Left atrial flow and thrombosis risk from 4D CT contrast dynamics by physics-informed neural network and indicator dilution theory

Atrial fibrillation (AF) promotes blood stasis and thrombus formation, most often within the left atrial appendage (LAA), and can lead to stroke or transient ischemic attack (TIA). Time-resolved contrast-enhanced computed tomography (4D CT) captures left atrial (LA) opacification and washout, but it does not directly provide quantitative stasis metrics such as blood residence time. Patient-specific computational fluid dynamics (CFD) can quantify LA/LAA residence time, yet routine clinical use is limited by computational cost and sensitivity to patient-specific boundary conditions. Here, we present two complementary approaches to infer time-resolved 3D residence time fields directly from contrast dynamics. First, a physics-informed neural network (PINN) treats contrast as a passive scalar and jointly reconstructs velocity and residence time by enforcing the incompressible Navier-Stokes equations and transport equations for contrast concentration and residence time in moving, patient-specific LA anatomies. Second, an indicator dilution theory (IDT) formulation computes voxelwise, time-resolved residence time maps from contrast time curves alone by constructing a PV-referenced impulse response and modeling transport with a tank-in-series model with spatially dependent parameters. Both methods are benchmarked against patient-specific CFD in six cases spanning diverse LA function, including three patients with TIA or thrombus in the LAA and three patients free of events. Both approaches reproduce expected spatial and temporal trends, with higher residence time in the distal LAA and higher LAA residence time in cases with TIA or thrombus. IDT demonstrates the closest agreement with CFD across the full range of residence times and produces maps in seconds, facilitating clinical translation. In contrast, the PINN additionally recovers phase-dependent atrial flow structures, but tends to smooth and underestimate the highest residence-time regions and requires hours of training. Together, these results support a scalable workflow in which IDT enables rapid stasis screening from contrast CT, and PINNs provide a complementary pathway for detailed, patient-specific hemodynamic inference when full-field flow information is needed.