Ontogenetic patterns in human frontal sinus shape: A longitudinal study using elliptical Fourier analysis

Abstract

Frontal sinus morphology is highly variable across individuals, but little is known regarding how or at what age that variation is reached. Existing ontogenetic studies are conflicting and often cross‐sectional in nature, limiting understanding of individualistic growth. Studies investigating sinus growth with longitudinal series often focus on lateral cephalograms and consequently do not capture the sinus morphological features that are most relevant to clinical and medicolegal settings (e.g., arcade/scalloping, width‐to‐height dimensions, asymmetry). Longitudinal analysis of sinus morphology from frontal radiographs is important to understand when sinus morphology stabilizes. The purpose of this study was to investigate at what age the frontal sinus attains its final shape, and whether sex‐based differences in ontogeny are evident, using a longitudinal sample of posterior‐anterior (PA) frontal radiographs from the AAOF Legacy Collection. Frontal sinus outlines were manually traced in 935 radiographs from 111 individuals (55F/56M) spanning 8–29 years of age. Outlines were subjected to elliptical Fourier analysis (EFA) and underwent principal components analysis (PCA). PC1 (51.02% of variation) appears to represent the relative height and breadth of the sinus, PC2 (11.73%) and PC3 (10.03%) captures the degree of relative complexity in the outlines. Individual PC scores were plotted against age‐in‐months with individual Loess growth curves. Overall, younger individuals typically display relatively shorter, flatter sinuses, increasing in vertical complexity with age. Mixed‐effect models on PC1 indicate significant effects for the repeated measure of years (p < 0.001). Within individuals, Euclidean distances of PCs between each sinus outline and their oldest‐age outline (i.e., final morphology) were calculated and plotted against age‐in‐months with Loess growth curves. The results indicate that final frontal sinus morphology is mostly attained by 20 yoa regardless of sex. There is sexual dimorphism in ontogenetic trajectories: females attain frontal sinus shape earlier than males. Specifically, Loess growth curves of the Euclidean distances to final sinus shape indicate that female shape shows decreased development at 14–16 yoa, with males approaching stabilization at 18–20 yoa. These trends were supported by paired t‐tests on PC1 between each year and the oldest age, whereby significant differences end for females starting at 15 and 18 yoa for males. The timing of shape‐stabilization in the current study closely aligns with previous studies on linear and size dimensions, indicating a close relationship between the ontogeny of frontal sinus shape and size. This research has several implications in diverse fields. Documenting ontogenetic patterns in modern humans could lead to more accurate interpretations of frontal sinus variation in hominin lineages. Understanding the age at which frontal sinus shape and size stabilizes in pediatric populations has important clinical implications, with future studies needed to investigate if/how sinus development directly relates to sinonasal disease susceptibility (e.g., sinusitis), surgical complications, and/or expected trauma patterns. For forensic practitioners utilizing frontal sinus comparisons for decedent identifications, it is important to know at what age these features stabilize to understand how much change may be expected between antemortem and postmortem radiographs.

This longitudinal, radiographic study investigates the age at which the frontal sinus attains its shape using elliptical Fourier analyses on sinus outlines. As expected, younger individuals typically display relatively shorter, flatter sinuses, increasing in vertical complexity with age. The results indicate that final frontal sinus morphology is mostly attained by 20 years of age, but sexual dimorphism is evident: stabilization occurs around 14–16 in females and 18–20 in males.

1. INTRODUCTION

The frontal sinus is considered the most variable of the paranasal sinuses in terms of asymmetry, presence/absence, and overall morphology across adult individuals. Numerous studies have investigated patterns of adult frontal sinus morphological variation in terms of sex differences, population variation, and individuating characteristics. Overall, studies suggest that males tend to possess larger sinuses than females (Asirdizer et al., 2017; Čechová et al., 2019; Michel et al., 2015; Tatlisumak et al., 2016). In addition to females being more likely to possess hypoplastic (small) sinuses, they are also more likely to present with aplasia (absent sinuses) (Aydinhoğlu et al., 2003; Belaldavar et al., 2014; Gotlib et al., 2015; Kim et al., 2013). Population‐level variation in the size, shape, and presence/absence of the frontal sinus has also been documented, with Inuit, Australian, and some African populations (regardless of sex) tending to present with hypoplastic, often absent, sinuses (see Butaric et al., 2020 and Trant & Christensen, 2018 for reviews).

Although there are general population‐level trends, the frontal sinus is known to be highly individualistic. In fact, several studies indicate that even monozygotic twins possess uniquely shaped frontal sinuses (Asherson, 1965; Schuller, 1943). Owing to this individualistic nature, forensic literature has also focused on the utility of frontal sinuses for the positive identification of decedents (see Christensen & Hatch, 2018 and Ubelaker et al., 2018 for reviews).

Despite the wide range of studies investigating adult variation, little is known regarding exactly when and how adult frontal sinus morphology is reached. The frontal sinus has two routes of embryological origin: the air space that will become the frontal sinus either emerges as an outpouching of the frontal recess directly off the nasal capsule, or it may indirectly emerge from the ethmoidal air cells (Weiglein, 1999), typically around the third to fourth fetal months (Kasper, 1936; Schaeffer, 1916). Regardless of its specific embryological origin, most gross frontal sinus development occurs postnatally. Unlike other paranasal sinuses, the frontal sinus is not developed enough at birth to be radiologically observed. Among ontogenetic studies that have been conducted, there are conflicting reports concerning the ages at which the frontal sinus emerges, the age it appears radiologically, and when the sinus reaches its adult form.

The earliest appearance data vary depending on sample composition and definitions of what constitutes the “presence” of a frontal sinus (see Butaric et al., 2020 and Weiglein, 1999 for reviews). Imaging modality also contributes to variations in definitions and results. For example, the superimposition of structures in frontal radiographs makes delineating a potential frontal sinus from surrounding ethmoidal air cells challenging. In these situations, more conservative definitions are used with frontal sinus presence scored only if the airspace pneumatizes above the superior orbital borders (e.g., Christensen, 2004; Hanson & Owsley, 1980; Libersa et al., 1981). Some even argue a frontal sinus is only present if it extends both superiorly above the superior orbital margins and laterally past the medial orbit walls (e.g., Çakur et al., 2011; Duzer et al., 2017; Eggesbø et al., 2001). When using less restrictive definitions of a sinus (i.e., any indication as present), the actual emergence of a frontal sinus distinct from the ethmoidal cells has been reported as early as 2–3 yoa (e.g., Davis, 1914; Maresh, 1940; Park et al., 2010; Weiglen et al., 1992). However, pneumatization (i.e., aeration) into the frontal bone itself usually occurs later, around 4–6 yoa (see Libersa et al., 1981; Som et al., 2011; Weiglein, 1999), with males typically presenting earlier than females (Brown et al., 1984; Gagliardi et al., 2004). Despite the potential of earlier emergences, the frontal sinus is clearly radiographically apparent among most individuals by 8 yoa, as the sinus grows superiorly past the superior orbital borders (Dolan, 1982; Duque & Casiano, 2005; Scuderi et al., 1993; Tatlisumak et al., 2007).

Growth of the frontal sinus continues with primary expansions documented through puberty (Brown et al., 1984). However, reported ages at which the frontal sinus ceases growth vary widely amongst studies. Most studies support cessation in the mid‐to‐late teenage years (Brown et al., 1984; Gagliardi et al., 2004; Sardi et al., 2018; Spaeth et al., 1997), although a few studies suggest later cessation in the early‐to‐mid 20s (Karakas & Kavakli, 2005; Prossinger, 2001). Despite these differences in age of growth cessation, most studies agree that females attain adult size a few years earlier than males. Thus, with later appearance dates and earlier maturation, females tend to have a shorter growth period compared to males (see Brown et al., 1984; Gagliardi et al., 2004). This is one possible explanation for the smaller frontal sinus sizes typically found among females (see above).

As mentioned above, noted discrepancies in the ontogenetic literature are likely due to a multitude of reasons, including sample composition, imaging modality (e.g., traditional radiographs versus CT scans), imaging orientation, variables of interest, and overall research design. The use of cross‐sectional samples (e.g., Bargouth et al., 2002; Buyuk et al., 2017; Fatu et al., 2006; Mahmood et al., 2016; Moore & Ross, 2017; Park et al., 2010; Patil & Revankar, 2013; Prossinger, 2004; Sardi et al., 2018; Spaeth et al., 1997; Tehranchi et al., 2017; Weiglein et al., 1992; Yun et al., 2011), particularly those with limited sample sizes at each group, may also impact results. Both factors limit the amount of ontogenetic variation captured and can contribute to reported discrepancies. Several longitudinal studies do exist in the literature (e.g., Brown et al., 1984; Gagliardi et al., 2004; Nathani et al., 2016; Ruf & Pancherz, 1996a, 1996b; Shah et al., 2003); however, these studies utilize lateral radiographs, typically have small numbers of individuals per age cohort, only have a few images per individual (e.g., <4), and/or often do not look at older subadults (e.g., the sample stops at 11 yoa). While lateral cephalograms allow more clear visualization of the inferior aspect of the frontal sinus (i.e., there is less interference of the ethmoidal air cells) and permit measures of superior‐inferior height and anterior‐posterior depth, this view does not capture frontal sinus breadth nor overall shape.

The highly individualistic morphology of the frontal sinus is best appreciated in the frontal view, by which its full extension into the frontal bone and expression of variable arcades, septa, and asymmetry in the right/left lobes can be observed. Frontal sinus ontogeny in frontal views—which are arguably most informative for a variety of anatomical, forensic, and clinical studies concerned with frontal sinus size and shape—remains largely undocumented. The present study aims to address this gap in the literature. By collecting and analyzing frontal sinus outlines from a longitudinal sample of posterior‐anterior (PA) frontal radiographs, the goal of this study is to evaluate at what age males and females attain “adult” frontal sinus shape and whether ontogenetic trends in frontal sinus shape differ significantly between sexes. Although the precise relationships between frontal sinus size (e.g., linear dimensions) and shape (e.g., number and configuration of arcades) are unclear, similar ontogenetic trends are likely. Thus, based on previous studies on frontal sinus size and linear dimensions, we expect to find that females attain final shape earlier compared to males.

2. MATERIALS AND METHODS

2.1. Sample

Posterior‐anterior (PA) frontal radiographs were obtained from the American Association of Orthodontists Foundation (AAOF) Craniofacial Growth Legacy Collections Project (https://www.aaoflegacycollection.org/aaof_home.html), which is a free online resource housing longitudinal radiographs from several growth series. For the current study, individuals originated from several collections in this resource, including the Bolton‐Brush, Burlington, Matthews, Oregon, and Forsyth‐Twin studies. The inclusion of multiple collections allowed a robust sample size, which is often difficult to attain in longitudinal studies. However, as each collection utilized different equipment and scales were not consistently provided, the use of multiple collections precluded the ability to measure the accurate size (see data collection section below). Although exact ancestral demographic information is not provided for each individual, collections predominately consist of individuals of European ancestry residing in the United States and Canada.

A preliminary review was conducted, and only those individuals without obvious pathologies and with radiographs in which frontal sinuses pneumatized above the superior orbital borders were included in this study. While not necessarily biologically accurate (see Butaric et al., 2020 and discussion above), utilizing the superior orbital border as an inferior boundary is common practice (e.g., Christensen, 2004; Hanson & Owsley, 1980; Libersa et al., 1981; Yoshino et al., 1987) and ensures that the air space being measured is actually the frontal sinus, not ethmoidal air cells or other potential spaces that become difficult to discern due to radiographic superimposition. While there are several frontal sinus studies on traditional radiographs that do not utilize the superior orbital border (e.g., Fatu et al., 2006; Quatrehomme et al., 1996; Yoshino et al., 1987), most of these studies utilize dry crania from museum collections or anatomical teaching collections, which present with no superimposed soft tissue, are radiographed in AP versus PA view, and/or often have broken ethmoidal bones, allowing a clearer view of the inferior aspect of the frontal sinus.

Additionally, individuals included in this study had to have a minimum of four radiographs between the ages of 8 and 30 yoa, with the oldest‐aged radiograph being at least 18 yoa. The average number of images registered per individual was 8.35, with a minimum of four and a maximum of 22 images. Although the frontal sinus may appear above the orbits earlier in some individuals, most literature agrees that an observable frontal sinus is generally present on radiographs by 8 yoa. Given that previous studies have suggested the frontal sinus may attain its adult size in the mid‐teens (e.g., Brown et al., 1984; Gagliardi et al., 2004; Sardi et al., 2018), requiring individuals to have at least one radiograph at 18 yoa or older should provide a final, or near‐final, adult morphology for comparison. Radiographs of individuals 30 yoa or older were not included in the study given their small sample sizes in the AAOF Legacy Collection.

After exclusion criteria, a total of 935 radiographs (aged 8–29 yoa) from 111 individuals (55M/56F) were utilized in this study. Sex and age were recorded directly from the AAOF Legacy Collection website, which provides age in terms of years and months (i.e., 12 years 05 months). For this study, these ages were converted to total months for a continuous age variable and binned into year‐long cohorts for a categorical age variable. The year value was assigned based on their year of age; for example, an individual at 12 years 01 months and one at 12 years 11 months would both be considered as 12 yoa. Note, if an individual had two radiographs in a given year both were included in analyses except where noted. Table 1 provides an overview of the total number of radiographic images (i.e., number of outlines) utilized in the current study each year, as well as the number of individuals in each sample. Table 2 provides the distribution of the oldest‐age radiographs obtained per individual, which were used in some analyses to represent the final adult morphology (see details below).

TABLE 1.

The number of images and individuals (in parentheses) across years of age (yoa) and by sex

	8 yoa	9 yoa	10 yoa	11 yoa	12 yoa	13 yoa	14 yoa	15 yoa	16 yoa	17 yoa	18 yoa	19 yoa	20 yoa	21+ yoa	Totals
Males	9 (6)	15 (14)	19 (18)	25 (23)	36 (35)	40 (39)	39 (39)	33 (33)	46 (45)	39 (39)	46 (43)	24 (23)	26 (25)	19 (19)	409 (55)
Females	20 (15)	23 (17)	30 (22)	43 (31)	49 (39)	56 (42)	52 (51)	32 (32)	50 (49)	37 (36)	51 (50)	27 (27)	26 (26)	22 (21)	518 (56)
Total	29 (21)	38 (31)	49 (40)	68 (54)	85 (74)	96 (81)	91 (90)	65 (65)	96 (94)	76 (75)	97 (93)	51 (50)	52 (51)	41 (40)	927 (111)

TABLE 2.

Distribution of the oldest radiograph obtained per individual across years of age (yoa) and by sex

	18 yoa	19 yoa	20 yoa	21 yoa	22 yoa	23 yoa	24 yoa	25 yoa	26 yoa	27 yoa	28 yoa	29 yoa	Totals
Males	14	13	22	0	1	0	1	1	0	2	0	1	55
Females	10	13	19	2	4	2	3	1	2	0	0	0	56
Total	24	26	41	2	5	2	4	2	2	2	0	1	111

2.2. Data collection

Radiographic images were downloaded from the AAOF website and imported into ImageJ (Schneider et al., 2012), where image size was enhanced to 3000 pixels. Image contrast and brightness levels were adjusted to best visualize the sinus. The steps for outlining the frontal sinus largely followed protocols established by Christensen (2004); also see Figure 1). First, using the line tool, a supraorbital line was drawn across the superior orbital border (i.e., the roof of the orbital cavity) to demarcate the inferior boundary of the frontal sinus outline. Next, the free‐form tool was used to trace the superior borders of the frontal sinus from left to right, starting and ending at the intersections with the supraorbital line. The outline adhered to the outer contours of the sinus and did not follow septa inferiorly within the sinus. In the case of disconnected sinuses (e.g., if the right and left sinuses did not connect above the supraorbital line), a thin (~2 pixels) straight line was drawn at the inferior boundary to connect them. This created a single, closed outline as required for elliptical Fourier analysis (EFA, see below). Once a closed outline was completed, the outline was filled in, the background was cleared, and the isolated outline was saved as a .BMP file. This outlining process was repeated for each frontal sinus. To gain a baseline of error and potential noise in the frontal sinus data, 101 outlines across 47 individuals were re‐traced and used to evaluate intra‐reliability error, as described below. Individuals in this sample were limited to outlines registered at 18 yoa or older, to minimize potential age variation and maximize frontal sinus complexity. Re‐tracings occurred at a minimum of three weeks after the original tracings.

FIGURE 1.

Example of original PA‐frontal radiograph (left) with open frontal sinus outline (right), following Christensen (2004). Note inferior demarcation of sinus at the supraorbital border.

Once all outlines were collected, the .BMP files were imported into the software SHAPE (Iwata & Ukai, 2002) for EFA. This statistical technique uses harmonics to describe closed outlines (Kuhl & Giardina, 1982) and, thus, does not require homologous landmarks, making it an ideal method to capture frontal sinus shape variations. EFA has been used to analyze adult frontal sinus shape (e.g., Christensen, 2004, 2005; also see Ubelaker et al., 2018 for a review), and is well‐established in differentiating structures with complex morphology (see Caple et al., 2017 for a general review of EFA in forensic anthropology). EFA can also be performed in the absence of size information, which was necessary for this study given that the radiographic samples did not have scales and originated from multiple institutions. Following Christensen (2004, 2005), EFA was performed utilizing 20 harmonics and orientation was normalized along the major axis of the first harmonic. During EFA, each harmonic is described by four EF coefficients (a, b, c, and d), representing the cosine and sine of the x and y dimensions (Caple et al., 2017). The first harmonic, represented by a simple ellipse, captures a general height/breadth component, while each consecutive harmonic provides increasingly detailed information about the sinus shape. Collectively, the EF coefficients of the 20 harmonics provide a detailed representation of the sinus shape. These procedures were performed on all pooled outline data, including the re‐traced outlines collected for the intra‐observer error study.

2.3. Data analysis

The resultant EFA coefficients were subjected to a principal component analysis (PCA) in the SHAPE software to obtain independent shape variables, facilitate the visual assessment of shape variation among the outlines, and reduce the number of variables (given that each outline is represented by 20 harmonics, each with four EF coefficients). The PCA is commonly utilized after EFA, as it efficiently summarizes the information contained within the EF coefficients. The resulting effective principal components (PCs) (i.e., those PCs whose proportion is >1 divided by the total number of analyzed coefficients) were utilized in subsequent analyses. It is important to clarify here that two separate PCAs were conducted: 1) the main PCA investigated the overall shape differences (n = 935 outlines total), which did not include the redundant outlines, and 2) the PCA focused on error rates, which included the full outlines plus the redundant outlines (n = 1036 outlines total). The PCs from the main analysis were utilized in all subsequent analyses examining age and sex tends in sinus shape, while the PCs run with the duplicated outlines were only used in the error rate analyses. By including all outlines in the error analysis, the distance between the redundant error study outlines could be assessed in the context of full sinus variation.

2.3.1. Age and sex variation

To gain a better understanding of how frontal sinus shape was distributed across the sample, the shape variations (i.e., sinus contours) captured by the PCs were visualized and interpreted. Specifically, scatterplots of each PC representing >10% of the variation (i.e., PC1, PC2, PC3) against age‐in‐months with added Loess curves were created in the statistical software program NCSS (NCSS, 2020). Loess curves are a type of non‐parametric “smoothing” line that, unlike traditional parametric lines of fit, do not require a priori specifications of functional relationships between the variables in question (Chen et al., 2010; Cleveland & Devlin, 1988; Jacoby, 2000).

While the primary purpose of this paper is a descriptive overview of shape changes and stabilization of the frontal sinus, we conducted a generalized linear mixed‐effect model (GLMM) to statistically test for potential sex‐based ontogenetic trajectories using the lme4 package in Rv4.1.3 (Bates et al., 2015; R Core Team, 2022). Due to the amount of missing data (i.e., years not radiographed) within each individual, mixed‐effects models are more appropriate in our data set versus the more well‐known and simpler repeated measures of analysis of variance (see Krueger & Tian, 2004; West, 2009). Primary assumptions of GLMM include normality of the random effects and appropriateness of the link function. A third assumption typical of GLMMs is that the variance is estimated well when it has a fixed relationship to the mean; however, this is not required in models with an estimated scale parameter. Preliminary investigations indicated that the data were not linearly distributed and were heavily skewed. A detailed investigation of the distribution pattern indicated that the data were most reflective of a Gamma distribution; it was also discovered that the third assumption regarding the estimation of variance was not required. As such, the PC values were transformed to more closely match the assumptions of the GLMM statistical tests by first adding the value of “1” to all scores (simply to change all negative values to positive) and then transforming those values using the R package LambertW (Georg, 2015). This package allows data with heavy tails to be “Gaussianized” as close to normal as the data permits. For consistency, we refer to this transformation as “W‐transformed.”

Three GLMMs were developed with the W‐transformed values for PC1, PC2, and PC3 considered as the dependent value in each; note, these three PCs were chosen as they each contributed over 10% of the variation. For each model, individuals were considered as the subjects and random effects, sex was used as the fixed factor, and age (logged‐transformed calendar year) was considered the repeated measure. For age, we binned individuals into calendar years, from 8 to 21 yoa. Owing to the smaller sample sizes, individual outlines over 21 yoa were not included. Further, if individuals had two registered outlines within a calendar year, we removed the younger duplicate. When setting up the models, slopes were allowed to vary over subject, meaning that our expectation of compound asymmetry, or autoregression, is constrained within the model code. The model was developed using a Laplace approximation as the parameter estimation method and an inverse Gaussian link function for the Gamma distribution (see Ju et al., 2020). The final model was selected based on the Bayes Factors and the Akaike information criterion. Finally, in order to ensure that the GLMM results are not largely influenced by autocorrelation in the variables and assess how well the model performed, we plotted and visually assessed the residuals. If the visual assessment were normal, residuals were then approximated with a Durbin‐Watson test (White, 1992). This test is typically conducted in linear regression studies to quantify the amount of autocorrelation in the residuals of the final model.

2.3.2. Age at stabilization

To preliminarily assess within‐individual changes in the actual stabilization of frontal sinus shape with age, Euclidean distances between within‐individual outlines in shape space were calculated and used as a measure of deviation between sinus outlines. Given that the primary aim of the study is to determine at what age frontal sinus shape stabilizes (i.e., attains its adult shape), Euclidean distances for each PC score (e.g., PC1 only) and across the effective PCs (e.g., PC1–PC9) were calculated from each outline to the oldest‐aged outline within each individual, which is presumed to represent final adult shape. For example, if an individual had outlines for 9, 12, 16, 18, and 20 yoa, Euclidean distances were calculated between the following pairs: 9–20 yoa, 12–20 yoa, 16–20 yoa, and 18–20 yoa. Note that the oldest‐aged outline varied between 18 and 29 yoa across individuals (Table 2; see below for further discussion). This provided a value representing how far away a sinus was from its final morphology.

The resulting distances to the oldest‐age PC were plotted against age‐in‐months with Loess curves (see description above) to examine ontogenetic trends in shape changes in the pooled and sex‐specific samples across all individuals. It was hypothesized that the distances from the younger‐aged outlines would be greatest, with distances decreasing with age as sinus morphology approached its final adult shape. At the point of stabilization in growth and development, the trend line was expected to level out and approach zero. While the oldest‐age sinuses used as the final adult morphology varied between 18 and 29 years of age, which could introduce some variation in analyses, the use of this final adult range was necessary to incorporate the largest sample possible given that the ages at which radiographs were taken varied across individuals. To investigate the possible effects of this methodological decision, distances were also calculated for each oldest age (e.g., 18, 19, 20, and 21+yoa) and Loess curves fit the data, with results presented in the Supplementary Materials (Figs S1 and S3).

To statistically assess the age‐at‐stabilization pattern observed in the Loess curves, paired t‐tests were conducted for males and females separately between the W‐transformed PC values at each age cohort and the W‐transformed PC values of the oldest‐age sinus. For example, paired t‐tests were run between PC1 of 8yo males and PC1 of oldest‐age males, between PC1 of 9yo males and oldest‐age males, etc. While implementing numerous paired t‐tests introduces the problem of multiple comparisons, these exploratory analyses were conducted to compare to observed trends in the Loess curves. To control for the false discovery rate, we selected the Benjamini‐Hochberg (BH) procedure with α = 0.05 set as the critical value. It was hypothesized that a trend would be observed where statistical differences would be obtained up until the age at which stabilization and adult morphology is attained, as observed in the Loess curves described above. The BH procedure helps to identify a clear sectioning point at which the frontal sinus stabilizes. These analyses used the same reduced sample as with GLMM models, whereby we limited analyses to 21 yoa, removed the youngest iterations of individuals within the same calendar year, and focused analyses on W‐transformed PC1, PC2, and PC3 values. A Shapiro‐Wilk test of normality on the possible sex‐age groups (e.g., males at 8 yoa) confirmed our data adhered to the assumptions of normality as required for paired t‐tests, with minimal exceptions (see Supplementary Materials, Table S1).

2.3.3. Error reporting

The act of manually tracing the frontal sinus outlines is expected to introduce some degree of error or noise to the shape analyses. To examine this potential source of error/noise, Euclidean distances between the original and re‐traced outlines (n = 101 pairs) were calculated for each effective PC (from the full sample + error PCA), as well as across the multidimensional distance between the cumulative effective PCs (PC1–PC9). These error distances were utilized to investigate whether any specific PC component was more affected by tracing errors and gain an understanding of the amount of deviation that should be expected from tracing versus ontogenetic changes. To further statistically evaluate potential error, pairwise testing between the two trials of PCs was conducted in SPSSv28 (IBM Corp. Released, 2021) and the technical error of measurements was calculated (see Langley et al., 2018; Zeman & Beňuš, 2020).

3. RESULTS

The main PCA on all outlines (excluding the duplicates for error testing) resulted in nine effective PCs, explaining a total of 92.44% of the variation. Figure 2 provides scatter plots for PCs presenting >10% of the variation across age‐in‐months to visualize individual variation; for example sinus outlines at the extreme axes are also provided, as well as sex‐based Loess curves. Plots showcasing Loess curves for each of the 111 individuals are provided in the Supplemental Materials (Figure S1). PC1 (51.02% of variation) largely tracks overall height‐to‐breadth dynamics. Outlines with increasingly positive PC1 scores exhibit superiorly‐inferiorly taller sinuses relative to medial‐lateral breadth, while those with more negative scores exhibit broad sinuses relative to height (i.e., “flat” sinuses).

FIGURE 2.

Scatterplots for PC1–PC3 across age‐in‐months (years labeled for ease of interpretation) by sex, from top to bottom: PC1 (51.02%); PC2 (11.73%); PC3 (10.03%). Loess lines were added for sex with symbol shapes distinguishing males (circles; dashed line) and females (triangles; solid line). PC contours: dashed black outline represents example individual outlines along the represented axes. Solid yellow (minimum extremes) and blue outlines (maximum extremes) correspond to +/‐2SD shape variations captured by the EFA.

PC2 (11.73% of variation) tracks asymmetry, as related to the location of a dominant arcade (right vs. left side) and extended “tail” on the contra‐lateral side. Outlines along the negative PC2 axes tend to possess an anatomically left‐sided dominant arcade with an extended right‐sided tail, with outlines along the positive axes possessing a right‐sided dominant arcade and extended left‐sided tails. Note that this pattern does not necessarily distinguish between right‐ versus left‐sided sinus lobe dominance (with the right and left lobes defined by an inter‐sinus septum), just the location of a dominant arcade (i.e., loop, scallop, expansion) regardless of side; in this pattern, an individual who only possesses a right frontal sinus (i.e., left sinus aplasia) could still be located along the negative PC2 axis if that right lobe had a dominant arcade on its left portion. PC3 (10.03% of variation) appears to capture some degree of relative complexity in sinus shape, which is most evident when looking at actual example outlines (black dashed lines in Figure 2) versus the averaged contours. Outlines on the negative PC3 axis tend to present with more complex arcades, as well as slight right dominance in arcade height, while outlines on the positive PC3 axis tend to present with a smoother single arcade, indicating less complexity, and slight left dominance in arcade height. The remaining PCs each explain less than 10% of the variation and are not further discussed here.

In terms of the sex‐based ontogenetic trendlines, both the male and female trend lines show a positive relationship between PC1 and age (Figure 2, top), such that younger individuals tend to possess sinuses that are wider and superior‐inferiorly flatter (negative PC1 loadings), with vertical growth increasing with age. Further, as indicated by the relative location of the trend lines, females (solid line) tend to possess more positive PC1 loadings for a given age compared to their male counterparts, until 22‐plus years of age where the lines cross. The Loess lines for PC2 (Figure 2, middle) and PC3 (Figure 2, bottom) do not seem to indicate strong sex‐based or age‐based patterns of variation. The results of GLMM for W‐transformed PC1, PC2, and PC3 with sex and age somewhat reflect these visible trends (see Table 3). The variable of age presented as a significant effect in the models for W‐transformed PC1 and PC3 (t _PC1 = −6.336, t _PC3 = 5.508, p‐values <0.001), but not for PC2 (t _PC2 = 1.751, p‐value = 0.08). The fixed effect of sex in relation to repeated years was not significant in any of the models, though PC2 approached significance (t _PC2 = −1.849, p‐value = 0.06). In all models, autocorrelation was successfully accounted for, with visual assessment of the residuals indicating normality and Durbin‐Watson tests returning relatively acceptable values (d_PC1 = 1.88, d_PC2 = 1.76, d_PC3 = 1.93).

TABLE 3.

Generalized linear mixed effect model (GLMM) results for W‐transformed PC1–PC3

Model Parameter		w PC1				wPC2				w PC3
		Est	Err	Stat	Sig	Est	Err	Stat	Sig	Est	Err	Stat	Sig
Fixed	Intercept	1.470	0.077	19.121	0.001	0.936	0.043	21.976	0.001	0.817	0.034	24.315	0.001
	Age	−1.160	0.025	−6.336	0.001	0.028	0.016	1.751	0.080	0.070	0.013	5.508	0.001
	Sex	0.014	0.033	1.428	0.669	−0.021	0.011	−1.849	0.064	−0.007	0.011	−0.687	0.492

		Var	SD	d	Var	SD	d	Var	SD	d
Random (Ind.)	Intercept	0.162	0.403	1.884	0.051	0.225	1.757	0.031	0.177	1.926
	Year	0.021	0.144		0.007	0.086		0.005	0.068
	Residual	0.003	0.057		0.001	0.038		0.001	0.034

Note: In each model, PCs were considered dependent variables, age as the repeated measure, sex as the fixed factor, and individuals as the random effects. Results include parameter estimates (Est), standard Error (Err), t‐values (Stat), and p‐values (Sig); random effect results are Durbin‐Watson estimates (d), variance (Var), and standard deviation (SD).

Note: Bold p‐values indicate significance at 0.05; d results between 1.5 and 2.5 are relatively acceptable for residual autocorrelation (d = 2 indicates no autocorrelation).

3.1. Oldest‐Age PC distances

To better examine the age at which frontal sinus shape actually stabilizes, the within‐individual Euclidean distances to the oldest‐age outline (referred to here as oldest‐age distances) were plotted against age‐in‐months and Loess curves were applied to the male and female groups. Figure 3 illustrates these trends for the multivariate distances across PC1–PC9, thereby capturing the overall shape of the sinus as explained by these nine PCs. The oldest‐age distances presented here varied across individuals (see Materials and Methods section); plots for separate distances to 18, 19, 20, and 21+yoas are available in Supplemental Materials (Figure S2). Plots of individual‐based Loess curves for specific PC distances (i.e., PC1, PC2, PC3) across age were also visualized, highlighting the individualistic noise inherent to the dataset (Figure S3). The Supplemental Materials also include sex‐based Loess curves for specific PC distances (i.e., PC1, PC2, PC3) across age (Figure S4), with male and female PC2 and PC3 trend lines displaying relatively little change as compared to PC1.

FIGURE 3.

Multivariate PC1–PC9 distances to oldest age versus age‐in‐months (years labeled for ease of interpretation). Female (open triangles) ontogenetic trends are represented with a solid Loess curve; male (grey circles) ontogenetic trends are represented with a dashed Loess curve. The solid red line represents the PC error mean at 0.056 with dashed red lines at 0.027 standard deviations above/below (see Table 5). A1 and A2 indicate outliers, and their outlines as compared to the oldest age are presented in the lower box (see text for details).

The sex‐based Loess curves indicate similar female and male general trends, with greater distances represented in earlier years, as expected. Some slight differences, however, can be observed between the sexes. The female line (thick solid line) is lower than the male line (thick dashed line) at the earlier ages until they cross around 17–18 yoa. The female curve also appears to stabilize, or level out, earlier than the male curve (Figures 3, S2). Specifically, initial stabilization appears to occur around 14–16 yoa for females and 18 yoa for males. Final stabilization (leveling out) appears to occur by 16–18 yoa for females and 20 yoa for males. The results of the paired t‐tests largely confirm these initial interpretations (see Table 4). Specifically, PC1 values of the younger ages were significantly different (p < 0.05) from oldest‐age values until 15 yoa in females and 18 yoa in males (except for 15 yoa males with a BH adjusted p‐value of 0.058). Paired t‐tests performed on PC2 were mostly non‐significant across all male and female ages (Table S2). PC3 returned a similar trend as PC1 for females (significant differences until 15 yoa, even with the BH correction), but this variable was generally non‐significant across the male ages (Table S3).

TABLE 4.

Paired t‐test results for W‐transformed PC1between each year and oldest age, separated by sex

Year ‐ oldest	Females						Males
	n	Mean Diff	Std Dev	T	Sig	BH Adj	n	Mean Diff.	Std Dev	T	Sig	BH Adj
8 yoa	15	1.009	0.086	−2.384	0.032	0.052	7	0.931	0.107	−5.637	0.001	0.004
9 yoa	17	0.996	0.116	−3.282	0.005	0.011	14	0.890	0.067	−5.356	0.000	0.001
10 yoa	22	0.994	0.125	−3.766	0.001	0.004	19	0.945	0.104	−4.047	0.001	0.003
11 yoa	31	0.984	0.125	−4.373	0.000	0.001	22	0.950	0.099	−4.915	0.000	0.001
12 yoa	39	0.995	0.137	−2.973	0.005	0.011	33	0.952	0.094	−7.523	0.000	0.000
13 yoa	42	1.014	0.143	−2.383	0.022	0.038	31	0.946	0.109	−5.199	0.000	0.000
14 yoa	51	1.027	0.145	−2.394	0.020	0.038	39	0.971	0.096	−4.351	0.000	0.001
15 yoa a	32	1.045	0.131	−0.874	0.389	0.460	33	0.971	0.103	−2.167	0.038	0.058
16 yoa	49	1.015	0.146	−1.433	0.158	0.217	45	0.989	0.100	−2.580	0.013	0.027
17 yoa	36	1.052	0.141	−0.160	0.874	0.874	39	0.979	0.077	−3.414	0.002	0.004
18 yoa b	50	1.042	0.132	−0.424	0.673	0.729	43	1.006	0.100	−1.443	0.157	0.217
19 yoa	27	1.070	0.139	−0.893	0.380	0.460	23	0.987	0.098	−0.485	0.633	0.715
20 yoa	26	1.051	0.127	0.215	0.832	0.865	25	1.020	0.112	1.000	0.327	0.425

Note: Results include sample sizes (n), difference of means (Mean Diff), standard deviations for the difference of means (Std Dev), t‐test statistics (T), and p‐values (Sig), and BH adjusted p‐values (BH Adj).

Note: Bold p‐values indicate significance at 0.05 and BH values below critical value α = 0.05.

^a Age at stabilization for female shape on PC1.

^b Age at stabilization for male shape on PC1.

3.2. Error rates

The PCA on the full sample including duplicate outlines resulted in nine effective PCs cumulatively explaining 92.48% of the variation. Distances (combined PC1–PC9) calculated between the duplicate outlines in this full‐PC configuration reveal an average error distance of 0.056 (std dev = 0.027), with 17 out of 101 paired outlines exceeding a distance of 0.080 (see Table S4). This average level of “noise” introduced by tracing is plotted in Figure 3, to assist in interpreting at which point any deviations in PC distances could be solely from outlining errors and may not represent ontogenetic changes. In looking at the individual PCs, the majority of intra‐observer error was seemingly captured in PC3 (9.86% of the variation), which had the highest average of error distances (avg = 0.024, std dev = 0.022). This error can be visualized by outlines in Figure 3, whereby the A1 and A2 datapoints show the appearance of larger oldest‐age distances in the older individual datapoints. A visual analysis of these two outlines, which are from the same individual, indicates that these deviations are likely due to noise related to the level of detail captured in each tracing. Noise is also evident in the individualistic Loess curves (Figure S3).

Given the non‐parametric nature of the PCs (see Table S5), Wilcoxon signed‐rank tests were conducted to test for significant differences between the repeated measures for each PC. The results, provided in Table 5, indicate three PCs where the first and second measures are significantly different: PC1 (p = 0.004), PC3 (p < 0.001), and PC4 (p = 0.006). Subsequent technical error measurements were calculated, with all relative error rates scoring <2% except PC3 (2.3%). These tests support the initial conclusion above, suggesting most of the noise in the data is related to outline complexity captured by PC3. The implications of these error rates on the results of this study are discussed further below. Note, unlike the tests above, the error rate tests utilized raw (not transformed) PC values to properly calculate the technical error measurement.

TABLE 5.

Error reporting for each of the effective components, including averaged mean differences (Mean Diff) and standard deviations (Std Dev) between observations for each PC, Wilcoxon signed‐ranks test results with Z‐scores (Z) and p‐values (Sig.), and the calculated absolute and relative technical error of measurement (Abs TEM and Rel TEM, respectively) with the reliability coefficient (R)

PC	Mean Diff	Std Dev	Z	Sig	Abs TEM	Rel TEM	R
PC1	−0.007	0.022	−3.643	<0.001	0.016	0.016	0.983
PC2	−0.002	0.022	−1.614	0.106	0.016	0.016	0.937
PC3 a	0.016	0.029	−5.730	<0.001	0.023	0.023	0.739
PC4	−0.006	0.022	−2.600	0.009	0.016	0.016	0.907
PC5	0.000	0.017	−0.456	0.649	0.012	0.012	0.876
PC6	0.000	0.016	−0.195	0.846	0.011	0.011	0.806
PC7	0.003	0.021	−1.089	0.276	0.015	0.015	0.549
PC8	−0.001	0.012	−0.635	0.525	0.009	0.009	0.798
PC9	−0.001	0.013	−1.313	0.189	0.009	0.009	0.776

Note: Bold p‐values indicate significance at 0.05.

^a PC3 also has the highest maximum value and mean for error distances; see text for details.

4. DISCUSSION

This paper represents the first investigation into the ontogeny of frontal sinus shape from a longitudinal sample of posterior‐anterior radiographs. Overall, the descriptive and statistical results indicate that final frontal sinus morphology is mostly attained by 20 yoa regardless of sex. Age had a significant effect on PC1 (51.03% variation) representing the relative height and breadth of the sinus, as well as PC3 (10.03% variation) capturing the degree of relative complexity in the outlines. Younger individuals tend to have superior‐inferiorly flatter sinuses relative to their medial‐lateral breadth. This is in concordance with previous literature suggesting vertical pneumatization further into the frontal squama occurs in later years (Brown et al., 1984; Dolan, 1982; Duque & Casiano, 2005; Scuderi et al., 1993; Tatlisumak et al., 2007). It is important to note, however, that most previous literature either 1) is cross‐sectional in nature, with actual individualized trends unknown, or 2) used lateral cephalograms, for which medial‐lateral breadth dimensions cannot be accounted for. As might be expected, younger individuals also tend to have less complex frontal sinus outlines (indicated by PC3), supporting an increase in the number of arcades with age.

Figure 4 illustrates six individuals (three males, three females) with overlaid frontal sinus outlines to provide within‐individual examples of sinus development across ontogeny. These individuals were chosen as they had the most data points available across ontogeny from 8 yoa to at least 20 yoa. These individuals provide interesting insight into the progression of shape change over the years. The increase in relative height and complexity with age is evident. More specifically, there is overall superior and lateral expansion of the sinus, as well as increased complexity in the numbers of arcades. Most interestingly, however, is that the overall shape of the sinus (in terms of arcade presentation) seems to be established early, even while superior and lateral expansion continues.

FIGURE 4.

Overlaid frontal sinus outlines across ontogeny for six selected individuals (with AAOF identification numbers; OR, Oregon collection; BUR, Burlington collection; M, male; F, female); dashed line represents the superior orbital border demarcating the inferior boundaries of the frontal sinus.

Sex differences in frontal sinus ontogeny are also apparent. Similar to several previous studies on various frontal sinus sizes and linear dimensions (Brown et al., 1984; Gagliardi et al., 2004; Karakas & Kavakli, 2005; Prossinger, 2001; Prossinger & Bookstein, 2003; Sardi et al., 2018; Spaeth et al., 1997), the current study suggests that females attain their adult shape earlier than males. This trend is evident in the exemplar individuals (Figure 4) and was statistically supported by the GLMM models. As indicated by the leveling of the Loess growth curves, we specifically found that frontal sinus shape in females (Figure 3, solid line) approaches stabilization around 16 yoa, with a change in slope suggesting decreased development between 14–16 yoa. In males (Figure 3, dashed line), stabilization is not observed until 18–20 yoa. These interpretations were also statistically supported by the paired t‐tests investigating within individual distances to oldest age along PC1. In those results, significant differences in the paired distances stopped for females at 15 and 18 yoa for males considering (an alpha critical value of 0.05), suggesting that females approach adult morphology earlier than males.

Although not exact, these results are also similar to those of several studies: Brown et al. (1984) suggest sinus size should reach its adult state around 14.95 yoa for females and 17.51 yoa for males based on lateral radiographs; Spaeth et al. (1997) report cessation at 15–16 yoa for females and 18 yoa for males for linear data; and, more recently, Sardi et al. (2018) indicate cessation at 14.6 yoa for females and 20 yoa for males for volumetric and linear data. Note that these studies focused on frontal sinus size (as measured by area, volume, and/or general linear measures such as height and breadth), while this study focused on outline shape (i.e., the contours of the sinus arcades). As mentioned previously, due to the nature of our radiographic sample, we were unable to directly assess size. It is possible to get additional development of outline shape (e.g., expanding of certain arcades, the inclusion of additional arcades) without affecting the maximum height and width of a sinus. Thus, some variation in results from this study could also be due to the use of a frontal view and the specific incorporation of outline shape. Still, there appears to be a general alignment between the timing of cessation of frontal sinus shape and size across multiple studies.

While these general trends in shape stabilization are noted, pin‐pointing an exact year of cessation is challenging for several reasons. First, as with any ontogenetic variable, there is individual variation in the age at which final frontal sinus morphology is attained. In fact, studies already point to inherent noise in frontal sinus ontogenetic data (see Prossinger, 2004; Prossinger & Bookstein, 2003; Sardi et al., 2018). Radiographs were not available at every age for every individual in this study, and toward the older ages (20 yoa and above), sample sizes are greatly reduced—thus, there are some inherent gaps in the data. However, we accounted for some of these limitations by incorporating linear mixed effect models able to accommodate missing data. Further, slight variations in orientation during radiography could artificially affect the shape of the sinus outlines and placement of the supraorbital line. For example, an upward turn of the head would artificially shorten the height of a sinus and may result in arcades close to the supraorbital line being excluded from the supraorbital region (thus changing the degree of complexity). These variations can create noise in the data, adding ambiguity to the trend lines. However, longitudinal samples of radiological images of subadult crania are rare given the risks associated with radiation, so research is limited to these available collections. Furthermore, given the lack of homologous landmarks available on the highly variable frontal sinus, outline analyses are beneficial regardless of these limitations to capture the full shape of the frontal sinus (as would be required to assess final shape attenuation).

Another complication in determining the precise year of cessation is the fact that the within‐individual distances to the oldest‐aged radiograph do not actually reach zero. Noise introduced in the manual tracing of the outlines is one source contributing to outline errors. The intra‐reliability aspect of this study revealed that even when the same radiographs were outlined by the same observer, there was an average distance of 0.056 between multivariate PC distances (with a standard deviation of 0.027). If we can expect this amount of PC distance from the same exact radiograph, then we can only be sure distances outside of this range are due to actual anatomical variance. In short, distinguishing between shape variation introduced in outlining and slight variations that may be due to small amounts of ontogenetic change is not possible. This complication is further highlighted by the fact that PC3, which corresponds with aspects of sinus complexity, contributed the most to these intra‐reliability distances. The evidence of tracing “noise” can be seen in Figure 3, with an example of an outlier in the older‐aged individuals provided. In the outlines A1 and A2 (Figure 3), the oldest‐aged outline was traced slightly down into a septum unlike the prior two outlines, again along with slight differences in the complexity of the tracing. Given that sample sizes are relatively lower post‐20 yoa, outliers such as these individuals can impact results. This is most evident along PC3, the PC that was most associated with tracing errors, whereby the trendline lines increase in older ages (Figure S4, bottom graph).

Tracing noise can also be visualized in older‐aged outlines in Figure 4; although overall sinus morphology appears consistent, there are slight variations in the outlines. These deviations could be the result of human tracing error, as to keep the continuity of the outline, each sinus had to be outlined in a single stroke. It could also reflect radiograph quality or superimposition of structures obscuring the exact contour. Given these possibilities and the orientation issues described above, EFA may be too sensitive for some shape analyses, particularly when small shape deviations are important to the research question. Future studies could utilize coding methods, in which the number of septa, arcades, and other features is scored, to assess when those variables stabilize; however, such an analysis would still not capture the comprehensive shape of the frontal sinus.

There is also the possibility that some frontal sinus shape change continues after 20 yoa. As noted in the introduction, several studies report much later periods of growth cessation (Karakas & Kavakli, 2005; Prossinger, 2001; Prossinger & Bookstein, 2003). However, these studies are largely limited by being cross‐sectional in nature with few examples of individuals in each age cohort. For example, Prossinger (2001) was based on a cross‐sectional sample of children ranging from 3 to 11 yoa, with the adult growth‐cessation dates estimated by a logistical function. Even with a later addition of adults and older children to the dataset (Prossinger & Bookstein, 2003), the age cohorts 10–23 yoa for males and 10–16 yoa for females were not available, rendering large portions of the growth model still unaccounted. Fatu et al. (2006) found a significant difference in frontal sinus volume among younger and older adults, suggesting that the frontal sinus may experience changes in volume with senescence (also see McLaughlin et al., 2001). However, while some studies found sinus enlargement with older age indicative of bone resorption, others found sinus volume reduction (Akhlaghi et al., 2016; Emirzeoglu et al., 2007).

When looking at the actual outline tracings in the current study, it seems unlikely that there are significant ontogenetic changes in frontal sinus shape in these “older” individuals studied here (i.e., mid‐to‐late twenties). As discussed above, the outlines of individuals in Figures 3, 4, suggest that the shape changes captured by EFA in these older‐aged individuals are more likely the result of radiographic orientation, tracing noise, and/or radiographic limitations such as superimposition of structures or radiographic quality resulting in slight deviations in outlines. Of importance, however, is that despite these limitations discussed above, a general pattern of sinus shape ontogeny has emerged.

Although a pattern is evident, additional research is required to better understand how the actual ontogenetic processes may affect sinus pneumatization across diverse groups; indeed, overall pneumatization processes of the paranasal sinuses are still largely unknown (but see Zollikofer & Weissmann, 2008 for one hypothesis). Several studies suggest that frontal sinus pneumatization may relate to growth with brain expansion during growth and development (Enlow, 1975:120; Shapiro & Schorr, 1980; Takahashi, 1984). For example, during enlargement of the frontal cerebral lobe, both the internal and external tables of the frontal participate in an “anterior drift” with the enlarging brain and neurocranium. Once anterior brain growth stops, the internal table position remains relatively stable. However, the anterior drift of the outer table continues, with osteoblastic (bone deposition) and osteoclastic (bone resorption) activity on its external and internal surfaces, respectively. This differential growth between the outer and inner tables coincides with the additional vertical expansion of the frontal sinus.

Continued vertical expansion of the frontal sinus superior to the supraorbital borders may be related to frontal bone morphology. Several individuals have suggested that the sinuses will opportunistically invade neighboring bone unless constraints are present. For example, Zollikofer and colleagues (Zollikofer et al., 2008; Zollikofer & Weissmann, 2008) suggest that a more acute supraglabellar depression acts as a spatial constraint, resulting in smaller frontal sinuses (also see Maddux & Butaric, 2017 for similar spatial‐constraint arguments for the maxillary sinus). This hypothesis is somewhat supported in the paleoanthropological literature, based on visual assessment of large browed hominins with depressed supraglabellar regions (e.g., Sungir‐1, Forbes'Quarry, Saccopastore‐2, Ceprano, Mladeč), who tend to present with small, often absent, frontal sinuses (Bruner & Manzi, 2005; Buck et al., 2019; Butaric et al., 2019; Tillier, 1975; Zollikofer et al., 2008). However, this spatial‐constraint hypothesis does not fully explain why modern human females, with less pronounced supraorbital ridges and lacking supraglabellar depressions, also often present with small, often absent, frontal sinuses (Aydinhoğlu et al., 2003; Belaldavar et al., 2014; Gotlib et al., 2015; Kim et al., 2013).

Further, Sardi et al. (2018) highlight a complicated ontogenetic relationship between frontal bone morphology and frontal sinus dimensions. Specifically, the cranial and sinus dimensions analyzed in their study showed drastically different ontogenetic trajectories across their sample. For example, while frontal sinus volume did not correlate with nasal dimensions and endocranial volumes, as expected based on previous studies, it did correlate with glabellar thickness. While these authors utilized CT scans, allowing more accurate and robust measures of frontal sinus size and cranial morphology that cannot be captured by 2D radiographs, they were limited to cross‐sectional data as radiation exposure makes most longitudinal studies with CT scans unethical. As such, these authors acknowledge that the cross‐sectional nature of their study and high inter‐individual variability may occlude accurate models of growth. Although more limited in terms of data collection, longitudinal studies incorporating lateral radiographs could be conducted to directly investigate the timing of the vertical expansion of the frontal sinus in conjunction with the overall development of the supra‐glabellar depression.

When possible, such studies should incorporate more diverse groups to gain a better understanding of frontal sinus and cranial growth development. The current study was limited in this regard, as most of the sample was of European‐American ancestry. Initial evidence does suggest some overall trends across groups of varying ancestry. For example, as mentioned above these results match relatively well with Sardi et al. (2018), who measured Argentinian samples, and Gagliardi et al. (2004), who measured Australian Aborigines. Still, caution is warranted in applying these results to other populations. Population variation in frontal sinuses among adults is well‐established in the literature (see Introduction section), and studies indicate that differences in adult form are known to be the result of several potential ontogenetic trajectories. For example, population‐level differences could be the result of early (prenatal) development, divergent trajectories occurring later in ontogeny, and/or the extension or truncation of size‐related ontogenetic scaling (Sardi & Rozzi, 2012; Strand Viðarsdóttir et al., 2002). Fully understanding frontal sinus ontogenetic trajectories across sexes and populations, and unraveling potential influencing variables, will continue to be a challenge without large, diverse longitudinal samples.

Although questions remain, the results of this study contribute to knowledge of frontal sinus growth and development, which can have implications in various disciplines. The role of the paranasal sinuses has a long history in the paleoanthropological literature (e.g., Blake, 1864; Bruner & Manzi, 2005; Buck et al., 2019; Busk, 1865; Butaric et al., 2019; Coon, 1962; Koppe et al., 1999; O'Higgins et al., 2006; Prossinger, 2008; Rae & Koppe, 2004; Rossie, 2008; Stansfield et al., 2021; Tillier, 1975, 1977; Vlćek, 1967). Understanding the ontogenetic processes of these structures in modern humans, for which larger sample sizes are available, could lead to more accurate interpretations of the ontogenetic and phylogenetic processes acting on hominin craniofacial morphology. In contemporary populations, frontal sinus development has long been an area of interest in pediatric medicine, particularly in otolaryngology, maxilla‐facial surgery, orthodontics, and related fields. Specifically, studies note the importance of understanding the anatomical variations and craniofacial relationships of the frontal sinus among pediatric populations, largely due to potential relationships with sinonasal disease susceptibility (e.g., sinusitis), surgical complications, and/or expected trauma patterns (e.g., Shah et al., 2003; Sivaslı et al., 2002; Whatley et al., 2005; Wolf et al., 1993; Wright et al., 1992; Zimmerman et al., 2006).

Finally, these results also have direct forensic implications. In conjunction with other methods, (e.g., visual identification, fingerprints, dental comparisons, DNA analysis), medicolegal agencies also utilize frontal sinus comparisons to make positive identifications in decedents. Typically, antemortem and postmortem radiographs are compared and, if there is a morphological match, a positive identification is made (see Christensen & Hatch, 2018 and Ubelaker et al., 2018 for reviews). Making a false positive identification or excluding a true identification has major impacts on the family of the decedent, as well as potential legal implications. Therefore, it is particularly important for practitioners to know at which age frontal sinus shape stabilizes or how much shape change can be expected given the timing between the antemortem and postmortem radiographs. Future studies directly testing the impact of age‐related changes on forensic identification methods utilizing the frontal sinus would be beneficial.

5. CONCLUSION

The current study provides a first look at changes in frontal sinus shape with age. Longitudinal assessments of posterior‐anterior frontal sinus outlines indicate that final frontal sinus shape is attained by 20 yoa in most individuals, regardless of sex. Still, sex differences were observed in frontal sinus ontogeny: females attain their adult shape earlier than males. Although pinpointing an exact year of cessation is challenging for several reasons, overall stabilization of frontal sinus shape appears to occur around 14–16 yoa for females and around 18–20 yoa for males, which largely agrees with previous growth studies investigating frontal sinus size. Additionally, this study highlights the methodological difficulties in frontal sinus imaging studies, with issues of varying radiographic orientation and manual outline tracing with EFA introducing additional noise to the ontogenetic data. Statistical analyses across longitudinal data are challenged by missing radiographs at varying ages across individuals. Despite these limitations and sources of “noise” in the data, the current study contributes novel information to the existing literature by utilizing one of the largest available longitudinal (versus cross‐sectional) samples, examining sinus morphology in a frontal (versus lateral) view, and investigating the ontogeny of frontal sinus shape (versus size or linear dimensions). As such, the results of this study may provide important insights for clinical, paleoanthropological, and medicolegal fields, particularly regarding pediatric medicine and forensic identification. Additional studies further exploring the connection between sinus morphology, ontogeny, and medicolegal applications would be valuable.

AUTHOR CONTRIBUTIONS

LNB participated in concept/design, acquisition of data, data analysis/interpretation, and drafting of the manuscript. HMG participated in concept/design, data analysis/interpretation, and critical revision of the manuscript. JLC participated in data analysis/interpretation. KMF participated in the acquisition of data and approval of the article. All authors read and approved the final manuscript.

CONFLICT OF INTEREST

The authors declare no conflicts of interest.

Supporting information

Appendix S1

Butaric, L.N. , Campbell, J.L. , Fischer, K.M. & Garvin, H.M. (2022) Ontogenetic patterns in human frontal sinus shape: A longitudinal study using elliptical Fourier analysis. Journal of Anatomy, 241, 195–210. Available from: 10.1111/joa.13687

DATA AVAILABILITY STATEMENT

DATA AVAILABILITY STATEMENT Data available on request from the authors