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Modeling an aortic dissection represents a particular challenge from a numerical perspective, especially when it comes to the interaction between solid (aortic wall) and liquid (blood flow). The complexity of patient‐specific simulations requires a variety of parameters, modeling assumptions and simplifications that currently hinder their routine use in clinical settings. We present a numerical framework that captures, among other things, the layer‐specific anisotropic properties of the aortic wall, the non‐Newtonian behavior of blood, patient‐specific geometry, and patient‐specific flow conditions. We compare hemodynamic indicators and stress measurements in simulations with increasingly complex material models for the vessel tissue ranging from rigid walls to anisotropic hyperelastic materials. We find that for the present geometry and boundary conditions, rigid wall simulations produce different results than fluid–structure interaction simulations. Considering anisotropic fiber contributions in the tissue model, stress measurements in the aortic wall differ, but shear stress‐based biomarkers are less affected. In summary, the increasing complexity of the tissue model enables capturing more details. However, an extensive parameter set is also required. Since the simulation results depend on these modeling choices, variations can lead to different recommendations in clinical applications. [ABSTRACT FROM AUTHOR]

The modeling and simulation of fluid‐structure interaction (FSI) involve the two‐way coupling of a fluid flow and a deforming structure. The fluid exerts a load on the structure, the structure deforms, and, hence, the fluid flow changes, which leads to an altered loading on the structure. To accomplish this coupling, the fluid domain has to be updated after each time step, leading to a change in the fluid mesh. Various mesh update methods have been presented where an initial mesh is generated and then updated after each time step. Each method comes with different levels of complexity and has its own advantages and disadvantages. Herein, FSI simulations with fully integrated mesh generation, rather than updates, are proposed. Instead of updating the mesh at each time step, a new mesh for the fluid domain is generated based on the deformation of the solid domain. An advanced structured meshing algorithm, based on a block structure, enables this integrated mesh generation approach. An initial set of coarse‐scale conforming blocks is generated by the user, representing the topology and rough initial position of the solid and the fluid. Further information is the exact geometry at the boundary and the deformed position of the fluid‐structure interface, plus grading information to obtain a high‐quality fluid mesh. Transfinite maps are used to generate elements inside the blocks with any desired resolution and order. [ABSTRACT FROM AUTHOR]

In aortic dissections blood flows not only in the regular, true lumen but also between separated lamellae within the media of the aortic wall, in the so‐called false lumen. Both lumina are separated by a dissection membrane, which may move substantially during the cardiac cycle, linking blood flow and vessel deformation. We employ strongly coupled fluid‐structure interaction simulations incorporating an anisotropic, fiber‐reinforced, hyperelastic continuum including layer‐specific tissue parameters. [ABSTRACT FROM AUTHOR]

The numerical modeling of aortic dissection (AD) is a particularly challenging biomechanical application, since the underlying coupling of tissue deformation and blood flow has to be considered, leading to a fluid‐structure interaction (FSI) problem. To improve clinical relevance, patient‐specific data and state‐of‐the‐art constitutive models have to be incorporated. Computational methods to consider for tissue prestress and fiber orientation are presented herein. [ABSTRACT FROM AUTHOR]

In aortic dissection, the layers composing the aorta rupture, allowing blood to enter the vessel wall. This process is modeled applying a monolithic fluid‐structure interaction framework, formulating the Navier‐Stokes equations for incompressible flows as well as the mixed finite strain elastodynamics equations in the Lagrangian frame of reference. Continuous test‐ and trial function spaces are employed in the whole domain, rendering the coupling straightforward. Within this contribution, a predefined function indicating failure is used to convert solid to fluid elements, thereby mimicing tissue rupture. [ABSTRACT FROM AUTHOR]

• Split-step fluid-structure interaction scheme allowing equal-order interpolation. • An added-mass-stable, semi-implicit, relaxed coupling yields fast convergence. • Incompressible generalised Newtonian fluid flows are considered. • A pressure Poisson equation with fully consistent boundary conditions is derived. • Performance is shown via exact solutions, a benchmark and flow through an aneurysm. Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the engineering design process. Therefore, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluid models, as used, e.g., for blood or polymer flows. In these fluids, subtle differences in the local shear rate can have a drastic impact on the flow and hence on the coupled problem. There, existing (semi-) implicit solution strategies based on split-step or projection schemes for Newtonian fluids are not applicable, while extensions to non-Newtonian fluids can lead to substantial numerical overhead depending on the chosen fluid solver. To address these shortcomings, we present here a higher-order accurate, added-mass-stable fluid–structure interaction scheme centered around a split-step fluid solver. We compare several implicit and semi-implicit variants of the algorithm and verify convergence in space and time. Numerical examples show good performance in both benchmarks and an idealised setting of blood flow through an abdominal aortic aneurysm considering physiological parameters. [ABSTRACT FROM AUTHOR]

Fluid–structure interaction (FSI) incorporates effects of fluid flows on deformable solids and vice versa. Complex biomedical problems in clinical applications continue to challenge numerical algorithms, as incorporating the underlying mathematical methods can impair the solvers' performance drastically. In this regard, we extend a semi-implicit, pressure Poisson-based FSI scheme for non-Newtonian fluids to incorporate several models crucial for biomechanical applications. We consider Windkessel outlets to account for neglected downstream flow regions, realistic material fibre orientation and stressed reference geometries reconstructed from medical image data. Additionally, we incorporate vital numerical aspects, namely, stabilisations to counteract dominant convective effects and instabilities triggered by re-entrant flow, while a major contribution of this work is combining interface quasi-Newton methods with Robin coupling conditions to accelerate the partitioned (semi-)implicit coupling scheme. The numerical examples presented herein aim to finally bridge the gap to real-world applications, considering state-of-the-art modelling aspects and physiological parameters. FSI simulations of blood flow in an iliac bifurcation derived from medical images and vocal folds deforming in the process of human phonation demonstrate the versatility of the framework. • FSI scheme for incompressible non-Newtonian fluids and hyperelastic continua. • Semi-implicit Robin- and IQN-ILS-accelerated, pressure-Poisson-based coupling. • Consistently incorporates Windkessel models, backflow- and GLS stabilisations. • Considers tissue models with realistic fibre orientation in prestressed geometries. • Versatility and robustness is shown in aortic blood flow and human phonation. [ABSTRACT FROM AUTHOR]