral acute angle formed by the Mx-SP and the projection of molar long axes onto MxCP is calculated
Mandibular body
Frontal ramus inclination	FRA D-ND	The difference between the internal inferior angle formed by the projection of the bilateral Rmn-Go line onto the coronal plane and the horizontal plane
Ramus height	Co-Go D-ND	The value calculated by subtracting the distance from Co to Go on D from that on ND
Mandibular body length	Go-Me D-ND	The value calculated by subtracting the distance from Me to Go on D from that on ND
Width
Yonsei’s analysis	YTI’width	The distance between the maxillary bilateral U6F subtracted by the distance between the mandibular bilateral L6F
Penn’s analysis	Penn’width	The distance between the maxillary bilateral Uw subtracted by the distance between the mandibular bilateral Lw

D, deviated side; ND , nondeviated side.

Statistical analysis

PCA was conducted on 18 important variables (Me-SP, Mn-yaw, Mnd-yaw, Mx-yaw, Mxd-yaw, Mx-SP D-ND, Mx-FH D-ND, U6F-MSP D-ND, U6F-FH D-ND, Co-Go D-ND, Go-Me D-ND, MtF-MSP D-ND, MtF-FH D-ND, MdF-MSP D-ND, MdF-FH D-ND, L6F-MSP D-ND, L6F-FH D-ND, and FRA D-ND) that affected asymmetry characteristics in the asymmetry group. The Kaiser-Meyer-Olkin test and Bartlett’s test of sphericity were employed to examine the suitability of the data for PCA. The Kolmogorov-Smirnov test was used to evaluate whether the data followed a Gaussian distribution. Before performing PCA, the variables were standardized by subtracting the mean and scaling them to obtain a unit variance. The varimax method was employed to obtain a rotated component matrix to assess the principal components (PCs) derived from PCA. Subsequently, we identified the main explanatory variables for each PC by selecting factor loadings that exceeded 0.5. PCs with a cumulative variance >80% were used as indicators for K-means clustering analysis. K-means clustering analysis was performed separately for the range 2-5. One-way analysis of variance, the Kruskal-Wallis H test, the least significant difference post-hoc test, and Bonferroni correction were used to compare all measured variables and determine the main differences among each cluster group and symmetry group.

Forty of the 161 patients were randomly selected, and repeated measurements were taken every 2 weeks by the same operator (L.L.Z.) to determine the intrarater reliability of the examiner. The within-group correlation coefficient was used to compare 2 sets of measurement values. The method error was calculated using the Dahlberg formula. All analyses were performed using SPSS (version 21.0; IBM, Armonk, NY), and a 95% confidence level was considered statistically significant ( P < 0.05).

A decision tree model was built using the 18 important independent variables and the category of each sample as the dependent variable using the method of minimizing the Gini coefficient. The maximum depth of the tree was set to 5, the minimum number of patients for parent nodes was set to 2, and the minimum number of patients for child nodes was set to 5. All samples were split into training and validation sets at a 70:30 ratio. The classification and regression tree (CART) algorithm was used to construct a classification decision tree model.

Results

The intraclass correlation coefficients for all measurements ranged 0.91-0.95, indicating sufficient reliability. The linear measurement error ranged 0.14-0.20 mm, and the angular measurement error ranged 0.11°-0.15°. All statistical analyses used the initial measurement data.

According to the Kolmogorov-Smirnov test, the data had a Gaussian distribution. The Kaiser-Meyer-Olkin test statistic (0.771) and Bartlett’s sphericity test ( P <0.001) indicated that the data were suitable for PCA. Six PCs, explaining 80.622% of the data variability, were extracted. Table III shows the variance and constituent variables explained for each PC: (1) PC1 contributed to the most data variation (30.437%) and mainly included the transverse shift of the facial units and maxillary roll; (2) PC2 explained 19.488% of the variation and mainly included the roll of the maxillary dentition, mandible, and mandibular dentition; (3) PC3 represented the yaw of the mandible and mandibular dentition, explaining 11.432% of the variation; (4) PC4 represented the yaw of the maxilla and maxillary dentition (8.864%); (5) PC5 represented the ramus height and body length (6.27%); and (6) PC6 represented the frontal ramus inclination (4.13%).

Table III

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