Nonunion scaphoid bone shape prediction using iterative kernel principal polynomial shape analysis

The scaphoid is an important mechanical stabilizer for both the proximal and distal carpal columns. The precise estimation of the complete scaphoid bone based on partial bone geometric information is a crucial factor in the effective management of scaphoid nonunion. Statistical shape model (SSM) could be utilized to predict the complete scaphoid shape based on the defective scaphoid. However, traditional principal component analysis (PCA) based SSM is limited by its linearity and the inability to adjust the number of modes used for prediction.

This study proposes an iterative kernel principal polynomial shape analysis (iKPPSA)-based SSM to predict the pre-morbid shape of the scaphoid, aiming at enhancing the accuracy as well as the robustness of the model.

Sixty-five sets of scaphoid images were used to train SSM and nine sets of scaphoid images were used for validation. For each validation image set, three defect types (tubercle, proximal pole, and avascular necrosis) were virtually created. The predicted shapes of the scaphoid by PCA, PPSA, KPCA, and iKPPSA-based SSM were evaluated against the original shape in terms of mean error, Hausdorff distance error, and Dice coefficient.

The proposed iKPPSA-based scaphoid SSM demonstrates significant robustness, with a generality of 0.264 mm and a specificity of 0.260 mm. It accounts for 99% of variability with the first seven principal modes of variation. Compared to the traditional PCA-based model, the iKPPSA-based scaphoid model prediction demonstrated superior performance for the proximal pole type fracture, with significant reductions of 25.2%, 24.7%, and 24.6% in mean error, Hausdorff distance, and root mean square error (RMSE), respectively, and a 0.35% improvement in Dice coefficient.

This study showed that the iKPPSA-based SSM exploits the nonlinearity of data features and delivers high reconstruction accuracy. It can be effectively integrated into preoperative planning for scaphoid fracture management or morphology-based biomechanical modeling of the scaphoid.