Zingaro Alberto, Bucelli Michele, Fumagalli Ivan, Dede' Luca, Quarteroni Alfio
MOX, Laboratory of Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy.
ELEM Biotech S.L., Barcelona, Spain.
Int J Numer Method Biomed Eng. 2023 Dec;39(12):e3767. doi: 10.1002/cnm.3767. Epub 2023 Aug 24.
A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement. During such phases, both atrioventricular and semilunar valves are closed: consequently, the ventricular pressure may not be uniquely defined, and spurious oscillations may arise in numerical simulations. These oscillations can strongly affect valve dynamics models driven by the blood flow, making unlikely to recovering physiological dynamics. Hence, prescribed opening and closing times are usually employed, or the isovolumetric phases are neglected altogether. In this article, we propose a suitable modification of the Resistive Immersed Implicit Surface (RIIS) method (Fedele et al., Biomech Model Mechanobiol 2017, 16, 1779-1803) by introducing a reaction term to correctly capture the pressure transients during isovolumetric phases. The method, that we call Augmented RIIS (ARIIS) method, extends the previously proposed ARIS method (This et al., Int J Numer Methods Biomed Eng 2020, 36, e3223) to the case of a mesh which is not body-fitted to the valves. We test the proposed method on two different benchmark problems, including a new simplified problem that retains all the characteristics of a heart cycle. We apply the ARIIS method to a fluid dynamics simulation of a realistic left heart geometry, and we show that ARIIS allows to correctly simulate isovolumetric phases, differently from standard RIIS method. Finally, we demonstrate that by the new method the cardiac valves can open and close without prescribing any opening/closing times.
心脏功能的计算流体动力学建模中的一个主要挑战是，当血流动力学问题由规定的边界位移驱动时，对等容相进行模拟。在这些阶段，房室瓣和半月瓣均处于关闭状态：因此，心室压力可能无法唯一确定，并且在数值模拟中可能会出现虚假振荡。这些振荡会强烈影响由血流驱动的瓣膜动力学模型，使得恢复生理动力学变得不太可能。因此，通常采用规定的打开和关闭时间，或者完全忽略等容相。在本文中，我们通过引入一个反应项来正确捕捉等容相期间的压力瞬变，对电阻浸入隐式表面（RIIS）方法（费代莱等人，《生物力学模型与分子生物力学》，2017年，16卷，1779 - 1803页）提出了一种合适的改进。我们将该方法称为增强RIIS（ARIIS）方法，它将先前提出的ARIS方法（西斯等人，《国际数值方法在生物医学工程中的应用》，2020年，36卷，e3223）扩展到网格未贴合瓣膜的情况。我们在两个不同的基准问题上测试了所提出的方法，包括一个保留了心动周期所有特征的新简化问题。我们将ARIIS方法应用于一个真实左心几何形状的流体动力学模拟，并表明与标准RIIS方法不同，ARIIS能够正确模拟等容相。最后，我们证明通过新方法，心脏瓣膜可以在不规定任何打开/关闭时间的情况下打开和关闭。
