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Vortex Ring Propagation in Confined Spheroidal Domains and Applications to Cardiac Flows

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Vortex Ring Propagation in Confined Spheroidal Domains and Applications to Cardiac Flows VORTEX RING PROPAGATION IN CONFINED SPHEROIDAL DOMAINS AND APPLICATIONS TO CARDIAC FLOWS By MILAD SAMAEE Bachelor of Science in Mechanical Engineering Khaje Nasir Toosi University of Technology Tehran, Iran 2008 Master of Science in Biomedical Engineering Amirkabir University of Technology Tehran, Iran 2011 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December, 2019 ii VORTEX RING PROPAGATION IN CONFINED SPHEROIDAL DOMAINS AND APPLICATIONS TO CARDIAC FLOWS Dissertation Approved: Dr. Arvind Santhanakrishnan Dissertation Adviser Dr. Jamey Jacob Dr. Khaled Sallam Dr. Sundar Madihally Dr. Yu Feng ii Name: MILAD SAMAEE Date of Degree: DECEMBER, 2019 Title of Study: VORTEX RING PROPAGATION IN CONFINED SPHEROIDAL DOMAINS AND APPLICATIONS TO CARDIAC FLOWS Major Field: MECHANICAL ENGINEERING Abstract: Vortex ring formation is observed in the human cardiac left ventricle (LV) during diastole. Numerous studies to date have examined the intraventricular filling vortex for potential use in the diagnosis of cardiac dysfunction. However, a systematic understanding of the effects of LV size on vortex ring properties is currently unavailable. In diastolic dysfunction (LVDD), heart muscles can thicken and decrease the internal volume of the LV. On the other hand, by progressing diastolic dysfunction, the transmitral inflow changes and the impact of inflow altering on vortex ring properties is also unknown. In contrast to the considerable body of research on vortex ring propagation in semi-infinite domains and interaction with walls, only a limited number of studies have examined confined vortex ring dynamics. The latter studies only considered radially confined domains, which are a simplification to the combined radial and axial confinement observed in spheroidal domains such as the LV. We experimentally examined vortex ring propagation within three flexible-walled, semi-spheroidal physical models (semi-oblate, hemisphere, and semi-prolate) that presented both axial and radial confinement. 2D time-resolved particle image velocimetry (TR-PIV) measurements showed that while the formation process and peak circulation were nearly unaffected with changing geometry, increasing axial confinement increased the rate of normalized circulation decay. We next examined vortex propagation in an in-vitro model of the LV, under physiological hemodynamic. Two flexible-walled, anatomical physical models representative of a normal LV and an LV with asymmetric wall thickening characteristic of hypertrophic cardiomyopathy (HCM) were examined. We varied the end- diastolic volume (EDV) of the models to change the confinement level. Peak circulation was lowered in the HCM model and also in the normal LV model with lower EDV when compared to the normal LV model with normal EDV. In the end, we examined the role of transmitral inflow on vortex ring properties under different grades of diastolic dysfunction. The normal transmitral flow showed higher circulation strength, momentum flux, and stronger vortex ring compared to those of diastolic dysfunction. Our results suggest that peak circulation and normalized circulation decay rates have the potential link with LVDD from the fluid mechanics’ point of view. iii TABLE OF CONTENTS Chapter Page I. INTRODUCTION .................................................................................................. 1 1.1. Motivation ....................................................................................................... 1 1.2. Aims of the study ............................................................................................ 3 Aim I: Vortex ring propagation in flexible-walled semi-spheroidal domains.. ....................................................................................................................3 Aim II: Effects of varying LV confinement severity on the intraventricular filling vortex ..........................................................................................................4 Aim III: Effects of varying transmitral inflow profile on filling vortex properties ................................................................................................................ 5 1.3. References ....................................................................................................... 6 II. BACKGROUND .................................................................................................... 8 2.1. Cardiac Anatomy and Physiology ................................................................... 8 2.2. Left ventricular disease ................................................................................... 12 Left ventricular diastolic dysfunction (LVDD) ....................................... 13 cardiomyopathy........................................................................................ 13 2.3. Transmitral inflow in different grades of diastolic dysfunction ...................... 15 Grade I: Delayed relaxation .................................................................... 16 Grade II: Pseudonormal inflow ................................................................ 17 Grade III: Restrictive pattern ................................................................... 18 2.4. Left ventricular fluid dynamics ....................................................................... 18 2.5. Vortex ring formation...................................................................................... 19 Slug flow model ....................................................................................... 20 Semi-infinite domains .............................................................................. 21 Confined domains .................................................................................... 22 Intraventricular vortex rings .................................................................... 23 2.6. In vivo and in vitro experiments ..................................................................... 24 2.7. References ....................................................................................................... 26 III. VORTEX RING DECAY IN FLEXIBLE-WALLED SPHEROIDAL CONFINED DOMAINS ..................................................................................................................... 32 iv 3.1. Introduction ..................................................................................................... 33 3.2. Material and methods ...................................................................................... 35 Experimental setup................................................................................... 35 Vortex ring formation under active filling ............................................... 40 Validation ................................................................................................. 42 Particle image velocimetry (PIV) ............................................................ 42 Definitions of calculated quantities ......................................................... 44 Defining the vortex ring pinch-off time (formation time) ....................... 47 3.3. Results and discussion ..................................................................................... 48 Experimental setup Validation ................................................................. 48 Effects of semi-spheroidal confinement aspect ratio on vortex ring properties ................................................................................................................ 50 Effects of AT/DT on vortex ring properties ............................................ 59 Effects of filling time on vortex ring properties ...................................... 62 Effects of Re on vortex ring properties .................................................... 65 Peak circulation and pinch-off time ......................................................... 68 Circulation decay ..................................................................................... 71 Vortex circulation and circulation decay for active-filling ...................... 74 Pressure field for active and passive filling ............................................. 76 3.4. Conclusion ....................................................................................................... 77 3.5. References ....................................................................................................... 79 IV. DIASTOLIC VORTEX ALTERATION WITH REDUCING LEFT VENTRICULAR VOLUME: AN IN VITRO STUDY .............................................................................. 82 4.1. Introduction ..................................................................................................... 83 4.2. Experimental Methods .................................................................................... 85 Physical modeling .................................................................................... 85 Left heart simulator .................................................................................. 88 Experimental protocols ............................................................................ 89 2D Time-resolved particle image velocimetry (TR-PIV) ........................ 91 Definitions of calculated quantities ......................................................... 92 4.3. Results ............................................................................................................
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