A computational framework for simulating cardiovascular flows in patient specific anatomies

A COMPUTATIONAL FRAMEWORK FOR SIMULATING CARDIOVASCULAR FLOWS IN PATIENT-SPECIFIC ANATOMIES A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Trung Bao Le IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy Professor Fotis Sotiropoulos December, 2011 c Trung Bao Le 2011 ALL RIGHTS RESERVED Acknowledgements I gratefully acknowledge the instruction of my advisor, Professor Sotiropoulos, who guided me all the ways through a series of challenges during my time at Saint Anthony Falls Lab I am in debt of his encouragement and belief in my capability of putting out my curiosity into actual research projects I believe that his advices will go a long way with me throughout the rest of my scientific adventure Thanks to my committee members Professor Voller, Hondzo, Candler, Mahesh and Cockburn, whom I greatly admire their knowledge and instruction during my course work, for giving me kind advices on my research Thanks extended to Dr Kallmes at Mayo Clinic who provided me all the medical scanned images in the aneurysm project I would also like to thank Professor Yoganathan at Georgia Tech, who provided me the experimental data for the left ventricle Sincere thanks to Professor Webster at Georgia Tech, Professor Longmire at U of Minnesota and Dr Troolin at TSI for their dataset of the inclined nozzle case, which intrigued me so much for its beauty and simplicity Thanks to my friend, Iman Borazjani, who constantly gives me kind advices and supports at the initial stages of my research Thanks to my friends at the room 370: Fan Yi, Paola Passalacqua, Arvind Singh, Bereket Yohannes Tewoldebrhan, Ted Fuller, Man Liang, Vamsi Ganti and Mohammad Hajit The members of my research group: Seokkoo Kang, Liang Ge, Cristian Escauriaza provided me lots of feedback from my research questions I would like to thank all people at SAFL for being kind, supportive and empathetic Finally, I would also like to acknowledge Vietnam Education Foundation and United States National Academies for the fellowship, which provide me the opportunity to expand my horizon on science This work is also supported by grant NIH RO1-HL07262, the Minnesota SuperComputing Institute and Mayo Clinic i Dedication To my wife and my son, who have constantly supported me throughout challenging years ii Abstract The goal of the thesis is to develop a computational framework for simulating cardiovascular flows in patient-specific anatomies The numerical method is based on the curvilinear immersed method approach and is able to simulate pulsatile flow in complex anatomical geometries, incorporates a novel, lumped-parameter kinematic model of the left ventricle wall driven by electrical excitation, and can carry out fluid-structure interaction simulations between the blood flow and implanted bi-leaflet mechanical heart valves (BMHV) The ability of the method to resolve and illuminate the physics of dynamically rich vortex phenomena is demonstrated by carrying out simulations of impulsively driven flow through inclined nozzles and comparing the computed results with experimental measurements The method is subsequently applied to simulate: 1) vortex formation and wall shear-stress dynamics inside an intracranial aneurysm; 2) the hemodynamics of early diastolic filling in a patient-specific left ventricle (LV); and 3) and fluid-structure interaction of a BMHV implanted in the aortic position of a patientspecific LV/aorta configuration driven by electrical excitation of the LV wall motion For all cases the computed results yield new, clinically-relevant insights into the underlying flow phenomena and underscore the potential of the numerical method as a powerful tool for carrying out high-resolution simulations in patient-specific anatomic geometries Future work will focus on extending the fluid-structure interaction scheme to simulate soft tissues and other medical devices, such as stents, bio-prosthetic tri-leaflet and percutaneous heart valves iii Contents Acknowledgements i Dedication ii Abstract iii List of Tables vii List of Figures ix Introduction 1.1 Motivation 1.2 Literature review 1.2.1 In − vivo and In − vitro studies 1.2.2 Computational studies Thesis objectives and outlines 1.3 Methodology 10 2.1 Problem statements 10 2.2 Governing equations and boundary conditions for fluid domain Ωf 12 2.3 Governing equations for solid domain Ωs 14 2.4 The Fluid-Structure Interaction algorithm to calculate ΓF SI 16 2.5 Numerical discretization and integration 18 2.5.1 Governing equations in generalized coordinate system 19 2.5.2 Hybrid staggered/non-staggered grid approach 20 iv 2.5.3 Velocity reconstruction at the immersed boundary nodes 22 2.5.4 Time integration and fractional step method 23 2.5.5 Iterative methods for the non-linear momentum equation 24 2.6 Poisson solver 26 2.7 Domain decomposition 27 2.8 Load calculation 29 The dynamics of vortex rings in impulsively driven flow through inclined nozzles 31 3.1 Introduction 32 3.2 Governing equations and numerical method 37 3.3 Description of simulated test cases 37 3.4 Computational details 41 3.5 Validation of the numerical method 43 3.5.1 Case 1: The axisymmetric nozzle 43 3.5.2 Case 2: The D/2 inclined nozzle 45 3.5.3 Case 3: The D inclined nozzle 49 3.6 3D vortex dynamics at the exit of inclined nozzles 50 3.7 The kinematics of the circumferential flow 64 3.8 Conclusions 65 The hemodynamics of intracranial aneurysms 4.1 Introduction 4.2 Vortex formation and wall shear stress dynamics in side-wall aneurysms: 4.3 69 The effect of flow wave form 73 4.2.1 Introduction 73 4.2.2 Materials and methods 74 4.2.3 Results 83 4.2.4 Discussion 94 Conclusions 100 The kinematic model of the left ventricle 5.1 69 101 The left ventricular anatomy 101 v 5.2 Left ventricular modeling 103 5.3 A cell-based electrical activation model for the left ventricle 106 5.4 5.3.1 The anatomic model 106 5.3.2 Derivation of the kinematics model 107 5.3.3 Results 115 Conclusions 121 Hemodynamics of the left ventricle 122 6.1 Introduction 122 6.2 Computational setup 124 6.3 Results and discussions 6.4 Conclusions 135 126 Fluid-Structure Interaction of an aortic mechanical heart valve prosthesis in the left heart 140 7.1 Introduction 140 7.2 Computational setup 143 7.3 Results and discussions 7.4 Conclusions 158 146 Summary and conclusions 159 8.0.1 Summary and conclusions 159 8.0.2 Future work 162 Bibliography 164 vi List of Tables 3.1 Summary of geometrical parameters for the three simulated test cases With reference to Fig 3.2, I is the initial position of the piston S is the axial distance from the stopping location of the piston to the shortest lip of the nozzle, T is the location of the average nozzle exit lip along the cylinder centerline (it is also the distance from origin O to the tank top along Z direction) C is the angle of the cutting plane to the nozzle axis 3.2 41 The computational grids used for the grid sensitivity study 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Type waveforms were obtained by appropriately scaling the same original waveform-Case 1a Waveform 1a is constructed following a typical waveform in Middle Cerebral Artery Waveform 2a is a typical... ii Abstract The goal of the thesis is to develop a computational framework for simulating cardiovascular flows in patient- specific anatomies The numerical method is based on the curvilinear immersed... vortex formation, instabilities and breakdown Apply the computational framework to calculate the hemodynamic environment in an anatomic LV/aorta geometry with an implanted mechanical heart valve in