Preliminary study on ultrasound-based quantitative assessment of epiphyseal ossification angle for bone age evaluation in children

Introduction

Skeletal growth and development in children are influenced by multiple factors, including genetics, endocrine regulation, nutrition, and environment, resulting in considerable inter-individual variability (1,2). Bone age (BA) is defined as an index that quantifies skeletal maturity by assessing the appearance, morphological evolution, and fusion of ossification centers (3). As skeletal development spans the entire period of childhood growth, BA is regarded as the “gold standard” for evaluating skeletal maturation, providing a more accurate reflection of an individual’s developmental status than chronological age (4,5). As an independent and reliable indicator, BA plays a critical role in diagnosis, therapeutic monitoring, and adult height prediction, particularly in conditions associated with growth and pubertal disorders such as precocious puberty and familial short stature (6,7).

Currently, BA assessment is routinely performed using left hand and wrist radiography. However, this approach involves ionizing radiation, which poses potential health risks, especially for young children requiring repeated follow-up examinations, thereby limiting its clinical utility. Ultrasonography, as a radiation-free and convenient imaging modality, has shown substantial progress in BA assessment research in recent years, yet a widely accepted standardized protocol remains unavailable (8,9).

Previous studies have demonstrated that with increasing BA, epiphyseal morphology undergoes characteristic changes, including enlargement of bone size, thickening of the diaphysis, reduction in femoral inclination, and progressive thickening of the cartilage (10-12). Based on these morphological alterations, ultrasound-derived parameters such as epiphyseal cartilage thickness (ECT) and ossification ratio (OR) have been proposed as potential indicators for BA estimation, with preliminary evidence supporting their feasibility (13,14). However, large-scale validation is still lacking. Most existing ultrasound parameters assess epiphyseal maturation along the axial dimension. However, ossification of the secondary center progresses radially from the center towards the periphery. We therefore hypothesized that the angle formed between the advancing front of the secondary ossification center and the diaphysis—the ossification angle (OA)—would decrease with skeletal maturation and could serve as a novel geometric descriptor for BA assessment. Although more advanced approaches such as machine learning-based analysis of ultrasound images or artificial intelligence (AI)-enhanced radiographic interpretation are emerging, this study focused on establishing the fundamental validity of a novel, simple, and quantitative morphometric parameter (OA) that could potentially be integrated into such automated systems in the future.

If validated, a radiation-free method such as ultrasound-based OA measurement could be particularly valuable in clinical scenarios requiring serial monitoring of skeletal maturation, such as in children with precocious puberty receiving gonadotropin-releasing hormone (GnRH) agonist therapy or those with growth hormone deficiency undergoing treatment, where frequent BA assessments are needed to guide therapy and minimize cumulative radiation exposure. We present this article in accordance with the STROBE reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-2009/rc).

Methods

Study population

In this prospective study, a total of 201 Han Chinese girls aged 5–14 years were enrolled from the pediatric clinic of a single tertiary care center between August 2024 and May 2025. The study was initially restricted to Han Chinese girls to control for potential confounding by sex and ethnicity in this preliminary investigation. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the institutional ethics committee of Fuqing City Hospital Affiliated to Fujian Medical University (No. K (2024)49) and informed consent was provided by the guardians of all individual participants. A formal sample size calculation was not performed a priori for this preliminary feasibility study. The sample size of 201 was deemed sufficient to provide initial estimates of correlation coefficients and reliability for the novel OA parameter.

Inclusion criteria

• Female children of Han ethnicity residing in Fujian Province, China;
• Aged 5–14 years;
• Underwent standard left hand and wrist radiography within one week prior to ultrasonography;
• No history of trauma, infection, or tumor in the wrist or knee joints.

Exclusion criteria

• Previous pharmacological treatment for growth or developmental disorders;
• Presence of malignancy, cachexia, psychiatric disorders, or inability to cooperate with the examination.

Data collection

Height, weight, chronological age, and medication history were recorded for all participants.

Radiographic BA assessment

All participants underwent standard posteroanterior radiography of the left wrist (tube-to-film distance: 91.4 cm) within one week before ultrasonography. BA was evaluated using the Tanner-Whitehouse 3 (TW3) method by two radiologists with >5 years of experience in BA interpretation. Both radiologists were blinded to the participants’ clinical data. Consensus was reached either by agreement or through discussion in cases of discrepancy.

Ultrasonographic image acquisition

Ultrasound examinations were performed using an Aixplorer system (SuperSonic Imagine, Aix-en-Provence, France) equipped with a high-frequency linear probe (L15–4, 4–15 MHz) in musculoskeletal imaging mode. Typical settings included a depth of 2–3 cm for the wrist and 3–4 cm for the knee, with gain adjusted to optimize visualization of the bony interfaces and cartilage. Images were obtained by a sonographer with >5 years of experience, blinded to the participants’ clinical information and to the radiographic TW3 BA results.

• Distal radius: supine position, left forearm in neutral position, probe placed longitudinally along the radial styloid in the coronal plane.
• Distal ulna: forearm pronated, probe placed longitudinally along the ulnar styloid in the coronal plane.
• Medial femoral condyle: the knee was flexed approximately 20–30° and abducted about 15–20 degrees. The probe was placed in the coronal plane at the distal femur, posterior to the medial collateral ligament. Only the left knee was examined to maintain consistency with the standard left-sided radiographic BA assessment.

Ultrasonographic parameter measurement

Two experienced sonographers independently measured the following parameters:

• OA (Figure 1, Figures S1-S3):
  • A baseline was drawn along the medial border of the diaphyseal hyperechoic band. A perpendicular line was extended from the most distal point of the diaphysis to the baseline (point K). A tangent was drawn from point K to the secondary ossification center’s hyperechoic band. The angle between the tangent and baseline was recorded as OA.
  • Total ossification angle (TOA): sum of OA values at the distal radius, distal ulna, and medial femoral condyle.
• OR (Figure 2):
  • For each site, the maximum vertical diameter of the secondary ossification center (d) and the corresponding epiphyseal cartilage (D) were measured. OR = (d / D) × 100%.
  • Skeletal maturity score (SMS): sum of OR values across the three sites.

Figure 1 Schematic representation of OA measurement. (A) Distal radius. (B) Distal ulna. (C) Distal femur. The baseline (red line) is drawn along the diaphyseal margin. From the furthest point of the diaphysis, a perpendicular line (yellow line) is dropped to intersect the baseline at point K. A tangent line (blue line) is drawn from point K to the hyperechoic band of the secondary ossification center. The OA is defined as the angle between this tangent line and the baseline. OA, ossification angle.

Figure 2 Schematic representation of OR measurement. (A) Distal radius. (B) Distal ulna. (C) Distal femur. The maximal vertical diameter of the secondary ossification center (d) is indicated by the red dashed line. The corresponding maximal vertical thickness of the epiphyseal cartilage (D) is indicated by the yellow dashed line. The OR is calculated as OR = (d/D) × 100%. OR, ossification ratio.

Inter- and intra-observer consistency

A total of 30 randomly selected cases were measured by both sonographers to assess inter-observer agreement for OA and OR at the three sites. After a 2-month interval, the same sonographers repeated the measurements to evaluate intra-observer consistency.

Statistical analysis

Statistical analyses were performed using SPSS 22.0 (IBM Corp., Armonk, NY, USA). Categorical variables were presented as frequencies (percentages), normally distributed continuous variables as mean ± standard deviation (SD), and non-normally distributed data as median (interquartile range, IQR). Intraclass correlation coefficients (ICC) were used to assess measurement consistency. Pearson’s correlation coefficients (with Spearman’s rank correlation used as a robustness check, which yielded similar results) were used to analyze the relationship between SMS, TOA, and radiographic BA. Linear regression models were constructed to explore the predictive value of ultrasound parameters for BA. A 2-tailed P value <0.05 was considered statistically significant. This was a complete-case analysis, as no data were missing for the variables included in this study. A post-hoc power analysis was conducted using G*Power software (https://www.gpower.hhu.de/) for the primary correlation between TOA and BA (r=−0.808). With a sample size of 201 and an alpha of 0.05, the analysis yielded a statistical power of >0.99, indicating that the study was sufficiently powered to detect this strong relationship.

Results

Participant characteristics

Of 225 female children screened, 24 were excluded due to prior pharmacological treatment for growth disorders, and 201 were included in the final analysis. The mean age was 9.24±2.15 years. The main clinical complaints were short stature (n=35, 17.41%), breast development (n=44, 21.89%), obesity (n=38, 18.91%), and vaginal discharge (n=12, 5.97%).

Inter- and intra-observer agreement

As shown in Table S1, both inter- and intra-observer agreement for OA and OR measurements at all three sites were excellent. Intra-observer ICCs (2-way random effects model for absolute agreement, single rater) ranged from 0.81 to 0.92 [95% confidence intervals (CIs): 0.65–0.96], and inter-observer ICCs ranged from 0.78 to 0.89 (95% CIs: 0.60–0.94; all P<0.001). A sample size of 30 was considered adequate for reliability assessment in methodological studies.

Correlation between ultrasonographic parameters and BA

OA: OA at all three sites was negatively correlated with BA (radius: r=−0.686; ulna: r=−0.650; femur: r=−0.721; all P<0.001). TOA showed a strong negative correlation with BA (r=−0.808, P<0.001).

OR: OR at all three sites was positively correlated with BA (radius: r=0.807; ulna: r=0.632; femur: r=0.708; all P<0.001). SMS exhibited a strong positive correlation with BA (r=0.813, P<0.001).

Parameter correlations: OA and OR were negatively correlated at all sites (radius: r=−0.603; ulna: r=−0.635; femur: r=−0.554; all P<0.001). TOA was strongly negatively correlated with SMS (r=−0.826, P<0.001) (Table 1).

No statistical adjustment for multiple testing was applied for the correlation analyses, as the primary relationships between the key ultrasound parameters (TOA, SMS) and BA were pre-specified hypotheses, and other correlations were considered exploratory.

Age-stratified OA values are presented in Table 2. Minor non-monotonic variations in mean OA values between successive age groups (e.g., ulna) are likely attributable to sampling variability and the cross-sectional nature of the study, which captures natural biological variation in the timing and tempo of skeletal maturation. A linear regression model was developed based on TOA and BA (Figure 3). The linear regression model based on TOA and BA was defined by the equation: BA =15.58−0.11× TOA. The model R² was 0.653 [95% CI: (−0.115, −0.095), P<0.001], indicating that TOA explains approximately 65.3% of the variance in BA.

Figure 3 Scatter plot and linear regression line illustrating the relationship between TOA and BA assessed by TW3. The regression equation is BA =15.58–0.11× TOA, with R²=0.653. BA, bone age; TOA, total ossification angle; TW3, Tanner-Whitehouse 3.

An exploratory Bland-Altman analysis was conducted to assess the agreement between the BA predicted by the TOA model and the reference TW3 BA. The mean difference (bias) was −0.249 years, with 95% limits of agreement ranging from −4.994 years to +4.496 years (Figure S4).

Discussion

This study quantified epiphyseal OA using ultrasonography and explored its utility for BA assessment in children. Our findings demonstrated a strong negative correlation between OA and BA. Moreover, OA correlated significantly with the conventional parameter OR, suggesting OA as a potential noninvasive indicator for skeletal maturity assessment, warranting further optimization and validation.

Epiphyseal ossification is predominantly driven by endochondral ossification. Mechanical loading is thought to initiate secondary ossification center formation, during which cartilage canals form, allowing vascular invasion and cellular recruitment. Hypertrophic chondrocytes proliferate and secrete alkaline phosphatase, facilitating matrix calcification, while osteoprogenitor and mesenchymal cells participate in trabecular bone formation and remodeling (15-17). Secondary ossification centers grow radially from the center toward the periphery. Morphological changes during this process form the basis of ultrasound-based BA evaluation, including alterations in tangent angles, OR, and ECT (10,12,18,19).

Most existing parameters assess epiphyseal maturation along the axial dimension, whereas ossification progresses radially (20,21). Our study extends this perspective by evaluating the angle between the secondary ossification center and the diaphysis, revealing that OA decreases progressively with increasing BA and is highly correlated with radiographic BA. This provides new morphological evidence for ultrasound-based BA assessment. Although our study demonstrated a strong correlation, the Bland–Altman analysis revealed limits of agreement that are too wide for clinical application. This underscores that our findings establish a proof-of-concept association rather than a clinically ready tool, and it clearly identifies the reduction of this variability as the primary goal for future model development.

Combining measurements from multiple sites (radius, ulna, medial femoral condyle) improved predictive performance compared with single-site assessment, consistent with previous findings (13,18). Multi-site evaluation helps to mitigate local developmental variability and better reflects overall skeletal maturation. Comparing the performance of OA with other ultrasound parameters, the correlation between TOA and BA (r=−0.808) in our study appears comparable or superior to correlations reported for ECT and similar to those for OR-based scores in some previous studies, although direct comparisons are limited by population and methodological differences (13,14,22). This suggests that OA captures unique morphological information that complements existing parameters.

This study focused on girls aged 5–14 years, considering that female puberty and skeletal maturation typically occur earlier than they do in boys, with estrogen exerting a pronounced effect on epiphyseal closure (23). Growth disorders such as precocious puberty and idiopathic short stature are also more prevalent among girls, increasing the clinical demand for noninvasive monitoring (24). Furthermore, substantial variations in skeletal maturation rates across different ethnicities are well-documented (25). Therefore, our findings must be tempered by the recognition that they are specific to this demographic and cannot be directly extrapolated to other populations without further validation. It is therefore important to interpret our results within this specific context. The strong correlations observed between TOA and radiographic BA are indicative of association but are exploratory in nature and fall short of establishing immediate clinical utility. Therefore, a necessary future direction is the development and rigorous validation of a calibrated predictive model based on TOA. We envision and are already developing integrated multivariable models that combine TOA with key clinical variables [e.g., chronological age, body mass index (BMI), pubertal stage] to improve assessment accuracy for conditions such as precocious puberty. Finally, expanding this research to include boys and wider age ranges is essential for establishing universally applicable, sex- and age-specific standards. For clinical translation, future models must demonstrate acceptable accuracy. Although defined thresholds vary, a mean absolute error (MAE) of less than 6–12 months compared to the reference standard is often cited as desirable for clinical utility in growth disorders. Our exploratory analysis suggests that current limits of agreement are wider than this, highlighting the need for model refinement, potentially incorporating non-linear terms or additional covariates.

Limitations and future directions

This study is subject to several limitations. Firstly, as a single-center investigation utilizing operator-dependent ultrasound techniques, the generalizability of our findings may be limited, a concern compounded by the lack of external validation. Secondly, the exclusive focus on a clinic-referred cohort of Han Chinese girls introduces spectrum bias and precludes the extrapolation of our results to the general pediatric population, including boys and other ethnicities. Furthermore, from an analytical perspective, our work establishes correlation but not causation. The exploratory agreement analysis indicated proportional bias and limits of agreement that currently fall short of clinical requirements. Additionally, potential confounders such as BMI and precise pubertal stage were not adjusted for in the analysis. Finally, this preliminary study deliberately stopped at establishing correlation and did not develop a validated predictive model for clinical use.

Conclusions

In this preliminary study of female children aged 5–14 years, the ultrasound-derived epiphyseal OA, particularly when combined across multiple sites as TOA, showed a strong correlation with radiographic BA. This radiation-free method represents a promising conceptual approach for noninvasive BA assessment. However, these findings are exploratory and require further development and validation in larger, more diverse populations, including the creation of predictive models with robust agreement testing, before any clinical application can be considered.

Acknowledgments

We would like to express our sincere gratitude to the staff of the Ultrasound Department of the participating institution for their invaluable assistance in case collection for this study. Their expertise and support were essential in the successful completion of this research. We deeply appreciate their dedication and hard work throughout the study period.

Footnote

Reporting Checklist: The authors have completed the STROBE reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-2009/rc

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-2009/dss

Funding: This work was supported by the Social Development Indicative Project of Fujian (grant No. 2021Y0012; recipient: S.C.), the Joint Fund Project for Scientific and Technological Innovation of Fujian (grant No. 2021Y9092; recipient: S.C.) and Fujian Medical University Starter Grant Program (grant No. 2024QH1059; recipient: M.L.). The sponsors played no role in the study design, conduct, analysis, interpretation of data, writing, review, approval of the manuscript, or decision to submit for publication.

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-2009/coif). S.C. reports that this work was supported by research grants from Fujian Provincial Department of Science and Technology (Nos. 2021Y0012, 2021Y9092). M.L. reports that this work was supported by Fujian Medical University (No. 2024QH1059). The other authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the institutional ethics committee of Fuqing City Hospital Affiliated to Fujian Medical University (No. K (2024)49) and informed consent was obtained from the guardians of all individual participants.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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