2.1 Setting and study procedures

Of all the untreated patients enrolled for orthodontic treatment during January 2017 to April 2021 in Xinhua Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, 635 adolescents of Chinese ethnicity were selected. After checking the selection criteria through patients’ medical journal and cone-beam computed tomography (CBCT), and eliminating the unqualified dental casts and cephalograms, 100 eligible patients diagnosed with moderate crowding in the early permanent dentition phase from their records were selected as the BDC-c study group, while another 100 adolescents with no BDC, PDC and crowding were selected as the control group (Table 1).

2.2 Inclusion criteria

The inclusion criteria for the study group were designed as shown below:

1. Either maxillary unilateral or bilateral BDC with crowding and insufficient space for maxillary canine to occupy.

2. Early permanent dentition with completely erupted canines.

3. Adolescents of Chinese ethnicity age between 12 and 16 years old.

4. No premature loss of any primary tooth (information assessed from patients’ medical journal).

5. No retained primary teeth or impacted tooth.

6. No abnormal tooth including fused tooth, germinated tooth, concrescence of tooth, hypodontia, hyperdontia (e.g., supernumerary teeth), etc.

7. No previous orthodontic treatment.

8. No congenital diseases or anomalies such as cleft lip and palate.

2.3 3D measurement method variables

Within this study, the variables are comprised of both 3D model measurements of the dental casts and 2D lateral cephalometric measurements for all participants. For 3D measurements, inter-canine (W3), inter-first premolar (W4), inter-second premolar (W5), and inter-molar (W6) transverse widths at the buccal cusps were chosen for further evaluations. Depths at the buccal cusps levels of canine (D3), first premolar (D4), second premolar (D5), and first molar (D6) as well as the palatal surface area (SA) and volume (VOL) were measured. To identify dental variables which is served to distinguish BDC-c patients from control group, W3 and D3 were particularly included in the logistic regression model due to the salient feature from the control group (i.e., buccally displaced reference point for the BDC-c patients versus the non-displaced point for the control) in order to understand if it can capture the effect of other dental variables. As for 2D lateral cephalometric measurements, 17 cephalometric measurements were recorded.

2.4 3D measurement method

A 3D scanner (3 Shape 3D Scanner, D800, 3Shape A/S, Copenhagen, Denmark) was used to analyse the dental casts. Collected data further were exported to the Geomagic Wrap 2015 software (Geomagic, Research Triangle Park, NC, USA) for manual processing. Following the detailed study by our group, three planes were set up by using customised method which is described here. The gingival plane was created by connecting the midpoints (the lowest points) of the dentogingival junction of all permanent teeth. The distal plane was set up through two points at the distal surface of the first molar perpendicular to the gingival plane. Both the gingival plane and distal plane were defined as the boundaries of the palate such that the surface area and volume can be easily measured. The sagittal plane was created by passing through the frontmost anterior point of the incisive papilla which is considered to be stable point. The three planes were chosen to be perpendicular to each other as much as possible (Fig. 1A–C). The palatal surface area and volume were calculated by software analysis. The transverse widths were measured directly between the buccal cusps of contralateral teeth, while the depths of the palate vault were measured as the vertical distances from the palate vault to the connecting lines between the contralateral buccal cusps (Fig. 1D–G) [13, 14, 15]. All lateral cephalogram (LC) data were imported to the Dolphin Imaging software (Dolphin Imaging 11.95 Premium, Patterson Dental Supply Inc., Chatsworth, CA, USA) and orientated at the Frankfort-horizontal plane. 20 landmarks were then marked later to obtain 17 skeletal cephalometric measurements (Fig. 2).

Fig. 1.The customised method of setting up three planes and 3D measurements. A. Gingival plane (GP). B. Distal plane (DP). C. Sagittal plane (SP). D. Palatal surface area. E. Palatal volume. F. Transverse widths between inter-canines (W3), inter-first premolars (W4), inter-second premolars (W5), and inter-molars (W6) respectively. G. Depths between inter-canines (W3), inter-first premolars (W4), inter-second premolars (W5), and inter-molars (W6), respectively.

Fig. 2.The cephalometric landmarks. 1. Sella, S. 2. Nasion, Na. 3. Orbitale, Or. 4. Porion, Po. 5. Articular, Ar. 6. Point A, A. 7. Point B, B. 8. Anterior nasal spine, ANS. 9. Posterior nasal spine, PNS. 10. Menton, Me. 11. Gonion, Go. 12. Pogonion, Pog. 13. Upper central incisor cusp tip, U1. 14. Lower central incisor cusp tip, L1. 15. Upper first molar buccal-mesial cusp, U6M. 16. Lower first molar buccal-mesial cusp, L6M. 17. Upper central incisor root, U1R. 18. Lower central incisor root, L1R. 19. Condyloid process, Co. 20. Basion, Ba.

2.5 Statistical analysis

The effects of the research variables were analysed by using SPSS 24.0 (SPSS Inc., Chicago, IL, USA). All 3D model measurements and cephalometric measurements were performed three times independently by the same practitioner with an interval of one week for three consecutive weeks to ensure the data were measured accurately and consistently. Single rater measurement error is assessed with an ICC (Intraclass correlation coefficient) Index by use of absolute agreement between repeated measurement definition to confirm the reliability of measurements.

Independent-samples T tests were conducted to evaluate any dental and cephalometric variable’s differences between BDC-c and control groups. For 3D models, multiple binary logistic regression models were employed to evaluate any of the above predictor’s effects on the odds of predicting the BDC-c study group, using 0.5 as the endpoint of cut-off from the default control group.

Logistic Regression analysis was used to identify the joint effects of the dental variables’ 3D measurements; however, the sample size of the current study precluded the inclusion of the 17 cephalometric variables into the model. Various assumptions of logistic regression were tested. Spearman’s rho was used to identify issue of multi-collinearity, and any predictor pair with correlation coefficient of over 0.8 would signal the need to drop either one of the pair from the model. Box-Tidwell transformation technique was applied to identify nonlinearity of the independent variables, and both VOL and SA were therefore excluded from the model. Outlier detection was performed by comparing the Mahalanobis distance with a critical value of χ² (Chi-Square) distribution. Any value less than 0.001 would suggest an outlier and to be examined. Only one BDC-c case had a p-value (0.0004) due to its large Mahalanobis distance. Further inspection of the participant’s dental variables did not show any special differences from all other cases. Hence it was decided not to exclude it.

4.1 3D analysis of the maxilla abnormality with BDC-c

Larsen et al. [12] described that transverse distance between molars was significantly larger in both BDC and PDC group of subjects around 13 years old. Meanwhile, Ikoma and Aria [11] did not find any significant differences in the inter-canine transverse widths in adults with BDC. In the present study, we focused on the early permanent dentition and found that in participants with BDC-c, W3 was greater while W4, W5 and W6 were smaller. Our finding clearly suggests that participants with BDCs have a narrower posterior dental arch than those in control group.

Bizzarro et al. [13]’s observation in children with BDC by using cusps of primary canines as reference points revealed that the anterior depths increased slightly whilst posterior depths decreased insignificantly in comparison with control group. In contrast, Ikoma and Aria [11] stated that women with BDC had smaller anterior depths, which agrees with the current results that the anterior vertical depths were smaller and posterior vertical depths were larger in BDC-c group. The reference points selected in previous studies were the cusps of the ectopic permanent canine, and hence it was referred as landmarks in our study, hinting that the smaller anterior depths can be due to the eruption height of the ectopic permanent canines at the transition stage and affected by the participants’ ethnicity, races, growth or tooth sizes, and thus, more stable landmarks for measuring ectopic permanent canines still need to be evaluated. Seto et al. [16] revealed that palatal height itself is not a reliable indicator of maxillary constriction and that the width must also be taken into account when assessing constriction. To avoid the confusion of the contradictory results, SA and VOL were introduced in our study to avoid biases caused by tooth position and angulation. Moreover, these two 3D measurements have been previously verified as reliable indicators of palatal and maxillary arch growth [14]. Meanwhile, adolescents with BDC-c were found to establish a smaller palatal volume and surface area than control group, suggesting that crowding due to smaller palatal vault in all three-dimensions might attribute to BDC-c. Furthermore, logistic regression model was used to investigate whether BDC-c is the result of the deviated growth of the maxillary complex or whether deviation in eruption is independent from morphology of the maxillary complex. Besides, it also suggested that these variables should be considered simultaneously as a whole. The need for 3D measurement is justified by statistical outcome of the model, which had a high correct prediction rate of 91%. As implied from the statistical outcome, reduced W4 and D3 with greater W3 and W6 together tend to relate to the occurrence of BDC-c, suggesting that BDC-c would more likely to appear with a narrower dental arch at corresponding first premolar region. Such phenomenon could possibly be caused by earlier eruption of premolar, leaving insufficient space for the canine, and resulting in a higher and/or more buccal positioned canine, thus a shorter D3 and wider W3. Growth in widths of dental arches tends to be completed before adolescent growth spurt, and therefore it is affected minimally even if there is growth change in which inter-canine width also seems to decrease after age 12 [17]. At the same time, most canines have erupted by age 12–13. In this way, the arch width not only provides little space for canine, but also it might attribute to a future chance of ectopic position. Consequently, smaller D3 and larger W3 can be speculated as a result instead of the causes of BDC-c.

Dimensions of the palate can provide clinical signs and it determines degrees of crowding, since earlier research had shown that children with BDC demonstrated a smaller palatal VOL and SA compared with non-BDC [13]. Most research suggests that a larger tooth size is not responsible for maxillary crowding and that smaller dental arch could be the main factor, providing evidence that smaller maxilla dimensions including arch lengths, widths, and perimeters are found along with asymmetric and irregular arch in the crowded arch [8]. In the present study, adolescents with BDC-c also had a smaller palatal volume and surface area, suggesting that crowding due to smaller palatal dimensions can be the main factor to BDC-c. Thus, according to the results of this study, if signs of a narrower W4 and palatal dimensions are identified clinically in the mixed dentition, early intervention such as maxillary expansion, may be recommended to increase the palatal surface area and volume to encourage normal canine eruption.

In addition, our results indicated that participants with a BDC-c have some level of phenomenon similar to that of mouth-breathers. As reported by Lione et al. [18], greater narrowing and higher depths at the level of posterior teeth and smaller palatal VOL and SA were found in mouth-breathers. Thus, oral breathing might be related to BDC-c, and therefore further research can be considered, as mouth-breathers were not specified in the present study.

4.2 Cephalometric characteristics of BDC-c dentition

The present results clearly indicate that participants with a BDC-c demonstrate a significantly smaller SN, SNA, SNB, and ANB, implying that the maxilla of participants with a BDC were more underdeveloped or retrusive than those observed in control group, agreeing with the previous studies that BDCs featured with a shorter maxilla sagittally [11, 12]. Other clinical research has suggested that cranial base length and angle are main factors leading to retrusive maxilla because cranial base offers a central supportive structure for craniofacial region [19]. Hence, shorter anterior cranial base can lead to a retrusive maxilla and is interrelated to a smaller palatal volume and surface area. Chang et al. [20] concluded that retrusion of nasomaxillary complex could cause facial flatness and anterior displacement of temporomandibularjoint.

On the other hand, we found that the FMA, anterior facial height, and lower facial height were larger with a retrusive and narrower maxilla in the BDC-c, supporting the conclusion that hyperdivergent skeletal pattern is highly correlated with a smaller maxilla in the sagittal and transverse dimensions, thereby with less increase in inter-molar width [11]. We also found that larger SN-PP angle was a factor to imply the maxilla rotated downward and backward more as ANS moved more inferiorly than the PNS. This might be the reason why larger SN-PP angle usually associates with longer lower facial height [21]. In addition, it has been reported that a greater obtuse cranial base angle and shorter posterior cranial base length can lead to a higher positioned glenoid fossa and condyle, causing a backward rotation of the mandible and thus resulting in a hyperdivergent-angled face [22]. These all serve to add clues to the existence of racial/ethnic influence on facial structure. Nevertheless, there were no significant differences in both cranial base angle and posterior cranial base length between the BDC-c group and control group in the present study.

4.3 Limitations

The sample size of the studying subjects should be increased in order to elaborate on the outcomes of the BDC. The observational study only described a correlation between BDC and craniofacial morphology and further study is needed for analysing why and how it occurred.