Unsupervised physics-informed deep learning for assessing pulmonary artery hemodynamics

Deep learning advancements have significantly benefited medical applications. One such helpful application is noninvasive fractional flow reserve (FFR) evaluation along the pulmonary artery tree, which aids in planning optimal balloon pulmonary angioplasty. This study proposes a surrogate model that employs an unsupervised physics-informed neural network (UPNN) to predict FFR based on pulmonary CT angiography. To ensure the UPNN strictly follows the unique solution of the governing equations, we implemented a hard boundary conditions enforcement approach. Subsequently, a finite difference convolutional filter was developed to enhance connectivity among neighboring points. This allows the neural networks to propagate boundary conditions into the unseen vessel interior and perceive the geometric structure of the computational domain. We also introduced regularization constraints on the three components contributing to pressure drop within the artery tree. A total of 4500 synthetic pulmonary artery trees were used to train the UPNN with impedance outlet boundary conditions. We found that the limits of agreement of FFR trained by UPNN ranged from −0.05 to 0.04 with computational fluid dynamics (CFD) simulation results. The testing results showed that the correlation coefficient between FFR predicted by UPNN and CFD were 96.1% and 94.7% for synthetic and patient-specific data, respectively. Using invasive FFR as reference, the accuracy of FFR predicted by UPNN and CFD was 81.4% and 84.8%, respectively. These results demonstrate that our UPNN-based surrogate model's performance in evaluating FFR aligns closely with CFD simulations.