Wall shear stress in coronary arteries and grafts using computational fluid dynamics and physics-informed neural networks

Abstract

Computational fluid dynamics (CFD) were used to quantify wall shear stress (WSS) in 12 patient-specific coronary geometries, including four healthy cases, five coronary artery bypass graft cases with saphenous vein grafts, and three coronary artery disease cases without bypass grafts, under both Newtonian and Carreau–Yasuda blood viscosity models. The analysis focused on area-weighted average WSS, average WSS at bifurcations, the area fraction where WSS exceeds 40 dynes/cm2 normalized by the total vessel area, area-weighted average WSS above 40 dynes/cm2, and the interquartile range (IQR) of WSS. Diseased coronary arteries and diseased grafts (DGs) exhibited elevated WSS compared with healthy arteries and healthy grafts. The area-weighted average WSS above 40 dynes/cm2 in DGs reached up to ∼148 dynes/cm2, while healthy vessels showed lower values in the present cohort. IQR values were also higher in diseased vessels, indicating increased spatial heterogeneity of WSS. An exploratory elevated WSS threshold of 40 dynes/cm2 effectively differentiated healthy and diseased regions. Compared with the Newtonian model, the Carreau–Yasuda formulation captured shear-rate-dependent viscosity effects in stenotic and bifurcation regions. Furthermore, physics-informed neural network surrogate models incorporating random Fourier feature encoding were trained to reconstruct the CFD fields for the 12 patient-specific cases. Under a dense 20% within-geometry holdout of CFD target values, the Newtonian surrogate achieved a mean normalized root mean square error of 0.93% with a coefficient of determination (R2) of 0.98, while the Carreau–Yasuda surrogate achieved 0.97% with a coefficient of determination of 0.98, with both rheologies evaluated on a common per-patient vessel subset so that the comparison is strictly like-for-like. Both models showed strong agreement with CFD results within their respective training geometries, with holdout Pearson correlation coefficients of 0.99 and 0.99, respectively.