Deep Learning-Based Surrogate Model of Subject-Specific Finite-Element Analysis for Vertebrae

Subject-specific finite-element analysis (FEA) models enable accurate simulation of vertebral biomechanics but are often time-consuming to construct and solve under varying conditions. This study presents a novel deep learning (DL)/machine learning (ML)-based surrogate model that predicts stress distributions in vertebral bodies with high efficiency. The model integrates vertebral shape encoding and employs separate decoding branches for surface and internal nodes. It was trained on 3,960 synthetic L1 vertebrae generated via data augmentation from 42 real computed tomography (CT) scans. Evaluation on independent test samples yielded a mean absolute error (MAE) of 0.0596 MPa and an $\mathrm{R}^{2}$ of 0.864 for von Mises stress. Visualization results confirm strong agreement between predicted and FEA-computed stress patterns, with localized discrepancies observed at the anteroinferior margin and pedicles. Moreover, an end-to-end automated pipeline was established based on the developed model, reducing the total processing time from 90-120min to approximately 134-154s per subject. These findings highlight the potential of the proposed surrogate model to facilitate rapid, subject-specific biomechanical assessments in clinical workflows.