Age-dependent changes in infant head shape: a smartphone app-based study in Japan

Abstract.

Head shape undergoes rapid changes during infancy, but the age-dependent changes in cranial asymmetry remain inadequately characterized. This study aims to analyze factors associated with these parameters, and to establish reference curves in Japanese infants. Two indices of head shape, the cranial vault asymmetry index (CVAI) and cranial index (CI) were collected from 127,605 Japanese infants via a smartphone app. We performed univariate and multivariate analyses to identify factors associated with CVAI and CI. Using 72,726 data derived from infants born via spontaneous vaginal delivery with normal birth weight, reference curves for CVAI and CI were constructed. CVAI exhibited a peak at 3–4 mo of age, followed by a gradual decline, whereas CI increased until approximately 6 mo of age. Boys had significantly higher CVAI than girls. Low birth weight was associated with low CI. Reference curves revealed distinct age-specific patterns, with CVAI peaking at 3–4 mo and declining thereafter, and CI increasing until around 6 mo. In conclusion, this study provides the first reference curves for CVAI and CI that can be applied for Japanese infants. The findings highlight the natural course of cranial asymmetry and proportionality, emphasizing the importance of age-specific assessment.

Highlights

● We aimed to clarify the natural course of infant head shape by constructing reference curves using large-scale, app-based data.

● Among 72,726 Japanese infants, cranial asymmetry peaked at 3–4 mo and then improved, while cranial proportionality increased until 6 mo.

● These findings support age-specific assessment of head shape and may promote more rational approaches to positional plagiocephaly.

Introduction

Because infants’ heads grow rapidly in size, measurement of head circumference has been established worldwide as a standard item in child health surveillance. In contrast to size, less is known about age-dependent changes in infant head shape. The incidence of deformational skull deformities has increased dramatically since the widespread implementation of supine sleeping recommendations in the 1990s, and it has become a common health concern brought to pediatricians in clinical practice (1). The cranial vault asymmetry index (CVAI) is a quantitative measure of cranial asymmetry, and is calculated based on the difference in diagonal cranial measurements (2). The cranial index (CI) is a quantitative measure that represents the proportional relationship between cranial width and length. Physiological or pathological changes in head shape can be expressed by CVAI and CI, with large CVAI indicating plagiocephaly (asymmetrical head), small CI indicating dolichocephaly (long head), and large CI indicating brachycephaly (short head).

Previous studies have shown that CVAI shows age-dependent changes during infancy, with CVAI peaking around 3–4 mo of age and then gradually improving as infants acquire gross motor skills such as head control, turning over and sitting up (3). However, there are no widely accepted references for CVAI and CI, and criteria for clinical intervention vary among studies and guidelines (4). Since the “Back to Sleep” campaign of the 1990s, the mean CI of infants has increased, and several studies have warned of overtreatment of infants with cranial remodelling therapy when the conventional reference interval is applied (5, 6). To address these gaps, we conducted a large-scale study to analyze CVAI and CI in modern Japanese infants using a smartphone app “Akachan No Atama No Katachi Sokutei” (translated as “Measuring the Shape of the Baby’s Head”). By utilizing data from over 100,000 infants, the objectives of this study were to construct reference curves for CVAI and CI, and to measure the effects of key perinatal and postnatal factors associated with CVAI and CI.

Methods

Smartphone app

A smartphone app “Akachan No Atama No Katachi Sokutei” was developed by Japan Medical Company, Inc. The app is freely available on Apple App Store and Google Play. Caregivers of children can use the app anonymously, as it does not collect names, addresses, or other personally identifiable information. To use the app, the caregiver first takes a photograph of the child’s head from a parietal view. Then, the caregiver identifies the positions of the nose and ears in the app. Based on the image and these landmarks, CVAI and CI were calculated (Supplementary Fig. 1) (7). In a validation study using ten 3D-printed head models with predetermined CVAI and CI values, 91 individuals photographed the models. The mean error from the true values ranged from 1.0% to 3.2% for CVAI and from 1.3% to 4.1% for CI, demonstrating acceptable measurement accuracy (7).

Because the app is designed and provided in Japanese and primarily distributed through domestic app stores, its use is largely limited to caregivers in Japan. Therefore, while individual-level ethnicity was not recorded, the dataset can reasonably be regarded as predominantly representing Japanese infants.

Correlation between app-based measurements and 3D scanner-based measurements

We recruited healthy Japanese infants at 4-mo-old health checkup in Goto Fukue, Nagasaki prefecture, Japan between May 2023 and March 2025. The subjects were evaluated for CVAI and CI using two methods (app-based and 3D scanner-based).

Before imaging, a measurement cap was placed on each child’s head. Imaging was performed with the child seated on their caregiver’s lap, supported by the caregiver. Each child’s head was photographed from seven directions—front, left lateral, left posterior oblique, right lateral, right posterior oblique, posterior, and superior—using a 3D scanner Vectra H2 (Canfield Scientific Inc, Parsippany, NJ, USA). After the scanning, an additional top-down image was obtained using an iPad. The 3D cranial model was constructed as previously described (8) to calculate CVAI and CI.

Collection, cleaning and selection of data

The original data obtained through “Akachan No Atama No Katachi Sokutei” between February 2021 and November 2024 comprises 583,687 CVAI and CI data derived from 213,558 smart devices (Fig. 1). During the data collection period, there were approximately 2.8 million births in Japan, and the app was estimated to have been used by approximately 8% of caregivers. The anonymized dataset was provided directly by Japan Medical Company, Inc. after the approval of the study protocol by the ethics committee.

Fig. 1.

Flow of data processing. From 583,687 entries, 127,605 initial clean data (Dataset 1) were extracted after outlier removal and filtering. Dataset 2 included information on delivery mode and maternal age. Dataset 3 comprised infants with spontaneous delivery and normal birth weight for reference curve construction.

The original data contained extreme outliers. By referring to the images, we inferred that they were due to improper input of landmarks (nose and ears). To remove these outliers, we calculated the interquartile range (IQR; difference between the 75th and 25th percentile values) of CVAI and CI and excluded 36,538 data (6.3%) that were below the 25th percentile –1.5 × IQR or above the 75th percentile +1.5 × IQR, resulting in extraction of 547,149 clean data. Next, we extracted 341,661 clean data with valid inputs of sex, age at measurement, and birth weight as minimal covariates. In this study, the valid age was defined as 7–300 d, and the valid birth weight was set at 500–4,500 g. Finally, to avoid bias associated with repeated measurements, 214,056 data recorded after the initial measurement were excluded. Repeated measurements were identified and removed when the following information matched: sex, birthdate, birth weight, mode of delivery, maternal age, and prefecture of residence. This procedure left 127,605 initial clean data with information on sex, age and birth weight (Dataset 1, Fig. 1).

Subgroup analysis and multiple regression analysis

The 127,605 initial clean data were categorized based on three variables: sex (male or female), age (d) (30–59; 60–89; 90–119; 120–149; 150–179; 180–209; 210–239; 240–269; 270–300), and birth weight (g) (500–1,999; 2,000–2,499; 2,500–2,999; 3,000–3,499; 3,500–4,500). For each category, means and 95% confidence intervals were calculated. For analysis on delivery mode (spontaneous vaginal delivery; vacuum extraction; cesarean section; and others), and maternal age (10s; 20s; 30s; and 40s), 25,408 data that were derived from infants aged 90–119 d and had the two additional covariates were used (Dataset 2, Fig. 1). We also used Dataset 2 for the multiple regression analysis: CVAI (or CI) was used as the objective variable, and sex, age, presence of low birth weight (i.e., 500–2499 g), delivery mode and maternal age were calculated as predictor variables.

Construction of reference curves of CVAI and CI

To construct percentile reference curves of CVAI and CI, we used 78,081 outlier-removed data derived from infants born with normal vaginal delivery and normal birth weight (2,500–4,000 g) (Dataset 3, Fig. 1). For CVAI showing a sex difference, reference curves were constructed separately for boys and girls; for CI with no sex difference, a single reference curve was constructed. The three sets of data (boy CVAI, girl CVAI and CI) were subject to calculation with the generalized additive models for location, scale and shape (GAMLSS) distributional regression framework using the R package gamlss version 5.4-22 (https://cran.r-project.org/web/packages/gamlss/index.html) (9). To find appropriate fitting methods, we calculated Akaike information criterion (AIC), an estimator of prediction error, for each of three data with six models (gamma distribution, normal distribution, Box-Cox t distribution, Box-Cox power exponential distribution, Johnson’s SU distribution and Sinh-Arcsinh original distribution) that are commonly applied in growth curve modeling for their balance between flexibility and parsimony. We used default settings of degree of freedom (dF) (μ dF = 3; σ dF = 2; υ dF = 1; τ dF = 1). After determining the distribution model with the lowest AIC, we optimized the dF for μ, σ, υ, and τ in the model. Based on AIC and the shape of the reference curves, we determined dF to be applied in the final model. The final selection of dF was based not only on AIC but also on visual assessment of curve shapes. The fitted trajectories were confirmed to reflect age-related patterns consistent with clinical observations, ensuring both statistical adequacy and clinical plausibility.The codes are available in Supplementary Methods.

Statistics

Correlations between app-based measurements (CVAI and CI) and 3D scanner-based measurements were evaluated using correlation coefficients. Calculation of means and 95th percentile confidence intervals for measurements (CVAI and CI), comparison of means of two groups in univariate analysis (Welch’s t test), and multiple regression analysis were performed on Microsoft Excel 2023. The significance level was set at P < 0.001 to account for multiple comparisons and the large sample size, minimizing the risk of Type I error.

Ethics statement

For the study of correlation between app-based measurements and 3D scanner-based measurements, the study protocol was reviewed and approved by Nagasaki University Graduate School of Biomedical Sciences Ethics Committee (No. 23020901-3).

For the study of app-based measurements, the study protocol was reviewed and approved by the Ethics Committee of Keio University School of Medicine (Approve number, 2024-1107). The requirement for obtaining individual informed consent was waived by the Ethics Committee, as the study used fully anonymized data. An opt-out method was employed, whereby participants were provided with information about the study and given the opportunity to decline participation.

Results

Correlation between app-based measurements and actual measurements

To verify whether app-based measurements correctly reflect infant head shape, we analyzed the correlation between app-based measurements and highly accurate 3D scanner-based measurements using a dataset obtained from 269 Japanese infants enrolled at 4-mo-old health checkup in Nagasaki Prefecture, Japan. Both CVAI and CI showed moderate to strong correlation (R² = 0.585 and 0.706, respectively), indicating that infant head shape can be assessed with our app-based method (Supplementary Fig. 2).

Characteristics of infants evaluated by the app

The app originally collected 583,687 pairs of CVAI and CI data. After removing of outliers and restricting the dataset to initial measurements with covariates for analysis (i.e., sex, age and birth weight), 127,605 data (derived from 127,605 infants) were set as the analysis target (Fig. 1, Dataset 1). The characteristics of the analyzed infants are shown in Table 1. In brief, the study population had a median age of 100 d, approximately 10% had low birth weight, and about 60% were born by spontaneous vaginal delivery.

Table 1. Characteristics of the subjects.

Analysis on age, sex and birth weight

As a first-stage analysis of app-based data, we conducted a subgroup analysis on sex, age and birth weight using Dataset 1 (Fig. 2). There was an age-dependent change in means of both CVAI and CI, with a gradual increase after birth to form a peak, followed by a decline in late infancy. For CVAI, the peak was observed around ages 3–4 mo, whereas it was seen around ages 6–7 mo for CI. The mean CVAI tended to be high for boys in most subgroups. On the other hand, sex difference was not evident for CI. Trends based on birth weight were observed in mean CIs. At ages 2–8 mo, mean CIs were about 5% lower in infants with birth weights of 2,000 g or less compared to those with normal birth weight.

Fig. 2.

Subgroup analysis of CVAI and CI stratified by age, gender, and birth weight. Circles and bars indicate means and 95% confidence intervals, respectively. Birth weights are ordered from light to heavy from left to right. Turquoise indicates boys; coral indicates girls.

Analysis on delivery mode and maternal age

Because nonlinear age-dependent changes in CVAI and CI were observed, we used 25,408 data derived from infants aged 90–119 d for univariate analyses on delivery mode and maternal age (Dataset 2) (Table 2). Sexually dimorphic CVAI was analyzed stratified by sex. As for CVAI, a common difference between boys and girls was found in maternal age: when the mother was in 20s, mean CVAI was 0.22% lower for boys and 0.27% lower for girls as compared to those in 30s. There was also a difference in CI based on maternal age, with mean CI being 0.93% higher when the mother was in 20s compared to those in 30s. Delivery mode was associated with mean CI: the value was 1.7% lower for infants delivered by cesarean section than for those delivered by spontaneous vaginal delivery.

Table 2. Univariate analysis on CVAI and CI at ages 90-119 d.

Multivariate analysis

In the univariate analysis, several factors were found to be associated with CVAI and CI. However, since these factors were interrelated (e.g., relationship between higher maternal age and lower birth weight), there was a potential for confounding effects. To identify independent associated factors, we conducted a multivariate analysis using Dataset 2 (Table 3). Boys had higher CVAI than girls (β = 0.41 to 0.59, P = 1 × 10^–29). Low birth weight infants showed significantly higher CVAI than those without (β = 0.23 to 0.53, P = 4 × 10^–7). Infants born to mothers in their 20s had lower CVAI compared to those born to mothers in their 30s (β = –0.31 to –0.14, P = 7 × 10^–7). For CI, no sex difference was observed. Low birth weight infants had lower CI compared to those without (β = –2.07 to –1.43, P = 2 × 10^–26). Infants delivered by cesarean section had lower CI compared to those delivered by spontaneous vaginal delivery (β = –1.55 to –1.07, P = 5 × 10^–27). Infants born to mothers in their 20s had higher CI compared to those born to mothers in their 30s (β = 0.61 to 1.00, P = 6 × 10^–16).

Table 3. Multiple regression analysis on CVAI and CI at ages 90-119 d.

Reference curves of CVAI and CI

Finally, we constructed reference curves for head shape of Japanese infants using app-based CVAI and CI data. Since multivariate analysis revealed that low birth weight and delivery mode were associated with CVAI and CI, we used 72,726 data (Fig. 1; Dataset 3) derived from infants born via spontaneous vaginal delivery with normal birth weight (2,500–4,000 g). For CVAI, reference curves were constructed separately for boys and girls. Modelling with seven GAMLSS distributions showed that the Box-Cox power exponential distribution was the best fit for the three data (boy CVAI, girl CVAI and CI) (Supplementary Fig. 3). After optimization of dF of the four parameters (μ, σ, υ, and τ) (Supplementary Fig. 4), percentile reference curves (10, 25, 50, 75, and 90 percentiles) were drawn (Fig. 3). CVAI has a right-skewed distribution, showing peaks at ages 3–4 mo and then gradually decreases. The decline is particularly pronounced in higher percentiles (75th and 90th), which was contrasting to relatively stable lower percentiles (10th and 25th) throughout the observed period. CI showed a near normal distribution, with peaks around age 6 mo.

Fig. 3.

CVAI and CI percentile reference curves constructed by GAMLSS based on data from 72,726 Japanese infants born via spontaneous vaginal delivery and with normal birth weight. Curves for CVAI were constructed separately for boys and girls because of the sex difference.

Discussion

This study comprehensively analyzed the head shape of Japanese infants using a large smartphone app-based dataset, and for the first time, elucidated the detailed age-dependent changes in CVAI and CI. In the reference curves of CVAI, the degree of asymmetry gradually increased from early infancy, peaked at 3–4 mo, and then declined toward late infancy. There are very few reports addressing the age-related changes in CVAI from early infancy. An observational study conducted in New Zealand in 2004, which measured approximately 200 infants at ages 6 wk, 4 mo, 8 mo, 12 mo and 2 yr, reported changes consistent with our findings (3). The sex differences in the prevalence of positional plagiocephaly has been repeatedly reported in observational studies (10, 11). In our study, the adjusted sex difference in CVAI, based on multivariate analysis using the data from 3-mo-old infants, was 0.5%. In the reference curves, the sex difference was more pronounced at higher percentiles. Our data suggest that the higher prevalence of positional plagiocephaly in boys is not due to an exceptional subgroup of boys (e.g., X-linked muscular disorders) being associated with plagiocephaly, but rather due to a rightward shift in the continuous distribution of CVAI.

In this study, the infants exhibited an increase in CI over the first six months of life. A similar age-dependent change has been reported in a 3D scanner-based longitudinal study of 88 Japanese infants (12). However, previous studies conducted in Caucasians have not observed such an age-dependent increase in CI (3, 13). A study on infants and adolescents (aged 12–14 yr) in Massachusetts reported that mean CIs of Asians were approximately 5% higher than those of other ethnic groups (Caucasian, African American and Hispanic) (6). Although the underlying mechanism remains unclear, these findings suggest the possibility of ethnic differences in absolute value of CI and its age-dependent changes.

The dominant factor associated with CI identified in this study was birth weight of less than 2,000 g. Multiple 3D scanner-based studies have repeatedly shown preterm delivery as a risk factor for dolichocephaly (14,15,16). In this study, infants born via cesarean section had a lower CI than those born through spontaneous vaginal delivery. Several previous studies have reported cesarean section as a risk factor for dolichocephaly (14, 16). The present study is the first to estimate the adjusted effect size of cesarean section on CI, showing a difference of 1.3% at age 3 mo. There are two possible explanations: (i) vaginal delivery increases CI; (ii) obstetricians tend to choose cesarean delivery for dolichocephalic babies because transvaginal delivery is relatively difficult. A stratified analysis based on indication for cesarean section may elucidate the underlying mechanism(s) for the difference.

This study has several limitations. First, because the app was primarily used by caregivers who were interested in or concerned about their infants’ head shape, such individuals may be overrepresented among the users. This self-selection could result in slightly higher mean CVAI values compared with those in the general population. Therefore, while the present reference curves provide valuable information for population-level monitoring, they should be interpreted with caution when applied to individual clinical decision-making. As compared with the general Japanese population, the study population included slightly more boys (57.9% vs. 51.3%). However, the mean (SD) of CVAI reported in a 3D scanner-based study of 165 Japanese 1-mo-old infants was 5.0% (2.8%) (16), which did not seem to be different from that observed in the age-matched subgroup of our study 4.1% (3.1%). Second limitation is the moderate correlation between app-based and 3D scanner-based measurements. This likely reflects the inherently lower precision of the simplified photographic method. However, because our primary aim was to describe age-dependent changes of CVAI and CI, the impact of random measurement error is mitigated by the large sample size. Importantly, app-based measurements alone should not guide clinical decision-making; accurate evaluation in individual patients is best achieved using 3D scanner-based methods. Third, this study was limited to Japanese infants, and further investigation is needed to determine its generalizability to other populations. Since infant head shape exhibits ethnic differences (6), comparative studies across populations are necessary. Fourth, in this study, we did not collect data on genetic or nutritional factors that are known to influence head circumference; therefore, the effects of these potential influencing factors should be assessed in future studies.

In conclusion, we have performed an app-based investigation on infant head shape, and provided unique insights into age-dependent changes. We stress the importance of age-specific assessment of infant head shape, and decisions on medical intervention should be based on evidence regarding its natural course. The reference curves presented in this study are primarily intended for population-level surveillance, research purposes, and caregiver education. They provide a framework for understanding age-related trends in cranial shape within the Japanese infant population, rather than serving as diagnostic thresholds for individual clinical use. In clinical practice, these curves may assist healthcare professionals in the early detection and longitudinal monitoring of positional plagiocephaly, but they should not replace direct clinical assessment. Previous studies have described ethnic or racial variations in cranial indices, but the underlying causes remain poorly understood. The present study may help clarify these differences in future comparative studies and contribute to a more comprehensive understanding of cranial development across populations.

Conflict of interests

Hideki Kajita received travel fees from Japan Medical Company, Inc. and serves as a consultant for the company. Atsuko Nakahari and Yoshiaki Sakamoto received a research grant from Japan Medical Company, Inc. Shigeharu Hosono received lecture fees from Sanofi, AstraZeneca, and Japan Medical Company, Inc.