Network analysis of three-dimensional hard-soft tissue relationships in the lower 1/3 of the face: Skeletal Class I-normodivergent malocclusion versus Class II-hyperdivergent malocclusion

doi:10.21203/rs.3.rs-4279114/v1

Background

The determining effect of facial hard tissues on soft tissue morphology in orthodontic patients has yet to be explained. The aim of this study was to clarify the hard-soft tissue relationships of the lower 1/3 of the face in skeletal Class II-hyperdivergent patients compared with those in Class I-normodivergent patients using network analysis.

Methods Fifty-two adult patients (42

females, 10 males; age, 26.58 ± 5.80 years) were divided into two groups: Group 1 (G1), 25 subjects, skeletal Class I normodivergent pattern with straight profile (Class I-norm-straight); Group 2 (G2), 27 subjects, skeletal Class II hyperdivergent pattern with convex profile (Class II-hype-convex). Pretreatment cone-beam computed tomography (CBCT) and three-dimensional (3D) facial scans were taken and superimposed, on which 3D landmarks were identified manually, and their coordinate values were used for network analysis.

Results

(1) In sagittal direction, G2 correlations were generally weaker than G1. In both the vertical and sagittal directions of G1, the most influential hard tissue landmarks to soft tissues were located between the level of cemento-enamel junction (CEJ) of upper teeth and root apex of lower teeth. In G2, the hard tissue landmarks with the greatest influence in vertical direction were distributed more forward and downward than in G1. (2) In G1, all the coefficients in the correlation matrix of sagittal and vertical positions of hard tissue landmarks were positive. In G2, the values of those coefficients decreased. In G1, all the correlations for vertical-hard tissue to sagittal-soft tissue position and sagittal-hard tissue to vertical-soft tissue position were positive. However, G2 correlations between vertical-hard tissue and sagittal-soft tissue positions were mostly negative. Between sagittal-hard tissue and vertical-soft tissue positions, G2 correlations were negative for mandible, and were positive for maxilla and teeth.

Conclusion

Compared with Class I-norm-straight patients, Class II-hype-convex patients had more variations in soft tissue morphology in sagittal direction. In vertical direction, the most relevant hard tissue landmarks on which soft tissue predictions should be based were distributed more forward and downward in Class II-hype-convex patients. Class II-hype-convex pattern was an imbalanced phenotype concerning sagittal and vertical positions of maxillofacial hard and soft tissues.

Network analysis

Data mining

Skeletal Class I malocclusion

Skeletal Class II malocclusion

Vertical pattern

Facial soft tissue

Three-dimensional measurement

Morphology

Harmonious facial soft tissue morphology, as a treatment goal in orthodontics, has become increasingly important but is sometimes difficult to achieve. This is partly due to the highly variable soft tissues. The variation results from the irregular shape of dental and skeletal structures and individual variations in thickness and tension of soft tissues. Orthodontic treatment directly changes the position of hard tissues such as teeth or bones, and subsequently affects the soft tissue contour. However, patients are always more concerned about the shape of the facial soft tissue rather than about the underlying hard tissue [1].

Skeletal Class II hyperdivergent malocclusion is a common condition in orthodontic patients and is often accompanied by increased difficulty in treatment and compromised orthodontic outcomes. This skeletal pattern has an obvious negative effect on human facial beauty, resulting in the common chief complaint to improve facial aesthetics. Some patients with this condition seek orthognathic surgery for better facial appearance, but the high cost and risk of surgery and the demand for both surgeons and equipment hinder the selection of this surgery for many patients. To improve the outcome of camouflage orthodontic treatment, controlling the vertical position of hard tissues is often important and challenging. Various methods have been used, such as premolar extraction, posterior bite blocks, high-pull headgear, mini screw implants, and clear aligners [2, 3]. However, to achieve an ideal facial profile in the treatment of skeletal Class II hyperdivergent malocclusion, it is vital to clarify the relationships between hard and soft tissue contours.

Previous studies concerning skeletal Class II hyperdivergent malocclusion have been carried out, most of which were two-dimensional (2D) analysis using lateral cephalograms [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. Kasai K [4] reported that the vertical dimension of the lower facial height and the position of the lower incisors were associated with the thickness of the upper-lip vermilion and soft tissue B. Lee YJ et al. [6] found that the perioral soft tissue measurements of skeletal Class II were correlated with the inclination and anteroposterior position of the maxillary and mandibular incisors along with facial depth (Nasion-Gonion) and facial length (Sella-Gnathion). It is well known that the relationship between craniomaxillofacial (CMF) hard and soft tissues is very complicated. Previous studies used correlation analysis or multiple regression analysis [4, 5, 6, 10, 11, 12, 13, 14] to learn the relationship between soft and hard tissues, but the overall relationship of the CMF system could not be explored or visualized. For now, the most advanced artificial intelligence algorithm [7] for predicting soft tissue contour from hard tissue shape calculates only two line distances (the distance between labrale superius or labrale inferius to the esthetics plane), which essentially predicts the position of merely two points, and cannot reflect the complex soft tissue contour. In addition, most studies have focused on the correlation between lip thickness, length and hard tissue measurements due to the adoption of linear distance and angle for analysis [6, 8, 9, 11, 12, 13, 14]. However, the position of the soft tissue surface is more critical than the lip thickness.

The CMF system can be abstracted as a combination of two layers, the internal hard tissues and the external soft tissues. With many representative landmarks distributed on each layer of tissue, the role of hard tissues in determining soft tissue contour can be abstracted as a many-to-many problem. Dealing with many-to-many relationships is the strength of network analysis. Network analysis, as an advanced data mining method based on graph theory, has been widely applied in epidemics [15], genomics and proteomics, such as tumor stratification [16] and discovery of biomarker genes for diseases [17, 18]. In clinical orthodontic studies, network analysis has also been proven to be a promising methodology [19, 20, 21, 22]. The main idea is that a system of elements that interact with each other can be represented by a mathematical object called a ‘network’ (or a ‘graph’, Fig. 1) [23]. The elements can be abstracted to a series of ‘nodes’ that are connected to each other by ‘links’ which represent the interaction between two nodes. Graph theory provides a powerful representation of these functional interactions and highlights their global interdependence. The pattern and architecture of relationships matter more than the precise identities of the elements themselves [24].

In contrast to conventional methods, by calculating from correlation matrix, network analysis can visualize multiple relationships among all the elements at the same time, find closely interrelated components, and identify the strongest interrelated elements as ‘regulatory hubs’. Due to this comprehensiveness, it can identify unexpected correlations and quantify their strengths [25]. Moreover, certain parameters that describe the overall features of the network can also be calculated, allowing direct and convenient comparisons between networks.

There are only a few studies of network analysis in the field of clinical orthodontic research, all of which were 2D [19, 20, 21, 22], using cephalometric and clinical measurements, such as the ANB angle and overbite, as variables. They only reflected the relationships among discrete measurements and could not be translated into an overall understanding of 3D CMF morphology. Moreover, despite finding key measurements of a certain type of malocclusion, they had the disadvantage that a measurement was determined by more than one point, and it could not be specified which point was actually responsible for the significance or influence of the measurement. For example, if they found that the ANB angle was a crucial measurement for skeletal Class III patients, weather the impact ANB angle had was attributed to the position of point A, B or N was not clarified, and it is unclear how to change the ANB angle in clinical practice to achieve a better outcome. In addition, the mechanism by which hard tissues determine soft tissue contour was still difficult to explain simply by analysing cephalometric and clinical measurements, such as how the vertical position of one hard tissue point affects the vertical and sagittal positions of soft tissue contour, and which are the most influential hard tissue points.

Since 2D cephalogram data lack massive amounts of important information and soft tissues are not necessarily in relaxed condition, the extensive application of CBCT and 3D facial scans in clinical examination has led to the rapid development of 3D research. CBCT can reveal the complexity of dental and skeletal structures [26], while 3D facial scans can provide significantly more accurate soft tissue surface information than can CBCT [27].

In this study, for the first time, we introduced network analysis to the study of the 3D CMF hard-soft tissue relationships. We adopted 3D landmarks of hard and soft tissue in the lower 1/3 of the face, and separated the influence of hard tissues on soft tissue contour into sagittal and vertical directions, thus removing the interference of other dimensions when clarifying the impact of a certain dimension. The aims of this retrospective study were to clarify the hard-soft tissue relationships of the lower 1/3 face in Class II-hype-convex patients compared with those in Class I-norm-straight patients, identify key hard tissue points that are most influential on soft tissue contour, deepen the understanding of the morphology and pathogenesis of skeletal Class II hyperdivergent malocclusion, and provide new perspectives for orthodontic treatment planning.

Subjects

Patients data before orthodontic treatment were retrospectively collected at Peking University School and Hospital of Stomatology from 2020 to 2023. The inclusion criteria were as follows: (1) Age: 18 ~ 40 years old; (2) Body Mass Index (BMI): 18.5 ≤ BMI < 24; (3) Group 1, skeletal Class I, normodivergent, straight profile (ANB 0.7° ~ 4.7°, SN-MP 27.3° ~ 37.7°, FCA 7° ~ 15°) ; Group 2, skeletal Class II, hyperdivergent, convex profile (ANB > 4.7°, SN-MP > 37.7°, FCA > 15°) [28, 29, 30, 31]; (4) Complete permanent dentition (not considering third molars) with crowding of less than 4 mm; (5) Good health with no chronic disease or disability. The exclusion criteria were as follows: (1) Moderate or severe periodontitis; (2) Severe maxillofacial skeletal asymmetry or open bite deformity; (3) History of maxillofacial trauma, surgery, or orthodontic treatment; (4) Maxillofacial soft tissue defect or asymmetry larger than 5mm.

Twenty-five G1 subjects and 27 G2 subjects were included in the study, according to the sample size of previous network analysis in clinical orthodontic research [21]. Patients had cephalogram, CBCT and 3D facial scan images taken on the same day before orthodontic treatment. CBCT images were taken using NewTom Scanner (NewTom AG, Marburg, Germany) with 0.3 mm axial slice thickness, 15 × 15 cm field of view, 3.6 s scan time, 110 kV tube voltage, and 2.81 mA tube current. The 3D facial scan images were captured using 3dMD imaging system (3dMD, Atlanta, Ga) and were stored in obj files. The patients were instructed to maintain a neutral facial expression in their natural head position when scanned, with lips and mouth at rest and teeth in intercuspation to minimize involuntary movement [32].

Ethical approval

for this study was obtained from the Ethics Committee of Peking University Biomedical Sciences (PKUSSIRB-202058145). All patients signed informed consent forms before enrollment. All the procedures were followed in accordance with the Declaration of Helsinki.

Cephalometric analysis

The cephalograms were uploaded to an open-source cephalometric website (https://cephnex.aishinye.com) to manually identify landmarks and measure cephalometric variables (Table 1, Fig. 2). The Frankfort Horizontal Plane (FHP, the plane passing through Po and O) of each subject was set parallel to the ground. All the 2D landmarks were manually identified twice by a previously calibrated examiner with a time interval of more than 7 days, and the measurement values were computed automatically. To determine the intraoperator reliability of the measurements, the values were exported to SPSS 26.0 (IBM SPSS Statistics, IBM Corp, Armonk, NY) to calculate intraclass correlation coefficient (ICC). Independent 2-sample t tests or Mann-Whitney U tests were used to determine the differences in the values between groups. For all the comparisons in this study, P < 0.05 indicated statistical significance.

Table 1

Landmarks and measurements of cephalograms
Names	Definitions
Landmark
S	Sella
N	Nasion
Po	Porion
O	Orbitale
Go	Gonion
Gn	Gnathion
A	Subspinale
B	Supramental
G	Glabella
Sn	Subnasale
Pog’	Soft-tissue pogonion
UL	The most anterior point of upper lip
LL	The most anterior point of lower lip
U1L	The point on the intersection of the labial surface of upper incisor and the horizontal line passing through UL
L1L	The point on the intersection of the labial surface of lower incisor and the horizontal line passing through LL
Measurement
ANB	A-N-B angle
SN-GoGn	Angle formed by the SN plane and mandibular plane
FCA	Facial Convexity Angle, the Angle at Sn subtended by G and Pog'
Upper Lip Thickness (ULT)	Distance between UL and U1L
Lower Lip Thickness (LLT)	Distance between LL and L1L

Superimposition of CBCT and 3D facial scan images

The CBCT images were exported in Digital Imaging and Communications in Medicine (DICOM) format, and then transferred into Dolphin 3D Imaging software (version 11.8, Dolphin Imaging and Management Solutions, Chatsworth, Calif). In the 3D coordinate system, X-axis represented transverse direction, Y-axis represented sagittal direction and Z-axis represented vertical direction. To set identical orientation for different subjects, right and left Orbitale and right Porion of each CBCT were selected to form the FHP which was adjusted parallel to the XY plane. Meanwhile, the mid-sagittal plane formed by Nasion, Sella, and Basion was set to be parallel to the YZ plane.

Then, the reoriented CBCT images were imported into imaging program 3D Slicer (open-source, multiplatform, software package, version 4.11.0, http://www.slicer.org). The soft tissue surface (skin) of each CBCT image was extracted by a thresholding process in the segment editor tab and then exported in stereolithography (STL) file format. The 3D facial scan file was exported in object (OBJ) file format.

To integrate the CBCT and facial scan images for each patient, the two imaging modalities were imported into Geomagic Studio 11.0 software (Raindrop Geomagic, Inc., NC, USA) for superimposition (Fig. 3). CBCT was set as the base for registration (Fig. 3A), offering a fixed position for the corresponding facial scan image. As unnecessary areas such as hair and ears can increase the error range, the facial images were trimmed along the hair line and in front of the tragus (Fig. 3B). These two models were then superimposed using an iterative closest point (ICP) algorithm [33] to minimize the difference between them. Initial (global) registration was achieved through the selection of three corresponding points on CBCT and facial scans. Then, regional registration was used to optimize the registration, with the relatively stable forehead, nasal bridge and malar areas as the registration regions (Fig. 3A) [34]. The registration areas were selected by using the function of colouring the area in the software. The average surface distance (ASD) between the two surfaces, as registration error, was automatically calculated by measuring the closest 3D Euclidean distances between surface points on the two models using the iterative closest algorithm [35]. Meanwhile, Geomagic studio visualized the registration errors through a 3D colour map (Fig. 3C). An independent 2-sample t test was used to analyse the difference in ASD between G1 and G2 using SPSS 26.0.

3D landmark identification

The definitions of the 3D landmarks were shown in Table 2, and the landmark distribution was visualized in Fig. 4. The superimposed CBCT and facial scan images were imported to imaging program 3D Slicer to manually identify landmarks in transverse, coronal, and sagittal views (Fig. 5). To assess the reliability of this method, landmark positioning of ten randomly selected patients was repeated by two calibrated operators. Pearson’s correlation was performed to calculate ICC for interoperator reliability.

Table 2

Landmarks of hard tissues on CBCT and soft tissues on 3D facial scans
Landmarks	Definitions
Hard tissue
S	Sella (The center point of the sella turcica)
N	Nasion (Nasal root point: the most convex point on the nasal frontal suture)
O	Orbitale (The most inferior point of the orbital margin)
Po	Porion (The most superior and lateral point of bony external acoustic meatus image)
Ba	Basion (The midpoint of the anterior edge of the foramen magnum)
A	Subspinale (The most concave point of the maxillary on the maxilla midline)
ANS	Anterior nasal spine (The most anterior point of the anterior nasal spine)
PNS	Posterior nasal spine (The most posterior point of the posterior nasal spine)
PRO	The most inferior and anterior point of the alveolar process between the upper central incisors
ID	Infradentale (The most superior and anterior point of the alveolar process between the lower central incisors)
B	Supramental (The most concave point of the mandibular labial surface on the mandibular midline)
POG	Pogonion (The most anterior point of mandibular sysmphysis on the midline of mandibular)
ME	Menton (The most inferior point of the mandibular sysmphysis on the midline of mandibular)
RF	The most concave point/middle point of the the anterior margin of the mandibular ramus
RMP	The point located on the transition site of the anterior margin of the mandibular ramu to the upper edge of the mandibular body with the maximum curvature
RP	The most concave point/middle point of the the posterior margin of the mandibular ramus
GO	Gonion (The point located on the mandibular angle with the maximum curvature)
U1J	The midpoint of labial CEJ of upper central incisor
U2J	The midpoint of labial CEJ of upper lateral incisor
U3J	The midpoint of labial CEJ of upper canine
U6J	The midpoint of buccal CEJ of upper first molar
L1J	The midpoint of labial CEJ of lower central incisor
L2J	The midpoint of labial CEJ of lower lateral incisor
L3J	The midpoint of labial CEJ of lower canine
L6J	The midpoint of buccal CEJ of lower first molar
U1	The midpoint of the incisal margin of upper central incisor
U2	The midpoint of the incisal margin of upper lateral incisor
U3	The cusp of upper canine
U6	The mesio-labial cusp of upper first molar
U1a	The root apical of upper central incisor
U2a	The root apical of upper lateral incisor
U3a	The root apical of upper canine
L1a	The root apical of lower central incisor
L2a	The root apical of lower lateral incisor
L3a	The root apical of lower canine
Soft Tissue
ULP	Upper lip (Most prominent point of the upper lip on the mid-saggital plane)
LLP	Lower lip (Most prominent point of the lower lip on the mid-saggital plane)
Ch	Cheilion (Left or right corner of the mouth)
A'	Soft-tissue A-point
B'	Soft-tissue B-point
2&1	Most prominent point of the upper lip on the saggital plane that passing through the midpoint of ULP and Ch
4&3	Most prominent point of the lower lip on the saggital plane that passing through the midpoint of LLP and Ch
6&5	Point of the upper lip on the intersection of saggital plane that passing through the midpoint of ULP and Ch and the horizontal plane that passing through A’
8&7	Point of the lower lip on the intersection of saggital plane that passing through the midpoint of LLP and Ch and the horizontal plane that passing through B’
Pog'	Soft-tissue pogonion
Me'	Soft-tissue menton

Network analysis

Networks or graphs are mathematical objects formed by vertices (nodes) and links (edges) connecting them (Fig. 1). They are often used as models to extract useful structural information from a variety of mechanical and biological systems. Structural aspects are vital in problems involving multiple interacting elements. We used the coordinate values of 3D landmarks as vertices (nodes). The ‘degree’ corresponds to the number of nodes adjacent (directly connected) to a given node and is a measure of the centrality of a node. In biological terms, the ‘degree’ allows an immediate evaluation of the regulatory relevance of a node. For instance, in cellular signalling networks, protein with a very high degree interacts with several other signalling proteins, suggesting that it is a central regulatory node (Fig. 1B).

The Ba point was set as the origin (coordinate values = 0, 0, 0) for each subject, generating adjusted coordinate values for every other landmark. In each group, the adjusted Y or Z-axis coordinate value of each landmark was used to calculate Pearson correlation coefficient to analyse relationship between points. On a certain axis, all the coefficients among coordinate values generated a correlation matrix, from which a network was extracted using Cytoscape 3.10 [36], an open-source software project (http://www.cytoscape.org/). The composition of each network was shown in Fig. 6.

In a network, each node represented the position (coordinate value) on Y or Z-axis of a landmark, and each link represented the correlation between two landmarks [19]. The networks were built by fixing a threshold value T: two nodes were linked if the correlation between them was greater than T. For each network, T was different corresponding to the certain condition. Several global network metrics were computed to convey biological meaning to network (Table 3). We detected the dominant landmarks by computing the ‘degree’ for each landmark and by visual inspection (Figs. 8 ~ 11), also using Cytoscape 3.10.

Table 3

Global network metrics *
Network Metrics	Meaning
number of nodes	the total count of nodes in a network
number of edges (links)	the total count of edges (links) in a network
average degree	the mean of the number of neighbors of a node
network density	the density of a network
*Global network metrics provide information about the general properties of each skeletal pattern owing to the structure of their entire networks. All the reported metrics are pure numbers

The demographic and cephalometric information of the two groups were shown in Table 4. No statistically significant difference in age, BMI, ULT or LLT was detected between Class I-norm-straight and Class II-hype-convex subjects (Table 4). ANB, SN-MP, and FCA angle were remarkably different among subjects with different classifications.

Table 4

The demographic and cephalometric comparison between Class I-norm-straight (G1) and Class II-hype-convex (G2) patients*
	Class I-norm-straight (M ± SD)	Class II-hype-convex (M ± SD)	t value	Z value	P value
Age(y)	26.20 ± 5.24	26.93 ± 6.35	-0.448		0.656
BMI	21.35 ± 1.84	20.68 ± 1.95	1.279		0.207
ANB(°)	3.46 ± 0.24	6.55 ± 0.27		−6.181	0.000^{ƚ, ǂ}
SN-MP(°)	30.73 ± 0.47	40.83 ± 0.73		−6.181	0.000^{ƚ, ǂ}
FCA(°)	10.18 ± 0.48	18.30 ± 0.57		−6.181	0.000^{ƚ, ǂ}
ULT(mm)	12.06 ± 0.47	11.51 ± 0.34	0.963		0.340
LLT(mm)	15.03 ± 0.39	15.25 ± 0.42	−0.372		0.711

M, mean; SD, standard deviation.

^ƚ Significant difference between Class I-norm-straight and Class II-hype-convex groups, P < 0.05; *If the data conformed to a normal distribution and variances were uniform, an independent 2-sample t test was used; ^ǂIf the data did not conform to a normal distribution and uniform variances, a Mann-Whitney U test was used

The ASD between CBCT surfaces and 3D facial scans was 0.35 ± 0.10 mm in G1 and 0.30 ± 0.08 mm in G2, indicating an accurate registration [34]. No statistically significant difference was in registration error between the two groups (t = 1.912, P = 0.062). The ICCs for the intraobserver reliability were greater than 0.94 for all the 2D cephalometric measurements. Moreover, the ICCs for the interobserver reliability were greater than 0.95 for all the 3D landmark positions on each axis in the ten randomly selected patients, supporting a high consistency and reliability in landmark identification.

In the networks, square nodes (Fig. 7B) represented hard tissue landmarks, and the redder the colour of the node was, the more soft tissue landmarks were connected to the node (Fig. 7A). The landmarks on teeth were arranged on the left, and the bony landmarks were on the right (Fig. 7B). Round nodes represented soft tissue landmarks that had no difference in colour. The nodes were arranged from top to bottom according to the biological spatial position. The thickness of the link represented the strength of the correlation.

The network of hard tissue Y-axis and soft tissue Y-axis was shown in Fig. 8. The threshold was set as 0.9. In G1 (Fig. 8B), according to the bluer colour of the links, the impact of hard tissues on lower lip (LLP, 4&3, B’, 8&7) was greater than that on upper lip (A’, 6&5, ULP, 2&1). The dental landmarks most relevant to soft tissues are those in redder node colours (higher ‘degree’), which were located at CEJ of upper and lower teeth, incisor margin or cusp of upper teeth, and root apex of lower teeth. A higher ‘degree’ meant that there were more soft tissue landmarks connected to these hard tissue landmarks than to other landmarks. The bony landmarks most related to soft tissues were B point, ID and PRO. In G2 (Fig. 8C), the landmarks most related to soft tissues were CEJ of upper incisors, PRO and A point. Compared with G1, G2 network was sparser, and its global network metrics decreased (Table 5).

Table 5

Global metrics of hard tissue Y-axis and soft tissue Y-axis networks
Network Metrics	Class I-norm-straight	Class II-hype-convex
number of nodes	35	31
number of edges (links)	192	88
average degree	10.971	5.677
network density	0.161	0.095

The network of hard tissue Z-axis and soft tissue Z-axis was shown in Fig. 9. The threshold was set as 0.8. In G1 (Fig. 9B), according to the bluer colour of the links, upper lip (A’, 6&5, ULP, 2&1) was more strongly correlated with hard tissues than lower lip. The most related hard tissue landmarks were located at the level of upper incisal margin or cusp and CEJ of upper and lower tooth. Compared to those in G1, the correlations of upper lip were weaker in G2 (Fig. 9C), and the ‘degree’ of posterior landmarks (molar points, PNS and RMP) decreased. The node colours of molar points lightened, indicating that fewer soft tissue landmarks were related to them in G2. Moreover, PNS and RMP failed to survive the thresholding process, so they did not appear in G2 network. In contrast, the ‘degree’ of anterior tooth points, B point, and Pog increased, as shown by their redder node colour. Overall, the global network metrics of the two groups were similar (Table 6).

Table 6

Global metrics of hard tissue Z-axis and soft tissue Z-axis networks
Network Metrics	Class I-norm-straight	Class II-hype-convex
number of nodes	36	35
number of edges (links)	173	175
average degree	9.611	10.000
network density	0.137	0.147

The network of hard tissue Z-axis and soft tissue Y-axis was shown in Fig. 10. The threshold was set as 0.2. In G1 (Fig. 10B), all the correlations were positive (blue links). Posterior hard tissue landmarks had stronger correlation than anterior landmarks (bluer links). In G2 (Fig. 10C), the correlations were mostly negative (red links), and hard tissues were mainly correlated with lower lip and chin.

The network of hard tissue Y-axis and soft tissue Z-axis was shown in Fig. 11. The threshold was set as 0.2. In G1 (Fig. 11B), all the correlations were positive (blue links). In G2 (Fig. 11C), the correlations between teeth or maxilla and soft tissues were positive (blue links). In contrast, the correlations between mandibular and soft tissue landmarks were negative (red links).

In G1, the correlation coefficient matrix of hard tissues (Fig. 12A) showed that the correlation between the sagittal position of any hard tissue landmark and the vertical position of any other hard tissue landmark was positive (green). Compared with G1, the correlation coefficient matrix of G2 (Fig. 12B) showed that the correlations decreased (lighter in green) or became negative (red).

Facial soft tissue aesthetics are an increasingly common concern of orthodontic patients [37]. In the lower 1/3 of the face, by applying network analysis to coordinate values of 3D landmarks in Class I-norm-straight and Class II-hype-convex patients, we found major hard-soft tissue relationships and differences between the two groups. The networks allowed the visualization of malocclusion information (Figs. 8 ~ 11), while the global network metrics conveyed biological meaning to the networks (Tables 5, 6). We found that in Class II-hype-convex patients, soft tissue morphology was more variable, mainly due to the greater variation in sagittal direction. The most relevant hard tissue landmarks on which soft tissue predictions in vertical direction should be based tended to be distributed more forward and downward in G2. Moreover, Class II-hype-convex pattern was not proportionate between sagittal and vertical positions of the lower 1/3 of the face as was Class I-norm-straight pattern.

We selected young adult subjects to exclude dynamic changes in the hard-soft tissue relationship during the growth and development period [38]. Previous studies have shown that the hard-soft tissue correlation is different in patients with various skeletal types, for example, Class II hyperdivergent and Class II hypodivergent patterns [6]. Therefore, in this study, sagittal and vertical skeletal types were defined simultaneously to obtain more accurate correlation data. A previous study also showed that the convexity of the face is one of the main factors causing variations in soft tissue contour [39]. In this research, G1 patients were limited to a straight profile in order to set patients with the most standard and harmonious profile as the control group. Meanwhile, G2 subjects were limited to a convex profile so as to exclude atypical ones with straight profile, who had good soft tissue compensation and a relatively aesthetic profile. The morphological characteristics of Class II-hype-convex pattern are mainly manifested in sagittal and vertical dimensions. As for the transverse dimension, which mainly reflects facial width and symmetry in orthodontics, is not directly related to the study. Thus, the landmark coordinate values on X-axis were not analysed by network. However, since our materials (CBCT and facial scan) were 3D, multiple non-midline landmarks were taken into consideration, covering more information than did previous 2D studies.

The traditional multivariate linear regression model could not accurately predict lip positions of new patients [40]. This was partly because it calculated many-to-one relationships, ignoring the relationships among independent variables. Systems biology theory holds that for a complex biological system, the relationships among variables are more important to the system than the variables themselves [41]. If the intricate interrelation network of variables cannot be mined sufficiently, it is impossible to accurately predict soft tissue morphology. The advantages of network analysis are that it can concentrate on relationships between components, visualize and quantify multiple relationships as a whole, find out easily overlooked relationships, and reflect rules of complex systems comprehensively [42].

An appropriate threshold is necessary for the clear visualization and description of a system. In general, the lower the threshold is, the denser the network is. It would be difficult to make a network effective if it were too dense or too sparse. By selecting the appropriate threshold according to the specific values of correlation coefficient matrix, we could obtain a network with moderate density, which well reflected the diverse correlations among various parts of the CMF system or the differences between the two groups. In the present study, the threshold values in networks of the same axis were high. For the network of hard tissue Y-axis and soft tissue Y-axis, T was set as 0.9, whereas for the network of hard tissue Z-axis and soft tissue Z-axis, T was set as 0.8. These threshold values were higher than those of previous orthodontic studies using cephalometric measurements as variables [19, 20, 21, 22]. This was because the correlations between landmarks (e.g., A and A’) were greater than those between cephalometric measurements with large differences in composition (e.g., ANB and ULT). Thus, higher thresholds were needed to generate effective networks of the same axis. Moreover, the thresholds of the networks of the same axis were higher than those in the networks of different axes (T = 0.2). These thresholds were set according to the overall coefficient values in the correlation matrix of each network, indicating that the final and actual positions of soft tissues in certain dimension (e.g., sagittal) were more related to the hard tissue positions on the same axis (e.g., sagittal) than to the hard tissue positions on other axes (e.g., vertical). Therefore, while discussing the actual position of soft tissues, we ignored the influence of the hard tissue positions on other axes.

For the network of hard tissue Y-axis and soft tissue Y-axis, in G1 (Fig. 8B), the effect of hard tissues on lower lip was stronger than that on upper lip. Therefore, the estimation of sagittal upper lip position may be more inaccurate. The most relevant hard tissue landmarks were located between the level of cemento-enamel junction (CEJ) of upper teeth and root apex of lower teeth. This suggested that soft tissue prediction in sagittal direction should be based on these areas, excluding the less relevant landmarks (e.g., root apex of upper teeth). In G2 (Fig. 8C), the relevance of lower tooth and mandibular landmarks decreased, and the connection between lower lip and hard tissues was weakened. Compared with G1, the G2 network was sparser, and the values of the global network metrics decreased (Table 5), indicating that the correlation between hard and soft tissues was weaker. Consequently, the accuracy of predicting the anteroposterior soft tissue position might decrease. In clinical practice, skeletal Class I-norm-straight pattern is often considered as the ‘standard’ phenotype, in which soft tissue surface in the lower 1/3 of the face is more consistent with the underlying hard tissue morphology. For example, variation of the mentolabial fold is uncommon in Class I-norm-straight patients, in whom it mostly shapes along the contour of the skeletal chin, well reflecting the concave curve of the anterior mandible. However, in Class II-hype-convex patients, the shape of the mentolabial fold could be typical and could also be wavy with twists and turns or nonexistent, even if the underlying hard tissue shapes were similar. This variation was partly a result of the difficulty in obtaining a relaxed muscle condition [6]. Even though the 3D facial scans were taken when the patients were instructed to relax all the facial muscles, a strained lip and chin position could occur because of unconscious muscle hyperactivity.

For the network of hard tissue Z-axis and soft tissue Z-axis (Fig. 9), the correlation coefficients were generally lower than those of Y-axis, indicating increased uncertainty of soft tissue positions in vertical dimension. In G1 (Fig. 9B), upper lip had stronger connections with hard tissues than did lower lip, contrary to the result on Y-axis. The hard tissue landmarks with the most links were similar to those of Y-axis. These findings suggested that these landmarks were vital for soft tissue position prediction in both the vertical and sagittal directions in G1. In G2 (Fig. 9C), the hard tissue landmarks with higher ‘degrees’ (redder nodes) tended to be distributed more forward and downward than those in G1, suggesting that the areas that should be used for soft tissue prediction differed from those in G1. In vertical dimension, the general hard-soft tissue correlation strengths of the two groups were similar (Table 6). Thus, the above-mentioned larger morphological variation in soft tissues in Class II-hype patients was mainly caused by sagittal variation rather than vertical variation. Moreover, the positive hard-soft tissue correlations of G2 were in accordance with the conclusion of a previous study that the height of the lips was greater in hyperdivergent patients [8].

Due to the elasticity of soft tissues, the hard tissue position on one axis (e.g., vertical) will affect soft tissue positions on other axes (e.g., sagittal). The overall correlation coefficients of the hard-soft tissue relationships were lower for different axes than for the same axis. Accordingly, the threshold in the networks of different axes was set at 0.2. Although 0.2 ~ 0.4 represented only a weak correlation, the distinction of the hard-soft tissue relationship between G1 and G2 could be clearly shown by comparison.

In G1, the correlation coefficient matrix of hard tissues (Fig. 12A) showed that the correlation between sagittal position of any hard tissue landmark and vertical position of any other hard tissue landmark was positive. This meant that if hard tissues became vertically farther away from Ba point, they would also become sagittally farther away from Ba point. Thus, the G1 hard tissues were proportionate and harmonious in sagittal and vertical directions. For the network of hard tissue Z-axis and soft tissue Y-axis, in G1 (Fig. 10B), the correlation between Z-axis value of any hard tissue landmark and Y-axis value of any soft tissue landmark was positive, mainly owing to the positive correlation between Y and Z-axis value of hard tissues (Fig. 12A). Similarly, the correlation between Y-axis value of any hard tissue landmark and Z-axis value of any soft tissue landmark was positive (Fig. 11B), reflecting a harmonious hard-soft tissue relationship in G1 with regard to sagittal and vertical directions. Compared with G1, the hard tissue correlation matrix of G2 (Fig. 12B) showed that the correlation decreased (lighter green) or even became negative (red). This indicated that if hard tissues became vertically farther away from Ba point, their trend of becoming sagittally farther away from Ba point would be weakened or even reversed, suggesting that the sagittal and vertical sizes of hard tissues were not as consistent as those in G1. In G2, the correlations were mostly negative (Fig. 10C), meaning that the more downward (vertically farther away from Ba point) the hard tissues were, the more backward (sagittally closer to Ba point) the soft tissues were.

Riesmeijer AM et al. [43] reported that Class II samples had greater SN-MP angles than Class I growth patterns, indicating a more downward (increased vertical size) and backward (decreased sagittal size) growth pattern that could result in inconsistency in these two directions, as revealed in the present study. They found no significant difference in mandibular length or mandibular body length between the two groups with basically complete growth and development. Thus, it can be deduced that the inconsistency between vertical and sagittal mandibular positions of G2 was mainly caused by the clockwise growth direction rather than the actual shape of the mandible. In a longitudinal study [44], Yoon SS et al. concluded that the overall craniofacial growth patterns of Class I and Class II girls were similar, with the face becoming more flattened, the ANB angle decreasing, and the mandible demonstrating forward rotation with a decrease in the SN-MP angle. In G2 subjects of the present study, we found that this growing trend might only have reduced the CMF discrepancy, but not diminished it completely. Chung CH et al. [45] compared craniofacial growth of untreated skeletal Class II subjects with different vertical patterns (hypodivergent, normodivergent, and hyperdivergent). Their results showed that for 9-year-old children, the hyperdivergent group had greater facial convexity, larger Y-axis and gonial angles, and greater anterior facial height. From ages 9 to 18, all the groups showed changes in accordance with the findings of Yoon SS et al. [44]. However, the hyperdivergent group displayed significantly less facial flattening and less mandibular forward rotation than did the hypodivergent group. Thus, among skeletal Class II patients, the hyperdivergent ones have the worst initial facial profile and the least improvement from growth. This can result in the obvious disharmony of facial appearance in adulthood, as shown in the present study in many ways compared with Class I-norm patients.

For the network of hard tissue Y-axis and soft tissue Z-axis, in G1 (Fig. 11B), as mentioned above, all the correlations were positive. In G2, all the correlations of the mandible landmarks were negative (Fig. 11C), meaning that the more backward (sagittally closer to Ba point) the mandible was, the more downward (vertically farther away from Ba point) the soft tissues were. This could result in the classic facial appearance of skeletal Class II-hype patients with a long lower 1/3 face. This finding was also consistent with our experience in orthodontic treatment to avoid clockwise mandibular rotation [2]. It is known that muscle dysfunctions and oral habits have great influence on the facial soft tissue contour [4]. Attempts to gain lip closure in patients with protrusive incisors or hyperdivergent skeletal pattern result in greater lip strain accompanied by hyperactive mentalis function and elevation of the chin integument. The retrusive mandible directly pulled the lower lip and chin soft tissue downward. Subsequently, to get closure with the lower lip, the upper lip muscles were also forced downward. Eventually, all the soft tissues of the lower 1/3 of the face were adjusted downward due to the retrusive mandible. In contrast, all the correlations of teeth and maxilla were positive (Fig. 11C).

In summary, we found that there were major differences in the hard-soft tissue relationships between the two types of patients, and in Class II-hype-convex pattern:

The soft tissue morphology was more variable than that of Class I-norm-straight pattern, mainly due to the greater variation in sagittal direction;

The most relevant hard tissue landmarks on which soft tissue predictions in vertical direction should be based tended to be distributed more forward and downward than Class I-norm-straight pattern;

Class II-hype-convex pattern was not harmonious or proportionate between sagittal and vertical positions of the lower 1/3 of the face, as was Class I-norm-straight pattern. From this point of view, it is an unbalanced CMF phenotype.

However, many previous studies [4, 5, 7, 11, 12, 13, 14] have analysed patients with different skeletal types as a whole when looking for the morphological mechanism of soft tissues or making predictions. This might be one of the reasons for their limited accuracy. Therefore, similar studies should distinguish among different skeletal and profile patterns to achieve higher accuracy.

Network analysis is essentially a deep data mining method for extracting key information from complex systems. Once the network (“graph”) is computed, the topological structure of the data (input) is abstracted and encoded in simpler structures, on which the machine learning algorithms can be run [42]. Hence, our work provided a basic data environment for machine learning algorithms to further data mining and prediction by building neural network regression models.

The present study was limited in the relatively small sample size, whereas a larger group collected in multiple centers would have been a better representation of the two malocclusion patterns. Moreover, the study proposed that there could be differences in the accuracy of predicting soft tissue contour among different skeletal patterns or different areas and suggested a few hard tissue landmarks on which soft tissue prediction should be based. Further studies that validate these assumptions are needed. In addition, a future study utilizing both pre- and post-treatment data would provide us with more beneficial information about the mechanism of facial soft tissue contour change caused by tooth movement in orthodontic treatment.

There were major differences in the hard-soft tissue relationships between the two types of patients, and in Class II-hype-convex pattern:

The soft tissue morphology was more variable than that of Class I-norm-straight pattern, mainly due to the greater variation in sagittal direction;

The most relevant hard tissue landmarks on which soft tissue predictions in vertical direction should be based tended to be distributed more forward and downward than Class I-norm-straight pattern;

Class II-hype-convex pattern was not harmonious or proportionate between sagittal and vertical positions of the lower 1/3 of the face, as was Class I-norm-straight pattern. From this point of view, it is an unbalanced CMF phenotype.

This study introduced network analysis to the evaluation of the 3D hard-soft tissue morphological relationships in the CMF system, and provided a basic data environment for machine learning algorithms to further data mining and soft tissue prediction. It was pioneering for deepening the understanding of facial soft tissue morphology, and pushed the application of network science forward in clinical orthodontic field.

2&1	Most prominent point of the upper lip on the saggital plane that passing through the midpoint of ULP and Ch
2D	two-dimensional
3D	three-dimensional
4&3	Most prominent point of the lower lip on the saggital plane that passing through the midpoint of LLP and Ch
6&5	Point of the upper lip on the intersection of saggital plane that passing through the midpoint of ULP and Ch and the horizontal plane that passing through A’
8&7	Point of the lower lip on the intersection of saggital plane that passing through the midpoint of LLP and Ch and the horizontal plane that passing through B’
A'	Soft-tissue A-point
A	Subspinale (The most concave point of the maxillary on the maxilla midline)
ANB	A-N-B angle
ANS	Anterior nasal spine (The most anterior point of the anterior nasal spine)
ASD	average surface distance
B'	Soft-tissue B-point
B	Supramental (The most concave point of the mandibular labial surface on the mandibular midline)
Ba	Basion (The midpoint of the anterior edge of the foramen magnum)
CBCT	cone-beam computed tomography
Ch	Cheilion (Left or right corner of the mouth)
Class II-hype-convex	skeletal Class II hyperdivergent pattern with convex profile
Class I-norm-straight	skeletal Class I normodivergent pattern with straight profile
CMF	craniomaxillofacial
DICOM	Digital Imaging and Communications in Medicine
FCA	Facial Convexity Angle, the Angle at Sn subtended by G and Pog'
G	Glabella
G1	Group1
G2	Group2
Gn	Gnathion
Go	Gonion (The point located on the mandibular angle with the maximum curvature)
ICC	intraclass correlation coefficient
ICP	iterative closest point
ID	Infradentale (The most superior and anterior point of the alveolar process between the lower central incisors)
L1a	The root apical of lower central incisor
L1J	The midpoint of labial CEJ of lower central incisor
L1L	The point on the intersection of the labial surface of lower incisor and the horizontal line passing through LL
L2a	The root apical of lower lateral incisor
L2J	The midpoint of labial CEJ of lower lateral incisor
L3a	The root apical of lower canine
L3J	The midpoint of labial CEJ of lower canine
L6J	The midpoint of buccal CEJ of lower first molar
LL	The most anterior point of lower lip
LLP	Lower lip (Most prominent point of the lower lip on the mid-saggital plane)
Lower Lip Thickness (LLT)	Distance between LL and L1L
M	mean
ME	Menton (The most inferior point of the mandibular sysmphysis on the midline of mandibular)
Me'	Soft-tissue menton
N	Nasion (Nasal root point: the most convex point on the nasal frontal suture)
O	Orbitale (The most inferior point of the orbital margin)
OBJ	object
PNS	Posterior nasal spine (The most posterior point of the posterior nasal spine)
Po	Porion (The most superior and lateral point of bony external acoustic meatus image)
POG	Pogonion (The most anterior point of mandibular sysmphysis on the midline of mandibular)
Pog’	Soft-tissue pogonion
PRO	The most inferior and anterior point of the alveolar process between the upper central incisors
RF	The most concave point/middle point of the the anterior margin of the mandibular ramus
RMP	The point located on the transition site of the anterior margin of the mandibular ramu to the upper edge of the mandibular body with the maximum curvature
RP	The most concave point/middle point of the the posterior margin of the mandibular ramus
S	Sella (The center point of the sella turcica)
SD	standard deviation
Sn	Subnasale
SN-GoGn	Angle formed by the SN plane and mandibular plane
STL	stereolithography
U1	The midpoint of the incisal margin of upper central incisor
U1a	The root apical of upper central incisor
U1J	The midpoint of labial CEJ of upper central incisor
U1L	The point on the intersection of the labial surface of upper incisor and the horizontal line passing through UL
U2	The midpoint of the incisal margin of upper lateral incisor
U2a	The root apical of upper lateral incisor
U2J	The midpoint of labial CEJ of upper lateral incisor
U3	The cusp of upper canine
U3a	The root apical of upper canine
U3J	The midpoint of labial CEJ of upper canine
U6	The mesio-labial cusp of upper first molar
U6J	The midpoint of buccal CEJ of upper first molar
UL	The most anterior point of upper lip
ULP	Upper lip (Most prominent point of the upper lip on the mid-saggital plane)
Upper Lip Thickness (ULT)	Distance between UL and U1L

Acknowledgements

None.

Authors’ contributions

TW conceptualized this study, performed the analysis and wrote the first draft of this manuscript. KN offered technical support in data processing and implemented the calculation of correlation matrix. KX performed the validation test. YF, GC, BH and TX provided valuable suggestions on the study design. GS provided generous help in sample collection. YP and TX supervised the study. All authors contributed to the manuscript content and revisions and gave final approval of the manuscript. All authors gave final approval of the version of the manuscript to be published. All authors read and approved the final version of the manuscript.

Funding

This work was supported by National Natural Science Foundation of China (82071172).

Data availability

The datasets used during the current study are available from the corresponding author on reasonable request.

Ethics approval and consent to participate

Ethics approval for this study was obtained by the Ethics Committee of Peking University Biomedical Sciences (PKUSSIRB-202058145). All parents and/or their legal guardian(s) signed informed consent forms before enrollment. All the procedures were followed in accordance with the Declaration of Helsinki.

Consent for publication

Written informed consent from all subjects for publication of identifying information/images has been obtained.

Competing interests

The authors declare no competing interests.

Author details

¹Department of Orthodontics, Peking University School and Hospital of Stomatology & National Center for Stomatology & National Clinical Research Center for Oral Diseases & National Engineering Research Center of Oral Biomaterials and Digital Medical Devices, Beijing, China

²Beijing Key Laboratory of Digital Stomatology, Peking University School and Hospital of Stomatology, Beijing, China

³Key Laboratory of Machine Perception (MOE), Department of Machine Intelligence, School of Artificial Intelligence and Technology, Peking University, Beijing, China

⁴Third Clinical Division, Peking University School and Hospital of Stomatology & National Center for Stomatology & National Clinical Research Center for Oral Diseases & National Engineering Research Center of Oral Biomaterials and Digital Medical Devices, Beijing, China

⁵Second Clinical Division, Peking University School and Hospital of Stomatology & National Center for Stomatology & National Clinical Research Center for Oral Diseases & National Engineering Research Center of Oral Biomaterials and Digital Medical Devices, Beijing, China

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No competing interests reported.

Network analysis of three-dimensional hard-soft tissue relationships in the lower 1/3 of the face: Skeletal Class I-normodivergent malocclusion versus Class II-hyperdivergent malocclusion

Status:

Journal Publication

Version 1

Abstract

Background

Methods Fifty-two adult patients (42

Results

Conclusion

Figures

Introduction

Methods

Subjects

Cephalometric analysis

Superimposition of CBCT and 3D facial scan images

3D landmark identification

Network analysis

Results

Discussion

Conclusions

Abbreviations

Declarations

References

Additional Declarations

Status:

Journal Publication

Version 1