High-fidelity CFD framework for solution of Cahn–Hilliard and Navier–Stokes equations for blood-clot interaction in the left atrium

Atrial fibrillation (AF) disrupts left atrial (LA) contraction, impairing blood flow and promoting thrombosis in the left atrial appendage (LAA). AF increases the risk of ischemic stroke fivefold and is implicated in up to one-third of all stroke cases. Despite this strong association, clinical data show no clear temporal alignment between AF episodes and stroke events, suggesting that factors beyond thrombosis, such as clot formation, migration, and stability, play a key role in embolic risk. Modeling these processes remains challenging.

We present a high-fidelity CFD framework that couples blood flow and clot dynamics in patient-specific LA geometries. The clot is modeled as a porous, viscoelastic material using a diffuse-interface phase-field formulation. Blood-clot interaction is captured by coupling the incompressible Navier-Stokes equations with the Cahn-Hilliard equation, where a double-well potential drives phase separation. Two-way coupling includes advection and deformation of the clot by the flow, as well as momentum source terms: a Darcy resistance scaled by the clot volume fraction and elastic stresses representing internal clot mechanics. Large deformations are tracked by evolving the deformation gradient tensor F.

We solve the Navier-Stokes equations using a fractional step method with immersed boundaries for atrial walls. Time integration employs a three-stage, low-storage Runge-Kutta scheme. The biharmonic term in the Cahn-Hilliard equation is decomposed into two Helmholtz problems, and a WENO scheme ensures stable evolution of F.

We benchmark the solver on idealized domains and demonstrate scalability on patient-specific LA and LAA reconstructions from 4D CT. The method captures clot growth and embolization dynamics, enabling mechanistic studies of thromboembolism in AF and enhancing risk stratification.