Anisotropic adaptive finite element method for modelling blood flow

Müller, Jens; Sahni, Onkar; Li, X.; Jansen, Kenneth E.; Shephard, Mark S.; Taylor, Charles A.

doi:10.1080/10255840500264742

Cited by 62 publications

(42 citation statements)

References 27 publications

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“…Blood was assumed to be a Newtonian fluid with a density of 1.06 g/cm 3 and a viscosity of 4 cP consistent with a previous report (74) in rabbits and upon consideration of the shear rates observed in the present investigation. Computational meshes contained ϳ4 mil-lion tetrahedral elements, and localized refinement was performed using an adaptive technique to deposit more elements in regions prone to flow disruption (45). Simulations were run for four to six cardiac cycles until the flow rate and BP fields yielded periodic solutions.…”

Section: Methodsmentioning

confidence: 99%

Altered hemodynamics, endothelial function, and protein expression occur with aortic coarctation and persist after repair

Menon

Eddinger

Wang

et al. 2012

American Journal of Physiology-Heart and Circulatory Physiology

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Coarctation of the aorta (CoA) is associated with substantial morbidity despite treatment. Mechanically induced structural and functional vascular changes are implicated; however, their relationship with smooth muscle (SM) phenotypic expression is not fully understood. Using a clinically representative rabbit model of CoA and correction, we quantified mechanical alterations from a 20-mmHg blood pressure (BP) gradient in the thoracic aorta and related the expression of key SM contractile and focal adhesion proteins with remodeling, relaxation, and stiffness. Systolic and mean BP were elevated for CoA rabbits compared with controls leading to remodeling, stiffening, an altered force response, and endothelial dysfunction both proximally and distally. The proximal changes persisted for corrected rabbits despite >12 wk of normal BP (∼4 human years). Computational fluid dynamic simulations revealed reduced wall shear stress (WSS) proximally in CoA compared with control and corrected rabbits. Distally, WSS was markedly increased in CoA rabbits due to a stenotic velocity jet, which has persistent effects as WSS was significantly reduced in corrected rabbits. Immunohistochemistry revealed significantly increased nonmuscle myosin and reduced SM myosin heavy chain expression in the proximal arteries of CoA and corrected rabbits but no differences in SM α-actin, talin, or fibronectin. These findings indicate that CoA can cause alterations in the SM phenotype contributing to structural and functional changes in the proximal arteries that accompany the mechanical stimuli of elevated BP and altered WSS. Importantly, these changes are not reversed upon BP correction and may serve as markers of disease severity, which explains the persistent morbidity observed in CoA patients.

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Section: Methodsmentioning

confidence: 99%

Altered hemodynamics, endothelial function, and protein expression occur with aortic coarctation and persist after repair

Menon

Eddinger

Wang

et al. 2012

American Journal of Physiology-Heart and Circulatory Physiology

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“…As a result, many complex features observed in experimental studies of aneurysm flow (152,153) have not been replicated in computational simulations. Muller et al (154) and Sahni et al (155) recently described anisotropic adaptive finite element methods that are well suited for resolving complex, 3-D pulsatile flow dynamics as occur in aneurysms. A posteriori error estimators, based on the Hessian of the velocity magnitude (speed) field, yield directional information on the solution error.…”

Section: Fsi During a Cardiac Cyclementioning

confidence: 99%

Intracranial and Abdominal Aortic Aneurysms: Similarities, Differences, and Need for a New Class of Computational Models

Humphrey

Taylor

2008

Annu. Rev. Biomed. Eng.

269

238

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Intracranial and abdominal aortic aneurysms result from different underlying disease processes and exhibit different rupture potentials, yet they share many histopathological and biomechanical characteristics. Moreover, as in other vascular diseases, hemodynamics and wall mechanics play important roles in the natural history and possible treatment of these two types of lesions. The goals of this review are twofold: first, to contrast the biology and mechanics of intracranial and abdominal aortic aneurysms to emphasize that separate advances in our understanding of each disease can aid in our understanding of the other disease, and second, to suggest that research on the biomechanics of aneurysms must embrace a new paradigm for analysis. That is, past biomechanical studies have provided tremendous insight but have progressed along separate lines, focusing on either the hemodynamics or the wall mechanics. We submit that that there is a pressing need to couple in a new way the separate advances in vascular biology, medical imaging, and computational biofluid and biosolid mechanics to understand better the mechanobiology, pathophysiology, and treatment of these lesions, which continue to be responsible for significant morbidity and mortality. We shall refer to this needed new class of computational tools as Fluid-Solid-Growth (FSG) Models.

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“…where P D has been defined in Equation (3), underlining the fact that the method defined in Equations (10) and (11) belongs to the class of projection methods. From Equation (11), it is possible to derive that ∇ 2 (ũ k+1 −ũ k )·n| * = 0, and accordingly…”

Section: Velocity-correction Schemementioning

confidence: 99%

An adaptive mesh refinement solver for large‐scale simulation of biological flows

Botti

Piccinelli

Ene-Iordache

et al. 2009

Numer Methods Biomed Eng

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SUMMARYThe observation that hemodynamic forces play an important role in the pathophysiology of the cardiovascular system has led to the need for characterizing in vivo hemodynamics on a patient-specific basis. However, the introduction of computational hemodynamics in clinical research contexts is bound to the availability of integrated workflows for analyses on large populations. Since such workflows must rely on automated geometry-driven mesh generation methods, the availability of robust solvers featuring adaptive mesh refinement strategies is essential to ensure that the approach can be adopted on a large scale. In this paper, we present an open-source solver for the incompressible Navier-Stokes equations based on the libMesh finite elements library, featuring adaptive mesh refinement and parallelization. The solution scheme is a second-order velocity correction in rotational form. By presenting numerical tests on benchmark cases, we demonstrate that the coupling of this solution strategy with adaptive mesh refinement leads to a solver with good accuracy characteristics despite the relative simplicity of the scheme adopted. The availability of this solver within the Vascular Modeling Toolkit project leads to a widely available, seamless pipeline from images to simulation ready to be applied in clinical research environments.

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Anisotropic adaptive finite element method for modelling blood flow

Cited by 62 publications

References 27 publications

Altered hemodynamics, endothelial function, and protein expression occur with aortic coarctation and persist after repair

Altered hemodynamics, endothelial function, and protein expression occur with aortic coarctation and persist after repair

Intracranial and Abdominal Aortic Aneurysms: Similarities, Differences, and Need for a New Class of Computational Models

An adaptive mesh refinement solver for large‐scale simulation of biological flows

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