Fluid-solid interaction (FSI) phenomena play an important role in many biomedical engineering applications. While FSI techniques and models have enabled detailed computational simulations of flow and tissue motion, the application of FSI can present challenges, particularly when data for constraining models is sparse and/or when fast computational simulations are required for assessment. In this paper, we propose a novel method for flexible-wall fluid dynamics in an ALE framework applicable for cardiovascular applications where adaptive fluid motion that emulates patient data is required. Efficiency and model simplicity are gained by a physics-based reduction to solid membrane formulations at the fluid-tissue interface combined with a Galerkin projection to a subspace spanned by boundary motion modes, leveraging snapshots observed from imaging data by use of Proper Orthogonal Decomposition (POD). The resulting fluid-reduced-solid interaction (FrSI) model is verified for a series of examples, illustrating efficacy and efficiency. Focusing on an idealized left ventricle model, we demonstrate homogenization of transmural active stress along with the capacity to accommodate prestress in the FrSI model, accounting for whole cycle mechanics by coupling to 0D pre- and afterload models (showing end-diastolic and end-systolic projected endocardial surface position errors of less than 1.5% and 3.5%, respectively). Further, we present strategies to compensate for the inherent approximation errors of the FrSI model, allowing for minimizing both the integral and spatial error between reduced and full-order model by re-calibrating parameters that govern diastolic and systolic function. Finally, the ability of FrSI to extrapolate to impaired system states (increased afterload, localized region of infarct) is shown, providing a simple yet effective strategy to enhance the POD subspace to further reduce errors. These results illustrate the potential of FrSI to streamline the simulation of hemodynamics in the heart and cardiovascular system.

中文翻译：

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流体简化固体相互作用（FrSI）：心血管应用中基于物理和投影的模型简化

流固相互作用（FSI）现象在许多生物医学工程应用中发挥着重要作用。虽然 FSI 技术和模型已经能够对流动和组织运动进行详细的计算模拟，但 FSI 的应用可能会带来挑战，特别是当约束模型的数据稀疏和/或需要快速计算模拟进行评估时。在本文中，我们提出了一种在 ALE 框架中实现柔性壁流体动力学的新方法，适用于需要模拟患者数据的自适应流体运动的心血管应用。通过在流体-组织界面处对固体膜配方进行基于物理的简化，并结合对边界运动模式跨越的子空间的伽辽金投影，利用本征正交分解 (POD) 从成像数据中观察到的快照，获得了效率和模型简单性）。由此产生的流体减少固体相互作用 (FrSI) 模型经过一系列示例的验证，说明了功效和效率。着眼于理想化的左心室模型，我们展示了透壁主动应力的均质化以及 FrSI 模型中适应预应力的能力，通过耦合到 0D 前负荷和后负荷模型（显示舒张末期和收缩末期）来解释整个循环力学。预计心内膜表面位置误差分别小于 1.5% 和 3.5%）。此外，我们提出了补偿 FrSI 模型固有近似误差的策略，通过重新校准控制舒张和收缩功能的参数来最小化降阶模型和全阶模型之间的积分和空间误差。最后，显示了 FrSI 外推受损系统状态（后负荷增加、梗塞局部区域）的能力，提供了一种简单而有效的策略来增强 POD 子空间以进一步减少错误。这些结果说明了 FrSI 简化心脏和心血管系统血流动力学模拟的潜力。