Orthognathic surgery repositions jaw bones to restore occlusion and enhance facial aesthetics. Accurate simulation of postoperative facial morphology is essential for preoperative planning. However, traditional biomechanical models are computationally expensive, while geometric deep learning approaches often lack interpretability. In this study, we develop and validate a physics-informed geometric deep learning framework named PhysSFI-Net for precise prediction of soft tissue deformation following orthognathic surgery. PhysSFI-Net consists of three components: a hierarchical graph module with craniofacial and surgical plan encoders combined with attention mechanisms to extract skeletal-facial interaction features; a Long Short-Term Memory (LSTM)-based sequential predictor for incremental soft tissue deformation; and a biomechanics-inspired module for high-resolution facial surface reconstruction. Model performance was assessed using point cloud shape error (Hausdorff distance), surface deviation error, and landmark localization error (Euclidean distances of craniomaxillofacial landmarks) between predicted facial shapes and corresponding ground truths. A total of 135 patients who underwent combined orthodontic and orthognathic treatment were included for model training and validation. Quantitative analysis demonstrated that PhysSFI-Net achieved a point cloud shape error of 1.070 +/- 0.088 mm, a surface deviation error of 1.296 +/- 0.349 mm, and a landmark localization error of 2.445 +/- 1.326 mm. Comparative experiments indicated that PhysSFI-Net outperformed the state-of-the-art method ACMT-Net in prediction accuracy. In conclusion, PhysSFI-Net enables interpretable, high-resolution prediction of postoperative facial morphology with superior accuracy, showing strong potential for clinical application in orthognathic surgical planning and simulation.

翻译：正颌外科手术通过重新定位颌骨以恢复咬合关系并改善面部美学。准确模拟术后面部形态对于术前规划至关重要。然而，传统的生物力学模型计算成本高昂，而几何深度学习方法往往缺乏可解释性。在本研究中，我们开发并验证了一个名为PhysSFI-Net的物理信息几何深度学习框架，用于精确预测正颌手术后的软组织变形。PhysSFI-Net包含三个组成部分：一个结合颅面与手术方案编码器及注意力机制的分层图模块，用于提取骨骼-面部交互特征；一个基于长短期记忆网络（LSTM）的序列预测器，用于增量式软组织变形预测；以及一个受生物力学启发的模块，用于高分辨率面部表面重建。模型性能通过预测面部形状与对应真实值之间的点云形状误差（豪斯多夫距离）、表面偏差误差以及标志点定位误差（颅颌面标志点的欧几里得距离）进行评估。研究共纳入135名接受正畸-正颌联合治疗的患者用于模型训练与验证。定量分析表明，PhysSFI-Net实现了1.070 +/- 0.088 mm的点云形状误差、1.296 +/- 0.349 mm的表面偏差误差以及2.445 +/- 1.326 mm的标志点定位误差。对比实验表明，PhysSFI-Net在预测精度上优于当前最先进的方法ACMT-Net。总之，PhysSFI-Net能够以卓越的精度实现可解释、高分辨率的术后面部形态预测，在正颌外科手术规划与模拟的临床应用中展现出巨大潜力。