Sexual dimorphism and sex-specific features of pediatric hand bone shapes via statistical shape modeling

1 Introduction

• Population-level characterization of anatomical shape variation across developmental stages remains an open challenge because temporal change compounds inter-individual variability.The paper frames this as a complex spatiotemporal shape space.Source: §1 · p. 2
• Hand-bone morphology matters for mobility, early-life health, and age estimation, but osteometric analyses depend on consistent landmarks that can be unreliable.The authors motivate alternative methods whose efficacy can be quantified.Source: §1 · p. 2
• PDM-based statistical shape models summarize populations through a mean shape and principal modes of variation derived from corresponding landmarks.The study uses this framework to investigate shape variation across developmental time points.Source: §1 · p. 2
• Prior work leaves a gap in broad hand-bone coverage across age: studies often use small 3D datasets, few bones, and narrow, mostly mature age ranges.Earlier studies include pediatric lower-limb models, phalangeal-joint modeling, and sex comparisons of carpometacarpal bones.Source: §1 · pp. 2–3
• The study builds separate PDM-based models for metacarpals and proximal, medial, and distal phalanges, then examines sex- and age-stratified shape spaces.The stated aim is to characterize the overall shape envelope and offer a potential framework for other anatomical structures.Source: §1 · p. 3

2.1 Datasets and pre-processing

• 1,456 RSNA radiographs were selected to provide relatively balanced sex representation and a homogeneous age distribution, after CLAHE preprocessing.The dataset comprises unique radiographs from individual subjects.Source: §2.1 · p. 3

2.2 Detection – segmentation framework

• The two-stage pipeline first detects labeled bounding boxes for individual bones, then applies a universal segmentation head to produce 27,664 bone masks.Detection configurations were compared using mAP50-95; segmentation models were evaluated using ASSD plus HD95, with Dice and IoU also calculated.Source: §2.2 · pp. 3–4

2.3 Statistical shape modeling

• PDM-based models align shapes, register corresponding landmarks, center and scale configurations, and use PCA modes retaining 90% of variation.The analyses group bone masks and focus on the third ray in the main text, with remaining-bone results in supplementary material.Source: §2.3 · pp. 4–5

2.4 Sexual dimorphisms

• Sexual dimorphism is assessed from each bone’s shape parameters using Hotelling’s T² and per-mode Welch tests with Benjamini-Hochberg correction.The multivariate test compares sex-specific mean vectors; Mahalanobis distance measures centroid separation independently of sample size, while Cohen’s d quantifies per-mode separation.Source: §2.4 · pp. 5–6

2.5 Association between sexual dimorphism and age

• Cubic-age multivariate models include skeletal age, sex, and their interaction to test whether sex-specific shape trajectories differ.The interaction is tested jointly with Pillai’s trace, using Freedman-Lane residual sampling because residuals were often age-heteroskedastic and heavy-tailed; per-mode follow-ups use HC3 variance estimates and corrected tests.Source: §2.5 · pp. 6–7

3.1 Detection – segmentation framework

• YOLOv12s led detection with mAP50-95 0.9711, while SegFormerB4 was selected for segmentation with HD95 1.512 ± 0.005 and ASSD 0.449 ± 0.001.SAM2 Hiera Large had the best ASSD, Dice, and IoU, but required 354 PFLOPs versus 45 PFLOPs for SegFormerB4.Source: §3.1 · p. 7

3.2 Statistical shape models

• Seven modes captured 90% of variation for each hand bone except the proximal phalanx, which required eight; leading modes encoded aspect ratio, shear, taper, thickness, and head/base form.The reported modes included distal phalanx tapering, medial phalanx diaphysis and head/base morphology, proximal phalanx aspect ratio, and metacarpal size and thickness.Source: §3.2 · pp. 7–8

3.3 Sexual dimorphism

• All four third-ray bones showed significant sexual dimorphism, with Hotelling’s T 2 values of 66.656–142.01, p < 0.001, and Mahalanobis D values of 0.4279–0.6246.Source: §3.3 · p. 8
• Sex differences were localized to distal phalanx head and metaphysis shape, medial phalanx width, proximal phalanx base and shaft thickness, and metacarpal base, metaphysis, and shaft width.The metacarpal showed relatively smaller-magnitude dimorphism.Source: §3.3 · pp. 8–9
• The first shape mode was significantly dimorphic across all bones, with Cohen’s d of 0.1333–0.4806, broadly reflecting size and aspect-ratio variation.Source: §3.3 · p. 9

3.4 Sexual dimorphism over time

• Interaction-block results from a multivariate general linear model showed sexes did not follow parallel age trajectories; Freedman–Lane resampling found significant differences across all bones, with normalized Pillai/s values of 0.032–0.058 for distal and proximal phalanges, respectively, relatively modest.Source: §3.4 · p. 9
• Mode-wise trajectory differences varied by bone: distal phalanx differences appeared only on PC1, PC4, PC5, and PC6; proximal phalanx differences spanned all modes; metacarpals differed except on PC2 and PC4.For the medial phalanx, all modes except PC7 differed significantly.Source: §3.4 · pp. 9–10
• With age, the distal phalanx lengthened and changed proportions, the medial phalanx thinned and lengthened, the proximal phalanx developed concave articulating surfaces, and the metacarpal shaft elongated.Sex differences were bone- and age-specific: proximal phalanx dimorphism peaked at 204 months, while metacarpal dimorphism was most apparent at 36 months.Source: §3.4 · p. 10

4 Discussion

• The first shape modes generally captured growth-associated changes, including aspect-ratio shifts and formation of proximal and distal articular interfaces across the third ray.The fitted models represented 1456 subjects and 19 bones across sex and age.Source: §4 · p. 11
• Analyzing sex-stratified shape parameters within SSM subspaces quantifies dimorphism while accounting for covariance across the whole bone rather than isolated measurements.The authors position this as an addition to population-level SSM analysis.Source: §4 · p. 12
• Sex-stratified shape modes and parameters differed significantly across all bones, with dimorphism most evident in proximal phalanx base width and diaphysis thickness, metacarpal thickness, and phalanx widths.These patterns align with observations in existing morphometric studies.Source: §4 · p. 12
• Pediatric-to-NSM radiographs showed discernible dimorphism whose form aligned with findings in skeletally mature subjects, despite the challenge of identifying sex from pediatric images.The paper presents shape-parameter variation as a data-driven way to highlight and quantify these features.Source: §4 · p. 12
• Comparisons with Tanner-Whitehouse and Greulich-Pyle methods showed similar age-related morphology, including head rounding in metacarpals and concave phalanx interfaces after epiphyseal capping and fusion.The authors note Greulich-Pyle is simpler, while Tanner-Whitehouse is more accurate but time-intensive.Source: §4 · p. 13
• The study’s shape coverage is constrained by 2D radiographs, unavailable provenance and acquisition metadata, landmark scaling, and PDM-based masks that generally exclude uncapped epiphyses.These limits may underrepresent shape variation, obscure size-related variation, and omit radiographic features relevant to growth assessment.Source: §4 · pp. 12–14

5 Conclusions

• The study charts age-related hand-bone shape variation and uses stratified SSM parameters to quantify sexual dimorphism and sex-based developmental changes across a population.The authors identify longitudinal data and other tissues and imaging modalities as directions for further work.Source: §5 · p. 14

• The study used the open-source RSNA Pediatric Bone Age Challenge 2017 image dataset.Source: Acknowlegements · p. 15

E. Oei, and M. v. Middelkoop, “FACTORS ASSOCIATED TO A DISTINCTIVE

• The 2024 cited item concerns three-dimensional patellar shape variation in an adolescent population.Source: E. Oei, and M. v. Middelkoop, “FACTORS… · p. 18

Table Captions

• Table 1 reports demographic characteristics for the full RSNA dataset and the study subset.Source: Table 1 · p. 24
• Table 2 covers a detector-model sweep with a 200-epoch cap and patience of 15; runs were early-stopped, so reported epochs reflect actual training duration.Source: Table Captions · p. 24, Table 2
• Table 3 covers the universal bone segmentation-head sweep; configurations were trained in triplicate with randomized seeds, and results are means with standard deviations.Source: Table 3 · p. 24, Table Captions · p. 24
• Table 4 reports Hotelling’s T² across retained shape modes; T² and D quantify male–female distance, while F and p-values indicate statistical significance.Source: Table 4 · p. 24, Table Captions · p. 24
• Table 5 reports per-mode sexual-dimorphism tests using Welch’s t-tests, with p-values corrected by the Benjamini-Hochberg method and significance defined at p ≤ 0.05.Source: Table 5 · p. 25, Table Captions · p. 25
• Table 6 reports Pillai’s trace for sex × age interactions; permutation tests using Freedman-Lane sampling with Rademacher sign flipping provide a more robust significance indicator under heteroskedastic residuals.Source: Table 6 · p. 25, Table Captions · p. 25
• Table 7 reports per-mode sex × age tests, with p-values corrected by the Benjamini-Hochberg method and p ≥ 0.05 marked not significant.Source: Table 7 · p. 26, Table Captions · p. 26

Figure Captions

• Figure 1 outlines the workflow: radiographs are selected, bones detected and segmented into masks, then masks are aligned, landmarked, and analyzed with PCA for shape modeling.Source: Figure Captions · p. 27, Figure 1 · p. 28
• Figure 2 compares detector model sizes by mAP50-95, calculated across ten intersection-over-union thresholds from 50% to 95%, with higher scores indicating better performance.Source: Figure Captions · p. 27, Figure 2
• Figure 3 shows third-ray SSM mean shapes and the first three shape modes, alongside cumulative variance by mode and a 90% analysis threshold.Source: Figure Captions · p. 27, Figure 3
• Figure 4 presents sex-stratified mean-shape differences as landmark heatmaps and first-five-mode parameter distributions as violin plots, with Welch-test significance marked by asterisks.Source: Figure Captions · p. 27, Figure 4
• Figure 5 plots shape parameters against skeletal age with sex-specific trajectories fitted by a multivariate general linear model; joint F-tests with Benjamini-Hochberg corrections determine significance.Source: Figure Captions · p. 27, Figure 5
• Figure 6 visualizes estimated third-ray mean shapes at different skeletal ages, predicting shape parameters from fitted multivariate general linear models before overlaying shapes and highlighting differences.Source: Figure Captions · p. 27, Figure 6

A Form-fitting for age term

• A cubic form fit best across all third-ray bones and shape modes, so it was selected as the representative age term for later analyses.The comparison used Bayesian information criterion (BIC).Source: A Form-fitting for age term · p. 34
• Table A1 reports the lowest-BIC candidate and its margin over the runner-up for each third-ray bone and shape mode; margins below 2 indicate no meaningful preference.Candidate forms include cubic, quadratic, and linear.Source: Table A1 · p. 34
• Figure 1 compares the age-term fits, with lower BIC indicating a better fit.Each subfigure title denotes the difference in BIC.Source: A Form-fitting for age term · p. 35

B Results from remaining bones

• All bones were sexually dimorphic in the sex-stratified shape parameters encompassing the retained shape modes.The analysis reports Hotelling’s T^2, with F and p-values for significance and T^2 and D quantifying male–female distance.Source: Table B1 · p. 36
• All bones showed sex-specific ontogeny in the sex × age interaction results.Pillai’s trace was normalized by s degrees of freedom, and permutation tests were used as a more robust significance indicator because residuals were heteroskedastic.Source: Table B2 · p. 36
• For the sex × age interaction, significance was assessed with permutation tests using Freedman-Lane sampling and Rademacher sign flipping.The table also reports raw p-values based on analytic F.Source: Table B2 · p. 36