Physics-Informed Emulation of Systemic Circulation for Fast Parameter Estimation and Uncertainty Quantification

There are many computational models set up to predict blood flow and pressure in vascular networks. Methods for a single forward solution of such models are well established but become problematic in clinical applications, where model calibration and patient-specific parameter estimation call for repeated forward simulations of the model requiring substantial computational costs. A potential workaround is emulation, which approximates the original mathematical model by a statistical or machine learning surrogate model. Our methodological framework is based on physics-informed neural networks, with a particular focus on patient-specific model calibration. Once fully trained, our machine learning model predicts flow and pressure waveforms in a fraction of the time required by the numerical solver, enabling fast parameter inference and inverse uncertainty quantification. The proposed framework is applied to clinical data from four patients diagnosed with a Double Outlet Right Ventricle (DORV), a congenital heart defect where both the aorta and main pulmonary artery connect to the right ventricle, potentially leading to insufficient oxygen delivery to the body and hence requiring careful blood flow monitoring. We assess the performance of our method in a comparative evaluation study that includes several alternative state-of-the-art machine learning methods, and we quantify the improvement achieved in terms of accuracy and efficiency gains.