Sexual dimorphism and sex-specific features of pediatric hand bone shapes via statistical shape modeling
Authors: Edwin Tay, Amir A. Zadpoor, Nazli Tümer
Organizations: Department of Biomechanical Engineering, Faculty of Mechanical Engineering, Delft University of Technology (TU Delft), Mekelweg 2, 2628CD, Delft, The Netherlands
Understanding the envelope of shape variation encompassing both sexual dimorphism and growth-related changes in living tissue is a non-trivial task. In this work, we use statistical shape models (SSMs) and analyze demographic-stratified shape parameters to quantify sexual dimorphism and sex-specific shape changes. To this end, we developed a two-stage detection-segmentation framework that accurately segmented n=27664 unique bone masks from a radiographic dataset of n=1456 subjects with diverse ages and sexes (HD95 = 1.512±0.005, ASSD 0.449±001, Dice = 0.987±0.00004, IoU = 0.975±0.0001). Following SSM fitting, our follow-up analyses of stratified shape parameters highlighted the morphology of sexual dimorphisms for each bone and demonstrated sex-specific differences in shape development. Our results were consistent with existing literature and provided an unambiguous, data-driven methodology for characterizing tissue shape and its population-scale variation. This approach provides a potential methodological foundation for developing population-based models of anatomical variation and could be extended to investigate tissue growth and shape changes over time. Future work should evaluate the applicability of this methodology on alternative anatomical structures and imaging modalities, with the goal of validating these growth trajectories on longitudinal data.
Table A1: Age term elected per shape mode for bones of the third ray. Each cell names the lowest-BIC candidate for that bone and mode, and its BIC margin over the runner-up. cub denotes cubic, quad denotes quadratic, and lin denotes linear. ∼ marks a margin below 2, which is no meaningful preference.
Figure 1: Comparison of the different fits of varying forms for the age terms. Each subfigure title denotes the difference in the Bayesian information criterion (BIC); a lower BIC indicates a better fit.
Bone
modes
T2
F
df
D
p
Distal phalanx 1
PC1–8
61.712
7.677
8, 1447
0.4118
p≤0.001
Distal phalanx 2
PC1–7
65.67
9.343
7, 1448
0.4248
p≤0.001
Distal phalanx 4
PC1–7
51.661
7.35
7, 1448
0.3767
p≤0.001
Distal phalanx 5
PC1–7
69.628
9.906
7, 1448
0.4374
p≤0.001
Medial phalanx 1
PC1–7
108.65
15.46
7, 1448
0.5464
p≤0.001
Medial phalanx 3
PC1–7
97.191
13.83
7, 1448
0.5167
p≤0.001
Appendix
Table B1: Hotelling’s T2 over sex-stratified shape parameters encompassing c shape modes retained for analysis. F and p -values denote statistical significance whilst T2 and D quantifies the distance between males and females. Results indicate that all bones are sexually dimorphic.
Bone
Pillai
s
Pillai /s
F
df
p ( F )
p (Freedman–Lane)
Distal phalange 1
0.07335
3
0.02445
4.521
24, 4329
p≤0.001
p≤0.001
Distal phalange 2
0.07228
2
0.03614
7.74
14, 2890
p≤0.001
p≤0.001
Distal phalange 4
0.1063
3
0.03542
7.576
21, 4332
p≤0.001
p≤0.001
Distal phalange 5
0.1161
3
0.03869
8.302
21, 4332
p≤0.001
p≤0.001
Medial phalange 1
0.1503
3
0.05008
10.88
21, 4332
p≤0.001
p≤0.001
Medial phalange 3
0.2033
3
0.06777
15
21, 4332
p≤0.001
p≤0.001
Appendix
Table B2: Results from Pillai’s trace on sex × age interaction. Raw Pillai’s trace magnitudes are normalized with respect to s degrees of freedom, giving Pillai /s . We report raw p -values based on analytic F , but because residuals are heteroskedastic, we used permutation tests via Freedman-Lane sampling with Rademacher sign flipping to obtain a more robust indicator of significance. Results indicate that all bones have sex-specific ontogeny.
Accurate segmentation and statistical shape modeling of hand anatomy have significant implications for medical diagnostics, ergonomics, and biomechanics. This study proposes an AI-assisted reconstruction pipeline for segmenting and analyzing hand anatomy from 1,271 elbow-to-hand (e2h-CT) computed tomography scans. A Pix2Pix-based conditional generative adversarial network is first employed to remove plaster cast and background artifacts from CT volumes. The cleaned scans are then processed in 3D Slicer to extract skin and bone masks, which are converted into closed-surface mesh models. Segmented bone meshes are used to construct skeletal representations, enabling implicit skinning to align all hand models into a standardized anatomical configuration. Subsequently, non-rigid registration is performed on the hand skin surfaces using the Geodesic Based Coherent Point Drift++ (GBCPD++) algorithm to establish point-wise correspondence across subjects. Principal Component Analysis (PCA) is then applied to the registered models to quantify anatomical shape variability. The Pix2Pix preprocessing stage achieved a Dice coefficient of 0.9856 and an IoU of 0.9720 on the held-out test set. Statistical modeling was performed on a subset of 90 scans in which the fingers were fully visible and anatomically separated. The resulting statistical shape distributions demonstrate strong agreement with the U.S. Army Anthropometric Survey (ANSUR II), supporting the anatomical validity of the reconstructed models. The proposed methodology demonstrates significant potential for advancing biomechanical modeling, ergonomic optimization, prosthetic design, and precision medical diagnostics.
Gokce Guven, Hasan Fehmi Ates, Deniz Karasahin +1
Dept. of Computer Science and Engineering Özyeğgin University İstanbul, Türkiye · Dept. of Artificial Intelligence and Data Engineering Özyeğgin University İstanbul, Türkiye · Osteoid Inc. İstanbul, Türkiye
Three-dimensional femoral reconstruction from radiographs supports surgical planning, implant sizing, and post-operative follow-up, but remains ill-posed as X-ray projections discard depth information. Existing methods often incorporate a 3D statistical shape model (SSM) as a shape prior to guide reconstructions toward anatomically plausible shapes, relying on iterative 3D-to-2D projection matching. Yet, these approaches are computationally expensive and constrain their SSM to a single dimensionality, leaving the statistical relationship between 2D observations and 3D geometry largely unexploited and unexplored. We instead propose a joint 2D-3D SSM that explicitly captures the co-variation between 2D and 3D segmentations in a shared latent space. During training, 2D and 3D segmentations are registered to a common 3D template and its corresponding 2D projections, and the resulting stationary velocity fields are jointly decomposed using principal component analysis (PCA). This joint modeling allows the 2D-to-3D mapping to be learned directly from data rather than computing correspondences at inference time. For unseen subjects, the 3D shape is recovered directly by lifting the 2D latent coordinates to the 3D PCA subspace, thereby eliminating the need for iterative 3D-to-2D projection. Experiments on NMDID demonstrate that the proposed joint 2D-3D SSM outperforms a widely-used 3D-only SSM baseline while achieving inference approximately 4 times faster, at under 3 seconds per subject. The code is available at: https://github.com/florence-dellaniello-picard/joint2d3d-ssm.
We present BoneAgeTW2, the first fully open-source system to automate the complete Tanner-Whitehouse 2 (TW2) clinical protocol for skeletal maturity assessment end-to-end. The system employs YOLOv8 for precise detection and localization of the 20 TW2 hand bones from radiographic images, and an EfficientNet-B3 backbone with 20 independent classification heads to assign maturation stages (A-I) to each bone simultaneously. From these predictions, the system automatically generates clinical PDF reports including interactive Gaussian distribution curves for all 20 bones, enabling direct comparison with population norms. The model is trained on the public RSNA Pediatric Bone Age Challenge dataset (12,611 hand radiographs) using a pseudo-labeling strategy to derive per-bone stage labels from global bone age annotations. The full codebase is publicly available at https://github.com/jmmana/BoneAgeTW2.
Juan Manuel Castillo Pinto
Maestria en Inteligencia Artificial Universidad de La Salle, Bogota, Colombia