随机电极位置下ECG的快速准确不确定度量化
Fast and Accurate Uncertainty Quantification for the ECG with Random Electrodes Location
摘要：
标准心电图（ECG）是对某些给定位置的身体电位的逐点评估。这些位置具有不确定性，可能因患者而异，甚至可能因单个患者而异。在这项工作中，我们估计的不确定性，在心电图时，来自前向bidomain模型的电极位置不确定引起的。为了避免在整个躯干的bidomain模型的解决方案相关联的高计算成本，我们提出了一种低秩的方法来解决不确定性量化（UQ）问题。更准确地说，我们利用稀疏的心电图和铅域论，将其转化为一组确定性的，与时间无关的问题，其解决方案是最终用来评估期望和协方差的心电图。我们评估的方法与数值实验在一个简单的几何形状。
英文摘要：
The standard electrocardiogram (ECG) is a point-wise evaluation of the body potential at certain given locations. These locations are subject to uncertainty and may vary from patient to patient or even for a single patient. In this work, we estimate the uncertainty in the ECG induced by uncertain electrode positions when the ECG is derived from the forward bidomain model. In order to avoid the high computational cost associated to the solution of the bidomain model in the entire torso, we propose a low-rank approach to solve the uncertainty quantification (UQ) problem. More precisely, we exploit the sparsity of the ECG and the lead field theory to translate it into a set of deterministic, time-independent problems, whose solution is eventually used to evaluate expectation and covariance of the ECG. We assess the approach with numerical experiments in a simple geometry.
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