Background
Fractures of the radius and ulna are common injuries in children, with improper healing potentially leading to limitations in forearm rotation affecting function and quality of life. Understanding the normal three-dimensional, age-related morphological variation and spatial relationship of the radius and ulna is essential to support clinical decision-making regarding surgical correction. Previous statistical shape models (SSMs) analyzed the radius and ulna separately, without considering their combined morphological and positional interaction during growth. This study aimed to develop a multi-object SSM of the pediatric forearm to capture combined age-related morphological and spatial variation and to compare its performance with single-object SSMs.

Methods
A cross-sectional dataset of 3D models of healthy pediatric forearms (n = 155; ages 3.8–18.8 years), reconstructed from computed tomography scans, was used to develop a multi-object SSM based on principal component analysis (PCA) and partial least squares regression (PLSR). The model captured the combined shape and position of both bones and enabled prediction of individual forearm geometry across ages during growth. Predictions were validated against follow-up scans of six participants. Morphological accuracy was assessed by root mean squared error (RMSE) and bone length error. Inter-bone spatial relationships were evaluated by comparing normalized distances and bounding box ratios between predicted and original meshes.

Results
The multi-object model captured age-related diaphyseal scaling and epiphyseal development. Absolute distance between the radius and ulna decreased with age, while their relative separation increased due to positional shifts. The PCA-based model achieved superior prediction accuracy (mean RMSE: 2.0 mm) compared to PLSR (3.5 mm). Morphological prediction accuracy was lower than that of single-object SSMs (mean RMSE: 2.4 and 1.7 mm vs. 0.9 and 1.0 mm). However, the multi-object model preserved inter-bone spatial relationships with good agreement longitudinally and reasonable consistency in transverse and sagittal dimensions.

Conclusion
While the multi-object SSM of the forearm does not outperform single-object models in predicting bone morphology, it enables combined modeling of morphology and spatial alignment. This approach provides additional insights into coordinated forearm development and may support future clinical applications in growth assessment and surgical planning.

Introduction: Unrestricted elbow range of motion (ROM) is essential for daily function, yet flexion and extension limitations frequently occur following elbow trauma. These restrictions may result from osseous deformities, soft tissue contracture, or both, requiring accurate identification of the dominant cause to guide treatment. Although CT imaging provides detailed evaluations of bony pathology, conventional single CT lacks functional information, and dynamic 4D-CT faces clinical limitations. Therefore, alternative approaches to assess osseous contributions to motion restrictions are needed.

Objective: This study aims to introduce and validate a 3D computational kinematic bone model based on segmented single CT scans. The model enables patient-specific simulation of elbow flexion and extension, enabling quantifiable assessment of osseous related motion restrictions to support clinical decision making.

Methods: Eight non-affected cadaveric elbows were scanned using computed tomography in seven positions ranging from full extension to full flexion and segmented into 3D models. Anatomical landmarks were automatically identified to define a landmark-based rotation axis (LMA), which was validated against a kinematically derived average helical axis (AHA). The primary outcomes were the angular deviation and the minimal distance between the axes. The simulated ulnar motion was generated by applying finite helical axis-derived rotations to the neutral ulnar pose. Predicted poses were compared to scanned poses at each flexion angle, with translational and rotational deviations calculated to assess simulation accuracy. Clinical applicability was evaluated by applying the model to bilateral CT scans of ten patients with elbow flexion and extension restrictions. Model-based ROM was determined by simulating flexion and extension and identifying the onset of osseous impingement, and compared to clinically recorded ROM.

Results: Alignment between the LMA and the AHA showed a mean positional difference of 0.41 mm (SD 0.22) and an angular deviation of 2.76° (SD: 1.32). LMA-based simulated ulnar poses demonstrated increasing translational and rotational errors with flexion, predominantly in distal, lateral and valgus directions. Specimens exhibited impingement exclusively in the ulnohumeral region at the trochlea and the greater sigmoid notch. In patients, model-based ROM showed a mean absolute difference of 6.7° for terminal extension and 14.2° for terminal flexion, with false-positive impingement primarily observed in the ulnohumeral region.

Conclusion: This study validated a 3D computational model for simulating elbow flexion and extension using single CT scans. The model accurately estimated ROM and identified osseous impingement locations. Although it demonstrated sensitivity to false-positive detections, it provides a clinically applicable tool for assessing osseous motion restrictions. Future improvement should focus on enhancing landmark accuracy and potentially restricting impingement detection to anatomically relevant regions.

Objective
Insight into the three-dimensional (3D) healthy growth of the radius and ulna remains limited, as orthopedics rely primarily on simple two-dimensional radiographic measurements. In this study, we used statistical shape modeling (SSM) to explore 3D forearm shape variations during healthy growth and predict individual radial and ulnar anatomy over time.

Methods
We trained SSMs using CT segmentations of 117 healthy radii and 116 ulnae. Principal Component Analysis (PCA), with and without Procrustes scaling, extracted general shape variation, while we used Partial Least Squares Regression (PLSR) to create an average growth model and prediction models. We developed several methods using age, sex, bone length and/or initial anatomy to predict bone anatomy over time. The models were validated by comparing the predicted bone models to the original segmentations of follow-up samples of 22 radii and 19 ulnae. The primary outcome measure was Root Mean Squared Error (RMSE), complemented by bone length error and mean and maximum distance errors.

Results
Size differences dominated the unscaled PCA- and PLSR-based SSMs, while the scaled PCA captured more subtle shape variations. With PLSR, we extracted the longitudinal growth trajectory for boys and girls aged 4 to 18 in 3D from the cross-sectional data. Using initial anatomy and age as input, the validation samples were predicted with RMSEs of less than 1 mm. The lowest bone length errors were reached using age, sex, and bone length as predictors.

Conclusion
We successfully utilized SSM to investigate and predict healthy growth of the radius and ulna in 3D. The current models are clinically viable as reference anatomy in pre-operative planning, and the methodology shows promise to support diagnosing and treating forearm deformities.