This study investigated the potential of end-to-end deep learning tools as a more effective substitute for FEM in predicting stress-strain fields within 2D cross sections of arterial wall. We first proposed a U-Net based fully convolutional neural network (CNN) to predict the von Mises stress and strain distribution based on the spatial arrangement of calcification within arterial wall cross-sections. Further, we developed a conditional generative adversarial network (cGAN) to enhance, particularly from the perceptual perspective, the prediction accuracy of stress and strain field maps for arterial walls with various calcification quantities and spatial configurations. On top of U-Net and cGAN, we also proposed their ensemble approaches, respectively, to further improve the prediction accuracy of field maps. Our dataset, consisting of input and output images, was generated by implementing boundary conditions and extracting stress-strain field maps. The trained U-Net models can accurately predict von Mises stress and strain fields, with structural similarity index scores (SSIM) of 0.854 and 0.830 and mean squared errors of 0.017 and 0.018 for stress and strain, respectively, on a reserved test set. Meanwhile, the cGAN models in a combination of ensemble and transfer learning techniques demonstrate high accuracy in predicting von Mises stress and strain fields, as evidenced by SSIM scores of 0.890 for stress and 0.803 for strain. Additionally, mean squared errors of 0.008 for stress and 0.017 for strain further support the model's performance on a designated test set. Overall, this study developed a surrogate model for finite element analysis, which can accurately and efficiently predict stress-strain fields of arterial walls regardless of complex geometries and boundary conditions.

翻译：本研究探索了端到端深度学习工具作为有限元法替代方案，预测二维动脉壁截面应力-应变场的潜力。我们首先提出基于U-Net的全卷积神经网络，根据动脉壁截面的钙化空间分布预测von Mises应力与应变分布。进一步开发条件生成对抗网络，从感知层面提升对不同钙化数量及空间构型动脉壁应力-应变场图的预测精度。在U-Net与cGAN基础上，分别提出其集成方法以进一步优化场图预测性能。通过施加边界条件并提取应力-应变场图，构建了由输入与输出图像组成的数据集。经训练，U-Net模型在保留测试集上对von Mises应力场与应变场的结构相似性指数评分分别达0.854与0.830，均方误差分别为0.017与0.018。采用集成学习与迁移学习技术组合的cGAN模型在预测von Mises应力场与应变场时展现出高精度，其SSIM得分分别为0.890（应力）与0.803（应变），指定测试集上的均方误差分别为0.008（应力）与0.017（应变）。本研究开发的有限元分析替代模型，能够独立于复杂几何构型与边界条件，准确高效地预测动脉壁应力-应变场。