Craniofacial growth percentile curves: A clinical tool from the Craniofacial Growth Consortium Study

Abstract

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 2100 subjects (1056 males and 1044 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.

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.^1,2 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).^1–5

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.^2–5 The AAOF platform (https://www.aaoflegacycollection.org/aaof_home.html) has since become a vital resource for researchers and educators.⁵ 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.^6,7 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.² By merging data across studies, the CGCS increases statistical power and enhances generalizability beyond what individual datasets can offer.^8–10 Comparative analyses across studies demonstrated no significant differences in core growth trajectories, justifying the combination of these datasets into one unified framework.²

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.² Overall, the CGCS comprises 17,290 lateral cephalometric radiographs encompassing ages ranging 2.5–31.3 years and including 1056 males and 1044 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 2100 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	4065
Burlington	49	48	97	1023
Denver	50	44	94	968
Fels	281	267	548	5208
Forsyth	50	40	90	844
Iowa	44	47	91	1067
Michigan	326	349	675	2921
Oregon	47	56	103	1194
Total	1056	1044	2100	17,290

Fig 2.

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.

Fig 3.

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.² 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.²

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).^11,12

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

Fig 4.

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.¹³ 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 (https://www.aaoflegacycollection.org/AAOF_Images/AAOFScaledMeasurement.pdf).

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,^14–16 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.⁹ 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.^17,18

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,¹⁹ 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 Scammon²⁰ and Scott.²¹ A summary of the technical details is provided below for interested readers, with additional details of model implementation available elsewhere.^2,9

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 (a₁), separate initial rates at the start of periods of rapid growth (b₁ and b₂; in millimeters per year), and ages (c₁ and c₂; in years) at associated with periods of rapid growth:

$$y(age)=\frac{a_1}{1+\exp \left(-b_1\left(age-c_1\right)\right)}+\frac{f-a_1}{1+\exp \left(-b_2\left(age-c_2\right)\right)}$$

In addition, we included a 0-centered, normally distributed individual-specific random-effects intercept, which allowed the mean intercept to vary by individual.² Models were written using the Stan programming language²² and fit using Hamiltonian Monte Carlo sampling²³ via the cmdstanr package in R (R Foundation for Statistical Computing, Vienna, Austria).²⁴ Sampling included 4 parallel chains, each sampled for 10,000 iterations after 10,000 iterations of warmup, which yielded approximately 4000 effective samples and $\widehat{\text{R}}$ values of approximately 1.^2,9 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.²⁵ 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.²⁶

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.²

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.^27,28 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.⁹ This approach has proven effective in providing biologically meaningful estimates of PGV, aPGV, and age at cessation of growth periods in most traits.^2,9

Table IV.

Population models for 24 linear craniofacial measurements

	aPGV (y)		PGV (mm/y)
Measurements	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

NA, not applicable.

In certain measurements, however, the modeled curve displays modest incremental growth without rapid changes in velocity, resulting in the absence of distinct inflection points. This may occur in measures of small magnitude (eg, sella-basion; Fig 5, A) or in individuals in which the growth period is of shorter duration, as in females (Fig 5, A and B). Such a growth pattern makes estimation of milestones challenging when employing a double logistic growth model (eg, aPGV for sella-basion for both females and males and N-ANS in females).

Fig 5.

Examples of the double logistic growth curves: A, The distance from sella to basion; B, The distance from condylion to pogonion using the CGCS sample (black, the growth trajectories of individuals in the CGCS; red, percentile curves across the age range estimated from the double-logistic model).

The PGV of different components of the craniofacial complex is attained at ages ranging 8.11–13.6 years for females and 12.63–16.6 years for males (with 1 outlier each of aPGV at 7.1 years for females and 8.1 years for males, both for the measure S-Ba). Overall, females, on average, reach their PGV approximately 2.9 years earlier than males, emphasizing the importance of sex-specific considerations in assessing craniofacial growth. For example, in males, the population estimate of aPGV for condylion-gnathion was 14.0 years, with a PGV of 3.3 mm/yr. In females, the population estimate of aPGV was 11.6 years, with a PGV of 2.5 mm/yr.

Figure 5, A and B, presents examples of the percentile curves resulting from the present study. The graphs show that most observations fall within the 98% interval, with an increased density close to the 50th percentile. As noted, the 10-fold cross-validation was used to assess the predictive accuracy of growth percentile intervals (Table V). Across all measurements and for both sexes, observations in the test fell within the middle 50% and middle 98% ranges about as often as would be predicted.

Table V.

Cross-validation

	Percent in the middle 50%		Percent in the middle 98%
Measurements	Female	Male	Female	Male
S-N	50.3 (46.4–54.1)	50.2 (48.2–52.3)	98.1 (97.3–99.0)	98.5 (97.6–99.3)
S-Ba	50.5 (47.9–53.2)	52.8 (49.8–55.8)	97.9 (96.9–98.9)	97.6 (96.9–98.3)
N-Ba	51.2 (49.3–53.1)	49.7 (45.9–53.5)	97.7 (96.7–98.7)	98.3 (97.8–98.8)
Ba-ANS	51.7 (49.4–54.1)	52.6 (48.8–56.4)	97.6 (97.0–98.2)	97.6 (96.7–98.5)
S-ANS	51.3 (48.3–54.2)	51.3 (48.4–54.1)	97.7 (96.9–98.5)	98.0 (97.3–98.6)
S-PNS	51.1 (47.1–55.1)	52.0 (48.8–55.1)	97.8 (96.6–99.0)	97.9 (97.4–98.3)
S-Ar	50.0 (46.9–53.1)	50.5 (46.4–54.6)	97.4 (96.4–98.4)	97.7 (96.8–98.6)
S-Go	51.0 (49.1–52.9)	53.9 (49.9–57.9)	97.9 (97.1–98.6)	97.3 (96.3–98.3)
S-Pog	50.9 (47.5–54.4)	53.9 (50.6–57.1)	97.7 (96.7–98.8)	97.6 (96.7–98.5)
S-Me	50.4 (47.3–53.6)	54.7 (52.1–57.3)	97.8 (97.0–98.6)	97.4 (96.6–98.2)
N-ANS	51.2 (48.2–54.1)	52.2 (49.8–54.6)	97.6 (96.6–98.6)	97.4 (96.6–98.2)
ANS-Me	49.9 (46.7–53.1)	51.1 (49.1–53.1)	97.6 (96.5–98.7)	97.9 (97.1–98.7)
N-Me	50.3 (47.0–53.6)	52.3 (50.2–54.4)	97.7 (96.8–98.6)	97.8 (97.1–98.5)
ANS-PNS	51.6 (50.2–53.1)	51.4 (48.2–54.6)	97.4 (96.7–98.1)	97.2 (96.3–98.2)
PNS-point A	50.9 (48.0–53.8)	51.0 (47.2–54.9)	97.8 (97.1–98.5)	97.6 (96.8–98.4)
Co-point A	50.8 (48.7–53.0)	52.0 (48.1–56.0)	97.6 (97.0–98.2)	97.7 (97.0–98.3)
Co-Go	51.0 (48.0–54.1)	52.1 (49.0–55.2)	97.9 (97.0–98.9)	97.7 (97.1–98.2)
Ar-Go	51.3 (48.2–54.4)	53.0 (51.6–54.4)	97.8 (97.1–98.6)	97.6 (97.0–98.2)
Ar-Me	50.6 (46.7–54.5	54.1 (51.4–56.9)	98.4 (97.8–99.0)	97.1 (95.9–98.3)
Ar-Pog	51.3 (47.4–55.2)	53.8 (50.0–57.7)	97.9 (97.4–98.4)	97.5 (96.6–98.3)
Co-Pog	50.1 (46.8–53.5)	53.1 (49.4–56.8%)	98.1 (97.4–98.8)	97.6 (96.7–98.5)
Ar-G	51.0 (47.3–54.7)	53.7 (51.0–56.5%)	98.0 (97.4–98.6)	97.4 (96.3–98.4)
Co-Gn	50.8 (48.2–53.5)	53.1 (51.0–55.2)	98.0 (97.2–98.7)	97.7 (96.8–98.5)
Go-Pog	50.6 (48.1–53.1)	52.6 (47.7–57.5)	97.9 (97.6–98.3)	97.5 (97.0–98.1)

All data are presented as percentages.

The study generated percentile values for each percentile from 1%−99% for 24 cephalometric linear measurements at each age, ranging 4–25 years, for males and females separately. These data have been integrated into an interactive web-based percentile tool to provide interested parties with a user-friendly tool to calculate percentile scores for craniofacial measurements quickly) (https://www.aaoflegacycollection.org/aaof_craniofacialGrowth.html).

Users can save percentile images similar to Figures 5, 6, and 7 to their computer, although no personal data is stored on the platform. Users can input their patients’ or subjects’ sex and age, select the desired cephalometric measure from the provided list, and enter the corresponding values.

Fig 6.

Serial lateral cephalometric radiographs and measurements of 2 untreated subjects: A, A male subject (Michigan Growth Collection-2000) with a Class II malocclusion presented at 7 years, 10 years 1 month, 13 years, and 14 years 11 months; B, A female subject (Michigan Growth Collection-2125) with a Class III malocclusion presented at 7 years, 9 years, 11 years 1 month, 13 years 2 months, and 14 years 10 months. Study-specific magnification factors shown in Table II were applied to correct measurements.

Fig 7.

Single timepoint evaluation for a 13.8-year-old boy with a Class II malocclusion, indicating a significant discrepancy in sagittal jaw relationship characterized by a short mandibular length (Co-Pog) and a short lower anterior face height (ANS-Menton).

Once the information is provided, the tool calculates the percentile, which can be updated for different measurements or ages, and displays the results graphically. This web interface also allows for the assessment of multiple measurements from a single lateral cephalogram to identify growth discrepancies among different craniofacial structures. Furthermore, the same measurements for multiple time points can be employed to track growth changes over time in the growth curve, enabling the visualization of an individual’s growth trajectory. Figures 6–8 illustrate the clinical application of this web interface.

Fig 8.

Multiple time points evaluation for a 10-year-old male patient presenting with a Class III jaw relationship primarily because of maxillary deficiency. Facemask therapy was initiated for 12 months, with phase 1 treatment completed at 12 years. Subsequent monitoring included tracking the growth of the maxilla and mandible. The records of this patient were not included in the database, but are used here only for illustrative purposes.

In Figure 6, 2 untreated subjects from the CGCS are presented: In Figure 6, A, a male subject at 7 years exhibits maxillary length (ANS-PNS) over the 50th percentile, mandibular length (Co-Pog) at the 25th percentile, and lower face height (ANS-Me) at the 70th percentile, contributing to his Class II malocclusion. Although his mandibular size gradually reaches the 50th percentile, his lower face height increases closer to the 70th percentile, perpetuating his Class II skeletal jaw relationship. In Figure 6, B, a female subject exhibits maxillary length (ANS-PNS) at the 10th percentile, remaining consistent for 7–15 years, whereas the anterior cranial base length (S-Na) remains at the 10th percentile, but declines to less than the fifth percentile after age 11 years, without further increase. On the other hand, mandibular length (Co-Pog) presents at the 50th percentile at 7 years, but advances to the 75th and 90th percentiles during the pubertal growth peak, exacerbating Class III skeletal discrepancy over time.

Figures 7 and 8 demonstrate the clinical application of the percentile growth curve website through examples of clinical scenarios. In Figure 7, a 13.8-yearold male patient presents with severe Class II malocclusion. The growth percentile scores for various facial structures indicate short mandibular length (Co-Pog) at the ninth percentile and lower anterior face height (ANS-Menton) at the 31st percentile, contributing to a significant sagittal skeletal discrepancy compared with within the 40–50th percentiles of the cranial base (S-Na, N-Ba) and ramus height (Co-Go), along with increased maxillary length (ANS-PNS) at the 65th percentile.

In Figure 8, a 10.3-year-old male presents with a Class III skeletal relationship primarily attributed to a deficient maxilla, measuring below the fifth percentile of the anterior cranial base (S-Na) and the first percentile of maxillary length (ANS-PNS), whereas mandibular length is at the 25th percentile (Co-Pog). Although his overall craniofacial growth falls below 25 percentiles, a noticeable discrepancy between upper and lower facial structures is apparent. Treatment with maxillary protraction face mask therapy was initiated for 12 months, resulting in successful overcorrection of the Class III malocclusion with improved maxillary length to the 18th percentile and reduced mandibular length to the 10th percentile at the end of phase 1 treatment. During observation, the maxillary length continues at the 18th percentile, which marks a significant improvement compared with the initial first percentile. However, continued observation is necessary as mandibular length progresses to over the 50th percentile, indicating a potential catch-up growth in the sagittal jaw relationship toward a Class III pattern.

This web application will be available through the existing AAOF Craniofacial Growth Legacy Collection website. A full set of results from the growth models is available in the supplementary data.

DISCUSSION

Growth standards for craniofacial growth have previously been based on small samples, samples with a limited age range, cross-sectional analyses (even when longitudinal data are present), or a limited number of measures. In addition, standards are frequently presented as simple averages for a categorical age period.

This study developed a comprehensive set of growth standards for craniofacial cephalometric linear measurements using a high-density, long-term longitudinal cephalometric dataset from the CGCS. By integrating multiple historical growth studies after correcting various image-specific radiographic enlargements, we generated robust percentile growth curves that enhance our understanding of the extent of variation in craniofacial growth trajectories. These percentile references provide clinicians and researchers with a valuable tool for assessing individual growth patterns in the context of normative data in craniofacial regions.

One notable finding is the variation in growth timing patterns across different craniofacial structures. Although the growth of some measures exhibits the classic sigmoid curve with discernible inflection points, indicating distinct phases of acceleration, peak, and deceleration, a small subset of traits shows more gradual and steady incremental growth without a marked growth spurt. This highlights the complexity of craniofacial growth and underscores the need for flexible modeling approaches that can capture these varying growth trajectories. In this study, the inflection point corresponds to the maximum rate of change in the growth curve (ie, PGV), a widely used definition in statistical growth modeling²⁷

A shared objective among the various historical growth collections comprising the CGCS was the establishment of growth standards that could serve as benchmarks for comparing individuals and evaluating a child’s growth in relation to their peers. Deviations from these standards may indicate potential growth issues, warranting further investigation. It is important to recognize that although the current craniofacial growth standards provide a population average with normal variations for males and females separately, they do not represent an idealized norm typically derived from individuals with balanced facial attributes, Class I skeletal and dental features, and normal Class I occlusion. Existing cephalometric norms, based on such balanced features, retain their own significance in orthodontic and craniofacial surgical practices, providing clinicians with essential reference values for diagnosis and treatment planning. Contrary to these idealized norms, the current study offers sex-specific normative cephalometric standards spanning childhood to adulthood, enhancing representativeness by including individuals across North America and various malocclusion types. This feature strengthens the dataset’s applicability in various orthodontic conditions, making it a clinically valuable tool for assessing individual growth trajectories.

Before integrating data across collections, we validated that growth trajectories were generally consistent across studies.² Previous research has shown that craniofacial growth tends to follow predictable patterns with considerable consistency in milestone estimates and overall growth curve shape across different studies.² Combining datasets enhanced statistical power and expanded the age range and geographic diversity of the reference sample, strengthening the clinical use of the resulting growth standards.

A significant methodological challenge involved correcting for radiographic enlargement differences across collections. Historical cephalograms were often acquired without scaling tools. During the initial periods of lateral cephalometric analyses, the adjustment for enlargement was not considered essential, as practitioners primarily used analog films without such adjustment. However, to make meaningful comparisons between historical growth data and contemporary samples, especially those acquired through modern imaging modalities, such as 2-dimensional (2D) digital radiographs with scale rulers, cone-beam computed tomography (CBCT), or magnetic resonance imaging, it is now imperative to apply correction factors accounting for magnification and ensuring anatomic accuracy. We applied rigorous correction protocols using original documentation and cross-validation of measurement consistency, ensuring reliable modeling and meaningful interpretation of growth data across all contributing collections.

Despite the strengths of this large, longitudinal dataset, some limitations should be recognized. Merging data from multiple longitudinal studies introduces trade-offs. Although it increases sample size, age range, and statistical power, it may also introduce heterogeneity because of cohort effects and regional sampling differences. In addition, the dataset is predominantly of European ancestry, which may limit generalizability to more diverse populations. This study, nonetheless, represents an important step toward establishing percentile-based growth references for the general North American population. Ethnicity and secular trends may influence craniofacial development, yet few longitudinal studies have conducted a detailed exploration of these effects across the entire craniofacial complex. Expanding the CGCS to include more diverse populations is essential for addressing these knowledge gaps.

Although each cephalogram was independently traced by 3 trained assessors with systematic outlier handling and redigitization, small residual fluctuations may remain because of landmarking challenges, head posture differences, or projection effects. These were addressed through the Bayesian model fitting, but their potential influence should be acknowledged.

Numerous growth models have been used to characterize and quantify growth curves.^17,28–36 Based on our extensive previous work with a wide variety of models, we have chosen to use the double-logistic model, presented here, as it provides the benefits of including naturally interpretable model parameters, such as ages at prepubertal and adolescent growth spurts, as well as timing of growth cessation. The additive nature of the double logistic growth model means that if a trait does not exhibit a clear adolescent growth spurt, the parameters f, b_2, and c₂ are estimated as being close to 0. In this case, the trait is effectively modeled as following a single logistic growth pattern, in which the growth rate is initially high and gradually slows to 0 at cessation. Importantly, a by-product of the method we have chosen is the generation of data used to create the percentile curves.

A major contribution of this study is the development of an interactive, web-based tool that allows visualization of percentile-based growth trajectories in real time. This tool enables clinicians and researchers to input individual measurements from lateral cephalograms and assess growth across 24 linear cephalometric dimensions. Users can assess the harmony or discrepancy of growth patterns in various craniofacial areas, including the cranial base, maxilla, mandible, face height, depth, and others, as presented in Figure 7. The dynamic interface allows for both quantitative and visual tracking of changes over time, enhancing clinical insight into growth progression.

Future directions will also include the expansion of this framework into 3D growth modeling using CBCT-derived growth standards. Although CBCT offers greater anatomic detail and measurement accuracy, it will not be possible to collect extensive longitudinal data similar to that of the lateral cephalometric radiograph collection because of radiation exposure concerns. However, the Bayesian modeling framework applied in the present study provides a pathway for integrating existing 2D growth models as informative priors, in combination with new 3D reference datasets from diverse populations. This integration of 3D imaging (CBCT-derived growth models) will further improve the accuracy of growth predictions, enabling a transition from 2D-based growth standards to more precise 3D growth models.

CONCLUSIONS

1. By leveraging the CGCS as a representative dataset, this study generated population-level percentile standards that provide a comprehensive reference framework for assessing craniofacial growth across a broad age range.

2. The percentile curves developed using a Bayesian nonlinear growth model serve as a valuable tool for assessing individual growth trajectories and identifying deviations from normative growth patterns.

3. This study also underscores the enduring value of large historical craniofacial growth collections, while addressing the challenges in combining data from multiple sources. In particular, it emphasizes the critical importance of correcting for radiographic enlargement when using historical cephalometric radiographs, especially in assessing growth and treatment outcomes.

4. The web-based growth percentile tool introduced in this study provides clinicians with an interactive platform to visualize craniofacial growth patterns, track changes, and estimate future growth potential. By providing sex-specific percentile scores and real-time visual analysis, the tool enhances clinical decision-making regarding growth modification and treatment timing.

Supplementary Material

SUPPLEMENTARY DATA

Supplementary data associated with this article can be found, in the online version, at 10.6084/m9.figshare.29424749.