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. 2025 Jan 8;25:42. doi: 10.1186/s12903-024-05345-9

Feasibility of occlusal plane in predicting the changes in anteroposterior mandibular position: a comprehensive analysis using deep learning-based three-dimensional models

Bingran Du 1,#, Kaichen Li 2,#, Zhiling Shen 3, Yihang Cheng 3, Jiayan Yu 3, Yaopeng Pan 1, Ziyan Huang 3, Fei Hu 3, Xiaohui Rausch-Fan 4, Yuanpeng Zhu 2,✉, Xueyang Zhang 1,3,✉
PMCID: PMC11707869  PMID: 39780117

Abstract

Background

A comprehensive analysis of the occlusal plane (OP) inclination in predicting anteroposterior mandibular position (APMP) changes is still lacking. This study aimed to analyse the relationships between inclinations of different OPs and APMP metrics and explore the feasibility of OP inclination in predicting changes in APMP.

Methods

Overall, 115 three-dimensional (3D) models were reconstructed using deep learning-based cone-beam computed tomography (CBCT) segmentation, and their accuracy in supporting cusps was compared with that of intraoral scanning models. The anatomical landmarks of seven OPs and three APMP metrics were identified, and their values were measured on the sagittal reference plane. The receiver operating characteristic curves of inclinations of seven OPs in distinguishing different anteroposterior skeletal patterns and correlations between inclinations of these OPs and APMP metrics were calculated and compared. For the OP inclination with the highest area under the curve (AUC) values and correlation coefficients, the regression models between this OP inclination and APMP metrics were further calculated.

Results

The deviations in supporting cusps between deep learning-based and intraoral scanning models were < 0.300 mm. The improved functional OP (IFOP) inclination could distinguish different skeletal classification determinations (AUC Class I VS Class II = 0.693, AUC Class I VS Class III = 0.763, AUC Class II VS Class III = 0.899, all P values < 0.01) and the AUC value in skeletal Classes II and III determination was statistically higher than the inclinations of other OPs (all P values < 0.01). Moreover, the IFOP inclination showed statistical correlations with APMP metrics (rAPDI = -0.557, rANB = 0.543, rAF−BF = 0.731, all P values < 0.001) and had the highest correlation coefficients among all OP inclinations (all P values < 0.05). The regression analysis models of IFOP inclination and APMP metrics were yAPDI = -0.917x + 91.144, yANB = 0.395x + 0.292, and yAF−BF = 0.738x − 2.331.

Conclusions

Constructing the OP using deep learning-based 3D models from CBCT data is feasible. IFOP inclination could be used in predicting the APMP changes. A steeper IFOP inclination corresponded to a more retrognathic mandibular posture.

Keywords: Deep learning, Occlusal plane, Anteroposterior mandibular position

Background

The three-dimensional (3D) spatial position of the mandible, particularly its anteroposterior position, is crucial in human facial growth [1, 2]. An imbalance in the anteroposterior mandibular position (APMP) can lead to poor oral function [3] and concerns regarding facial aesthetics [4], which impair social and psychological quality of life [5]. With the advancement of technology, camouflage orthodontic treatment has rapidly progressed [6]. For adults with APMP imbalances who refuse the orthognathic surgery due to the economic and psychological burdens, camouflage orthodontic treatment ca.n be used to improve the facial aesthetics and oral function by promoting favorable mandibular rotation [7, 8].

Considering the complexity of the regulatory mechanism of orthodontics-induced mandibular rotation, a parameter in predicting changes in APMP is needed for orthodontists to conduct effective and efficient treatment. The occlusal plane (OP) refers to an imaginary surface at the level of occlusion [9]. Since the 1940s, numerous scholars have observed a fact that individuals with retrognathic or prognathic mandibular posture tend to show steeper or flatter OP [10–13], which indicates that OP inclination may be an important parameter in predicting APMP. However, this finding has not been consistently observed in all clinical orthodontic practices [14, 15], reflecting the uncertainty regarding the OP inclination as a predictive parameter for APMP. Therefore, further analysis is required to explore the relationship between OP inclination and APMP.

The inaccurate representation of various OPs may be the most limiting factor in analysing the relationship between OP inclination and APMP. Traditionally, many OPs used in clinical practice are represented by straight lines on two-dimensional radiographs, which are prone to inaccuracies due to landmark errors and image magnification [16]. Although cone-beam computed tomography (CBCT) can address these issues [17], achieving accurate and reliable representations of some OPs in maximum intercuspation remains challenging. Therefore, it is crucial to explore a more accurate method for representing various OPs in clarifying the relationship between OP inclination and APMP.

Recently, CBCT imaging-based deep neural networks have demonstrated high performance in segmenting teeth, alveolar bone, and other structures, significantly aiding clinical diagnostics, treatment, and evaluation [18–20]. Given the remarkable achievements of deep learning in the field of dentistry, the precise representation of OP in 3D models using deep learning-based CBCT segmentation would be possible.

This study aimed to analyse the relationships between the inclinations of different OPs and APMP metrics using deep learning-based 3D models and explore the feasibility of OP inclination used in predicting the changes in APMP. We hypothesised that there are differences in the relationships between the inclinations of various OPs and APMP metrics and that the inclination of specific OP can be used as a parameter in predicting changes in APMP.

Methods

CBCT images of 115 patients (63 females and 52 males, age range of 18–39 years) were obtained from our institution using NewTom VGi (Cefla, Imola, Italy). CBCT images were captured by the same technician under consistent settings, with a tube voltage of 110 kV and a current of 3 mA. The CBCT scans were taken with the patients seated, with their heads positioned according to three light beams. The upper horizontal light beam passed through the subnasale, the lower horizontal light beam passed through the anterior-most point on the chin, and the sagittal light beam was aligned with the midline of the patient’s face. During the scanning, the patients were required to remain still and refrain from swallowing. All patients provided informed consents to participate in this study, and the study was approved by the ethics review board of our institution (Approval No.: KYLS20220913).

The inclusion criteria were as follows: (1) fully erupted permanent dentition; (2) no previous orthodontic treatment; (3) no bone defects, severe mandibular skeletal asymmetry (menton deviation > 4 mm) [21], or other craniomaxillofacial deformities; and (4) no tooth loss, severe tooth wear, dental prosthesis, or posterior crossbite. All included patients were categorised into skeletal Classes I, II, and III based on the results of the majority of the APMP metrics, including the anteroposterior dysplasia indicator (APDI) [22], ANB angle [23], and AF-BF distance [24]. In cases where all metrics for diagnosing anteroposterior skeletal classes did not align, a decision was made by an orthodontist based on radiographic evaluation and clinical judgment [25]. The final classification of the patients resulted in the following groups: skeletal Class I (n = 30), Class II (n = 51), and Class III (n = 34).

CBCT data were automatically segmented using deep learning technology (3D U-Net Convolution Neural Network) and reconstructed into 3D models in Remebot Jaw Motion Analyser (Beijing Ruiyibo Technology Co., Ltd., Beijing, China). Based on these 3D models, 13 landmarks on craniofacial hard tissues (Table 1) [26–29] and 70 landmarks on tooth cusps (Fig. 1), respectively, were marked by a trained resident using the 3D marking method that incorporates multi-planar reformations [30]. Subsequently, three reference planes were constructed in Geomagic Studio 2014 (3D Systems Inc., Rock Hill, SC, USA), including the Frankfort horizontal plane (FHP) [27], the sagittal reference plane (SRP) [26], and the coronal reference plane (CRP) (Fig. 2). The coordinates of corresponding landmarks and the reference plane information were then imported into MATLAB (MathWorks Inc., Natick, MA, USA), where the three APMP metrics and the inclinations of seven OPs were calculated.

Table 1.

Landmarks on craniofacial hard tissue

Landmark Abbreviation Definition
Nasion N Medial (and upper) point of the frontonasal suture[26]
Sella S Central point of the sella[26]
Anterior nasal spine ANS Medial and most anterior point of the nasal spine [26]
Posterior nasal spine PNS Medial and most distal point of the osseous palate [26]
Orbitale Or-L/Or-R The lowest point of the orbital rim L/R [26]
Pogonion Pog Medial and most anterior point of the mandible [26]
Internal Acoustic Foramen IAF-L/IAF-R The most lateral point of the internal auditory meatusat the skull base L/R[27]
Incisive foramen IF Anteroposterior and me-diolateral center of the incisive foramen [28]
Basion Ba Middorsal point of the anterior margin of the foramen magnum on the basilar part of the occipital bone [28]
A-point A The deepest bony point on the contour of the premaxilla below ANS [29]
B-Point B The deepest bony point on the contour of the mandible above the Pog [29]
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Fig. 1.

Fig. 1

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Landmarks on tooth cusps

Fig. 2.

Fig. 2

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Construction of reference planes. a: Front view of relevant anatomical landmarks. b: Top view of relevant anatomical landmarks. c: Three reference planes—SRP, sagittal reference plane (plane through N, Ba, and IF); FHP, Frankfort horizontal plane (plane perpendicular to the SRP and passing through two points: the midpoint of IAF-L and IAF-R and the midpoint of Or-L and Or-R); and CRP, coronal reference plane (plane passing through S and perpendicular to the SRP and FHP)

The APMP metrics included the APDI, ANB angle, and AF-BF distance, which were calculated as angular values or linear distances formed by the landmarks projected onto the SRP (Table 2; Fig. 3). OPs included the posterior OP [31], anterior OP [31], bisected OP [32], maxillary OP [33], mandibular OP [33], and functional OP (FOP) [34], which have been described in previous studies, as well as the improved FOP (IFOP), which we created according to the definition that FOP divides posterior occlusal contacts [35]. OP inclination was defined as the angle between the FHP and the sagittal projected line of OP. A negative value indicated that the projected line was angled above the FHP, whereas a positive value showed that the lines were angled below the FHP. The sagittal projected line was generated by projecting the corresponding cusps onto the SRP using the minimum distance method (Table 3; Fig. 4). The formula is as follows:

Table 2.

Metrics of APMP

Metrics Definition
APDI (°)

NP-FH ± NP-AB ± PP-FH.

NP-FH, the angle made by the the N-Pog* line and FHP;

NP-AB, the angle made by the the N-Pog* line and A*-B* line;

PP-FH, the angle made by the the ANS*-PNS* line and FHP;
ANB (°) The angle made by N-A* line and N-B* line
AF-BF (mm) The linear distance between points A* and B* projected onto the FHP
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*Corresponding points projected onto the sagittal reference plane (SRP)

Fig. 3.

Fig. 3

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Calculation of APMP metrics (with ANB as an example). a: Landmarks of the craniofacial hard tissue. b: Calculation of ANB on SRP. A' and B’, the corresponding points of A and B projected onto the SRP. APMP, Anteroposterior mandibular position; SRP, Sagittal reference plane

Table 3.

Corresponding cusps of occlusal planes (OPs)

OPs Abbreviation Corresponding cusps
Anterior OP AOP 21-M, 15-B, 25-B
Posterior OP POP midpoint (15-B, 25-B), 17-B2, 27-B2
Bisected OP BOP midpoint (21-M, 31-M), midpoint (16-B2, 46-B2), midpoint (26-B2, 36-B2)
Maxillary OP MxOP 21-M, 16-B1, 26-B1
Mandibular OP MnOP 31-M, 36-B1, 46-B1
Functional OP FOP midpoint (14-B, 44-B), midpoint (24-B, 34-B), midpoint (15-B,45-B), midpoint (25-B, 35-B), midpoint (16-B1, 46-B1), midpoint (16-B2, 46-B2), midpoint (26-B1, 36-B1), midpoint (26-B2, 36-B2)
Improved functional OP IFOP 14-B, 15-B, 16-B1, 16-B2, 17-B1, 17-B2; 24-B, 25-B, 26-B1, 26-B2, 27-B1, 27-B2; 14-L, 15-L, 16-L1, 16-L2 17-L1, 17-L2; 24-L, 25-L, 26-L1, 26-L2, 27-L1, 27-L2; 34-B, 35-B, 36-B1, 36-B2, 36-B3, 37-B1, 37-B2; 44-B, 45-B, 46-B1, 46-B2, 46-B3, 47-B1, 47-B2; 34-L, 35-L, 36-L1, 36-L2, 37-L1, 37-L2; 44-L, 45-L, 46-L1, 46-L2, 47-L1, 47-L2 (The tooth cusp tips mentioned without occlusal contacts in intercuspal position would be excluded.)
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Note: midpoint (cusp tip 1, cusp tip 2) refers to the midpoint between cusp tip 1 and cusp tip 2

Fig. 4.

Fig. 4

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Calculation of OP inclination (with MnOP as an example). a: Landmarks of cusps. b: Inclination of MnOP. Blue line, the sagittal projected line of MnOP. OP, Occlusal plane; MnOP, Mandibular occlusal plane

graphic file with name M1.gif

where Inline graphic is the error function representing the sum of squared distances; Inline graphic is the total number of cusps; Inline graphic) are the coordinates of the ith cusps; Inline graphic,Inline graphicand Inline graphic are parameters of the line equation Inline graphic; and Inline graphic represents the signed distance from the ith cusp to the line. The objective of this analysis was to determine the values of Inline graphic,Inline graphicand Inline graphic that minimise the sum of squared distances.

Before analysing the relationship between the inclinations of different OPs and APMP metrics, Trios 3 scanner-acquired intraoral scanning models (3Shape, Copenhagen, Denmark) of 25 randomly selected patients among 115 patients were collected and imported into Geomagic Control X v2020.1.1 (3D Systems Inc.) to evaluate the accuracy of supporting teeth cusps on deep learning-based 3D models. Deviations between deep learning-based and intraoral scanning 3D models were subsequently calculated using the following parameters: overall positive deviation, overall negative deviation, and absolute deviation of supporting cusps.

In this study, 60 samples were randomly selected 2 weeks after the initial landmarking and were re-landmarked by another resident to evaluate inter-examiner reliability. The resident also received standardised training to ensure consistency in the landmarking process.

Statistical analysis

Statistical analyses were performed using Microsoft Excel (Microsoft Corp., Redmond, WA, USA) and IBM SPSS for Windows, version 27.0 (IBM Corp., Armonk, NY, USA). P values < 0.05 were considered statistically significant. The Shapiro–Wilk test was used to assess the normality of the data.

Sex-based differences were determined using the Mann–Whitney U test and independent-samples t-test for non-normally and normally distributed data, respectively. Receiver operating characteristic (ROC) curve analysis was used to test the ability of the inclinations of different OPs to distinguish various anteroposterior skeletal patterns. The correlations between the inclinations of different OPs and APMP metrics were calculated and compared using Spearman’s rank correlation analysis and the method proposed by Meng et al. [36]. Moreover, the simple linear regression models were calculated to explore the precise relationship between the inclination of specific OP and each APMP metric. The intraclass correlation coefficient (ICC) [37] and measurement errors (Dahlberg’s formula) [38] of landmarks on craniofacial hard tissues and the cusps were calculated to assess the inter-examiner reliability.

Based on our preliminary research and clinical perspective, this study concentrated on examining the correlation between the IFOP inclination and APMP metrics, and the correlation coefficient was conservatively estimated to be 0.3. PASS15.0 (NCSS, LLC. Kaysville, UT, USA) software was used to calculate the sample size, with a type I error (α) of 0.05 and a power of 0.9 for hypothesis testing. This analysis yielded a required sample size of 112. Therefore, the CBCT images of 115 patients collected for this investigation were deemed sufficient.

Results

The values of overall positive deviation, overall negative deviation, and absolute deviation of supporting cusps between deep learning-based and intraoral scanning 3D models were 0.191 (0.095), -0.200 (0.103), and 0.231 (0.163) mm, respectively. Considering the clinically acceptable error (a threshold of < 0.300 mm) [39], the accuracy of supporting cusps on deep learning-based 3D models was acceptable.

The evaluation of the reliability of the measured landmarks revealed that the Dahlberg errors of the coordinate values of landmarks on tooth cusps (Tx, Ty, and Tz) were 0.529, 0.776, and 0.503 mm, respectively, and those of landmarks on craniofacial hard tissues (Cx, Cy, and Cz) were 0.935, 0.814, and 0.932 mm, respectively. Furthermore, the ICC scores of measured landmarks were all > 0.800, indicating a good level of reliability.

Given that no statistically significant differences were observed between sexes (all P values > 0.05), the evaluations were conducted on pooled data without distinguishing based on sex. The ability test results of inclinations of seven OPs in distinguishing different anteroposterior skeletal patterns are shown in Fig. 5. In distinguishing skeletal Classes II and III, the area under the curve (AUC) value of IFOP inclination was 0.899, statistically higher than the values of inclinations of other OPs (all P values < 0.01). Although no statistical differences were observed between the AUC values of IFOP inclination and those of other OPs in distinguishing the Class I and the other two skeletal classes, the AUC values of IFOP inclination were the highest (AUC Class I VS Class II = 0.693; AUC Class I VS Class III = 0.763). Moreover, the correlations between the inclinations of different OPs and APMP metrics are presented in Table 4. As shown in Fig. 6, the correlation coefficients between IFOP inclination and APMP metrics were statistically different from those between the inclinations of other OPs and APMP metrics (all P values < 0.05).

Fig. 5.

Fig. 5

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ROC curves of the inclinations of different OPs for anteroposterior skeletal pattern determinations. OP, Occlusal plane; ROC, Receiver operating characteristic

Table 4.

Correlations between inclinations of different occlusal planes (OPs) and APMP metrics

APDI (°) ANB (°) AF-BF (mm)
AOP (°) Correlation -0.362*** 0.327*** 0.493***
POP (°) Correlation -0.433*** 0.361*** 0.530***
BOP (°) Correlation -0.414*** 0.371*** 0.575***
MxOP (°) Correlation -0.378*** 0.326*** 0.515***
MnOP (°) Correlation -0.306*** 0.282** 0.450***
FOP (°) Correlation -0.488*** 0.451*** 0.679***
IFOP (°) Correlation -0.557*** 0.543*** 0.731***
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*, P value < 0.05; **, P value < 0.01; ***, P value < 0.001

Fig. 6.

Fig. 6

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Correlation coefficients between the inclinations of different OPs and APMP metrics. OP, Occlusal plane; APMP, Anteroposterior mandibular position; *, P value < 0.05; **, P value < 0.01; ***, P value < 0.001

To further analyse the relationships between IFOP inclination and APMP metrics, the regression model of IFOP inclination and APMP metrics were obtained, which are as follows: yAPDI = -0.917x + 91.144, yANB = 0.395x + 0.292, and yAF−BF = 0.738x − 2.331. The corresponding R2 values were 0.325, 0.311, and 0.474, respectively.

Discussion

In orthodontic practice, how to use the OP inclination to predict changes in APMP remains uncertain, which may lead to difficulty in establishing diagnosis, prognosis, and treatment plans for adults with mild to moderate APMP imbalance. To address this issue, our study aimed to analyse the relationship between OP inclination and APMP using deep learning-based 3D models, and to explore the feasibility of using OP inclination as a parameter for predicting the changes in APMP. The results from the ROC curve and correlation analyses of this study confirmed our hypothesis that the inclination of the IFOP formed by the contacting cusps of the posterior teeth could be used in predicting changes in APMP. Moreover, we found a steeper IFOP inclination corresponded to a more retrognathic mandibular posture.

Accurate representation of OP is foundational for analysing the relationship between OP inclination and APMP. While intraoral scanning can accurately capture the occlusal surface of the tooth for better OP representation [40], its limitations in application and high management costs hinder the acquisition of sufficient samples [41]. Therefore, we opted for deep learning-based CBCT segmentation to create OP instead of intraoral scanning. Although this technology has been successfully applied in maxillofacial disease diagnosis [42], its feasibility in creating OPs has not been thoroughly explored. Our study demonstrated that deep learning-based CBCT segmentation could identify the supporting cusps of both upper and lower teeth, indicating its promising potential for OP construction.

Accurate evaluation of APMP is the key to analysing the relationship between OP inclination and APMP. Considering that no single measurement is currently accepted as the “gold standard” to diagnose the APMP imbalance [43, 44], APDI, ANB, and AF-BF were employed in this study. APDI was selected because of its advantages in small measurement variability [45]. ANB was selected because of its convenience in assessing mandibular relationships only using NA and NB lines [46]. Additionally, we used AF-BF because of its advantages in eliminating the nasion’s effect [24]. Undoubtedly, the Wits appraisal is also an important metric for assessing APMP [47]. However, its measurement relies on OP as a reference plane, which exhibited uncertainty and variability in present study; therefore, we did not consider the Wits appraisal in this study.

Many studies have analysed the relationship between OP inclination and APMP [10–13]; however, few have explored the feasibility of OP inclination used in predicting changes in APMP. In the current study, we compared the ability test results of seven OP inclinations in distinguishing different anteroposterior skeletal patterns. The results showed that IFOP inclination had a significantly higher discrimination ability than did the other OP inclinations in skeletal Classes II and III, which indicated the higher feasibility of IFOP inclination used as a parameter in predicting the APMP changes. Furthermore, we also compared the correlation coefficients of inclinations of these OPs to validate the feasibility of IFOP inclination in predicting the APMP changes. These results showed that IFOP inclination, comprising contacted cusps from posterior teeth, had the strongest correlation with each APMP metric, and its correlation coefficient with each APMP metric was higher than that of the inclinations of other OPs. The superior performance of IFOP may be attributed to the cusps used used to represent this OP. As is well known, the mandibular condyle is an important growth site in the developing mandible, and is closely associated with maxillofacial skeleton morphogenesis [48, 49]. Mechanical loading is one of the local factors that could affect the growth of condylar cartilage [49, 50]. Differential condylar loading depends on the bite point of the dentition [51]. Therefore, the occlusal contact pattern may significantly contribute to the development of the APMP. Compared with other OPs, the IFOP, constructed by the contacted supporting cusps, more accurately represents the true occlusal contact pattern of the dentition. As a result, it may have a stronger correlation with each APMP metric.

To further explore the effect of the IFOP inclination on the change in each APMP metric, we constructed the regression models of the IFOP inclination and APMP metrics. According to the slope of regression models, the deeper the IFOP inclination, the smaller the APDI, and the greater the ANB and AF-BF. Specifically, the deeper the IFOP inclination, the more retrognathic the mandibular posture. This finding is consistent with that of a study by Coro et al. [12], despite the difference in the focused OP. Nevertheless, we also observed that the IFOP inclination accounted for 32.5%, 31.1%, and 47.4% of the variation in APDI, ANB, and AF-BF, respectively. This suggests that the predictive effect of the IFOP inclination on the changes in each APMP metric is not uniform. Specifically, in predicting changes in APDI and ANB, the effect of IFOP inclination appears to be more limited.

The OP is considered as the “workbench of orthodontics,” and the OP inclination is a key parameter need to be focused in the orthodontic treatment [52]. Previous studies have shown that orthodontists can distal en-masse move the dentition or adjust the vertical dimension of dental arches to achieve the control of OP inclination, which leads to the changes of APMP related metrics and improves oral function and facial aesthetics for adult patients with different skeletal malocclusions [53, 54]. Therefore, a quantitative evidence on the feasibility and efficiency of OP inclination to predict APMP changes is crucial for achieving the satisfied outcomes in camouflage treatment. The potential clinical applications of this study could be reflected in the identifying specific OP that need to be controlled and predicting changes in APMP metrics. The orthodontist could avoid the unfavorable rotation of mandible by controlling IFOP inclination during the treatment and develop an appropriate treatment strategy by evaluating the effect of IFOP inclination control on APMP. Considering that orthodontic treatment is oriented toward obtaining an acceptable aesthetic and functional mandibular position for the patient [55, 56], the more predictable of the IFOP inclination on the APMP changes, the better of treatment outcomes.

This study had some limitations. First, we only analysed the OPs formed by the cusps, which may overlook potential contributions from other anatomical structures. Future research will explore the different combinations of OPs and analyse their effect in predicting the changes in APMP. Second, the findings of this study require further clinical validation. In our next study, we will design a cohort study to measure and compare the aesthetic and functional metrics of adult patients with APMP imbalances who receive IFOP control and those who do not, at different stages of orthodontic treatment, to further validate our findings. Finally, the underlying reasons for the superior performance of IFOP than the other OPs need further investigation. Future studies will involve animal experiments and finite element analysis to validate the proposed mechanism.

Conclusion

This study demonstrated that using deep learning-based 3D models to construct the OP formed by the cusps from CBCT data is a feasible approach. Compared with other reported OPs, the IFOP is more suitable to be used as a parameter for predicting APMP changes. Within the range of inclinations that IFOP can achieve, a steeper IFOP inclination corresponded to a more retrognathic mandibular posture.

Acknowledgements

Not Applicable.

Abbreviations

3D

Three-dimensional

APDI

Anteroposterior dysplasia indicator

APMP

Anteroposterior mandibular position

AUC

Area under the curve

CBCT

Cone-beam computed tomography

FHP

Frankfort horizontal plane

ICC

Intraclass correlation coefficient

IFOP

Improved functional occlusal plane

OP

Occlusal plane

ROC

Receiver operating characteristic

SRP

Sagittal reference plane

Author contributions

B.D. conducted the investigation, methodology, and original draft preparation. K.L. handled software development, validation, and investigation. Z.S. was responsible for writing the original draft and formal analysis. Y.C. contributed to measurement and formal analysis. J.Y., Y.P., and Z.H. managed data curation and investigation. F.H. oversaw project administration. X.R.F. reviewed and edited the draft. Y.Z. worked on software, visualization, and methodology. X.Z. provided resources, supervision, and conceptualization. All authors have read and approved the final manuscript.

Funding

This work was supported by the Key Fields Special Project of Guangdong Universities (2021ZDZX1024), Foshan Engineering Technology Research Center for Oral Functional Occlusion Reconstruction of Periodontal Disease (GCJSYJZX2024-008), Guangdong Basic and Applied Basic Research Foundation (2024A1515010413), and the 2023 Provincial College Student Innovation and Entrepreneurship Training Program of Southern Medical University (S202312121171).

Data availability

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

Declarations

Ethics approval and consent to participate

All patients provided informed consents to participate in this study, and the study was approved by the Research Ethics Commission of the Department of Stomatology, Shunde Hospital, Southern Medical University (Approval No.: KYLS20220913). All procedures of this study were performed in accordance with the relevant guidelines and regulations.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Bingran Du and Kaichen Li contributed equally to this work as first authors.

Contributor Information

Yuanpeng Zhu, Email: zhuyuanpeng@csu.edu.cn.

Xueyang Zhang, Email: zxy123@smu.edu.cn.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

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

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