Numerical investigation of abdominal aortic aneurysm hemodynamics using the reduced unified continuum formulation for vascular fluid-structure interaction

Abstract

We recently demonstrated the reduction of the unified continuum and variational multiscale formulation to a computationally efficient fluid-structure interaction (FSI) formulation via three sound modeling assumptions pertaining to the vascular wall. Similar to the coupled momentum method introduced by Figueroa et al., the resulting semi-discrete formulation yields a monolithically coupled FSI system posed in an Eulerian frame of reference with only a minor modification of the fluid boundary integral. To achieve uniform second-order temporal accuracy and user-controlled high-frequency algorithmic damping, we adopt the generalized-α method for uniform temporal discretization of the entire coupled system. In conjunction with a fully consistent, segregated predictor multi-corrector algorithm preserving the block structure of the incompressible Navier-Stokes equations in the implicit solver's associated linear system, a three-level nested block preconditioner is adopted for improved representation of the Schur complement. In this work, we apply our reduced unified continuum formulation to an appropriately prestressed patient-specific abdominal aortic aneurysm and investigate the effects of varying spatial distributions of wall properties on hemodynamic and vascular wall quantities of interest.

Validation of the Reduced Unified Continuum Formulation Against In Vitro 4D-Flow MRI

“…21 The RUC formulation, which achieves monolithic coupling of the fluid and solid subproblems in an Eulerian frame, was found to offer computational cost as low as 1.3 times that of rigid-walled CFD simulations. 22 While the coupled momentum method (CMM) 7 similarly embeds a linear elastic membrane into an Eulerian fluid subproblem, key theoretical and numerical differences exist with regard to the fluid-solid coupling, spatiotemporal discretization, vascular wall dynamics, and linear solver technology. 21 In our verification against Womersley's deformable wall theory, we demonstrated notable agreement between analytical and numerical solutions.…”