Growing InSight: Developing a 3D growth model for the healthy radius and ulna using statistical shape modeling

Abstract

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.