标题： 使用谱代理和维数约简评估血流动力学偏微分方程模型的参数可识别性 显示英文标题

标题： Assessing parameter identifiability of a hemodynamics PDE model using spectral surrogates and dimension reduction

摘要： 生物医学模拟器的计算逆问题由于数据有限和相对较高的参数维度而面临困难。 这通常需要敏感性分析，其中模型参数根据它们对特定感兴趣的量的影响程度进行排名。 这对于用于构建医疗数字孪生的模拟器尤其重要，因为数据量通常有限。 对于昂贵的模型（例如血液流动模型），采用代理模型来加速模拟时间。 然而，参数排名和固定通常依赖于启发式方法，并且会随着具体应用或使用的模拟器而变化。 本研究通过利用多项式混沌展开（PCE）为多输出全局敏感性分析和正式参数可辨识性提供了一种创新的解决方案。 对于前者，我们使用降维技术高效地量化一维肺动脉血流动力学模型的时间序列敏感性。 我们考虑了Windkessel和结构化树边界条件。 然后，我们使用PCE构建似然置信区间，以正式评估参数可辨识性，并展示实验设计的变化如何改善可辨识性。 我们的工作提出了一种确定参数可辨识性的新方法，并利用一种常见的代理建模策略，以实现受偏微分方程控制的问题中的似然分析。 显示英文摘要

摘要： Computational inverse problems for biomedical simulators suffer from limited data and relatively high parameter dimensionality. This often requires sensitivity analysis, where parameters of the model are ranked based on their influence on the specific quantities of interest. This is especially important for simulators used to build medical digital twins, as the amount of data is typically limited. For expensive models, such as blood flow models, emulation is employed to expedite the simulation time. Parameter ranking and fixing using sensitivity analysis are often heuristic, though, and vary with the specific application or simulator used. The present study provides an innovative solution to this problem by leveraging polynomial chaos expansions (PCEs) for both multioutput global sensitivity analysis and formal parameter identifiability. For the former, we use dimension reduction to efficiently quantify time-series sensitivity of a one-dimensional pulmonary hemodynamics model. We consider both Windkessel and structured tree boundary conditions. We then use PCEs to construct profile-likelihood confidence intervals to formally assess parameter identifiability, and show how changes in experimental design improve identifiability. Our work presents a novel approach to determining parameter identifiability and leverages a common emulation strategy for enabling profile-likelihood analysis in problems governed by partial differential equations.