Modelling the cardiac electrophysiology entails dealing with the uncertainties related to the input parameters such as the heart geometry and the electrical conductivities of the tissues, thus calling for an uncertainty quantification (UQ) of the results. Since the chambers of the heart have different shapes and tissues, in order to make the problem affordable, here we focus on the left ventricle with the aim of identifying which of the uncertain inputs mostly affect its electrophysiology. In a first phase, the uncertainty of the input parameters is evaluated using data available from the literature and the output quantities of interest (QoIs) of the problem are defined. According to the polynomial chaos expansion, a training dataset is then created by sampling the parameter space using a quasi-Monte Carlo method whereas a smaller independent dataset is used for the validation of the resulting metamodel. The latter is exploited to run a global sensitivity analysis with nonlinear variance-based indices and thus reduce the input parameter space accordingly. Thereafter, the uncertainty probability distribution of the QoIs are evaluated using a direct UQ strategy on a larger dataset and the results discussed in the light of the medical knowledge.

中文翻译：

---

左心室电生理模型的敏感性分析

心脏电生理建模需要处理与输入参数相关的不确定性，例如心脏几何形状和组织的电导率，因此需要对结果进行不确定性量化 (UQ)。由于心脏的腔室具有不同的形状和组织，为了使问题能够负担得起，这里我们将重点放在左心室，目的是确定哪些不确定的输入主要影响其电生理。在第一阶段，使用文献中可用的数据评估输入参数的不确定性，并定义问题的感兴趣的输出量 (QoI)。根据多项式混沌展开式，然后通过使用准蒙特卡罗方法对参数空间进行采样来创建训练数据集，而较小的独立数据集用于验证生成的元模型。后者被用来运行基于非线性方差的指数的全局敏感性分析，从而相应地减少输入参数空间。此后，在更大的数据集上使用直接 UQ 策略评估 QoI 的不确定性概率分布，并根据医学知识讨论结果。