Simulation of Aortic Valve Dynamics During Left Ventricular Support

GRADUATE SCHOOL OF BIOMEDICAL ENGINEERING

Simulation of Aortic Valve Dynamics during Left Ventricular Support

Khalid.A.Alonazi

B.BiomedE, King Saud University M.BiomedE, University of New South Wales

A dissertation submitted for the degree of Doctor of Philosophy

February 2015

ORIGINALITY STATEMENT

‘I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at

UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.’

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AUTHENTICITY STATEMENT

‘I certify that the Library deposit digital copy is a direct equivalent of the final officially approved version of my thesis. No emendation of content has occurred and if there are any minor variations in formatting, they are the result of the conversion to digital format.’

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Table Contents

Acknowledgments ...... i Abstract ...... iii List of Abbreviations ...... iv List of Figures ...... vi List of Tables ...... xi Part I-Introduction, Background and Literature Review ...... 1 1 Chapter 1 - Introduction, Aims, and Outline ...... 2 1.1 Research Motivation ...... 2 1.2 Thesis Aims ...... 4 1.3 Thesis outline ...... 6 1.4 Publications ...... 9 1.4.1 Refereed Conference Proceedings and Abstracts ...... 9 2 Chapter 2 - Background...... 11 2.1 Overview ...... 11 2.2 Basic Anatomy and Physiology ...... 11 2.2.1 Cardiovascular system ...... 11 2.2.2 Control of Cardiac Output ...... 16 2.2.3 Aortic Valve Anatomy and Physiology ...... 19 2.2.4 Regulation of the Aortic Valve ...... 21 2.3 Heart Failure Pathology and Therapy ...... 24 2.3.1 Congestive Heart Failure ...... 24 2.3.2 Ventricular Assist Devices: an Emerging Therapy for CHF ...... 28 2.3.3 Abnormal pathophysiology in LVAD patients ...... 40 2.3.4 LVAD control systems ...... 40 2.4 Existing LVAD Models and Computational Methods ...... 54 2.4.1 Overview of Computational Techniques for LVAD-AV Modelling ...... 54 2.4.2 Finite Element Method ...... 56 2.4.3 Heart-Pump Interaction Models ...... 58

3 Chapter 3-Review of Modelling Approaches in Cardiac Dynamics ...... 60 3.1 Background ...... 60 3.2 Existing cardiac dynamics models ...... 63 3.3 Existing modelling studies of AV state under LVAD support ...... 68 Part II – Methods ...... 71 4 Chapter 4 -Development of Computational 2D LV-pump Models ...... 72 4.1 Introduction ...... 72 4.2 Geometrical models of LV-LVAD interaction ...... 75 4.2.1 Simplified LV-pump interaction model ...... 75 4.2.2 Simplified LV-pump interaction model with systemic circulation...... 83 4.2.3 Simplified LV-pump model with systemic circulation and heart contractility .. 89 4.2.4 Simplified LV-pump interaction model with systemic circulation, cardiac contractility and without AV ...... 95 4.2.5 Realistic LV-Pump geometry model with and without AV leaflets ...... 103 4.2.6 Simulating LV and AV dynamics ...... 119 4.2.7 Investigation of Cardiovascular Interaction with a Left ventricular Assist Device 120 Part III-Results and Discussion ...... 124 5 Chapter 5 - Fluid-Structure Interaction in a Simple Model of an Assisted Left Ventricle ...... 125 5.1 Introduction ...... 125 5.2 Simplified LV-pump model ...... 126 5.2.1 Results: ...... 126 5.2.2 Discussion ...... 128 5.3 Simplified LV-pump model with systemic circulation ...... 129 5.3.1 Results: ...... 129 5.3.2 Discussion ...... 139 5.4 Conclusion ...... 141 6 Chapter 6 - Simulation of Aortic Valve Response during Ventricular Assist Device Support ...... 142 6.1 Introduction ...... 142 6.2 Simplified LV-pump model ...... 143 6.3 Realistic LV-Pump model with AV leaflets ...... 147

6.3.1 Identification of aortic valve states for LV- pump interaction models with AV 148 6.3.2 Detection of AV State ...... 150 6.3.3 Discussion ...... 161 6.4 Limitations ...... 162 6.5 Conclusion ...... 163 7 Chapter 7 – Effect of Parameter Variations on Aortic Valve State under Rotary Blood Pump Assistance...... 165 7.1 Introduction ...... 165 7.2 Simplified LV-pump model ...... 168 7.2.1 Results and Discussion ...... 168 7.3 Realistic LV-Pump model ...... 174 7.3.1 Introduction ...... 174 7.3.2 Results: ...... 174 7.3.3 Discussion ...... 181 7.4 Model Limitations ...... 183 7.5 Conclusions ...... 183 8 Chapter 8 - Simulation of Motor Current Waveforms as an Index for Aortic Valve Condition during Ventricular Support ...... 184 8.1 Introduction ...... 185 8.2 Simplified LV-pump model ...... 187 8.2.1 Results: ...... 187 8.2.2 Discussion ...... 190 8.3 Realistic LV-Pump model Results ...... 192 8.3.1 Identification of AV state ...... 192 8.3.2 LV wall motion ...... 193 8.3.3 LV-Pump model simulations ...... 194 8.3.4 Discussion ...... 204 8.4 Model Limitations ...... 205 8.5 Conclusions ...... 206 9 Chapter 9 - Conclusions and Recommendations ...... 207 9.1 Conclusions ...... 207 9.2 Suggestions for Future Work ...... 209 9.2.1 Simulating chronic heart failure during exercise and postural change ...... 210

9.2.2 AV state detection validation ...... 210 9.2.3 Effect of blood viscosity on AV states ...... 211 Bibliography ...... 212

Acknowledgments

Writing these acknowledgements I look back and remember the time through the years I have spent in my Phd. Although the amount of studies never ends, it was a great experience. Praise

God for the blessing of science. Thanks to my professors and friends. For me it was the last stage of my long schooling life, but I will not stop in my research journey to serve my society and all of humanity. I would like to thank the Custodian of the two Holy Mosques King

Abdullah bin Abdul Aziz, the King of Saudi Arabia, for his support to Saudi students all over the world, as well as the Ministry of Defence representative, my commander Major General

Walid Khalil. I would also like to thank my mother for her patience, love, support, and encouragement. I would like to thank all those inspiring persons I have learnt from. In particular, I would like to thank all of my teachers who have taught me over the last 4 years, and all my friends in Australia and abroad for sharing this journey with me. In specific, my supervisors Professor Socrates Dokos, Professor Nigel Lovell, and Professor Andrey Savkin, because of their knowledge, guidance, assistance and follow-up to the completion of my thesis, giving me the opportunity to present my research at international conferences, and for giving me the confidence in myself to complete my research in the simulation of heart dynamics. Thank you Professor Socrates Dokos for your help in all aspects of this project, encouraging words at difficult times for the completion of my thesis. Thanks, Professor Nigel

Lovell for your advice. I wish to thank my friend Associate Professor Abdul Hakim for giving me a concrete base in the heart pump control systems. Special thanks to my friends

Amr, Mohammad, Fahad, Ammar, James, Adrian, Einly, Tianruo, Siwei ,Azam and Ulises.

thank you guys for your support. Finally, my gratitude is also extended to my family in Saudi

Arabia, my sisters and my brothers: thank you for all your support, encouragement and patience - without you this PhD would not have happened.

Abstract

Implantable Rotary Blood Pumps (IRBPs) for the left ventricle (LV) have become a

viable treatment and long-term option for heart failure (HF) patients. In addition,

development of valve abnormalities after Left Ventricular Assist Device (LVAD)

implantation is common among patients with advanced HF, likely due the fact that

the LVAD alters haemodynamics by changing the direction of blood flow from the

apex of the heart, largely bypassing the left ventricle (LV), directly to the aorta. The

aim of this thesis was to investigate the hemodynamic interaction between the

LVAD and aortic valve (AV) using 2D LV-LVAD computational models.

To investigate the correlation between AV status and LVAD motor speed, this study

perfomed a detailed computational analysis of left ventricular flow and mechanics

during LVAD support. Simulations were carried out using a 2D LV-pump Fluid-

Structure Interaction (FSI) approach, examining LVAD intrinsic motor current and

motor speed waveforms. AV state was assessed by analysing the pump motor

current waveform, investigating its association with open-close valve state and pump

impeller speed. Results show that there is a significantly higher motor current during

the valve open state, which has the potential of being utilized in future LVAD

control systems to ensure patient safety and comfort, and reduce the incidence of AV

pathologies during heart pump support, as well as for optimal management of pump

outﬂow, paving the way for more sophisticated pump control algorithms, which take

into account heart valve state.

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List of Abbreviations

AC aortic valve open ECG electrocardiogram

ACE angiotensin converting enzyme EDV end-diastolic volume

AI aortic insufficiency ESV end-systolic volume

AR aortic regurgitation EDP end-diastolic pressure

AS aortic stenosis ESP end- systolic pressure

AO aortic valve closed FDA food and drug administration

AG aqueous glycerol FD fictitious domain

ALE Arbitrary Lagrangian Eulerian FE finite element

ALI activity level index FSI fluid structure interaction

ANO aortic valve not open H pump head

AP arterial pressure HCT haematocrit

AoP aortic pressure HR heart rate

ARX autoregressive with exogenous IRBP implantable rotary blood pump input LV left ventricle

AV aortic valve LVAD left ventricular assist device

CHF congestive heart failure LVP left ventricular pressure

CO cardiac output MV mitral valve

CFD computational fluid dynamics NYHA New York Heart Association method PV pulmonary valve

CHF congestive heart failure rpm pump rotational speed

CVS cardiovascular system RV right ventricle

SOV2 mixed venous oxygen saturation Q flow rate

WHO world health organization Qa aortic flow rate

ΔP pump differential pressure Qav aortic valve flow rate

SV stroke volume Qp pump flow rate

SVR systemic vascular resistance rpm revolutions per minute

TAH total artificial heart ω pump impeller speed

VAD ventricular assist device I pump electrical current

VI electrical input power 2D two dimensional

Vtotal inlet-flow rate to LV model.

List of Figures

Figure 2.1:A longitudinal view of the heart and its main components (adapted ...... 12 Figure 2.2: Distribution of blood volume in the different parts of the ...... 13 Figure 2.3: “Syncytial” interconnecting nature of cardiac muscle ﬁbers (adapted from Guyton et al. [12])...... 14 Figure 2.4 : Ventricular pumping action; systole and diastole (adapted from Mohrman et al. [13])...... 14 Figure 2.5: Left ventricular function during cardiac cycle illustrating variations in left atrial pressure, left ventricular pressure, aortic pressure, pressure gradient, the electrocardiogram (ECG), and the phonocardiogram (adapted from Yellin et al. [14]). 15 Figure 2.6 : Heart pump function. The gray arrow indicates the influence of increased ventricular filling, while the black arrows indicate the findings of Frank and Starling .. 17 Figure 2.7 : Typical pressure-volume relationship of the left ventricle. The letters indicate valve action: A. mitral valve (MV) opens; B. mitral valve closes; C. aortic valve opens; D. aortic valve closes. (adapted from Vandenberghe [15])...... 18 Figure 2.8 : Schematic representation of the aortic valve: (a) side view of the complete valve, (b) after dissection of one leaflet with corresponding sinus wall and, (c) aortic view, (ada pted ...... 20 Figure 2.9 : Pressure and ﬂow curves for aortic and mitral valves (adapted from Yoganathan et al. [21])...... 22 Figure 2.10: Aortic (Pao: dashed line) and left ventricular (Plv: solid line) pressure curves during the cardiac cycle. The associated flow curve is also given (Q: dotted line). AO denotes the onset of valve opening and AC the moment of complete closure (adapted from Yoganathan et al. [22])...... 23 Figure 2.11 : Cardiovascular alterations with compensated systolic heart failure. Point (A) illustrates the intersection of normal CO and normal venous function curves (adapted from Alomari et.al [13])...... 26 Figure 2.12 : Left ventricular pressure-volume loops during heart failure ...... 27 Figure 2.13 : Prof. Christiaan Barnard with the first recipient of a donor heart (adapted from Vandenberghe [15])...... 30 Figure 2.14: Schematic of the myocardial wedge excised from the left ventricle in the Batista procedure. The resulting exposed edges of the ventricle are subsequently sewn together to yield a ‘remodelled’ ventricle (adapted from Starling et al. [38])...... 32 Figure 2.15 : Pulsatile-Flow (Panel A) and continuous-Flow (Panel B) Left Ventricular Assist Devices (LVADs) (adapted from Slaughter et al. [5])...... 37 Figure 2.16 : VentrAssistTM pump ( adapted from Gosline [17])...... 38 Figure 4.1 : Simplified 2D representation of the LV, aortic valve ...... 76

Figure 4.2 : (a) a fluid and structural element meshes in the simplified LV-pump model. The outer and inner AV segment lengths are 13 and 15.3 mm, respectively. (b) zoomed view of the AV highlighting the leaflet thickness, AV mesh and chamber element details. ... 78 Figure 4.3 : Sinusoidal velocity profile multiplied by an instantaneous step starting at ...... 82 Figure 4.4 : (a) Fluid and structural element meshes of simplified LV with pump and CVS model. The length and diameter of the pump cannula are 0.6 and 0.6 mm, respectively. (b) Zoomed view of the AV highlighting the leaflet thickness, AV and chamber mesh element details...... 84 Figure 4.5 : Windkessel model of the circulation where is the left ventricular outlet pressure, is the arterial systemic pressure, is atrial inflow to the LV, is the pump flow rate (L/min), is the blood flow ejected from the LV, is the characteristic aortic impedance, is the peripheral resistance and is the arterial systemic compliance...... 85 Figure 4.6 : Sinusoidal velocity profile applied to the inlet boundaries to simulate diastolic inflow. The inflow velocity oscillated in a sinusoidal pattern with period 1 s and a magnitude 0.75ms−1 about a mean level of 0.25 ms-1...... 88 Figure 4.7 : (a) Fluid and structural domain meshes for the simplified LV-LVAD interaction model with heart wall contraction. The length and diameter of the pump cannula were 0.6 and 0.6 mm respectively. (b) Zoomed view of upper AV leaflet highlighting the leaflet domain and LV chamber mesh element details...... 90 Figure 4.8 : Windkessel model of the circulation where is the left ventricular outlet pressure, is the arterial systemic pressure, is atrial inflow to the LV, is the pump flow rate (L/min), is the blood flow ejected from the LV, is the characteristic aortic impedance, is the peripheral resistance, is the arterial systemic compliance and P is the pressure differential head of the LVAD pump...... 94 Figure 4.9 : 2D representation of the LV chamber and pump cannula without AV ...... 95 Figure 4.10 : (a) Fluid and structural domain meshes for the simplified LV model without AV. (b) Mesh element detail at the sink outflow boundary. (c) Zoomed view of theoutflow bo und-ary highlighting the mesh element detail around the aortic outflow...... 97 Figure 4.11 : Windkessel model used with simplified LV-pump model without AV leaflets...... 100 Figure 4.12 : 2D geometry of the LV and AV (long axis plane) with LVAD cannula attached at the apex. The diameter of the LVAD cannula was 0.87 cm...... 104 Figure 4.13 .Two-dimensional geometry of the LV (long axis plane), LA, and ...... 106 Figure 4.14 : (a) 2D realistic LV model mesh. (b) Zoomed-in view of boundary mesh layers at the interface between the LV walls and fluid. (c) Zoomed-in view of AV leaflet tips highlighting the mesh element detail...... 108 Figure 4.15 : Mesh element size in 2D realistic LV model showing the aorta (Ao) and AV leaflet regions. (a) Boundary layer sizes at the Ao (b) zoomed view of the AV leaflet tips highlighting the element sizes in mm...... 110 Figure 4.16 : (a) Element quality of realistic LV model (q) in the range from 0 to 1. (b) Zoomed-in view of boundary element quality at the interface between the LV wall and

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fluid. (c) Zoomed-in view of AV leaflet tips, highlighting the element quality around the AV...... 110 Figure 4.17 : 2D realistic representation of the LV, AV, pump cannula and ...... 113 Figure 4.18 : Two-dimensional realistic representation of the LV, pump cannula ...... 114 Figure 4.19 : Boundary conditions of realistic LV-pump model...... 118 Figure 5.1 : Simulated pressure at pump outlet over a single 1 s cardiac cycle, where ...... 127 Figure 5.2 : Snapshots of simulated LV blood velocity magnitude during LVAD support at128 Figure 5.3 : (a) Simulated pressure from the pump outlet over a single, 1 s cardiac cycle, where ' * ' and ' ● ' indicate aortic valve opening and closing times, respectively. ‘c’ represents the period during which the aortic valve is closed, and ‘o’ is the period in which the aortic valve is open. (b) Zoomed-in view of pumpoutlet pressure. T-he pressure shown at the position of the arrows increases transiently on aortic valve closure...... 130 Figure 5.4 : Snapshots of computed LV blood velocity magnitude during LVAD support at various phases during the ...... 132 Figure 6.1 : Simulated motor electric current and pump impeller speed at two motor speed set points (100 and 150 rad/s), where ' ■ ' and ' ● ' indicate AV opening and closing times, respectively, (a) Simulations using a motor speed set point of set =100 rad/s. Periods 'O' and 'C' represent the phases during which the AV is open and valve closed respectively. (b). Simulations using a motor speed set point of set =150 rad/s. Periods 'O' and 'C' represent the phases during which the AV is open and closed, respectively. Max PCT and Min PCT are the maximum and minimum values of current threshold during AV closure, respectively. The motor current waveform at Max PCT begins to decrease more rapidly once the aortic valve is closed at the closing notch (CN)...... 144 Figure 6.2 : Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle...... 146 Figure 6.3 : Simulated left ventricular pressure (sold black line) and aortic pressure (dotted149 Figure 6.4 : AV state in 2D LV-LVAD realistic geometry simulations. The left pa- ...... 150 Figure 6.5 : Simulated electric current and pump impeller speeds at four motor speed set points (50, 100, 150 and 180 rad/s), where ' ■ ' and ' ● ' indicate AV opening and closing times, respectively. Periods 'O' and 'C' represent the phases during which the AV is open, referred to as ventricular ejection (VE), and valve closed (VC), respectively. Max PCT and Min PCT are the maximum and minimum values of motor current during AV closure, respectively. The motor current waveform at Max PCT further decreases once the aortic valve is closed at the closing notch (CN). (a) set = 50 rad/s (b) set = 100 rad/s) (c)set = 150 rad/s) (d)set = 180 rad/s...... 154 Figure 6.6 : Simulated electric current (black line) and distance between aortic valve (AV) lea fl-ets (red line) at a motor speed set points of 200 rad/s, where '●' and '■' indicate AV o pening an-d closing times, respectively. The duration of the closing phase was increased from lower set p-oint values, with the VC state beingcontinuously maintained (ANO). A R denotes the aortic val-ve regurgitant period through the cardiac cycle...... 155

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Figure 6.7 : Average inflow rate Qin (dashed line) applied at the inlet (source) boundaries, and the inlet pump flow rate Qp (solid line)...... 155 Figure 6.8 : LVP–peak (red dotted line) and LVAD motor current ...... 157 Figure 6.9 : Closure time against motor speed in LV model ...... 157 Figure 6.10 : Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle. For each panel, the three snapshots illustrate AV closing phase (left), opening phase (middle) and fully-open (right). (a) set = 50 rad/s. (b) set = 100 rad/s...... 159 Figure 6.11 : Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle. For each panel, the three snapshots illustrate AV closing phase (left), opening phase (middle), and fully-open phase (right). (c) set = 150 rad/s. (d) set = 180 rad/s...... 160 Figure 6.12 :Average pump inflow rate (Qp) at a motor speed set points of 100 rad/s, where ' ●' and '■' indicate AV opening and closing times, respectively...... 162 Figure 7.1 : Simulated electric current and pump impeller speed at two motor speed set points of 100 rad/s (top) and150 rad/s (bottom), where ' ● ' and ' ■ ' indicate AV opening and closing times, respectively, the periods 'O1', 'O2', 'O3' and 'C1', 'C2' and 'C3' represent the periods during which the AV is open and closed, respectively at conditions H1, H2 and H3 respectively. MAX C1PT, MAX C2PT and MAX C3PT, and MIN C1PT, MIN C2PT and MIN C3PT are the maximum and minimum values of motor current during AV closure...... 169 Figure 7.2 : Simulated distance between AV leaflets at two motor speed set points of 100 rad/s (top) and150 rad/s (bottom), where ' ● ' and ' ■ ' indicate AV opening and closing times, respectively. The periods 'O1', 'O2', 'O3' and 'C1', 'C2' and 'C3' represent phases during which the AV is open and closed, respectively, for conditions H1, H2 and H3 respectively...... 171 Figure 7.3 : Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle for = 100 rad/s...... 173 Figure 7.4 : Simulated motor electric current at three motor speed set points (50, 100, and150 rad/s), where ' ● ' and ' ■ ' indicate AV opening and closing times, respectively. The periods 'O1', 'O2', 'O3' and 'C1', 'C2' and 'C3' represent the phases during which the AV is open and closed respectively, at conditions H1, H2 and H3 respectively...... 175 Figure 7.5 : (a), (b) and (c). Simulated motor current waveform during AV closure/open phases, where ' ● ' and ' ■ ' indicate AV opening and closing times, respectively. Current levels MAX C1PT, MAX C2PT and MAX C3PT, and MIN C1PT, MIN C2PT and MIN C3PT denote the maximum and minimum values of motor current during AV closure, whilst MAX O1PT, MAX O2PT and MAX O3PT are the maximum current values during AV open phases. From top to bottom, the panels show pump speed set points of (a) set = 50 rad/s, (b) set 100 rad/s and (c) set = 150 rad/s)...... 177 Figure 7.6 : Simulated open and closed states of AV leaflets at two motor speed set points of (a) 50 rad/s and (b) 100 rad/s). The waveforms show the distance between AV leaflets, where the distance in the open state the distance was measured with a positive value in ix

millimeters. This open state is referred to as ventricular ejection (VE), whilst the valve closed (VC) state is when the distance was zero. Periods 'O1', 'O2', 'O3' and 'C1', 'C2' and 'C3' represent the phases during which the AV is open and closed, respectively at conditions H1, H2 and H3 respectively...... 178 Figure 7.7 : Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle for = 150 rad/s. (a) Aortic valve closing and opening phases under condition H1. (b) Aortic valve closing and opening phases under condition H2. (c) Aortic valve cl osing and opening phases under condition H3...... 180

Figure 8.1 : Simulated aortic valve flow (Qav), pump flow (Qp), left ventricular pressure (Plv) and aortic pressure (Pao), ...... 189 Figure 8.2 : Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle. (a) = 50 rad/s. (b) = 100 rad/s. (c) = 150 rad/s...... 191 Figure 8.3 : Left ventricular wall simulated cavity dimension during contractile motion. ... 193 Figure 8.4 : Top panels: left ventricular pressure (black line) and aortic valve pressure (do tted red line) at variouspump speeds. Lower panels: ...... 196 Figure 8.5 : Simulated aortic valve flow (Qav), (black line) and pump flow ...... 198

Figure 8.6 : Simulated pump motor current (black) and reference aortic flow (Qav) (red) at fou r motor s-peed set points corresponding to (a) 50 rad/s, (b) 100 rad/s, (c) 150 rad/s and (d) 200 rad/s, where '■' and '●' indicate AV opening and closing times, respectively. Qav > 0 represents the periods when the AV is open, referred to as ventricular ejection (VE), and Qav =0 represents the valve closed (VC) state. Note that in panel (d), Qav = 0 at all times, indicating the AV remains closed throughout the cardiac cycle (ANO) for this pump set point speed of 200 rad/s...... 199

Figure 8.7 : Simulated aortic valve flow (Qav), (black line) and pump flow (Qp) (red line) at a pump set point of 50 rad/s...... 201 Figure 8.8 : Simulated left ventricular pressure (sold black line) and aortic pressure (dotted bl ack line) and pump differential pressure head (red line) at the low pump speed set point of 50 rad/s...... 202 Figure 8.9 :Snapshot of simulated LV blood velocity magnitude during LVAD support at various phases i.e. AV closure time (left figure in all panels), LV opening phase (two figures at the centre in all panels) and next cycle closure phase (right in all panels) during the cardiac cycle. (a) = 50 rad/s. (b) = 100 rad/s. (c) = 150 rad/s...... 203

List of Tables

Table 4 -1: Material properties used for the simplified LV model ...... 80 Table 4 -2: Mesh properties of simplified CVS LV-pump model...... 86 Table 4 -3: Material properties of the LV-LVAD interaction model incorporating CVS and heart contraction...... 90 Table 4 -4: Mesh properties of simplified LV-pump model with CVS and heart contraction. 92 Table 4 -5: Mesh properties of simplified LV-pump model without AV leaflets...... 98 Table 4 -6: Material properties of the myocardium in simplified LV model without AV ...... 99 Table 4 -7. Material properties of 2D realistic LV model ...... 107 Table 4 -8. Material properties of the myocardium ...... 107 Table 4 -9. Mesh properties of realistic LV model...... 109 Table 4 -10 Fluid material properties in 2D realistic LV model...... 115 Table 4 -11 Material properties for the solid model...... 119 Table 4 -12. Simplified LV-pump model parameters for the healthy and abnormal condition subjects: Systemic peripheral resistance, Rsa; and total blood volume, Vtotal...... 122 Table 4 -13: Realistic 2D LV-LVAD model parameters for healthy and abnormal conditions: Systemic peripheral resistance, Rsa; and total blood volume, Vtotal...... 123 Table 6 -1 A summary of physiological and pump basic parameters identifying AV state...... 148 Table 8 -1. A summary of physiological and pump basic parameters identifying the aortic valve conditions...... 193

Part I-Introduction, Background and Literature Review

1 Chapter 1 - Introduction, Aims, and Outline

1.1 Research Motivation

Congestive heart failure (CHF) is a serious health condition resulting in diminished

blood flow to the tissues and organs in the body. More than 5 million people will

develop some degree of heart failure (HF) in their lifetime in the United States,

where its prevalence averages 2.1% of the normal population [1]. According to the

World Health Organization (WHO), a total of 17.3 million people died from

cardiovascular diseases (CVDs) in 2008, representing 30% of global deaths. Of

these, 7.3 million were due to coronary heart disease and 6.2 million were due to

stroke. This figure will increase to 23.3 million by 2030 [2].

Due to advancements in the medical treatment of HF, continuous flow Left

Ventricular Assist Devices (LVADs), known as Implantable Rotary Blood Pumps

(IRBPs), represent promising therapies for congestive HF patients [3]. A variety of

ventricular assist devices (VADs) have previously been effectively used in end-stage

heart failure patients, either as a bridge to heart transplant or to provide permanent

support. Patients alive on VAD therapy display significant improvements in heart

failure symptoms (New York Heart Association (NYHA) class II vs. IV), mood,

exercise capacity, and survival (1-year survival 52% vs. 25%; median survival 408

days vs. 150 days) [4].

More recent IRBPs are non-pulsatile blood pumps, representing the third generation of LVAD development. These non-pulsatile pumps are frequently used due their advantages of small size, efficiency, and reliability, which render them easily implantable, help improve patient health outcomes and increase the likelihood that patients resume normal lives [5]. Due to the shortage of appropriate heart donors,

LVADs are often used as permanent support, i.e. a destination therapy. They are also used as support to heart transplantation, i.e. bridge-to-transplant [6]. However, the increased use of LVAD for long-term mechanical support necessitates a better understanding of resulting hemodynamic changes in the left ventricle (LV), as well as the aortic valve (AV) state.

In addition, VADs can revise the systematic abnormalities in advanced CHF by improving systemic end-organ perfusion. Currently, VADs treat end-stage heart failure refractory to medical therapy [3]. A detailed understanding of the impact of the device on ventricular hemodynamic variables such as flow and pressure, as well as cardiac valve motion, is necessary to optimize LVAD use in unloading the ventricle.

On the other hand, in order to provide appropriate control strategies which accommodate heart valve state for the purpose of patient safety and recovery, an increased understanding of the interaction between the cardiovascular system (CVS), the LVAD, as well as the AV state under LVAD support, may allow the detection of the open/closed state of the AV from LVAD non-invasive parameters alone, paving

the way for more sophisticated pump flow control algorithms which take into

account the state of the aortic valve.

It is, therefore, important to understand the LV response to the pumping action of

these devices when connected to the heart, which can help improve the accuracy of

existing LVAD controllers which require feedback data such as blood flow and

pressure.

1.2 Thesis Aims

This thesis aims to examine the AV response to LV rotary blood pump assistance,

using 2D computational simulations of LV-pump interaction, investigating AV state

from LVAD non-invasive parameters. AV open-close state was assessed by

analysing pump motor current waveform (I) and pump impeller speed (ω).

The main hypothesis of this thesis was that AV state during LVAD support could

be detected and classified using non-invasive intrinsic pump parameters (i.e. pump

electrical current and pump impeller speed).

Using non-invasive pump parameters to investigate the impact of patient

physiological conditions on AV dynamics under different LVAD operating speeds,

may provide an insight to cardiovascular responses to these devices without using rotational examination (i.e. echocardiology). Furthermore, the AV is observed to be closed in most LVAD patients [7, 8]. However, with postural change, cardiac recovery and exercise, it may open on occasion. The AV may well offer a lower resistance path than the LVAD bypass route, with the native heart pumping significant flow relative to that via the LVAD [9]. These AV conditions under LV-

AD support could greatly influence greatly the current pump speed control strategy, and therefore would benefit from AV state detection.

AV state detection during LVAD support is challenging, and will greatly help to avoid high stress and pressure to prevent AV complications such as stenosis and thrombogenesis during LVAD support. Since implantable flow and pressure sensors are correlated with increase of the system cost and reduced reliability, this thesis will focus on using only non-invasive feedback measurements (i.e. motor electrical current and pump speed), as simulated from a 2D LV-LVAD interaction model, to develop all the necessary detection algorithms for AV state. Therefore, this thesis aims to achieve the following two objectives:

 To develop a numerical 2D LV-LVAD model using Finite Element (FE), Fl-

uid Structure Interaction (FSI) methods, to enhance the development of AV

state (open/close) detection methods during LVAD support. The model was

formulated with the aim of providing insights into the dynamics of heart-

pump interaction that cannot readily be obtained experimentally.

 To develop a novel approach to detect and monitor AV function during LV-

AD support by using simulated LVAD motor current waveform as an index

signal. Such information will lead to a more precise evaluation of AV functi-

on, helping reduce the risk of aortic insufficiency and other AV problems.

 This AV dynamics data could be used in developing a LVAD feedback

controller with the objective of recognizing pump speed set points within a

safe range of pump operating speeds, where the LVAD could be driven at a

pump speed between the starting point of 1) partial assistance (i.e. pump

assistance ratio < 100% where the net positive flow through both the aortic

valve and the LVAD) and 2) total assistance (i.e. pump assistance ratio =

100% where the AV remains closed throughout the entire cardiac cycle).

1.3 Thesis outline

This thesis is presented in nine chapters describing some background of HF, possible

treatments, modelling methods used, and simulation results of LV-LVAD fluid-

structure interaction in two-dimensional models that mimic the status of the aortic

valve during LVAD support.

Chapter 2 of this thesis introduces basic cardiovascular physiology, including AV

function and a brief discussion of HF and AV abnormal pathophysiology in

LVAD patients. Methods for HF treatment are briefly explained, focussing on LVADs and their various types (i.e. continuous blood flow and pulsatile flow) an d their applications. A summary of computational FE, FSI methods are also included in this chapter, as well as some details on existing LVAD control systems with methods of estimating pump parameters.

Chapter 3 continues with a review of the literature into this emerging field of FSI

LVAD modelling, allowing the reader to understand accumulated work done to resolve the problem of AV state detection and function. A survey will be presented regarding LV modelling, examining Computational Fluid Dynamics (CFD) approaches which have been used to model the cardiac cycle including LV and AV dynamics. Various studies that have attempted to simulate AV function under

LVAD support will be also be discussed.

Chapter 4 defines the computational methods used in this thesis, outlining two major geometrical LV-pump models. The first describes a modelling approach based on highly-simplified LV-Pump geometries, including dimensional definitions and numerical settings. The second model describes a geometric approach based on a more-realistic LV-Pump anatomy, including dimensional definitions and numerical settings. These models are used for various purposes:

(i) to simulate and predict AV status during LVAD support.

(ii) to examine the resulting data for pump current, average aortic outflow and distance between leaflets waveforms, under pulsatile flow conditions.

(iii) to validate the simulated models.

(iv) to estimate average pump differential pressure and average pump flow rate from average pump input power.

Lastly, in this chapter I have underlined the methods and protocols of simulation used to investigate LV-pump interaction over a wide range of pump and physiological operating conditions, including variations in:

(i) systemic vascular resistance; and

(ii) total blood volume, by varying the inlet-flow rate to the LV.

The primary focus of Chapters 5 and 6 is to use the 2D LV-pump model to simulate the AV open-closed state, and determine the effect of intra-ventricular flow on AV state within the LV chamber under LVAD support. Chapter 6 was divided into two sections: the first presents a systematic approach using a simplified LV-Pump interaction model to predict the AV state during LVAD support, whilst the second describes a more-realistic LV-Pump geometry with AV, to predict AV dynamics during LVAD support.

Chapter 7 represents an extension to Chapter 6. Three pump speed set points were used to investigate LV-pump interaction over a wide range of pump operating conditions and physiological states, including normal heart condition as well as alterations in systemic vascular resistance and total blood volume.

Chapter 8 represents an extension to Chapter 6, in which the aortic valve model was replaced with a computational representation of a pressure valve to mimic aortic 8

outflow. The AV state was predicted during LVAD support by using aortic flow and

non-invasive pump parameters.

Finally, recommendations for future research, along with the main conclusions of

this thesis are presented in chapter 9.

1.4 Publications

The work presented in this thesis was published in the following refereed conference

proceedings and abstracts during my PhD candidacy:

1.4.1 Refereed Conference Proceedings and Abstracts

K. A. Alonazi, A. V. Savkin, N. H. Lovell, and S. Dokos, ".Use of an implantable rotary blood pump for sensorless estimation of ECG isoelectric potential in a model of heart failure," in Engineering in Medicine and Biology Society (EMBC), 2012 34th Annual International Conference of the IEEE, 2012.

K. A. Alonazi, N. H. Lovell, and S. Dokos, "Modelling aortic valve open-close events during left ventricular support," Australian Biomedical Engineering Conference (ABEC), 2013.

K. A. Alonazi, N. H. Lovell, and S. Dokos, "Simulating assist device motor current waveform in monitoring aortic valve state during left ventricular support," Australian Biomedical Engineering Conference (ABEC), 2014.

K. A. Alonazi, A. V. Savkin, N. H. Lovell, and S. Dokos, "Modelling aortic valve closure under the action of a ventricular assist device," in Engineering in Medicine and 9

Biology Society (EMBC), 2013 35th Annual International Conference of the IEEE, 2013, pp. 679-682.

K. A. Alonazi, N. H. Lovell, and S. Dokos, "Simulation of motor current waveform as an index for aortic valve open-close condition during ventricular support," in Engineering in Medicine and Biology Society (EMBC), 2014 36th Annual International Conference of the IEEE, 2014, pp. 3013-3016.

K. A. Alonazi, N. H. Lovell, and S. Dokos, "Simulation of motor current waveforms in monitoring aortic valve state during ventricular assist device support," in Engineering in Medicine and Biology Society (EMBC), 2014 IEEE Conference on Biomedical Engineering and Sciences (IECBES), 2014.

2 Chapter 2 - Background

2.1 Overview

This chapter provides a brief background to the research area of this thesis. Basic

cardiovascular anatomy and physiology related to both the heart and the aortic valve

are presented in sections 2.2, followed by an overview of congestive heart failure and

its treatments in section 2.3, since this thesis aims to detect and monitor AV function

during LVAD support in heart failure. This section also includes a brief overview of

various pump outflow control strategies currently adopted (section 2.3.4), since this

thesis aims to provide insights into LVAD control based on simulated pump motor

current to monitor AV function. Section 2.4 then presents an overview of existing

heart-pump interaction computational techniques and models. More detailed literature

reviews are given in subsequent chapters in order to complement the distinct topics

presented.

2.2 Basic Anatomy and Physiology

2.2.1 Cardiovascular system

The human heart is located in the mediastinum (the space between the lungs in the

thoracic cavity), and weighs approximately 300 grams. The heart incorporates the

right and left atrium, the right and left ventricle (LV) and valves. The atria pass the

blood into the ventricular chambers. In contrast, the right and the left ventricles have

a thicker muscular wall to generate significant force to pump the blood through either the pulmonary or the systemic circulation [10] (see Figure 2.1).

The valves are located at the outlet and inlet of both ventricles to prevent the blood from backflow. For example, the mitral and tricuspid valves, during systole, prevent blood from returning to the atria from the ventricles. Likewise, the pulmonary and aortic valves prevent backflow to the ventricles from the aorta and pulmonary arteries during diastole.

Figure 2‎ .1:A longitudinal view of the heart and its main components (adapted from [10]) .

The cardiovascular system is comprised of both the heart and circulation, and functions to distribute essential elements to the tissues and organs to regulate and adjust oxygen supply and nutrients. It includes the heart, blood vessels, as well as major arteries, and veins which carry the blood (i.e. oxygenated and deoxygenated) 12

from the heart to the body tissues and back to the heart through the systemic and pulmonary systems [11] (see Figure 2 .2). The blood circulates through a closed system starting from the heart, passing through arteries, capillaries and veins. The systemic circulation covers the greater proportion of the blood in the circulation

(84%).

Figure 2‎ .2: Distribution of blood volume in the different parts of the circulatory system, (adapted from John et al. [11]).

The systemic circulation originates from the LV through the aorta, an elastic artery approximately 2.5cm in diameter, passing through various systemic tissues via the large arteries, small arteries, capillaries, small veins, and large veins before flowing back to the heart into the right atrium and right ventricle (RV). Blood return to the right atrium occurs via the superior and inferior venae cavae. Then RV then pumps the deoxygenated blood to the lung, through the pulmonary arteries, for gas exchange. The blood is then returned to the left atrium through the pulmonary veins

(see Figure 2.1), flowing to the LV to be pumped again into the systemic circulation as shown in Figure 2 .2 [11]

Figure 2‎ .3: “Syncytial” interconnecting nature of cardiac muscle ﬁbers (adapted from Guyton et al. [12]).

Heart muscle is constructed of cells known as myocytes, connected together via intercalated discs, formed by cell membranes, and specific for cardiac muscle [12].

Cardiac muscle is made from bundles of myofibrils, which contain the contractile elements (see Figure 2 .3).

Figure 2‎ .4: Ventricular pumping action; systole and diastole (adapted from Mohrman et al. [13]).

Heart muscle contracts by electrical stimulation from impulses arising from excitation of neigbouring cells. This excitation (known as an action potential) travels 14

from cell to cell. As a result, free diffusion of ions occurs and the action potential

spreads from one cell to another if these cells are excited.

The cardiac cycle begins from action potentials which originate in the sinoatrial

(SA) node located in the right atrial wall. These travel through both left and right

Figure 2‎ .5: Left ventricular function during cardiac cycle illustrating variations in left atrial pressure, left ventricular pressure, aortic pressure, pressure gradient, the electrocardiogram (ECG), and the phonocardiogram (adapted from Yellin et al. [14]).

atria causing contraction. The action potential is then conducted through the atrio-

ventricular bundle into the venricles. During the contraction period, blood is pumped

from the left ventricle through the aorta to the rest of the body, and this phase is

called systole [13] (see Figure 2 .4). Diastole is the period when the ventricles relax,

in order that they refill with blood returning via the venae cavae. Slow passive filling

of the ventricles marks this initial diastole phase (diastasis), with the final phase of

ventricular diastole known as atrial systole, where the atria contract with an ‘atrial 15

kick’, to fill the ventricles with 20% of their blood capacity. As shown in Figure 2 .5,

once the blood is transferred to the ventricles, they then contract, with this

contraction revealed as QRS waves on the ECG trace about 0.16 second after the

onset of the P wave [14]. Ventricular pressure then rises, causing both the mitral and

tricuspid valves to close. After this period when both valves are closed, the

isovolumic phase of contraction begins, where the pressure continues to build up

inside the ventricle.

When ventricular pressure rises above that of the pulmonary trunk or aortic pressure

at the end of isovolumic contraction, the aortic and pulmonary valves open, forcing

blood flow from the ventricles. Following this phase of ejection, the heart undergoes

a period of ventricular repolarization and relaxation, evidenced as a T wave on the

ECG [14] (see Figure 2 .5). As a result, ventricular relaxation starts and ventricular

pressure drops below that of the pulmonary arteries or aorta. The blood flows back

to the ventricles, resulting in both aortic and pulmonary valve closure, holding the

blood volume inside the ventricular chambers fixed. The ventricular pressure falls

rapidly below the atrial pressure causing the mitral and tricuspid valves to open,

allowing the blood to pass to the ventricles again, starting a new cycle of cardiac

contraction and relaxation.

2.2.2 Control of Cardiac Output

The heart in its natural environment pumps more than 7 tons of blood daily, beating

more than 100,000 times per day to meet the perfusion demands of the tissues and 16

organs. Due to this complex pumping action to maintain the pulmonary and systemic circulations, the heart requires a significant control system to guarantee accurate, continuous, and constant regulation of its haemodynamic parameters (i.e. pressure and heart rate), adjusting in response to external factors like stress, exercise or haemorrhage [13]. Heart function can also be described by the mean left ventricular pressure and volume of blood pumped per unit time (i.e. cardiac output). Heart pumping power is altered in HF patients, and can be severely diminished to the extent that the heart is unable to supply enough blood to meet the body’s metabolic needs.

Figure 2‎ .6: Heart pump function. The gray arrow indicates the influence of increased ventricular filling, while the black arrows indicate the findings of Frank and Starling ( adapted from Vandenberghe [15]).

The heart operates and is intrinsically controlled according to Starling’s law of the heart, known as the Frank-Starling mechanism which states that, Stroke volume increases as the volume of blood returning to the ventricle (end-diastolic volume

(EDV) or preload) increases [13] (see Figure 2 .6 ). This can be explained by the intrinsic mechanical properties of heart muscle: the greater a heart fibre is stretched, 17

the greater the extent of overlap between thick (myosin) and thin (actin) filaments,

leading to the formation of more cross-bridges and an increase in the fibre’s

contractile force. In other words, for a given afterload, increasing the preload to the

heart increases the active tension produced by the heart muscle fibres.

However, another approach for measuring cardiac function is via the LV pressure-

volume relationship. As illustrated in Figure 2.7 the LV pressure volume loop indi-

cates four phases that are representative of ventricular function: isovolumic relaxati-

on, filling, isovolumic contraction, and ejection [15].The relation between preload

(filling pressure) and end-diastolic volume has vital physiological and clinical

consequences. For example, in a normally functioning cardiac muscle, the actual

relationship is curvilinear, especially at very high filling pressures; it is

linear over normal operating range of the heart [16]. However, HF is characterized

by an abnormal pressure-volume relationship.

Figure 2‎ .7: Typical pressure-volume relationship of the left ventricle. The letters indicate valve action: A. mitral valve (MV) opens; B. mitral valve closes; C. aortic valve opens; D. aortic valve closes. (adapted from Vandenberghe [15]).

Other factors that have an effect in controlling the function of the heart include the

systemic arterial pressure (AP) effect on end-systolic volume during heart failure.

Furthermore, cardiac sympathetic and parasympathetic nerve activity also affects

contractility of the heart as well as its rate of contraction [17].

2.2.3 Aortic Valve Anatomy and Physiology

The heart has four valves that control the direction of blood ﬂow through the heart.

Heart valves play a crucial role in regulating the flow of blood between chambers.

Their function is to control the direction of blood flow during the cardiac cycle, or in

other words, to prevent the backflow of blood. Essentially, heart valves are passive

tissues that open and close due to inertial forces exerted by the surrounding blood.

There are two types of valves: semilunar and sigmoidal (see Figure 2.1). The

semilunar valves, (pulmonary valve (PV) and aortic valve (AV)), control the ﬂow of

oxygenated blood from the left side of the heart to the body, and are open during

systole when the ventricles are contracting to prevent the blood from flowing back

into the ventricle during diastole [10]. During isovolumic contraction and relaxation,

both valves are closed. These types of valves have different size and leaflet

dimensions.

Figure 2‎ .8: Schematic representation of the aortic valve: (a) side view of the complete valve, (b) after dissection of one leaflet with corresponding sinus wall and, (c) aortic view, (adapted from De Hart et al. [18]).

On the other hand, the aortic valve acts as a one way valve between the left ventricle

and the ascending thoracic aorta, as shown in Figure 2 .8. Basically, the valve

consists of three membranous leaflets and three sinuses [18]. These structures form a

cylindrical wall to which three crescent-shaped leaflets are attached. These leaflets

are attached to the aorta, and with their free edges, they fold back towards the wall

of the aorta to permit blood to flow from the left ventricle during systole. The

leaflets come together during diastole to prevent backflow and assist in the efficient

LV filling with blood.

As shown in Figure 2 .8, the cusp adjacent to the aortic valve is designated as the

anterior or aortic cusp, while the one closer to the ventricular wall is designated as

the posterior or mural cusp. Behind the cusps, the aortic root forms bulges known as

the sinuses of Valsalva, which, as reported by Bellhouse et al. [19], play a role in the

closure mechanism of the valve. They intersect the aortic root wall on the ventricular

side in a crown-like shape. The upper level where the sinuses merge into the aorta is

known as the sinotubular junction, and corresponds to the upper reach of the leaflets

in the open position.

2.2.4 Regulation of the Aortic Valve

During systole, which normally lasts 200 to 300 ms [20], the LV contracts and the

aortic valve opens. This valve closes during diastole when the LV is ﬁlling through

the open mitral valve. During isovolumic contraction, both valves are closed [21]

(Figure 2 .9). If the heart beats at 65 times per minute, which is a normal heart rate at

rest, then a whole heart cycle would last 0.95 seconds. The duration of ventricular

diastole would be almost two thirds of the beat, while systole would last about one

third of the cardiac cycle and begin when the aortic valve opens. During systole,

blood quickly rushes through the valve and reaches a peak velocity during the ﬁrst

third of systole after the leaﬂets have opened to their full extent and are beginning to

close again. The ﬂow starts to slow rapidly after the peak is reached. The developed

adverse pressure gradient affects the low momentum ﬂuid near the wall of the aorta

more than that at the centre: this causes reverse ﬂow in the sinus regions [21].

Figure 2‎ .9: Pressure and ﬂow curves for aortic and mitral valves (adapted from Yoganathan et al. [21]).

The pressure difference between the ventricle and aorta determines blood flow

through the aortic valve. Figure 2 .10 illustrates the pressure and ﬂow relations across

the aortic valve during the cardiac cycle [22]. During systole, the pressure difference

required to drive the blood through the aortic valve is small; however, the diastolic

pressure difference reaches 80 mmHg in normal individuals. The aortic valve closes

near the end of systole with very slight reverse ﬂow through the valve.

Figure 2‎ .10: Aortic (Pao: dashed line) and left ventricular (Plv: solid line) pressure curves during the cardiac cycle. The associated flow curve is also given (Q: dotted line). AO denotes the onset of valve opening and AC the moment of complete closure (adapted from Yoganathan et al. [22]).

Furthermore, the heamodynamics of the heart are responsible for shaping aortic

valve functionality, and knowing these effects are essential to understand the heart

response under LVAD support. For example, in healthy individuals, blood flows

through the aortic valve and may reach a peak velocity of 1.35±0.35m/s [23,

24]. Blood flow through the aortic valve is affected by the state of the valve.

Therefore, the complete closure and opening of the valve during and at the end of

systole is controlled by the inertial flow produced from the pressure difference

developed in the boundary layer along the aortic valve wall.

In addition, development of vortices in all the three sinuses behind the AV leaﬂets,

have a function was ﬁrst described by Leonardo da Vinci in 1513. With help of these

vortices during systole in the sinuses, the leaflets are pushed away from the wall to

close the valve, and prevent blood from returning to the ventricle during the closing

process, assisting in the efficient closure of the valve [25].

There are various studies that have investigated the action of vortices on AV closure

[26, 27], including the role of transverse pressure differences created by vortices that

push the leaﬂets toward the centre of the aorta and each other at the end of systole.

They concluded that this transverse pressure difference alone is enough to close the

valve, but is not as efﬁcient and rapid in the presence of vortices. The next section

will provide a brief overview of the of congestive heart failure and its treatments,

since this thesis aims to detect and monitor AV function during LVAD support in

heart failure.

2.3 Heart Failure Pathology and Therapy

2.3.1 Congestive Heart Failure

Congestive Heart Failure (CHF), or Heart failure (HF), is characterized as a serious

condition caused when cardiac pumping function reduces to such an extent that the heart is

unable to supply sufficient blood to cope with the body's physiological needs. The resulting

weak pumping action of the heart leads to a build-up a fluid (congestion) in the lungs and

other body tissues including the legs and feet. According to the World Health Organization,

the global incidence of CHF is increasing each year, with an estimated 9.4 million deaths

each year caused by heart disease [28]. CHF always results from an underlying disease

primarily affecting heart function such as heart valve disease or cardiomyopathy. It occurs

when the heart is unable to deliver sufficient cardiac output (CO) to prevent venous

congestion. When blood is not adequately returned to the heart, increasing pressure in the

lung and the veins leads to a build-up of fluid in different parts of the body. 24

Moreover, Gary et al. [29] describes heart failure as a “complex syndrome that can result from any structural or functional cardiac disorder that impairs the ability of the heart to function as a pump to support a physiological circulation”. Furthermore, the severity of CHF is difficult to quantify as it has various potential causes: it may arise from a number of defects such as myocardial failure where the cause is due to damaged myocardium (structural abnormalities), or mechanical factors where some obstruction to the pumping action of the myocardium leads to a decrease in its effectiveness, or from a combination of both the above. Increased understanding of the causes of CHF will lead to better therapeutical approaches. Patients suffering from end-stage CHF due to a damaged heart such as ventricular hypertrophy or dilatation are mainly treated with cardiac assist devices.

Indices used to predict cardiac function include ejection fraction, end-systolic volume (ESV), mean velocity of circumferential fibre shortening, end-systolic pressure-volume relationship, end-systolic stiffness, preload recruitable stroke work and first time-derivative of ventricular pressure [30]. In addition, increased pumping power of the heart in a CHF patient is accompanied by a reduction in stroke volume and cardiac output, as well as an increase in end-diastolic pressure (EDP), end- systolic volume and end-diastolic volume (EDV) of the failing ventricle [31, 32]. In the presence of reduced cardiac function, a number of natural body mechanisms occur to manage cardiac output including reflex control mechanisms which improve

abnormal contractility, left and right heart remodelling, as well as fluid retention

[31, 33, 34].

Figure 2‎ .11: Cardiovascular alterations with compensated systolic heart failure. Point (A) illustrates the intersection of normal CO and normal venous function curves (adapted from Alomari et.al [13]).

During HF, regardless of the cause, the pumping power of the heart and the Frank-

Starling mechanism are both degraded. The conditions of chronic heart failure are illustrated by the CO and venous function curves, as shown in Figure 2 .11 Alomari et.al [13]. These curves illustrate the normal operating point of the heart, defined as the intersection between the normal CO and normal venous function curves. In the healthy heart state, CO is 5 L/min and venous pressure almost 2 mmHg, whereas in the HF condition, the CO will be lower than normal at any given filling pressure causing a shift from the normal operating point as shown in Figure 2 .11. In addition, for the HF condition, the decline in SV and CO will cause an increase in all heart dynamics parameters such as contractility, total blood volume, and myocardial

remodelling, due to the increase in sympathetic neural activity, coupled with the increase in end-diastolic pressure as well as increased end-systolic and end-diastolic volumes [34, 35].

Due to HF, the relationship between ventricular pressure and volume is affected by a decrement in stroke volume and ejection fraction. Figure 2 .12 Alomari et.al [13] shows these phenomena along with a high filling pressure, marked by a decrease in contractility of the heart, as evidenced by the downward shifting of the slope of the end-systolic pressure volume relationship.

Figure 2‎ .12: Left ventricular pressure-volume loops during heart failure ( adapted from Alomari et. [13]).

Due to the complexity of CHF and its different possible causes and symptoms, the severity of HF is commonly gauged using the New York Heart Association (NYHA)

Functional Classification method based on the function condition of the patient. It

provides a way of classifying the extent of HF in patients according to their

symptoms [36]. These are:

I. Patients with no limitation in physical activities; they suffer no symptoms when

undertaking such activities.

II. Patients with slight, mild limitation during physical activity; they are comfortable

with rest or with mild physical exertion.

III. Patients with marked limitation of physical activity; they are comfortable only at

rest.

IV. Patents unable to carry out any physical activity without discomfort; they should be

at complete rest, confined to a bed or chair.

2.3.2 Ventricular Assist Devices: an Emerging Therapy for CHF

Therapeutic options for treating end-stage heart failure have evolved significantly in

recent years. Transplantation of the heart remains the traditional treatment, and is the

only therapy offering a real solution for the chronic HF patient. The ratio of the

number of donor hearts available to the number of potential recipients is declining.

This due to the fact that CHF is the main cause of death in comparison with

other diseases [15]. Due to the lack of donor organs, various alternative therapies for

CHF have emerged in the healthcare system. These include medical therapies such

as pharmacological treatment and surgery. However, mechanical therapies such as

total artificial heart replacement and ventricular assist devices (mechanical 28

circulatory support) are alternative treatments for heart failure. This thesis will focus

on left ventricular assist devices.

2.3.2.1 Surgical Therapies for Heart Failure

2.3.2.1.1 Heart transplantation

Despite advances in new technologies for the treatment of severe HF, the numbers of

myocardial failure patients have failed to drop considerably. The American Heart

Association’s latest update estimates that nearly 5,000,000 Americans suffer from

heart failure. Nearly 10 % of the population over 75 years old have been diagnosed

with HF [37].

Heart transplantation has become the standard therapy for these patients, and is

commonly accepted to reduce mortality and morbidity, as well as improve quality of

life. However, heart transplantation is a major surgical procedure carried out on end-

stage HF or severe coronary artery disease patients. Nonetheless, it is still the most

reliable solution for patients who have reached end-stage HF.

Figure 2‎ .13: Prof. Christiaan Barnard with the first recipient of a donor heart (adapted from Vandenberghe [15]).

The first successful human heart transplant was performed by Christian Barnard in

1967 in the Groot Schuur Hospital in South Africa (Figure 2 .13 Vandenberghe [15]),

followed by Shumway in 1968 in the United States at Stanford. Currently, more than

5000 heart transplant procedures are performed annually worldwide [29]. Although

heart tran-splantation still remains the standard treatment for heart failure, as

reported by Hardy et al. [38], due to the limited number of donors and graft failure,

multi-organ-system failure, infection, and acute rejection are the major leading

causes of death following transplation, minimizing the applicability of this

treatment. However, alternative medical therapies are increasingly being recognized

through medical trails as options for restoring heart function, alleviating symptoms,

and improving clinical outcomes.

2.3.2.1.2 Surgical reshaping

HF can also be treated with a number of innovative surgical approaches, which aim

to improve ventricular function, quality of life, and eventually, survival. These

approaches include coronary artery bypass surgery, aortic valve replacement, mitral

valve repair, ventricular restoration and passive restraints. In the following section,

two surgical treatments will be elaborated briefly.

2.3.2.1.2.1 Ventricular volume reduction Ventricular restoration, also known as the “Batista procedure”, is a treatment for

dilated cardiomyopathy which focuses on the reduction of ventricular volume to

restore ventricular function, by removing a wedge shaped piece of the LV wall of

about 100 g [34]. (see Figure 2 .14 Starling et al. [38]). In 1994, this treatment was

first implemented by Randas Batasta as a new surgical technique called partial left

ventriculectomy, He developed this technique because he lacked the technology that

was available in Europe and North America to use other therapies. His technique

was used to correct the pathologic alteration in cardiac geometry from its abnormal

spherical shape, caused by infraction, to its normal elliptical shape. Furthermore, this

procedure was performed by removing a wedge piece from the left ventricular wall.

However, in 2004 Dor [39] modified this technique, resulting in improvements in

the functional limitations of patients with heart failure end-systolic volume index

(ESVI) was calculated as end-systolic volume (ESV) divided by body surface area

[40]. Hence, this procedure can be used with transplant candidates, so it is also

applicable to carry out heart transplantation.

Figure 2‎ .14: Schematic of the myocardial wedge excised from the left ventricle in the Batista procedure. The resulting exposed edges of the ventricle are subsequently sewn together to yield a ‘remodelled’ ventricle (adapted from Starling et al. [38]).

2.3.2.1.2.2 Dynamic Cardiomyoplasty Another important surgical therapy for HF is dynamic cardiomyoplasty or passive

restraints. This procedure is based on hemodynamic factors to improve the structural

deterioration linked with heart failure. It is performed by wrapping the left latissmus

dorsi skeletal muscle around the dilated heart and stimulating it to contract

synchronously with the heartbeat by applying a regiment of electrical pulses. The

key issue in this concept is the training and stimulation of the muscle.

Cardiomyoplasty, as stated by Stijn [41], was first used by Carpentier following

testing with animal experiments. Today, this procedure is sufficient in patients with

congestive heart failure, by keeping the heart dimensions stable over a long period,

thus eliminating further dilation and remodelling of the heart [38].

2.3.2.2 Pharmacological therapy

Drugs have always been part of HF treatment, since they unload the heart by

controlling its activity or decreasing the afterload pressure from the arterial system.

However, the goals of pharmacological treatment are to minimize the likelihood of

death, alleviate symptoms, and improve the quality of life. These are achieved

through the use of inotropic agents such as digitalis, which increase the power of

contraction of the heart by increasing the amount of calcium ( released in the

myocytes. However, it is only in the early stage of heart failure that such drugs are

utilized [42]. Furthermore, β-Blockers and angiotensin-converting enzyme (ACE)

inhibitors are also very popular drugs for the treatment of HF. ACE is an enzyme

that is produced in the kidney, responsible for maintaining the tone in the blood

vessels as well as relaxation of the vessels and reduction in afterload. Unfortunately,

some of these drugs have unknown biochemical mechanisms, and can have toxic

side effects which result in excessive lowering of blood pressure to undesirable

levels [31]. However these treatments are also limited in their effectiveness, with an

associated increase in mortality by almost 18% every 6 months [29]. In addition,

these types of drugs may initially worsen ventricular haemodynamics, including the

β-blockers which affect heart rate and contractile power of the heart, decreasing

oxygen demand.

2.3.2.3 Mechanical therapies

Physicians nominated the option of replacing a defected heart with an artificial one,

even before even heart transplantation was available. The first successful total

artificial heart (TAH) was developed in 1953 by Gibbon, who developed the first

heart-lung machine during a cardiopulmonary bypass (CPB) surgical operation for

45 min [38]. However, due to the complications linked to these devices, total

artificial hearts are still being researched as a viable mechanical option for HF.

Currently, there are many disadvantages and challenges to deal with before any

TAH is globally accepted and used on patients, including life-threatening infection,

bleeding and thromboembolism [36] .

Another mechanical treatment for end-stage HF patients is the use of a cardiac assist

device (CAD) also referred to as a ventricular assist device (VAD). VADs are now

accepted as alternative treatment therapies for congestive HF patients. Because the

number of donors are limited, VADs are often essential, and are used to assist the

failing heart by pumping blood from the left or the right atrium or ventricle through

the ventricular assist device to a major artery [43]. In some cases, they can be used

to support both ventricles, left and right, also known as bi-ventricular assist devices

(BVADs or BiVADs)

Ventricular assist devices were first used in 1961 to support a patient whose right

ventricle exhibited impaired pumping [44]. The first implantable left VAD was rep-

orted in 1963 by Liotta et al. [7]. Furthermore, VADs can be implanted as a bridge to heart transplantation, or even as a destination therapy. They can improve end- organ function and reduce morbidity. To this end, pulsatile and non-pulsatile pumps have been developed to provide support of the natural heart. Eventually, it is desirable to establish a controller for such blood pumps, utilizing information such as blood pressure and pump flow rate. These two types of pumps are illustrated in

Figure 2 .15 [5]. Implanted LVADs draw blood from the apex of the left ventricle and pump it to the ascending aorta. Both pulsatile and non-pulsatile types are electrically energized by means of a percutaneous lead that connects the pump to an external system controller and power source.

DeBakey implanted the first ventricular assist device in 1963, to successfully treat a patient who had suffered a cardiac arrest following an aortic valve replacement.

Although the patient subsequently died, this operation proved the feasibility of mechanical circulatory assistance [37]. The limitations of these early devices, however, provided the motivation for the development of an intracorporeal LVAD powered from an external power supply. Currently, with the development of these devices, VADs are being successfully used as a bridge to recovery. This means the device does not only prolong life, but also improves the quality of life for HF patents with short life expectancy. For example, the Randomized Evaluation of Mechanical

Assistance for the Treatment of Congestive Heart Failure trial (REMATCH) was preformed over 3 years with over 120 patients being under observation with implanted ventricular assist devices. The outcomes established survival rates with a significant reduction of 33% in mortality, as well as significantly higher quality-of-

life benchmarks [45]. Furthermore, the expansion of the VAD spectrum is clearly evident today, and various studies have shown that LVADs can be successfully used as a bridge to transplantation. For example, a study designed for the second- generation LVADs showed successful outcomes with patients being assigned to ventricular assist devices, with survival rates 70% in the second year post- implantation [5, 44]. Consequently, these patients were able to return to normal daily activities. Despite the significant developments in LVAD technology, major problems such as thrombosis, bleeding and LVAD failure have not yet been solved, indicating much more room for LVAD improvement.

The LVAD results in a decrease in patient morbidity at the time of transplant, rendering the patient a better candidate and improving his/her post-transplant outcomes. The LVAD takes over the work of the LV by decreasing the filling pressure and increasing CO. Clearly, it will increase blood perfusion in organ systems, allowing HF patients to stabilize as they wait for a heart transplant. Another study in 10 patients who received an LVAD as a bridge to transplantation was maintained for up to 214 days. It found that LVADs maintain renal and hepatic function throughout the period of circulatory assistance [46].

According to the pumping principle of VADs, two major types can be classified: pulsatile-flow pumps and continuous-flow pumps. It is not the intention here to provide an overview of all the available devices. However, a short summary of current devices along with some new types will be given below.

Figure 2‎ .15: Pulsatile-Flow (Panel A) and continuous-Flow (Panel B) Left Ventricular Assist Devices (LVADs) (adapted from Slaughter et al. [5]).

2.3.2.3.1 Pulsatile-Flow ventricular assist devices

The Pulsatile-Flow VAD has been used medically since the late 1970s. It

consists of a chamber that fills and empties intermittently. In other words,

these devices have a chamber that fills with blood during one stage of the

operation cycle and pumps out the blood during the subsequent phase of the

cycle. This type of assist device may be divided into centrifugal, axial and

diagonal rotary pumps that differ in their appearance and inflow blood path.

In the device shown in Figure 2.15 (Panel A) Slaughter et al. [5], the motor withi n the device is powered from an external supply box. The motor drives a pusher

plate up and down frequently, that presses on a polyurethane diaphragm, whic h will maxim-ize and minimize the chamber’s volume and deliver a pulsatile flow to the aorta. In addition, it has a built-in valves at the inflow and outflow to control the direction of blood flow.

Furthermore, the TAH may also be considered a type of pulsatile-flow pump, where the patient’s ventricles are removed and the pump is inserted orthotopically [47]. Another example of this device is the third generation of the impeller rotary pumps with free contacting components and virtual shafts

Figure 2‎ .16: VentrAssistTM pump ( adapted from Gosline [17]).

supported by magnetic bearings, such as the VentrAssistTM pump (Ventracor Li-

mited, Sydney, Australia). In these devices, hydrodynamic forces offer a simple

means of suspending the impeller, preventing the complexity of active magnetic

bearings and reducing wear of contact pivot bearings. Consequently, these

devices are small, light, resistant to infection and durable, which makes this

generation of IRBPs easily to implant. Subsequently, good performance has

been achieved in device efficiency and prevention of haemolysis [8, 16, 48]. The

limitations of this type of LVAD are that the pump is noisy and the valve inside

the pump will decay over time. In this thesis, the LVAD that will be modelled is

the VentrAssistTM device, shown in Figure 2 .16 [17].

2.3.2.3.2 Continuous-Flow ventricular assist devices

As the blood moves through the systemic circulation, the initial pulsatile flow in the

aorta is gradually reduced, becoming continuous flow at the level of the capillaries.

Accordingly, pulsatile flow may not be necessary for humans. The non-pulsatile-

flow pump shown in Figure 2 .15 (Panel B) Slaughter et al. [5] contains a titanium-

coated rotor that curves around a central shaft with helical blades and an impeller.

An external drive line provides electrical power to a motor that drives the rotation of

the impeller by electromagnetic induction. The spinning impeller draws blood from

the inflow cannula to the outflow cannula. With this design, the continuous-flow

device has only one moving part and does not require valves, minimizing the long-

term risk of mechanical failure. In addition, the pump is smaller and lighter than the

first generation LVADs and functions in virtual silence.

Early concerns about the adverse effects of continuous flow on end organs have

been alleviated with successful long term use of this device [3]. Currently, the

HeartMateTM II is the only Food and Drug Administration (FDA)-approved

continuous flow pump.

2.3.3 Abnormal pathophysiology in LVAD patients

2.3.3.1 LVAD-Related Aortic Valve Dysfunction

In the past decade, studies have shown a potential correlation between LVAD

support and heart valve dysfunctions, in both pulsatile and non-pulsatile pump types

[49-54]. However, many studies did find a link between AV complications and

LVAD use. For example, one study found evidence of AV commissural fusion (i.e. a

remodelling process in which the aortic valve leaflets adhere together to prevent

complete opening of the valve) explanted from hearts supported by an LVAD [8,

51].

2.3.4 LVAD control systems

The centrifugal blood pump LVAD has been developed in many research

laboratories world-wide to understand its impact on the CVS with the aim of

developing a robust, implantable mechanical support device. Efforts have been made

to study and develop a variety of LVAD control systems in order to achieve the 40

optimal pump output demanded by the patient’s circulatory system. However, many

research groups have agreed that the main purpose of these control systems is to

provide a long-term treatment for heart failure. On the other hand, the implantation

of additional sensors is not desirable, as they may result in thrombus formation and

require regular calibration due to measurement drifts, which makes long-term

implantation of such devices problematic.

2.3.4.1 Dynamic modelling and estimation of LVAD pump parameters

The LVAD drives blood through the circulation by supporting the function of the

heart. In fact, it mimics the natural heart function. According to the Frank-Starling

law, the output of the ventricles depends upon the preload in such a way as to

provide blood flow that is equal to venous return. However, most researchers have

aimed at simply representing the function of the heart by monitoring LVAD

performance. One approach is to apply the intrinsic characteristics of the pump to

estimate the hemodynamic state of the patient. The second approach directly moni-

itors pressure and flow through the pump.

Blood pump operation requires the blood pressure and flow as parameters to the

controller, which can either be directly measured or predicted by an estimation

technique. Funakubo et al. proposed a method of estimating rotary pump flow rate

and pressure head from its motor speed and torque [55]. This approach was to be

used with a conventional positive-displacement type pump, where differential

pressure is estimated from the power supplied to the pump [56]. However, this type of pump failed when pump speed set point was increased because of back-flow, resulting in negative pressure or suction. More extensive control is obviously needed, not only for the pumping action of the VAD, but also considering the factors which the characteristic curve of the pump is highly sensitive to. These factors include physiological and mechanical properties such as blood viscosity and impeller inertia of the pump. Therefore, another scheme has been proposed to control the pump speed by adjusting the available supplied power. This means identifying the pump suction state according to an intrinsic motor signal such as electrical current. However, this method did not prevent the suction condition, but it helped to prevent over-pumping [57].

Another approach has been developed where the pump is attached to one of ventricles of the heart, as a left or right assist device. This model consists of a ventricular assist device, cannula, controller, and the recipient’s cardiovascular system. For example, Yih-Choung et al. and Lim et al. [58] claimed that their esti- mator could identify cardiovascular system parameters such as atrial compliance, peripheral resistance, and inertial properties of the blood as inputs to the controller to facilitate an effective control strategy [57-59]. These variables could be obtained in principle by sensor technology, but because of the disadvantages of sensors, researchers have looked to find alternative methods. Existing models have also been used to investigate pump control strategies that can respond to hemodynamic changes. However, the need to transform sensor measurements, such as flow rate and pressure, into the desired cardiovascular variables is recommended. Hence, flow 42

and pressure are mathematically estimated through the use of non-invasive

measurements of motor current and pump speed.

2.3.4.2 Estimation of pump flow and pressure head in LVADs

The non-invasive estimation of LVAD flow rate and pressure has attracted the

attention of many researchers. Various pump control algorithms have been designed

by different research groups, operating under steady-state or transitory conditions,

who have shown that pump flow rate and differential pressure head can be

accurately estimated. Kitamura et al. showed that continuous measurements of pump

pressure and flow are not attempted in long-term clinical use of artificial hearts due

to disadvantages such as catheter blockage with a thrombus, or septicaemia in the

recipient [60]. The proposed method first estimates blood viscosity by linear

equation 2.3 (see below) and then solves a set of three equations for the pump

system to calculate flow rate and pressure head. The three equations are as follows:

where denotes pressure differential from the aorta through the pump to the left

atrium, is the output flow of the centrifugal pump, is the natural heart output,

is the total systemic resistance, and is the compliance of the aorta.

The equation governing the centrifugal pump is:

Where is the rotational speed of the impeller, is the total inertance of the blood within the inlet and outlet pump cannulae, and are viscosity-dependent parameters.

The rotor equation is given by:

Where is the DC-motor current, is the inertia of all the motor rotating parts, are viscosity-dependent parameters, is the kinetic friction coefficient of the rotor axis, and is the torque constant of the DC motor.

However, pulsatile flow estimation was covered by only a few studies. This may be

due to a number of factors, such as the use of pump characteristic curves which are sensitive to many physiological and mechanical parameters such as blood viscosity and pump impeller inertia. The design characteristics for each pump can contribute to the proposed estimation algorithms: this means that different unique equations can be obtained. Wakisaka et al. [61, 62] noted that it is important to determine the pump flow rate for a mechanical heart in clinical use after implantation in a recipient. Flow rate can be estimated by power consumption and the rotating speed of the motor, but because of fluctuations in blood viscosity, there is a need to understand the factors affecting this. He suggested a non-invasive method for correcting this estimation for centrifugal blood pumps (National Cardiovascular 44

Centre -NCVC-2™,Tokyo, Japan). Output power, pump speed and the haematocrit are measured, and their flow rate estimation method is shown in equation (2.4):

is the estimated flow rate (L/min), is the power consumption of the motor

(watts), is the rotating speed (rpm), and is the haematocrit (HCT). The values for parameters , and , were determined by least squares fits to data.

Tanaka et al. [63] proposed a new method for estimating instantaneous pump flow rate and pressure, based on motor voltage, current and rotational speed. They used two auto-regressive exogenous (ARX) models where the current and past values of power and speed were used as inputs to another ARX model. Their estimation method has been validated on-line in acute animal experiments, with actual measured values of blood viscosity. Their method was successfully able to estimate pump flow and pressure when the blood viscosity changed.

Yoshizawa et al. [64] utilized power and pump speed to estimate pulsatile pump flow and pressure as the output of a two dynamic time series ARX models, as shown below in equations 2.5-2.6. This was performed by employing six fluid solutions, representing various levels of viscosity, as input parameters. After collecting the values of input and output, the coefficients were identified, the pulsatile flow and pump head pressure were estimated by employing two ARX models together. In the

first model, the coefficients were identified before pump implantation (off-line) using two inputs: pump speed and power. The second ARX model identified the steady state gain of the system, estimating blood viscosity on the basis of two inputs: power and rotational pump speed on-line (i.e. after implantation of the pump).

Furthermore, these two ARX models were combined to complete the estimation process with changing of blood viscosity each time and steady state gain recorded at these time changes. Furthermore, a mock loop system was used for the validation, with an error of 1.66 L/min which was affected by the input gain. The first ARX model was given by:

where is the electrical power, is rotational speed, and b1 – b6 are parameters to be identified by measured data. The second ARX model was given by:

where is the discrete time index satisfying , is the sampling period,

is the residual assumed to be white noise, is the order of the output, is the order of the input, are six kinds of exogenous input and and are coefficient parameters.

Furthermore, due to the insensitivity of LVADs to overflow and underflow, together with uncertainties in estimating pump flow, it is appropriate for pump control

strategies to prevent uncomfortable pumping conditions for the recipient. Malagutti et al. [65] investigated the role of the blood hematocrit (HCT) on a non-invasive iRBP flow estimation algorithm. Three input variables were used for flow estimation: the electrical power, pump speed and HCT. The resulting algorithm was then tested with a validation data set using different blood viscosities. Since iRBP flow depends upon the amount of blood in the LV, estimating blood flow and differential pressure is essential in designing an automatic, robust, and responsive control system that can effectively control the pump flow according to the body’s physiological needs and perturbations [66].

Most LVADs currently function at a fixed speed, which is controlled by the medicalspecialist. On the other hand, Bertram has found that detection of pump flow and differential pressure alone can be the basis of an adequate control strategy to assist the failing heart [66]. Wu et al. [67] based their algorithms on the control of aortic pressure rather than pump differential pressure. Other investigators have estimated pump pressure and flow in cardiac failure conditions, represented these as dynamic functions of the motor variables, and identifying the unknown coefficients mathematically. However, these coefficients depend on which specific pump and motor are used. For example, the fluid-dynamic design of the left ventricular assist device (VentrAssistTM) produces a particularly flat head-flow (HQ) curve [68]. Lim e t al. [69] proposed a dimensional analysis method for the estimation of implantable rotary pump flow and head pressure. This method utilizes theoretical principles of fluid mechanics, which provides a valuable understanding of the parameter relationships. Furthermore, their flow and pressure estimates were validated with two LVADs from VentrAssist™. Linear regression between the estimated and measured flow and head pressure values was plotted over a flow range 0.5 L/min to 47

8.0 L/min. Resultant slopes were 0.98 and 1.027 respectively, with respective errors of 5.79% and 1.51%.

Moreover, Ayre et al. [70] have used static, non-pulsatile and pulsatile mock loops with aqueous glycerol (AG) solutions and ovine blood to estimate average flow for a single viscosity. The static equation for the estimated flow was of the form:

(2.7) where Qest denotes estimated flow rate (L/min); denotes pump rotational speed

(rpm), and VI represents input electrical power (W). The values obtained for each of the six parameters (a, b, c, d, e, and f) were then plotted against blood viscosity, in order ascertain how to incorporate blood viscosity in a comprehensive relationship.

In this study, the authors proposed a non-invasive method to estimate iRBP flow in various hydrodynamic states using mock-loops and in-vivo experiments. Although these studies showed successful results when used to estimate the pump flow and pressure head, they did not focus on the stability of transient changes in pump flow.

However, Alomari et al. [71] proposed a dynamic model for pulsatile flow estimation of LVAD pressure and flow. The inputs of this model were acquired from the pump electrical power ( ), impeller rotational speed ( ) togther with HTC measured non-invasively. A viscosity range of 20% -50% was implemented in the mock loop using various AG solutions. Furthermore, a linear regression analysis between the measured and estimated pulsatile flow revealed a highly significant

correlation ( = 0.957) and mean absolute error of 0.902 L/min. In addition, further validations were undertaken using six sets of ex-vivo animal data. Their model provided accurate estimation of the transient response and the dynamics of pulsatile flow. The investigators utilized the steady-state solution given by equation 2.8:

where and are constants and the power coefficients and were found to have a linear relationship with the HCT. The dynamic version of the model defined an input to the dynamic system f(t) as follows:

f(t) =

where , is the sampling period and

The dynamic model for the left ventricular assist device was given by:

where is the output of the system which represents the estimated instantaneous value of the pulsatile flow is the input to the dynamic system model defined in Eq. 2.9, is the shift operator, whilst are polynomials defined as:

where is the model output order, and is the model input order satisfying condition .

In addition, AlOmari et al. [72] proposed a dynamic model for LVAD inlet pressure

estimation during the diastolic period. This model was used to design a controller to

regulate mean diastolic pump inlet pressure. Non-invasive variables such as pump

speed and power as well as a pulse width modulation signal (PWM) were used as

inputs to an ARX model to estimate inlet pressure during the diastolic period. The

model was validated using in-vivo animal data under a wide range of pump speeds

under various heart conditions.

2.3.4.3 Existing LVAD control strategies

Ventricular assist devices are used for long-term therapy for congestive heart failure

patients. Among these devices, iRBPs have been increasingly popular due to their

small size, and simple design. However, one of the disadvantages of rotary blood

pumps lies in their control strategy for maintaining outflow under different

physiological HF conditions. Most implanted LVADs are controlled manually by a

trained physician, using fixed procedures to adjust the outflow rate for patient

comfort. However, automatic and robust control systems have seen the steady

replacement of the role of clinicians to maintain physiological perfusion under

various conditions. This will hopefully contribute in helping LVAD patients live normal lives and continue their regular activities.

Efforts have been made to study and develop a variety of controllers for implantable ventricular assist devices. These can be classified according to controller input variables such invasive and non-invasive data. However, there are two designs of non-invasive controllers which have been used to control rotary blood pumps for maintaining physiological perfusion, which will be briefly explained. The invasive method of implanting more sensors is not recommended for long-term therapy, since additional sensors can result in inflammation and thrombus formation.

The first non-invasive control technique uses physiological variables as the inputs for the controller to determine the pulsatile and continuous pump flow rate. These variables include atrial pressure, blood oxygen saturation and lactic acid levels in the blood. Moreover, a number of physiological control strategies have been proposed for iRBPs, and many research groups have decided that maintaining atrial pressure within limits that balance blood volume in both sides of the heart is a practical method. Mclnnis et al. [73] proposed a physiological control system that incorporated LVAD and CVS models, which was controlled by a self-tuning PID- controller to control pulsatile blood flow [74]. This controller was designed to cope with different types of physiological demand to regulate left atrial pressure (LAP), and was validated by using mock-loop circulation system data. The controller

performed well when LV physiological conditions were simulated in the mock-loop.

The stroke volume (SV) of the assist device was adjusted by the control system so that the mean left atrial pressure remained at the desired level. Kitamura et al. proposed a new method to avoid using pressure sensors for measuring atrial pressure

[75]. The authors used a dynamic compensator technique for left atrial control for use with an artificial heart drive system. The goal here was to improve optimal pump output for the volume that the patient's circulatory system required.

Most recently, Karantonis et al. [76] proposed a control algorithm for an implantable centrifugal rotary blood pump based on non-invasive indicators of the implant recipient’s activity level. The authors used the Activity Level Index (ALI) as input to the controller. ALI was based on two variables: tri-axial acceleration and heart rate

(HR), which together can be used to estimate metabolic energy expenditure. This non-invasive method makes it possible to control left ventricular stroke volume to compensate for changes in LV end-diastolic volume or its correlate preload.

However, Nakamura et al. [77] proposed mixed venous oxygen saturation

(SVO2) as an input variable for physiological control of a TAH. However, use of SV-

O2 sensors is not recommended because of the likelihood of thrombosis and inflammation in the patient.

The second non-invasive control technique to estimate pump flow and pressure is by using non-physiological input variables such as pump electrical current, voltage, and rotational speed. In this technique, flow and differential pressure used for the control algorithms are empirically estimated typically through experimental recordings of 52

pump flow and differential pressure. For instance, Giridharan et al. [78] proposed an effective proportional integral PI feedback controller to maintain a reference differential pressure between the LV and aorta. This model-based control system was able to regulate the pump speed within physiological limits, minimizing the difference between the reference pressure and the actual differential pressure.

Alomari et al. [79, 80] proposed a deadbeat controller to control pulsatile pump flow using a tested algorithm for steady and pulsatile reference pump flows. Pump speed, power and pulse width signals were used to estimate the pulsatile flow and inlet pressure. These values were used together with servo parameters as inputs to the control system, with pulsatile flow and pressure head as the output. In addition, both constant and sinusoidal reference pump flow inputs were used to test the controller algorithm under healthy and HF conditions. This controller showed that the simulated flow accurately tracked the reference input signal with an error of ±0.7

L/min [81].

Moreover, there are several varieties of non-invasive control methods which include suction limit control and preload control; all of which require demand-responsive control algorithms for implantable centrifugal pumps.

2.4 Existing LVAD Models and Computational Methods

2.4.1 Overview of Computational Techniques for LVAD-AV Modelling

Numerous computational methods have been used to simulate mechanical

interaction between blood and AV motion in the heart. This section will provide an

overview of fully-coupled fluid-structure interaction numerical techniques, whereby

fluid flow in the model affects mechanical defamation of solid structures and vice-

versa. This fully-coupled approach forms the basis of models developed in this

thesis.

2.4.1.1 Fluid-structure interaction

Fluid-Structure Interaction (FSI) was developed in the 1970’s to simulate the

interaction between a deformable solid in contact with fluid. FSI research initially

focused largely on aerospace applications, as reported by Farhat et al. [82]. It is now

used for a range of engineering applications dealing with the multi-physics

relationships between deformable solid structures with a surrounding and/or internal

fluid. To date, three main aspects of FSI methods have been developed. First, is the

technique used to discretise the governing equations for the solid and fluid domains,

which include the Finite Element Method (FEM) and Finite Volume Method (FVM).

The FEM will be discussed in more detail in the subsequent section of this chapter.

Second, is the coupling interface between the fluid and solid. For cardiovascular models involving structural motion change (e.g. AV deformation) due to fluid flow

(e.g. blood flow), the FSI method is very practical and accurate in simulating native heart physiological behaviour in terms of wall contraction and valvular conditions during the cardiac cycle. The computational models developed in this thesis are governed by the complex interaction between the heart wall, valve leaflets and blood flow. The coupling method used to link cardiac geometry with blood on the solid- fluid interface is a key issue. Existing coupling methods are categorized into two categories, partitioned and monolithic. The one-way method, used by most FSI approaches, is a partitioned approach [83]. The monolithic method represents a strong-coupling approach, a two-way mathematical or computational process which relates the solution method with the movement of the solid structure and thereby affects the blood flow which, in turn, affects the motion of the structure. The partitioned method, is weakly-coupled, separating the fluid and solid structure and then solving their governing equations with two different solvers until both solutions converge.

The next section will provide a brief overview of the finite element method, which was used to numerically implement the FSI models of this thesis.

2.4.2 Finite Element Method

Finite element methods are employed extensively in the analysis of solid structures

and fluids, and indeed are useful in almost every field of biomedical engineering

design. FEMs are the numerical tools of choice for solving partial differential

equations (PDEs) and are widely used in biomedical engineering applications, with

this use expected to increase significantly in the coming years. Complex

physiological systems require appropriate methods for structural analyses, with

numerical techniques for structural analyses such as FEM and boundary element

methods (BEMs), are promising approaches used from the 1950s, with the help

of advanced computer systems [84].

Accurate prediction of fluid dynamics and solid mechanical response is essential in

the simulation of native heart valve dymanics, particularly, the opening and closing

behaviour of the aortic valve during LVAD support. Finite Element Analysis, or

FEA, involves using mesh generation for dividing a complex problem into small

elements with the use of computational software programs coded with FEM

algorithms. Domain meshing is an important step in the prediction of native heart

responses and potential abnormalities in heart valves (i.e. thromboembolic

complications and AV stenosis) to LVAD support, with underlying physics such

as the Navier-Stokes fluid equations given as PDE or integral equations solved over

each element.

In addition, simulation methods are highly useful and efficient, since in-vivo

experimental approaches often require the creation of expensive, time-intensive 56

prototypes and evaluations. Therefore, numerical methods such as FEM are often preferred for investigating complex dynamic systems, including the interaction of the valves with the blood to understand their function in the human heart during

LVAD support.

FSI when combined with FEM, aims to simulate the motion of solid structures (i.e.

AV leaflets) due to a surrounding fluid. In contrast, in purely structural FEM, there is no fluid-solid coupling; the loads must be assigned before the solution can be found. Using FEM, the irregular geometries of human organs or tissues are replaced by discrete models developed by subdividing into a number of finite elements. These discretised, as an assemblage (mesh) models, are composed of appropriately shaped elements represented by a chain of interconnected points known as nodes. Elements can be rectilinear or curvilinear, forming a grid. Implicit within each element is its force/displacement function which, in terms of parameters to be determined, defines how the force/displacements (i.e. element stiffness properties) are interpolated from the nodes over each element. This may be either an external force applied as a load to the structure, or an internal force that transfers loads between elements. The equations of equilibrium are solved for each element, and variables in time can be modelled using either implicit or explicit methods by dividing into a number of time steps. When applied to the analysis of a continuum fields over a domain, either solid or fluid, the spatial discretisation forms a matrix assembly consisting of a number of degrees of freedom. Using the implicit method, acceleration is assumed to vary linearly within each time step, which gives a more accurate representation. In the

explicit technique, the equations of motion are solved at every time step by assuming

that acceleration is constant over the step.

A major advantage of FEM is that relatively moderate finite degrees of freedom can

model a range of complex forms (i.e. one or two dimensional shells or solid

elements), and can be handled with ease, and numerically solved with system

algebraic equations. The essential characteristic of FEM is that the solution of the

discrete system is assumed, a priori, to have a prescribed form. Also, the solution is

strongly linked to the geometric representation of the domain, which is an integral

(or weak) form of the PDE. Generally, this integral (weak) equation is developed

using a weighted residual method which can include differential type boundary

conditions. A final characteristic of FEM is the modular way in which the

discretization is achieved, which is assembled from an element-element level to

define a global matrix system of equations [85].

The next section will provide a brief overview of existing computational studies of

ventricular support devices and their interaction with the cardiovascular system. This

thesis aims to extend the scope of such models to incorporate AV motion.

2.4.3 Heart-Pump Interaction Models

Implanted LVADs are difficult to monitor using standard medical image modalities

such as MRI and echocardiography due to limitations with device positioning as

well as the metallic parts of the pump and impeller. Consequently, numerical simulations using CFD and FSI schemes solved with the Arbitrary Lagrangian–

Eulerian Finite Element Method have been important tools for cardiac function research, providing a crucial visualisation of cardiac function, blood haemodynamics and abnormalities in the circulatory system. Since this approach is based entirely on non-invasive tests using computer software, issues of reduced experimental reliability and relatively higher costs associated with incorporating in vivo tests are avoided.

Non-invasive experiments such as computational simulations, have emerged as key tools for directly analysing the complex mechanics and dynamics of the heart. Such numerical simulations have been used ny many investigators for evaluating heart function, simulating the dynamic changes in the cardiovascular system (CVS) under healthy, diseased, and VAD-supported conditions. Such numerical models could be used to simulate CVS behaviour in the presence of an LVAD, providing additional insights into the dynamics of assisted circulation. This could provide insights into the performance characteristics of the blood pump and its interaction with the pulsating heart. Non-invasive computational methods of heart-pump interaction can be categorized into lumped parameter and finite element models.

3 Chapter 3-Review of Modelling Approaches in Cardiac Dynamics

3.1 Background

Understanding the fundamental response mechanisms of fluid/solid coupling in the

heart is crucial for characterizing normal heart function and its behaviour in disease.

Although flow in the human heart, particularly the left ventricle (LV), has been

investigated by invasive and non-invasive imaging [86, 87], there is still only a

limited understanding of blood and heart tissue interaction, particularly if the LV is

assisted with a pump device. The latter scenario is the basis for the modeling work of

this thesis.

Lumped parameter models have increased our knowledge and understanding of

cardiac function and the interaction between the LV and its valves [88]. FSI is

commonly used as an important modelling approach to acquire an understanding of

cardiac hemodynamic and heart valve behavior [89-91].

In recent years, cardiac CFD simulations, including studies of blood flow patterns,

have played an important role in investigating heart wall motion and valve function.

More detailed understanding of the coupled relationship between blood flow patterns 60

and the myocardial valves can be further enhanced by the combined use of CFD and patient specific geometries. It represents a reliable tool that can be used to improve our understanding of heart changes during the cardiac cycle such as relaxation and contraction, as well as the pathophysiology of heart valves, which could be very useful in the investigation of AV status during LVAD support. AV dynamics has been largely ignored in previous modelling studies of the LVAD-supported heart.

Although LV-pump interaction may be partially understood through in-vivo animal studies, such studies are unconvincing at present due to a shortage of animal models of heart failure [92]. The primary advantage of computational models is that they play a significant role in simulating heart failure experiments under similar conditions. Therefore, such models offer an excellent platform for the development and evaluation of cardiac physiological dynamics.

On the other hand, there are three types of in-vitro based methods to simulate blood flow within the ventricles to reconstruct the mechanical behaviour of the LV and aortic valve: the geometry-prescribed CFD method, the fictitious FSI method, and the realistic FSI method. These methods offer full flow features in the ventricle, such as velocity profiles, pressure, shear rate and recirculation. They have been commonly used in the simulation of heart valve function during cardiac cycle [93].

In this thesis, the realistic fluid-structure-coupled simulation of the AV and left ventricle during ejection phase under LVAD support is utilized.

Realistic FSI requires at least three aspects to accurately simulate heart dynamics, as reported by Cheng et al. [94]. First, the structure solver must be able to define the nonlinear, anisotropic and inhomogeneous tissue characteristics. Next, the CFD method must be able to solve the large deformations at the boundaries of the fluid domains, updating the meshes accordingly. Last and most importantly, the coupling algorithm must be able to couple the fluid (i.e. blood) and structural elements (i.e. heart valves and inner walls) correctly and ensure convergence. In this thesis, this approach is applied to specifically investigate LV fluid/solid coupling, allowing quantitative examination of blood flow through the LV, pressure distributions and

AV movement.

The survey of literature presented in this chapter, regarding cardiac dynamics modelling, will focus on two aspects. The first is a review of CFD studies which have been undertaken using realistic simulations of the LV, including simulating AV dynamics. The second will examine studies that have simulated AV function under

LVAD support. However, none of these models include a two dimensional (2D) model of AV state during LVAD support under pulsatile flow conditions, as presented in this thesis.

3.2 Existing cardiac dynamics models

Numerical simulations of the mechanics of the heart may be divided into three

general categories, solid-only, fluid-only, and fluid-structure interaction. Many

studies have focused on solid-only simulations that compute the deformations of the

heart walls by specifying inner boundary conditions for the pressure [95] [. Fluid

only simulations simulate the flow of blood through the heart by assigning prescribed

wall motions in patient-specific geometries, according to data collected from

magnetic resonances edition imaging (MRI) techniques [96].

ALE methods employ a grid that is modified to, and deforms with, the moving

boundary. It has many advantages for finding solutions to a wide range of time-

dependent complex fluid dynamics problems such as three dimensional (3D)

simulations and studies of blood flow in arteries [44]. In addition, the method uses a

finite difference mesh with vertices that may be moved with the fluid (Lagrangian

frame), be held fixed (Eulerian frame), or be moved in any other prescribed manner.

The theoretical framework for mixed Lagrangian-Eulerian finite element

descriptions has been established by Hughes et al. [97] in the context of

incompressible and viscous flows.

A large number of investigations have been carried out on the haemodynamics of the

left ventricle using CFD techniques. This computational method has been widely

used since the early 1970s: for example, Bellhouse et al. [98] provided a LV model

incorporating the mitral and aortic valve to investigate the effect of LV vortices in

mitral valve open and closed states. Reul et al. [99] investigated the forces causing

mitral valve closure under an adverse pressure gradient, incorporating valve leaflet

motion. Taylor et al. [100, 101] simulated haemodynamics within the left ventricle,

including detailed flow and pressure gradient behaviour. Their computation used a

3D realistic LV anatomy. Jones et al. [102] extended this work to more accurately

simulate blood flow within the LV. Vierendeels et al. [103] developed a 2D axi-

symmetrical model of detailed LV flow during filling, examining the flow patterns

produced during the diastolic phase. These studies have provided important results

on the role of the LV wall stiffness on blood flow during the filling cycle.

In addition, pioneering 2D and 3D simulations in cardiac dynamics include the studies of Peskin and McQueen [104-109]. These investigators incorporated a left chamber into their heart models using the immersed boundary method. The solid domain was not explicitly characterized within the fluid field, however it was represented by an additional force field that the solid applies on the fluid where the two fields overlap.

As a result, the first model of left ventricular valve function using the immersed boundary method was due to Peskin [110], who detailed the fluid-ventricular wall interaction scheme [105].

Vesier et al. [111] have developed a 3D ventricular thin-walled model, which gives a realistic behaviour of LV function when compared with clinical data. In addition,

Lemmon et al. [112] have used the same realistic approach to cardiac modelling with the immersed boundary method in a 3D heart model to simulate the blood-tissue interaction. This technique offered a significant tool in various studies to assess cardiovascular function and investigate the phenomena of vortex and swirling motions within the LV interacting with heart valves [113-115], inflow velocity and pressure, particularly intraventricular ﬂow dynamics on mitral [116] and aortic valve [117]

ﬂow. Long et al. [118] determined that CFD simulations of left ventricular ﬂow are highly sensitive to the boundary conditions imposed. In addition, Vierendeels et al.

[103] proposed a 2D axisymmetric ventricular model based on the ALE method, to examine the formation of pressure and vortex patterns during the filling phase.

These simulations did not take FSI into account. FSI needs to be carried out using different, albeit tightly coupled, sets of equations for the fluid and solid domains, using either a monolithic or a partitioned coupling method [119, 120]. The differences between these is that the monolithic method solves two sets of governing equations (i.e. solid and fluid) at the same time and is computationally challenging.

However, the partitioned scheme computes the solid and fluid fields individually, coupling these together through iterative updating of boundary conditions at the interfaces. Consequently, it can minimize the computational process time by taking advantage of sophisticated codes that have been developed to solve pure fluid or structural problems. Borazjani et al. [121] have identified the relationship between the background grid and the moving bodies. They conclude that the stability

of FSI code depends both on the properties of the structure (mass and geometry) and on the sign of the local progressive force imposed by the local flow on the structure.

Hence the FSI method, which is more accurate and realistic, directly couples both the solid wall motion of the heart and the blood flow. For example, Chahboune et al. [122] proposed an FEM based FSI scheme for 2D simulation of blood flow inside the LV over a complete cardiac cycle. Patterson et al.[123] and Carmody et al. [11] have developed a significant 3D FSI model of the mitral valve, known as the Sheffield bicuspid valve model. Their studies have included the simulation of blood pulsatile flow for one cardiac cycle along with LV wall motion using distinct methods, using the outlet flow pattern as the input for AV and aortic root flow profile. Their LV model was geometrically built from MRI data, and results corresponded well with physiological AV opening times and flow velocities. Vierendeels et al. [124] coupled the fluid and solid equations to simulate haemodynamics for a 2D axisymmetric LV. Their

simulated blood flow field was achieved using the ALE method combining the full

Navier-Stokes equations on a moving mesh and computed from the movement of boundaries developed by Riemslagh et al. [125].

In addition, De Hart et al. [18, 126-128] published an important FSI study of the aortic valve, which incorporated a 2D AV model. Their method was focused on solving for the fluid system variables first (i.e. pressure and stress), while the structural variables

(i.e. displacements) were kept constant. They investigated the application of strong coupling to the problem of a flexible aortic valve during systole. Their FEM m-

odel utilized the fictitious domain technique to couple the fluid and structural domains.

It was extended to a 3D model in later studies [18, 128].

The model of Hunter et al. [129] goes a long way towards achieving the whole-organ model objective of integrating cardiac anatomy, electrical activation, mechanics, metabolism and fluid mechanics together, although their model does not incorporate

AV leaflet motion. Vierendeels et al. [124] proposed a 2D axisymmetric FSI model to simulate passive filling of the ventricle, providing pressure and vortex pattern results.

Loon et al. [130] link fictitious domain (FD) with adaptive meshing for flexible valve leaflets. Stijnen et al. [131] use FD to predict the dynamic behaviour of a 2D moving rigid heart valve .

Watanabe et al. developed a three dimensional, FEM-based model which incorporated

blood flow inside the LV using FSI, examining the contraction and relaxation of the

LV during the cardiac cycle in normal activation as well as arrhythmia [132, 133].

Cheng et al. [94] developed an FSI method to analyse the velocity, vortex and pressure distributions under LV contraction and relaxation, regardless of the interaction with the mitral and aortic valves. Kittian et al. [120] modelled a LV FSI model, including both passive inflation and active contraction, based on patient-specific MRI datasets to evaluate the quality of pressure distribution results, which showed an overall agreement with experimental data.

However, the above models did not include simulation of the closing state of

the aortic valve during LVAD support, and ignored its interaction with the blood and

solid wall structures. Specifically, how does the AV behave under LVAD support?

Most of these studies support only the design of prosthetic valves and its influence on

surgical techniques required to repair mitral and aortic valves. In addition, none of

these studies provide full FSI models of the AV during LVAD support.

3.3 Existing modelling studies of AV state under LVAD support

Aortic valve state forms an important consideration in regards to thrombus formation

in assisted hearts due to its influence on intraventricular flow distribution in the LV.

Simulating the interaction between the blood and AV is challenging due to the

complex dynamics of the AV, the potential contact between AV leaflets, basic flow

instability, and intense velocity and pressure gradients local to the AV. However,

many CVS-LVAD interaction studies have been undertaken to investigate the impact

of rotary pumps on heart valve function. Lim et al. [86, 104] have developed a

lumped-parameter model of the CVS based on in-vivo experimental data recorded in

healthy animals combined with a dynamical model of a left ventricular device. This

model was used to evaluate the impact of LVADS on heart dynamics, including heart

valves.

Another approach to in-vitro experiments is to use a mock circulation loop system

(MCLs): this has been employed by various research groups to mimic LVAD-heart valve interactions [134]. A study by Shi et al. [135] presented a numerical model of the CVS, including the AV, under the pumping action of a pulsatile VAD connected in-series with the native heart. Their model was used to predict the change in aortic pressure (Aop) and coronary flow under different physiological conditions with

LVAD support. In addition, Endo et al. [136] have estimated the AV state during pump support using a closed-loop mock circulation with pulsatile pump simulating the natural LV.

In terms of numerical simulations, the Arbitrary Lagrangian Eulerian method

(ALE) is able to provide a suitable solution of the Navier–Stokes equations for ﬂuid

ﬂow with structural interactions characteristic of AV simulations. However, due to the large leaflet deformations, as reported by Horsten [137], it is important to adapt the fluid-domain mesh in such a way that proper mesh quality is maintained to model the

AV motion. We have used the ALE finite element method in our 2D AV models of this thesis to simulate leaflet motion with blood flow.

Accurate simulation of fluid/solid coupling mechanisms are crucial for characterizing normal heart valve function and its behaviour during LVAD support. To investigate these mechanisms, Nordsletten et al. [138] implemented an FSI LV model by integrating multiple physiological data to characterize the haemodynamics of the LV, including passive diastolic and active systolic phases. Su et al. [84] modelled the first

patient-specific left ventricular flow in two-dimensions, taking into account both the mitral and aortic valves.

Understanding how the AV behaves under LVAD support may allow the detection of its open/closed state from LVAD pressure/flow sensor transducers alone, paving the way for more sophisticated pump control algorithms which take into account such AV state. A particular problem of interest here is the effect of outlet pump outflow on AV closure of the human heart assisted by an implantable blood pump, and how it could be estimated from non-invasive pump variables. The aim of the computational models of this thesis is to simulate the interaction between the LV and aortic valve under

LVAD support. It is clear that this is a challenging task that needs to be addressed one stage at a time.

Part II – Methods

4 Chapter 4 -Development of Computational 2D LV-pump Models

4.1 Introduction

Many computational studies have been undertaken to simulate the behaviour of the

aortic valve, ignoring its interaction with the blood, during LV support [89-91].

However, several studies have also been published incorporating full-FSI of the AV

leaflets in contact with blood [18, 131, 139-141]. This chapter presents the

methodology we have developed in this thesis for a 2D LV-pump-AV model using a

simplified LV chamber with AV leaflets and LVAD blood flow. Although recent

imaging-based works can produce 3D patient-specific geometry over time, this

thesis have focused on more simpler 2D models to better understand the LVAD

factors affecting AV state during the cardiac cycle. These 2D simplified models

represent important pioneering steps on the way to more refined models, including

those based on patient-specific data.

Initially, our simplified LV dimensions were adapted from the study of McQueen et

al. [109] however we later modified the LV geometry to a more-realistic shape with

appropriate measurements from the literature. COMSOL Multiphysics (COMSOL

AB, Sweden, Version 4.3a) was used to develop the geometry models and the FEM 72

meshes of the fluid and solid domains. The more-realistic model represents a 2D section through the left side of the heart and is based on a study by Peskin [142]. Our purpose here is to modify the model’s dimensions and parameters so it mimics a human LV and to validate simulation results with previous studies. The more- realistic model describes blood flow in the LV and the movement of heart walls during a cardiac cycle. We also generalised the boundary representation so that it included not only the LV cavity and AV leaflets but also the LV walls.

The computational meshing process was unique to the individual geometries, involving mesh parameters such as element type, size and resolution of elements in high-curvature regions. The modelling process included specifying the model geometry, assigning the material properties, and applying appropriate boundary conditions. Our models aim to illustrate how fluid flow (i.e. blood) can deform the

LV and AV leaflet structures, solving for the flow in a continuously deforming geometry using the Arbitrary Lagrangian-Eulerian technique.

Fluid-structure interaction (FSI) deals with the multi-physics relations between deformable solid structures and a surrounding and/or internal fluid. FSI deals with structural motion change (i.e. LV wall and AV leaflet deformation) due to fluid (i.e. blood) flow, and is ideally suited to simulating AV behaviour in terms of opening and closing times during LVAD support. This behaviour is governed by the complex interaction between the valve leaflets, blood flow and blood pressure, as well as 73

LVAD pumping action. In FSI simulations, the coupling method used to solve for

deformations and flow at the boundary interface is a key issue. FSI coupling

methods are categorized into a three approaches: weak, strong and constrained met-

hods. COMSOL FEM software by default is set to fully-coupled (i.e. strong).

FSI simulations were performed for two LV geometrical groups. For each group, A-

V state was detected and analysed for various modelling scenarios. First we simulat-

ed the LV using a simplified rectangular chamber, whilst for the second group, a rea-

listic LV geometry was implemented based on previous literature. These simulation

scenarios were investigated under various LV dynamics, including the presence of

systemic circulation and LV contraction.

In this chapter, we define each group’s dimensional and numerical settings,

including the LVAD pump model. Adapted geometric methods have been used for

various purposes:

i. to detect AV status during LVAD support.

ii. to examine the resulting data for pump current, average aortic outflow

waveforms and distance between AV leaflets under various pump speed set

points and physiological conditions. iii. to estimate average pump differential pressure and average pump flow rate

from average pump input power.

The last part of this chapter describes the simulation protocols used to investigate

the LV-pump interaction model over a wide range of physiological operating condit-

ions, including variations in:

i. systemic vascular resistance (SVR); and

ii. total blood volume Vtotal by varying the inlet-flow rate to LV model.

The above variations are common in real life scenarios, and could lead to adverse

patient states with intolerable risk.

4.2 Geometrical models of LV-LVAD interaction

4.2.1 Simplified LV-pump interaction model 4.2.1.1 Computational approach and geometric definition:

The geometry of the simplified 2D LV-pump model was chosen to reflect that of

simple LV dimensions, with the domain having the same dimensions as a slice

through the measurement section. The ALE-based finite element method was used to

implement a fluid-structure interaction solver, which allows for deformation of

flexible structures such as the valve leaflets within the LV chamber. Our objective

was to analyse the motion of the AV in a highly-simplified LV model, without

taking into account the effects of heart wall contraction.

Figure 4‎ .1: Simplified 2D representation of the LV, aortic valve and pump cannula.

The model geometry consisted of a horizontal flow channel of diameter 2.0 cm and length 3.5 cm representing the LV, an appended 2.5 cm length representing the aorta

(Ao), and narrow curved structures representing the AV leaflets, as shown in Figure

4 .1. The AV consisted of two flexible leaflets of length 1.25 cm, idealized as rounded arcs with rounded tips. Although a native aortic valve has three leaflets, only two leaflets of equal length were modelled here, with assumed 0.1 cm thickness. To maintain a continuous flow domain, a 0.2 mm gap between the leaflets was preserved at the fully closed position (Figure 4 .2 (b)). A thin-walled cannula of width 0.8 cm and length 0.8 cm, representing the LV-AD inlet, was inserted into the simplified ventricular chamber wall. The model also included blood outflow from the LV: aortic outflow was modelled using four outlet boundaries defining a square- shaped ‘sink’, as illustrated in Figure 4 .1. Inflow to the LV was produced from four 76

inlet boundaries in the form of a square ‘source’, placed at the left end of the channel

(Fig. 4.1).

4.2.1.2 Mesh Generation

For most applied problems in fluid dynamics, it is essential to solve the governing

equations numerically with the assistance of computers. The formulation of the

equations into a form for numerical solution generally requires that the flow and

structure domains be discretised using a set of points or nodes which can be

connected to produce elements.

To obtain accurate simulation results, and using special meshing tools provided by

COMSOL, we combined two types of meshing methods and resolutions in the

model, as shown in Figure 4 .2,. These were a “fine” resolution for the fluid domain,

with maximum and minimum element sizes of 0.98 mm and 0.028 mm respectively,

and a “free triangular” mesh resolution for the remaining domains.

Solution accuracy with the finite element method is known to be influenced not only

by the element size, but also by the element quality – a measure indicating how close

the triangular or quadrilateral elements are to regular polyhedrons. A number of

measures are in use for the quality of an element, the most obvious being the

smallest and largest angles associated with the element [143]. In COMSOL, the

Figure 4‎ .2: (a) a fluid and structural element meshes in the simplified LV-pump model. The outer and inner AV segment lengths are 13 and 15.3 mm, respectively. (b) zoomed view of the AV highlighting the leaflet thickness, AV mesh and chamber element details.

mean element quality ( ) of triangular/ quadrilateral meshes was calculated by

dividing the area of each element by the sum of squares of its sides. The element

quality (q) is then scaled to range from zero to one such that an equilateral triangular

or square element has a quality of one. Therefore, for a triangular element we have:

and for a quadrilateral element:

where A is the area, and h1, h2, h3, h4 are the sidelengths of the element. The mean

element quality of the triangular and quadrilateral elements used ( =0.95 and 0.45

respectively), were significantly greater than the value known to affect the

accuracy of a solution (see Figure 4 .16), as determined by COMSOL to be =0.3

for triangular and quadrilateral meshes [85].

During movement of the leaflet structures, the nearby triangular elements will

deform according to COMSOL's in-built moving mesh interface, so that the mesh

quality remains as high as possible. If however the triangles do degenerate, there is

an option in the interface to perform a remesh if the overall mesh quality falls below

a threshold value. This option, however, was not required in the simulations of this

thesis, but could be implemented if larger deformations were imposed onto the

model.

4.2.1.3 Material properties

The viscosity of blood and elastic properties of the valve leaflets were obtained from

the literature to represent healthy human blood and valve properties [144, 145]. The

properties of blood used in this simulation are shown in Table 4 -1.

Table 4‎ -1: Material properties used for the simplified LV model

Parameter Value

Blood density ( ) 1.06 × 103

Blood viscosity (Pa.s) 2.70 × 10-3

Leaflet density ( ) 1.06 × 103

Aortic leaflet Young’s 1.0 × 106 modulus (Pa)

Leaflet Poisson’s ratio 0.49

4.2.1.4 Model equations

A two-dimensional FSI model of aortic valve dynamics was implemented using the

COMSOL Multiphysics finite element numerical software platform (COMSOL AB,

Sweden, Version 4.3a). The software utilized the moving grid method, whereby the

fluid mesh was adjusted to move with the moving solid-fluid interface boundary

throughout the numerical calculation. This technique is known as the Arbitrary

Lagrangian-Eulerian (ALE) formulation, first proposed by Donea et al. [146],

coupling the Lagrangian and Eulerian descriptions of the Navier-Stokes equations on

the moving grid.

Blood pulsatile flow was characterized as laminar, Newtonian, viscous and

incompressible. The fluid was described by the Navier-Stokes equations (4.1) and

the mass continuity equation for incompressible flow (4.2). 80

(4.1)

(4.2)

where is the fluid density, is the velocity of the fluid in the fixed Lagrangian coordinate system, is the velocity of the fluid in the moving Eulerian coordinate system, is the pressure,  is the fluid viscosity, and I is the unit tensor.

The fluid flows into the LV chamber from the left source (inlet) boundaries (see Fig.

4.1). At this inlet, the flow is assumed to have fully developed a laminar profile, changing with time as described in the next section. The valves are modeled as a linear elastic material, formulated as an isotropic Hookean elastic solid expressed using Einsteinian indicial notation as:

(4.3)

where is the Young’s modulus, is Poisson’s ratio, are the strain and stress tensors respectively, and represent the Kronecker-delta tensor such that:

Values of E and  for the AV leaflets are given in Table 4 -1

4.2.1.5 Boundary Conditions

The fluid flow boundary conditions of the model included the following: laminar

inflow conditions at the inlet boundaries were applied using a sinusoidal velocity

profile with a period of 1 s and amplitude 0.12 m/s, as shown in Figure 4.3, a 0

mmHg pressure outlet was specified at the sink outlet boundaries, a 0.014 m/s

velocity was applied at the outflow of the pump cannula, the fixed walls of the

model were set to be no-slip boundaries, and the valve leaflets were assigned a

'moving-wall' boundary condition whereby the velocity of fluid at these leaflet

boundaries was set equal to the velocity of the moving wall. Finally, the stress on the

valve leaflets was set to equal to the fluid stress (pressure plus viscous stress), with

the leaflet root boundaries set to a fixed displacement of zero.

Figure 4‎ .3: Sinusoidal velocity profile multiplied by an instantaneous step starting at 0.2 s applied at the inlet to simulate inflow.

4.2.1.6 Computational settings

The FSI simulations were performed on a computational workstation using a 64-bit 82

windows platform with 3.20 GHz processor and an Intel Core i7-3930K processor,

with an applicable memory allocation of 32 GB. The fully-meshed model exhibited

approximately 15,000 degrees of freedom.

4.2.1.7 Numerical Settings

The simplified LV pump model was implemented over two mesh geometries using

one setting for the integration time stepping algorithm: namely, absolute tolerance

0.001, relative tolerance 0.01, maximum integration time step 0.01s, maximum order

of the Backward Differential Formula (BDF) integration scheme at 2, saved sample

rate of the output at 100 Hz.

4.2.2 Simplified LV-pump interaction model with systemic circulation

4.2.2.1 Computational approach and geomtry definition

LVAD cannula placement influences the dynamics of flow within the ventricle,

however, placing the cannula near the centre of the LV leads to high velocities in

order to ensure ventricular washout as reported by Laumen et al. [18]. In our model,

the LVAD cannula was placed in the center of the ventricle between the inlet

boundaries (source) and the AV as shown in Figure 4 .4.

Figure 4‎ .4: (a) Fluid and structural element meshes of simplified LV with pump and CVS model. The length and diameter of the pump cannula are 0.6 and 0.6 mm, respectively. (b) Zoomed view of the AV highlighting the leaflet thickness, AV and chamber mesh element details.

The simplified LV-pump CVS interaction model geometry consisted of a rectangular

flow channel of diameter 2.5 cm and length 5.0 cm, representing the ventricle, along

with narrow curved structures representing the AV leaflets (see Figure 4 .4). The

latter were two flexible leaflets of length 1.65 cm and thickness 0.1 cm. A thin-

walled cannula of width 0.6 cm and length 0.6 cm was also placed into the

ventricular chamber wall. The model included blood outflow from the LV, which

was sourced from inlet boundaries placed at the left end of the chamber (labelled

“source” in Figs 4.4 and 4.5), whilst aortic outflow was modelled as a fixed pressure

boundary condition. Outflow from the aorta "sink" boundaries was calculated using

a Windkessel model of the circulation, connecting the aortic "sink" boundaries to the

atrial "source" boundaries, as shown in Figure 4 .5. In this version of the simplified

model, heart wall contraction was not considered.

Figure 4‎ .5: Windkessel model of the circulation where is the left ventricular outlet pressure, is the arterial systemic pressure, is atrial inflow to the LV, is the pump flow rate (L/min), is the blood flow ejected from the LV, is the characteristic aortic impedance, is the peripheral resistance and is the arterial systemic compliance.

In addition, blood pulsatile flow was characterized as laminar, Newtonian, viscous

and incompressible, and described by the incompressible Navier-Stokes (4.1) and

mass continuity (4.2) equations. The fluid flows into the model from the left source

(inlet) boundaries. At the entrance, the flow is assumed to have fully developed a

laminar characteristic with flow changing with time as described in the subsequent

fluid boundary condition section (4.2.2.5).

4.2.2.2 Mesh Generation

Three types of meshing algorithms and resolutions were used in this version of the

model: an “extremely fine” mesh setting was used for the fluid domain with

maximum and minimum element sizes of 0.80 mm and 0.0016 mm respectively.

Furthermore, due to the importance of simulating an accurate distance between the

leaflets to identify AV open and closed states, a small element size around the

leaflets tips (see Table 4 -2) was required. Therefore, AV boundaries adjacent to the

blood were discretised with 8 boundary layers and with 1 thickness adjustment

factor, producing thin quadrilateral elements parallel to the boundary. Finally, a

“free triangular” mesh was used for the remaining domains (Figure 4 .4). The fluid

and solid domains were discretised with triangular elements, as summarised in Table

4 -2. The total number of triangular and quadrilateral mesh mesh elements for this

model were 11696 and 2816 respectively.

Table 4‎ -2: Mesh properties of simplified CVS LV-pump model.

Regional of interest Simplified models with system circulation

valve leaflet edges Number of edge elements: 176

Mean element size: 0.58 (mm)

valve leaflet tips Number of edge elements: 32

Mean element size: 0.09 (mm)

Fluid domain Number of elements: 12236

Triangular: 10828

Quadrilateral: 1408

Mean element size: 0.75(mm)

Valve leaflet domains Number of elements:2110

Triangular:702

Quadrilateral:1408

Mean element size: 0.61(mm)

4.2.2.3 Material properties

In this version of the model, the viscosity of blood and elastic properties of the valve

leaflets were similar to that of the previous model (see Table 4 -1). However, for

improved accuracy the AV leaflet Young’s modulus was increased to 30 × 107 Pa.

4.2.2.4 Model equations 4.2.2.4.1 Windkessel model

To simulate the systemic circulation, a windkessel model was employed [147],

characterized by the following equations (see Figure 4 .5):

(4.4)

(4.5)

+ (4.6)

where P is the aortic pressure, Pout is the left ventricular outlet pressure, PS is the

arterial systemic pressure, is the pump flow rate, is the blood flow ejected

from the aorta, Rout is the characteristic aortic root impedance, RS is the total periph-

eral resistance and CS is the arterial systemic compliance. The following values we-

re employed for these Windkessel parameters: =0.006 mmHg.s/ , =1.0 m

mHg.s/ and =2.75 /mmHg These parameter values are adapted from

Danielsen [148].

4.2.2.5 Fluid boundary conditions

Boundary conditions applied to the model included the following: laminar inflow conditions were applied at the inlet source and outlet sink boundaries. For the inlet boundaries, a sinusoidal velocity profile with offset, having a period of 1 sec and maximum and minimum magnitudes of 1 m/s and -0.5 m/s respectively, was applied as shown in Figure 4 .6. For the outlet boundaries, we have used the Windkessel model to determine the pressure (Pout). For the LVAD, a fixed 2 m/s average velocity was applied over the outflow boundary of the cannula. Finally, the LV walls of the model were set to be no-slip boundaries.

Figure 4‎ .6: Sinusoidal velocity profile applied to the inlet boundaries to simulate diastolic inflow. The inflow velocity oscillated in a sinusoidal pattern with period 1 s and a magnitude 0.75ms−1 about a mean level of 0.25 ms-1.

4.2.3 Simplified LV-pump model with systemic circulation and heart contractility

4.2.3.1 Computational approach and Geometry definition

In this version of the model, the geometry similarly consisted of a horizontal flow

chamber of diameter 2.5 cm and length 5 cm representing the ventricle, and narrow

curved structures representing the AV leaflets, as shown in Figure 4 .7. Key model

parameters shown in Table 4 -3 were: blood density, blood viscosity, leaflet density,

aortic leaflet Young’s modulus and leaflet Poisson’s ratio. The AV consisted of two

flexible leaflets of length 1.25 cm and thickness 1 mm. A thin-walled cannula of

width 0.6 cm and length 0.6 cm, representing the LVAD inlet, was placed in the

ventricular chamber wall.

The model also included blood inflow into the LV on boundaries placed at the left

end of the channel (labelled as "source" in Figure 4 .7), whilst aortic outflow was

modelled as a varying pressure boundary condition (labelled "sink" in Figure 4 .7).

Outward flow at the atrial "sink" boundaries was simulated using a

Windkessel model of the circulation as previously defined, connecting aortic

pressure and ﬂow. These equations governing the Windkessel circuit were

implemented as global differential equations in the COMSOL solver. Heart wall

contraction on the upper boundary of the ventricular chamber was also incorporated,

labelled as “moving-wall” in Figure 4.7.

Figure 4‎ .7: (a) Fluid and structural domain meshes for the simplified LV-LVAD interaction model with heart wall contraction. The length and diameter of the pump cannula were 0.6 and 0.6 mm respectively. (b) Zoomed view of upper AV leaflet highlighting the leaflet domain and LV chamber mesh element details.

Table 4‎ -3: Material properties of the LV-LVAD interaction model incorporating CVS and heart contraction.

Parameter Value

Blood density ( ) 1.06 × 103

Blood viscosity (Pa.s) 1.00 × 10-3

Leaflet density ( ) 1.06 × 103

Aortic leaflet Young’s 4.7 × 107 modulus (Pa)

Leaflet Poisson’s ratio 0.49

4.2.3.2 Mesh Generation

In this version of the simplified model, three types of COMSOL automated meshing

methods were combined: 1) an “extremely fine” free-triangular mesh was used for

the fluid domain with maximum and minimum element sizes of 0.85 mm and 0.0017

mm minimum respectively, 2) due to the important role of the upper LV chamber

wall, incorporating contractility to force the fluid (i.e. blood) through the AV, this

upper wall boundary, along with the AV leaflet edges, was discretised with 8

boundary layers made up of quadrilateral elements, and 3) a “free triangular” mesh

was employed for all remaining domains (see Figure 4 .7). Properties of the mesh for

the model are listed in Table 4 -4. The total number of triangular and quadrilateral

mesh elements was 11224 and 5394 respectively.

4.2.3.3 Material properties

For this version of the simplified model, the viscosity of blood and the elastic

properties of the valve leaflets are shown in Table 4 -3. However, for more accurate

simulation, the model dimensions were changed to represent LV dimensions, the

Young’s modulus for the AV leaflets was changed to 4.7 × 107 Pa and fluid viscosity

decreased to 1 mPa.s.

Table 4‎ -4: Mesh properties of simplified LV-pump model with CVS and heart contraction. Region of interest Mesh Properties

valve leaflet edge Number of edge elements: 192

Mean element size: 0.656 (mm)

Fluid domain Number of elements: 14494

Triangular: 10500

Quadrilateral: 3994

Mean element size: 0.822 mm

Valve leaflets thickness Number of elements: 2124

Triangular: 724

Quadrilateral: 1400

Mean element size: 0.665 mm

LV outer boundaries Number of edge elements: 360

Mean element size: 0.65 mm

4.2.3.4 Boundary Conditions

Fluid flow boundary conditions for the simplified LV-pump interaction model with

contraction included the following: a sinusoidal flow pattern with period 1 sec, mean

25 mL/s and amplitude 50 mL/s was applied at the inlet (source) boundaries, we

have used the Windkessel model to determine the pressure (Pout) according to the

equation (4.6), and was specified at the outlet (sink) boundaries and a pressure of

was applied at the outflow of the pump cannula, where PS is the systemic pressure of the circulation and P is the pressure differential head of the LVAD pump (see Figure 4 .8). The fixed walls of the model were set to be no-slip boundaries, and the valve leaflets were assigned a 'moving-wall' boundary condition

(Figure 4 .7), whereby the velocity of the fluid at these leaflet boundaries was set equal to the velocity of the moving wall. The stress on the valve leaflet boundaries was set to equal the fluid stress, with the leaflet root boundaries fixed.

Finally, heart wall contraction was simulated by moving the upper boundary of the ventricular chamber with a velocity according to:

(4.7)

where is the wall velocity, is the x coordinate measuring the arc length across this boundary from the left (as referenced from Figure 4.7), is the maximum velocity, and L is the total length of the upper boundary segment, equal to 5 cm. As with the valve leaflets, the fluid velocity at this boundary was set equal to the wall velocity.

Figure 4‎ .8: Windkessel model of the circulation where is the left ventricular outlet pressure, is the arterial systemic pressure, is atrial inflow to the LV, is the pump flow rate (L/min), is the blood flow ejected from the LV, is the characteristic aortic impedance, is the peripheral resistance, is the arterial systemic compliance and P is the pressure differential head of the LVAD pump.

4.2.3.5 Computational Settings

FSI simulations for this model were performed on a 3.20 GHz Intel Core i7-3930K

PC workstation, using a 64-bit Windows platform, with an applicable memory

allocation of 32 GB. The fully-meshed model exhibited approximately 65,500

degrees of freedom.

4.2.3.6 Numerical Settings

The above simplified valve-pump model with CVS and heart contraction

was implemented using a BDF integration time stepping algorithm. The followed

settings were used for this time-dependent solver: absolute tolerance 0.001,

relative tolerance 0.01, maximum time step 0.01s, maximum order of BDF method

set at 2, and sampling rate of saved model output set to 100 Hz.

4.2.4 Simplified LV-pump interaction model with systemic circulation, cardiac contractility and without AV

4.2.4.1 Geometry definition

Similar to the previous simplified models described, this model also utilized

the ALE finite element method to simulate the fluid/structural domain interactions

using a strong coupling method by default.

Figure 4‎ .9: 2D representation of the LV chamber and pump cannula without AV leaflets.

However, for a more simplified and computationally efficient simulation of aortic pressure (AoP) and left ventricular pressure (LVP), the geometry of this simplified model was based on the previous 2D LV-pump simplified models, however this time by excluding the AV leaflets (see Figure 4 .9). A thick homogeneous upper LV moving wall was added to implement LV contraction, with length 5.0 cm and width

0.4 cm.

Instead, AV behaviour was represented mathematically by a resistance and diode to allow flow only in one direction out of the sink boundaries representing the aorta.

Blood will flow out of these boundaries when the pressure gradient across the LV and aorta is positive, according to:

(4.8)

where Q denotes the aortic outflow, PAo denotes the aortic pressure, R is the AV resistance, and PLV is the upstream pressure within the LV chamber.

Figure 4 .10: (a) Fluid and structural domain meshes for the simplified LV model without AV. (b) Mesh element detail at the sink outflow boundary. (c) Zoomed view of theoutflow boundary highlighting the mesh element detail around the aortic outflow.

4.2.4.2 Mesh Generation

To capture sufficient detail of AV state, mesh element size was finer around the

aortic outflow boundaries than the previous simplified models (see Figure 4 .10).

Therefore, the upper LV wall moving boundary and the outflow boundary layers

were discretised with 8 boundary layers, using 1 thickness adjustment factor. For

the fluid domain, an “extremely fine” free triangular mesh was used, as listed in

Table 4 -5.

Table 4‎ -5: Mesh properties of simplified LV-pump model without AV leaflets.

Region of interest Simplified model without AV leaflets

LV outer boundaries Number of edge elements: 301

Mean element size: 0.80 (mm)

Outflow inner boundaries Number of edge elements: 356

Mean element size: 0.089 (mm)

Fluid structure Number of elements: 24213

Triangular: 19483

Quadrilateral: 4730

Mean element size: 0.77 (mm)

Myocardial internal boundaries Number of edge elements: 31

Mean element size: 0.7 (mm)

4.2.4.3 Material properties

The viscosity of blood was similar to the previous model (see Table 4 -3). The

moving myocardial wall was modelled as being linear elastic, with properties as

shown in Table 4 -6.

Table 4‎ -6: Material properties of the myocardium in simplified LV model without AV

Parameter Value

Wall density ( ) 1.06 × 103

Myocardial Young’s 1.0 × 107

modulus (Pa)

Myocardial Poisson’s ratio 0.49

4.2.4.4 Model equations

4.2.4.4.1 Windkessel model

To simulate the systemic circulation, a simple Windkessel model was employed,

characterized by the following equations (see Figure 4 .11):

(4.9)

(4.10)

(4.11)

where P is the aortic pressure, is the left ventricular outlet pressure, is the

arterial systemic pressure, is the pump flow rate (L/min), is the blood flow

ejected from the LV, is the characteristic aortic impedance, is the peripheral

resistance and is the arterial systemic compliance.

Figure 4 .11: Windkessel model used with simplified LV-pump model without AV leaflets.

4.2.4.4.2 Pump model

The differential pressure head (ΔP) across the pump outlet was modeled using three

equations as reported by Lim et al. [149]; the motor windings electrical equation

(4.12), the electromagnetic torque transfer equation (4.16), and the pump hydraulic

equation linear equation (4.17).

100

i) Motor windings electrical equation

(4.12)

where V is the motor terminal voltage, I is the motor current, is motor winding

resistance (1.38 ) and is the motor winding reactance. is the back

electromotive force (BEMF) given by:

(4.13)

where = 8.48 and is the motor electrical speed ( , where is

the impeller speed in rad/s). Due to the synchronization between BEMF and motor

electrical current to produce maximum torque efficiency, equation (4.12) can be

written as:

(4.14)

where L = 0.439 is the motor winding inductance. V was determined using a

proportional controller to track the desired pump speed according to:

(4.15)

where K is constant (1 V.s/rad) and is the pump speed set point. ii) Electromagnetic torque transfer equation

(4.16)

101

Where Te is the output electromagnetic torque and J is the moment of inertia of the

-6 2 impeller (7.74×10 kg/m ). The coefficients c1, c2, c3 and c4 are viscosity-

4 dependent parameters, set to constant values of c1=1576.8 kgs/m , c2=0.0119

-5 2 -10 2 kgs/m, c3=1.92×10 m kg/s, and c4=3.14×10 m kg/s.

iii) Pump hydraulic equation

(4.17)

where c5, c6, c0 are viscosity-dependent parameters, fixed to values of c5= -32343

10 5 kg/(m s ), c6=0.25331kgs/m, and c0= -39.463 Pa.

4.2.4.5 Boundary Conditions

To simulate a periodic diastolic inflow, a sinusoidal flow pattern with period 1 sec,

mean flow rate 40 mL/s and amplitude 80 mL/s was applied at the inlet (source)

boundaries. Furthermore, we have used the Windkessel model to determine the

pressure (Pout) according to the equation (4.6), and this pressure was specified at the

outlet (sink) boundaries, a pressure of was applied at the

outflow of the pump cannula, where the Lf is the blood inertance, and the fixed walls

of the model were set to be no-slip boundaries, as shown in Figure 4 .11. To simulate

LV contraction, an external force was applied to the upper LV moving boundary

given by Equation 4.18:

(4.18)

102

where F is a periodic forcing function, and Fmax is the value of maximum

force when the wall is fully contracted.

4.2.4.6 Computational Settings

The FSI simulations were performed on a 3.20 GHz Intel Core i7-3930K PC

workstation, using a 64-bit Windows platform, with an applicable memory

allocation of 32 GB. The fully-meshed model exhibited approximately 76,819

degrees of freedom.

4.2.4.7 Numerical Settings

The realistic LV-pump model was implemented using the following numerical

integration settings: absolute tolerance 0.001, relative tolerance 0.01, maximum time

step 0.01s, maximum BDF order set to 2, and sampling rate of saved model output set

to 100 Hz.

4.2.5 Realistic LV-Pump geometry model with and without AV leaflets

4.2.5.1 Computational approach and geometry definition

This section outlines the scheme developed for simulating aortic valve function

inside the left ventricle and under LVAD support using a more realistic LV

103

geometric shape. This model characterizes a 2D section through the left side of the

heart, lying in a long axis plane passing through the apex of the heart, bisecting the

mitral valve leaflets, and passing through the aortic outlet flow tract. Our purpose

has been to change the model’s dimensions and parameters so it models a human

heart. The model consists of the left ventricle of height 7 cm from base to the apex,

with a diameter of 5.18 cm and a varying wall thickness of 0.8 to 0.95 cm (see Fig.

4.11). The model also includes narrow curved structures representing the AV

leaflets. The LV boundaries consisted of an endocardial (inner) border lining the

cavity of LV, and an epicardial (outer) border, as shown in Figure 4 .12.

Figure 4‎ .12: 2D geometry of the LV and AV (long axis plane) with LVAD cannula attached at the apex. The diameter of the LVAD cannula was 0.87 cm. 104

Key model parameters including blood density, blood viscosity, leaflet density, aortic leaflet Young’s modulus, leaflet Poisson ratio and myocardium properties are shown in Table 4 -7 and Table 4 -8. The ALE FSI method was used to simulate the dynamics of the aortic valve and the LV wall. The shape of the aortic root was based on the idealized geometric description of De Heart et al. [18]. The AV was simplified with an outflow region of diameter of 2.1cm, consisting of two flexible curved shape leaflets with equal length of 1.25 cm and thickness 1 mm. The myocardium wall thickness of around 0.90 cm was modified from Bogaert et al.[150].

A thin-walled cannula of width 0.87 cm and length 0.8 cm, representing the LVAD, was inserted into the ventricular chamber wall. The dimensions of all these structures were adapted from McQueen et al. [109] and were arranged so that the geometry of the 2D left ventricle closely matched echocardiographic data of the normal human heart. However, this LV-pump model was also modelled using version without the AV leaflets, to produce a more computationally-efficient model, as shown in Figure 4 .13. The ALE Navier-Stokes equations [151] were used to model the blood inflow into the LV on boundaries placed at the left end of the channel (labelled as "source" in Figure 4 .13), whilst aortic outflow was modelled as a varying pressure boundary condition (labelled "sink" in Figure 4 .13). Outward flow at the "sink" boundaries was simulated using a Windkessel model of the circulation, connecting aortic pressure and ﬂow. These equations governing the

Windkessel circuit were implemented as global differential equations in the 105

COMSOL solver. Heart wall contraction on the outer boundaries of the ventricular

chamber was also incorporated by applying an external periodic sinusoidal load

profile on the LV epicardial boundaries.

Figure 4‎ .13.Two-dimensional geometry of the LV (long axis plane), LA, and LVAD cannula without the AV leaflets.

4.2.5.2 Material properties

In this model, the viscosity of blood and the elastic properties of the valve leaflets

were obtained from the literature to represent healthy human values [144, 145]. The

main properties of blood used in this simulation are shown in Table 4-7. 106

In addition, the ventricular wall was modelled as being linear elastic with appropriate Young’s modulus and Poisson’s ratio properties, are shown in Table 4-8.

Table 4‎ -7. Material properties of 2D realistic LV model

Parameter Value

Blood density ( ) 1.06 × 103

Blood viscosity (Pa.s) 1.00 × 10-3

Leaflet density ( ) 1.06 × 103

Aortic leaflet Young’s 4.2 × 107

modulus (Pa)

Leaflet Poisson’s ratio 0.49

Table 4‎ -8. Material properties of the myocardium

Parameter Value

Wall density ( ) 1.06 × 103

Young’s modulus (Pa) 1.0 × 107

Poisson’s ratio 0.49

107

4.2.5.3 Mesh Generation and Quality

A fine mesh resolution was used for the fluid domain and AV leaflet boundaries, as

illustrated in Figure 4 .14 and Figure 4 .15. Figure 4 .16 shows the element quality (q)

over the whole model in the range 0 to 1. The mean element quality of the triangular

and quadrilateral elements in the fluid domain, myocardial walls and AV leaflets

were 0.91, 0.93 and 0.88 respectively (Table 4 -9), which were significantly greater

than the q thresholds known to affect solution accuracy [85].

Figure 4‎ .14: (a) 2D realistic LV model mesh. (b) Zoomed-in view of boundary mesh layers at the interface between the LV walls and fluid. (c) Zoomed-in view of AV leaflet tips highlighting the mesh element detail.

However, to obtain accurate simulation results, we utilized three types of automated

meshing methods as provided by COMSOL: (1) a “fine” resolution for the fluid

domain with maximum and minimum element sizes of 3.22mm and 0.092mm

respectively, (2) a boundary layer mesh was used for all fluid-LV cavity boundaries

with two boundary layers and 6 thickness adjustment factors, and (3) “free 108

triangular” meshing was used for the remaining domains (Figure 4 .14). The total number of mesh elements in the fluid domain was 17777 (see Table 4 -9).

Table 4‎ -9. Mesh properties of realistic LV model.

Region of interest Realistic LV model

Valve leaflet edge Number of edge elements: 398

Mean element size: 1.16 (mm)

Valve leaflet tips Number of edge elements: 87

Mean element size: 0.084 (mm)

Myocardial wall edges Mean element size: 2.44(mm)

Number of edge elements: 1237

Mean element size: 2.5 (mm)

Myocardial thickness Number of elements: 663

Mean element size: 3.00(mm)

Average element quality: 0.93

Fluid domain Number of elements: 17777

Triangular: 17117

Quadrilateral: 660

Mean element size: 0.822(mm)

Average element quality:0.91

Valve leaflets thickness Number of elements: 2218

Triangular: 2218

Quadrilateral: 0

Mean element size: 1.23(mm)

Average element quality: 0.91

109

Figure 4‎ .15: Mesh element size in 2D realistic LV model showing the aorta (Ao) and AV leaflet regions. (a) Boundary layer sizes at the Ao (b) zoomed view of the AV leaflet tips highlighting the element sizes in mm.

Figure 4 .16: (a) Element quality of realistic LV model (q) in the range from 0 to 1. (b) Zoomed-in view of boundary element quality at the interface between the LV wall and fluid. (c) Zoomed-in view of AV leaflet tips, highlighting the element quality around the AV.

110

During movement of the heart wall and the AV leaflets, adjacent triangular elements

will deform in accordance to COMSOL's in-built moving mesh interface, so that the

mesh quality remains as high as possible. If however the triangles do degenerate,

there is an option in the interface to perform a remesh if the overall mesh quality

falls below a threshold value. This option, however, was not required in the

simulations of this section, but could be implemented if larger deformations were

imposed onto the model.

4.2.5.4 Model Equations 4.2.5.4.1 LV model

Pulsatile flow blood was characterized as being laminar, Newtonian, viscous and

incompressible. The fluid was described by the Navier-Stokes equations for

incompressible flow:

where  is the fluid density,  is the viscosity, u is the velocity of the fluid and p is the pressure.

The fluid flowed into the ventricle from the right source (inlet) boundaries (see

Figure 4.12). At these entrance boundaries, the flow is assumed to have fully

developed a laminar profile. The valves were modelled as an isotropic Hookean

elastic solid, with constitutive law expressed with Einsteinian indicial notation as:

111

(4.20)

where E is the Young’s modulus, is Poisson’s ratio, are the Cauchy strain and

stress tensors respectively, and represents the Kronecker-delta tensor:

This modelling was carried out automatically using the Parallel Direct Sparse Solver

(PARDISO) solver in COMSOL using the FSI module [152].

4.2.5.4.2 Windkessel model of the CVS

To simulate the systemic circulation, a simple Windkessel model was employed,

characterized by the following equations (see Figure 4 .17):

(4.21)

(4.22)

(4.23)

where P is the aortic pressure, is the left ventricular outlet pressure, is the

arterial systemic pressure, is the pump flow rate, is the blood flow ejected

from the LV, is the characteristic aortic impedance, is the peripheral

resistance and is the arterial systemic compliance. 112

The fluid density and viscosity are listed in Table 4 -10. These values correspond to the physical properties of blood in the large arteries and heart cavities as reported by

Yilmaz et al. [153].

Figure 4‎ .17: 2D realistic representation of the LV, AV, pump cannula and Windkessel model of the circulation.

113

Figure 4‎ .18: Two-dimensional realistic representation of the LV, pump cannula and Windkessel model of the circulation without the LV leaflets.

In the realistic version of the LV-pump model without AV leaflets ( Figure 4 .18), the aortic valve was represented by a resistance (Rout) and a diode (Dout) to allow flow only in one direction from the sink boundaries, representing flow in the aorta. Blood flow across the aortic valve was non-zero only when the pressure gradient across the

LV and aorta was positive:

114

(4.24)

where Q is the blood flow through the AV, R is the resistance of the aortic valve, P1

the upstream LV pressure, and P2 the downstream aortic pressure.

Table 4‎ -10 Fluid material properties in 2D realistic LV model.

Density (kg/m3) viscosity (mPa.s)

1060 1

4.2.5.4.3 Pump model

4.2.5.4.3.1 Average pump flow and differential pressure estimation model

Due to the insensitivity of IRBPs to preload, overpumping or underpumping

conditions, which can potentially endanger implant recipients, such scenarios can

readily occur if pump control is not properly implemented. One design goal of an

IRBP controller is to be able to accurately and reliably predict pump flow as well as

differential pressure without the need for additional implantable sensors. Additional

complications such as residual ventricular function dependent on the amount of

residual contractility, as well as insufficient venous return, may also influence the

occurrence of undesirable conditions [136].

115

The differential pressure head (ΔP) across the pump outlet was therefore modelled using three equations, as reported by Lim et al. [149]: (1) the motor windings electrical equation (4.25), (2) the electromagnetic torque transfer equation (4.29), and (3) the pump hydraulic linear equation (4.30).

i) Motor windings electrical equation

(4.25) where V is the motor terminal voltage, I is the motor current, is motor winding resistance (1.38 ) and is the motor winding reactance. is the back electromotive force (BEMF) given by:

(4.26) where = 8.48 and is the electrical speed ( , where is the impeller speed in rad/s). Due to the synchronization between BEMF and motor electrical current to produce maximum torque efficiency, equation (4.25) can be written as:

(4.27)

where L = 0.439 is the motor winding inductance. V was determined using a proportional controller to track the desired pump speed according to:

116

(4.28)

where K is constant (1 V.s/rad) and is the pump speed set point.

ii) Electromagnetic torque transfer equation

(4.29)

where Te is the output electromagnetic torque and J is the moment of inertia of the

-6 2 impeller (7.74×10 kg/m ). The coefficients c1, c2, c3 and c4 are viscosity-

dependent parameters fixed to values of c1, c2, c3, and c4.

iii) Pump hydraulic equation

(4.30)

where c5, c6, c0 are viscosity-dependent parameters, fixed to values of c5, c6, c0.

4.2.5.5 Boundary Conditions

Fluid flow boundary conditions of the model included the following: a sinusoidal

flow pattern with period 1 sec, mean flow rate 40 mL/s and amplitude 80 mL/s was

applied at the inlet (source) boundaries, we have used the Windkessel model to

determine the pressure (Pout) and was specified at the outlet (sink) boundaries, a

117

pressure of was applied at the outflow of the pump cannula,

where the Lf is the blood inertance, the fixed walls of the model were set to be no-

slip boundaries, the valve leaflets were assigned a 'moving-wall' boundary condition,

as shown in Figure 4 .19, and LV contraction was implemented by applying a load on

the endocardium of the septum and the posterior left ventricular wall according to

Equation 4.31, which will be detailed section 4.2.6. The stress on the valve leaflet

boundaries was set to equal the fluid stress.

Figure 4‎ .19: Boundary conditions of realistic LV-pump model.

4.2.5.6 Computational settings

118

FSI simulations were performed using COMSOL finite element software on a

Windows 64-bit platform with 3.20GHz processor employing an Intel Core i7-3930K

PC workstation, with an applicable memory allocation of 32 GB.

4.2.5.7 Numerical Settings

The realistic LV-pump model was implemented using the following numerical

integration settings: absolute tolerance 0.001, relative tolerance 0.01, maximum

integration time step 0.01s, maximum BDF order set to 2, and sampling rate of saved

model output set to 100 Hz.

4.2.6 Simulating LV and AV dynamics

To model the dynamic contraction and relaxation of the ventricle, the myocardial

and septal walls were modelled as an incompressible elastic isotropic materials with

properties shown in Table 4 -11.

Table 4‎ -11 Material properties for the solid model.

Density (kg/m3) Young’s Poisson ratio modulus (MPa)

LV wall 1040 100 0.49

AV leaflets 1060 470 0.49

For the LV wall structural mechanics computations, a time- and coordinate-

dependent load was applied at the LV outer boundaries (i.e. myocardial and

interventricular septal walls) according to:

(4.31) 119

where F is the force per unit area, and Fmax is the maximum force when the walls are

fully contracted.

In this method, the incorporation of dynamic heart wall motion into simulations

plays an important role in modelling the open/closed state of the AV, thus regulating

flow during the cardiac cycle. The fluid boundary conditions at these contacting

regions was set at moving-wall. The apex outer walls were set to be free-wall, and

all sides of the cannula were set to be fixed (i.e. zero displacement).

4.2.7 Investigation of Cardiovascular Interaction with a Left ventricular Assist Device 4.2.7.1 Speed and Parameter Variation studies

Numerical models, able to simulate CVS response in the presence of an implantable

rotary blood pump (IRBP), have been widely used as predictive tools to investigate

the interaction between the CVS and the LVAD under various operating conditions.

Contractility, ventricular preload, and afterload, which may endanger patients, can

be investigated individually using a numerical model. In addition, such models can

provide additional understanding of the dynamics of the assisted circulation, sheding

light on research questions not easily answered in vivo. Specifically, such models

can help investigate the impact of circulatory perturbations on the haemodynamics

of the heart.

120

This section describes an extension of the previous method sections to investigate

LV-pump interaction over a wide range of operating conditions, including

alterations in systemic vascular resistance and total blood volume by varying the rate

of inlet flow. These variations are important tools in testing the interaction between

the heart and the LVAD under different operating scenarios and to avoid

unacceptable dangers to recipients if pump control is not appropriately implemented.

4.2.7.2 Simulation Protocols

In this set of numerical experiments, model parameters illustrated in Table 4‎ -12,

which correspond to the Healthy condition (H1), were used as starting point values

for a normal subject. To allow simulation of various physiological conditions, two

cardiovascular parameters were altered: afterload and preload.

4.2.7.3 Effect of speed ramp

The model was tested under one physiological “Healthy condition” (H1), with syst-

em parameters set at baseline values. The simulation was first carried out using a

constant reference pump speed input, starting at 50 rad/s at t=0 s. During this

test, the impeller speed set point ωset was steadily increased from 50 rad/s to 200 rad/

s in 50 rad/s steps, then increased from 150 rad/s to 200 rad/s in 30 rad/s steps, in o-

rder to cover the full range of pumping states. The physiological signals, instantane-

121

ous pump impeller speed (ω) and motor current (I), were post-processed and saved

from the pump model.

4.2.7.4 Effect of parameter variations

In order to evaluate the response of the AV for different cardiovascular states, the m-

odel was tested under two sets of parameters for a wide range of pump operating set-

tings:

i. varying SVR.

ii. changing the total blood volume Vtotal, (see Table 4‎ -12 and Table 4‎ -13).

These settings were evaluated using both the simplified and realistic versions of the

2D LV-LVAD models.

Table 4 -12. Simplified LV-pump model parameters for the healthy and abnormal condition subjects: Systemic peripheral resistance, Rsa; and total blood volume, Vtotal.

Variable H1 H2 H3

-1 Rsa (mmHg.mL ) 0.74 0.74 0.40

Vtotal (mL) 5600 3400 5600

First, the “Volume low condition” (H2) (or preload), was simulated for both simplif-

ied and realistic LV-LVAD models by varying the blood volume input and the pump

speed: Vtotal was decreased to 3400mL and 1875ml respectively, and the simulation

was continued for 6 seconds to allow the system to reach steady state. 122

Next, an “Afterload condition” (H3) was simulated. In this test, the SVR parameter

was decreased by 50% for both models. This H3 simulation was conducted to deter

mine whether the model, in combination with alteration of LV parameters, was able

to provide normal AV open-close functionality during afterload decrease.

Table 4 -13: Realistic 2D LV-LVAD model parameters for healthy and abnormal conditions: Systemic peripheral resistance, Rsa; and total blood volume, Vtotal.

Variable H1 H2 H3

-1 Rsa (mmHg.mL ) 0.74 0.74 0.40

Vtotal (mL) 5600 1875 5600

123

Part III-Results and Discussion

124

5 Chapter 5 - Fluid-Structure Interaction in a Simple Model of an Assisted Left Ventricle

This chapter presents the first steps in simulating the effects of outlet pump pressure

on aortic valve closure of the heart assisted by an implantable blood pump. A 2D

fluid structure interaction aortic valve model is presented with blood flow in the left

ventricular chamber using the Arbitrary Lagrangian–Eulerian finite element

formulation to predict AV closure during outflow of blood from the left ventricle

into the left ventricular assist device (LVAD).

5.1 Introduction

Heart disease represents one of the biggest causes of death in the world [2]. Due to

the shortage in donor hearts, an artificial heart can be a bridge to transplantation or

serve as a destination therapy for patients with heart failure. It is well known that the

changes in hemodynamic behaviour of the heart can alter the physiological structure

of heart valves during LVAD support [154]. There are various imaging tools that can

visualize mechanical characteristics of the left ventricle (LV) as well as blood flow

inside the ventricle, qualitatively, but they do not provide a complete picture of the

status of heart valves during LVAD support following implantation [155-157].

125

FSI simulations have been extensively used for the purposes of heart function

assessment and heart disease diagnosis. A model of human left ventricular-pump

interaction by the finite element method was developed to simulate the

haemodynamics inside the assisted LV. The model was formulated with dimensions

and parameters to mimic simple 2D AV dynamics and LVAD behaviour. The

primary focus of this chapter is to present results using a simplified model of the LV

chamber to examine the effect of intra-ventricular flow under the action of an assist

device on AV status. The simulations of this chapter provide a first step in

investigating the effect of outlet pump pressure on AV closure. This will potentially

provide significant insights into LV function under LVAD assistance.

The main results of this chapter were published in Alonazi et al. [158].

5.2 Simplified LV-pump model

5.2.1 Results:

Simulations using the simplified LV-pump model revealed that model behaviour

could effectively be separated into two phases: aortic valve closed and open, as

shown from the simulated outlet pump pressure result of Figure 5 .1 , which has

been calculated from the cannula inlet pressure minus the differential pressure head.

The AV closed phase was characterized by increasing pressure in the LV during the

early stage of filling. Moreover, the LVAD pumping action kept the LV pressure

126

lower. However, during the second phase, this pressure dropped from its peak when the aortic valve opened.

Figure 5‎ .1: Simulated pressure at pump outlet over a single 1 s cardiac cycle, where ' * ' and ' ● ' indicate AV closing and opening times, respectively. Label 'c' represents the period during which the AV was closed, and 'o' is the period in wh- ichthe valve was open.

From Figure 5.1, we see that a low blood velocity occurs at the source boundaries during the closing phase (t=0.4s), rising sharply and accelerating while the aortic valve was in its closed state (t=0.4-0.675s), reaching its maximum value of 0.25m/s at t=0.675 s.

It can be observed that during this period, blood moves toward the LVAD inlet due to suction created by the pump. Meanwhile, the pressure at the pump outlet increases before reaching its maximum value of 35.0 Pa at t=0.675s, as illustrated in Figure

5 .1. In this phase, the aortic valve is closed, however during the AV opening phase 127

starting at t=0.7s, the pump pressure starts to increase gradually, reaching its

maximum value of 185.8 Pa at t= 1s. The valve leaflets, as observed from Figure 5 .2,

are fully opened at t=1s, before starting to close again. The leaflets are fully closed

by t=1.56s resulting in an open phase duration of 0.86s.

Figure 5‎ .2: Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle. (a) Aortic valve at closing phase. (b) Aortic valve at opening phase.

5.2.2 Discussion We have presented results from a two-dimensional FSI ALE model of aortic valve

motion in a simplified LVAD-assisted LV chamber. The simulations confirmed that

when the AV opens, pressure falls at the LVAD inlet, similar to the findings obtained

by Shi et al. [135]. However in their model, they did not incorporate any 128

computational fluid dynamics to determine pressure and velocity distributions during

LVAD support, ignoring the effects of aortic valve interaction between the blood and

moving solid structures.

This simulated pressure variation during AV movement, particularly during its

closure phase, provides significant insight into LV function under LVAD assistance,

offering the potential of improving the accuracy of current LVAD control systems to

ensure patient safety and comfort.

5.3 Simplified LV-pump model with systemic circulation

5.3.1 Results:

In this section, results are presented from a 2D LV chamber model with CVS,

capable of simulating aortic valve dynamics (closure/opening) under LVAD support,

which can be useful in the design and evaluation of physiological pump control

algorithms to ensure patient safety and comfort, as well as evaluating aortic valve

pathologies.

As in the previous results, model behaviour could effectively be divided into two

phases: aortic valve closed and open, as shown from the outlet pump pressure in

Figure 5 .3. AV open/close state was characterized from two simulated signals: the

distance between the valve leaflets and the outlet pump pressure during the early 129

stage of filling. During the first closed phase, the pumping action of the LVAD kept

the AV pressures low. During the second phase, this pressure dropped from its peak

value when the aortic valve opened.

From Figure 5 .3(b) a low fluid velocity is observed at the source boundaries during

the closing phase (t=1.51s), rising sharply and accelerating whilst the aortic valve is

still in its closed state (t=1.51-1.88s), reaching a maximum value of 4m/s at t=2.00 s

when the valve has fully opened.

Figure 5 .3: (a) Simulated pressure from the pump outlet over a single, 1 s cardiac cycle, where ' * ' and ' ● ' indicate aortic valve opening and closing times, respectively. ‘c’ represents the period during which the aortic valve is closed, and ‘o’ is the period in which the aortic valve is open. (b) Zoomed-in view of pumpoutlet pressure. T- he pressure shown at the position of the arrows increases transiently on aortic valve closure.

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It can be observed that during the first phase, blood moves toward the pump inlet due to the suction created by the pump and closure of the aortic valve. Meanwhile, the pressure at the pump outlet shown at the position of the arrows in Figure 5.3 (i.e. at the instant of AV closure) reveals a transient increase on aortic valve closure, before reaching its maximum negative amplitude of -7000 Pa at t=1.45s, as illustrated in

Figure 5 .3(b). After this instant, the aortic valve remains closed until the AV opens at t=1.88s. After this opening, the pump pressure begins to decrease gradually (Figure

5 .3 (b)). The aortic leaflets, as observed from Figure 5 .4, are fully opened at t=2.03s before starting to close again. The leaflets are fully closed by t=2.44s resulting in an open phase duration of 0.56s.

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Figure 5‎ .4: Snapshots of computed LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle. (a) Aortic valve in the closed phase. (b) Aortic valve in the open phase.

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5.3.2 Discussion

Development of valve abnormalities after LVAD placement is common among

patients with advanced heart failure, likely due to the fact that the LVAD induces

different haemodynamics by changing the direction of blood flow from the apex of

the heart, largely bypassing the LV, directly to the aorta. This abnormal recirculation

modifies the pressure and stress on the AV leaflets, leading to remodelling of the

valve [159]. In particular, aortic valve functional problems have been reported by

Rose et al. [2] and Letsou et al. [3], who note that that aortic insufficiency (AI) and

Aortic stenosis (AS) are more prevalent in LVAD patients. In addition, Park et al.

[48] reported that within 6–12 months of LVAD implantation, 50% of patients with

pulsatile LVADs developed AI or AS. A major consequence of LVADs is excessive

flow bypassing the AV, resulting in diminished and infrequent AV opening which

could also extend to the systolic phase [5].

Managing native aortic valve insufficiency during LVAD placement is very

challenging. A variety of procedures to prevent aortic insufficiency have been

reported, including aortic valve replacement with a bioprosthetic valve, or primary

closure of the aortic valve opening [160-162]. However, these surgical techniques

could cause further complications, impairing the LVAD as being a viable alternative

to transplantation [163, 164]. Currently, MRI and Echocardiography are the only

techniques used clinically to evaluate aortic valve abnormal pathophysiology in

LVAD recipients in real-time [52, 165].

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Alternatively, computational modelling of blood flow has been used extensively to study LV haemodynamics. Several FEM models of the left ventricle and aortic valve have been developed to simulate leaflet motion due to blood flow. Early studies of heart valve FSI models include the work of Peskin [110], who used an immersed boundary method to describe a 2D model of the left heart. Watanabe et al. [166] addressed the limitations of the Peskin approach, using instead the ALE approach to simulate cardiac mechanics during cardiovascular flow. Alternately, De Hart et al.

[18, 127] used a fictitious domain (FD) method to simulate closure of a flexible heart valve during systole. Loon et al. [130], extended this approach by linking fluid dynamics with adaptive meshing for the flexible leaflet. Stijnen et al. [131] also simulated the dynamic behaviour of a two-dimensional moving rigid heart valve using the FD method. Lastly, McCormick et al. formulated an FSI model of the left ventricle with LVAD using a modification of the Newton–Raphson/line algorithm and optimizing the interpolation scheme at the fluid–solid boundaries [167, 168].

However, these models did not include simulation of AV closure during LVAD support. Understanding how the AV behaves under LVAD support may allow the detection of the open/closed state of the valve from LVAD pressure/flow sensor transducers alone, paving the way for more sophisticated pump control algorithms which take into account the AV state.

In this chapter, a simplified 2D FSI model of the aortic valve and ventricle during

LVAD support has been presented, including the systemic circulation. The results

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confirm that when the AV opens, less blood flows through the LVAD compared to

when the valve is closed, similar to the results reported by Shi et al. [135].

However, our simulated pressure variations during AV movement, particularly

during its closing phase, provide significant insight into LV function under LVAD

assistance, offering the potential of improving current LVAD control systems to

ensure patient safety and comfort.

5.4 Conclusion

Previous FSI models of ventricular function with LVAD support have ignored the

impact of AV closure on blood dynamics in the assisted left ventricle, as presented in

this chapter. Blood flow in a 2D model of the left ventricle with aortic valve was

simulated using the finite element model. This model can be used to investigate heart

aortic valve closure during LVAD support. The next chapter includes results from

modelling a realistic ventricular geometry, as well as adding the contractile activity

of the LV in order to simulate an entire cardiac cycle. To date, few modeling studies

which have considered valve-blood interaction in addition to ventricular wall-blood-

interaction have incorporated LVAD pumping action.

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6 Chapter 6 - Simulation of Aortic Valve Response during Ventricular Assist Device Support

In this chapter, analysis of simulated LVAD motor current waveform was

performing to derive useful parameters for evaluating aortic valve status. A 2D fluid

structure interaction model of the LV and aortic valve in the presence of LVAD flow

are presented to predict AV closure during LVAD outflow of blood to derive an

automatic pump speed control method.

6.1 Introduction

Congestive heart failure (CHF) is a serious health condition characterized by the

inability of the heart to supply sufficient blood flow to tissues and organs in the body.

Left ventricular support with pump devices has been an essential element in cardiac

health care for several decades. It is therefore important to understand the interaction

between the cardiovascular system and a cardiac pump device. Furthermore, to avoid

valvular stenosis and thrombogenesis reported in previous investigations [49, 169],

the monitoring of aortic valve opening and closing is important during pump support.

This chapter provides preliminary steps in simulating the role of outlet pump pressure

on aortic valve function of the heart assisted by an implantable blood pump. A simple

2D FSI aortic valve model is presented with blood flow in the left ventricular

chamber using the ALE Finite Element Method to predict AV closure during blood

outflow from a left ventricular assist device (LVAD).

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The aim here is to:

● Simulate the response of the aortic valve in the presence of an LVAD in the 2D

simplified and realistic LV geometries.

Simulate the response of the models over a range of pump operating points (i.e. over

a wider pump speed range).

AV state was evaluated using the simulated LVAD motor current waveform as an

index, using two 2D simplified computational models of AV dynamics

(closure/opening) under heart pump support. Such models will be useful in the design

and evaluation of physiological heart pump control algorithms to achieve the balance

between LVAD pumping and mechanical circulatory support against disruption to

AV movement, which may lead to various AV pathologies. Therefore, the objective

of this chapter is to investigate how the motor electrical current profile changes with

AV state and pump speed. Identifying the AV state according to the non-invasive

motor current signal could serve as a useful an input to a pump speed controller to

prevent highly negative pressures from occuring in the left ventricle leading to wall

suction, as well as ensuring the AV properly opens and closes over the complete

cardiac cycle.

The main results of this chapter were published in Alonazi et al. [170].

6.2 Simplified LV-pump model

Model behaviour could effectively be divided into two phases: aortic valve closed and open, as shown from pump motor current in

Figure 6 .1. The valve ejection phase (VE) was characterized by two waveforms: the

pump motor current and the pump

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Figure 6‎ .1: Simulated motor electric current and pump impeller speed at two motor speed set points (100 and 150 rad/s), where ' ■ ' and ' ● ' indicate AV opening and closing times, respectively, (a)

Simulations using a motor speed set point of set =100 rad/s. Periods 'O' and 'C' represent the phases during which the AV is open and valve closed respectively. (b). Simulations using a motor speed set point of set =150 rad/s. Periods 'O' and 'C' represent the phases during which the AV is open and closed, respectively. Max PCT and Min PCT are the maximum and minimum values of current threshold during AV closure, respectively. The motor current waveform at Max PCT begins to decrease more rapidly once the aortic valve is closed at the closing notch (CN).

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speed. In each simulation, the impeller speed set point was increased from 50 rad/s to

200 rad/s in 50 rad/s increments, in order to cover the full range of aortic valve state transitions (from ventricular ejection (VE) to aortic valve closed (VC)). The physiological signals, instantaneous pump impeller speed (ω) and motor current (I), were simulated from the pump model equations.

Figure 6 .1 shows the waveforms obtained at two different speed set points of 100 rad/s and 150 rad/s, illustrating the relationship between the peak motor current and instantaneous pump speed in the 2D model, indicating an inverse correlation of motor current with pump speed.Transition from state VE to state VC occurred with increasing pump speed. However, at a pump speed set point of 200 rad/s, VC state was continuously maintained, whereby the AV remained closed throughout the entire cardiac cycle (ANO) with no blood flow to the proximal aorta. Furthermore, a peak motor current (MAX PCT) of 0.203A was observed during the AV closing phase

(t=3.15s) for 100 rad/s, decreasing rapidly throughout the AV closed state

(t=3.15-3.85s), reaching a minimum value (MIN PCT) of 0.1067A at t=3.49s.

Figure 6 .2 shows the simulation results of AV movement during LVAD support, where the opening time at t=2.85 s was approximately the same for both speed set points. However, the closure time was delayed by 10 ms to t = 3.16s at the motor speed set point of 150 rad/s. During AV opening, there were also small oscillations in the current waveform, probably due to mechanical flutter of the valve leaflets.

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Figure 6‎ .2: Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle. (a) Aortic valve and blood motion for = 100 rad/s. (b) Aortic valve and blood movement for = 150 rad/s

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6.3 Realistic LV-Pump model with AV leaflets

In the section, we present results of AV dynamics simulated from a 2D realistic LV

computational model under heart pump support. AV state is examined from non-

invasive simulated LVAD motor current as an index. The model could serve as a

useful tool in the design and evaluation of physiological pump control algorithms to

achieve a balance between LVAD speed and disruption to AV movement which can

lead to various AV pathologies. Therefore, the objective of these simulations was to

investigate the correlation between AV status and the motor electrical current

waveform using the 2D LV-pump interaction model. Also, identification of AV state

according to motor current could provide an input to a pump speed controller to

prevent highly negative pressures in the left ventricle leading to wall suction, as well

as ensuring the AV opens and closes over the cardiac cycle.

The hypothesis examined with this set of simulations is that by using the non-

invasive measures of instantaneous pump electrical current and impeller speed, it is

possible to detect various AV states including:

 Open AV state during Ventricular ejection (VE)

 Closed AV state during diastole (AC)

 AV remaining closed over the entire cardiac cycle (ANO).

 AV regurgitation (AR), which frequently occurs in LVAD heart failure

patients. 147

6.3.1 Identification of aortic valve states for LV- pump interaction models with AV

In order to assess whether pump speed and motor current are potential indicators of

aortic valve state transitions, it is necessary to independently verify the physiological

state of the aortic valve in the simulations. This was achieved by using the pump int-

rinsic parameters indicated in Table 6-1. Model behaviour can effectively be divided

into two phases: systole and diastole. An initial inspection of the distance between l-

eaflets and the difference between left ventricular pressure (LVP) and Aortic pressu-

re (AoP), indicated the presence of two physiologically significant aortic valve state-

s (i.e. open and closed) (see Figure 6.4).

Table 6‎ -1 A summary of physiological and pump basic parameters identifying AV state.

Physiological Pump Basic Parameters Parameters AV State Motor Pump Distance between AV LVP current speed leaflets

AC decreasing

VE increasing >AoP decreasing > 0

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Figure 6‎ .3: Simulated left ventricular pressure (sold black line) and aortic pressure (dotted

red line) at a low pump speed set point of set = 50 rad/s.

The method here is that by using only the non-invasive measure of instantaneous

pump current to evaluate AV dynamics during LVAD support, it is possible to detect

a range of AV states according to these classifications:

1. In the systolic phase, due to the positive difference between left ventricular pressure

and aortic pressure (LVP > AoP), (see Figure 6 .3), blood flows through the AV

from the ventricle to the aorta causing the AV to open. During this state, LVAD

pump flow is also increased. Following LV contraction, the pump differential

pressure decreases, increasing the pump flow and torque on the impeller, causing the

impeller speed to fall and the motor current to increase (see Figure).

2. During isovolumic relaxation, left ventricular pressure (LVP) decreases, causing the

aortic valve to close, (LVP < AoP), increasing the differential pressure across the

pump, causing the pump flow to fall. Subsequently, the torque on the impeller

decreases, causing impeller speed to increase and motor current to decrease.

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3. If the aortic valve remains closed throughout the entire cardiac cycle (ANO), the

aortic flow (Qav) will equal zero at all times. This condition could not be maintained

in our model, due to the difficulty in simulating permanently contacts AV leaflets..

4. In the aortic valve regurgitation state (AR), LV pressure is excessively low due to

high pump speed, aortic root pressure is always higher than the left ventricular

pressure (AoP>LVP) as a result of LVAD unloading. This occurs during diastole.

6.3.2 Detection of AV State The realistic 2D LV-Pump interaction model was used to simulate the AV dynamics

within the LV cavity (see Figure 6 .4) and to identify AV state by analysing the

LVAD current motor waveform.

Figure 6‎ .4: AV state in 2D LV-LVAD realistic geometry simulations. The left panel represents cross-sections of the heart and LVAD during isovolumic relaxation when the aortic valve is closed(AC), with blood flow path indicated by the black arrows. The right panel illustrates the AV open (AO) state during LV ejection. Both

panels show LV flow for a pump speed set point of set = 100 rad/s).

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In another set of simulations, the impeller speed set point was increased from 50 rad/s to 150 rad/s in 50 rad/s increments, then increased to 180 rad/s and 200 rad/s in order to cover the full range of aortic valve state transitions (from ventricular ejection (VE) to aortic valve closed (VC)). The instantaneous pump impeller speed

(ω) and motor current (I) for all five set points are shown in Figure and Figure , illustrating that the pump motor current undergoes signiﬁcant changes at each impeller set point. Figure 6.8 shows the relation between the peak motor current and the instantaneous pump speed, revealing an inverse correlation between the two.

In addition, the relationship between motor current, AV closure time and closed duration, exhibited good correlation. As shown in Figure, transition from state VE to state VC occurred with increasing pump speed. Where the VE state corresponded to left ventricular ejection during systole, increasing motor speed set point produced an upward shift of the motor current amplitude, resulting in an increased AV closing time, significantly increasing peak motor current by at least 50% compared to the next lowest speed set point. However, during increase of the set point to 200 rad/s,

(see Figure), VC state was continuously maintained, with the distance between AV leaflets decreasing to zero at t= 0.45s, after which the AV remained closed (ANO) with no further blood flow to the proximal aorta.

Furthermore, at a set point of 50 rad/s, a low motor current of 0.044A was observed during the AV closing phase (t=1.72s) with a close phase duration of 0.20 seconds.

This current then increased throughout the AV open state (t=1.72-2.52s), reaching a

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maximum value of 0.0733A at t=2.29s. At a set point of 180 rad/s, a low motor current of 0.6246A was observed during the AV closing phase (t=1.77s) with a close phase duration of 0.62 seconds, an increase of 0.42 seconds compared to 50 rad/s.

The motor current then increased throughout the AV open state (t=2.05-2.43s), reaching a maximum value of 0.8056A at t=2.29s. Furthermore, at speed set points of 100 and 150 rad/s, low motor currents of 0.150 A and 0.391 respectively were observed during the AV closing phase (t=1.76s) and (t=1.78s), with closed phase durations of 0.38 seconds and 0.52 respectively. The motor current also increased throughout the AV opened state (t=1.90-2.52s, and (t=1.97-2.45s respectively), with delay in open time of 0.14 seconds compared to 150 rad/s. The current reached maximum values of 0.232A and 0.526A respectively at t=1.31s and t=1.28s.

However, AV closure durations for set points of 100, 150 and 180 rad/s were increased by 0.18 s, 0.32 s and 0.42 s compared to the 50 rad/s set point, respectively. Ho- wever, the AV fully-open instant at 100 rad/s and 150 rad/s occurred at approximately the same time (t=2.21s), whereas this time occurred earlier for 50 rad/s and 180 r- ad/s at t=2.12s and t=2.17s, respectively. In addition, during AV opening, there were small oscillations in the current waveform at a set point of 180 rad/s, probably due to mechanical flutter of the valve leaflets.

As Figure 6.6 illustrates, aortic valve regurgitant flow during high pump speed (i.e.,

200 rad/s), occurs during diastole, LV pressure is low with a concomitant reduction in LVAD flow as illustrated in Figure 6.7. It was observed that the pump average

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flow (Qp=1.4 L/min) at pump speed of 200 rad/s was decreased by 0.6 L/min compared with pump speed of 100 rad/s which was 2L/min Figure , due to the increase in pump speed and the need for a higher LVAD speed to compensate for the back flow of the blood from the aorta, as reported by Rasalingam et al. [171]. These investigators claimed it was caused by aortic root pressure being higher than instantaneous LV pressure as a result of LVAD unloading. In addition, AR, or the inability of the aortic valve to close

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Figure 6‎ .5: Simulated electric current and pump impeller speeds at four motor speed set points (50, 100, 150 and 180 rad/s), where ' ■ ' and ' ● ' indicate AV opening and closing times, respectively. Periods 'O' and 'C' represent the phases during which the AV is open, referred to as ventricular ejection (VE), and valve closed (VC), respectively. Max PCT and Min PCT are the maximum and minimum values of motor current during AV closure, respectively. The motor current waveform at Max PCT further decreases once the aortic valve is closed at the closing notch (CN). (a) set = 50 rad/s (b) set = 100 rad/s) (c)set = 150 rad/s) (d)set = 180 rad/s.

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Figure 6‎ .6 : Simulated electric current (black line) and distance between aortic valve (AV) leafl-ets (re d line) at a motor speed set points of 200 rad/s, where '●' and '■' indicate AV opening an-d closing ti mes, respectively. The duration of the closing phase was increased from lower set p-oint values, with t he VC state beingcontinuously maintained (ANO). AR denotes the aortic val-ve regurgitant period thr ough the cardiac cycle.

Figure 6‎ .7 : Average inflow rate Qin (dashed line) applied at the inlet (source) boundaries, and the inlet pump flow rate Qp (solid line).

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completely during diastole, results in the backflow of blood from the aorta into the left ventricle to the LVAD.

However, during our simulation, the AR was developed by the result of the high pump speed (i.e. 200 rad/s), low blood flow from the left atrium, the left ventricle is in diastolic phase, and aortic pressure (AoP) is larger than LVP at all times. In addition, the aortic valve was not open during the entire cardiac cycle (ANO), since all the blood flowing thru pump cannula. Therefore, the CO (total flow of mean 1.3

L/min) is equal to the pump flow (see Figure ), meaning that the CO is totally provided by the LVAD at high pump speed. In addition, during AR (t=0.51-0.97s), it was observed that the pump average flow (Qp=1.4 L/min) was increased by 0.4

L/min due to aortic valve regurgitation and the need for a higher LVAD speed to compensate for the back flow of the blood from the aorta, which may lead to premature device failure.

In addition, the relationship between motor current amplitude and LV pressure versus motor pump speed (rad/s) exhibited an excellent correlation: as shown in

Figure , peak motor current increased with decreases in LVP with the increase in the pump speed. Figure 6.9 shows the relation between the AV closure time and motor pump speed. The closure time increased with the increase in the motor pump speed, indicating that AV closure time reaches a point when stays closed during all cardiac cycle.

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Figure 6‎ .8 : LVP–peak (red dotted line) and LVAD motor current (black solid line) against pump speed in LV model.

Figure 6‎ .9 : Closure time against motor speed in LV model

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Figure and Figure illustrate simulation results of blood flow AV movement during

LVAD support, where the closure time is approximately the same at both (50 and 100 rad/s) speed set points. However, the opening time is delayed by 0.18 s at the motor speed set point of 100 rad/s. At 150 and 180 rad/s speed set points, the opening time is approximately the same for both, however the closure time was delayed by 20 ms at the set point of 180 rad/s.

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Figure 6‎ .10 : Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle. For each panel, the three snapshots illustrate AV closing phase (left),

opening phase (middle) and fully-open (right). (a) set = 50 rad/s. (b) set = 100 rad/s.

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Figure 6‎ .11 : Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle. For each panel, the three snapshots illustrate AV closing phase (left),

opening phase (middle), and fully-open phase (right). (c) set = 150 rad/s. (d) set = 180 rad/s.

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6.3.3 Discussion

The simplified and realistic LV models described in this chapter were

developed with the aim of providing insights into the dynamics of LV-LVAD

interaction as well as detecting AV status. The simulation data in Figure show

a progressive increase of AV closure duration with increasing pump speed set

point and pump electrical current amplitude. During the ventricular ejection

state, the LV begins to pressurize, forcing the AV leaflets to open, blood to

flow through the aortic valve, and pressure differential head across the pump to

decrease. The latter leads to an increase in pump flow and motor current, with

a decrease in pump speed that continues throughout systole. However, in the

AV closed state, the LV pressure falls, causing AV flow to decrease and

differential pressure across the pump (head) to rise. The latter results in a

decline in pump flow motor electrical current during diastole. In addition,

Figure and Figure illustrate that during both systole and diastole, there was

continual blood flow through the pump (see Figure ), and this flow begins to

increase as a result of LV contraction at t=1.65s, even before the AV opens at

t=1.90s..

The state in which the AV remains closed throughout the entire cardiac cycle,

with aortic flow (Qav) being zero and pump flow Qp equal to the CO,

indicates that the left ventricular pressure (LVP) is less than the aortic pressure

(AoP) and is not enough to open the AV. In our simulations, this state arises

when the pump speed is too high, substantially lowering the LV pressure. In 161

terms of simulations of the mechanics of the left ventricle, the real heart

exhibits more complex motion and can be modelled with more realistic active

contractile properties, such as a time-varying elastance. This may affect the

onset of AV open-close times. However, such detailed modelling was beyond

the scope of this thesis work. Furthermore, the model may be extended in

future to incorporate a range of heart failure conditions including changes in

cardiac contractility.

Figure 6‎ .12 :Average pump inflow rate (Qp) at a motor speed set points of 100 rad/s, where '●' and ' ■' indicate AV opening and closing times, respectively.

6.4 Limitations

Modelling LV geometry in a congestive heart failure patient remains a challenge,

due to the limited available in vivo data of the remodelled myocardium during

LVAD support. One option is to compare simulation results with existing studies.

The LV has a complex geometry with a smooth endocardial surface and anisotropic

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material properties. However, our results were obtained using an idealized geometry

with smooth surface and isotropic material properties, which may alter the flow

patterns in the myocardium. However, in this study, our LV model was used only to

supply fluid velocity loading conditions for the AV. Since the behaviour of the

ventricle was not the focus of the study, it was not necessary to represent its

structural properties accurately.

A final limitation of the present model is that the measured LV pressure during

ventricular ejection (Figure 6.3) was much lower (i.e. maximum LVP during AV

open was 40 mmHg at pump speed 150 rad/s) compared to previous modelling data

(i.e. 120 mmHg during AV open) [141]. However, we found that LVP is highly

variable from one study to the other, probably due to the simplified LV geometry

used, and the simplified ventricular contractility settings during systole.

6.5 Conclusion

In this chapter, simulation results were presented from simplified 2D FSI models of

the LV in the presence of LVAD, based on the ALE method. The models were

formulated with the aim of providing insights into the dynamics of heart-pump

interaction, and to simulate LVAD motor current waveform in relation to the AV

state. The results confirmed that when the AV opens, there is a higher motor current

compared to when the valve is closed. However, our computational model of motor

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current variations during AV movement, particularly during its closing phase, and under pulsatile flow conditions, will provide significant insights into LV function during LVAD support, particularly as the model is further developed to incorporate physiological heart failure conditions. Moreover, our simulations offer the potential for improving current LVAD control systems to ensure patient safety and comfort, reducing the incidence of AV pathologies during heart pump support, and in helping reduce the risk of aortic insufficiency.

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7 Chapter 7 – Effect of Parameter Variations on Aortic Valve State under Rotary Blood Pump Assistance

7.1 Introduction

The use of a left ventricular assist device (LVAD) as mechanical assistance for heart

failure disease is of great importance, due to its ability to stabilize heart function until a

suitable donor heart becomes available, or to allow adequate mechanical assistance for the

native heart to heal itself. Due to advances in LVAD development, as well as the shortage

of appropriate heart donors, LVADs are often used as a bridge to transplant, or more

frequently nowadays, a destination therapy [6, 172]. However, since patients undergo

different activity levels from sleep to exercise, underpumping or overpumping can often

occur, leading to undesired consequences in LV haemodynamics, as well as abnormalities

in AV state [168].

Numerical models [92, 173-175], mock loop experimental studies [176-178], animal

studies [156, 179] and human studies [180, 181] have been used to examine the effect of

LVADs on the cardiovascular system (CVS). On the contrary, FSI models are able to

simulate the response of the CVS in the presence of left ventricular support devices, and

can provide additional insight into the dynamics of the assisted circulation under different

operating conditions. Numerical models also offer a stage for refining existing techniques

used to control the speed of the implantable rotary pump. Consequently, monitoring of AV

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opening and closure during heart pump support is crucial in preventing AV abnormalities and remodelling caused by anomalous recirculation.

Previous LVAD experiments have concluded that the ideal control set-point is where left ventricular ejection is occurring and there is a net positive flow through both the aortic valve and the pump [182-184]. However, implanted LVADs alter the haemodynamics of the heart, leading to the necessity of determining the optimal speed set point to satisfy the varying physiological needs of the patient, and to ensure maximum end-organ perfusion

[185]. Consequently, the identification of AV state during LVAD support is necessary to prevent complications reported in previous studies such as recirculation and stasis inside the LV cavity [186, 187], as well as aortic valve fusion [7]. Clinically, AV state is measured using echocardiography, whilst aortic flow is assessed using pulsed Doppler

Ultrasound after LVAD implantation. Identifying heart state using non-invasive variables has concentrated on LV suction state detection and non-suction state [183, 188, 189], whereas few studies have focussed on detecting AV state during LVAD support using pump motor electrical current [136, 190-192].

Identifying AV state according to the LVAD motor current signal can provide a non- invasive input for a pump speed controller, in order to prevent highly negative pressures developing in the left ventricle when there is insufficient blood in the ventricle to sustain normal left ventricular ejection and the AV remains closed, as reported by Karantonis et al.

[183]. In this instance, there is no flow through the AV and the possibility of blood stasis distal to the AV could lead to significant complications from thrombus formation. This

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chapter will describe results from two LV pump geometry models, in order to evaluate the immediate response of the AV to different physiological states over a wide range of pump speed conditions.

Several studies [144, 145, 193, 194] have investigated non-invasive pump motor feedback signals (current or speed), to be used as useful indicators of LVAD pumping state for either overor under-pumping conditions. For example, Yuhki et al. [193] considered a waveform deformation index based on a spectral analysis of the speed signal; Oshikawa et al. [194] and Endo et al. [136] studied the pump motor current amplitude; and Voigt et al. [195] used the differentiated current waveform as an LV wall suction indicator. Most groups failed to show the impact of physiological conditions and other cardiovascular characteristics on the interaction of the ventricular assist device with both the LV and the aortic valve.

The results of this chapter are divided into two parts. In the first part, results from a simplified 2D FSI LV finite element model with implantable rotary pump are presented to predict AV state during LVAD outflow. In the second section, a realistic 2D left ventricle geometry is used. These models will be useful tools in the development of a pump speed controller for optimal management of pump outflow.

The main results of this chapter were published in Alonazi et al. [34].

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7.2 Simplified LV-pump model

7.2.1 Results and Discussion

In this section, we present results from a simplified 2D model of LVAD support,

investigating for the first time, the effect of variations in cardiovascular parameters on AV

open and closed states during LVAD assist. As demonstrated in Figure 7.1, model

behaviour could effectively be divided into two phases: aortic valve closed and open. In

this simulation, the impeller speed set points were 100 and 150 rad/s, covering the range of

aortic valve state transitions from ventricular ejection (VE) to aortic valve closure (VC).

Figure 7.1 shows the instantaneous pump motor current (I) for both set points for two

abnormal physiological conditions, H2 and H3, compared to the H1 (healthy) condition,

illustrating that the pump motor current undergoes signiﬁcant changes for each condition.

Furthermore, there was a good correlation between motor current, AV closure time and

AV closure duration.

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Figure 7‎ .1: Simulated electric current and pump impeller speed at two motor speed set points of 100 rad/s (top) and150 rad/s (bottom), where ' ● ' and ' ■ ' indicate AV opening and closing times, respectively, the periods 'O1', 'O2', 'O3' and 'C1', 'C2' and 'C3' represent the periods during which the AV is open and closed, respectively at conditions H1, H2 and H3 respectively. MAX C1PT, MAX C2PT and MAX C3PT, and MIN C1PT, MIN C2PT and MIN C3PT are the maximum and minimum values of motor current during AV closure.

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As shown in Figure 7.1 reduced Vtotal (H2 condition) produced a downward shift of the current amplitude, resulting in an increased AV closing time, significantly decreasing peak motor current by 50% compared to the healthy H1 condition under both speed set points.

Furthermore, at both set points of 100 and 150 rad/s, high motor currents of 0.31A and

0.67A respectively were observed for H1 (t=2.00s), decreasing rapidly throughout the AV c losed state (t=2.21-2.70s and t=2.20-2.75s respectively), reaching a minimum value of 0.09

5A at t=2.60s and 0.295A at t=2.53s respectively.

Figure 7.2 shows simulation results of AV movement during LVAD support, where the opening time at 100 rad/s was delayed by 0.12 sec for H2 compared to H3. However, opening time remained approximately the same for both H2 and H3 at 150 rad/sec. However, the closure time at speed points of 100 and 150 rad/s was delayed by 0.1 sec and 10 ms respectively between the two conditions, with the closure period under H3 and H2 being between 0.48 sec and 0.70 sec, and 0.67 sec and 0.66 sec, respectively, compared to the H1 values of 0.45 sec at 100 rad/s and 0.57 sec at 150 rad/s.

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Figure 7‎ .2: Simulated distance between AV leaflets at two motor speed set points of 100 rad/s (top) and150 rad/s (bottom), where ' ● ' and ' ■ ' indicate AV opening and closing times, respectively. The periods 'O1', 'O2', 'O3' and 'C1', 'C2' and 'C3' represent phases during which the AV is open and closed, respectively, for conditions H1, H2 and H3 respectively.

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However, the closure time was increased by 10 ms and delayed by 30 ms compared to H3, and was delayed by 0.1 sec and increased by 40 ms compared to H2. In addition, during

AV opening, there were small oscillations in the current waveform, probably due to mechanical flutter of the valve leaflets. Figure 7.2 shows the AV dynamics at different phas es in the cardiac cycle for the three physiological conditions (H1, H2 and H3), starting at t- he onset of AV opening and ending at AV closure. AV state during these physiological conditions was characterized by the measured distance between AV leaflets as shown in

Figure 7.2. Under each condition, the impeller speed was fixed at two speed set points of

100 and 150 rad/s. The figure shows the relation between the peak opening distance and the total duration of opening and closing AV times, revealing the correlation between the pump speed and distance between leaflets under each physiological condition. Results of blood flow and AV movement are shown in Figure 7 .3 for a speed set point of 100 rad/s.

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Figure 7‎ .3: Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle for = 100 rad/s. (a) Aortic valve closing and opening phases under condition H1. (b) Aortic valve closing and opening phases under condition H2. (c) Aortic valve closing and opening phases under condition H3.

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7.3 Realistic LV-Pump model

7.3.1 Introduction

In this section, we examined the response of the aortic valve (i.e. open and closed)

during a working range of pump speeds and changes in physiological condition. The

realistic 2D LV-Pump interaction model described in Chapter 6 was used. The main

finding of this set of simulations is the influence of rotary pump output on AV state

during three physiological conditions; healthy and two different physiological

conditions simulated by altering cardiovascular parameters:

i. by varying systemic vascular resistance (SVR) ( or afterload) (condition H3)

ii. by changing the total blood volume Vtotal (or preload) (condition H2), by

varying the rate of inflow to the model through the source inlet.

The pump set speed was increased from a speed of 50 to 150 rad/s

7.3.2 Results:

To investigate the effect of motor pump current on AV open and closed states, the

response of the AV under LVAD support was examined under three physiological

heart conditions using the realistic 2D LV-pump interaction model. As shown in

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Figure 7‎ .4: Simulated motor electric current at three motor speed set points (50, 100, and150 rad/s), where ' ● ' and ' ■ ' indicate AV opening and closing times, respectively. The periods 'O1', 'O2', 'O3' and 'C1', 'C2' and 'C3' represent the phases during which the AV is open and closed respectively, at conditions H1, H2 and H3 respectively.

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Figure 7.4, model behaviour could effectively be divided into two phases: aortic valve closed and open. In this simulation, the impeller speed set points were set to

(50, 100 and 150 rad/s), covering the full range of aortic valve state transitions from ventricular ejection (VE) to aortic valve closed (VC). To obtain the individual effect on AV state of two abnormal physiological conditions, H2 and H3, compared to the

H1 (healthy) state, pump impeller motor current (I) was simulated for all speed set points for all three physiological conditions, H1, H2 and H3, revealing that the pump motor current undergoes signiﬁcant change under each condition. In addition, the relationship between motor current, AV closure time and AV closure duration exhibited good correlation.

As shown in Figure 7.5, reduced Vtotal formed a downward shift of the current amplitude, resulting in a reduction in AV closing time by 80 ms, significantly decreasing peak motor current (MAX O2 PT) by approximately 50% compared to t- he healthy condition (H1) maximum current (MAX O1 PT) at 50 rad/s speed set points as shown in Figure 7 .5(a). On the contrary, at speed set points of 100 and 150 rad/s, AV closing times were increased by 130 and 160 ms, respectively, compared

to H1, whereas, at condition H3, the peak motor current (MAX O3 PT ) was increased slightly, but was almost the same as to the healthy condition under both speed s- et points. Moreover, at speed set points of 100 and 150 rad/s, high motor currents (

MAX O1 PT) of 0.23A and 0.52A, respectively, were observed for H1 (t=2.28s) during AV open state, decreasing rapidly throughout the AV closed state (t=2.52-2.90 s and t=2.45-2.98s respectively), reaching a minimum value (MIN C1 PT) of 0.151

A at t= 2.77s and 0.391A at t=2.78s, respectively, (see Figure 7 .5 (b and c)).

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Figure 7‎ .5: (a), (b) and (c). Simulated motor current waveform during AV closure/open phases, where ' ● ' and ' ■ ' indicate AV opening and closing times, respectively. Current levels MAX C1PT, MAX C2PT and MAX C3PT, and MIN C1PT, MIN C2PT and MIN C3PT denote the maximum and minimum values of motor current during AV closure, whilst MAX O1PT, MAX O2PT and MAX O3PT are the maximum current values during AV open phases. From top to bottom, the panels show pump speed set points of (a) set = 50 rad/s, (b) set 100 rad/s and (c) set = 150 rad/s).

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Figure 7.6 shows simulation results of AV movement during LVAD support, where

the opening time at 50 rad/s was delayed by 10 ms more for H2 than for H3, but r-

emaining approximately the same for both H2 and H3 at 100 rad/sec. The closure

time at speed points of 50 and 100 rad/s was shifted by 0.1 s and 40 ms respectively

between the two conditions. AV closure periods under conditions H2 and H3 were

between 0.13 sec and 0. 11 sec, and 0.27 sec and 0.31 sec, respectively, compared to

the H1 values of 0.20 sec at 50 rad/s and 0.34 sec at 100 rad/s.

Figure 7‎ .6: Simulated open and closed states of AV leaflets at two motor speed set points of (a) 50 rad/s and (b) 100 rad/s). The waveforms show the distance between AV leaflets, where the distance in the open state the distance was measured with a positive value in millimeters. This open state is referred to as ventricular ejection (VE), whilst the valve closed (VC) state is when the distance was zero. Periods 'O1', 'O2', 'O3' and 'C1', 'C2' and 'C3' represent the phases during which the AV is open and closed, respectively at conditions H1, H2 and H3 respectively.

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The closure time was delayed by 70 ms and decreased by 30 ms compared to H3, and was decreased by 70 ms and shifted by 90 ms compared to H2.

Figure shows the blood velocity and AV dynamics at different phases in the cardiac cycle for all three physiological conditions, starting at the onset of AV opening and ending at AV closure. Generally, we observe that with all conditions, AV opening time was reduced and the closure time was increased with the increase in pump speed from 50 rad/s to 100 rad/s.

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Figure 7‎ .7 : Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle for = 150 rad/s. (a) Aortic valve closing and opening phases under condition H1. (b) Aortic valve closing and opening phases under condition H2. (c) Aortic valve closing and opening phases under condition H3.

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7.3.3 Discussion

Endo et al. [136] and Oshikawa et al. [194] investigated the variation in pump motor

current amplitude to estimate motor pulsatility, without using specific sensors, and

ignoring the AV response to CVS parameter variations. However, in this chapter,

the impact on AV dynamics using an LV-pump interaction model with varying degre-

es of LVAD assistance under various heart failure conditions was investigated,

demonstrating that electrical motor current amplitude alters with variation of cardiova-

scular parameters due to changes in AV state.

The model was able to simulateAV state during three physiological conditions across

the full range of pump speeds (i.e. 50, 100 and 150 rad/s). Figure 7.6 shows various

AV dynamics states in one cardiac cycle. The AV state during different physiological

situations was characterized by the measured distance between aortic valve leaflets.

The relationship between the peak distance and duration of opening and closure AV

times revealed the correlation between the pump speed and extent of AV opening

under each physiological condition. During the healthy H1 condition, the leaflets were

able to reach a full opening diameter of 25.3 mm due to myocardial contraction,

causing the left ventricular pressure to increase (LVP) and expulsion of blood from the

ventricle. This result was perfectly matched by in vivo measurements of AV opening

diameter in the human heart of 24.4 mm, as measured by Doppler Ultrasound [196].

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In terms of simulating the mechanics of the LV, the actual heart is known to exhibit more complex motions and can be modelled with more realistic active contractile properties, such as a time-varying elastance. This may affect AV open-close times.

However, such detailed modelling was beyond the scope of this study. This simple method of classifying was based not only on the time of the systole as with other studies [191], but also on the diastolic portion of the pump current signal, and allowed a clear distinction between open and closed AV states in real time. Such information will lead to a more precise evaluation of AV function, helping to reduce the risk of aortic insufficiency. Furthermore, the model can be extended to incorporate a range of heart failure conditions including changes in cardiac contractility.

Currently, the only way to confirm myocardial recovery and ensure the opening of the aortic valve during LVAD support is to perform serial echocardiograms and adjust the pump speed accordingly [197]. However, our AV dynamics models could be used in developing a controller with the objective of maintaining the pump speed set point within safe pump operating ranges for heart recovery. Such controllers can estimate if the AV opens and closes normally at a given pump speed. As reported by Maybaum et al. [40], partial loading of the LV during LVAD support (i.e. pump assistance ratio < 100% where there is net positive flow through both the aortic valve and the LVAD), is associated with improved myocardial function.

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7.4 Model Limitations

Due to the lack of existing aortic valve and left ventricular assist device interaction

simulation and experimental studies, more data is needed to understand the native

heart responses to the changes in physiological parameters associated with varying

levels of HF. In the present model, we have not taken into account adding more

physiological parameters associated with varying levels of contractility, such as

exercise and postural changes, due to their complexity and to understand the native

heart responses to changes in these parameters associated with HF. However, careful

attention would have to be taken while modelling the response in a chronic heart

failure patient, since it may be significantly different from that of a healthy subject

[198].

7.5 Conclusions

In this chapter, we have investigated the effect of alterations in model parameter

values, namely SVR and Vtotal, on AV state under rotary pump assistance, using both a

simplified and realistic 2D LV-pump interaction model. In particular, the models were

able to simulate the response of the AV to changes in LV preload and afterload in the

presence of LVAD support for the proper management of pump speed settings.

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8 Chapter 8 - Simulation of Motor Current Waveforms as an Index for Aortic Valve Condition during Ventricular Support

Existing commercially-used left ventricular assist devices (LVADs) make no attempt

to automatically detect the aortic valve condition in their control methods to optimize

ventricular assistance. However, to develop such a control strategy, an important

design goal for iRBPs is the ability to reliably and accurately detect AV states that can

cause harmful effects on AV structure and function due to aortic valve backflow

(regurgitation) as a result of aortic root pressure being always higher than LVP as a

consequence of LVAD over-pumping [171], and the stress applied on AV leaflets due

to pump back flow (regurgitation) as a result of under-pumping [199].

In addition, varying LVAD pump speed can control the state of the aortic valve. By

increasing impeller speed, it is possible to transition from the normal physiological

state of AV opening during ventricular ejection to a state where the aortic valve

remains permanently closed throughout the cardiac cycle. The problem of AV state

detection has attracted substantial research interest [182, 189, 190, 197, 200-

202]. However, none of these studies have included aLV-pump FSI model to investig-

ate the impact on the AV during left ventricular assist.

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FSI and CFD have emerged as reliable tools that can provide mechanical and

dynamical field information as well as other variables essential for the assessment of

cardiac function under assist device support. The FSI method is utilised in this study

for examining the AV response during LVAD support. However, limited studies have

focused on identifying the aortic valve state, despite its importance in the

improvement of current LVAD control algorithms, which may offer better response

times and more normal cardiac output aiming for myocardial recovery to ensure

patient safety and comfort, as well as reduce the incidence of AV pathologies during

heart pump support.

In this chapter, we have investigated the correlation between the AV performance and

LVAD motor current as well as speed set points; simulating aortic valve blood flow,

pressure, pump flow and LV mechanics using a 2D LV-pump interaction model. The

model does not include physical AV leaflets, but these were replaced by a valve flow

equation and pressure gradient between chambers to mimic the AV function, for more

efficient computation of left ventricular pressure (LVP) and AV pressure (AoP) in the

model.

8.1 Introduction

Important improvements have been achieved in recent times in FSI simulations of

cardiac valves. Many problems in cardiac mechanics can be modelled as the dynamic

interaction of a fluid (the blood) and an elastic structure (the valves of the heart). Over

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the past years, medical societies have mostly accepted that valve dysfunction in

LVAD patients may be related to structural changes in the tissue induced by altered biomechanics and excessive stress, and a reliable assessment of full assist state requires an estimation of the aortic valve mechanism during LVAD support [203,

204].

In this chapter, we evaluate AV state using the LVAD motor current and aortic valve flow waveforms as an index, simulated from a 2D LV computational model without

AV leaflets under heart pump support. The objective was to investigate how motor electrical current waveform changes with AV state and with the increase in pump speed. Also, identifying AV state according to motor current signals may provide an additional input to a pump speed controller to prevent highly negative pressures in the left ventricle, leading to wall suction, as well as ensuring the AV opens and closes over the cardiac cycle.

The hypothesis here is that by using the FSI 2D LV-pump model and only the non- invasive measures of instantaneous pump electrical current and impeller speed, it is possible to automatically detect AV states including:

 AV open state during Ventricular ejection (VE)

 AV closed state during diastole (AC)

 AV not open state (ANO), remaining closed throughout the entire cardiac

cycle.

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 AV regurgitation state (AR), which frequently occurrs in heart failure patients

assisted by LVADs, caused by high pump speed.

Results show that when the AV opens, there is a higher motor current compared to

when the valve is closed. Also with the increase in pump speed, the AV state shifts

from the VE into the VC state. With high pump speeds, the AV shifts into the ANO

state. In addition, we observed a negative flow jet through the cardiac cycle which oc-

cured at lower relative pump speed (i.e; 50 rad/s) causing a pump regurgitant state.

8.2 Simplified LV-pump model

8.2.1 Results:

Figure 8.1 shows the waveforms obtained from a simplified 2D LV-pump interaction

model simulation. An initial inspection of the invasive variables of LVP, AoP, aortic

valve flow (Qav), pump flow (Qp) as well as the non-invasive variables of motor

electrical current (I) and pump impeller speed, indicated the presence of AV

physiological open/closed states under LVAD support. Three pump speed set points

are illustrated. The AV was open during systole, where blood flowed from both the left

ventricle and the pump, as seen from the positive Qp and Qav throughout the cardiac

cycle. VE was characterized by LV ejection during systole, with greater LVP

compared to Aop (LVP > AoP), and positive aortic valve flow (Qav > 0).

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In addition, during systole, the contracted LV model produced a low pump speed and high motor current, causing the pressure differential across the pump to decrease and pump flow to increase. Torque is proportional to input power for a constant coil drive voltage. This means that as torque fluctuates, so does motor current and input power.

As flow increases, it causes the impeller speed to fall and power to rise. This result is similar to that obtained in previous animal [183] and computational studies [149].

In addition, Figure 8.1 shows that the transition between AV states was induced by changes in LV wall contraction. During the end of the LV pressurization (diastole), the aortic valve opened and the LVP sharply declined. Aortic pressure gradually decreased, causing a rise in differential pressure across the pump (head) and Qp to fall away much later than the Qav (approximately 0.27 s) during diastole, with less torque on the impeller leading to an increase in speed.

Thus, as shown in Figure 8.1, the current waveform in both diastole and systole shows a sinusoidal profile, equally uniform, with adjacent cardiac cycles symmetrical between systole and diastole, and inversely related to the motor speed waveform (i.e.

as current increases, speed decreases). In addition, during AV opening at a pump speed of 150 rad/s, there was an increment in the current amplitude and small oscillations in the current waveform, probably due to turbulent blood flow patterns. On the other hand, the motor current waveform showed at low pump speed set point (i.e. 50 rad/s) along with a 50% decrement in amplitude compared to 150 rad/s.

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Figure 8‎ .1 : Simulated aortic valve flow (Qav), pump flow (Qp), left ventricular pressure (Plv) and aortic pressure (Pao), motor current and pump speed waveforms obtained from the combined simplified LV-Pump model. Three pump speed set points (50, 100, and 150 rad/s) are shown.

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Figure shows simulation results using the simplified LV-pump model without AV

leaflets during LVAD support. The motor speed set points start from 50 rad/s and

increase by 50 rad/s to 150 rad/s, where the opening time at lower motor speed (i.e. 50

rad/s) occurs much earlier than at high motor speed set point (i.e. 150 rad/s)

approximately by 0.12s, and 70ms less than that at 100 rad/s. However, at a low speed

set point of 50 rad/s, the closure time was delayed by approximately 0.1s than at a

motor speed set point of 150 rad/s and by 40ms compared to 100 rad/s.

8.2.2 Discussion

This set of simulations aimed to develop a simplified LV-pump model capable of

predicting the time course of simulated haemodynamic variables in a left ventricular

model. Furthermore, the model of the aortic valve and the rotary blood pump serves as

an important platform for the next stage of modelling realistic geometries of a LV-

pump model to investigate the aortic valve response under LVAD support.

It was observed that during high speeds (i.e.150 rad/s), LV contractions eventually dec-

reased and the model became akin to LV suction, as shown in Figure 8.2. However, fl-

uctuations in pump flow continued to occur due to turbulence as a result of the

high motor speed (i.e. 150 rad/s).

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Figure 8‎ .2 : Snapshots of simulated LV blood velocity magnitude during LVAD support at various phases during the cardiac cycle. (a) = 50 rad/s. (b) = 100 rad/s. (c) = 150 rad/s. 191

8.3 Realistic LV-Pump model Results

In this section, we presente results from the realistic 2D LV-pump FSI model without

AV leaflets. Due to the complexity of the real system, LV geometry and associated

structures have been idealised. The model did not include physical AV leaflets: these

were replaced by a valve flow equation to mimic the AV function for more

computationally-efficient simulations of left ventricular pressure (LVP) and AV

pressure (AoP).

8.3.1 Identification of AV state

In order to evaluate whether pump speed and motor current are potential indicators of

aortic valve state transition, it was necessary to independently verify the physiological

state of the AV in the simulations. Since this model did not include the AV leaflets, A-

V state was identified from model pressure and flow data, as well as pump intrinsic

variables, as indicated in Table 8 -1.

Model behaviour can effectively be broken up into two phases, systole and diastole.

An initial inspection of the invasive variables of aortic valve flow and the difference

between left ventricular pressure (LVP) and Aortic pressure (AoP) indicated the prese-

nce of open and closed aortic valve states (see Figure 8.4, top panel).

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By using only the non-invasive measures of instantaneous pump impeller current to

evaluate AV dynamics during LVAD support, it may be possible to detect a range of

AV states, as described in previous chapters. In this set of simulations, attempts were

made to identify the AV states using the criteria of Table 8.1.

Table 8‎ -1. A summary of physiological and pump basic parameters identifying the aortic valve conditions.

Physiological Pump Basic Variables Variables AV State Motor LVP Pump speed Qav current

AC decreasing

VE increasing >AoP decreasing >0

8.3.2 LV wall motion

Figure 8‎ .3 : Left ventricular wall simulated cavity dimension during contractile motion.

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Measurements of end-systolic cavity dimension and end-diastolic cavity dimension

were compared with echocardiographs data from human experiments [205].

However, since our model apex structure is fixed, and the LV walls were the only

moving boundaries, the model’s LV wall contraction was less when compared to a real

heart failure subject. Therefore, we have analysed only short axis displacement by

measuring the horizontal displacement of the LV cavity as an alternative. In our study,

the cavity dimension was measured as the maximum short axis displacement between

the septal endocardium and the posterior left ventricular wall, with dimension results

shown in Figure . Due to the impact of the LVAD on CVS dynamics, the maximum

short axis displacement of the model was 3.5 mm less than cavity displacement

dimension magnitude reported in a prior human echocardiography study for heart

failure subjects, which was 20 mm [253].

8.3.3 LV-Pump model simulations

To examine the change in model haemodynamic and pump variables with increasing

pump speed set point under fixed LV contractility, values of key variables from our

LV-pump interaction model study were plotted in Figure 8.4 and Figure 8.6. An initial

inspection was made of the invasive observations of LVP, AoP, Qav , as well as the

non-invasive variables of motor electrical current (I) and pump impeller speed. During

pump assist, most variables showed a change in the amplitude with respect to pump

speed. Qav was lower with increased pump speed (see Figure ). In addition, at a high

pump speed set point (i.e. 200 rad/s), Qp was higher due to lower differential pressure

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across the pump (head), producing a higher pump assistance as reported by Maybaum et al. [40] (i.e. pump assistance ratio = 100%) and transition into ANO state, as shown in Figure (d).

Figure 8.4 illustrates the waveforms obtained from a realistic 2D LV-pump interaction model simulation. Four pump speed set points were applied to the model from 50 rad/s to 200 rad/s in increments of 50 rad/s. The figure shows pressure patterns (LVP and

AoP) waveforms during speed changes in this 2D LV-pump model simulation.

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Figure 8‎ .4 : Top panels: left ventricular pressure (black line) and aortic valve pressure (dotted red line) at variouspump speeds. Lower panels: Corresponding pump speed waveforms from the LV-Pump model. Four pump speed set points (50, 100, 150 and 200 rad/s) are shown.

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The simulation data showed a decrease in pulsatility in aortic pressure with increasing pump speed until the point where the AV remained permanently closed ( Figure ,

200 rad/s). This was because LVAD support directly correlated with unloading of the

LV while maintaining aortic blood pressure, so this loss of pulsatility is as expected during LVAD support. This finding is similar to the experimental studies of Goldstein et al. [179] and Choi et al. [206]. Figure illustrates the motor current and aortic flow waveforms obtained from four different set points of 50, 100, 150 and 200 rad/s, illustrating that the pump motor current undergoes signiﬁcant change for each impeller speed set point. The result indicates the relationship between the peak impeller speed and Aop in our 2D LV-pump interaction model, revealing an excellent correlation with the aortic pressure.

In addition, due to absence of a mitral valve in the 2D realistic LV model, we have found that the LVP and Aop are lower than observed in a previous animal study by

Karantonis et al. [183] and a computational study by Lim et al. [149]. However, our low left ventricular pressure result was similar to that obtained from a numerical model study by Shi et al. [135] for investigating human CVDS response to LVAD, as well as previous animal [207] and mock-loop [208] experiments. In addition, Figure 8.4 shows time series plots calculated from the pump speed. The plots were obtained from our pump model at a certain value of the pump speed set points, providing another useful representation of the pump flow state characteristics.

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Figure 8‎ .5 : Simulated aortic valve flow (Qav), (black line) and pump flow (Qp) (red line) at a pump set point of 100 rad/s.

Contraction in the model results in distinct AV open/close phases. For example, the ideal AV state appeared to be that in which the aortic valve opened during systole, where blood flowed from both the left ventricle and the pump, as seen from the positive

Qp and Qav flows during systole (see Figure 8.5). Contraction of the ventricle caused th- e differential pressure across the pump to decrease, and the force or torque on the impeller to rise. As pump flow increases, it causes impeller speed to fall and electrical power to rise. In contrast, during diastole, impeller speed increased, causing motor current to decrease. This result is similar to that reported in previous animal [183] and computational studies [149].

From the pump motor current and aortic valve flow signals in Figure (a, b and c), model behaviour could effectively be divided into two states: aortic valve closed and open, similar to the previous simulation results. Furthermore, the relationship between motor current, AV closure time and closure duration exhibited good correlation.

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Figure 8‎ .6 : Simulated pump motor current (black) and reference aortic flow (Qav) (red) at four motor s- peed set points corresponding to (a) 50 rad/s, (b) 100 rad/s, (c) 150 rad/s and (d) 200 rad/s, where '■' and '●' indicate AV opening and closing times, respectively. Qav > 0 represents the periods when the AV is open, referred to as ventricular ejection (VE), and Qav =0 represents the valve closed (VC) state. Note that in panel (d), Qav = 0 at all times, indicating the AV remains closed throughout the cardiac cycle (ANO) for this pump set point speed of 200 rad/s.

As shown in Figure , transition from state VE to state VC occurred with increasing

pump speed. In addition, increases in motor speed set point produced an upward shift

of the motor current amplitude, resulting in an increased AV closing time, and

significantly increasing peak motor current by at least 50% compared to the next

lowest speed set point. However, at the increase of pump speed set point to 200 rad/s, 199

the aortic valve not opening (ANO) state was continuously maintained, with the AV remaining closed throughout the entire cardiac cycle (see Figure , d), with no blood flow to the proximal aorta. Such an ANO state during the LVAD support has been reported by limited studies [136, 182, 183, 190-192], occurring when AoP is continually higher than LVP with no sufficient pressure in the LV cavity to open the

AV (see Figure 8.4, top panels).

Furthermore, a low motor current of 0.021A was observed at 50 rad/s in the

AV closing phase, with this phase starting at t=1.89s and lasting for a duration of 0.57 seconds. Motor current increased throughout the AV open state (t=1.97-2.40s), reaching a maximum value of 0.052A at t=2.37s. In contrast with 150 rad/s, a low motor current of 0.375A was measured during the AV closing phase (t=1.70s), with a closing duration of 0.78 seconds, representing an increase of 0.21 seconds compared to 50 rad/s. The motor current increased throughout the AV open state

(t=2.13-2.34s), reaching a maximum value of 0.4947A at t=2.25s.

Furthermore, at a speed set point of 100 rad/s, a low motor current of 0.1143 A was observed during the AV closing phase (t=1.65s), with this phase lasting for a duration of 0.74 seconds. Motor current then increased throughout the AV open state (t=2.11-2.

35s), with an increase in the total open time of 30 ms compared to the 150 rad/s set point. Motor current, then reached a maximum value of 0.196 A at t=2.24s. The total closure durations for pump speed set points of 100 and 150 rad/s were increased by 0.1 and 0.21 s compared to the 50 rad/s set point, respectively. However, as shown in Fig-

200

ure 8.11, the fully-open AV instant at 50 rad/s and 100 rad/s remained approximately

the same (t=2.21 and t=2.22s respectively), whereas it was increased at 150 rad/s to o-

ccur at t=2.27s. In addition, we observe in Figure 8.6 a rightward shift of the pump

motor current from the aortic flow waveform, particularly, at AV fully-open times, at

all four pump speeds, most likely due to the motor winding inductance.

In Figure 8.9a, we observed a negative flow jet through the cardiac cycle which occu-r

ed at relatively low pump speed (i.e. 50 rad/s) causing a pump regurgitant state at t=1.

97s. This LVAD behaviour during low pump speed has been reported by previous

studies including that of Yuhki et al. [193] and Karantonies et al. [183]. This pheno-

menon was due to negative pump flow during VE (see Figure ), resulting in AoP

being higher than the LVP and the pump differential pressure (head) as shown in

Figure .

Figure 8‎ .7 : Simulated aortic valve flow (Qav), (black line) and pump flow (Qp) (red line) at a pump set point of 50 rad/s.

201

Figure 8‎ .8 : Simulated left ventricular pressure (sold black line) and aortic pressure (dotted black line) and pump differential pressure head (red line) at the low pump speed set point of 50 rad/s.

202

Figure 8‎ .9 :Snapshot of simulated LV blood velocity magnitude during LVAD support at various phases i.e. AV closure time (left figure in all panels), LV opening phase (two figures at the centre in all panels) and next cycle closure phase (right in all panels) during the cardiac cycle. (a) = 50 rad/s. (b) = 100 rad/s. (c) = 150 rad/s.

203

8.3.4 Discussion

Despite extensive studies previously being carried out on AV state detection using

intrinsic LVAD parameters [136, 190, 191, 207], and studies to detect pump

state [182, 183, 188, 201], only a limited number of studies have been conducted to

automatically detect AV state using LV-pump FSI models. In the simulations of his

chapter using a 2D LV-pump interaction model without AV leaflets, we concluded

that AV dynamics were affected by the pump speed set point. With increasing pump

speed, AV closing duration increased and open time was decreased, eventually

reaching a condition at high motor speeds where the AV remained closed throughout

the entire cardiac cycle. In order to evaluate whether pump current is a potential

indicator of aortic valve state transition, it was necessary to independently verify the

state of the aortic valve in the simulations. This was achieved through the use of aortic

valve flow and pressures. In addition, using the motor electrical current signal, it was

feasible to determine AV state as open, closed, or permanently closed. In addition,

using the motor electrical current signal, it was feasible to determine AV state as open,

closed, or permanently closed. Although beyond the scope of this thesis, there is

undoubtedly a need for more experimental studies in data-driven learning strategies

for the identification, classification, and recognition of AV state from pump current

waveform. Nonetheless, the modelling paradigm presented in this chapter should be

viewed as a first stage in the validation of suitable AV state detection techniques for

more robust LVAD control.

204

These results agreed with published experimental findings, which showed an increase

in aortic pressure with increasing pump speeds [209]. However, the increase in the

AoP and LVP in our simulation results was not as high as that reported clinically. This

may be due to the fact that we have used a simplified geometry and have not utilized a

sufficiently accurate model of LV contractility.

The model described in this chapter will prove useful in determining

safe pump speed ranges that can detect whether the AV open and closes normally at a

given pump speed. In addition, we have been able to identify pattern changes in the

LVAD electrical current, which may indicate if the AV is open, closed and continually

closed during the cardiac cycle. Hence, the model will provide a useful tool for

developing physiological responsive pump control strategies which could promote

myocardial recovery, minimizing the risk of LV pathologies in LVAD patients.

8.4 Model Limitations

A possible limitation of our AV state detection method was that the measurement of

either electrical current or power was based on fixed pump speed set point, ignoring

transient changes in set point characteristics. However, is not likely that set point

would need abruptly to change in vivo, even during sudden perturbations of the

cardiovascular system during pump operation.

205

Another limitation is that it has been reported that haemodynamic responses of the L-

VAD may be different under chronic heart failure and failing heart conditions [179].

Therefore, further simulation using our LV model with induced chronic heart failure

(i.e. enlarged heart) could be carried out to more accurately represent a wider range of

clinical scenarios.

8.5 Conclusions

We have presented a simplified two-dimensional FSI model of the ventricle during

LVAD support, without explicitly modelling the AV leaflet structures. The model was

formulated with the aim of providing computationally efficient simulations that can

provide insight into the dynamics of heart-pump interaction, and to simulate LVAD

motor current waveform in relation to AV state. The results confirmed that when the

AV opens (i.e. aortic outflow), there is a higher motor current compared to when the

valve is closed. This motor current result is similar to that obtained by Lim et al. [149].

Our computational model of motor current variations during AV movement,

particularly during its closing phase and under pulsatile flow conditions, will provide

significant insights into LV function during LVAD support, particularly if the model is

further developed to incorporate realistic anatomies. Moreover, our model is an

important tool for improving current LVAD control systems to ensure patient safety

and comfort, and reduce the incidence of AV pathologies during heart pump support

206

9 Chapter 9 - Conclusions and Recommendations

9.1 Conclusions

Despite extensive research in the area of implantable rotary blood flow devices,

interaction between the aortic valve and the heart assist device has not yet been

completely understood, to improve the treatment of heart failure patients.

Computational models of LVAD-AV interaction are economical and fit for

investigating AV dynamics under LVAD support. For example, specific

pump parameters that difficult to acquire in-vivo, or the impact of certain pump

outflow settings can be determined using LV computational models. This thesis was

able to address the aims the study in offering insights into AV state detection from

LVAD variables such as pump speed and motor current.

Chapter 5 presented a simplified two-dimensional LV-pump interaction model of

aortic valve motion, based on the the use of the Arbitrary Lagrangian–Eulerian

Finite Element Method and the time-dependent Navier-Stokes formulation of an

incompressible viscous fluid. The simulated pressure result was altered during AV

leaflet movement, particularly during AV closure, providing significant insights into

LV function under LVAD assistance. In the second part of Chapter 5 the simplified

model of LV-pump was combined with a Windkessel model of the systemic

207

circulation and heart contractility to correctly simulate AV open state during ventricular ejection (VE) and AV closed state (AC) during diastole.

Chapter 6 presented an approach for detecting AV states during LVAD support from basic pump variables (i.e. motor current and pump impeller speed), using a simplified 2D LV-pump interaction model. In addition, methods for estimating the average pump differential pressure (head) and flow rate from pump impeller speed, input power and fluid viscosity were presented for modelling the LVAD. This pump model is able to provide valuable insights into how various LVAD speed set points affect AV dynamics, whereas very few studies have examined AV state in simplified computational model with pulsatile LV contraction. In section two of this chapter, 2D realistic LV-LVAD geometries were used to simulate LV dynamics and pump motor current over a range of pump operating points. It also allowed ascertaining the performance of the AV under modified pump operating conditions.

Chapter 7 simulated the effect of alterations in CVS parameter values, namely total blood volume (Vtotal) and systemic vascular resistance (SVR), on AV close and open times during LVAD support. In addition, LV-pump parameters were altered to examine the correlation between simulated motor current and distance between

AV leaflets over a wide range of pump speed operating points and various CVS conditions, which may be encountered by LVAD patients in their daily activities. It was shown from the motor current simulation results that the AV open and closed durations were altered by these parameter changes.

208

Chapter 8 presented a number of model CVS dynamics features in a simplified LV-

pump model after excluding the AV leaflets. This computationally-efficient model

provided important insights into AV and LV behaviour under LVAD support. The

valve leaflets were substituted with a pressure gradient equation to describe aortic

valve flow. This simplified model was shown to be able to predict the time course

of simulated haemodynamic variables and pump intrinsic parameters (i.e. motor

current and impeller speed), as well as AV state, during LVAD support.

9.2 Suggestions for Future Work

While this thesis has addressed many of the important issues associated with AV

monitoring and detection in the LVAD-assisted heart, there were numerous areas

that still need to be investigated. These include the ability to simulate AV state

under a wider range of cardiovascular states and pump operation conditions (i.e.

myocardial contractile dysfunction), during exercise and postural changes with

more realistic heart geometry. In addition, in order to validate the outcomes of the

AV state detection resulting from our model, further in-vivo and in-vitro

experiments are required. Furthermore, the ability of the model to detect the level

of blood viscosity or HCT from pump intrinsic parameters (i.e. motor current

waveform) is an interesting area that needs further analysis.

209

9.2.1 Simulating chronic heart failure during exercise and postural change

Thus far, various states of heart failure severity have been defined by different

levels of myocardial contractility, changes in venous return blood volume and

different vascular resistance values (i.e. Chapter 7). A worthwhile goal for future

studies would be to expand the range of HF. One limitation of our model is that

myocardial contractility was fixed, and not able to be descreased (i.e. contractile dy

sfunction), which is usually determined through a decrease in wall motion. Alterna-

tively, methods can be used to achieve this objective (i.e. virtual heart with

myocardial fibre direction), and to more accurately simulate chronic heart failure

by modelling the LV with patient-specific realistic cardiac morphologies captured

from non-invasive imaging modalities such as computed tomography, magnetic re-

sonance imaging or echocardiography.

9.2.2 AV state detection validation

Evaluating the suitability of the proposed AV detection strategy was performed in

our study purely via software simulation. Although the model was validated with

limited previously developed in-vivo and in-vitro studies, further investigation and

validation of the LV-pump and AV dynamics results using animal experiments

under various physiological conditions, including postural changes and HF severity

are required. However, this experimental validation was beyond the scope of this

thesis. 210

9.2.3 Effect of blood viscosity on AV states

As been reported from various in-vitro studies [65, 69], different values

of haematocrit (HCT) may affect the estimation of pump flow rate at the same

pump power and impeller speed. In addition, it was observed from in-vitro experi-

ments by Wakisaka et al. [62] in the goat, that there is a strong correlation betwe-

en HCT levels and estimated pump flow. Chapter 6 of this thesis described a

model to estimate pump head differential pressure and flow rate from LVAD

pump power and impeller speed, which depends on changes in blood viscosity. Fu-

ture studies should investigate the effect of blood HCT or viscosity on AV state

during LVAD support.

211

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