Role of physics-informed constraints in real-time estimation of 3D vascular fluid dynamics using multi-case neural network

Numerical simulations of fluid dynamics in tube-like structures are important to biomedical research to model flow in blood vessels and airways. It is further useful to some clinical applications, such as predicting arterial fractional flow reserves, and assessing vascular flow wall shear stresses to predict atherosclerosis disease progression. Traditionally, they are conducted via computational fluid dynamics (CFD) simulations, which, despite optimization, still take substantial time, limiting clinical adoption. To improve efficiency, we investigate the use of the multi-case Neural Network (NN) to enable real-time predictions of fluid dynamics (both steady and pulsatile flows) in a 3D curved tube (with a narrowing in the middle mimicking a stenosis) of any shape within a geometric range, using only geometric parameters and boundary conditions. We compare the unsupervised approach guided by physics governing equations (physics informed neural network or PINN) to the supervised approach of using mass CFD simulations to train the network (supervised network or SN). We find that multi-case PINN can generate accurate velocity, pressure and wall shear stress (WSS) results under steady flow (spatially maximum error < 2-5 %), but this requires a specific enhancement strategies: (1) estimating the curvilinear coordinate parameters via a secondary NN to use as inputs into PINN, (2) imposing no-slip wall boundary condition as a hard constraint, and (3) advanced strategy to better spatially propagate effects of boundary conditions. However, we cannot achieve reasonable accuracy for pulsatile flow with PINN. Conversely, SN provides very accurate velocity, pressure, and WSS predictions under both steady and pulsatile flow scenarios (spatially and/or temporally maximum error averaged over all geometries <1 %), and is much less computationally expensive to train. To achieve this, strategies (1) and (2) above and a spectral encoding strategy for pulsatile flow are necessary. Thus, interestingly, the use of physics constraints is not effective in our application.