Towards fast and reliable estimations of 3D pressure, velocity and wall shear stress in aortic blood flow: CFD-based machine learning approach

In this work, we developed deep neural networks for the fast and comprehensive estimation of the most salient features of aortic blood flow. These features include velocity magnitude and direction, 3D pressure, and wall shear stress. Starting from 40 subject-specific aortic geometries obtained from 4D Flow MRI, we applied statistical shape modeling to generate 1,000 synthetic aorta geometries. Complete computational fluid dynamics (CFD) simulations of these geometries were performed to obtain ground-truth values. We then trained deep neural networks for each characteristic flow feature using 900 randomly selected aorta geometries. Testing on remaining 100 geometries resulted in average errors of 3.11% for velocity and 4.48% for pressure. For wall shear stress predictions, we applied two approaches: (i) directly derived from the neural network-predicted velocity, and, (ii) predicted from a separate neural network. Both approaches yielded similar accuracy, with average error of 4.8 and 4.7% compared to complete 3D CFD results, respectively. We recommend the second approach for potential clinical use due to its significantly simplified workflow. In conclusion, this proof-of-concept analysis demonstrates the numerical robustness, rapid calculation speed (less than seconds), and good accuracy of the CFD-based machine learning approach in predicting velocity, pressure, and wall shear stress distributions in subject-specific aortic flows.