This retrospective cross-sectional study involved CBCT images acquired between 2018-2022 from the Department of Imaging at the Faculty of Dentistry, National Autonomous University of Mexico (UNAM), for clinical purposes unrelated to this research. This study was approved by the UNAM ethics and research committee (Approval No. CIE/0105/11/2021). The images were anonymized by removing all personal identifiers, and a confidentiality-bound employee ensured that no identifiable information remained. Given anonymization, consent for publication was not required under ethical guidelines.

The CBCT scans were randomly selected from an external data storage unit in the Department of Imaging, UNAM. The inclusion criteria were as follows: patients aged 9-50 years, no history of prior treatment, no orthodontic appliances, craniofacial syndromes, or orthognathic fixation plates. The exclusion criteria were scans with image distortions that obstructed anatomic and facial structure identification.

The minimum required sample size for multivariate analysis of variance (MANOVA) was determined to be 264 patients using G∗Power software (version 3.1.9.7; Heinrich-Heine Universität Düsseldorf, Germany), with a Cohen d effect size of 0.04, an α level of 0.05, and statistical power of 0.90. Six age groups were considered, with the first response variable being the values of the first 11 principal components (PC1-PC11) and the second being the first 11 canonical variables (CV1-CV11). An additional 10% was added to account for data loss and to ensure representativeness, resulting in a final sample size of 282 CBCT pictures.

The images were obtained using a uniform protocol with a large field of view of 15 × 15 cm, with the patient placed in a standing position, occluding teeth on maximal intercuspation, and maintaining a natural head position without swallowing during image capture. A NewTom VGi tomograph (CEFLA sc, Verona, Italy) was used, with amperages ranging 3-7 mA for children (9-15 years) and 7-15 mA for adults, a kilovoltage of 110 kV, an exposure time of 18 seconds, and a 180° rotation. The voxel size was adjusted to 0.3 × 0.3 × 0.3 mm.

The Department of Imaging at the university created an anonymized database of CBCT scans from 2018-2022, organized chronologically. Stratified random sampling was used, with sample sizes proportional to available patients in the 6 age groups and defined by mandibular growth and dentoskeletal milestones. Patients were randomly selected within each group using random number generator app (Creations App, version 2.2; Mireia Lluch Ortola, Valencia, España, Spain), allowing analysis of mandibular morphology across relevant biological stages. ^, This stratification enabled the analysis of mandibular morphologic evolution across biologically relevant stages.

To classify the patients according to skeletal classes, all CBCT scans were imported into Dolphin Imaging software (version11.9; Patterson Dental Supply, Chatsworth, Calif). Lateral radiographs were generated from these CBCT scans (radiographs in orthogonal projection to guarantee a one-to-one evaluation of the structures). Skeletal classification was determined using the ANB angle from Steiner Analysis, defined as follows: Class I (ANB = 3.0°-1.0°), Class II (ANB >3.0°), and Class III (ANB <1°).

The tomographic data were imported into the 3D Slicer software (version 5.10.0; The Slicer Community, New York, NY) ( http://www.slicer.org ), selecting the CT-bone visualization preset to facilitate mandibular segmentation. A region of interest (ROI) was then defined using crop volume extension, delimiting the specific area for analysis, from which a new volume was generated. This volume was reconstructed with an isotropic spacing of 0.3 × 0.3 × 0.3 mm, preserving the original scale in each file.

The 282 CBCT images were semiautomatically segmented using the ROI tool and the segment editor module. A median smoothing filter of 0.75 mm was used, followed by Gaussian smoothing of 1.00 mm, all while keeping the original scale and RAS coordinate system, which refers to the standard Right–Anterior–Superior orientation used in 3D Slicer. ^,,, The segmented surfaces were exported as stereolithography files ( Fig 1, A-D ).

Workflow for 3D mandibular model preparation from CBCT scans. CBCT data were processed in 3D Slicer using Visualization Tool Kit (VTK) and Graphic Processor Unit (GPU) ray casting for volumetric rendering: A, The full craniofacial skeleton was visualized with multiplanar views (axial, coronal, and sagittal), and volumes were cropped to focus on the ROI; B, The mandible was segmented using thresholding and manually refined; C, The isolated mandible was further defined using the segment editor; D, The final stereolithography model was postprocessed for landmark placement and morphometric analysis.

Using SlicerMorph extension within the 3D Slicer (The Slicer Community/SlicerMorph Project, New York, NY) ( https://slicermorph.github.io/ ) environment, 32 anatomic type 1 (points at structural intersections, characterized by precision, high repeatability, and clear homology) landmarks based on their anatomic locations and biological significance were digitized on each mandibular surface model using the markups function: 4 midline and 14 landmarks on each side of the mandible, of which 12 were used in a previous study. The 3D coordinates (x, y, and z) of each anatomic landmark were saved in fiducial comma-separated value (.fcsv) format. The definitions of the anatomic landmarks are presented in Table I , and their anatomic locations are illustrated in Figure 2, A-D .

Distribution of 32 anatomic landmarks on 3D mandibular models. The landmarks are displayed from 4 different views ( right , points 1-18; left , corresponding landmarks marked by a prime symbol [eg, 5′, 7′, and 18′]). Consistent bilateral placement ensures symmetry and enables accurate shape comparisons across patients for morphometric analysis.

The coordinates of the 32 mandibular landmarks underwent Procrustes analysis using Morpho J software (Klingenberg Laboratory, Manchester, UK) ( https://morphometrics.uk/MorphoJ ), considering the mandible as a symmetrical structure, based on the recommendations of Klingenberg et al. The Procrustes analysis produces separate components of symmetrical variation and asymmetry. Only the symmetrical component of shape variation was considered for further analysis. The new coordinates are known as the Procrustes coordinates. These datasets were used in statistical analyses afterward, as dependent variables.

Intraexaminer reliability was determined by placing landmarks on 40 randomly selected mandibles; these 32 landmarks were placed 3 times by the same examiner, with 8-day gaps between measurements. The intraexaminer random error was calculated using Dahlberg’s formula, which was based on the discrepancies among the 3 repeated measurements for each of the 40 mandibles. The computed errors were 1.36, 1.49, and 1.63 Procrustes units for the x-, y-, and z-axes, respectively. These statistics show little variability owing to landmark relocation and digitalization, indicating that the associated inaccuracy has no meaningful effect on the results.

In addition, the landmark configurations were evaluated using Procrustes analysis of variance and MANOVA to determine the variation owing to interindividual differences against the variance caused by recurrent landmarking. ^, The ratio of mean squares revealed that the variation because of individual differences was 8.56 times greater than the variation because of triple digitization ( Table II ).

A total of 282 CBCT scans from participants aged 9-50 were included in the analysis. The samples were divided into 6 age groups: group 1 (G1, 9-15 years), n = 51 (18.1%); group 2 (G2, 16-21 years), n = 51 (18.1%); group 3 (G3, 22-27 years), n = 52 (18.4%); group 4 (G4, 28-33 years), n = 56 (19.9%); group 5 (G5, 34-39 years), n = 41 (14.5%); and group 6 (G6, 40-50 years), n = 31 (11.0%). Females represented 60.0% of the study population, whereas males accounted for 40%. Specifically, 32.6% (n = 92) were classified as Class I, 48.4% (n = 138) as Class II, and 19.0% (n = 52) as Class III ( Table III ).

The general variability of mandibular shape was described using the PCA. This analysis revealed that the first 11 components accounted for 80.10% of the total variation in the mandibular shape. PC1 accounted for the largest proportion of the individual variance (27.58%), followed by PC2 (10.67 %), with a cumulative variance of 38.25%. Afterward, the components contributed decreasingly: PC3 (9.43%), PC4 (6.75%), and PC5 (5.47%), reaching a cumulative of 59.89%. PC6 accounted for 5.03%, followed by PC7 (4.07%), PC8 (3.44%), PC9 (3.01%), PC10 (2.47%), and PC11 (2.18%). These findings indicate that most mandibular morphologic variability can be captured by a relatively small number of PCs ( Fig 3, A-D ).

PCA of mandibular shape by age group: A, All patients; B-D, Age group pairs have been displayed for clarity; B , G1 (9-15 years) and G2 (16-21 years) show greater shape dispersion along PC1; C, G3 (22-27 years) and G4 (28-33 years) show clearer shape differences; D, G5 (34-39 years) and G6 (40-50 years) show reduced variability.

Figure 3 depicts the graphical results from the 2 PCAs. Each panel in Figure 3 depicts the average mandibular shape associated with the extremes of PC1 and PC2, highlighting the primary morphologic distinctions recorded by these components. To visualize morphologic differences, the mean PC1 and PC2 scores were detected and superimposed with the appropriate mandibular shapes. Panel B ( blue , G1 vs purple , G2) depicts the form changes in the ramus, mandibular angle, condyle, sigmoid notch, and coronoid process. Panel C ( green , G3 vs beige , G4) reveals the primary variations in condyle and mandibular ramus morphology. Panel D ( yellow , G5 vs pink , G6) depicts differences in the posterior border of the ramus, condyle, mandibular angle, and coronoid process.

In order to determine whether there were any notable variations in mandibular shape among age groups, sexes, and skeletal Classes I, II, and III, the PC scores between PC1 and PC11 were used as input factors in the PERMANOVA analysis, which included 10,000 permutations.

Age group had a statistically significant impact on mandibular shape, according to the PERMANOVA ( P <0.001). Sex was only relevant when interacting with age groups, according to the PERMANOVA, which produced paired comparisons that are statistically significant but biologically irrelevant. The sex-age group interaction ( P <0.001) and the interaction between skeletal class and age group ( P <0.001) were also found to be statistically significant. In the case of skeletal class–age group interaction, which is relevant to the hypothesis of this work, the presence of irrelevant pairs that produced statistical significance was confirmed using CVA ( Table IV ).

Age groups and skeletal classes were compared for changes in mandibular morphology using CVA. Procrustes variables showed that when considering age differences, the influence of skeletal class is irrelevant within age groups. Accordingly, only differences that take into account both factors, for example, G1+Class I vs G4+Class III, are statistically significant but not biologically relevant. Comparing the 18 groups pairwise revealed that most mandibular shape differences were statistically significant ( P <0.05). The youngest groups (G1) exhibited significant differences from almost all other groups, particularly G2 and G3, regardless of skeletal class. As age increased, differences among groups became more variable. Some pairs showed significant differences, whereas others did not (eg, G6/Class III vs G1/Class III and G5/Class II vs G6/Class III), indicating that age has a stronger effect on mandibular shape than skeletal class. The differences tended to decrease in older groups, reflecting a relative stabilization of mandibular morphology in late adolescence and early adulthood. As detailed results are shown in the Supplementary Information, only age groups were considered for CVA afterward.

CVA did not identify any clear age-related changes in mandibular shape within each skeletal class. In Class I, the youngest group (G1) exhibited no significant difference from G2 ( P = 0.0627), but differed considerably from G3 ( P <0.0001), G4 ( P <0.0001), G5 ( P = 0.01), and G6 ( P = 0.0014). In Class II, G1 was significantly different from the following groups: G2 ( P = 0.0013), G3 ( P <0.0001), G4 ( P <0.0001), G5 ( P = 0.0005), and G6 ( P = 0.0001). In Class III, G1 was not substantially different from G2 ( P = 0.1004), but considerably different from G3 ( P = 0.0018), G4 ( P <0.0001), and G6 ( P = 0.0171). These findings show that mandibular shape variation appears greatest in the prepubertal and midgrowth groups, with variations gradually diminishing with age ( Supplementary Table IV ).

Figure 4 illustrates a scatterplot of CVA across all age groups, revealing that CVA1 (61.5%) and CVA2 (16.3%) accounted for 77.8% of the total variation in mandibular shape. CV1 revealed that age G1 (9-15 years) differed little from the other age groups, especially G5 (34-39 years). G1 was positioned at the negative end of CV1, with dispersion above and below CV2. G2 (16-21 years) was around the graph’s center. Finally, age G5 was positioned positively, although CV2’s negative side stood out among the other 4 age groups.

CVA of mandibular shape by age group ( blue , G1 clusters in the lower-left quadrant; beige , G4 appears mainly in the upper-right quadrant). The scatter plot shows CVA1 vs CVA2 with points color-coded by age group. Inset boxes display changes in mandibular shape associated with extreme CVA values.

According to the findings of the age-group (G1-G6) CVA, there was a significant difference ( P <0.0001) between the youngest group (G1) and the other groups. Though some differences were modest or nonsignificant, especially between the oldest groups (G5 vs G6, P = 0.4226), comparisons among the older groups were generally significant. With the biggest differences between the youngest and oldest groups and fewer noticeable variations among the older groups, these results suggest that age has a significant impact. The mandibles of the G1 and G2 age groups, as well as those of the G3 and G6 age groups, differed greatly in terms of mandibular form. G3 was not similar to G4, yet it was different from G5 and G6. Significant differences were between mandibular G4 and G5, and much more between the 2. There were no notable differences between the mandibles of G5 and G6. According to Table V , these findings demonstrate that G5 and G6’s mandibular morphologies are more stable throughout time.

Finally, a scaling factor based on the observed values at the negative and positive extremes of CV1 was applied to the mean mandibular shape, which is situated at the center of the scatterplot, in order to visualize variations in mandibular shape. This method made it possible to compare the form attributes of various age groups.

Transverse plane (side-to-side direction):

Compared with the blue mandible, the beige mandible exhibited transverse expansion: (1) ramus height: the rami in the blue mandible are more vertical and slightly taller, giving a more elongated appearance, (2) basal contour: the blue mandible shows a more rounded basal contour with outward flaring, whereas the beige mandible has a straighter and more defined outline, (3) chin position: the chin in the beige mandible is slightly more projected downward and forward compared with the blue mandible, and (4) ramus inclination: in the blue mandible, the rami tended to incline slightly outward, whereas in the beige mandible, they were more parallel to each other.

In the superior view, the key variations between the 2 mandibles are as follows: (1) vertical ramus height: the target mandible appeared taller in the posterior ramus region, particularly near the condylar process, (2) coronoid process: slight anterior-superior projection differences were visible in the coronoid region, (3) mandibular body thickness: variations along the buccal surface, especially in the premolar-molar region, indicate greater buccolingual thickness in the target mandible, (4) mandibular angle: the gonial angle region shows a marked difference, with increased width and contour changes, and (5) anterior body curvature: minor changes in the symphyseal and parasymphyseal curvatures suggest differences in chin prominence and lower border inclination ( Fig 5 ).

Superimposed 3D mandibular models comparing shape extremes along CV1 (+10 to–10) ( blue , CV1 [–10]; beige , CV1 [+10]). Views include frontal (arch), superior (basal contour), lateral (ramus and body), and posterior (condylar width and divergence) perspectives.

In the lateral view, the most notable differences between the 2 mandibles were as follows: (1) mandibular body length: the mandibular body length is shorter in the blue mandible than in the beige mandible, particularly in the posterior segment, (2) ramus height: the ramus in the blue mandible indicated less vertical growth with age, (3) posterior border of the ramus: the posterior border of the beige mandible is straighter and more vertically oriented, whereas the blue mandible is more curved, (4) mandibular angle: the gonial angle in the beige mandible appears more acute, whereas in the blue mandible, it is more obtuse, and (5) symphysis contour: the beige mandible presents a taller and less rounded symphysis, whereas the blue mandible displays a shorter and more curved profile ( Fig 6 ).

Comparison of mandibular shape extremes along CV1 (+8 to–8). Superimposed 3D models show overlap between CV1 (–8, green ) and CV1 (+8, beige ): top (a-c) presents anterior views, highlighting arch form and symphyseal morphology; second row (d-f) shows superior views of the basal contour and body width; third row (g-i) illustrates lateral views emphasizing ramus inclination and mandibular angle; bottom (j-l) displays posterior views showing condylar width and corpus divergence.

In our study, we identified age-related patterns in mandibular shape, with the youngest group showing a clear distinction from the others. Interestingly, we also found that neither skeletal class nor sex affected the difference among age groups, indicating a pattern of similar shape changes among skeletal classes and sexes.

The most notable differences were observed between the youngest group (G1) and all older groups, confirming that the early developmental stages are characterized by marked morphologic changes. In contrast, differences among the older groups were less consistent, with G5 and G6 showing no significant variation, suggesting greater stability of the mandibular shape in adulthood. This common pattern of change across age groups is supported by both the exploratory and confirmatory analyses. Age-related differences in mandibular morphology were evident in the first PCs of PCA, PC1 distinguishing the youngest groups, whereas PC6 highlighted differences among the older age groups. The CVA results further indicate that age, irrespective of skeletal class, exerts a significant influence on mandibular shape.

Our study focused on comparing differences in mandibular shape across age groups and skeletal classes, while controlling for the effect of sex. Understanding the shape differences among skeletal patterns during growth allows for more accurate diagnoses in patients requiring orthognathic surgery, orthodontics, and other related treatments. However, this study did not find that mandibular shape was influenced by skeletal class. Therefore, we accept our working hypothesis that mandibular shape differs across age groups, but without differences among skeletal classes and with distinct morphologic patterns expected between younger and older patients.

Over time, several authors have investigated mandibular shape in different populations using panoramic radiographs to evaluate mandibular ramus morphology in 500 panoramic view images of adult patients (age range, 21-58 years). Other methods for acquiring 3D models, such as multislice computed tomography of 160 adult patients aged 40-79 years, have employed geometric morphometric analysis with 14 anatomic landmarks, 4 located on the midline and 5 on each side of the mandible. Nonetheless, despite using the same method, mandibular shape was ultimately represented through a wireframe model, which allowed for the observation of age-related changes.

Studies based on children’s mandibles (dental age, 1-12 years) were digitized using a computed tomography scanner and reconstructed into 3D models, achieving point correspondence with the iterative closest point and coherent point drift algorithms and using the template-to-target registration, ^,, including larger sample sizes and reported the mean shape and variation of human mandibles, emphasizing the importance of assessing mandibular morphology across different age ranges. Growth increments were disproportionate, with the height increasing more than the length and the length increasing more than the width. In the present study, the mandibular basal contour appeared more rounded with outward flaring, whereas the G1 (9-15 years) mandible exhibited a straighter and more defined outline. The mandibular condyles (28-33 years of age) appeared wider and more rounded, with a more posterior orientation and less vertical projection. In comparison, the mandibular condyles of patients aged 34-39 years were more elongated, slightly narrower mediolaterally, and positioned more anteriorly and superiorly.

Previous studies, conducted with smaller sample sizes, have employed geometric morphometrics to examine mandibular shape between 2-14 years of age as a critical developmental period and have reported variability in mandibular width, ramus height, and alveolar process height. ^,,

Our approach allowed for a more detailed assessment of the changes in mandibular morphology across different age ranges. By performing direct comparisons among these age groups, we were able to identify age-related variations that may have been overlooked in previous studies. Although other studies used larger samples, they focused exclusively on children or adults with broad age ranges, such as 1-12 years or 4-14 years. ^,, In contrast, in the present study, patients were stratified into 6 specific age groups (9-50 years), allowing for multiple direct comparisons. Some studies analyzed mandibular development at birth, whereas others focused only on adults, missing differences between young and adult mandibles.

The results of this study provide newer insights into the mandibles of the youngest patients, which exhibited greater bicondylar and bigonial widths, a less projected chin, a shorter and more posteriorly positioned mandibular ramus, a shorter and lower mandibular body, a more obtuse gonial angle, and a lower, less curved symphysis. Some of these changes have been previously described in the literature, including a decrease in the gonial angle, modifications in the symphysis region, and variations in chin projection. Changes in mandibular ramus height and position have also been reported, whereas the wider triangular coronoid processes observed in adults are consistent. However, our findings highlight age-specific mandibular variations in young patients that have not been fully documented in previous studies, thus providing a more detailed understanding of early mandibular development.

In older age groups, we observed a decrease in ramus width, with the condyle positioned more anteriorly and superiorly, a forward-projected chin, and more acute mandibular angles. ^, The intermediate age group displayed a broader and narrower mandibular shape, whereas PC2 captured differences in ramus height and condylar position, features that may influence joint function and are relevant for comprehensive diagnosis and treatment planning in orthodontics, orthognathic surgery, total prosthetic rehabilitation, and related procedures. These findings are consistent with previous reports showing that mandibular shape and configuration change with age, ^,, highlighting that mandibular size is strongly influenced by growth and developmental stages.

Regarding skeletal classes, previous studies have evaluated mandibular variability across different classifications ^, and reported that vertical patterns exert a greater influence than sagittal patterns on sectional morphology, with a thinner symphysis observed in hyperdivergent patients. Similarly, patients with Class III and dolichocephalic facial patterns showed higher values than those with other skeletal and facial patterns.

Previous studies have reported that the variation in mandibular shape and sex dimorphism in adult humans differed significantly in shape space. Males’ mandibles were larger than females, had a higher ramus, a more pronounced gonial angle, a larger intergonial width, and a more distinct antegonial notch. Other studies reported marked sexual differences at 12 years and at 14 years, allowing quantification of distinct male and female traits. In contrast, our study did not show a significant effect on mandibular morphology when sex alone was considered.

The interactions between sex and age were significant, indicating that the influence of these factors on mandibular shape depends on the age range. This contrasts with other studies, which reported that the age-sex interaction was not significant, suggesting that the impact of sex on mandibular morphology may vary across populations or methodological approaches.

The clinical implications of these findings emphasize the importance of using 3D diagnostic tools in orthodontics and maxillofacial surgery. Identifying variations in mandibular shape across different age groups is crucial for improving orthopedic diagnosis, refining orthognathic surgery planning, and developing individualized approaches to orthodontic care.

Additional factors, including genetic, functional, and environmental influences, should be further investigated as they probably contribute to mandibular variability. The potential impact of masticatory habits, bite force, and upper airway development on mandibular shape warrants further exploration, given that previous studies have suggested that deficient growth patterns are associated with conditions such as obstructive sleep apnea, oral habits such as thumb sucking, and variations in facial biotype.

Future research should focus on longitudinal studies to explore the relationship between mandibular growth, masticatory load, airway structure, and genetic factors. Understanding the interactions among these variables is essential for improving diagnostic precision and optimizing treatment strategies in orthodontics and maxillofacial surgery. The results of this study reinforce the importance of considering age as the primary factor driving variation in mandibular shape while also highlighting the need to continue investigating other factors contributing to this variability.

Although this study provides valuable insights into mandibular shape variability across different age groups, some limitations must be acknowledged. A major limitation is its cross-sectional design, which restricts its ability to evaluate longitudinal changes in mandibular growth. Because growth is a continuous and dynamic process, a cross-sectional approach offers only a snapshot of mandibular shape at specific ages, without capturing individual developmental trajectories over time. Future studies using longitudinal data are needed to track mandibular changes at different life stages and to provide a more comprehensive understanding of growth patterns. However, studies with CBCT must follow the as low as reasonably achievable principle, minimizing radiation exposure and increasing the scan speed, while ensuring sufficient image quality for justified clinical purposes.

Another limitation is the sample size, which, despite the use of random selection and multivariate variance methods, may have limited the generalizability of the findings. Although this study is among the first to estimate the sample size and apply rigorous selection criteria before data analysis, larger datasets are required to confirm these results and strengthen statistical power. Expanding the study population to include different ethnicities and geographic regions will provide additional insights into potential population-specific differences in mandibular shape.

In addition, certain clinical variables were not included in the analysis, despite their potential influence on mandibular morphology. Factors, such as oral breathing patterns, masticatory function, bite force, and airway structure, are known to contribute to craniofacial development, but were not considered in this study because of reliance on pre-existing tomographic data. The exclusion of these variables has limited the ability to fully explain the observed mandibular variations. Future research should incorporate these factors to provide a more comprehensive understanding of the mechanisms underlying the differences in mandibular shape.

Finally, although CBCT provides highly accurate 3D reconstructions of the mandible, variations in imaging acquisition techniques and the identification of anatomic landmarks have the potential to introduce errors in shape variables. However, this effect is minor when the research question involves large-scale shape data. ^,,,, Nevertheless, greater standardization in imaging acquisition and analysis across studies would be beneficial to improve reproducibility and comparability.

Despite these limitations, this study contributes valuable knowledge regarding age-related mandibular shape variation and underscores the importance of incorporating 3D diagnostic tools into clinical practice. Future research should focus on longitudinal studies, larger sample sizes, and the inclusion of functional and genetic factors to deepen our understanding of mandibular development and variability.

Clinicians may use these findings to improve diagnostic accuracy at both the beginning and end of orthodontic and surgical treatments. Providing robust diagnostic options for children and adolescents may prevent or mitigate the onset of malocclusion or asymmetrical development during growth. In this study, differences were observed between subgroups aged 9-21 years (G1 and G2); however, the study design did not allow inferences regarding patient remodeling or growth trajectories.

These findings suggest that timing Class II treatment during periods of rapid mandibular growth may optimize outcomes, and that growth pattern analysis can help predict patient mandibular development for more personalized treatment planning.