Introduction
Accurate assessment of skeletal maturity is essential for orthodontic treatment planning and growth modulation. This study aimed to develop a comprehensive machine learning (ML) model to predict skeletal maturation stages using cervical vertebral morphology, dental maturation stage (DMS), gender, and age.
Methods
A total of 860 patients with lateral cephalograms, panoramic, and hand-wrist radiographs were included. A baseline model using 6 cervical morphologic parameters was compared with enhanced models incorporating DMS, gender, and age. Six ML algorithms were evaluated, with CatBoost showing the highest performance. Feature importance was analyzed using 2 methods, and the final model was assessed using a confusion matrix, receiver operating characteristic curves, and calibration curves.
Results
Incorporating DMS, gender, and age significantly improved predictive performance. The CatBoost model achieved an area under the receiver operating characteristic curve of 0.924, an area under the precision-recall curve of 0.806, and an F1-score of 0.752. Feature importance analysis confirmed the strong predictive contribution of DMS, especially the mandibular second molar. The final model demonstrated high accuracy, strong discrimination, and good calibration across all skeletal maturity stages.
Conclusions
This study presents a novel and clinically practical ML model for skeletal maturity prediction, integrating routinely acquired orthodontic records. The results demonstrate that combining DMS with cervical morphology, age, and gender enhances prediction accuracy, offering a reliable alternative to traditional hand-wrist assessments.
Highlights
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Dental maturation stage (DMS) shows a strong correlation with skeletal maturity.
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Skeletal maturity was predicted using routine radiographs and demographic data.
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Adding DMS, sex, and age improves prediction accuracy over cervical parameters alone.
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CatBoost outperformed five other models in predicting skeletal maturity stages.
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DMS ranked third in feature importance, highlighting its critical predictive role.
The timing of orthodontic and dentofacial orthopedic treatments is crucial for optimizing treatment outcomes in growing patients. Accurate assessment of skeletal maturity enables clinicians to estimate remaining growth potential and determine whether the pubertal growth spurt has commenced or concluded. Because chronological age does not reliably reflect individual variability in growth, alternative assessments using biological or physiological age indicators, such as somatic, sexual, skeletal, and dental maturation, have been proposed. ,
Among these, hand-wrist radiographs are considered the gold standard for skeletal maturity assessment, particularly using the Fishman skeletal maturity indicator (SMI). However, this method exposes patients to additional radiation exposure, prompting the exploration of alternative approaches. The cervical vertebral maturation (CVM) method, favored for its simplicity and clinical feasibility, has been widely adopted. Nonetheless, its diagnostic reliability remains contentious. For instance, Perinetti et al reported that one-third of CVM-based visual assessments were inaccurate, casting doubt on their clinical dependability.
To enhance objectivity, several researchers have attempted to quantify cervical morphologic features into CVM-based assessments. Perinetti et al introduced a CVM coding system, whereas Chen et al developed a quantified CVM scoring model based on its correlations with hand-wrist skeletal maturity. Despite these efforts, subsequent studies have indicated that CVM alone provides limited diagnostic accuracy. The accuracy varied across populations and malocclusion types, and the sensitivity for detecting maturation stages was low in certain subgroups. ,,
Given these limitations, our study aims to integrate additional clinically accessible parameters beyond cervical morphology to enhance the accuracy of skeletal maturity prediction. Notably, recent evidence has highlighted the use of dental maturation stages (DMS), particularly the mandibular second molars, as indicators of skeletal maturity. Rodrigo et al showed that the Demirjian method, when applied to mandibular second molars, can reliably predict the onset of pubertal growth spurt. Similarly, Luciana et al validated the use of panoramic radiographs— widely employed in orthodontics—as a viable screening tool for assessing pubertal growth timing.
In parallel, artificial intelligence (AI) has advanced the analysis and interpretation of complex medical data. , As a subfield of AI, machine learning (ML) enables computers to learn from data patterns and generate predictive models, proving especially useful in diagnostic applications. Because of ML’s ability to model complex, nonlinear relationships and incorporate diverse features, it presents a promising tool for determining growth and development stages. Although some ML-based skeletal maturity models have recently emerged using lateral cephalograms, they typically rely on CVM staging and retain a categorical classification approach.
In this study, we developed an ML model to predict skeletal maturity stages based on the gold standard SMI method. To our knowledge, this represents the first effort to construct a data-driven, SMI-based model that integrates multiple biological indicators, including chronological age, sex, cervical vertebral morphology, and DMS. This study aimed to establish a more objective, accurate, and clinically applicable method for skeletal maturity assessment, reducing dependence on hand-wrist radiographs and leveraging routine orthodontic imaging for improved diagnostics.
Material and methods
This study was approved by the ethics committee of Stomatological Hospital of Chongqing Medical University (2025-032). The overall workflow of the study is illustrated in Figure 1 .
Flowchart depicting the design of the study. Input features included multimodal indicators (DMS, cervical morphologic parameters, sex, and age). The model predicted skeletal maturity stages determined by SMI (clinical gold standard), which can be applied to support the timing of growth-modification therapy.
A retrospective dataset comprising 860 patients who sought orthodontic treatment at the Stomatological Hospital of Chongqing Medical University between 2010 and 2024 was collected. The inclusion criteria were as follows: (1) chronological age of 6-18 years; (2) availability of 3 radiographic images—cephalometric, panoramic, and hand-wrist radiographs—taken simultaneously; (3) no history of trauma or systemic or local diseases affecting the face, cervical vertebrae, or hand-wrist regions; (4) no history of endocrine or bone-related disease; (5) no previous history of orthodontic treatment; and (6) high-quality radiographic images free from motion blur or artifacts. Pretreatment records, including demographic data, cephalometric, panoramic, and hand-wrist radiographs, were collected for analysis. Patients who had not yet reached SMI stage 1 were excluded. All personally identifiable information was removed, and only age and sex were retained to ensure confidentiality. Cephalometric and panoramic radiographs were obtained using a ProMax system (Planmeca, Helsinki, Finland). Exposure parameters for lateral cephalometric images were set at 80 kV, 10 mA, and 0.5 seconds. For panoramic images, the parameters were 66 kV, 8 mA, and 15 seconds. Wrist radiographs were acquired with a CS 9000C system (Carestream Health, Rochester, NY) using exposure settings of 60 kV, 10 mA, and 0.5 seconds.
Each patient’s radiographs were assessed to evaluate hand-wrist maturation, dental maturation, and cervical vertebral morphology ( Fig 2 , A – C ). All radiographic evaluations were independently performed by 2 calibrated orthodontists, each with more than 5 years of clinical experience in growth and development assessment. Before the study, the examiners underwent reliability training to ensure consistency in staging criteria. Panoramic and hand-wrist radiographs were evaluated using Windows Photo (Microsoft, Redmond, Wash) on a 14.0-inch LED HD screen (2880 × 1800 pixels). Evaluations were conducted under dim lighting by 2 calibrated investigators (M.G. and Y.D.), who were allowed to zoom and adjust brightness and contrast as needed. In cases of disagreement, a third investigator (D.A.), a senior orthodontist with over 15 years of clinical practice, provided the final judgment. Each imaging modality was assessed independently and in duplicate. Maturation stages were determined as follows: (1) for DMS, the Demirjian method was applied to the mandibular second molar for panoramic radiographs ( Fig 2 , A and Table Ⅰ ) and (2) for SMI, the Fishman method was applied to hand-wrist radiographs ( Fig 2 , C and Table Ⅰ ). Consistent with previous studies that grouped the Fishman 11 SMIs (1-11) into broader developmental phases based on growth velocity patterns, the present study also categorized the stages into 4 clinically meaningful groups. ,, In our study, we adopted a 4-stage system: SMI 1-3 were combined into stage I (period of accelerating velocity), SMI 4-7 into stage II (period of high velocity), SMI 8-9 into stage III (period of deceleration velocity), and SMI 10-11 into stage IV (period of completing velocity).
Representative radiographic indicators of skeletal maturity: A, Representative images of each dental maturational stage according to the method proposed by Demirjian; B, Landmarks and measurement definitions for cervical vertebral morphology: reference points ( left ) include C2d-C4d (most superior points of the lower borders of C2-C4), C2a/C2p/C3la/C3lp/C4lp (most anterior and posterior points on the lower borders), C3ua/C3up/C4ua/C4up (most superior points on the anterior and posterior borders), C3um/C4um (midpoints of the upper borders), and C3am/C4am (midpoints of the anterior borders); corresponding quantitative parameters ( right ); C, Hand-wrist radiographs showing the Fishman SMIs (1-11).
Table I
Definitions of dental maturity stages, cervical morphologic parameters, and SMI
| Parameter | Definition |
|---|---|
| DMS | |
| a | Calcification of single occlusal points without different calcifications |
| b | Fusion of mineralization points; the contour of the occlusal surface is recognizable |
| c | Enamel formation has been completed at the occlusal surface, and dentine formation has begun. The pulp chamber is curved, and no pulp horns are visible |
| d | Crown completed to the cementoenamel junction; root formation begins |
| e | The root length remains shorter than the crown height. The walls of the pulp chamber are straight, and the pulp horns have become more differentiated than in the previous stage. In molars, the root bifurcation has commenced to calcify |
| f | The walls of the pulp chamber now form an isosceles triangle, and the root length is equal to or greater than the crown height. In molars, the bifurcation has developed sufficiently to give the roots a distinct form |
| g | The walls of the root canal are now parallel, but the apical end is partially open. In molars, only the distal root is rated |
| h | The root apex is completely closed (distal root in molars). The periodontal membrane surrounding the root and apex is uniform in width throughout |
| Morphologic features of the CV | |
| @2 | Anterosuperior angle of C2d-C2p connection to C2p-C2a connection |
| AH3 | Vertical distance of C3ua to the connection of C3ip and C3ia |
| PH3 | Vertical distance of C3up to the connection of C3ip and C3ia |
| AH3/PH3 | Ratio of AH to PH3 |
| H4 | Vertical distance of C4um to the connection of C4ip and C4ia |
| W4 | Vertical distance of C4m to the connection of C4um and C4lp |
| H4/W4 | Ratio of H4 to W4 |
| SMI | |
| SMI 1-3 | Epiphysis width approximating diaphysis width; observed in the third finger distal phalanx (SMI 1), third finger proximal phalanx (SMI 2), and fifth finger middle phalanx (SMI 3) |
| SMI 4 | Ossification indicated by the appearance of the adductor sesamoid of the thumb |
| SMI 5-7 | Capping of epiphysis observed in the third finger distal (SMI 5) and proximal phalanges (SMI 6), and in the fifth finger middle phalanx (SMI 7) |
| SMI 8-10 | Fusion of epiphysis and diaphysis in the third finger distal (SMI 8), proximal (SMI 9), and middle phalanges (SMI 10) |
| SMI 11 | Complete fusion of the radius bone |
CV, cervical vertebrae.
Cephalometric radiographs were imported into ImageJ open-source image-analysis software (version 1.53q for Windows; National Institutes of Health, Bethesda, Md), resized to their actual size, and anatomic landmarks were manually traced. Measurements were conducted independently by 2 investigators (M.G. and G.Y.), and mean values were used in the analysis. Interobserver reliability was assessed using the intraclass correlation coefficient. All features used to build the ML prediction model are illustrated in Figure 2 , B and Table Ⅰ .
ML models were constructed as outlined in Figure 1 . The target variable was the SMI stage. Input features included chronological age, sex, DMS, and cervical vertebral morphologic parameters. The Spearman rho (ρ) correlation coefficient was used to assess associations between these features and the SMI stage.
All modeling was performed using Python programming (version 3.8.0; Python Software Foundation, Wilmington, Del). The Scikit-learn framework was applied for model development and evaluation. Data preprocessing was carried out using the Python Pandas package. Categorical variables, such as gender, were converted into binary numeric values. The dataset was randomly divided into a training set (n = 602) and a testing set (n = 258). The training set was used for model derivation, whereas the testing set was used for independent evaluation. A 5-fold cross-validation strategy was applied to the training set to prevent overfitting and enhance model generalizability.
Six commonly used ML algorithms were compared, including gradient boosting (CatBoost, XGBoost), support vector machine, Naïve Bayes, random forest, and decision tree. , The model hyperparameters were determined through systematic grid search with 5-fold cross-validation. Detailed parameter settings and implementation procedures are provided in the Appendix.
To directly assess whether the performance gains justify added complexity, we fit a conventional multinomial logistic regression using the same predictors and preprocessing to serve as a baseline comparator. The performance of each model was evaluated using several standard classification metrics: accuracy, area under the receiver operating characteristic curve (AUC-R), area under the precision-recall curve (AUC-P), precision, recall, and F1-score (F1).
To better understand model performance and feature contribution, we compared models before and after incorporating DMS, sex, and age. In addition, we examined model performance across different sagittal skeletal patterns and between sexes. Feature importance analysis was conducted using 2 methods: (1) CatBoost’s built-in feature importance, which quantifies the average gain attributed to each feature across decision splits and (2) permutation importance, implemented using the scikit-learn library, which measures performance degradation when individual features are randomly shuffled. To further assess the final model’s classification performance and reliability, we generated a confusion matrix, a receiver operating characteristic (ROC) curve, and a calibration plot, thereby evaluating both the model’s discriminatory power and the agreement between predicted probabilities and actual outcomes.
Results
A heatmap visualizing SMI stage distribution across chronological age is presented in Figure 3 , A . The color intensity represents the frequency of patients at each age-SMI combination, with darker shades indicating higher counts. Table Ⅱ shows the mean chronological age, standard deviation, and age range for each SMI stage, stratified by sex and grouped into 4 skeletal maturation stages. The data confirmed that females generally reach skeletal maturity earlier than males.
Heatmaps illustrating skeletal maturity patterns and correlations: A, Distribution of SMI across chronological age; B, Spearman rho (ρ) correlation matrix among cervical morphologic parameters and SMIs.
Table II
Summary of stages and statistical measurements
| Stages | SMI | Sex | n | Mean | SD | Min | Max |
|---|---|---|---|---|---|---|---|
| I | 1 | M | 68 | 9.53 | 1.34 | 6 | 12 |
| F | 24 | 8.04 | 1.08 | 6 | 10 | ||
| 2 | M | 41 | 10.85 | 1.22 | 8 | 14 | |
| F | 27 | 9.11 | 1.34 | 7 | 14 | ||
| 3 | M | 70 | 11.01 | 0.99 | 8 | 13 | |
| F | 50 | 9.84 | 1.06 | 7 | 12 | ||
| II | 4 | M | 18 | 11.83 | 1.10 | 10 | 14 |
| F | 22 | 10.50 | 1.50 | 8 | 13 | ||
| 5 | M | 22 | 11.68 | 0.95 | 10 | 13 | |
| F | 20 | 10.50 | 0.76 | 9 | 12 | ||
| 6 | M | 35 | 12.17 | 0.95 | 11 | 14 | |
| F | 49 | 10.96 | 1.04 | 8 | 13 | ||
| 7 | M | 27 | 12.41 | 1.05 | 10 | 14 | |
| F | 59 | 11.00 | 0.89 | 8 | 12 | ||
| III | 8 | M | 19 | 13.32 | 1.06 | 12 | 15 |
| F | 54 | 11.76 | 1.03 | 9 | 14 | ||
| 9 | M | 17 | 12.94 | 1.25 | 10 | 15 | |
| F | 67 | 11.75 | 0.93 | 9 | 14 | ||
| IV | 10 | M | 13 | 13.69 | 1.11 | 12 | 16 |
| F | 71 | 12.48 | 1.18 | 10 | 16 | ||
| 11 | M | 14 | 15.21 | 1.12 | 14 | 18 | |
| F | 63 | 13.38 | 1.46 | 11 | 18 |
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