Boundary condition (BC) calibration to assimilate clinical measurements is an essential step in any subject-specific simulation of cardiovascular fluid dynamics. Bayesian calibration approaches have successfully quantified the uncertainties inherent in identified parameters. Yet, routinely estimating the posterior distribution for all BC parameters in 3D simulations has been unattainable due to the infeasible computational demand. We propose an efficient method to identify Windkessel parameter posteriors using results from a single high-fidelity three-dimensional (3D) model evaluation. We only evaluate the 3D model once for an initial choice of BCs and use the result to create a highly accurate zero-dimensional (0D) surrogate. We then perform Sequential Monte Carlo (SMC) using the optimized 0D model to derive the high-dimensional Windkessel BC posterior distribution. We validate this approach in a publicly available dataset of N=72 subject-specific vascular models. We found that optimizing 0D models to match 3D data a priori lowered their median approximation error by nearly one order of magnitude. In a subset of models, we confirm that the optimized 0D models still generalize to a wide range of BCs. Finally, we present the high-dimensional Windkessel parameter posterior for different measured signal-to-noise ratios in a vascular model using SMC. We further validate that the 0D-derived posterior is a good approximation of the 3D posterior. The minimal computational demand of our method using a single 3D simulation, combined with the open-source nature of all software and data used in this work, will increase access and efficiency of Bayesian Windkessel calibration in cardiovascular fluid dynamics simulations.

翻译：在心血管血流动力学的主体特异性仿真中，通过同化临床测量数据对边界条件进行标定是必不可少的关键步骤。贝叶斯标定方法已成功量化了参数辨识过程中固有的不确定性。然而，由于三维仿真计算成本过高，常规估计所有边界条件参数的后验分布一直难以实现。本文提出一种高效方法，仅需单次高保真三维模型评估结果即可辨识Windkessel参数的后验分布。我们仅对初始选择的边界条件执行一次三维模型计算，并利用其结果构建高精度的零维代理模型。随后采用序列蒙特卡洛方法，通过优化的零维模型推导高维Windkessel边界条件的后验分布。我们在公开可用的N=72例主体特异性血管模型数据集中验证了该方法。研究发现，通过先验优化零维模型以匹配三维数据，可将其中位数近似误差降低近一个数量级。在部分模型中，我们证实优化后的零维模型仍能泛化至广泛的边界条件范围。最后，我们利用序列蒙特卡洛方法展示了不同测量信噪比下血管模型的高维Windkessel参数后验分布，并进一步验证了零维推导后验分布对三维后验分布的良好近似性。本方法仅需单次三维仿真的极小计算需求，结合本研究所有软件与数据的开源特性，将显著提升贝叶斯Windkessel标定在心血管血流动力学仿真中的可及性与效率。