Multiscale and monolithic arbitrary Lagrangian–Eulerian finite element method for a hemodynamic fluid-structure interaction problem involving aneurysms

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.