Analysis of finite element and finite volume methods for fluid-structure interaction simulation of blood flow in a real stenosed artery

Abstract This paper presents a qualitative and quantitative comparison between the finite element and the finite volume methods for the fluid-structure interaction simulation of blood flow through a real stenosed artery. The artery geometry corresponds to a severely stenosed (around 75% lumen reduction) portion of the brachiocephalic trunk, located immediately upstream of the bifurcation of this vessel into the right subclavian and right common carotid arteries. The patient-specific geometry was segmented from medical images of a computerized tomography scanner from an individual with the subclavian steal syndrome. Doppler ultrasound velocity measurements were used to determine and impose patient-specific boundary conditions. The numerical simulations were performed in commercial software, Ansys and COMSOL, with a comparative second order discretization for the pressure, velocity and displacement variables. The results of this research disclosed a reasonable overall agreement between the predicted hemodynamics for both approaches. The finite volume method software (Ansys) proved to be more efficient in computational time and memory requirements.

[1]  M. Hamady,et al.  A Computational Study of the Effect of Stent Design on Local Hemodynamic Factors at the Carotid Artery Bifurcation , 2020 .

[2]  E. Dick,et al.  Introduction to Finite Element Methods in Computational Fluid Dynamics , 2009 .

[3]  Murray Rudman,et al.  Direct numerical simulation of turbulent non-Newtonian flow using OpenFOAM , 2019, Applied Mathematical Modelling.

[4]  W Riley,et al.  Hypertension and arterial stiffness: the Atherosclerosis Risk in Communities Study. ARIC Investigators. , 2000, American journal of hypertension.

[5]  S. Alper,et al.  Hemodynamic shear stress and its role in atherosclerosis. , 1999, JAMA.

[6]  Christopher J. Arthurs,et al.  Impact of Patient-Specific Inflow Velocity Profile on Hemodynamics of the Thoracic Aorta. , 2018, Journal of biomechanical engineering.

[7]  Gelin Xu,et al.  Carotid Geometry as a Predictor of In-Stent Neointimal Hyperplasia　- A Computational Fluid Dynamics Study. , 2019, Circulation journal : official journal of the Japanese Circulation Society.

[8]  Nitesh Kumar,et al.  Fluid Structure Interaction Study of Stenosed Carotid Artery Considering the Effects of Blood Pressure and Altered Gravity , 2020, Finite Element Methods and Their Applications [Working Title].

[9]  A D Hughes,et al.  Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation. , 2000, Journal of biomechanics.

[10]  D. O’Regan,et al.  A numerical study of aortic flow stability and comparison with in vivo flow measurements. , 2013, Journal of biomechanical engineering.

[11]  T. Seo.  Hemodynamic Characteristics in the Human Carotid Artery Model Induced by Blood-Arterial Wall Interactions , 2013 .

[12]  C. Tegeler,et al.  Subclavian Steal Syndrome: Can the Blood Pressure Difference Between Arms Predict the Severity of Steal , 2002, Journal of neuroimaging : official journal of the American Society of Neuroimaging.

[13]  D. Ghista,et al.  Correlation between quantitative analysis of wall shear stress and intima-media thickness in atherosclerosis development in carotid arteries , 2017, BioMedical Engineering OnLine.

[14]  Mohamad Shukri Zakaria,et al.  Computational Fluid Dynamics Study Of Blood Flow In Aorta Using OpenFOAM , 2018 .

[15]  Claudio Chiastra,et al.  Computational replication of the patient-specific stenting procedure for coronary artery bifurcations: From OCT and CT imaging to structural and hemodynamics analyses. , 2016, Journal of biomechanics.

[16]  S. Turek,et al.  Benchmark computations based on Lattice-Boltzmann, Finite Element and Finite Volume Methods for laminar Flows , 2006 .

[17]  A. Abbas Nejad,et al.  Pulsatile flow of non-Newtonian blood fluid inside stenosed arteries: Investigating the effects of viscoelastic and elastic walls, arteriosclerosis, and polycythemia diseases , 2018, Comput. Methods Programs Biomed..

[18]  Seongwon Kang,et al.  A fluid-structure interaction analysis on hemodynamics in carotid artery based on patient-specific clinical data , 2012, Journal of Mechanical Science and Technology.

[19]  Olaf Schenk,et al.  Solving unsymmetric sparse systems of linear equations with PARDISO , 2004, Future Gener. Comput. Syst..

[20]  N. Fatouraee,et al.  Fluid structure interaction modeling of aortic arch and carotid bifurcation as the location of baroreceptors , 2020 .

[21]  Alison L. Marsden,et al.  SimVascular: An Open Source Pipeline for Cardiovascular Simulation , 2017, Annals of Biomedical Engineering.

[22]  Giulio Lorenzini,et al.  CFD analysis of pulsatile blood flow in an atherosclerotic human artery with eccentric plaques. , 2008, Journal of biomechanics.

[23]  Gábor Székely,et al.  Simulation of oscillatory flow in an aortic bifurcation using FVM and FEM: A comparative study of implementation strategies , 2011 .

[24]  S. Kulshrestha,et al.  Blood clots in COVID-19 patients: Simplifying the curious mystery , 2020, Medical Hypotheses.

[25]  M. Walsh,et al.  Mechanical properties and composition of carotid and femoral atherosclerotic plaques: A comparative study. , 2016, Journal of biomechanics.

[26]  S. Mirsadraee,et al.  Association of hemodynamic factors and progressive aortic dilatation following type A aortic dissection surgical repair , 2021, Scientific Reports.

[27]  L. Antiga,et al.  Outflow conditions for image-based hemodynamic models of the carotid bifurcation: implications for indicators of abnormal flow. , 2010, Journal of biomechanical engineering.

[28]  D. Gallo,et al.  Insights into the co-localization of magnitude-based versus direction-based indicators of disturbed shear at the carotid bifurcation. , 2016, Journal of biomechanics.

[29]  Marshall W. Bern,et al.  Mesh Generation , 2020, Handbook of Computational Geometry.

[30]  Vijaya B Kolachalama,et al.  Geometric determinants of local hemodynamics in severe carotid artery stenosis , 2019, Comput. Biol. Medicine.

[31]  Raghuvir B Pai,et al.  Haemodynamics Study in Subject Specific Carotid Bifurcation Using FSI , 2015 .

[32]  R. Poole,et al.  Closure technique after carotid endarterectomy influences local hemodynamics. , 2014, Journal of vascular surgery.

[33]  B. Jiang.  The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics , 1998 .

[34]  Dalin Tang,et al.  Sites of Rupture in Human Atherosclerotic Carotid Plaques Are Associated With High Structural Stresses: An In Vivo MRI-Based 3D Fluid-Structure Interaction Study , 2009, Stroke.

[35]  Christopher J. Arthurs,et al.  CRIMSON: An open-source software framework for cardiovascular integrated modelling and simulation , 2020, bioRxiv.

[36]  Michail I. Papafaklis,et al.  Local Low Shear Stress and Endothelial Dysfunction in Patients With Nonobstructive Coronary Atherosclerosis. , 2018, Journal of the American College of Cardiology.

[37]  A. Hughes,et al.  Image-based carotid flow reconstruction: a comparison between MRI and ultrasound. , 2004, Physiological measurement.

[38]  Weeratunge Malalasekera,et al.  An introduction to computational fluid dynamics - the finite volume method , 2007 .

[39]  N. Cheshire,et al.  Fluid structure interaction of patient specific abdominal aortic aneurysms: a comparison with solid stress models , 2006, Biomedical engineering online.

[40]  K. Bathe.  Finite Element Procedures , 1995 .

[41]  D Lopes,et al.  Blood flow simulations in patient-specific geometries of the carotid artery: A systematic review. , 2020, Journal of biomechanics.

[42]  Fei Liu,et al.  Patient-specific artery shrinkage and 3D zero-stress state in multi-component 3D FSI models for carotid atherosclerotic plaques based on in vivo MRI data. , 2009, Molecular & cellular biomechanics : MCB.

[43]  M. Darwish,et al.  The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab , 2015 .

[44]  J. Pepper,et al.  Computational study of aortic hemodynamics for patients with an abnormal aortic valve: The importance of secondary flow at the ascending aorta inlet , 2018, APL bioengineering.

[45]  J. Pepper,et al.  On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics. , 2017, Journal of biomechanics.

[46]  P. Jagad,et al.  ANALYSIS OF THE EFFECTS OF PLAQUE DEPOSITS ON THE BLOOD FLOW THROUGH HUMAN ARTERY , 2015 .

[47]  Alireza Karimi,et al.  Measurement of the uniaxial mechanical properties of healthy and atherosclerotic human coronary arteries. , 2013, Materials science & engineering. C, Materials for biological applications.

[48]  Dalin Tang,et al.  Advanced human carotid plaque progression correlates positively with flow shear stress using follow-up scan data: an in vivo MRI multi-patient 3D FSI study. , 2010, Journal of biomechanics.

[49]  Raad H. Mohiaddin,et al.  Fluid–solid interaction simulation of flow and stress pattern in thoracoabdominal aneurysms: A patient-specific study , 2008 .

[50]  Thierry Boulard,et al.  Comparison of finite element and finite volume methods for simulation of natural ventilation in greenhouses , 2010 .

[51]  Alvaro Valencia,et al.  Unsteady flow and mass transfer in models of stenotic arteries considering fluid-structure interaction ☆ , 2006 .

[52]  Jiyuan Tu,et al.  Analysis of patient-specific carotid bifurcation models using computational fluid dynamics , 2011 .

[53]  B. Bou-Saïd,et al.  The Role of Biomechanics in the Assessment of Carotid Atherosclerosis Severity: A Numerical Approach , 2018 .

[54]  S. Teixeira,et al.  Fluid–Structure Interaction study of carotid blood flow: Comparison between viscosity models , 2020 .

[55]  Mária Lukáčová-Medvid’ová,et al.  Comparison study of some finite volume and finite element methods for the shallow water equations with bottom topography and friction terms , 2006 .

[56]  D. Fernandes,et al.  Hemodynamic Forces in the Endothelium: From Mechanotransduction to Implications on Development of Atherosclerosis , 2018 .

[57]  R. Anderson,et al.  The Leading Causes of Death in the US for 2020. , 2021, JAMA.

[58]  A. Marsden,et al.  Use of patient-specific computational models for optimization of aortic insufficiency after implantation of left ventricular assist device. , 2020, The Journal of thoracic and cardiovascular surgery.

[59]  Seungik Baek,et al.  Computational fluid dynamic simulation of human carotid artery bifurcation based on anatomy and volumetric blood flow rate measured with magnetic resonance imaging , 2016, International Journal of Advances in Engineering Sciences and Applied Mathematics.

[60]  Muhammad Amir,et al.  Coupled Fluid-Structure Interaction Modelling of Loads Variation and Fatigue Life of a Full-Scale Tidal Turbine under the Effect of Velocity Profile , 2019 .

[61]  M. Wintermark,et al.  Carotid Atheroma Rupture Observed In Vivo and FSI-Predicted Stress Distribution Based on Pre-rupture Imaging , 2010, Annals of Biomedical Engineering.

[62]  Jaehoon Seong,et al.  Comparison of effects on technical variances of computational fluid dynamics (CFD) software based on finite element and finite volume methods , 2014 .

[63]  C. Yuan,et al.  Correlations between carotid plaque progression and mechanical stresses change sign over time: a patient follow up study using MRI and 3D FSI models , 2013, Biomedical engineering online.

[64]  I. Zun,et al.  Modeling the Effect of Red Blood Cells Deformability on Blood Flow Conditions in Human Carotid Artery Bifurcation. , 2017, Journal of biomechanical engineering.

[65]  L. Antiga,et al.  Modeling hemodynamics in intracranial aneurysms: Comparing accuracy of CFD solvers based on finite element and finite volume schemes , 2018, International journal for numerical methods in biomedical engineering.

[66]  T. Hatsukami,et al.  Ultrasound determination of total arterial wall thickness. , 1994, Journal of Vascular Surgery.

[67]  Yu Zhang,et al.  Multiphase particle-in-cell simulation in severe internal carotid artery stenosis , 2019 .

[68]  Christian Vergara,et al.  Computational Comparison Between Newtonian and Non-Newtonian Blood Rheologies in Stenotic Vessels , 2018 .

[69]  J. Montanero,et al.  Numerical and experimental analysis of the transitional flow across a real stenosis , 2017, Biomechanics and Modeling in Mechanobiology.

[70]  C. Vergara,et al.  Computational fluid dynamic comparison between patch-based and primary closure techniques after carotid endarterectomy. , 2017, Journal of vascular surgery.

[71]  I. Marshall,et al.  MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models. , 2004, Journal of biomechanics.

[72]  R. Tubbs,et al.  A review of subclavian steal syndrome with clinical correlation , 2012, Medical science monitor : international medical journal of experimental and clinical research.

[73]  L. Antiga,et al.  Geometry of the Carotid Bifurcation Predicts Its Exposure to Disturbed Flow , 2008, Stroke.

[74]  Michael C. McDaniel,et al.  Low Coronary Wall Shear Stress Is Associated With Severe Endothelial Dysfunction in Patients With Nonobstructive Coronary Artery Disease. , 2018, JACC. Cardiovascular interventions.

[75]  S. Teixeira,et al.  Influence of arterial mechanical properties on carotid blood flow: Comparison of CFD and FSI studies , 2019, International Journal of Mechanical Sciences.

[76]  Michael J. Pencina,et al.  Arterial Stiffness and Cardiovascular Events: The Framingham Heart Study , 2010, Circulation.

[77]  M. Hamady,et al.  Hemodynamic Functions of Fenestrated Stent Graft under Resting, Hypertension, and Exercise Conditions , 2016, Front. Surg..

[78]  Laura Hansen,et al.  Is increased arterial stiffness a cause or consequence of atherosclerosis? , 2016, Atherosclerosis.