Efficient, Multi-Fidelity Modelling of the Coagulation Cascade in Patient-Specific Left Atrial Flow*

The left atrium (LA) is the most common site of cardiac thrombosis, associated with up to 30% of ischemic strokes. The coagulation cascade regulates thrombosis via a large biochemical network. Under flow, this cascade is governed by a system of dozens of 3D advection-reaction-diffusion partial differential equations (PDE). Solving these PDEs is computationally challenging due to their high dimensionality and multi-scale nature. Here, we leverage a recently developed Multi-Fidelity (MuFi) coagulation model that  reduces the 3D PDE system into an equivalent ordinary differential equation (ODE) system. The MuFi model represents species concentration u_i(x,t) as a function of the statistical moments of blood residence time, which are the only PDEs we need to solve. We apply a 9-species MuFi model to a database of LA flows (N=6 patients, 3 thrombus negative and 3 thrombus/TIA positive) to quantify patient-specific thrombin production. Residence time moments are obtained from the LA velocity fields calculated by LA with CFD analysis of 4D CT patient-specific images. Taking advantage of the MuFi model's low computational cost, we also present a sensitivity analysis of the effect of reaction kinetic constants.