Physically Informed Deep Learning Technique for Estimating Blood Flow Parameters in Four-Vessel Junction after the Fontan Procedure

This study introduces an innovative approach leveraging physics-informed neural networks (PINNs) for the efficient computation of blood flows at the boundaries of a four-vessel junction formed by a Fontan procedure. The methodology incorporates a 3D mesh generation technique based on the parameterization of the junction's geometry, coupled with an advanced physically regularized neural network architecture. Synthetic datasets are generated through stationary 3D Navier-Stokes simulations within immobile boundaries, offering a precise alternative to resource-intensive computations. A comparative analysis of standard grid sampling and Latin hypercube sampling data generation methods is conducted, resulting in datasets comprising 1.1x104 and 5x103 samples, respectively. The following two families of feed-forward neural networks (FFNNs) are then compared: the conventional "black-box" approach using mean squared error (MSE) and a physically informed FFNN employing a physically regularized loss function (PRLF), incorporating mass conservation law. The study demonstrates that combining PRLF with Latin hypercube sampling enables the rapid minimization of relative error (RE) when using a smaller dataset, achieving a relative error value of 6% on the test set. This approach offers a viable alternative to resource-intensive simulations, showcasing potential applications in patient-specific 1D network models of hemodynamics.