Efficient multi-fidelity computation of blood coagulation under flow

Abstract

Clot formation is a crucial process that prevents bleeding, but can lead to severe disorders when imbalanced. This process is regulated by the coagulation cascade, a biochemical network that controls the enzyme thrombin, which converts soluble fibrinogen into the fibrin fibers that constitute clots. Coagulation cascade models are typically complex and involve dozens of partial differential equations (PDEs) representing various chemical species' transport, reaction kinetics, and diffusion. Solving these PDE systems computationally is challenging, due to their large size and multi-scale nature. We propose a multi-fidelity strategy to increase the efficiency of coagulation cascade simulations. Leveraging the slower dynamics of molecular diffusion, we transform the governing PDEs into ordinary differential equations (ODEs) representing the evolution of species concentrations versus blood residence time. We then Taylor-expand the ODE solution around the zero-diffusivity limit to obtain spatiotemporal maps of species concentrations in terms of the statistical moments of residence time, [Formula: see text], and provide the governing PDEs for [Formula: see text]. This strategy replaces a high-fidelity system of N PDEs representing the coagulation cascade of N chemical species by N ODEs and p PDEs governing the residence time statistical moments. The multi-fidelity order (p) allows balancing accuracy and computational cost providing a speedup of over N/p compared to high-fidelity models. Moreover, this cost becomes independent of the number of chemical species in the large computational meshes typical of the arterial and cardiac chamber simulations. Using a coagulation network with N = 9 and an idealized aneurysm geometry with a pulsatile flow as a benchmark, we demonstrate favorable accuracy for low-order models of p = 1 and p = 2. The thrombin concentration in these models departs from the high-fidelity solution by under 20% (p = 1) and 2% (p = 2) after 20 cardiac cycles. These multi-fidelity models could enable new coagulation analyses in complex flow scenarios and extensive reaction networks. Furthermore, it could be generalized to advance our understanding of other reacting systems affected by flow.