Cardio-mechanical models can be used to support clinical decision-making. Unfortunately, the substantial computational effort involved in many cardiac models hinders their application in the clinic, despite the fact that they may provide valuable information. In this work, we present a probabilistic reduced-order modeling (ROM) framework to dramatically reduce the computational effort of such models while providing a credibility interval. In the online stage, a fast-to-evaluate generalized one-fiber model is considered. This generalized one-fiber model incorporates correction factors to emulate patient-specific attributes, such as local geometry variations. In the offline stage, Bayesian inference is used to calibrate these correction factors on training data generated using a full-order isogeometric cardiac model (FOM). A Gaussian process is used in the online stage to predict the correction factors for geometries that are not in the training data. The proposed framework is demonstrated using two examples. The first example considers idealized left-ventricle geometries, for which the behavior of the ROM framework can be studied in detail. In the second example, the ROM framework is applied to scan-based geometries, based on which the application of the ROM framework in the clinical setting is discussed. The results for the two examples convey that the ROM framework can provide accurate online predictions, provided that adequate FOM training data is available. The uncertainty bands provided by the ROM framework give insight into the trustworthiness of its results. Large uncertainty bands can be considered as an indicator for the further population of the training data set.

翻译：心脏力学模型可用于辅助临床决策。遗憾的是，尽管此类模型可能提供有价值的信息，但许多心脏模型所涉及的大量计算工作阻碍了其在临床中的应用。在本工作中，我们提出了一种概率降阶建模（ROM）框架，可在提供可信区间的同时，显著降低此类模型的计算成本。在线阶段采用一个快速评估的广义单纤维模型。该广义单纤维模型通过引入修正因子来模拟患者特异性属性，例如局部几何形状变化。离线阶段则采用贝叶斯推断方法，基于全阶等几何心脏模型（FOM）生成的训练数据对这些修正因子进行校准。在线阶段使用高斯过程来预测训练数据中未包含的几何形状所对应的修正因子。通过两个示例展示了所提出框架的应用。第一个示例考虑理想化的左心室几何形状，借此可详细研究ROM框架的行为特性。第二个示例将ROM框架应用于基于扫描的几何形状，并在此基础上讨论了ROM框架在临床环境中的应用前景。两个示例的结果表明，只要具备充足的FOM训练数据，ROM框架能够提供精确的在线预测。该框架提供的不确定性区间有助于理解其结果的可靠性程度。较大的不确定性区间可视为需要进一步扩充训练数据集的指示信号。