Blood vessel tissue prestress modeling for vascular fluid-structure interaction simulation

In this paper we present a new strategy for obtaining blood vessel tissue prestress for use in fluid-structure interaction (FSI) analysis of vascular blood flow. The method consists of a simple iterative procedure and is applicable to a large class of vascular geometries. The formulation of the solid problem is modified to account for the tissue prestress by employing an additive decomposition of the second Piola-Kirchhoff stress tensor. Computational results using patient-specific models of cerebral aneurysms indicate that tissue prestress plays an important role in predicting hemodynamic quantities of interest in vascular FSI simulations.

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

[2]  C. Putman,et al.  Hemodynamics of Cerebral Aneurysms. , 2009, Annual review of fluid mechanics.

[3]  Jean-Frédéric Gerbeau,et al.  Algorithms for fluid-structure interaction problems , 2009 .

[4]  H. Kikuchi,et al.  Cerebral aneurysms arising at nonbranching sites. An experimental Study. , 1997, Stroke.

[5]  Zhijie Wang,et al.  Complex Hemodynamics at the Apex of an Arterial Bifurcation Induces Vascular Remodeling Resembling Cerebral Aneurysm Initiation , 2007, Stroke.

[6]  Shmuel Einav,et al.  Abdominal aortic aneurysm risk of rupture: patient-specific FSI simulations using anisotropic model. , 2009, Journal of biomechanical engineering.

[7]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[8]  Alfio Quarteroni,et al.  Cardiovascular mathematics : modeling and simulation of the circulatory system , 2009 .

[9]  Charles A. Taylor,et al.  A Computational Framework for Fluid-Solid-Growth Modeling in Cardiovascular Simulations. , 2009, Computer methods in applied mechanics and engineering.

[10]  S. Govindjee,et al.  Computational methods for inverse finite elastostatics , 1996 .

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

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

[13]  T. Hughes,et al.  Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow , 2006 .

[14]  J. Humphrey,et al.  Open Problems in Computational Vascular Biomechanics: Hemodynamics and Arterial Wall Mechanics. , 2009, Computer methods in applied mechanics and engineering.

[15]  G. Hulbert,et al.  A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method , 2000 .

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

[17]  Charles A. Taylor,et al.  Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries , 2006 .

[18]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[19]  Pascal Frey,et al.  Fluid-structure interaction in blood flows on geometries based on medical imaging , 2005 .

[20]  A. Shaaban,et al.  Wall shear stress and early atherosclerosis: a review. , 2000, AJR. American journal of roentgenology.

[21]  Ender A. Finol,et al.  Compliant biomechanics of abdominal aortic aneurysms: A fluid-structure interaction study , 2007 .

[22]  John A. Evans,et al.  Robustness of isogeometric structural discretizations under severe mesh distortion , 2010 .

[23]  B J B M Wolters,et al.  A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms. , 2005, Medical engineering & physics.

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

[25]  Toshio Kobayashi,et al.  Fluid-structure interaction modeling of blood flow and cerebral aneurysm: Significance of artery and aneurysm shapes , 2009 .

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

[27]  Kenji Takizawa,et al.  Patient‐specific arterial fluid–structure interaction modeling of cerebral aneurysms , 2011 .

[28]  K. Katada,et al.  Magnitude and Role of Wall Shear Stress on Cerebral Aneurysm: Computational Fluid Dynamic Study of 20 Middle Cerebral Artery Aneurysms , 2004, Stroke.

[29]  Wolfgang A. Wall,et al.  A computational strategy for prestressing patient‐specific biomechanical problems under finite deformation , 2010 .

[30]  M. Vidrascu,et al.  A partitioned Newton method for the interaction of a fluid and a 3D shell structure , 2010 .

[31]  Yuri Bazilevs,et al.  High-Fidelity Tetrahedral Mesh Generation from Medical Imaging Data for Fluid-Structure Interaction Analysis of Cerebral Aneurysms , 2009 .

[32]  Thomas J. R. Hughes,et al.  Multiscale and Stabilized Methods , 2007 .

[33]  K. Hayashi Cardiovascular solid mechanics. Cells, tissues, and organs , 2003 .

[34]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .

[35]  R M Nerem,et al.  Correlation of Endothelial Cell Shape and Wall Shear Stress in a Stenosed Dog Aorta , 1986, Arteriosclerosis.

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

[37]  Tayfun E. Tezduyar,et al.  Finite element stabilization parameters computed from element matrices and vectors , 2000 .

[38]  Tayfun E. Tezduyar,et al.  Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces , 1994 .

[39]  W A Wall,et al.  Prestressing in finite deformation abdominal aortic aneurysm simulation. , 2009, Journal of biomechanics.

[40]  T. Hughes,et al.  Isogeometric fluid-structure interaction: theory, algorithms, and computations , 2008 .

[41]  T. Tezduyar,et al.  Fluid–structure Interaction Modeling of Aneurysmal Conditions with High and Normal Blood Pressures , 2006 .

[42]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

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

[44]  Thomas J. R. Hughes,et al.  Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device , 2009 .

[45]  A. Quarteroni,et al.  On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels , 2001 .

[46]  Gerhard A. Holzapfel,et al.  Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science , 2000 .

[47]  Jay D Humphrey,et al.  Growth and remodeling in a thick-walled artery model: effects of spatial variations in wall constituents , 2008, Biomechanics and modeling in mechanobiology.

[48]  Y. Yoshida,et al.  Junction complexes of endothelial cells in atherosclerosis-prone and atherosclerosis-resistant regions on flow dividers of brachiocephalic bifurcations in the rabbit aorta. , 1994, Biorheology.

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

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

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

[52]  Alastair J. Martin,et al.  Aneurysm Growth Occurs at Region of Low Wall Shear Stress: Patient-Specific Correlation of Hemodynamics and Growth in a Longitudinal Study , 2008, Stroke.

[53]  Thomas J. R. Hughes,et al.  Encyclopedia of computational mechanics , 2004 .

[54]  J D Humphrey,et al.  A theoretical model of enlarging intracranial fusiform aneurysms. , 2006, Journal of biomechanical engineering.

[55]  Fabio Nobile,et al.  Robin-Robin preconditioned Krylov methods for fluid-structure interaction problems , 2009 .

[56]  Yuri Bazilevs,et al.  A fully-coupled fluid-structure interaction simulation of cerebral aneurysms , 2010 .