In this paper, a multiscale and monolithic arbitrary Lagrangian–Eulerian finite element method (ALE-FEM) is developed for a multiscale hemodynamic fluid-structure interaction (FSI) problem involving an aortic aneurysm growth to quantitatively predict the long-term aneurysm risk in the cardiovascular environment, where the blood fluid profile, the hyperelastic arterial wall, and the aneurysm pathophysiology are integrated into one hemodynamic FSI model, together with no-slip interface conditions between the blood fluid and the arterial wall. Additionally, two different time scales are involved: a fast time scale for the blood fluid-arterial wall interaction process in terms of seconds, and a slow time scale for the biological (abdominal aortic aneurysms (AAA) progression) process in terms of years. Two types of multiscale methods, the heterogeneous multiscale method (HMM) and the seamless multiscale method (SMM), are employed to tackle different time scales while the arbitrary Lagrangian–Eulerian (ALE) method is adopted to generate the moving blood fluid meshes that adapt to the deformation of the hyperelastic arterial wall all the time, based on which the variable time-stepping/mixed finite element method (FEM) is defined in the ALE frame to discretize the developed hemodynamic FSI model involving aneurysms. A two-dimensional schematic blood fluid-artery-aneurysm interaction example and a three-dimensional realistic cardiovascular FSI problem with an aortic aneurysm growth based upon the patients' CT scan data are simulated to validate the accuracy and the efficiency of our developed HMM(SMM)/ALE-FEM, and a medically reasonable long-term prediction is obtained for the aneurysm growth as well.

本文针对涉及主动脉瘤增长的多尺度血流动力学-结构相互作用（FSI）问题，开发了一种多尺度和整体式的任意拉格朗日-欧拉有限元方法（ALE-FEM），以定量地预测长期主动脉瘤的风险心血管环境，其中血液流体的轮廓，超弹性动脉壁和动脉瘤的病理生理学被整合到一个血液动力学FSI模型中，以及血液和动脉壁之间的无滑动界面条件。另外，涉及两种不同的时间标度：以秒为单位的用于血液-动脉壁相互作用过程的快速时间标度，以秒为单位的用于生物学（腹主动脉瘤（AAA）进展）过程的慢速标度。两种多尺度方法，分别采用异质多尺度方法（HMM）和无缝多尺度方法（SMM）来处理不同的时间尺度，而采用任意拉格朗日-欧拉（ALE）方法来生成适应超弹性变形的运动血液网格动脉壁始终存在，在此基础上，在ALE框架中定义了可变时间步长/混合有限元方法（FEM），以离散化已开发的涉及动脉瘤的血液动力学FSI模型。基于患者的CT扫描数据，模拟了二维示意性血液-动脉-动脉瘤相互作用示例和具有主动脉瘤生长的三维逼真的心血管FSI问题，以验证我们开发的HMM（SMM）的准确性和效率）/ ALE-FEM，