Modelling of fluid–structure interactions with the space–time finite elements: Arterial fluid mechanics

Abstract

SUMMARYThe stabilized space-time fluid-structure interaction (SSTFSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T AFSM) are applied to FSI modelling in arterial fluid mechanics. Modelling of flow in arteries with aneurysm is emphasized. The SSTFSI techniques used are based on the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation and include the enhancements introduced recently by the T AFSM to increase the scope, accuracy, robustness and efficiency of these techniques. The arterial structures can be modelled with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element can be made of linearly elastic or hyperelastic material. Test computations are presented for cerebral and abdominal aortic aneurysms and carotid-artery bifurcation, where the arterial geometries used in the computations are close approximations to the patient-specific image-based data.

Computational vascular fluid–structure interaction: methodology and application to cerebral aneurysms

“…6, the models are superposed in the configurations corresponding to low diastole and peak systole for better visualization of the relative displacement results. The relative displacement predicted is quite modest and is in good agreement with the observed vessel motions during aneurysm surgery in the clinical practice of one of the authors and predicted in computations by other researchers (see, e.g., Tezduyar et al 2007;Torii et al 2008Torii et al , 2009). Figure 7 shows a distribution of principal in-plane strain (Green-Lagrange strain measure is employed) at peak systole.…”

“…Numerous advances in the simulation technology were proposed, such as imposition of physiologically-realistic outflow boundary conditions (Formaggia et al 2001;Lagana et al 2002;VignonClementel et al 2006), simulation of stenting technology in the context of cerebral aneurysms (Appanaboyina et al 2009) and coronary arteries (Zunino et al 2009), optimization of cardiovascular geometries for surgical treatment (Marsden et al 2008), inclusion of the effects of wall elasticity Bazilevs et al 2006Bazilevs et al , 2008Tezduyar et al 2007;Torii et al 2008Torii et al , 2009, and growth and remodeling (Figueroa et al 2009) in the simulations. Nowadays, the state-of-the-art in computational hemodynamics involves fully coupled fluid-structure patient-specific simulations of large portions of the human cardiovascular system.…”

Geometric multiscale modeling of the cardiovascular system, between theory and practice

“…In this case, the schemes feature in general poor convergence properties due to the added mass effect, that predicts a breakdown of performances when the values of the densities of fluid and structure are close as it happens in hemodynamics [10,39,69,76,137]. Alternatively, one could consider space-time finite elements, see, e.g., [17,187], or the iso-geometric analysis, see [15].…”

Inexact accurate partitioned algorithms for fluid–structure interaction problems with finite elasticity in haemodynamics

“…This leads to the solution of a fluid-structure interaction (FSI) problem in three-dimensional (3D) real geometries [44,7,18,47,15,3,20,21]. To capture the complex dynamics characterizing such a problem, non-linear fluid and structure models have to be taken into account, leading to a complex non-linear coupled problem, formed also by the fluid domain subproblem when the fluid equations are written in Arbitrary Lagrangian-Eulerian (ALE) formulation [29,14].…”