Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need to be thoroughly demonstrated through verification, validation, and uncertainty quantification. When results depend on multiple uncertain inputs, sensitivity analysis is typically the first step required to separate relevant from unimportant inputs, and is key to determine an initial reduction on the problem dimensionality that will significantly affect the cost of all downstream analysis tasks. For computationally expensive models with numerous uncertain inputs, sample-based sensitivity analysis may become impractical due to the substantial number of model evaluations it typically necessitates. To overcome this limitation, we consider recently proposed Multifidelity Monte Carlo estimators for Sobol' sensitivity indices, and demonstrate their applicability to an idealized model of the common carotid artery. Variance reduction is achieved combining a small number of three-dimensional fluid-structure interaction simulations with affordable one- and zero-dimensional reduced order models. These multifidelity Monte Carlo estimators are compared with traditional Monte Carlo and polynomial chaos expansion estimates. Specifically, we show consistent sensitivity ranks for both bi- (1D/0D) and tri-fidelity (3D/1D/0D) estimators, and superior variance reduction compared to traditional single-fidelity Monte Carlo estimators for the same computational budget. As the computational burden of Monte Carlo estimators for Sobol' indices is significantly affected by the problem dimensionality, polynomial chaos expansion is found to have lower computational cost for idealized models with smooth stochastic response.

翻译：心血管系统计算模型日益广泛用于心血管疾病的诊断、治疗与预防。在用于转化应用之前，这些模型的预测能力需通过验证、确认及不确定性量化进行全面展示。当结果依赖于多个不确定输入时，灵敏度分析通常是区分相关输入与不相关输入的首要步骤，也是确定问题维度初始缩减的关键，这将显著影响所有下游分析任务的成本。对于具有大量不确定输入且计算成本高昂的模型，基于采样的灵敏度分析可能因所需大量模型评估而变得不切实际。为克服这一局限，本研究采用近期提出的用于Sobol灵敏度指数的多保真蒙特卡洛估计器，并证明其在理想化颈总动脉模型中的适用性。通过将少量三维流固耦合模拟与低成本的零维和一维降阶模型相结合，实现了方差缩减。我们将这些多保真蒙特卡洛估计器与传统蒙特卡洛及多项式混沌展开估计进行了比较。具体而言，双保真（1D/0D）和三保真（3D/1D/0D）估计器均呈现一致的灵敏度排序，且在相同计算预算下，其方差缩减效果优于传统单保真蒙特卡洛估计器。由于Sobol指数蒙特卡洛估计器的计算负担受问题维度显著影响，对于具有平滑随机响应的理想化模型，多项式混沌展开被发现具有更低的计算成本。