Coupled multiphysics modeling of aortic dissection

Computational modeling of the cardiovascular system plays an increasingly important role in biomedicine, as it allows for non-invasive investigations of the status-quo and studying the influence of different treatment options available. The goal is to incorporate patient-specific datasets to obtain socalled digital twins to increase relevance of virtual surgery and support clinical decision making. In this context, aortic dissection is particularly challenging, since the overall system behavior strongly depends on the interplay between tissue deformation and blood flow, giving rise to a fully coupled fluid-structure interaction problem. To account for the complex physics, several additional modeling aspects such as prestress, advanced constitutive models respecting fibre orientation and suitable boundary conditions for the fluid and solid phases have to be considered. Within this study, these special techniques are applied to a patient-specific dataset, for which first results are presented highlighting their relevance

A concept for aortic dissection with fluid‐structure‐crack interaction

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

Multi‐layered tissue models in patient‐specific simulations of aortic dissection

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

Coupled Multiphysics Modeling of Aortic Dissection

Computational modeling of the cardiovascular system plays an increasingly important role in biomedicine, as it allows for non-invasive investigations of the status-quo and studying the influence of different treatment options available. The goal is to incorporate patient-specific datasets to obtain socalled digital twins to increase relevance of virtual surgery and support clinical decision making. In this context, aortic dissection is particularly challenging, since the overall system behavior strongly depends on the interplay between tissue deformation and blood flow, giving rise to a fully coupled fluid-structure interaction problem. To account for the complex physics, several additional modeling aspects such as prestress, advanced constitutive models respecting fibre orientation and suitable boundary conditions for the fluid and solid phases have to be considered. Within this study, these special techniques are applied to a patient-specific dataset, for which first results are presented highlighting their relevance

Efficient split-step schemes for fluid–structure interaction involving incompressible generalised Newtonian flows

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

Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow

[EN] In numerous engineering applications, such as polymer or blood flow, the dependence of fluid viscosity on the local shear rate plays an important role. Standard techniques using inf-sup stable finite elements lead to saddle-point systems posing a challenge even for state-ofthe-art solvers and preconditioners. Alternatively, projection schemes or time-splitting methods decouple equations for velocity and pressure, resulting in easier to solve linear systems. Although pressure and velocity correction schemes of high-order accuracy are available for Newtonian fluids, the extension to generalised Newtonian fluids is not a trivial task. Herein, we present a split-step scheme based on an explicit-implicit treatment of pressure, viscosity and convection terms, combined with a pressure Poisson equation with fully consistent boundary conditions. Then, using standard equal-order finite elements becomes possible. Stability, flexibility and efficiency of the splitting scheme is showcased in two challenging applications involving aortic aneurysm flow and human phonation.The authors gratefully acknowledge Graz University of Technology for the financial support of the Lead-project: Mechanics, Modeling and Simulation of Aortic Dissection.Schussnig, R.; Pacheco, D.; Kaltenbacher, M.; Fries, T. (2022). Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 335-344. https://doi.org/10.4995/YIC2021.2021.12217OCS33534

An efficient split-step framework for non-Newtonian incompressible flow problems with consistent pressure boundary conditions

Incompressible flow problems with nonlinear viscosity, as they often appear in biomedical and industrial applications, impose several numerical challenges related to regularity requirements, boundary conditions, matrix preconditioning, among other aspects. In particular, standard split-step or projection schemes decoupling velocity and pressure are not as efficient for generalised Newtonian fluids, since the additional terms due to the non-zero viscosity gradient couple all velocity components again. Moreover, classical pressure correction methods are not consistent with the non-Newtonian setting, which can cause numerical artifacts such as spurious pressure boundary layers. Although consistent reformulations have been recently developed, the additional projection steps needed for the viscous stress tensor incur considerable computational overhead. In this work, we present a new time-splitting framework that handles such important issues, leading to an efficient and accurate numerical tool. Two key factors for achieving this are an appropriate explicit–implicit treatment of the viscous and convective nonlinearities, as well as the derivation of a pressure Poisson problem with fully consistent boundary conditions and finite-element-suitable regularity requirements. We present first- and higher-order stepping schemes tailored for this purpose, as well as various numerical examples showcasing the stability, accuracy and efficiency of the proposed framework

Robust stabilised finite element solvers for generalised Newtonian fluid flows

Various materials and solid-fluid mixtures of engineering and biomedical interest can be modelled as generalised Newtonian fluids, as their apparent viscosity depends locally on the flow field. Despite the particular features of such models, it is common practice to combine them with numerical techniques originally conceived for Newtonian fluids, which can bring several issues such as spurious pressure boundary layers, unsuitable natural boundary conditions and coupling terms spoiling the efficiency of nonlinear solvers and preconditioners. In this work, we present a finite element framework dealing with such issues while maintaining low computational cost and simple implementation. The building blocks of our algorithm are (i) an equal-order stabilisation method preserving consistency even for lowest-order discretisations, (ii) robust extrapolation of velocities in the time-dependent case to decouple the rheological law from the overall system, (iii) adaptive time step selection and (iv) a fast physics-based preconditioned Krylov subspace solver, to tackle the relevant range of discretisation parameters including highly varying viscosity. Selected numerical experiments are provided demonstrating the potential of our approach in terms of robustness, accuracy and efficiency for problems of practical interest

Fully integrated mesh generation in fluid-structure interaction

In fluid-structure interaction (FSI), the fluid and solid domains are permantently changing, coupled along a time-dependent, moving fluid-structure interface. The update of the fluid domain, i.e., in the numerical context, the mesh update is critical for robust and efficient simulations. Herein, we propose to inherently embed the mesh generation into the simulation.The FSI domain is defined based on structured building blocks that imply all the relevant information needed for the automatic mesh generation: Topology, geometry, and grading information. Transfinite maps play a crucial role for the definition of sub-meshes with any desired order and resolution in each building block. In every time step, a new mesh is generated, taking into account the deforming FSI interface. This generation is fast compared to the overall work load in each time step which is still dominated by the (iterative) solutions of the systems of equations. It is also very robust and removes any mesh entanglement by construction provided that suitable building blocks are selected once initially. Numerical results confirm the success of the proposed FSI strategy with integrated mesh generation

Higher-order block-structured hex meshing of tubular structures

Numerical simulations of the cardiovascular system are growing in popularity due to the increasing availability of computational power, and their proven contribution to the understanding of pathodynamics and validation of medical devices with in-silico trials as a potential future breakthrough. Such simulations are performed on volumetric meshes reconstructed from patient-specific imaging data. These meshes are most often unstructured, and result in a brutally large amount of elements, significantly increasing the computational complexity of the simulations, whilst potentially adversely affecting their accuracy. To reduce such complexity, we introduce a new approach for fully automatic generation of higher-order, structured hexahedral meshes of tubular structures, with a focus on healthy blood vessels. The structures are modeled as skeleton-based convolution surfaces. From the same skeleton, the topology is captured by a block-structure, and the geometry by a higher-order surface mesh. Grading may be induced to obtain tailored refinement, thus resolving, e.g., boundary layers. The volumetric meshing is then performed via transfinite mappings. The resulting meshes are of arbitrary order, their elements are of good quality, while the spatial resolution may be as coarse as needed, greatly reducing computing time. Their suitability for practical applications is showcased by a simulation of physiological blood flow modelled by a generalised Newtonian fluid in the human aorta