Introduction
This study aimed to develop new cephalometric standards incorporating samples from across North America, focusing on creating sex-specific percentile growth curves for craniofacial cephalometric measures using the extensive longitudinal data from the Craniofacial Growth Consortium Study.
Methods
This study comprised 2,100 subjects (1,056 males and 1,044 females) with 17,290 lateral cephalometric radiographs, spanning ages of 2.5-31.3 years. Twenty-four linear cephalometric measurements were calculated, including traits from the basicranium, maxilla, and mandible. For each measurement, multilevel nonlinear growth models were used to estimate growth milestones by sex, percentile growth curves were created, and a web-interface tool was developed to facilitate the practical application of these growth curves.
Results
Growth milestones, including age at peak growth velocity and peak growth velocity, were estimated for each sex using double logistic growth models. The timing of peak growth velocity varies across different regions of the craniofacial complex. Craniofacial growth percentile curves were created and cross-validated. A web interface tool was created to allow users to retrieve individual-specific percentile scores.
Conclusions
The developed percentile growth curves and web-based tool offer a robust framework for clinicians to assess individual growth patterns, identify deviations from normative growth, and estimate future growth potential, supporting more personalized treatment planning and timing.
Highlights
-
•
Correcting for enlargement in cephalograms is vital for accurate growth assessment.
-
•
Craniofacial growth percentiles allow individualized growth evaluation.
-
•
Nonlinear modeling identifies growth disparities, improving treatment precision.
-
•
A web tool provides percentile scores and dynamic growth analysis.
The timing of orthodontic interventions and the assessment and prediction of craniofacial growth are paramount for orthodontists, oral and maxillofacial surgeons, and other clinicians treating functional and esthetic anomalies of the face. Accurate growth standards help guide decisions regarding the timing of orthopedic, orthodontic, and surgical treatments. Although traditional cephalometric norms—mean values with standard deviations by age and sex—have served as reference points for decades, they offer only static snapshots and are limited in capturing the full spectrum of individual growth variation over time.
Longitudinal cephalometric radiographs from historical growth collections have long been a cornerstone for studying craniofacial development. These unique datasets contain serial radiographs from untreated, healthy people tracked through childhood and adolescence, offering unparalleled insight into the timing, direction, and variability of craniofacial growth. , During the mid-20th century (1930-1985), multiple North American studies systematically collected these records, focusing on healthy children, predominantly of European ancestry ( Fig 1 ). ,,,,
Timeline showing activity in each of the 9 growth studies comprising the AAOF Craniofacial Growth Legacy Collection. For each study, the period when cephalometric images were collected is highlighted by skull marks.
Recognizing the enduring scientific value of these datasets, the American Association of Orthodontists Foundation (AAOF) launched the Craniofacial Growth Legacy Collection in 2008, a digital repository providing open access to multiple longitudinal craniofacial growth studies. ,,, The AAOF platform ( https://www.aaoflegacycollection.org/aaof_home.html ) has since become a vital resource for researchers and educators. Although each collection has contributed extensively to the field, previous studies typically analyzed growth within single cohorts and focused on average trends rather than population-based growth percentiles. , As a result, percentile-based reference standards for craniofacial growth remain largely undeveloped.
To address this gap, the Craniofacial Growth Consortium Study (CGCS) was established to integrate multiple historical longitudinal datasets into a single comprehensive resource. By merging data across studies, the CGCS increases statistical power and enhances generalizability beyond what individual datasets can offer. ,, Comparative analyses across studies demonstrated no significant differences in core growth trajectories, justifying the combination of these datasets into one unified framework.
This study builds on that foundation by introducing sex-specific craniofacial growth percentile curves based on cephalometric measurements derived from the CGCS dataset. Similar to the way pediatricians use height and weight percentiles to monitor child development, these craniofacial percentiles enable clinicians to dynamically evaluate a patient’s growth relative to population-based norms. These curves are not intended to replace established cephalometric norms but rather to augment them—offering a complementary, time-sensitive framework for detecting delayed, accelerated, or atypical craniofacial growth.
A primary goal of this study was to develop and publicly share an interactive, web-based tool that allows users to visualize individual craniofacial growth trajectories in the context of these percentile curves. By providing real-time age- and sex-specific reference standards, this platform equips users with a more nuanced and accessible method for growth assessment. Although the current dataset reflects a population of predominantly European ancestry, this framework establishes a foundation for future expansion to more diverse populations and integration with 3-dimensional (3D) imaging modalities.
Material and methods
The University of Missouri Institutional Review Board approved all procedures used in this study (institutional review board number: 2008393).
The sample for the current study comes from the CGCS. Overall, the CGCS comprises 17,290 lateral cephalometric radiographs encompassing ages ranging 2.5-31.3 years and including 1,056 males and 1,044 females. Table I provides a breakdown of the sample size based on growth collections of origin. Notably, the median number of cephalograms per subject is 9, with many subjects represented by 15 or more images ( Fig 2 , A ). The graphical representation, shown in Figure 2 , B , illustrates the distribution of observations by age, highlighting a particularly dense concentration of data between ages 6-16 years—a critical period during craniofacial growth. The overall sample characteristics are summarized by 2 common cephalometric measurements: the ANB angle is used to represent the sagittal jaw relationship, and the mandibular plane angle relative to sella-nasion (SN-MPA) reflects the vertical pattern of growth ( Fig 3 ). Both measurements are shown at the observation point closest to age 13 years for each subject, which provides an overview of the variation present in the 2,100 untreated subjects included in the study. For the current study, only subjects with 2 or more cephalographs available were included.
Table I
Sample size and number of images of CGCS by growth collection
| Growth collection | Male | Female | Total number of subjects | Total number of radiographs |
|---|---|---|---|---|
| Bolton Brush | 209 | 193 | 402 | 4,065 |
| Burlington | 49 | 48 | 97 | 1,023 |
| Denver | 50 | 44 | 94 | 968 |
| Fels | 281 | 267 | 548 | 5,208 |
| Forsyth | 50 | 40 | 90 | 844 |
| Iowa | 44 | 47 | 91 | 1,067 |
| Michigan | 326 | 349 | 675 | 2,921 |
| Oregon | 47 | 56 | 103 | 1,194 |
| Total | 1,056 | 1,044 | 2,100 | 17,290 |
The number of images comprising the CGCS: A, The number of images per subject by study; B, The number of images per age group (years) by growth collections. Total number of images in the CGCS = 17,290.
Sample distribution by ANB angle and mandibular plane angle (SN-MPA).
The challenges related to the use of historical radiographic archives and the steps taken to minimize systematic errors and bias and improve image quality have been documented in detail elsewhere. Protocols related to radiography, specifically as it relates to radiographic enlargement, were identified by Sherwood and colleagues through careful examination of historic accounts and publications.
A set of 69 craniofacial landmarks was digitized as Cartesian coordinates using the eDigit software (Craniofacial Research Instrumentation Lab; University of Pacific Arthur A Dugoni School of Dentistry, San Francisco, Calif). ,
Using 12 landmarks, the 24 linear cephalometric measurements, which broadly describe the dimensions of the basicranium, face height and depth, maxilla, and mandible, were calculated ( Table II , Fig 4 ). These measurements include S-N, S-Ba, N-Ba, Ba-ANS, S-ANS, S-PNS, S-Ar, S-Go, S-Pog, S-Me, N-ANS, N-Me, ANS-Me, ANS-PNS, PNS-point A, Co-point A, Co-Go, Ar-Go, Ar-Me, Ar-Pog, Co-Pog, Ar-Gn, Co-Gn, and Go-Pog.
Table II
Cephalometric landmarks used in the current study (See Fig 4 )
| No. | Name | Symbol | Definition |
|---|---|---|---|
| 1 | Sella | S | The midpoint of the pituitary fossa |
| 2 | Nasion | N | The most anteroinferior point on the frontal bone at the nasofrontal suture |
| 3 | Basion | Ba | The most inferior point on the anterior margin of the foramen magnum in the midsagittal plane |
| 4 | ANS | ANS | The most anterior point of the anatomic anterior nasal spine |
| 5 | PNS | PNS | The intersection between the posterior extension of the superior surface of the palate and the downward extension of the pterygomaxillary fissure |
| 6 | Point A | Point A | The deepest point on the curvature of the surface of the maxillary bone between the ANS and the alveolar crest of the maxillary central incisor |
| 7 | Condylion | Co | The point on the posterosuperior contour of the condyle that is the longest distance from the pogonion |
| 8 | Articulare | Ar | The intersection between the basisphenoid synchondrosis and the posterior border of the neck of the condyle |
| 9 | Gonion | Go | The lowest point of the curvature of the angle of the mandible, in which the inferior surface of the body of the mandible meets the ramus (average of upper and lower gonion points) |
| 10 | Menton | Me | The most inferior point on the mandible at the symphysis |
| 11 | Pogonion | Pog | The most anterior point of the bony chin at the midline |
| 12 | Gnathion | Gn | The midpoint between pogonion and menton of the bony chin |
A total of 12 cephalometric landmarks and 24 linear measurements were used in the study: S-N; S-Ba; N-Ba; Ba-ANS; S-ANS; S-PNS; S-Ar; S-Go; S-Pog; S-Me; N-ANS; ANS-Me; N-Me; ANS-PNS; PNS-point A; Co-point A; Co-Go; Ar-Go; Ar-Me; Ar-Pog; Co-Pog; Ar-Gn; Co-Gn; and Go-Pog.
Correction factors for radiographic enlargement are based on the formula (X[TH-D])/TH, in which X is the radiographic measurement, TH is the tube-to-film distance, and D is the distance from the object (in this case, the cranial midline) to the film. Raw linear measures (in millimeters) collected from Legacy collection radiographs were multiplied by the study-specific correction factor for radiographic enlargement before analysis to avoid introducing systematic error to the dataset ( Table III ). Measures adjusted in this way more closely represent the dimensions of the actual structures being imaged (ie, anatomic truth) than do the raw distances from the radiographs. Angular measures, such as ANB and MPA, collected from the radiographs are not subject to enlargement and do not require correction.
Table III
List of factors to correct for radiographic enlargement for each growth collection
| Growth collection | Correction factor |
|---|---|
| Michigan | 87.10% |
| Bolton Brush | 92% |
| Denver | 96% |
| Oregon | 92.20% |
| Fels | Variable 89.6%-96.8% (complete summary in supplement) |
| Burlington | 90% or 90.16% |
| Forsyth | 94% |
| Iowa | 94% before March 16, 1956 |
| 91% between March 16, 1956 and September 19, 1957 | |
| 87% for films on or after September 19, 1957 and before 1970 | |
| 87.75% for films in 1970 and later |
Note. Raw linear measures from each radiograph must be multiplied by the study-specific factor before any analysis occurs.
It was discovered that several errors regarding enlargement factors were reported in previous publications or originally provided by the AAOF Legacy Collection. The Legacy Collection scaling document has been updated to match the values reported here ( ).
Statistical analysis
Growth, the change in a linear measurement across age, can be studied using a wide range of methods. At its simplest, growth may progress at an unchanging rate as a person ages. Such linear growth is uncommon. More commonly, growth rate changes over time relative to baseline, with notable increases during growth spurts followed by decreased rates. Thus, even though the magnitude of a linear cephalometric measurement is constantly increasing, the rate of that increase varies.
As an individual reaches skeletal maturity, the rate of growth slows greatly, identifiable as a gradual deceleration to a near-0 rate of growth. Although craniofacial measures can continue to change past the attainment of maturity, ,, the rate and magnitude of this change are small compared with those occurring during the childhood and adolescent periods. We previously defined the end of adolescence as marking the cessation of growth and the beginning of an adaptive phase. Important milestones during the growth period include the age at the onset of an adolescent growth spurt, age and size at peak growth velocity (PGV), and age and size at cessation of growth. Different statistical approaches to modeling changes in the rate of growth across age have been used in the past, with polynomial models and spline models among the most common. ,
In the present study, we used a Bayesian double-logistic growth model to characterize craniofacial growth in the CGCS sample. In this model, 2 separate growth periods, preadolescent and adolescent, are summed to produce a characteristic S-shaped growth pattern with 2 periods of rapid growth. This model also provides estimates for key growth milestones. Originally proposed for stature growth, this model is biologically appropriate for studying craniofacial growth, in which most traits follow a similar pattern: rapid early growth, slowed growth, a rapid adolescent growth spurt, and gradual slowing as the individual reaches adulthood, as described by Scammon and Scott. A summary of the technical details is provided below for interested readers, with additional details of model implementation available elsewhere. ,
Six parameters define the double logistic growth model as a function of age, including the asymptomatic trait measurement (measured in millimeters) at growth cessation (f) and prepubertal contribution (a 1 ), separate initial rates at the start of periods of rapid growth (b 1 and b 2 ; in millimeters per year), and ages (c 1 and c 2 ; in years) at associated with periods of rapid growth:
In addition, we included a 0-centered, normally distributed individual-specific random-effects intercept, which allowed the mean intercept to vary by individual. Models were written using the Stan programming language and fit using Hamiltonian Monte Carlo sampling via the cmdstanr package in R (R Foundation for Statistical Computing, Vienna, Austria). Sampling included 4 parallel chains, each sampled for 10,000 iterations after 10,000 iterations of warmup, which yielded approximately 4,000 effective samples and R ˆ values of approximately 1. , Complete details of the model fitting procedure are provided in the supplementary information (available online at: https://doi.org/10.6084/m9.figshare.29424749 ).
In addition to returning the posterior samples of estimates for the 6 parameters of the model, the sampling process was designed to simultaneously produce posterior distributions for each trait at monthly intervals from the age of 4-25 years. There are 2 important features of these samples. First, they represent the predicted trait values at each age in proportion to their probability and the probability of parameter estimates (ie, higher probability measurements are observed more frequently because those parameter estimates are more common). Second, the predicted values take advantage of the full observed variation in the CGCS, and thus represent the distribution of new, unobserved measurements. The latter makes these posterior predicted distributions ideal for establishing growth percentiles for craniofacial traits. For each monthly interval (approximately 0.083 years between ages), the sampling process produced 10,000 trait value estimates. These estimates follow a roughly normal distribution, with the median centered on the most probable trait value in the population. We then calculated the quantiles from 1%-99% in 1% increments for the estimates.
To ensure the accuracy of the growth model and validate the estimated percentiles for each measurement, a 10-fold cross-validation was conducted. This process involved dividing the data into 10 equal parts. For each fold, 90% of the participant IDs, along with all their related observations, were used as the training set, whereas the remaining 10% formed the test set. The double logistic growth model was fitted to the training set.
For each observation in the test set, it was determined whether each observation fell within the middle 50% and middle 98% percentile intervals of the model’s predictions. This step produced a set of results indicating whether each observation was inside (yes) or outside (no) the expected percentile range. The effectiveness of the cross-validation was assessed by calculating the mean and 95% confidence interval for the proportion of observations that fell within the 50th and 98th percentiles. The expectation is that approximately 50% of test observations will fall within the middle 50% confidence interval and that 98% will fall within the middle 98% confidence interval.
Whereas stature represents a single measurement with a single set of growth percentiles for each sex, the current study generated percentiles for 24 linear cephalometric measurements, each having its own sex-specific set of growth percentiles. To facilitate user access to these percentiles, a web interface was developed using the Shiny web framework for R.
The percentile curves are made publicly available through an interactive web-based platform, designed for educational, research, and reference use. The platform allows users to visualize an individual’s measurements against age- and sex-specific normative percentiles derived from a large pooled longitudinal dataset.
Results
To provide context for the percentile curves developed, we provide a brief analysis of the growth models. More detailed analyses of the growth models and milestones are available elsewhere.
Table IV presents the estimates of key growth milestones derived from the population models for 24 selected linear measurements, including age at PGV (aPGV) and PGV. The inflection point, defined here as the point of maximal curvature change on the fitted growth curve, corresponds to the aPGV and is widely used in biological growth modeling to estimate key developmental milestones. , It is interesting to note that the timing of PGV varies across different regions of the craniofacial complex, occurring at different ages. The growth models generated for the cephalometric measurements in the craniofacial region display a sigmoid curve characteristic of a growth pattern that includes an adolescent growth spurt. These curves typically begin with a phase of slow growth, transition into rapid growth with the onset of the spurt, reach a period of maximal growth (PGV), gradually decelerate, and eventually, plateau, indicating the end of the growth period, as defined by Hardin et al. This approach has proven effective in providing biologically meaningful estimates of PGV, aPGV, and age at cessation of growth periods in most traits. ,
Table IV
Population models for 24 linear craniofacial measurements
| Measurements | aPGV (y) | PGV (mm/y) | ||
|---|---|---|---|---|
| Female | Male | Female | Male | |
| S-N | 10.05 | 14.26 | 0.75 | 1.08 |
| S-Ba | 7.05 | 8.11 | 1.03 | 1.00 |
| N-Ba | 10.37 | 13.37 | 1.48 | 1.75 |
| Ba-ANS | 9.37 | 13.37 | 1.34 | 1.74 |
| S-ANS | 10.37 | 13.53 | 1.29 | 1.58 |
| S-PNS | 10.21 | 13.32 | 0.98 | 1.09 |
| S-Ar | 8.11 | 12.63 | 0.89 | 0.89 |
| S-Go | 10.63 | 14.26 | 1.87 | 2.82 |
| S-Pog | 11.37 | 13.84 | 2.48 | 3.21 |
| S-Me | 11.42 | 13.89 | 2.67 | 3.59 |
| N-ANS | NA | 13.21 | NA | 1.32 |
| ANS-Me | 12.47 | 13.84 | 1.26 | 1.72 |
| Na-Me | 11.68 | 13.74 | 2.33 | 3.11 |
| ANS-PNS | 11.63 | 13.58 | 0.80 | 1.03 |
| PNS-point A | 11.74 | 13.11 | 0.79 | 0.90 |
| Co-point A | 11.00 | 13.42 | 1.50 | 1.71 |
| Co-Go | 12.05 | 14.63 | 1.53 | 2.35 |
| Ar-Go | 12.26 | 14.74 | 1.45 | 2.01 |
| Ar-Me | 11.58 | 14.05 | 2.44 | 3.20 |
| Ar-Pog | 11.47 | 14.00 | 2.27 | 2.83 |
| Co-Pog | 11.47 | 14.00 | 2.38 | 3.05 |
| Ar-Gn | 11.58 | 14.00 | 2.41 | 3.15 |
| Con-Gn | 11.58 | 14.00 | 2.51 | 3.28 |
| Go-Pog | 10.79 | 13.58 | 1.44 | 1.64 |
Stay updated, free dental videos. Join our Telegram channel
VIDEdental - Online dental courses
