Multi-Fidelity Models for Thrombosis Risk Evaluation in the Left Heart Using Patient-Specific Data
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This work proposes a methodology to reduce the computational complexity of coagulation models in complex geometries, with the goal of evaluating thrombosis risk in the left heart. The approach leverages the low diffusion of coagulation cascade species to derive a simplified system of ordinary differential equations (ODEs) that neglects the diffusion term in the high-fidelity (HiFi) model. The resulting multi-fidelity of first order (MuFi-1) model combines the set of ODEs and a single partial differential equation (PDE) integration. To account for internal variance in the concentrations within each fluid particle, an additional PDE for the variance of the residence time is considered, leading to a MuFi-2 model. The methodology was validated using an idealized aneurysm and a simplified model of the intrinsic pathway of the coagulation cascade. Then, the MuFi models were applied to a database of patient-specific left atrial flows to estimate the risk of thrombosis in the left atrium. The residence time and its variance were calculated for 20 consecutive cardiac cycles, and the first and second order multi-fidelity models were used to assess the likelihood of thrombosis in the LA. Overall, both MuFi-1 and MuFi-2 are cost-effective solutions that can be trivially extended to more complex models of the coagulation cascade. This approach can help in the uncertainty quantification of blood coagulation models, and in the development of more accurate patient-specific metrics of thrombogenesis risk.