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

Edwin Tay; Amir A. Zadpoor; Nazli Tümer

cs.CVOct 26, 2026

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

Abstract

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 = $1.512 \pm 0.005$ , ASSD $0.449 \pm 001$ , Dice = $0.987 \pm 0.00004$ , IoU = $0.975 \pm 0.0001$ ). 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.

Figures & tables

	Sex	Age (months)					Total
	Sex	0 - 43.2	43.2 - 86.4	86.4 - 129.6	129.6 - 172.8	172.8 - 230	Total
Full RSNA	Male	233	894	1164	3690	852	6833
Full RSNA	Female	249	970	1986	2223	350	5778
Analysis subset	Male	118	143	151	156	156	724
Analysis subset	Female	119	145	152	157	159	732

Table 1

Model	Size	Params (M) [#]	Epochs [#]	mAP50-95 ( $\uparrow$ ) [-]
YOLOv8	n	3.01	82	0.9526
	s	11.14	79	0.9622
	m	25.87	122	0.9705
YOLO11	n	2.59	81	0.9521
	s	9.44	94	0.9663
	m	20.07	76	0.9676

Table 2

Head	Encoder	Params [M]	Train [PFLOPs]	HD95 + ASSD ( $\downarrow$ ) [px]	HD95 ( $\downarrow$ ) [px]	ASSD ( $\downarrow$ ) [px]	Dice ( $\uparrow$ ) [-]	IoU ( $\uparrow$ ) [-]
SegFormer	mit_b0	3.7	6	2.027	$1.564\pm 0.010$	$0.463\pm 0.001$	$0.98683\pm 0.00003$	$0.97408\pm 0.00005$
	mit_b1	13.7	12	1.988	$1.531\pm 0.009$	$0.457\pm 0.001$	$0.98698\pm 0.00003$	$0.97438\pm 0.00006$
	mit_b2	24.7	15	1.978	$1.526\pm 0.015$	$0.452\pm 0.003$	$0.98713\pm 0.00007$	$0.97467\pm 0.00015$
	mit_b3	44.6	29	1.977	$1.524\pm 0.013$	$0.453\pm 0.003$	$0.98711\pm 0.00005$	$0.97462\pm 0.00010$
	mit_b4	61.4	42	1.962	$\mathbf{1.512\pm 0.005}$	$0.449\pm 0.001$	$0.98718\pm 0.00003$	$0.97476\pm 0.00006$
	mit_b5	82.0	45	2.003	$1.548\pm 0.025$	$0.455\pm 0.003$	$0.98705\pm 0.00006$	$0.97451\pm 0.00012$

Table 3

Bone	$T^{2}$	$F$	df	$\mathcal{D}$	$p$ -value
Distal Phalanx 3	66.656	9.483	7, 1448	0.4279	$p\leq 0.001$
Medial Phalanx 2	137.89	19.62	7, 1448	0.6155	$p\leq 0.001$
Proximal Phalanx 3	142.01	17.67	8, 1447	0.6246	$p\leq 0.001$
Metacarpal 3	71.562	10.18	7, 1448	0.4434	$p\leq 0.001$

Table 4

Bone	mode	$t$	Cohen’s $d$	$p$ -value (BH)
Distal phalange 3	PC1	6.604	0.3462	$p\leq 0.001$
	PC2	4.63	0.243	$p\leq 0.001$
	PC3	$-$ 0.7269	$-$ 0.03811	ns
	PC4	1.123	0.05891	ns
	PC5	1.578	0.08273	ns
	PC6	$-$ 0.6306	$-$ 0.03305	ns

Table 5

Bone	Pillai	$s$	Pillai $/s$	$F$	df	$p$ ( $F$ )	$p$ (Freedman–Lane)
Distal Phalanx 3	0.09712	3	0.03237	6.902	21, 4332	$p\leq 0.001$	$p\leq 0.001$
Medial Phalanx 2	0.1231	3	0.04104	8.828	21, 4332	$p\leq 0.001$	$p\leq 0.001$
Proximal Phalanx 3	0.1726	3	0.05752	11.01	24, 4329	$p\leq 0.001$	$p\leq 0.001$
Metacarpal 3	0.1498	3	0.04995	10.84	21, 4332	$p\leq 0.001$	$p\leq 0.001$

Table 6

Bone	mode	$F$	df	$p$ -value (BH)
Distal Phalanx 3	PC1	22.93	3, 1448	$p\leq 0.001$
	PC2	0.7691	3, 1448	ns
	PC3	1.357	3, 1448	ns
	PC4	7.259	3, 1448	$p\leq 0.001$
	PC5	4.457	3, 1448	$p\leq 0.01$
	PC6	12.69	3, 1448	$p\leq 0.001$

Table 7

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

mode	Metacarpal 3	Proximal phalange 3	Medial phalange 2	Distal phalange 3
PC1	cub +1.5~	cub +14.9	cub +52.2	cub +34.9
PC2	quad +1.1~	cub +52.5	cub +6.8	lin +1.6~
PC3	cub +26.5	lin +1.1~	cub +64.0	lin +0.1~
PC4	cub +4.9	cub +79.2	cub +2.9	cub +20.9
PC5	cub +53.1	quad +4.8	lin +7.2	quad +7.1
PC6	cub +107.4	cub +17.1	cub +45.2	cub +15.4

Appendix

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.

\sim

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	$T^{2}$	$F$	df	$D$	$p$
Distal phalanx 1	PC1–8	61.712	7.677	8, 1447	0.4118	$p\leq 0.001$
Distal phalanx 2	PC1–7	65.67	9.343	7, 1448	0.4248	$p\leq 0.001$
Distal phalanx 4	PC1–7	51.661	7.35	7, 1448	0.3767	$p\leq 0.001$
Distal phalanx 5	PC1–7	69.628	9.906	7, 1448	0.4374	$p\leq 0.001$
Medial phalanx 1	PC1–7	108.65	15.46	7, 1448	0.5464	$p\leq 0.001$
Medial phalanx 3	PC1–7	97.191	13.83	7, 1448	0.5167	$p\leq 0.001$

Appendix

Table B1: Hotelling’s

T^{2}

over sex-stratified shape parameters encompassing

c

shape modes retained for analysis.

F

and

p

-values denote statistical significance whilst

T^{2}

and

\mathcal{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	$p\leq 0.001$	$p\leq 0.001$
Distal phalange 2	0.07228	2	0.03614	7.74	14, 2890	$p\leq 0.001$	$p\leq 0.001$
Distal phalange 4	0.1063	3	0.03542	7.576	21, 4332	$p\leq 0.001$	$p\leq 0.001$
Distal phalange 5	0.1161	3	0.03869	8.302	21, 4332	$p\leq 0.001$	$p\leq 0.001$
Medial phalange 1	0.1503	3	0.05008	10.88	21, 4332	$p\leq 0.001$	$p\leq 0.001$
Medial phalange 3	0.2033	3	0.06777	15	21, 4332	$p\leq 0.001$	$p\leq 0.001$

Appendix

Table B2: Results from Pillai’s trace on sex

\times

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.

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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.

Abstract

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