While the potential groundbreaking role of mathematical modeling in electrophysiology has been demonstrated for therapies like cardiac resynchronization or catheter ablation, its extensive use in clinics is prevented by the need of an accurate customized conductivity identification. Data assimilation techniques are, in general, used to identify parameters that cannot be measured directly, especially in patient-specific settings. Yet, they may be computationally demanding. This conflicts with the clinical timelines and volumes of patients to analyze. In this paper, we adopt a model reduction technique, developed by F. Chinesta and his collaborators in the last 15 years, called Proper Generalized Decomposition (PGD), to accelerate the estimation of the cardiac conductivities required in the modeling of the cardiac electrical dynamics. Specifically, we resort to the Monodomain Inverse Conductivity Problem (MICP) deeply investigated in the literature in the last five years. We provide a significant proof of concept that PGD is a breakthrough in solving the MICP within reasonable timelines. As PGD relies on the offline/online paradigm and does not need any preliminary knowledge of the high-fidelity solution, we show that the PGD online phase estimates the conductivities in real-time for both two-dimensional and three-dimensional cases, including a patient-specific ventricle.

虽然已经证明了数学建模在电生理学中对诸如心脏再同步或导管消融等疗法的潜在突破性作用，但由于需要精确的定制电导率识别，因此无法在临床中广泛使用它。通常，数据同化技术用于识别无法直接测量的参数，尤其是在特定于患者的环境中。但是，它们可能在计算上要求很高。这与临床时间表和要分析的患者数量相矛盾。在本文中，我们采用了F. Chinesta及其合作者在过去15年中开发的模型简化技术，称为适当的广义分解（PGD），以加快对心脏电动力学建模所需的心脏电导率的估算。 。特别，在过去的五年中，我们采用文献中深入研究的单域逆电导率问题（MICP）。我们提供了一个重要的概念证明，PGD是在合理的时间内解决MICP的突破。由于PGD依赖于脱机/在线范例，并且不需要任何有关高保真度解决方案的初步知识，因此我们证明PGD在线阶段可以实时估算二维和三维情况下的电导率，包括特定于患者的心室。