Inferring left atrial stasis and flow from patient-specific 4D contrast dynamics -- physics-informed neural networks with hard constraints vs. indicator dilution theory

Atrial fibrillation (AF) is the most common cardiac arrhythmia, characterized by irregular left atrial (LA) contractions that impair blood flow and promote stasis, particularly in the left atrial appendage (LAA), increasing thrombosis risk. AF affects nearly one in three individuals over their lifetime and increases the ischemic stroke risk fivefold; it is estimated to be responsible for one third of all strokes. Current risk stratification methods lack patient-specific precision and offer moderate predictive accuracy, particularly in cases where the benefits of anticoagulation therapy are unclear.

Patient-specific computational fluid dynamics (CFD) has shown promise in predicting LAA blood stasis. However, CFD analysis requires high-quality segmentation and meshing of the left atrium and appendage --tasks that remain challenging to automate -- and is sensitive to modeling assumptions such as inflow boundary conditions and blood rheology. This study investigates an alternative approach: using a physics-informed neural network (PINN) to infer LAA flow and stasis directly from the 4D spatiotemporal dynamics of a contrast agent imaged over multiple heartbeats, thereby eliminating the need for LA segmentation and explicit specification of inflow or rheological parameters.

The underlying physical models in our method consist of Navier-Stokes, continuity, a contrast transport equation, and a residence time equation. We incorporated hard constraints in the PINN architecture to enforce initial conditions on residence time and ensure temporal periodicity. We validated PINN predictions for flow velocity and residence time using data from patient-specific CFD simulations as ground-truth data. We also compare these predictions with those obtained by a simplified compartment model of indicator dilution that fits the contrast profile at each image voxel by a gamma-variate function and approximates residence time as the first-order moment of the gamma-variate.