Estimation of Hemodynamic Parameters via Physics Informed Neural Networks including Hematocrit Dependent Rheology

Abstract

Physics-Informed Neural Networks (PINNs) show significant potential for solving inverse problems, especially when observations are limited and sparse, provided that the relevant physical equations are known. We use PINNs to estimate smooth velocity and pressure fields from synthetic 4D flow Magnetic Resonance Imaging (MRI) data. We analyze five non-Newtonian dynamic 3D blood flow cases within a realistic aortic model, covering a range of hematocrit values from anemic to polycythemic conditions. To enhance state estimation results, we consider various design and training techniques for PINNs, including adaptive loss balancing, curriculum training, and a realistic measurement operator. Regarding blood rheology, the PINN approach accurately estimates viscosity globally and locally under peak systolic conditions. It also provides a clear pattern recognition for diastolic stages. Regarding mass conservation, PINN estimations effectively reproduce the bifurcation of flow through the different branches of the aorta, demonstrate an excellent representation of the non-slip conditions at the walls, and accurately estimate pressure drops with relative errors below the 5% in the whole pressure field. We test our pressure drop estimations against the state of the art Virtual Work Energy Relative Pressure (vWERP) estimator, and we observe how our results outperform vWERP in terms of both accuracy and time resolution. Additionally, we find that the best results are achieved by computing the velocity field using the PINN, which is then integrated into the vWERP framework, leading to time super-sampled and high-order approximations, with a clinically admissible accuracy.