BackgroundThe 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.PurposeThis 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.MethodsSixty‐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.ResultsThe 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.ConclusionThis 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.

中文翻译：

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使用迭代核主多项式形状分析预测舟状骨骨不连形状

背景舟骨是近端和远端腕柱的重要机械稳定器。基于部分骨几何信息的完整舟骨骨的精确估计是有效治疗舟骨骨不连的关键因素。统计形状模型（SSM）可用于根据有缺陷的舟骨预测完整的舟骨形状。然而，传统的基于主成分分析（PCA）的SSM受到其线性度和无法调整用于预测的模式数量的限制。目的本研究提出了一种基于迭代核主多项式形状分析（iKPPSA）的SSM来预测预方法采用65组舟骨图像进行SSM训练，9组舟骨图像进行验证。对于每个验证图像集，虚拟创建了三种缺陷类型（结节、近极和缺血性坏死）。通过 PCA、PPSA、KPCA 和基于 iKPPSA 的 SSM 预测的舟状体形状，根据平均误差、Hausdorff 距离误差和 Dice 系数与原始形状进行了评估。结果所提出的基于 iKPPSA 的舟状体 SSM 表现出显着的鲁棒性，通用性为 0.264 毫米，特殊性为 0.260 毫米。它解释了前七种主要变异模式中 99% 的变异性。与传统的基于 PCA 的模型相比，基于 iKPPSA 的舟状骨模型预测在近极型骨折方面表现出优越的性能，平均误差、Hausdorff 距离和均方根分别显着降低了 25.2%、24.7% 和 24.6%误差（RMSE）分别提高，Dice 系数提高了 0.35%。结论本研究表明，基于 iKPPSA 的 SSM 利用了数据特征的非线性，并提供了较高的重建精度。它可以有效地融入舟骨骨折治疗的术前计划或基于形态的舟骨生物力学建模中。