The influence of geometric imperfections in cardiovascular FSI simulations

Abstract We present a study of the fluid–structure interaction in an idealized end-to-end anastomosis of a vascular bypass-graft and an artery. Special attention is paid to the impact of geometric imperfections in the artery and the flow path of the upstream vessel segment on the hemodynamics. A partitioned solution approach is applied and developed further to solve the coupled problem in an implicit manner. To stabilize and accelerate the convergence of the staggered coupling iterations, an interface quasi-Newton least squares method is applied. While the finite volume method is used for the fluid mechanics subproblem, high-order finite elements serve to discretize the structural subproblem. A convergence study shows the efficiency of the high-order elements in the context of nearly incompressible, anisotropic materials used to model circular and irregular-shaped segments of an artery. The fluid–structure interaction simulations reveal a dominant influence of the upstream vessel’s curvature, which, however, decays rapidly in straight sections where the influence of geometric imperfections is dominant. Based on the proposed simulation approach, hemodynamic parameters such as the oscillating shear index can be directly linked to the shape and the intensity of the imperfections.

[1]  T. Tezduyar,et al.  Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling , 2008 .

[2]  Z. Yosibash,et al.  p‐FEMs for hyperelastic anisotropic nearly incompressible materials under finite deformations with applications to arteries simulation , 2011 .

[3]  J. Reddy,et al.  The Finite Element Method in Heat Transfer and Fluid Dynamics , 1994 .

[4]  Manil Suri,et al.  Analytical and computational assessment of locking in the hp finite element method , 1996 .

[5]  T. Tezduyar,et al.  Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique , 2008 .

[6]  Marcel König,et al.  A flexible C++ framework for the partitioned solution of strongly coupled multifield problems , 2016, Comput. Math. Appl..

[7]  Charles A. Taylor,et al.  A coupled momentum method for modeling blood flow in three-dimensional deformable arteries , 2006 .

[8]  Tayfun E. Tezduyar,et al.  Estimation of element-based zero-stress state for arterial FSI computations , 2014 .

[9]  Gerhard A Holzapfel,et al.  A three-dimensional finite element model for arterial clamping. , 2001, Journal of biomechanical engineering.

[10]  Guang-Zhong Yang,et al.  Fluid-structure interaction analysis of a patient-specific right coronary artery with physiological velocity and pressure waveforms , 2009 .

[11]  S. Sherwin,et al.  Does low and oscillatory wall shear stress correlate spatially with early atherosclerosis? A systematic review , 2013, Cardiovascular research.

[12]  Thomas J. R. Hughes,et al.  On the one-dimensional theory of blood flow in the larger vessels , 1973 .

[13]  Z. Yosibash,et al.  Artery active mechanical response: High order finite element implementation and investigation , 2012 .

[14]  H. Emdad,et al.  Numerical simulation of blood flow in a flexible stenosed abdominal real aorta , 2011 .

[15]  Toshio Kobayashi,et al.  Influence of wall elasticity in patient-specific hemodynamic simulations , 2007 .

[16]  Alexander Düster,et al.  Partitioned coupling strategies for multi-physically coupled radiative heat transfer problems , 2015, J. Comput. Phys..

[17]  K. Bathe,et al.  Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction , 2009 .

[18]  A. Düster,et al.  Convergence acceleration for partitioned simulations of the fluid-structure interaction in arteries , 2016 .

[19]  A. Ibrahimbegovic.  Nonlinear Solid Mechanics , 2009 .

[20]  R. Ogden,et al.  A robust anisotropic hyperelastic formulation for the modelling of soft tissue. , 2014, Journal of the mechanical behavior of biomedical materials.

[21]  J. Vierendeels,et al.  Performance of partitioned procedures in fluid-structure interaction , 2010 .

[22]  Kenji Takizawa,et al.  FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta , 2014 .

[23]  Kenji Takizawa,et al.  Patient-Specific Cardiovascular Fluid Mechanics Analysis with the ST and ALE-VMS Methods , 2014 .

[24]  Ernst Rank,et al.  The p‐version of the finite element method for three‐dimensional curved thin walled structures , 2001 .

[25]  P. Wriggers.  Nonlinear Finite Element Methods , 2008 .

[26]  Tayfun E. Tezduyar,et al.  Wall shear stress calculations in space–time finite element computation of arterial fluid–structure interactions , 2010 .

[27]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[28]  Tayfun E. Tezduyar,et al.  Space–time finite element computation of arterial fluid–structure interactions with patient‐specific data , 2010 .

[29]  Ivo Babuška,et al.  The p-Version of the Finite Element Method for Parabolic Equations. Part 1 , 1981 .

[30]  Ernst Rank,et al.  The p‐version of the finite element method for domains with corners and for infinite domains , 1990 .

[31]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[32]  Vom Fachbereich,et al.  Finite-Elemente Berechnung inelastischer Kontinua Interpretation als Algebro-Differentialgleichungssysteme , 2003 .

[33]  Barna A. Szabó,et al.  Quasi-regional mapping for the p-version of the finite element method , 1997 .

[34]  Wolfgang A. Wall,et al.  Coupling strategies for biomedical fluid–structure interaction problems , 2010 .

[35]  Foad Kabinejadian,et al.  Compliant model of a coupled sequential coronary arterial bypass graft: effects of vessel wall elasticity and non-Newtonian rheology on blood flow regime and hemodynamic parameters distribution. , 2012, Medical engineering & physics.

[36]  Toshio Kobayashi,et al.  Computer modeling of cardiovascular fluid-structure interactions with the deforming-spatial-domain/stabilized space-time formulation , 2006 .

[37]  Alexander Düster,et al.  Cardiovascular fluid-structure interaction: A partitioned approach utilizing the p-FEM , 2014 .

[38]  Jan Vierendeels,et al.  Multi-solver algorithms for the partitioned simulation of fluid–structure interaction , 2011 .

[39]  Ming-Chen Hsu,et al.  Computational vascular fluid–structure interaction: methodology and application to cerebral aneurysms , 2010, Biomechanics and modeling in mechanobiology.

[40]  I. Babuska,et al.  Locking effects in the finite element approximation of plate models , 1995 .

[41]  I. Babuska,et al.  Finite Element Analysis , 2021 .

[42]  Alexander Düster,et al.  A partitioned solution approach for electro-thermo-mechanical problems , 2015 .

[43]  Hrvoje Jasak,et al.  Dynamic Mesh Handling in OpenFOAM , 2009 .

[44]  Z. Yosibash,et al.  On volumetric locking‐free behaviour of p‐version finite elements under finite deformations , 2007 .

[45]  Yuri Bazilevs,et al.  Determination of Wall Tension in Cerebral Artery Aneurysms by Numerical Simulation , 2008, Stroke.

[46]  Tayfun E. Tezduyar,et al.  Modelling of fluid–structure interactions with the space–time finite elements: Arterial fluid mechanics , 2007 .

[47]  Aleksandar Jemcov,et al.  OpenFOAM: A C++ Library for Complex Physics Simulations , 2007 .

[48]  M. Anliker,et al.  Nonlinear analysis of flow pulses and shock waves in arteries , 1971 .

[49]  R. Ogden,et al.  A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models , 2000 .

[50]  Yuri Bazilevs,et al.  Computational fluid–structure interaction: methods and application to a total cavopulmonary connection , 2009 .