Transverse Growth and Torque Compensation of First Molar in Adolescents Using 3D Digital Dental Analysis

Transverse Growth and Torque Compensation of First Molar in Adolescents Using 3D Digital Dental Analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Transverse Growth and Torque Compensation of First Molar in Adolescents Using 3D Digital Dental Analysis Shiyao Liu, Yun Ding, Tianmin Xu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8518955/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 16 You are reading this latest preprint version Abstract Background To investigate age-related changes in transverse intermolar width and crown torque of maxillary and mandibular first permanent molars in adolescents, and to explore torque as a compensatory mechanism for asymmetric transverse skeletal growth. Methods A total of 470 dental casts and corresponding posteroanterior cephalograms from 124 subjects (43 males and 81 females) aged 8–18 years were analyzed using a cohort-based design, incorporating repeated records when available to evaluate transverse growth. Maxillary and mandibular basal bone widths were measured on posteroanterior radiographs. Dental casts were digitized and analyzed to obtain intermolar width and molar crown torque. Statistical analyses included independent t tests, one-way ANOVA with Bonferroni correction, and Pearson correlation analysis. Results Both maxillary and mandibular basal bone widths increased with age, with mandibular basal growth exceeding maxillary growth. Despite this skeletal pattern, maxillary intermolar width increased more than mandibular intermolar width (3.16 mm vs. 1.44 mm). Maxillary intermolar width showed a moderate correlation with maxillary basal bone width (r = 0.552), whereas the corresponding mandibular correlation was weaker (r = 0.330). No significant association was observed between maxilla–mandible basal width ratios and intermolar width ratios. Maxillary first molars exhibited progressive palatal uprighting totaling 7.43°, while mandibular first molars demonstrated buccal uprighting of 14.04°. Conclusions During adolescence, transverse skeletal growth of the mandible exceeds that of the maxilla, whereas maxillary intermolar width increases more than mandibular intermolar width. Coordinated molar torque adjustments appear to compensate for this skeletal–dental discrepancy and contribute to transverse occlusal coordination, emphasizing the clinical relevance of physiologic torque compensation in orthodontic treatment planning. transverse growth basal bone width intermolar width crown torque dentoalveolar compensation adolescents digital model Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Background Harmonious transverse development of the dental arches is fundamental to the establishment and long-term stability of normal occlusion. Compared with sagittal and vertical growth, transverse craniofacial development has received increasing attention due to the prevalence of transverse discrepancies in orthodontic patients. Transverse skeletal growth provides the structural foundation of the dental arches, whereas dentoalveolar adaptation ultimately determines interarch occlusal relationships. Previous studies have demonstrated disproportionate transverse skeletal growth between the maxilla and mandible during development, with mandibular basal bone width increasing more than that of the maxilla [ 1 – 3 ]. Accordingly, transverse dental arch width has most commonly been assessed using intermolar width, particularly at the level of the first permanent molars. Owing to their early eruption and central role in arch coordination, the first permanent molars have long been regarded as the “key to occlusion” [ 4 , 5 ]. Numerous longitudinal studies have documented age-related increases in dental arch width followed by relative stabilization during childhood and adolescence [ 6 – 10 ]. However, most existing studies have focused primarily on linear arch width measurements, whereas age-related changes in buccolingual inclination of posterior teeth have received considerably less attention. Evidence regarding growth-related changes in first molar crown torque remains limited but suggestive. Marshall et al. [ 11 ] reported progressive palatal tipping of maxillary first molars (U6s) and buccal tipping of mandibular first molars (L6s) from childhood to early adulthood, indicating that molar crown torque may represent a dynamic dentoalveolar parameter during growth. Nevertheless, the relationship between transverse skeletal growth, dental arch width, and molar crown torque during adolescence has not been fully characterized. Therefore, the present study aimed to characterize growth-cohort-based changes in intermolar width and first molar crown torque in Chinese adolescents using three-dimensional digital dental models, and to test the hypothesis that molar crown torque functions as a compensatory mechanism in response to differential transverse skeletal growth between the maxilla and mandible. Materials and Methods Sample and Ethics Approval This study was approved by the Ethics Committee of Peking University School and Hospital of Stomatology (PKUSSIRB-201735070). Subjects were selected from the Craniofacial Growth Center database of Peking University School and Hospital of Stomatology. The inclusion criteria were as follows: (1) individual normal occlusion; (2) availability of at least one high-quality plaster dental cast and a corresponding posteroanterior cephalogram obtained between the ages of 8 and 18 years; (3) no history of orthodontic or orthopedic treatment; and (4) absence of systemic disease, craniofacial anomalies, or syndromes. All plaster dental casts were digitized using a 3Shape R700 scanner (3Shape, Copenhagen, Denmark), and all dental measurements were performed on the resulting digital 3D models. In this growth-cohort-based study, a total of 470 dental casts and corresponding posteroanterior cephalograms were collected from 124 Chinese subjects (43 males and 81 females), aged 8–18 years, with individual normal occlusion. Multiple records from the same subjects at different ages were included to capture transverse dentoalveolar and skeletal growth changes during development. The distribution of samples by age and sex is summarized in Table 1. Cephalometric Measurements for Basal Bone Width Posteroanterior cephalograms were digitized using MATLAB software (MathWorks, Natick, MA, USA). Landmarks and reference planes were defined according to Ricketts [12] and Snodell et al. [13]. Maxillary basal bone width was measured as the distance between the bilateral jugal points, and mandibular basal bone width as the distance between the bilateral antegonial notches, as previously described [12, 13], with both measurements taken parallel to the horizontal reference plane. Dental Measurements on 3D Digital Models The plaster models were scanned using the 3Shape R700 scanner (3Shape, Copenhagen, Denmark) to obtain digital models in STL format at time points T0 – T10 (ages 8 – 18 years). These models were then imported into Rapidform 2006 software (INUS Technology, Seoul, Korea) for measurements: ① Model superimposition (i) Maxillary superimposition: the T10 maxillary model was superimposed onto each maxillary model from T0 to T9 using the palatal stable structures as described by Chen et al. [14]. Fig. 1 illustrates a representative example of the superimposition procedure. (ii) Mandibular superimposition: mandibular digital models were aligned through occlusal transfer based on intercuspal relationships with the corresponding maxillary models, allowing consistent spatial orientation of the mandibular arch relative to the maxilla across different age stages. ② Establishment of reference planes The definitions of the occlusal, sagittal, and coronal reference planes followed previously published methods [15] and was applied consistently in the present analysis. ③ Measurement variables (i) Intermolar width was defined as the horizontal distance between the projected mesiobuccal cusp tips of the right and left first molars onto the occlusal plane. Fig. 2 illustrates the measurement of maxillary intermolar width; the same procedure was applied to the mandibular arch. (ii) Buccolingual inclination (torque) of the first molars was measured according to Andrews’ [5] and the American Board of Orthodontics (ABO) definitions [16], using the long axis of the clinical crown relative to the occlusal plane. This was done within a local molar coordinate system, following the method described by Dai et al. [17]. Specifically, a mesiodistal plane of the first molar was constructed based on marginal ridge landmarks and their projection onto the occlusal plane (Fig. 3a). A buccolingual plane perpendicular to both the occlusal plane and the mesiodistal plane was then established (Fig. 3b). The torque angle was defined as the angle, on the buccolingual plane, between the projection of the clinical crown long axis and the reference line extending from the most gingival point of the crown axis to the occlusal plane (Fig. 3c). Positive torque values were recorded when the projected facial axis of the clinical crown lay on the buccal side of the reference line; otherwise, torque was recorded as negative. ④ To minimize landmark identification errors, the crown surfaces of the maxillary and mandibular first molars were isolated and superimposed using a surface-based best-fit registration approach. The workflow of crown surface isolation and subsequent registration is illustrated in Supplementary Figure S1. Statistical Analysis All statistical analyses were performed using SPSS software (version 21.0; IBM Corp., Armonk, NY, USA). Data distribution was assessed for normality prior to analysis. Independent t tests were used to evaluate sex differences and left - right differences in molar crown torque. As no significant side differences were detected for molar crown torque, data from both sides were pooled for subsequent analyses. Age-related differences were assessed using one-way analysis of variance (ANOVA) with Bonferroni correction for multiple comparisons. Given the growth-cohort-based nature of the dataset and the absence of complete repeated observations for all individuals across every age point, age-group-based comparisons were adopted rather than true repeated-measures models, which may limit strict longitudinal inference. Pearson correlation coefficients were calculated to assess associations between basal bone width and intermolar width. Statistical significance was set at P < 0.05. Reliability Assessment To assess intra-examiner reliability, fifty models were randomly selected and remeasured by the same examiner after a two-week interval. Intraclass correlation coefficients (ICCs) were calculated for all variables to evaluate measurement reliability. The ICC values indicated good reliability for all measurements (ICC > 0.90). No statistically significant differences were observed between the repeated measurements (P > 0.05). Results Basal Bone Width Maxillary and mandibular basal bone widths increased with age across adolescence. Males consistently exhibited larger basal bone widths and greater growth increments than females (P < 0.05). From ages 8 to 18 years, maxillary basal bone width increased by 6.62 mm in males and 3.68 mm in females, whereas mandibular basal bone width increased by 11.28 mm and 6.47 mm, respectively, indicating a greater transverse growth of the mandible. Age- and sex-specific values are summarized in Supplementary Table S1. These skeletal changes provide the structural context for subsequent analyses of transverse dental arch development. Dental Width Intermolar width increased gradually in both arches across adolescence. Males consistently exhibited greater transverse dimensions than females (P < 0.05). From ages 8 to 18, U6 intermolar width increased by 3.16 mm (3.59 mm in males and 2.73 mm in females), whereas L6 intermolar width increased by 1.44 mm (1.54 mm in males and 1.34 mm in females), respectively. On an annual basis, the average increase in maxillary first molar width was 0.32 mm/year (0.36 mm/year in males and 0.27 mm/year in females), compared with 0.14 mm/year in the mandible (0.15 mm/year in males and 0.13 mm/year in females). After Bonferroni correction, no statistically significant differences were detected between any pair of age groups from 8 to 18 years in either sex (P > 0.05). Consistent with this finding, growth curves demonstrated a gradual increase in intermolar width without an identifiable growth spurt (Figure 4). Correlation Between Basal Bone and Dental Width Maxillary intermolar width demonstrated a moderate association with maxillary basal bone width (r = 0.552, P < 0.001), suggesting partial skeletal influence on maxillary arch development. In contrast, the correlation between mandibular basal bone width and mandibular intermolar width was weak (r = 0.330, P 0.05). Molar Torque No statistically significant differences were observed between left and right molar torque values or between sexes, allowing torque measurements to be pooled. The U6s showed a gradual palatal uprighting trend, with a mean torque reduction of 7.43° from ages 8 to 18 years. In contrast, the L6s demonstrated a consistent buccal uprighting of 14.04°. Using the Bonferroni correction, some pairwise age-group comparisons revealed statistically significant differences in torque for both U6s and L6s (P < 0.05; Supplementary Table S2). Discussion This growth-cohort-based study investigated age-related transverse dentoalveolar changes during adolescence, with particular emphasis on intermolar width and first molar crown torque. Despite greater transverse skeletal growth of the mandible, maxillary intermolar width increased more than mandibular intermolar width during adolescence. This discrepancy was evident both in cumulative changes and in annual growth rates. The moderate correlation between maxillary basal bone width and maxillary intermolar width is consistent with previous reports [ 18 , 19 ] suggesting that transverse maxillary dental development remains partially influenced by skeletal expansion during growth, particularly through midpalatal suture activity. In contrast, the weak association observed in the mandible supports the view that postnatal mandibular growth—occurring primarily through surface remodeling—has limited direct influence on transverse dental arch width [ 20 ]. A central finding of the present study is the distinct and opposing age-related crown torque trends of the first molars. From 8 to 18 years, U6s exhibited progressive palatal uprighting totaling 7.43°, corresponding to an average change of 0.74° per year, whereas L6s demonstrated buccal uprighting of 14.04° (1.40° per year). These findings are consistent with previous longitudinal studies that reported continuous changes in posterior tooth inclination during growth [ 21 , 22 ]. Mandibular molars demonstrated a larger cumulative buccal uprighting than maxillary molars (14.04° vs. 7.43°). Given the limited association between mandibular basal bone width and dental arch width, torque adjustment may represent an important dentoalveolar mechanism contributing to transverse adaptation in the mandible. From a functional perspective, these coordinated torque adaptations may represent a physiologic dentoalveolar compensation mechanism that facilitates transverse intercuspation in the presence of differential skeletal growth between the jaws. According to the functional matrix hypothesis, tooth position and axial inclination adapt in response to functional demands and muscular equilibrium rather than being solely genetically predetermined [ 23 , 24 ]. Similarly, equilibrium theory emphasizes that buccolingual tooth inclination reflects the balance between intraoral and perioral muscular forces [ 25 ]. The present findings align with these concepts, suggesting that molar crown torque plays an important role in maintaining transverse occlusal coordination during growth. From a clinical perspective, these observations suggest that molar torque compensation during adolescence is a biologic, dynamic, and individualized process. A uniform preset torque value may not reflect individual physiologic variability during growth, and in certain individuals, excessive expression of palatal molar torque may be associated with limited transverse dental arch development. Accordingly, during orthodontic treatment in the early permanent dentition, careful consideration of molar torque expression is warranted. Although preset torque values for U6s in commonly used bracket systems, such as Roth and MBT, are typically around − 14° [ 26 ], these values represent widely adopted clinical conventions rather than individualized growth-related targets. Selective modulation of molar torque expression may help support physiologic dentoalveolar adaptation during growth. This approach is consistent with contemporary orthodontic principles emphasizing biologically compatible mechanics and long-term stability [ 27 ]. Several limitations should be acknowledged. Although the dataset included repeated observations across multiple age groups, it did not constitute a strict longitudinal design with complete follow-up for each subject. In addition, transverse skeletal measurements were derived from posteroanterior cephalograms rather than three-dimensional imaging. While these methods are well established in craniofacial growth research, future studies using prospective designs and three-dimensional imaging modalities may further clarify the interaction between skeletal growth, dentoalveolar adaptation, and orthodontic intervention. In summary, this study provides quantitative evidence that molar crown torque serves as an important compensatory mechanism in transverse occlusal development during adolescence and highlights the clinical relevance of incorporating growth-related torque considerations into orthodontic diagnosis and treatment planning. Conclusion U6 and L6 intermolar widths exhibit gradual transverse widening from ages 8 to 18, with consistently larger dimensions observed in males than females. Maxillary intermolar width correlates moderately with maxillary basal bone width, whereas the mandibular correlation is weak, reflecting asymmetric skeletal–dental coupling. U6s upright palatally and L6s upright buccally during adolescence, indicating systematic torque compensation. Torque compensation represents an important adaptive mechanism for maintaining transverse occlusal stability during growth. These growth-cohort-based findings provide quantitative evidence supporting the role of dentoalveolar compensation in transverse occlusal development and emphasize the importance of molar torque control in orthodontic treatment planning. Abbreviations 3D Three-Dimensional U6 Maxillary First Molar L6 Mandibular First Molar Declarations Acknowledgements The authors would like to thank Yandong Sun for insightful discussions and constructive suggestions that contributed to the development of the study concept. Authors' contributions Conceptualization, T. M. X. and S. Y. L, methodology, S. Y. L. and Y. D, software, S. Y. L, validation, S. Y. L, formal analysis, S. Y. L, investigation, S. Y. L. and Y. D, data curation, S. Y. L. and Y. D , writing—original draft preparation, S. Y. L, writing—review and editing, T. M. X, visualization, S. Y. L, supervision, T. M. X.. All authors have read and agreed to the published version of the manuscript. Funding Not applicable. Data availability Data are available from the corresponding author upon reasonable request. Ethics approval and consent to participate This study was conducted in accordance with the principles of the Declaration of Helsinki. Ethical approval was granted by the Ethics Committee of Peking University School and Hospital of Stomatology, Beijing, China (Approval No. PKUSSIRB-201735070). In line with the Measures for the Ethical Review of Biomedical Research Involving Human Subjects issued by the National Health Commission of the People’s Republic of China, the institutional review board of the hospital granted a waiver of informed consent. Consent for publication Not Applicable. Competing interests The authors declare no conflicts of interest. 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Björk A, Skieller V. Normal and abnormal growth of the mandible. Eur J Orthod. 1983;5:1-46. Zhang HP, Xu TM, Zhang XZ, et al. Growth changes of normal incisor and molar positions during the mixed dentition period. Chin J Orthod. 2007;14:74-7. Sayania B, Merchant M, Josephs P, et al. Changes in the buccolingual inclination of first molars with growth in untreated subjects: a longitudinal study. Angle Orthod. 2017;87:681-7. Moss ML, Salentijn L. The primary role of functional matrices in facial growth. Am J Orthod. 1969;55:566-77. Moss ML. The functional matrix hypothesis revisited. Am J Orthod Dentofacial Orthop. 1997;112:8-11. Weinstein S, Haack DC, Morris LY, Snyder BB, Attaway HE. On an equilibrium theory of tooth position. Angle Orthod. 1963;33:1-26. McLaughlin RP, Bennett JC, Trevisi H. Systemized orthodontic treatment mechanics.St. Louis: Mosby; 2001. Proffit WR, Fields HW, Larson B, Sarver DM. Contemporary Orthodontics. 6th ed. St. Louis: Elsevier; 2019. Tables Table 1. Distribution of study subjects by age and sex Age (years) Male (N) Female (N) Total (N) 8 6 14 20 9 5 16 21 10 13 25 38 11 12 26 38 12 14 33 47 13 25 50 75 14 25 42 66 15 20 37 56 16 18 30 47 17 13 25 37 18 10 11 20 Total 161 309 470 Note: N = number of subjects. Table 2. Mean and SD of maxillary (U6) and mandibular (L6) intermolar width at different ages Age(years) U6 intermolar width (Mean ± SD, mm) L6 intermolar width (Mean ± SD, mm) Male Female Male Female 8 52.85 ± 4.11 50.99 ± 2.47 45.12 ± 2.40 44.22 ± 2.12 9 53.61 ± 4.44 52.17 ± 2.64 45.39 ± 2.48 44.89 ± 2.27 10 53.51 ± 4.23 51.92 ± 2.71 45.22 ± 3.32 44.43 ± 2.26 11 53.43 ± 4.27 51.85 ± 2.75 45.67 ± 3.69 44.08 ± 2.79 12 53.25 ± 3.60 52.00 ± 2.87 45.58 ± 2.90 44.68 ± 2.91 13 55.20 ± 3.49 53.13 ± 2.41 46.04 ± 3.17 45.81 ± 2.79 14 55.88 ± 3.15 53.70 ± 2.08 46.30 ± 3.27 45.32 ± 2.39 15 56.13 ± 2.91 53.49 ± 2.32 46.46 ± 3.31 45.83 ± 2.70 16 55.86 ± 2.46 53.49 ± 2.32 46.86 ± 2.77 45.74 ± 2.78 17 55.82 ± 2.68 53.31 ± 2.16 46.58 ± 3.03 45.65 ± 2.80 18 56.44 ± 2.96 53.72 ± 2.68 46.66 ± 3.38 45.56 ± 2.51 Note: SD = standard deviation. Table 3 Mean and SD of maxillary first molar torque (U6 torque) and mandibular first molar torque (L6 torque) at different ages Age(years) U6 torque (Mean ± SD, °) L6 torque (Mean ± SD, °) 8 -12.11 ± 5.91 -48.48 ± 5.61 9 -12.54 ± 3.28 -46.12 ± 6.98 10 -12.26 ± 8.30 -42.96 ± 7.15 11 -14.00 ± 7.83 -40.95 ± 8.43 12 -14.62 ± 5.54 -40.90 ± 9.07 13 -15.75 ± 6.95 -39.22 ± 9.64 14 -15.85 ± 7.64 -37.53 ± 9.83 15 -15.96 ± 8.34 -35.42 ± 6.80 16 -16.57 ± 8.02 -34.36 ± 7.21 17 -17.44 ± 4.84 -35.34 ± 6.67 18 -19.54 ± 6.20 -34.44 ± 5.35 Note: SD = standard deviation Table 4. Correlation Between Basal Bone and Dental Width Measurement Maxillary basal bone width Mandibular basal bone width Maxillary first molar intermolar width Mandibular first molar intermolar width Maxillary basal bone width — 0.552* Mandibular basal bone width — 0.330* Maxillary first molar intermolar width 0.552* — Mandibular first molar intermolar width 0.330* — Note:*p＜0.05 Additional Declarations No competing interests reported. Supplementary Files SupplementaryTableS1.docx SupplementaryTableS2.docx supplementfigures1.png Supplementary Figure S1. Illustration of first molar crown surface isolation and surface-based best-fit registration used to reduce landmark identification errors. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8518955","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":582348793,"identity":"f0c9bd0d-6a9f-43e6-8ee7-9ce32e29aebd","order_by":0,"name":"Shiyao Liu","email":"","orcid":"","institution":"Peking University Stomatological Hospital","correspondingAuthor":false,"prefix":"","firstName":"Shiyao","middleName":"","lastName":"Liu","suffix":""},{"id":582348794,"identity":"5a1ca94d-6d64-4e5f-9414-29c00f8aceab","order_by":1,"name":"Yun Ding","email":"","orcid":"","institution":"Peking University Stomatological Hospital","correspondingAuthor":false,"prefix":"","firstName":"Yun","middleName":"","lastName":"Ding","suffix":""},{"id":582348795,"identity":"903e0d16-ee7a-49a0-854b-b21bf6b15c69","order_by":2,"name":"Tianmin Xu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIie3PMUsDMRjG8YQXkuWBOuao6Fd4IXA6HPSDuFwRbjqhk1OHKwd1KfarODmfBOzY1cHhdKjruUgFQc3iuVxcHfIfXhLIjyRCxGL/MfKD/ZCLp26fYUR014YEekK1TVbFYXKlzjlI+qVeGiiX8RbpQYhMNO2eH2aP05tGVsaAYJ1IhZhnZ8MPUye25J3lb8KzU4XUiaIV98VFNfyXdFyyO/IkN4AnG5aVCxD95gk8aaAMbC2XJkzwc8uigmIwkQoTh0tPbNLImpJVDuMUcR74i15vbsflh5teN/rlvdt/Tkbr7WvbzbNB0nfc/trkfx6PxWKxWKgvCHhQWzJNsfkAAAAASUVORK5CYII=","orcid":"","institution":"Peking University Stomatological Hospital","correspondingAuthor":true,"prefix":"","firstName":"Tianmin","middleName":"","lastName":"Xu","suffix":""}],"badges":[],"createdAt":"2026-01-05 08:39:43","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8518955/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8518955/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101492107,"identity":"2152cb46-3e1a-4125-9c9e-4e7cfec92d71","added_by":"auto","created_at":"2026-01-30 10:56:38","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":438359,"visible":true,"origin":"","legend":"The schematic diagram of the overlapping model area at stages of T0 (blue) and T10 (black).","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8518955/v1/e62a5063dedc614d175ae6c4.png"},{"id":101752159,"identity":"f424b9d7-793e-48e5-aaa6-4f6db41c7f59","added_by":"auto","created_at":"2026-02-03 10:25:47","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":355442,"visible":true,"origin":"","legend":"Measurement of intermolar width on three-dimensional digital models.","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8518955/v1/899d55509187495df5cbc947.png"},{"id":101752032,"identity":"c8906677-b337-483a-8423-bc13d0c91347","added_by":"auto","created_at":"2026-02-03 10:24:59","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":721855,"visible":true,"origin":"","legend":"Measurement of buccolingual inclination (torque) of the first molar on three-dimensional digital models. (a) Construction of the mesiodistal plane; (b) Establishment of the buccolingual plane; (c) Measurement of molar crown torque.","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8518955/v1/1f4cfae4fe0e419cd2ff0924.png"},{"id":101751968,"identity":"de1f3d04-a76a-4e1a-84ce-773ca7e61341","added_by":"auto","created_at":"2026-02-03 10:24:34","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1160315,"visible":true,"origin":"","legend":"Age-related changes in maxillary (U6) and mandibular (L6) first molar crown torque from 8 to 18 years. Data are presented as mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation (\u0026deg;). Negative values indicate palatal inclination of maxillary molars and lingual inclination of mandibular molars.","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8518955/v1/0adc7b8ecd0376eec51fd8c4.png"},{"id":101751622,"identity":"3cffe48c-81e4-47f0-bf70-e1c646110b5b","added_by":"auto","created_at":"2026-02-03 10:21:52","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":50794,"visible":true,"origin":"","legend":"Age-related changes in maxillary (U6) and mandibular (L6) intermolar width from 8 to 18 years of age, stratified by sex. Data are presented as mean values with standard deviation (mm).","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8518955/v1/e4c8cc92df16c70d205e8ddf.png"},{"id":101942708,"identity":"0a74afd8-a9e9-4dfd-836a-690c705fb658","added_by":"auto","created_at":"2026-02-05 09:34:44","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3410241,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8518955/v1/cebc331b-09ff-42ff-8578-eba92427ed3a.pdf"},{"id":101752054,"identity":"0a7e97f4-0dcd-47db-a05a-a02541cc329e","added_by":"auto","created_at":"2026-02-03 10:25:07","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":17406,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryTableS1.docx","url":"https://assets-eu.researchsquare.com/files/rs-8518955/v1/4424aed43f59599fc202a6bc.docx"},{"id":101751952,"identity":"a2f9e6f6-e9b4-4d88-8de8-c0a9af016455","added_by":"auto","created_at":"2026-02-03 10:24:31","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":14274,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryTableS2.docx","url":"https://assets-eu.researchsquare.com/files/rs-8518955/v1/b407b0a4b5ca16ad0503dbfc.docx"},{"id":101751737,"identity":"5fa4f061-545b-4901-adc7-67911ccbf1ca","added_by":"auto","created_at":"2026-02-03 10:23:01","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":1354278,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSupplementary Figure S1. \u003c/strong\u003eIllustration of first molar crown surface isolation and surface-based best-fit registration used to reduce landmark identification errors.\u003c/p\u003e","description":"","filename":"supplementfigures1.png","url":"https://assets-eu.researchsquare.com/files/rs-8518955/v1/71b3dc0101ae09102799636f.png"}],"financialInterests":"No competing interests reported.","formattedTitle":"Transverse Growth and Torque Compensation of First Molar in Adolescents Using 3D Digital Dental Analysis","fulltext":[{"header":"Background","content":"\u003cp\u003eHarmonious transverse development of the dental arches is fundamental to the establishment and long-term stability of normal occlusion. Compared with sagittal and vertical growth, transverse craniofacial development has received increasing attention due to the prevalence of transverse discrepancies in orthodontic patients.\u003c/p\u003e \u003cp\u003eTransverse skeletal growth provides the structural foundation of the dental arches, whereas dentoalveolar adaptation ultimately determines interarch occlusal relationships. Previous studies have demonstrated disproportionate transverse skeletal growth between the maxilla and mandible during development, with mandibular basal bone width increasing more than that of the maxilla [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Accordingly, transverse dental arch width has most commonly been assessed using intermolar width, particularly at the level of the first permanent molars. Owing to their early eruption and central role in arch coordination, the first permanent molars have long been regarded as the \u0026ldquo;key to occlusion\u0026rdquo; [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Numerous longitudinal studies have documented age-related increases in dental arch width followed by relative stabilization during childhood and adolescence [\u003cspan additionalcitationids=\"CR7 CR8 CR9\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. However, most existing studies have focused primarily on linear arch width measurements, whereas age-related changes in buccolingual inclination of posterior teeth have received considerably less attention.\u003c/p\u003e \u003cp\u003eEvidence regarding growth-related changes in first molar crown torque remains limited but suggestive. Marshall et al. [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] reported progressive palatal tipping of maxillary first molars (U6s) and buccal tipping of mandibular first molars (L6s) from childhood to early adulthood, indicating that molar crown torque may represent a dynamic dentoalveolar parameter during growth. Nevertheless, the relationship between transverse skeletal growth, dental arch width, and molar crown torque during adolescence has not been fully characterized.\u003c/p\u003e \u003cp\u003eTherefore, the present study aimed to characterize growth-cohort-based changes in intermolar width and first molar crown torque in Chinese adolescents using three-dimensional digital dental models, and to test the hypothesis that molar crown torque functions as a compensatory mechanism in response to differential transverse skeletal growth between the maxilla and mandible.\u003c/p\u003e"},{"header":"Materials and Methods","content":"Sample and Ethics Approval\nThis study was approved by the Ethics Committee of Peking University School and Hospital of Stomatology (PKUSSIRB-201735070). Subjects were selected from the Craniofacial Growth Center database of Peking University School and Hospital of Stomatology. The inclusion criteria were as follows: (1) individual normal occlusion; (2) availability of at least one high-quality plaster dental cast and a corresponding posteroanterior cephalogram obtained between the ages of 8 and 18 years; (3) no history of orthodontic or orthopedic treatment; and (4) absence of systemic disease, craniofacial anomalies, or syndromes.\nAll plaster dental casts were digitized using a 3Shape R700 scanner (3Shape, Copenhagen, Denmark), and all dental measurements were performed on the resulting digital 3D models. In this growth-cohort-based study, a total of 470 dental casts and corresponding posteroanterior cephalograms were collected from 124 Chinese subjects (43 males and 81 females), aged 8–18 years, with individual normal occlusion. Multiple records from the same subjects at different ages were included to capture transverse dentoalveolar and skeletal growth changes during development. The distribution of samples by age and sex is summarized in Table 1.\nCephalometric Measurements for Basal Bone Width\nPosteroanterior cephalograms were digitized using MATLAB software (MathWorks, Natick, MA, USA). Landmarks and reference planes were defined according to Ricketts [12] and Snodell et al. [13]. Maxillary basal bone width was measured as the distance between the bilateral jugal points, and mandibular basal bone width as the distance between the bilateral antegonial notches, as previously described [12, 13], with both measurements taken parallel to the horizontal reference plane.\nDental Measurements on 3D Digital Models\nThe plaster models were scanned using the 3Shape R700 scanner (3Shape, Copenhagen, Denmark) to obtain digital models in STL format at time points T0 – T10 (ages 8 – 18 years). These models were then imported into Rapidform 2006 software (INUS Technology, Seoul, Korea) for measurements:\n① Model superimposition\n(i) Maxillary superimposition: the T10 maxillary model was superimposed onto each maxillary model from T0 to T9 using the palatal stable structures as described by Chen et al. [14]. Fig. 1 illustrates a representative example of the superimposition procedure.\n(ii) Mandibular superimposition: mandibular digital models were aligned through occlusal transfer based on intercuspal relationships with the corresponding maxillary models, allowing consistent spatial orientation of the mandibular arch relative to the maxilla across different age stages.\n② Establishment of reference planes\nThe definitions of the occlusal, sagittal, and coronal reference planes followed previously published methods [15] and was applied consistently in the present analysis.\n③ Measurement variables\n(i) Intermolar width was defined as the horizontal distance between the projected mesiobuccal cusp tips of the right and left first molars onto the occlusal plane. Fig. 2 illustrates the measurement of maxillary intermolar width; the same procedure was applied to the mandibular arch.\n(ii) Buccolingual inclination (torque) of the first molars was measured according to Andrews’ [5] and the American Board of Orthodontics (ABO) definitions [16], using the long axis of the clinical crown relative to the occlusal plane. This was done within a local molar coordinate system, following the method described by Dai et al. [17].\nSpecifically, a mesiodistal plane of the first molar was constructed based on marginal ridge landmarks and their projection onto the occlusal plane (Fig. 3a). A buccolingual plane perpendicular to both the occlusal plane and the mesiodistal plane was then established (Fig. 3b). The torque angle was defined as the angle, on the buccolingual plane, between the projection of the clinical crown long axis and the reference line extending from the most gingival point of the crown axis to the occlusal plane (Fig. 3c). Positive torque values were recorded when the projected facial axis of the clinical crown lay on the buccal side of the reference line; otherwise, torque was recorded as negative.\n④ To minimize landmark identification errors, the crown surfaces of the maxillary and mandibular first molars were isolated and superimposed using a surface-based best-fit registration approach. The workflow of crown surface isolation and subsequent registration is illustrated in Supplementary Figure S1.\nStatistical Analysis\nAll statistical analyses were performed using SPSS software (version 21.0; IBM Corp., Armonk, NY, USA). Data distribution was assessed for normality prior to analysis. Independent t tests were used to evaluate sex differences and left - right differences in molar crown torque. As no significant side differences were detected for molar crown torque, data from both sides were pooled for subsequent analyses.\nAge-related differences were assessed using one-way analysis of variance (ANOVA) with Bonferroni correction for multiple comparisons. Given the growth-cohort-based nature of the dataset and the absence of complete repeated observations for all individuals across every age point, age-group-based comparisons were adopted rather than true repeated-measures models, which may limit strict longitudinal inference. Pearson correlation coefficients were calculated to assess associations between basal bone width and intermolar width. Statistical significance was set at P \u003c 0.05.\nReliability Assessment\nTo assess intra-examiner reliability, fifty models were randomly selected and remeasured by the same examiner after a two-week interval. Intraclass correlation coefficients (ICCs) were calculated for all variables to evaluate measurement reliability. The ICC values indicated good reliability for all measurements (ICC \u003e 0.90). No statistically significant differences were observed between the repeated measurements (P \u003e 0.05).\n"},{"header":"Results","content":"\u003cp\u003e\u003cstrong\u003eBasal Bone Width\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMaxillary and mandibular basal bone widths increased with age across adolescence. Males consistently exhibited larger basal bone widths and greater growth increments than females (P \u0026lt; 0.05). From ages 8 to 18 years, maxillary basal bone width increased by 6.62 mm in males and 3.68 mm in females, whereas mandibular basal bone width increased by 11.28 mm and 6.47 mm, respectively, indicating a greater transverse growth of the mandible. Age- and sex-specific values are summarized in Supplementary Table S1. These skeletal changes provide the structural context for subsequent analyses of transverse dental arch development.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDental Width\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIntermolar width increased gradually in both arches across adolescence. Males consistently exhibited greater transverse dimensions than females (P \u0026lt; 0.05). From ages 8 to 18, U6 intermolar width increased by 3.16 mm (3.59 mm in males and 2.73 mm in females), whereas L6 intermolar width increased by 1.44 mm (1.54 mm in males and 1.34 mm in females), respectively. On an annual basis, the average increase in maxillary first molar width was 0.32 mm/year (0.36 mm/year in males and 0.27 mm/year in females), compared with 0.14 mm/year in the mandible (0.15 mm/year in males and 0.13 mm/year in females).\u003c/p\u003e\n\u003cp\u003eAfter Bonferroni correction, no statistically significant differences were detected between any pair of age groups from 8 to 18 years in either sex (P \u0026gt; 0.05). Consistent with this finding, growth curves demonstrated a gradual increase in intermolar width without an identifiable growth spurt (Figure 4).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrelation Between Basal Bone and Dental Width\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMaxillary intermolar width demonstrated a moderate association with maxillary basal bone width (r = 0.552, P \u0026lt; 0.001), suggesting partial skeletal influence on maxillary arch development. In contrast, the correlation between mandibular basal bone width and mandibular intermolar width was weak (r = 0.330, P \u0026lt; 0.001), indicating limited skeletal\u0026ndash;dental coupling in the mandible. No significant association was observed between basal bone width ratios and intermolar width ratios (P \u0026gt; 0.05).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMolar Torque\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo statistically significant differences were observed between left and right molar torque values or between sexes, allowing torque measurements to be pooled. The U6s showed a gradual palatal uprighting trend, with a mean torque reduction of 7.43\u0026deg; from ages 8 to 18 years. In contrast, the L6s demonstrated a consistent buccal uprighting of 14.04\u0026deg;. Using the Bonferroni correction, some pairwise age-group comparisons revealed statistically significant differences in torque for both U6s and L6s (P \u0026lt; 0.05; Supplementary Table S2).\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis growth-cohort-based study investigated age-related transverse dentoalveolar changes during adolescence, with particular emphasis on intermolar width and first molar crown torque. Despite greater transverse skeletal growth of the mandible, maxillary intermolar width increased more than mandibular intermolar width during adolescence. This discrepancy was evident both in cumulative changes and in annual growth rates. The moderate correlation between maxillary basal bone width and maxillary intermolar width is consistent with previous reports [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] suggesting that transverse maxillary dental development remains partially influenced by skeletal expansion during growth, particularly through midpalatal suture activity. In contrast, the weak association observed in the mandible supports the view that postnatal mandibular growth\u0026mdash;occurring primarily through surface remodeling\u0026mdash;has limited direct influence on transverse dental arch width [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eA central finding of the present study is the distinct and opposing age-related crown torque trends of the first molars. From 8 to 18 years, U6s exhibited progressive palatal uprighting totaling 7.43\u0026deg;, corresponding to an average change of 0.74\u0026deg; per year, whereas L6s demonstrated buccal uprighting of 14.04\u0026deg; (1.40\u0026deg; per year). These findings are consistent with previous longitudinal studies that reported continuous changes in posterior tooth inclination during growth [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Mandibular molars demonstrated a larger cumulative buccal uprighting than maxillary molars (14.04\u0026deg; vs. 7.43\u0026deg;). Given the limited association between mandibular basal bone width and dental arch width, torque adjustment may represent an important dentoalveolar mechanism contributing to transverse adaptation in the mandible. From a functional perspective, these coordinated torque adaptations may represent a physiologic dentoalveolar compensation mechanism that facilitates transverse intercuspation in the presence of differential skeletal growth between the jaws. According to the functional matrix hypothesis, tooth position and axial inclination adapt in response to functional demands and muscular equilibrium rather than being solely genetically predetermined [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Similarly, equilibrium theory emphasizes that buccolingual tooth inclination reflects the balance between intraoral and perioral muscular forces [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The present findings align with these concepts, suggesting that molar crown torque plays an important role in maintaining transverse occlusal coordination during growth.\u003c/p\u003e \u003cp\u003eFrom a clinical perspective, these observations suggest that molar torque compensation during adolescence is a biologic, dynamic, and individualized process. A uniform preset torque value may not reflect individual physiologic variability during growth, and in certain individuals, excessive expression of palatal molar torque may be associated with limited transverse dental arch development. Accordingly, during orthodontic treatment in the early permanent dentition, careful consideration of molar torque expression is warranted. Although preset torque values for U6s in commonly used bracket systems, such as Roth and MBT, are typically around \u0026minus;\u0026thinsp;14\u0026deg; [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], these values represent widely adopted clinical conventions rather than individualized growth-related targets. Selective modulation of molar torque expression may help support physiologic dentoalveolar adaptation during growth. This approach is consistent with contemporary orthodontic principles emphasizing biologically compatible mechanics and long-term stability [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSeveral limitations should be acknowledged. Although the dataset included repeated observations across multiple age groups, it did not constitute a strict longitudinal design with complete follow-up for each subject. In addition, transverse skeletal measurements were derived from posteroanterior cephalograms rather than three-dimensional imaging. While these methods are well established in craniofacial growth research, future studies using prospective designs and three-dimensional imaging modalities may further clarify the interaction between skeletal growth, dentoalveolar adaptation, and orthodontic intervention.\u003c/p\u003e \u003cp\u003eIn summary, this study provides quantitative evidence that molar crown torque serves as an important compensatory mechanism in transverse occlusal development during adolescence and highlights the clinical relevance of incorporating growth-related torque considerations into orthodontic diagnosis and treatment planning.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eU6 and L6 intermolar widths exhibit gradual transverse widening from ages 8 to 18, with consistently larger dimensions observed in males than females.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eMaxillary intermolar width correlates moderately with maxillary basal bone width, whereas the mandibular correlation is weak, reflecting asymmetric skeletal\u0026ndash;dental coupling.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eU6s upright palatally and L6s upright buccally during adolescence, indicating systematic torque compensation.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTorque compensation represents an important adaptive mechanism for maintaining transverse occlusal stability during growth.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThese growth-cohort-based findings provide quantitative evidence supporting the role of dentoalveolar compensation in transverse occlusal development and emphasize the importance of molar torque control in orthodontic treatment planning.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003e3D \u0026nbsp; Three-Dimensional\u003c/p\u003e\n\u003cp\u003eU6 \u0026nbsp; Maxillary First Molar\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eL6 \u0026nbsp; Mandibular First Molar\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to thank Yandong Sun for insightful discussions and constructive suggestions that contributed to the development of the study concept.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConceptualization, T. M. X. and S. Y. L, methodology, S. Y. L. and Y. D, software, S. Y. L, validation, S. Y. L, formal analysis, S. Y. L, investigation, S. Y. L. and Y. D, data curation, S. Y. L. and Y. D , writing\u0026mdash;original draft preparation, S. Y. L, writing\u0026mdash;review and editing, T. M. X, visualization, S. Y. L, supervision, T. M. X.. All authors have read and agreed to the published version of the manuscript.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was conducted in accordance with the principles of the Declaration of Helsinki. Ethical approval was granted by the Ethics Committee of Peking University School and Hospital of Stomatology, Beijing, China (Approval No. PKUSSIRB-201735070). In line with the \u003cem\u003eMeasures for the Ethical Review of Biomedical Research Involving Human Subjects\u003c/em\u003e issued by the National Health Commission of the People\u0026rsquo;s Republic of China, the institutional review board of the hospital granted a waiver of informed consent.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot Applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflicts of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eCortella S, Shofer FS, Ghafari J. Transverse development of the jaws: norms for the posteroanterior cephalometric analysis. Am J Orthod Dentofacial Orthop. 1997;112:519\u0026ndash;22.\u003c/li\u003e\n \u003cli\u003eYavuz, A Ikbal, B Baydaş, et al. Longitudinal posteroanterior changes in transverse and vertical craniofacial structures between 10 and 14 years of age. Angle Orthod. 2004;74:624-9.\u003c/li\u003e\n \u003cli\u003eHuertas D, Ghafari J. New posteroanterior cephalometric norms: a comparison with craniofacial measures of children treated with palatal expansion. Angle Orthod. 2001;71:285-92.\u003c/li\u003e\n \u003cli\u003eAngle EH. Classification of malocclusion. Dental Cosmos. 1899;41:248\u0026ndash;64.\u003c/li\u003e\n \u003cli\u003eAndrews LF. The six keys to normal occlusion. Am J Orthod. 1972;62:296\u0026ndash;309.\u003c/li\u003e\n \u003cli\u003eMoorrees CFA, Chadha JM. Changes in dental arch dimensions expressed on the basis of tooth eruption as a measure of biologic age. J Dent Res. 1965;44:129-41.\u003c/li\u003e\n \u003cli\u003eBishara S E, Jakobsen J R, Treder J E, et al. Changes in the maxillary and mandibular tooth size-arch length relationship from early adolescence to early adulthood. A longitudinal study. Am J Orthod Dentofacial Orthop. 1989;95:46-59.\u003c/li\u003e\n \u003cli\u003eTsujino K, Machida Y. A longitudinal study of the growth and development of the dental arch width from childhood to adolescence in Japanese. Bull Tokyo Dent Coll. 1998 ;39(2):75-89.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eCarter GA, McNamara JA Jr. Longitudinal dental arch changes in adults. Am J Orthod Dentofacial Orthop. 1998;114:88\u0026ndash;99.\u003c/li\u003e\n \u003cli\u003eKnott VB. Longitudinal study of dental arch widths at four stages of dentition. Angle Orthod. 1972 ;42:387-94.\u003c/li\u003e\n \u003cli\u003eMarshall S, Dawson D, Southard KA, et al. Transverse molar movements during growth. Am J Orthod Dentofacial Orthop. 2003;124:615-24.\u003c/li\u003e\n \u003cli\u003eRicketts RM. Perspectives in the clinical application of cephalometrics. The First Fifty Years Angle Orthod. 1981;51:115\u0026ndash;50.\u003c/li\u003e\n \u003cli\u003eSnodell SF, Nanda RS, Currier GF. A longitudinal cephalometric study of transverse and vertical craniofacial growth. Am J Orthod Dentofacial Orthop. 1993;104:471\u0026ndash;83.\u003c/li\u003e\n \u003cli\u003eChen G, Chen S, Zhang XY, et al. Stable region for maxillary dental cast superimposition in adults, studied with the aid of stable miniscrews. Orthod Craniofac Res. 2011;14:70-9.\u003c/li\u003e\n \u003cli\u003eLiu S, Fan Y, Gao L, et al. Maxillary molar distalization with Invisalign in adult patients: a preliminary study using iTero-created digital models. BMC Oral Health. 2025;25:1232.\u003c/li\u003e\n \u003cli\u003eCasko JS, et al. Objective Grading System for Dental Casts and Panoramic Radiographs[J]. Am J Orthod Dentofacial Orthop. 1998;114:589-99.\u003c/li\u003e\n \u003cli\u003eDai FF, Xu TM, Shu G. Comparison of achieved and predicted crown movement in adults after 4 first premolar extraction treatment with Invisalign. Am J Orthod Dentofacial Orthop. 2021;160:805-13.\u003c/li\u003e\n \u003cli\u003eBj\u0026ouml;rk, A., \u0026amp; Skieller, V. Growth in width of the maxilla studied by the implant method. Scandinavian Journal of Plastic and Reconstructive Surgery. 1974;8:26-33.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eEnlow DH, Hans MG. Essentials of Facial Growth. Philadelphia: Saunders; 1996.\u003c/li\u003e\n \u003cli\u003eBj\u0026ouml;rk A, Skieller V. Normal and abnormal growth of the mandible. Eur J Orthod. 1983;5:1-46.\u003c/li\u003e\n \u003cli\u003eZhang HP, Xu TM, Zhang XZ, et al. Growth changes of normal incisor and molar positions during the mixed dentition period. Chin J Orthod. 2007;14:74-7.\u003c/li\u003e\n \u003cli\u003eSayania B, Merchant M, Josephs P, et al. Changes in the buccolingual inclination of first molars with growth in untreated subjects: a longitudinal study. Angle Orthod. 2017;87:681-7.\u003c/li\u003e\n \u003cli\u003eMoss ML, Salentijn L. The primary role of functional matrices in facial growth. Am J Orthod. 1969;55:566-77.\u003c/li\u003e\n \u003cli\u003eMoss ML. The functional matrix hypothesis revisited. Am J Orthod Dentofacial Orthop. 1997;112:8-11.\u003c/li\u003e\n \u003cli\u003eWeinstein S, Haack DC, Morris LY, Snyder BB, Attaway HE. On an equilibrium theory of tooth position. Angle Orthod. 1963;33:1-26.\u003c/li\u003e\n \u003cli\u003eMcLaughlin RP, Bennett JC, Trevisi H. Systemized orthodontic treatment mechanics.St. Louis: Mosby; 2001.\u003c/li\u003e\n \u003cli\u003eProffit WR, Fields HW, Larson B, Sarver DM. Contemporary Orthodontics. 6th ed. St. Louis: Elsevier; 2019.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003e\u003cstrong\u003eTable 1. Distribution of study subjects by age and sex\u003c/strong\u003e\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003eAge (years)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eMale (N)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003eFemale (N)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003eTotal (N)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e47\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e75\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e66\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e56\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e47\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e37\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003eTotal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e161\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e309\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e470\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eNote: N = number of subjects.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2. Mean and SD of maxillary (U6) and mandibular (L6) intermolar width at different ages\u003c/strong\u003e\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003eAge(years)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 261px;\"\u003e\n \u003cp\u003eU6 intermolar width (Mean \u0026plusmn; SD, mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 262px;\"\u003e\n \u003cp\u003eL6 intermolar width (Mean \u0026plusmn; SD, mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003eMale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003eFemale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003eMale\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003eFemale\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e52.85 \u0026plusmn; 4.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e50.99 \u0026plusmn; 2.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e45.12 \u0026plusmn; 2.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e44.22 \u0026plusmn; 2.12\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e53.61 \u0026plusmn; 4.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e52.17 \u0026plusmn; 2.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e45.39 \u0026plusmn; 2.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e44.89 \u0026plusmn; 2.27\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e53.51 \u0026plusmn; 4.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e51.92 \u0026plusmn; 2.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e45.22 \u0026plusmn; 3.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e44.43 \u0026plusmn; 2.26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e53.43 \u0026plusmn; 4.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e51.85 \u0026plusmn; 2.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e45.67 \u0026plusmn; 3.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e44.08 \u0026plusmn; 2.79\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e53.25 \u0026plusmn; 3.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e52.00 \u0026plusmn; 2.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e45.58 \u0026plusmn; 2.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e44.68 \u0026plusmn; 2.91\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e55.20 \u0026plusmn; 3.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e53.13 \u0026plusmn; 2.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e46.04 \u0026plusmn; 3.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e45.81 \u0026plusmn; 2.79\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e55.88 \u0026plusmn; 3.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e53.70 \u0026plusmn; 2.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e46.30 \u0026plusmn; 3.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e45.32 \u0026plusmn; 2.39\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e56.13 \u0026plusmn; 2.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e53.49 \u0026plusmn; 2.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e46.46 \u0026plusmn; 3.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e45.83 \u0026plusmn; 2.70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e55.86 \u0026plusmn; 2.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e53.49 \u0026plusmn; 2.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e46.86 \u0026plusmn; 2.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e45.74 \u0026plusmn; 2.78\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e55.82 \u0026plusmn; 2.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e53.31 \u0026plusmn; 2.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e46.58 \u0026plusmn; 3.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e45.65 \u0026plusmn; 2.80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 132px;\"\u003e\n \u003cp\u003e56.44 \u0026plusmn; 2.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e53.72 \u0026plusmn; 2.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 129px;\"\u003e\n \u003cp\u003e46.66 \u0026plusmn; 3.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e45.56 \u0026plusmn; 2.51\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eNote: SD = standard deviation.\u003cstrong\u003e\u003cbr\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3 Mean and SD of maxillary first molar torque (U6 torque) and mandibular first molar torque (L6 torque) at different ages\u003c/strong\u003e\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" align=\"\" width=\"553\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003eAge(years)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003eU6 torque (Mean \u0026plusmn; SD, \u0026deg;)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003eL6 torque (Mean \u0026plusmn; SD, \u0026deg;)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-12.11 \u0026plusmn; 5.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-48.48 \u0026plusmn; 5.61\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-12.54 \u0026plusmn; 3.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-46.12 \u0026plusmn; 6.98\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-12.26 \u0026plusmn; 8.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-42.96 \u0026plusmn; 7.15\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-14.00 \u0026plusmn; 7.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-40.95 \u0026plusmn; 8.43\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-14.62 \u0026plusmn; 5.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-40.90 \u0026plusmn; 9.07\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-15.75 \u0026plusmn; 6.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-39.22 \u0026plusmn; 9.64\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-15.85 \u0026plusmn; 7.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-37.53 \u0026plusmn; 9.83\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-15.96 \u0026plusmn; 8.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-35.42 \u0026plusmn; 6.80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-16.57 \u0026plusmn; 8.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-34.36 \u0026plusmn; 7.21\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-17.44 \u0026plusmn; 4.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-35.34 \u0026plusmn; 6.67\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 137px;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 217px;\"\u003e\n \u003cp\u003e-19.54 \u0026plusmn; 6.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 199px;\"\u003e\n \u003cp\u003e-34.44 \u0026plusmn; 5.35\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eNote: SD = standard deviation\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 4. Correlation Between Basal Bone and Dental Width\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"738\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 235px;\"\u003e\n \u003cp\u003eMeasurement\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 110px;\"\u003e\n \u003cp\u003eMaxillary basal bone width\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 112px;\"\u003e\n \u003cp\u003eMandibular basal bone width\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 141px;\"\u003e\n \u003cp\u003eMaxillary first molar intermolar width\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 139px;\"\u003e\n \u003cp\u003eMandibular first molar intermolar width\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 235px;\"\u003e\n \u003cp\u003eMaxillary basal bone width\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 110px;\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e0.552*\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 139px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 235px;\"\u003e\n \u003cp\u003eMandibular basal bone width\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 110px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 139px;\"\u003e\n \u003cp\u003e0.330*\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 235px;\"\u003e\n \u003cp\u003eMaxillary first molar intermolar width\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 110px;\"\u003e\n \u003cp\u003e0.552*\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 139px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 235px;\"\u003e\n \u003cp\u003eMandibular first molar intermolar width\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 110px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 112px;\"\u003e\n \u003cp\u003e0.330*\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 141px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 139px;\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eNote:*p＜0.05\u0026nbsp;\u003cbr\u003e\u0026nbsp;\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-oral-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ohea","sideBox":"Learn more about [BMC Oral Health](http://bmcoralhealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/ohea/default.aspx","title":"BMC Oral Health","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"transverse growth, basal bone width, intermolar width, crown torque, dentoalveolar compensation, adolescents, digital model","lastPublishedDoi":"10.21203/rs.3.rs-8518955/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8518955/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eTo investigate age-related changes in transverse intermolar width and crown torque of maxillary and mandibular first permanent molars in adolescents, and to explore torque as a compensatory mechanism for asymmetric transverse skeletal growth.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eA total of 470 dental casts and corresponding posteroanterior cephalograms from 124 subjects (43 males and 81 females) aged 8\u0026ndash;18 years were analyzed using a cohort-based design, incorporating repeated records when available to evaluate transverse growth. Maxillary and mandibular basal bone widths were measured on posteroanterior radiographs. Dental casts were digitized and analyzed to obtain intermolar width and molar crown torque. Statistical analyses included independent t tests, one-way ANOVA with Bonferroni correction, and Pearson correlation analysis.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eBoth maxillary and mandibular basal bone widths increased with age, with mandibular basal growth exceeding maxillary growth. Despite this skeletal pattern, maxillary intermolar width increased more than mandibular intermolar width (3.16 mm vs. 1.44 mm). Maxillary intermolar width showed a moderate correlation with maxillary basal bone width (r\u0026thinsp;=\u0026thinsp;0.552), whereas the corresponding mandibular correlation was weaker (r\u0026thinsp;=\u0026thinsp;0.330). No significant association was observed between maxilla\u0026ndash;mandible basal width ratios and intermolar width ratios. Maxillary first molars exhibited progressive palatal uprighting totaling 7.43\u0026deg;, while mandibular first molars demonstrated buccal uprighting of 14.04\u0026deg;.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eDuring adolescence, transverse skeletal growth of the mandible exceeds that of the maxilla, whereas maxillary intermolar width increases more than mandibular intermolar width. Coordinated molar torque adjustments appear to compensate for this skeletal\u0026ndash;dental discrepancy and contribute to transverse occlusal coordination, emphasizing the clinical relevance of physiologic torque compensation in orthodontic treatment planning.\u003c/p\u003e","manuscriptTitle":"Transverse Growth and Torque Compensation of First Molar in Adolescents Using 3D Digital Dental Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-30 10:56:33","doi":"10.21203/rs.3.rs-8518955/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-25T13:43:17+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-23T20:19:49+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-23T12:39:37+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-18T19:41:58+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-17T07:09:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"308856092278744488415836404073702584013","date":"2026-02-06T15:20:56+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-02T19:00:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"7112074706126400172950652819009566144","date":"2026-01-29T09:56:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"86539467913080430537648395917617254033","date":"2026-01-29T03:02:30+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"141362488451913216436360313896789302629","date":"2026-01-28T07:59:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"329934390395801405788475688401660896528","date":"2026-01-28T07:03:53+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-28T02:22:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-16T11:48:19+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-01-09T11:46:38+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-08T15:29:31+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Oral Health","date":"2026-01-08T15:17:32+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-oral-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ohea","sideBox":"Learn more about [BMC Oral Health](http://bmcoralhealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/ohea/default.aspx","title":"BMC Oral Health","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"5c670519-b357-43b1-abb9-90713b206286","owner":[],"postedDate":"January 30th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-02T12:08:45+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-30 10:56:33","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8518955","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8518955","identity":"rs-8518955","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}