Reducing the computational burden of coagulation cascade models in cardiovascular simulations*

Thrombosis is a complex process that begins with the coagulation cascade, a series of biochemical reactions involving more than 40 species. Simulating the coagulation cascade requires solving tens of 3D unsteady advection-reaction-diffusion (ADR) equations, which is challenging. Here we present a novel approach to drastically reduce the computational burden of these simulations. Based on the observation that diffusive transport in arteries is low compared to advection, we model the Lagrangian evolution of the coagulation cascade following each fluid particle using the blood residence time as the independent variable. The ADR eqs. are then reduced to a system of ODEs. We test this methodology in an idealized aneurysm (a pulsating 2D cavity flow), using a simple coagulation model with three biochemical species (thrombin, factor XIa, and protein Ca). We show that the reduced model is cost-effective, accurately reproducing the spatio-temporal development of the coagulation cascade in the ADR system for up to ~15 cardiac cycles.