Enhanced physics-informed generative adversarial network to estimate spatial-temporal distribution of shear stress in carotid arteries

Estimations of blood flow shear stress and its distribution have great importance for preventing carotid artery stenosis and predicting plaque stability. Physics-informed neural network (PINN) can utilize less data points with unknown boundary conditions and obtain high-resolution and accurate solutions under the constraints of physical equations. This makes PINN well-suited to address clinical hemodynamic modeling problems. However, the basic structure of PINN might cause an imbalance among the loss function terms and is hard to converge. To overcome the above problems and estimate shear stress distribution with high accuracy, this study proposed a physical consistent score (PCS) guided generative adversarial network (GAN) (PCS-GAN), which combined GAN with PINN. Physical consistent scores calculated from Navier-Stokes equations for each sampled point were used as one of the criteria for discriminator classification. The constitutive equations and the score based adaptive weights were added to the loss function of generator in order to alleviate the possible unbalance problems in the loss function and accelerate convergence. We tested PCS-GAN in carotid arteries with different stenosis degrees. Ablation experiments and comparison experiments were conducted to further demonstrate the performance of PCS-GAN. In general, PCS-GAN accurately estimated the spatiotemporal distributions of velocity and shear stress, and values of 0.268 ± 0.066 of the relative two-norm error as well as 0.976 ± 0.012 of structural similarities were achieved in shear stress and velocity prediction, respectively. PCS-GAN has the potential to reveal the local mechanical parameters near the carotid bifurcation and predict carotid stenosis as well as plaque stability.