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：边界条件（BC）校准以同化临床测量数据，是任何个体化心血管流体动力学模拟中的关键步骤。贝叶斯校准方法已成功量化了识别参数中固有的不确定性。然而，由于不可行的计算需求，在3D模拟中对所有BC参数常规估计后验分布一直难以实现。我们提出了一种高效方法，利用单次高保真三维（3D）模型评估结果识别Windkessel参数后验分布。我们仅对初始BC选择进行一次3D模型评估，并利用其结果创建高精度的零维（0D）代理模型。随后，我们使用优化后的0D模型执行序列蒙特卡洛（SMC）方法，以推导高维Windkessel BC后验分布。我们在包含N=72个体化血管模型的公开数据集中验证了该方法。我们发现，先验地将0D模型优化以匹配3D数据，可将其近似中值误差降低近一个数量级。在模型子集中，我们确认优化后的0D模型仍能泛化至广泛的BC范围。最后，我们利用SMC展示了不同测量信噪比下血管模型中高维Windkessel参数后验分布。我们进一步验证了基于0D模型推导的后验分布能很好地近似3D后验分布。本方法仅需单次3D模拟的最小计算需求，加之本研究所有软件和数据的开源特性，将提升心血管流体动力学模拟中贝叶斯Windkessel校准的可及性与效率。