Patients and methods
The present study on mandibular deviation focused on only patients with mandibular prognathism. They were not classified using Me deviation on frontal cephalograms, though previous studies have tried to use to quantify jaw deviation [
10]. The mandibular deviation has been observed as an asymmetry of not only Me but also the gonial regions [
15], so that we attempted to quantify jaw deviation in patients with mandibular prognathism from the two perspectives of mandibular morphology and condylar position relative to the skull base. As a result, our study would enable depiction of features of jaw deviation that have not been considered to date and greatly contribute to the quantification of jaw deviation.
Setting the mid-sagittal reference plane is extremely important when performing 3D evaluation of jaw deviation and it is essential to set anatomical reference points that are as unaffected by jaw deviation as possible in order to ensure appropriate evaluation [
16]. Thiesen et al. noted that the mid-sagittal reference plane should a clinically feasible and highly reproducible reference line [
12]. Taking this into account, we looked for reference points that were as unaffected by jaw deviation as possible, easy to establish, and highly reproducible. In this study, for the mid-sagittal reference plane, we selected the plane perpendicular to the FH plane and passing through both N and Ba. N and Ba are both located on the midline and are some distance from the measurement points, so they are the least affected by jaw deviation. We also considered the possibility that FH may be affected by jaw deviation. However, FH is frequently used in clinical situation. For example, during evaluation of the face, we usually utilize images in which the FH plane is parallel to the floor. Therefore, we decided to adopt it as one of the reference planes in this study. Although the anterior nasal spine (ANS) was used as a reference point in previous report [
17], considering possible deviation of the maxilla also occur, we used no maxillary reference points when setting any of the reference planes and instead opted for measurement points on stable structures close to the cerebral cranium.
In the present study, only linear measurements were used and the differences between measurement values on the left and the right were analyzed in order to evaluate deviation properties. The reason for this is that the classification of characteristics would become more complicated if both linear and angular measurements were included in the measurement items, which would make it more difficult to capture the features of the deviation.
Jaw deviation and cluster analysis
Numerous studies to date have focused on the composition of deviation [
9‐
11,
18,
19], although the deviation features are complicated and there is enormous variation, so this issue has not yet been adequately clarified. In the present study, we focused on mandibular morphology and condylar position relative to the skull base. We then used cluster analysis to simplify the complicated features and attempted to quantify and classify jaw deviation. Cluster analysis [
13] is a method that facilitates division of various types of data into populations based on objective numerical standards, so we believe it is suited to the classification of complex jaw deviation. A few previous studies have classified the characteristics of maxillofacial morphology using cluster analysis. Hwang et al. used frontal cephalograms and performed cluster analysis to classify 100 patients diagnosed with facial asymmetry into five groups that exhibited definite characteristics [
18]. Meanwhile, Baek et al. used 3D CT images to perform cluster analysis of 43 patients diagnosed with facial asymmetry and reported that they could be classified into four groups [
11]. However, one of the four groups obtained by Baek et al. included only two individuals, suggesting that the classification may not have been statistically reliable. For this reason, in the present study, we set a sample size of 100 patients in order to avoid any issues in achieving accurate classification due to a small sample size after cluster analysis.
The branch points on the dendrogram obtained by cluster analysis were based on the squared Euclidean distance. The closer the branch points were on the dendrogram, the greater the similarity between arbitrary clusters, while greater distances between branch points indicated lower similarity. In other words, the shorter the long axis of the dendrogram, the higher the intercluster similarity becomes. As a result, when selecting the transection site on the dendrogram to divide subjects into groups, it is advisable to ensure that the squared Euclidean distance is adequately long, and that the number of clusters ensures that each cluster has distinct characteristics. When we created the dendrogram for the mandibular morphology items in this study, a squared Euclidean distance of approximately 10,000 points (branch (1) in Fig.
3) was first divided into two clusters. We then selected a squared Euclidean distance of approximately 5000 points (branch (2) in Fig.
3) in one of these clusters, and then divided it in two again. Meanwhile, when we created the dendrogram for items of condylar position relative to the skull base in this study, a squared Euclidean distance of approximately 7500 points (branch (1) in Fig.
4) was first divided into two clusters. We then selected a squared Euclidean distance of approximately 2500 points (branch (2) in Fig.
4) in one of these clusters, and then divided it in two again. If the dendrogram were transected at a point inferior to branches (3) on Figs.
3 and
4, the squared Euclidean distance would decrease, and the similarity between each cluster would increase, which would make the characteristics more indistinct. For this reason, by transecting the dendrogram between branches (2) and (3) on Figs.
3 and
4, we obtained three clusters each and determined that we had obtained a suitable number of clusters for clinical application.
Classification of jaw deviation
To divide the patients into groups based on the quantification of jaw deviation and deviation characteristics, we first investigated mandibles in which structural asymmetry tends to arise. Since jaw deviation commonly affects both the maxilla and mandible in cases of jaw deformity associated with facial asymmetry, we originally believed that we should focus on both structures during the investigation. However, we presumed that this would complicate the quantification, and that the morphological characteristics would not be expressed accurately. For this reason, in the present study, we focused on only the mandible in cases of mandibular prognathism to simplify the characteristics to be captured, and we attempted to classify the condition from the two perspectives of the mandibular morphology and condylar position relative to the skull base.
For mandibular morphology, we used the Steel–Dwass test to clarify the characteristics of each group obtained by cluster analysis. We found that all mandibular morphology items (ramus height-diff, body length-diff, Cd-Me-diff and coronoid-diff) were significantly smaller in group A. Ramus height-diff, body length-diff and Cd-Me-diff were significantly larger in group B, and there was a moderate difference in ramus height and a large difference in body length between the left and right sides. Ramus height-diff, Cd-Me-diff and coronoid-diff were significantly larger in Group C, and it was clear that this group included cases with large differences between the left and right sides in terms of ramus height and distance from the gonion to the apex of the coronoid process. Meanwhile, in terms of condylar position relative to the skull base, we found that the Cd-MSP-diff and Cd-FH-diff were significantly smaller in group D, and this group included cases in which virtually no differences in condylar head position were observed between the left and right sides. In group E, Cd-MSP-diff and Cd-FH-diff were significantly larger, and there was lateral and vertical deviation of the condylar head in these cases. However, in group F, Cd-FH-diff was significantly larger, and this group included cases with vertical deviation of the condylar head.
Based on the various cluster analysis results for mandibular morphology and condylar position relative to the skull base, we reclassified individual cases in order to integrate these two perspectives. These results showed that the mandibular morphology was approximately symmetrical and the condylar head was not deviated in relation to the base of the skull group 1, whereas there was deviation of mandibular morphology or condylar position relative to the skull base, or both in groups 2 to 7. Group 1 included 39 patients, which was approximately 40% of the total, while the remaining 60% of cases exhibited some kind of asymmetry or deviation. Severt et al. reported that 34% of patients with jaw deformity exhibit clinically obvious facial asymmetry [
20], while Oguri et al. performed an analysis in which they defined lateral deviation as ≥ 4 mm of deviation in the maxillary and mandibular midline and reported that lateral deviation was observed in 48.6% of patients in whom surgical orthodontic treatment was indicated [
1]. Compared with these studies, our study had a higher percentage of patients with asymmetry, although we believe that enabled detection of cases in which jaw deviation was previously difficult to diagnose, and particularly cases with deviation of the condylar head.
These cases could be classified into six groups (groups 2 to 7) in which there was asymmetry or deviation of the mandibular morphology or condylar position relative to the skull base, or both. Among these groups, groups 2 and 3 had deviation of only the condylar head and the deviation was both lateral and vertical in group 2 but only vertical in group 3. The frequencies of occurrence for these groups were 3% and 16%, respectively. We focused on only the mandible in this study, but groups 2 and 3 were characterized by a highly symmetric mandible although it was positioned asymmetrically on the left and right sides. We therefore believe that there may have been concomitant horizontal cant of occlusal plane or maxillary deviation. In addition, in group 4, the position of the condylar head was approximately symmetrical, but the mandibular morphology, and particularly the difference in mandibular body length between the left and the right, was large, appearing with a frequency of 25%. This was the highest frequency among the groups with asymmetry. In this group, we believe that the asymmetry arose in the mandibular morphology only, and therefore, a type of ramus osteotomy is likely indicated in these cases. However, Nishida et al. reported that the indications for ramus osteotomy are limited and that there may be residual postoperative deviation in cases with extreme deviation [
21], so correcting mandibular morphology by means of bimaxillary surgery, genioplasty, or mandibular angleplasty should be investigated. Accordingly, considering the degree of improvement in not only skeletal asymmetry but also soft tissue asymmetry among the groups obtained during this study, we believe that ramus osteotomy and bimaxillary surgery should be investigated in these groups.
For groups 5 and 6, the respective frequencies of occurrence were not high at 3% and 6% respectively. However, there were large differences in both ramus height and body length between the left and right sides. In addition, group 5 had both lateral and vertical displacement of the condylar head, whereas group 6 had only vertical displacement. As we used absolute values for differences in mandibular morphology and condylar head position between the left and right sides in this study, we cannot determine the direction of deviations. However, if the directions of mandibular morphological asymmetry and deviation of condylar position relative to the skull base were the same, then the jaw deviation would likely be severe. If the mandibular morphology were asymmetrical and the direction of the condylar position relative to the skull base were retrograde, aspects of so-called reverse cant cases would likely be present [
22] and many of these cases would meet the indications for maxillo-mandibular surgery.
In group 7, the position of the condylar head was approximately symmetrical, but there were large differences in mandibular body length and coronoid process length between the left and right sides. The frequency of occurrence for this group was 6%. Coronoid hyperplasia and coronoid hypoplasia are examples of conditions with a large difference between the left and right coronoid processes, but both are relatively rare disorders. According to Galie et al. [
23], unilateral coronoid hyperplasia may be common in patients with facial asymmetry. Yoshida et al. [
24] noted that first and second branchial arch syndrome and Treacher-Collins syndrome are examples of congenital disorders that cause coronoid hypoplasia, while acquired disorders include systemic scleroderma, trauma, tumors, and chronic inflammation. None of the patients included in the present study had obvious congenital abnormalities or syndromes that would affect craniofacial morphology. However, there was a significantly greater difference in the values for ramus height-diff and coronoid-diff mandibular morphology in group 7 than in the other groups. Therefore, these findings indicate that, despite the absence of congenital abnormalities, there were cases of jaw deformity with large differences between the left and right sides in the vertical morphology of the ramus and coronoid process.
Studies to date have investigated the mandibular morphology and condylar position relative to the skull base separately [
25‐
27], but none has attempted to classify jaw deviation using both of these characteristics in combination. Obwegeser et al. reported classifying mandibular asymmetry due to unilateral mandibular hyperplasia into three types: unilateral hyperplasia of the condylar head, condylar neck, and mandibular ramus; unilateral elongation of the mandibular body; and a mixture of these two types [
25]. We believe that this classification resembles the groups with a large difference in ramus height and the groups with a difference in body length between the left and right sides. Obwegeser et al. classified mandibular asymmetry characteristics from 2D images and histopathology images, whereas our morphological classification is based on distance measurements on 3D images. Jaw deviation causes 3D morphological abnormalities in maxillofacial bony tissue, so we expect that the classification derived in this study will be useful for capturing jaw deviation.
In terms of asymmetry of the condylar position relative to the skull base, Yorozuya et al. reported that the horizontal distance between the mid-sagittal reference plane and condylar head was shorter on the deviated side [
26]. In our study, we detected asymmetry using differences between the left and right sides, and performed classification based on the measurement results. Thus, we did not classify our findings into those on a deviated side or non-deviated side and perfect comparison is not possible. However, our study also revealed a group in which the condylar head is displaced laterally, so we believe that the jaw deviation characteristics indicated by Yorozuya et al. may correspond to cases included in this group. Meanwhile, using 2-dimentional axial cephalometric projection, O’Byrn found that the condylar head was in a posterosuperior position on the deviated side, meaning that there was a difference between the condylar position relative to the skull base on left and the right sides in the anteroposterior and vertical directions [
27]. In our present study, we found no significant differences in anteroposterior condylar position relative to the skull base on the left and right sides, so this was not expressed as a group characteristic, although it was consistent with the finding that there were differences in the vertical direction between the left and right sides. In the present study, we grouped patients based on 3D characteristics of jaw deviation from the two perspectives of the morphological characteristics of the mandible itself and the positioning of the condylar head in the maxillofacial region as an index. This approach should contribute to an accurate understanding of jaw deviation in cases of jaw deformity associated with facial asymmetry.
In this work, the three groups each that were obtained by cluster analysis of mandibular morphology and condylar position relative to the skull base were reclassified into seven groups. Then, we performed a statistical analysis comparing the groups to clarify the characteristics of each one. Results showed that although there were groups in which it was possible to elucidate characteristics for which they were statistically significant differences, there were also some groups between which no statistically significant differences were observed. Specifically, group 2 was characterized by asymmetry of condylar position relative to the skull base, groups 5 and 6 were characterized by asymmetry of the mandibular morphology and condylar position relative to the skull base in both directions, and group 7 was characterized by asymmetrical mandibular morphology. No statistically significant differences were detected during the comparison between these groups. After reclassifying the groups, there were less than 10 patients in several of the groups and we believe that it is highly likely that the small patient populations affected the statistical analysis. To avoid having groups with small sample sizes during the study, we decided to include 100 patients, but ultimately there were multiple groups that consisted of less than 10% of the overall sample size. Although we cannot rule out the possibility that the number of cases was inadequate, the results showing numerous groups with a small number of cases appear to reflect the high degree of variation in jaw deviation. We expect a greater number of cases will be needed to more accurately clarify the characteristics of each group in further study.