Grid refinement study.

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, , and provide the governing PDEs for . 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.

血凝块形成（clot formation）是防止出血的关键生理过程，但若其失衡则可引发严重的凝血功能紊乱。该过程受凝血级联反应（coagulation cascade）调控——这是一套控制凝血酶（thrombin）活性的生化网络，凝血酶可将可溶性纤维蛋白原转化为构成血凝块的纤维蛋白纤维。凝血级联反应模型通常结构复杂，涉及数十个偏微分方程（partial differential equations, PDEs），用以表征各类化学物质的输运、反应动力学与扩散过程。由于该方程组规模庞大且具有多尺度特性，通过数值计算手段求解极具挑战。我们提出一种多保真度（multi-fidelity）策略以提升凝血级联反应模拟的效率：利用分子扩散的缓慢动力学特性，将控制偏微分方程转化为表征物质浓度随血液驻留时间演化的常微分方程（ordinary differential equations, ODEs）。随后围绕零扩散极限对常微分方程解进行泰勒展开，以驻留时间的统计矩为变量得到物质浓度的时空分布，并推导了关于该统计矩的控制偏微分方程。该策略将用于表征N种化学物质凝血级联反应的N个高保真偏微分方程系统，替换为N个常微分方程与p个用于描述驻留时间统计矩的偏微分方程。其中多保真度阶数p可实现精度与计算成本的平衡，相较于高保真模型可实现最高达N/p的加速比。此外，在动脉与心腔模拟常用的大规模计算网格中，该方法的计算成本不再依赖于化学物质的数量。我们以包含N=9种物质的凝血网络以及带有脉动流的理想化动脉瘤几何模型为基准，验证了p=1与p=2的低阶模型具有优异的精度：经过20个心动周期后，两类模型的凝血酶浓度与高保真解的偏差分别低于20%（p=1）与2%（p=2）。这类多保真度模型可为复杂流动场景下的凝血分析以及大规模反应网络研究提供新的可能，同时也可被推广用于深化对其他受流动影响的反应系统的理解。