A Novel Design and Optimization of a Polymeric

Aortic Valve using Numerical and Experimental

Techniques

By Saleh Hassanzadeh Gharaie

A thesis submitted in fulfilment of the requirements for the degree of

Doctor of Philosophy

Faculty of Science, Engineering and Technology

Swinburne University of Technology

Hawthorn Campus, Australia

April 2016

i

Abstract

Heart stroke and vascular diseases kill more Australians than any other disease

group accounting for 50,294 deaths (37.6% of all deaths) in 2002. Valvular heart

disease (VHD) can be considered the next cardiac epidemic. VHD is described as

damage to or a defect in one of the four heart valves namely, the aortic, tricuspid,

pulmonary, and mitral (bicuspid). However, there is currently no medication to cure

VHD and treatment is either repair or total replacement with a prosthetic heart valve

(PHV). Currently, there are two types of prosthetic valves, known as mechanical and

bioprosthetic (tissue) valves. Generally, both of these prosthetic valves impose neo

disease with health risk complications. In this context, impaired hemodynamic

performance of mechanical valves is associated with thrombotic complications. Tissue

valves are also known to have progressive tissue degradation and deterioration. Despite

more than 60 years of research, both types of PHV are still far from ideal and a PHV

with lifelong durability without thrombotic complications is yet to be developed. In this

context, polymeric valves (PVs) have been the focus of research since the 1950s as

possible alternatives to improve the durability and haemodynamic performance of the

prosthetic valves. PVs, typically, have flexible leaflets similar to tissue valves that

enhance blood flow and improve blood disruption with lifelong biostability and

durability, although the clinical outcomes of these initial trials were not successful, as

the polymers available at the time did not provide sufficient biostability and durability

for the valve. Nevertheless, current advances in material sciences and new development

of super biostable materials may fulfil the clinical requirements of PVs. However,

advancements in the development of biocompatible polymers alone are not enough, as

there is always the need for superior manufacturing techniques combined with a good

valve design to achieve a functional PV.

Traditionally, the design and development of prosthetic valves is based on in

vitro experimental techniques before in vivo trials take place. However, currently most

researchers and designers take advantage of the advances in numerical simulations that

are capable of providing sufficient qualitative and quantitative data to initially gauge the

valve functionality in a “virtual lab”. It is now well recognised that numerical

techniques such as Finite Element (FE)/Finite volume (FV) methods are a very cost

effective alternative to traditional techniques for evaluating conceptual designs. In this

regard, developing a numerical method to accurately predict the kinematics of the valve

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leaflets as well as the flow characteristics passing through the valve is a crucial part of

the design and optimization of the valve.

In this Ph.D. research, a strongly coupled 2-way fluid-structure interaction

(FSI) simulation is developed in which the FSI model is validated as follows:

1) Numerical approach: by modeling a reference valve and comparing the

results obtained from the FSI simulation to previously published validated-data;

2) Leaflet kinematics approach: by comparing the numerical predictions of the

leaflet displacements to the in vitro experimental measurements.

In order to implement the latter approach, a pulse duplicator machine was

designed and manufactured in our lab to simulate the pulsatile loads applied to the valve

in the FSI simulation.

Moreover, to construct the valve in the experimental part, advanced

manufacturing techniques such as electron beam melting (EBM) and 3D printing

methods were utilized. This is the first time that this technique has been used to

construct a prosthetic valve. The lead manufacturing time of the proposed technique for

a customised prosthetic valve (patient match implant) was estimated to be less than four

hours.

The polymeric tri-leaflet heart valve is initially designed based on a patient’s

sinus of Valsalva (SOV) geometry, where the design aims at maximizing the valve

hemodynamic performance regarding the effective orifice area (EOA) and minimizing

the valve pressure drop. However, the durability of this class of PHVs has a substantial

effect on the valve performance. In this context, previous studies on the development of

a PV showed stress localizations and elevated stresses mainly close to the leaflet

attachment regions to the stent, and near the leaflet commissure area. Since the leaflets

are subjected to repeated cyclic load, the stress concentrations will result in more

aggressive fatigue failure of the valve. This could be improved by altering the valve

design to have a better stress distribution in the leaflets. In order to address this long-

standing issue in the literature, the numerical scheme is used to optimize the proposed

parametric design of the valve in a series of FSI simulations to improve the durability of

the valve by avoiding stress concentrations in the leaflets and reducing the maximum

stress level. In addition, a comprehensive study is carried out to fully characterize the

flow passing through the valve to investigate the possibility of red blood cell (RBC)

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damage, platelet activation, and thrombus formation due to implanting the proposed

valve.

Concisely, the results obtained from the FSI simulation show that the proposed

valve has superior hemodynamic performance and causes negligible blood damage.

These results and findings are compared to previously published data and are discussed

in detail. The discussion and the overall conclusion are presented in this thesis as well

as the future research direction.

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Acknowledgements

Firstly, I would like to express my sincere gratitude to my principal supervisor

Prof. Yos Morsi for his continuous support of my Ph.D. study, his patience, motivation

and immense knowledge. His guidance helped me in all aspects of my research and

writing of this thesis.

I thank the DSM material sciences company, for supplying Bionate ® polymer

sheets and for their technical support and help.

I would like to thank all my colleagues in the biomechanical and tissue

engineering group for their assistance during my Ph.D. candidature. To all my friends,

thank you for your understanding and encouragement. It is impossible to list all your

names here, but you are always on my mind.

I wish to thank my beloved parents, Mahmoud and Sousan, for their faith in

me, their everlasting support, their motivation and love throughout my life. Thank you

both for giving me the strength to reach for the stars and chase my dreams. Finally, and

most importantly, I would like to thank my wife, Sama. Her support, quiet patience,

love and sacrifice were undeniably the bedrock upon which the past nine years of my

life have been built. Thank you for having faith in me and making this journey possible.

Saleh Hassanzadeh Gharaie

Melbourne, Australia

April 2016

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Declaration

I declare that this thesis represents my own work and contains no material

which has been accepted for the award of any other degree, diploma or qualification in

any universities except where due reference has been made in the text of the

dissertation. To the best of my knowledge and belief, this thesis contains no material

published or written by another person except where due acknowledgement has been

made.

Saleh Hassanzadeh Gharaie

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Table of content

1 Chapter 1 Introduction ........................................................................................ 1 1.1 Introduction ...................................................................................................................... 1 1.2 Heart structure .................................................................................................................. 2 1.3 Cardiac cycle .................................................................................................................... 3

1.3.1 Atrial contraction phase .............................................................................................. 4 1.3.2 Isovolumetric phase ..................................................................................................... 4 1.3.3 Rapid ejection phase: .................................................................................................. 4 1.3.4 Reduce ejection phase ................................................................................................. 4 1.3.5 Iso-volumetric relaxation ............................................................................................ 5 1.3.6 Rapid filling ................................................................................................................. 5 1.3.7 Reduced filling ............................................................................................................. 5

1.4 Heart valves ..................................................................................................................... 5 1.5 Valvular heart disease ...................................................................................................... 6 1.6 Limitations of current treatment of VHD ........................................................................ 8 1.7 Motivation and objectives ................................................................................................ 8 1.8 Thesis outline ................................................................................................................... 9

1.8.1 Chapter 2 ..................................................................................................................... 9 1.8.2 Chapter 3 ..................................................................................................................... 9 1.8.3 Chapter 4 ................................................................................................................... 10 1.8.4 Chapter 5 ................................................................................................................... 10 1.8.5 Chapter 6 ................................................................................................................... 10 1.8.6 Chapter 7 ................................................................................................................... 11

2 Chapter 2 Literature review .............................................................................. 12 2.1 Introduction .................................................................................................................... 12 2.2 Currently available Prosthetic Heart Valves .................................................................. 12 2.3 Alternative approaches................................................................................................... 16

2.3.1 Tissue engineering of aortic PHV ............................................................................. 16 2.3.2 Polymeric Heart Valves ............................................................................................. 23

2.4 Manufacturing Technique of Polymeric Valves ............................................................ 35 2.4.1 Polysiloxane (Silicone) valve manufacturing technique: .......................................... 36 2.4.2 Polytetrafluoroethylene (PTFE) valve manufacturing technique .............................. 37 2.4.3 Polyurethane (PU) valves manufacturing technique ................................................. 38 2.4.4 Poly (styrene-block-isobutylene-block-styrene) (SIBS) valve manufacturing technique

39 2.5 Summary of findings...................................................................................................... 40

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3 Chapter 3 Design procedure .............................................................................. 42 3.1 Introduction .................................................................................................................... 42 3.2 The design parameters ................................................................................................... 42 3.3 Approaches to parameterise the leaflet geometry .......................................................... 45 3.4 Polymeric aortic valve design ........................................................................................ 54 3.5 Proposed Design ............................................................................................................ 57

3.5.1 Initial design .............................................................................................................. 57 3.5.2 Design optimization ................................................................................................... 64

3.6 Reference Valve design ................................................................................................. 65 3.7 Summary ........................................................................................................................ 66

4 Chapter 4 Numerical simulation theory and boundary condition ................. 67 4.1 Fluid Structure Interaction (FSI) analyses ..................................................................... 67 4.2 One way FSI evaluation ................................................................................................. 67 4.3 Two-way FSI evaluation ................................................................................................ 69 4.4 FSI Method .................................................................................................................... 73

4.4.1 Coupling Management .............................................................................................. 75 4.5 Material properties and effect of nonlinearity ................................................................ 79 4.6 Boundary Conditions ..................................................................................................... 81

4.6.1 Fluid domain ............................................................................................................. 81 4.6.2 Solid domain .............................................................................................................. 84

4.7 Governing Equations ..................................................................................................... 86 4.7.1 Fluid Domain Governing Equations ......................................................................... 87 4.7.2 Solid Domain Governing Equation ........................................................................... 93

4.8 Theory of elements ........................................................................................................ 94 4.8.1 Meshing and element configurations ......................................................................... 95

4.9 Hydrodynamic evaluation methods ............................................................................. 109 4.10 Optimization Process ................................................................................................... 110

5 Chapter 5 The valve construction and experimental setup ........................... 111 5.1 Overview ...................................................................................................................... 111 5.2 Introduction .................................................................................................................. 111 5.3 Pulse Duplicator machine design ................................................................................. 115 5.4 Valve construction ....................................................................................................... 117 5.5 Flow in the Pulse Duplicator Machine ......................................................................... 120 5.6 Flow rate ...................................................................................................................... 122 5.7 Data acquisition ........................................................................................................... 126 5.8 Summary and limitations ............................................................................................. 127

6 Chapter 6 Results and discussion .................................................................... 128

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Overview ...................................................................................................................... 128 6.1.

Velocity distribution .................................................................................................... 128 6.2.

Asymmetrical velocity profiles on YZ plane ........................................................ 130 6.6.1.

Cross-sectional velocity profile on XY plane ...................................................... 134 6.6.2.

Red blood cell damage ................................................................................................. 137 6.3.

Stress distribution in the leaflets .................................................................................. 155 6.4.

Hydrodynamic performance ........................................................................................ 160 6.5.

Validation of the FSI simulation .................................................................................. 165 6.6.

Computational validation .................................................................................... 165 6.6.1.

In Vitro Validation .............................................................................................. 166 6.6.2.

7 Chapter 7 Conclusion ....................................................................................... 170 7.1 Overall conclusion ....................................................................................................... 170 7.2 Limitations ................................................................................................................... 174 7.3 Future research and recommendations ......................................................................... 174

7.3.1 Computational research requirements .................................................................... 174 7.3.2 Future experimental requirements .......................................................................... 175

List of publications ...................................................................................................... 176

References .................................................................................................................... 177

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List of Figures

FIGURE 1.1. CROSS-SECTION VIEW OF A HUMAN HEART (BLACK AND DRURY, 1994) .................................. 2 FIGURE 1.2. BLOOD FLOW IN THE DIASTOLIC AND SYSTOLIC PHASES (PHYSIOLOGY, 2011) ......................... 3 FIGURE 1.3. PRESSURE DIAGRAM, LEFT VENTRICULAR VOLUME, AND ECG DIAGRAM OF ONE CARDIAC

CYCLE (PHYSIOLOGY, 2011). .................................................................................................. 3 FIGURE 1.4. CROSS-SECTIONAL VIEW OF THE HEART WITH HEART VALVES AND BLOOD FLOW DIRECTIONS

(DRUGS, 2015) ....................................................................................................................... 6 FIGURE 2.1. INSTRUCTIONS ON FIXING THE VALVE INSIDE THE CONDUIT. A) THE CONSTRUCTED VALVE IS

PUSHED INSIDE THE CONDUIT; B) THE VALVE IS SUTURED ONTO THE DACRON CONDUIT AT

THE TOP AND BOTTOM ENDS; C) COMMISSURAL SUTURES ARE PLACED AT A 1-MM DISTANCE

FROM THE COMMISSURE (ARROW IN C), D) THE OUTER LAYER OF THE

POLYTETRAFLUOROETHYLENE VALVE IS SUTURED TO THE CONDUIT AT THE MIDPOINT OF THE

SINUS (ANDO AND TAKAHASHI, 2009). ................................................................................ 26 FIGURE 2.2. THE ADIAM POLYURETHANE (PU) VALVE FOR THE MITRAL POSITION (DAEBRITZ ET AL.,

2003). ................................................................................................................................... 30 FIGURE 2.3. THE ADIAM POLYURETHANE VALVE FOR THE AORTIC POSITION (DAEBRITZ ET AL., 2004B). 31 FIGURE 2.4. A) POLYURETHANE COPOLYMER (ELAST-EONTM) TRILEAFLET PROTOTYPE VALVES WITH A

CLOSED COMMISSURAL DESIGN, B) POLYURETHANE COPOLYMER (ELAST-EONTM)

TRILEAFLET PROTOTYPE VALVES WITH AN OPEN COMMISSURAL DESIGN (LEO ET AL., 2005A).

............................................................................................................................................. 32 FIGURE 2.5. A) SCHEMATIC REPRESENTATION OF THE VALVE DESIGN B) THE TRILEAFLET PROTOTYPE

MADE OF A POSS-PCU MATERIAL WITH A SUTURE RING (GHANBARI ET AL., 2010) ........... 33 FIGURE 2.6. PAS MEASUREMENTS OF THE ST. JUDE TISSUE VALVE AND SIBS TRILEAFLET HEART VALVE

(CLAIBORNE ET AL., 2011). .................................................................................................. 34 FIGURE 2.7. PAS MEASUREMENTS OF THE ST. JUDE BILEAFLET MECHANICAL VALVE AND SIBS TRILEAFLET

HEART VALVE (CLAIBORNE ET AL., 2011). ........................................................................... 34 FIGURE 2.8. A) THE COMPRESSION MOLD USED TO FABRICATE THE OPTIMIZED VALVE, AND (B) THE

OPTIMISED XSIBS VALVE (CLAIBORNE ET AL., 2013)........................................................... 35 FIGURE 2.9. A SILICON VALVE, A) THE UPPER PICTURE SHOWS THE WHOLE VALVE, B) CROSS-SECTION OF

ONE LEAFLET FROM THE TOP (ESCOBEDO ET AL., 2006). ...................................................... 36 FIGURE 2.10. SCHEMATIC DRAWING OF HEART VALVE CONSTRUCTION FIXED IN A DACRON CONDUIT. ..... 37 FIGURE 2.11. THE MODIFIED EDWARD’S LIFE SCIENCES CRIBIER-SAPIEN STENT IS SHOWN WITH

COMPOSITE MATERIAL, AND THREE STAINLESS STEEL BALL BEARINGS USED TO SHAPE THE

LEAFLET INTO A SEMILUNAR SHAPE (CLAIBORNE ET AL., 2009). .......................................... 39 FIGURE 3.1. DIMENSIONLESS CONFIGURATION OF AV (SWANSON AND CLARK, 1974). ............................. 45 FIGURE 3.2. CONFIGURATION OF LEAFLET-FREE EDGE USING A HYPERBOLA (JIANG ET AL., 2004). ........... 48 FIGURE 3.3. CONFIGURATION OF THE LEAFLET-FREE EDGE USING TWO STRAIGHT LINES (JIANG ET AL.,

2004). ................................................................................................................................... 49 FIGURE 3.4. SCHEMATIC VIEW OF A LONGITUDINAL CROSS-SECTION OF THE AORTIC VALVE IN CLOSE

POSITION (LABROSSE ET AL., 2006). ..................................................................................... 51

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FIGURE 3.5. SCHEMATIC VIEW OF ONE LEAFLET IN BOTH THE OPEN AND CLOSED POSITIONS (LABROSSE ET

AL., 2006). ............................................................................................................................ 51 FIGURE 3.6. SCHEMATIC VIEW OF GENERATED 3D SURFACE OF THE LEAFLET. .......................................... 57 FIGURE 3.7. TRIMMED LEAFLET SURFACE TO THE STENT SIZE. ................................................................... 58 FIGURE 3.8. 3D REPRESENTATION OF THE ASSEMBLED TRI-LEAFLETS VALVE. ........................................... 58 FIGURE 3.9. CONFIGURATION OF THE LEAFLET CONSTRUCTIVE CURVE IN A CIRCUMFERENTIAL DIRECTION.

(A) THE BLUE AREA SHOWS THE CENTRAL OPENING AREA FOR ONE LEAFLET; (B) THE

CENTRAL OPENING AREA AFTER TRANSFERRING THE HYPERBOLIC CURVE. .......................... 59 FIGURE 3.10. CONFIGURATION OF THE LEAFLET-FREE EDGE DEFINED BY THE HYPERBOLIC CURVE WITH

ASYMPTOTE SUBTENDING ANGLE OF (A) 117°AND (B) 118°. ................................................. 61 FIGURE 3.11. (A) REPRESENTATION OF A PATIENT’S SOV AND THE LEAFLET RADIAL CURVE IN ZY-PLANE.

(B) CONFIGURATION OF LR IN ZY-PLANE, WHERE DNI IS THE DISTANCE OF POINT NI TO PLANE

(D) IN Y DIRECTION, AND DNꞌI IS THE DISTANCE OF POINT NꞌI TO PLANE (D) IN Y DIRECTION.

THE LR CURVE WAS DEFINED USING THE ILLUSTRATED PARAMETERS; PLANE (E) WAS

DEFINED TO SEPARATE THE SOV REGION FROM THE MAIN STREAM, PLANE (D) PASSES

THROUGH LEAFLET DISTAL POINTS IN THE XY-PLANE (SEE FIG 3.8) AND THE CENTRE OF THE

STENT RING CROSS-SECTION IN ZY-PLANE. ........................................................................... 63 FIGURE 3.12. SCHEMATIC VIEW OF THE OPTIMIZED LEAFLET GEOMETRY. THE VERTICES OF HYPERBOLIC

CURVE (LꞌC) IS LOCATED ON THE RADIAL CURVE. THE DISTANCE FROM THE XY-PLANE IS HALF

OF THE VALVE HEIGHT. ......................................................................................................... 65 FIGURE 3.13. SCHEMATIC VIEW OF THE REFERENCE VALVE. ...................................................................... 66 FIGURE 4.1. MAPPING TARGET NODE TO SOURCE ELEMENT, VALUES ARE THE RESULT OF THE

INTERPOLATION (ANSYS SYSTEM COUPLING USER'S GUIDE, 2013). .................................. 74 FIGURE 4.2. EXECUTION SEQUENCE OF THE COUPLING SERVICE (ANSYS SYSTEM COUPLING USER'S

GUIDE, 2013). ....................................................................................................................... 76 FIGURE 4.3. PROCESSING DETAIL OF THE COUPLING SYSTEM (ANSYS SYSTEM COUPLING USER'S GUIDE,

2013). ................................................................................................................................... 77 FIGURE 4.4. SCHEMATIC VIEW OF THE TWO-WAY STRONGLY COUPLING FSI FLOW CHART. ....................... 79 FIGURE 4.5. THE WIGGERS DIAGRAM SHOWING TWO CARDIAC CYCLE EVENTS OCCURRING IN THE LEFT

VENTRICLE (FRANZONE ET AL., 2012). ................................................................................. 81 FIGURE 4.6. CURVE FITTING TO THE WIGGERS DIAGRAM. .......................................................................... 83 FIGURE 4.7. OVERVIEW OF THE PRESSURE-BASED COUPLED ALGORITHM. ................................................. 87 FIGURE 4.8. SCHEMATIC OF ELEMENT TYPES. ............................................................................................ 94 FIGURE 4.9. SECTIONAL VIEW OF THE FLUID DOMAINS (A) FLUIDREF, AND (B) FLUIDPHV. ............................ 96 FIGURE 4.10. FLUIDPHV DOMAIN DISCRETIZATION WITH TETRAHEDRAL ELEMENTS. (A) SIDE VIEW OF THE

FLUID DOMAIN WITH POSITIONS OF INLET AND OUTLET, (LV =16MM, AND LO=57MM) (B) TOP

VIEW (DOWNSTREAM) OF THE FLUID DOMAIN. ...................................................................... 98 FIGURE 4.11. FLUIDREF DOMAIN DISCRETIZATION WITH TETRAHEDRAL ELEMENTS. (A) SIDE VIEW OF THE

FLUID DOMAIN WITH POSITIONS OF INLET AND OUTLET, (LV =16MM, AND LO=57MM) (B) TOP

VIEW (DOWNSTREAM) OF THE FLUID DOMAIN. ...................................................................... 98 FIGURE 4.12. MESH STATISTICS FOR THE FLUIDPHV DOMAIN (A) QUALITY, (B) ASPECT RATIO AND (C)

SKEWNESS. ......................................................................................................................... 102

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FIGURE 4.13. MESH STATISTICS FOR THE FLUIDREF DOMAIN (A) QUALITY, (B) ASPECT RATIO AND (C)

SKEWNESS. ......................................................................................................................... 103 FIGURE 4.14. DISCRETIZATION OF (A) THE OPTIMIZED VALVE, AND (B) THE REFERENCE VALVE. ............. 105 FIGURE 4.15. MESH STATISTICS FOR THE OPTIMIZED VALVE (A) QUALITY, (B) ASPECT RATIO AND (C)

SKEWNESS. ......................................................................................................................... 107 FIGURE 4.16. MESH STATISTICS FOR THE REFERENCE VALVE (A) QUALITY, (B) ASPECT RATIO AND (C)

SKEWNESS. ......................................................................................................................... 108 FIGURE 4.17. SCHEMATIC REPRESENTATION OF EOA AND GOA. ............................................................ 109 FIGURE 4.18. THE OPTIMIZATION PROCESS DIAGRAM. ............................................................................. 110 FIGURE 5.1. SCHEMATIC VIEW OF THE PULSE DUPLICATOR MACHINE (THE MOTOR AND CONTROLLER UNIT

IS NOT SHOWN). .................................................................................................................. 116 FIGURE 5.2. PICTURE OF THE PULSE DUPLICATOR MACHINE, INCLUDING THE MOTOR AND MOTION

CONTROLLER. ..................................................................................................................... 117 FIGURE 5.3. MOLDS CONSTRUCTED BY EBM TECHNIQUE TO FORM THE POLYMER FILMS INTO THE LEAFLET

GEOMETRY. ........................................................................................................................ 118 FIGURE 5.4. 3D PRINTED STENT (SUPPORTING FRAME) ............................................................................. 119 FIGURE 5.5. POLYMERIC LEAFLETS ATTACHED TO THE STENT. ................................................................ 119 FIGURE 5.6. SYSTOLIC FLOW DIRECTION IN THE PULSE DUPLICATOR MACHINE. ....................................... 120 FIGURE 5.7. DIASTOLIC FLOW DIRECTION (RED ARROWS) IN THE PULSE DUPLICATOR MACHINE. ............. 121 FIGURE 5.8. AORTIC VALVE FLOW RATE IN A FULL CARDIAC CYCLE. ....................................................... 122 FIGURE 5.9. PISTON SPEED IN FORWARD TRAVEL (SYSTOLE). ................................................................... 123 FIGURE 5.10. PISTON MOVEMENT BY CIRCULAR MOTION OF THE CRANKSHAFT. NOTE THAT CRANKSHAFT

SIZE IS EXAGGERATED TO SHOW THE DETAIL. ..................................................................... 124 FIGURE 5.11. SYSTOLIC ANGULAR VELOCITY OF THE CRANKSHAFT. ........................................................ 125 FIGURE 5.12. CONFIGURATION OF THE HIGH-SPEED CAMERA IN THE EXPERIMENTAL TEST. ..................... 126 FIGURE 6.1. 2D REFERENCE PLANES (A) ASYMMETRICAL YZ PLANE (B) CROSS-SECTIONAL XY PLANE. . 129 FIGURE 6.2. SCHEMATIC VIEW OF ASYMMETRICAL PLANES FROM SINUS CAVITY TO THE COMMISSURAL

END..................................................................................................................................... 130 FIGURE 6.3. ASYMMETRICAL 2D VELOCITY PROFILE ON YZ PLANE AT T=20MS. ..................................... 131 FIGURE 6.4. ASYMMETRICAL 2D VELOCITY PROFILE ON YZ PLANE AT T=84.25MS. ................................ 132 FIGURE 6.5. ASYMMETRICAL 2D VELOCITY PROFILE ON YZ PLANE AT T=168.5MS. ................................ 133 FIGURE 6.6. SCHEMATIC VIEW OF CROSS-SECTIONAL PLANES FROM THE VALVE INLET TO OUTLET. ........ 134 FIGURE 6.7. CROSS-SECTIONAL 2D VELOCITY PROFILE ON YZ PLANE AT T= 20MS. ................................. 135 FIGURE 6.8. CROSS-SECTIONAL 2D VELOCITY PROFILE ON YZ PLANE AT T= 84.25MS. ............................ 136 FIGURE 6.9. CROSS-SECTIONAL 2D VELOCITY PROFILE ON YZ PLANE AT T= 168.5 MS. ........................... 136 FIGURE 6.10. 3D PRESENTATION OF WSS DISTRIBUTION ON THE LEAFLETS AT T=69MS. ......................... 138 FIGURE 6.11. NODAL DISTRIBUTION OF WSS AT TIME STEP=69MS (PEAK WSS). .................................... 138 FIGURE 6.12. TEMPORAL DISTRIBUTION OF WSSMAX OVER THE ACCELERATION PHASE. ........................... 139 FIGURE 6.13. DISTRIBUTION OF MAX. REYNOLDS STRESSES MAPPING ON THE REFERENCE ZY PLANE AT

X=0MM AT T=168.5MS (PEAK SYSTOLE). ........................................................................... 140 FIGURE 6.14. PRESENTATION OF STREAMLINES AND SAMPLE PARTICLES ON THE LEAFLET. ..................... 142

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FIGURE 6.15. EXPOSURE TIME HISTORY OF SAMPLE PARTICLES PASSING THE PEAK SHEAR STRESS AT 69MS

AFTER THE VALVE OPENING. ............................................................................................... 143 FIGURE 6.16. CALCULATED BDI VALUES USING THE AVERAGE SHEAR STRESS METHOD. ........................ 145 FIGURE 6.17. CALCULATED BDI VALUES USING THE TEMPORAL DIFFERENTIAL METHOD. ..................... 148 FIGURE 6.18. BDI VALUES CALCULATED FROM THE AVERAGE SHEAR STRESS AND TEMPORAL

DIFFERENTIAL METHODS. ................................................................................................... 149 FIGURE 6.19. FITTED CURVES (RED LINES) ON THE SHEAR STRESS CURVES EXTRACTED FROM THE FSI

SIMULATION. ...................................................................................................................... 152 FIGURE 6.20. BDI VALUES CALCULATED FROM AVERAGE SHEAR STRESS, TEMPORAL DIFFERENTIAL AND

TOTAL DIFFERENTIAL METHODS. ....................................................................................... 154 FIGURE 6.21. STRESS DISTRIBUTION IN THE LEAFLET OF (A) THE REFERENCE VALVE, (B) THE INITIAL

DESIGN, (C) THE OPTIMIZED VALVE AT T=0.8S (END OF DIASTOLIC PHASE)......................... 156 FIGURE 6.22. EQUIVALENT VON MISES STRESS DISTRIBUTION IN THE LEAFLETS DURING SYSTOLE. ........ 159 FIGURE 6.23. PREDICTED BLOOD STREAM AT PEAK SYSTOLIC FLOW RATE (T=168.5MS) PASSINGTHROUGH

(A) THE OPTIMIZED VALVE, (B) THE REFERENCE VALVE. THE SOLID AREA REPRESENTS THE

CALCULATED CROSS-SECTIONAL AREA OF THE VC (RED AREA IN (A), AND BLUE AREA IN (B)).

........................................................................................................................................... 160 FIGURE 6.24. COMPARISON OF THE FE STRUCTURAL MODEL WITH IN VITRO LEAFLET MOTION. .............. 167 FIGURE 6.25. PROPOSED DEFORMATION MEASURES ON A) THE ACTUAL VALVE IN VITRO AND B) THE

OPTIMIZED VALVE IN THE FSI SIMULATION. ....................................................................... 168 FIGURE 6.26. COMPARING THE FE PREDICTIONS WITH THE EXPERIMENTAL VALUES. .............................. 169 FIGURE 6.27. MAXIMUM GOA AT PEAK SYSTOLE FOR A) THE ACTUAL VALVE B) FE STRUCTURAL MODEL.

........................................................................................................................................... 169

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List of Tables

TABLE 2.1. TISSUE PROSTHETIC HEART VALVES. ...................................................................................... 13 TABLE 2.2. MECHANICAL HEART VALVES. ................................................................................................ 14 TABLE 3.1. A0 COMPUTED BY VARIOUS ASYMPTOTES OF THE HYPERBOLIC CURVE. .................................... 60 TABLE 3.2. VALVE HEIGHT AND SOV MEASUREMENTS (DATA IS ROUNDED). ............................................ 62 TABLE 4.1. SUMMARY OF INITIAL CONTACT STATUS AND CONTACT DETECTION FOR THE PROPOSED PHV. 85 TABLE 4.2. SUMMARY OF INITIAL CONTACT STATUS AND CONTACT DETECTION FOR THE REFERENCE

VALVE. ....................................................................................................................................... 86 TABLE 4.3. MESH INDEPENDENCE STUDY OF THE FLUID PHV DOMAIN. ........................................................ 99 TABLE 4.4. MESH INDEPENDENCE STUDY OF THE FLUID DOMAIN FLUID REF DOMAIN. ................................. 99 TABLE 4.5. MESH INDEPENDENCE STUDY OF THE REFERENCE VALVE....................................................... 104 TABLE 4.6. MESH INDEPENDENCE STUDY OF THE OPTIMIZED VALVE. ....................................................... 105 TABLE 6.1. MAXIMUM REYNOLDS AND WSS STRESSES RECORDED FOR THE PROPOSED VALVE AT THE

CRITICAL TIME STEPS. .............................................................................................................. 139 TABLE 6.2. CONSTANT VALUES OF POWER LAW EQUATIONS PROPOSED BY (GIERSIEPEN ET AL., 1990). .. 142 TABLE 6.3 AVERAGE SHEAR STRESSES AND EXPOSURE TIMES CALCULATED FOR THE SAMPLE PARTICLES.

................................................................................................................................................. 145 TABLE 6.4 HYDRODYNAMIC QUANTITIES OF THE REFERENCE AND OPTIMIZED VALVE. ............................ 161 TABLE 6.5. SYSTOLIC PRESSURE DROP CAUSED BY THE PROPOSED VALVE COMPARED TO AORTIC PHVS.

DATA FOR PHVS WERE COLLECTED FROM THE TEXTBOOK OF CLINICAL ECHOCARDIOGRAPHY

(OTTO, 2013) ........................................................................................................................... 162 TABLE 6.6. EOA OF THE PROPOSED VALVE COMPARED TO AORTIC PHVS. DATA FOR PHVS WERE

COLLECTED FROM TEXTBOOK OF CLINICAL ECHOCARDIOGRAPHY (OTTO, 2013) .................... 163 TABLE 6.7. EOA INDEX OF THE PROPOSED VALVE COMPARED TO THE EOA INDEX OF AORTIC PHVS. .... 164 TABLE 6.8. COMPARISON OF THE EXPERIMENTAL RESULTS WITH THE PREDICTED RESULTS. .................... 166

xiv

List of Abbreviations

ALE Arbitrary-Lagrangian-Eulerian

AP Atrial Pressure

API Application Programing Interface

AR Aortic Regurgitation

AV Aortic Valve

AVA Aortic Valve Area

AVEC Autologous Vascular Endothelial Cell

BDI Blood Damage Index

BP Bovine Pericardium

BSA Body Surface Area

CAD Computer-Aided Design

CFD Computational Fluid Dynamics

DTE Device Thrombogenicity Emulation

EBM Electron Beam Melting

ECG Electrocardiogram

ECM Extracellular Matrix

EDTA Ethylenediaminetetraacetic Acid

EOA Effective Orifice Area

ERV Endogenous Retrovirus

FDA Food and Drug Administration

FDM Fuse Deposition Modelling

FE Finite Element

FEM Finite Element Method

FSI Fluid-Structure Interaction

FTIR Fourier Transform Infrared

FV Finite Volume

GAG Glycosaminoglycan

GOA Geometric Orifice Area

IB Immersed Boundary

LB Lattice Boltzmann

LBGK Bhatnagar-Gross-Krook

LDA Laser Doppler Anemometer

LHS Left Heart Simulator

xv

LVOT Left Ventricular Outflow Tract

MHV Mechanical Heart Valves

MPI Message Passing Interface

MV Mitral Valve

NEM Newton-Euler Method

P3HB Poly(3-hydroxybutrate)

P4HB poly(4-hydroxybutyrate)

PB Pneumatic Bioreactor

PCU Polycarbonate-Urethane

PDMS Polydimethylsiloxane

PEEK Polyetheretherketone

PEG Poly(ethylene glycol)

PEU Polyether Urethane

PGA Polyglycolic Acid

PHA Polyhydroxyalkanoate

PHV Prosthetic Heart Valve

PIB Polyisobutylene

PIV Particle Image Velocimetry

PL Platelet

PMSF Phenylmethylsulfonyl Fluoride

PPM Prosthetic Patient Mismatch

PTFE Polytetrafluoroethylene

PU Polyurethane

PV Polumeric valve

PVA Polyvinyl Alcohol

RBC Red Blood Cell

RP Rapid Prototyping

RSS Reynolds Shear Stress

SA Sinoatrial

SDS Sodium Dodecyl Sulphate

SEM Scanning Electron Microscope

SIBS Poly (styrene-b-isobutylene-b-styrene)

SOV Sinus of Valsalva

STL Stereolithographic

xvi

TEHV Tissue-Engineered Heart Valve

TPE Thermoplastic Elastomer

TPG Transvalvular Pressure Gradient

TPU Thermoplastic Polyurethane

UCC Umbilical Cord Cell

UDF User-defined Function

VAD Ventricular Assist Devices

VEC Valvular Endothelial Cells

VC Vena Contracta

VHD Valvular Heart Disease

VP Ventricular Pressure

WSS Wall Shear Stress

1

1 Chapter 1 Introduction

1.1 Introduction

The research in this dissertation primarily focuses on the development of an optimized

prosthetic aortic valve using numerical and experimental techniques. The research also aims

to broaden the knowledge foundation in terms of the design and development of the valve

which can be used in the future research and development of prosthetic heart valves. The key

objectives of this research will be achieved in a systematic approach by:

Thoroughly understanding the native heart structure and its function, in particular, the

function of heart valves, related diseases and available treatments;

Performing an extensive literature review on the previous studies and current

developments;

Identifying the limitations and advantages of the previously carried out experimental

and numerical techniques from the literature;

Designing and manufacturing a testing machine (for the in vitro experiment) to

validate the simulation predictions;

Developing a numerical simulation method to virtually evaluate the varying designs,

and to optimize the valve design.

In this chapter, general information on the problem is provided following by the

impetus and motivations of this research. Currently available treatments of the diseased heart

valve are also presented as well as their advantages and drawbacks in terms of durability,

functionality, and biocompatibility. Finally, the scope and objectives of this research are

defined to address the problem.

2

1.2 Heart structure

The heart of all vertebrates is a muscular organ that executes consistent rhythmic

contractions to pump blood through the blood vessels. Evidence-based research literature

describes human heart valves (see Figure 1.1) as passive devices that open and close in

response to pressure variations to maintain unidirectional blood flow (Black and Drury,

1994).

Figure 1.1. Cross-section view of a human heart (Black and Drury, 1994)

The human heart is in the centre of the chest between the third and sixth ribs,

surrounded by a rubbery sac called the pericardium. The pericardium is composed of fibres

and surrounds the heart to maintain its position as well as lubricating the outer side of the

heart. The weight of a human heart is around 300 grams; however, this weight varies in

accordance with the general health, weight, gender, and age of the individual. The human

heart consists of four chambers, the upper left and right atria and the lower left and right

ventricles. The ventricles constitute the lower chambers of the heart and the atria constitute

the upper chambers of the heart. The atria chambers are bifurcated by the inter-atrial septum

and the interventricular septum divides the ventricles chambers. These dividing walls are

composed of thick muscles and are responsible for sustaining the cardiac chambers under the

influence of consistent pressure from the circulating blood. The thickness of the walls of the

left ventricle chamber is 12~13mm and provides sufficient force for pumping the blood to all

the organs in the body.

3

1.3 Cardiac cycle

The cardiac cycle represents the consecutive events which occur during a single cycle

of a heartbeat. It is divided into two phases: the diastole and systole phases as shown in

Figure 1.2.

Figure 1.2. Blood flow in the diastolic and systolic phases (Physiology, 2011)

The systolic phase represents the period of time that both the right and left ventricles

contract and eject blood to the body (through the aorta artery) and lungs (through the

pulmonary artery) and the diastole phase represents the time during which both ventricles are

filled with blood. The cardiac cycle can be described in more detail by dividing one cardiac

cycle into seven consecutive phases, as shown in Figure 1.3 (Physiology, 2011).

Figure 1.3. Pressure diagram, left ventricular volume, and ECG diagram of one cardiac cycle (Physiology, 2011).

4

1.3.1 Atrial contraction phase

This phase is initiated by action potentials which are generated by the sinoatrial (SA)

node. The depolarization of these cells causes a wave of electrical activity across the atrium

and then to the ventricles. These electrical activities cause muscles to depolarize and contract.

The electrical depolarization of the atria, called P-Wave on the electrocardiogram (ECG)

initiates the atria contraction. When the atria contracts, the pressure in the atrial chambers

increases, which increases the blood flow into the ventricles through the opened

atrioventricular valves. The sound of the vibration of the ventricular wall that is generated in

this phase, called the fourth heart sound, is detectable (S4 on Figure 1.3).

1.3.2 Isovolumetric phase

After the ventricles are filled, all atrioventricular valves are closed. During this

period of time (between the opening of the aortic and pulmonic valves and the closure of the

atrioventricular valves), the pressure in the ventricles increases rapidly while the ventricle

volume is constant. Therefore, contraction is isovolumetric. The sound of the closure of the

AV valves in this phase causes the first heart sound (see S1 on Figure 1.3).

1.3.3 Rapid ejection phase:

This phase begins when the blood pressure in the ventricles exceed the pressure in the

aortic and pulmonic valves. Consequently, blood is ejected rapidly into the aorta and

pulmonary arteries. In this phase, no heart sounds are usually noted as the opening of healthy

valves is silent, if a sound can be detected in this phase, this indicates a valve disease.

1.3.4 Reduce ejection phase

In this phase, ventricular repolarization occurs which is shown on the ECG as a T-

Wave. When repolarization occurs, the ventricular active tension declines, therefore, the

ejection rate is reduced and the ventricular pressure drops slightly below the outflow

pressure. Nevertheless, outward blood flow still occurs because of the kinetic energy of

blood. Also, the returning blood from the lungs and the body results in an increase in the

pressure in the atrial.

5

1.3.5 Iso-volumetric relaxation

The blood pressure at the beginning of the last phase is at the maximum of its cycle

(around 120 mm/Hg), after which it declines. The decline in the pressure continues, causing

both the aortic and pulmonic valves to close abruptly. The sudden valve closure is audible

(second heart sound, S2 on Figure 1.3), and it is the beginning of isovolumetric relaxation. In

this phase, the blood volume remains constant due to the closure of all the valves.

1.3.6 Rapid filling

During the relaxation of the ventricles in the previous phase, the pressure in the

intraventricular drops below the atrial pressure. Therefore, the mitral and tricuspid valves

open rapidly and start filling the ventricles with blood, which is a new phase. Despite the

blood flowing into the ventricles through the atrioventricular valves, the intraventricular

pressure drops slightly as the ventricles are still relaxed. The pressure in the ventricles slowly

rises when they are completely relaxed and receive blood from the atria. Although filling

blood in the ventricles is usually silent, the third heart sound (S3 on Figure 1.3) of children is

audible in this phase. Nevertheless, the third heart sound of adults indicates a heart valve

disease, which is caused by ventricular dilation.

1.3.7 Reduced filling

The blood-filling rate in the ventricles falls as they fill with blood which leads to an

increase in the intraventricular pressure. Therefore, pressure differentiation between the

ventricles and atrioventricular valves become relevantly less, which causes the rate of filling

to drop. At the end of this phase, the ventricles are filled up to 90% of their blood capacity

and then will be fully filled in the first phase of the next cycle, which is atrial contraction.

1.4 Heart valves

A human heart has four unidirectional valves, the aortic valve (AV), mitral valve

(MV), tricuspid valve and pulmonary valve, as shown in Figure 1.4.

6

Figure 1.4. Cross-sectional view of the heart with heart valves and blood flow directions (Drugs, 2015)

These valves maintain the circulatory system while acting as gatekeepers for checking

the unidirectional flow of blood. In general, the valves are categorised into two types:

- Atrioventricular valves: The valves that are located between the atriums and

ventricles of the heart (tricuspid and mitral valves).

- Semilunar valve: The valves that are located in the arteries leaving the heart (aortic

and pulmonary valves).

1.5 Valvular heart disease

Heart valve disease or valvular heart disease (VHD) is a condition where a heart valve

does not execute its blood regulation task. This can occur in any of the four valves. VHD

represents significant health concerns across the globe and contributes to the high morbidity

and mortality rates, as evidenced by the findings in the academic literature. Rheumatic fever

is one of the main causes of VHD, particularly in young adults and paediatric patients in

developing nations (Morsi and Morsi, 2012).

7

However, the reported cause of VHD in developed nations is due to degenerative

pathological conditions that predominantly affect the elderly and is closely related to ageing.

A dysfunctional heart valve is either due to congenital heart pathology, leading to

stenosis or inefficiency of the valve or from an acquired disease such as calcification,

regurgitation, degeneration and stenosis or endocarditis. The frequency of the reported cases

of acquired VHD is higher than the number of congenital cases.

Endocarditis is an infection of the heart valves due to bacteria or rheumatic fever and

has a significantly adverse impact on the patient’s heart functionality.

In general, there is a greater incidence of aortic and mitral valve disease than

pulmonary and tricuspid valve disease. Aortic regurgitation and aortic stenosis are commonly

recognized as the two major abnormalities of aortic valves. Aortic stenosis causes the partial

or complete blockage of the atrial valve which restricts the flow of blood through the valvular

opening. Therefore, the body expends more kinetic energy forcing the blood through the

blocked valve which results in a proportionate increase in the circulatory pressure in the

accumulation of extra blood behind the stenosis leaflets. As a result, the cardiac muscles need

to apply extra energy to facilitate the blood flow to other organs of the body. The heart

muscles, therefore, experience a thickness of their density in order to maintain the circulatory

cycle. VHD significantly alters the pressure dynamics and blood flow of the cardiac cycle,

leading to secondary heart failure. The other factors that contribute to the development of

valvular stenosis in the context of facilitating the progression of calcification across the

arterial walls include bacterial infection and acute rheumatic fever (Morsi and Morsi, 2012).

Aortic regurgitation (AR) affects the functionality of the aortic leaflets and the aortic

root, thereby disrupting the physiology of valvular closure. The loss of flexibility of the valve

leaflets and its inability to adapt in the diastolic phase results in the abnormality of its closure,

leading to circulatory disturbances. In this scenario, the portion of blood doubly pumped and

some content of blood regurgitates and leads to the proportionate enlargement of cardiac

chambers. This phenomenon of accumulation of blood due to its backflow attributes to the

prolapse of leaflets resulting in the dilatation of the upper chamber of the heart during the

execution of a heartbeat.

8

1.6 Limitations of current treatment of VHD

The treatment of VHD varies in accordance with the type and severity of the cardiac

disease. In general, there is no medication to cure such a disease. Hence, the replacement of

the dysfunctional valve by a PHV is often the preferred approach (Morsi and Morsi, 2012).

There are two types of PHVs currently available, bioprosthetic heart valves and mechanical

heart valves (MHVs). Determining which type of prosthetic valve which will be the most

suitable for a patient depends on the nature of the VHD as well as the patient’s age and

medical history. For instance, patients with papillary muscle disease usually receive an MHV,

the general recommendation for patients below the age of 60~65 is also to receive an MHV,

and a tissue valve is recommended for older patients (Tillquist and Maddox, 2011).

However, the literature review (see Chapter 2) shows that both the current commercial

PHV, bioprostheticand MHVs, still suffer from a number of drawbacks. For example,

patients with an MHV are still required to take anticoagulant medication for the rest of their

lives which elevates the risk of haemorrhagic complications. Even the newer generation of

MHVs, including the third generation of bi-leaflet valves, still suffering from a high degree of

turbulence fluctuations and high shear stresses that induce platelet activation, aggregation,

and deposition (Yin et al., 2004). In addition, the current tissue valves have disadvantages

including less structural reliability compared to mechanical valves. The lifetime of tissue

valves is shorter than MHVs due to their progressive tissue deterioration and often, patients

require another operation.

1.7 Motivation and objectives

Two alternative types of PHVs, namely tissue engineered heart valves (TEHVs) and

polymeric valves (PVs), have been investigated to overcome the drawbacks of the currently

available valve substitutes. Despite the great potential of TEHV, there are still significant

barriers that persist in terms of achieving the desired cell adherence, proliferation, scaffold

heterogeneity, degradation rate, mechanical properties, microstructure and porosity. In

addition, the need for cell harvesting, scaffold seeding, and bioreactor culture for this

approach make the clinical application unrealistic (Mack, 2014).

In contrast, advances in material sciences and the recent development of super

biostable polymers may fulfil the clinical requirement of PVs, and make it more reachable in

the near future. However, the development of PVs is still under investigations, and there is no

9

clinically available polymeric valve substitute. The literature shows that the proposed valve

designs and approaches to developing PVs still suffer from impaired haemodynamic

performance compared to the native valve. In addition, the FSI models incorporated in these

methods are questionable in terms of the reliability of the FSI results and the validation

process.

Therefore, this research aims to:

- Develop a parametric design of a high performance polymeric aortic valve;

- Develop a two-way strongly coupled Fluid-Structure Interaction (FSI) model to

evaluate the valve performance;

- Optimize the valve design through a series of FSI simulations in order to improve the

valve fatigue life;

- Design and manufacture a testing machine (pulse duplicator) to validate the FSI

model.

1.8 Thesis outline

This thesis consists of seven chapters. The first chapter is dedicated to the

introduction and the rest are summarised as follows:

1.8.1 Chapter 2

A thorough review of the scientific literature concerning approaches to developing

prosthetic aortic heart valves is provided. The literature review comprises the limitations of

commercially available PHVs and approaches to develop alternative PHVs including the

valve deign procedures and validation techniques. In the conclusion of this chapter, a brief

summary of the findings is provided which outlines the drawbacks of the current PHVs and

describes approaches to the development of alternative PHVs. Finally, based on these

findings, a realistic solution to developing an alternative aortic PHV is proposed.

1.8.2 Chapter 3

In this chapter, a literature review of the previous approaches to parameterize the

aortic valve design as well as the current development of the polymeric aortic valve is given.

10

The design parameters are then defined, and a novel parametric design of the valve is

proposed. Furthermore, the rationale for using the reference valve and its geometry is given.

1.8.3 Chapter 4

In this chapter, the rationale for using the Fluid-Structure Interaction (FSI) simulation

for this research is provided and different types of FSI simulations, including one-way and

two-way simulation, are explained. Furthermore, a literature review of FSI simulations in the

previous studies is given. The modelling strategy of the proposed aortic valve is explained in

detail. This includes a complete description of the FSI method, the Computer-Aided design

(CAD) model, material properties and the effect of nonlinearity, boundary conditions,

discretization of fluid and solid domains, and the optimization process.

1.8.4 Chapter 5

This chapter provides a brief literature review of the existing experimental approaches

to the evaluation of the valve performance and validation of the numerical simulation. The

aim of this chapter is to define the most suitable technique to validate the numerical results,

taking into account the constraints related to the infrastructure available at Swinburne

University of Technology. A new advanced manufacturing technique is introduced to

construct the valve. In addition, the experimental equipment, setup and procedures used to

collect the data and validate the numerical simulation are described in detail.

1.8.5 Chapter 6

In this chapter, the results obtained from the FSI simulations and in vitro testing of

the proposed valve are presented. The hydrodynamic performance of the valve is evaluated

and compared to the previously published data, in which the hydrodynamic quantities of the

proposed and reference valves including the effective orifice area (EOA), the geometric

orifice area (GOA), the transvalvular pressure gradient (TPG), leakage volume, and

maximum Von Mises stress are computed and compared to the previously published data.

The complex flow regime past the optimized valve is thoroughly analysed during systole in

order to characterize regions of high turbulence as well as flow separation with eddy

formation and stagnation point. In addition, the shear stress distribution in the leaflet and flow

field are investigated to determine to which degree the proposed valve will damage blood

11

components. Importantly, the predicted deformation of the leaflets in the FSI simulation are

compared to the in vitro experimental values as part of the simulation validation.

1.8.6 Chapter 7

Chapter 7 concludes the work in this thesis and also discusses the limitations of the

current study and suggests directions for future research.

12

2 Chapter 2 Literature review

2.1 Introduction

The literature review presented in the following sections involves a thorough review of the

scientific literature concerning approaches to developing prosthetic aortic heart valves. The

literature review comprises the limitations of commercially available prosthetic heart valves

(PHVs), and approaches to developing an alternative PHV, including the valve deign

procedures and validation techniques. Finally, based on these findings, a realistic solution to

developing an alternative aortic PHV is proposed.

2.2 Currently available Prosthetic Heart Valves

Currently, there are no medications that can cure valvular heart disease, and surgical

treatment remains the only therapeutic option to prolong the patient’s life, and depending on the

severity and type of the disease, the treatment options are either repairing the valve or replacing

the valve with a PHV. In the case of replacing the valve, the type of prosthetic valve strongly

depends on the nature of the valvular disease, the patient’s age and medical history. For

instance, patients with papillary muscle disease mostly receive an MHV, the general

recommendation for patients below the age of 60~65 is to receive an MHV, and the tissue valve

is recommended for older patients (Tillquist and Maddox, 2011). Prosthetic heart valves have

been used since the 1950s with a limited option of the cage ball mechanical valve (Andersen,

1992), and later in the 1960s, with tissue valves (Barratt-Boyes, 1964, B.G. Barratt-Boyes,

1965, Murray, 1960). However, in the last few decades, treatment options have been extended

significantly to include procedures like the Ross Operation with a tissue-engineered heart valve

(Dohmen et al., 2011), transcatheter aortic valve implantation (Généreux et al., 2012), the

cryopreserved homograft replacement procedure (Knott-Craig et al., 1994) and the stentless

tissue valve. Nevertheless, the substitution of a diseased heart valve with an MHV or a tissue

valve (stented porcine aortic valve, and bovine pericardial valves) remains the most pervasive

procedures. Table 2.1 and Table 2.2 present the list of tissue valves and MHVs respectively

that are approved by the U.S. Food and Drug Administration (FDA).

13

Table 2.1. Tissue Prosthetic Heart Valves.

Valve Name Valve component FDA approval date

SOLO Smart Stentless Heart Valve-P130011

The stentless valve is made of natural tissue obtained from the sac that surrounds the heart of a cow.

June 24, 2014

Edwards SAPIEN XT Transcatheter Heart Valve

This valve is made of tissue obtained from the heart of a cow attached to a balloon-expandable made from a cobalt-chromium frame.

June 16, 2014

Medtronic CoreValve System-P130021/S002

This valve consists of pig heart tissue mounted on a self-expanding titanium frame.

June 12,2014

St. Jude Medical® Trifecta™ Valve – P100029

This valve is made of pericardial tissue obtained from bovine with titanium stent covered with polyester.

April 20, 2011

SJM Biocor™ and Biocor™ Supra Valves

This valve is made of three pieces of pig tissue (one for each of the cusps) attached to a round shape stent.

August 5, 2008

Mitroflow Aortic

Pericardial Heart Valve

This valve is made of single piece of pericardium obtained from a cow attached to a polyester covered polymer frame.

October 23, 2007

Carpentier-Edwards S.A.V. Bioprosthesis Model 2650 (Aortic)

This valve is comprised of a porcine aortic valve tissue attached to a flexible stent.

June 24, 2002

Edwards Prima™ Plus Stentless Bioprosthesis Model 2500P

This valve is a segment of a porcine aortic artery which contains the aortic valve.

February 27, 2001

Mosaic Porcine Bioprosthetic Model 305 (Aortic) and Model 310 (Mitral)

This valve is made of a porcine heart valve tissue attached to a stent.

July 14, 2000

14

Medtronic HANCOCK® II Bioprosthetic heart valve

This valve consists of a porcine aortic valve mounted to a flexible acetal homopolymer stent.

June 24, 1999

Medtronic FREESTYLE Aortic Root Bioprosthesis

This valve comprises a porcine aortic root. September 15, 1997

Carpentier-Edwards DURAFLEX Low-Pressure Porcine Mitral Bioprosthesis

This valve is made of tissue obtained from a porcine heart valve mounted on a stent.

November 25, 1991

Table 2.2. Mechanical Heart Valves.

Valve name Valve type FDA approval date

On-X® Prosthetic Heart Valve - P000037

Bileaflet May 30, 2001

ATS Open Pivot® Bileaflet Heart Valve

Bileaflet October 13, 2000

Monostrut Cardiac Valve Prosthesis Tilting disk November 30, 1997

Carbomedics Prosthetic Heart Valve Bileaflet November 29, 1993

Starr-Edwards Silastic Ball Heart Valve Prosthetic, Model 1260 and 6120

Cage ball November 27, 1991

Bileaflet-Center Opening Cardiac Valve Bileaflet December 17, 1982

15

In general, the complications associated with mechanical or tissue valves are different

in nature. The main issue with mechanical valves is thrombogenic complications. This risk is

persistent across all type of mechanical valves, however the intensity of anticoagulant treatment

varies depending on the type of MHV (Iung and Vahanian, 2002). Currently, the available

MHVs have been improved with respect to material biocompatibility and hemodynamic

performance with a lower thromboembolic risk (Iung and Vahanian, 2002) but the risk is still a

persistent issue. Patients with an MHV are required to take lifelong anticoagulant medication

which elevates the risk of haemorrhagic complication. Even the newer generation of MHVs,

including the third generation of bileaflet valves still have turbulence fluctuation and areas of

high shear stress which induce platelet activation, aggregation, and deposition (Yin et al., 2004,

Bluestein et al., 2004). The cumulative effect of repeated passage through the valve also results

in driving platelets beyond their activation threshold (Alemu and Bluestein, 2007).

Furthermore, flow abnormalities and blood disruption may also produce more blood cell

damage. However, despite this disadvantage, MHVs have high structural reliability. In contrast,

tissue valves derived from valvular or nonvalvular tissue from animals or humans present a

lower risk of thrombosis without antithrombotic agents and a lower risk of anticoagulant

bleeding complications (GL and Rahimtoola, 1990). However, tissue valves have less structural

reliability compared to MHVs. Tissue valves have a shorter lifetime due to progressive tissue

deterioration and most patient require another operation. However, a 20-year post operation

follow up on 2,533 patients aged 18 years or older who had received tissue and mechanical

valves was condcuted by (Khan et al., 2001) which showed that there were no overall

difference in survival rates for both type of valves, which also indicates that both type of valves

still need significant improvement.

In conclusion, patients who have received an MHV have an elevated risk of

haemorrhage, and the main concern for patients who have received a tissue valve is the risk of

needing another operation, which increases progressively with time. These risks and limitations

of current PHVs has led to current extensive research to find an alternative PHV. The current

studies mainly focus on developing two alternative prostheses, namely the tissue-engineered

PHV and the polymeric PHV. The following section is a brief literature review of the current

progress on developing these alternative PHVs.

16

2.3 Alternative approaches

2.3.1 Tissue engineering of aortic PHV

The previously mentioned disadvantages of currently available PHVs have caused

researchers to investigate a new approach for treating valvular heart diseases. The tissue-

engineered heart valve (TEHV) can potentially offer the ultimate solution for treating the

diseased heart valve. The hypothesis of this approach is to either 1) regenerate the heart valve

tissue by seeding the autologous cells on a biodegradable polymeric scaffold to form the valve

tissue; or 2) to form the tissue by seeding the cells on a decellularized valve derived from an

animal or human source. Ideally, the TEHV is biocompatible with no thromboembolic risk and

also has the ability to grow and repair itself and respond to hemodynamic forces similar to

native heart valves.

Numerous studies have been carried out on TEHVs, in respect to investigating different

materials and techniques to form the tissue valves. Nevertheless, none of them has developed a

fully functional heart valve as yet. One of the main factors that has a significant influence on

the success of TEHV approach is the type of scaffold (Sodian et al., 2000).

a) Biological scaffolds, including scaffolds made from fibrin, chitosan, chitin, and

collagen as well as scaffold obtained from the decellularization of the xenograft,

allograft or homograft heart valves scaffold;

b) Polymeric scaffolds.

Hence, the literature review of the TEHV approaches for polymeric scaffolds and

biological scaffolds is presented in sections 2.3.1.1 and 2.3.1.2, respectively.

2.3.1.1 Overview of Polymeric Scaffolds

Biodegradable polymers have been used to construct the scaffolds in tissue engineering

since the late 1970s for growing skin tissue. In general, the concept is to harvest autologous

cells then seed the cells on a biodegradable porous scaffold in vitro or in vivo or a combination

of both to generate the tissue as the scaffold degenerates (Hoerstrup et al., 2000). The first

attempt at TEHV dates back to 1995 when Shinoka et al. (1995) investigated the feasibility of

tissue engineering a heart valve in vivo by seeding the endothelial cells and fibroblast on

polyglycolic acid (PGA) scaffolds. Later Hoerstrup et al. (2000) used polyhydroxyalkanoates

17

(PHAs) for the scaffold which improved the process in terms of the handling of material due to

the thermal properties of PHA. Nevertheless, the PHA scaffold was found to prolong

biodegradation which caused synthetic scaffold to persist in vivo step. The same group

investigated the feasibility of fabricating the scaffold by three different materials PGA, poly-4-

hydroxylbutyrate (P4HB) and polyhydroxyalkanoate (PHA). However, they concluded that it

was impossible to construct a functional valve from PGA but scaffolds made from PHA and

P4HB opened and closed synchronously in the bioreactor.

Composite materials have been also studied to improve the scaffold properties.

Hoerstrup et al. (2000) investigated the composition of P4HB and PGA. It is noted that the

scaffold degraded within 6 to 8 weeks. However, the progression of regurgitation and stenosis

under low pressure was also observed. PGA composited with a copolymer of PLA was also

studied by Zund et al. (1997), which showed insufficient mechanical strength. Non-woven PGA

and PLLA (50% of each) is another type of composite material which has been studied for

TEHV.

Sutherland et al. (2005) investigated the effect of static and dynamic cells culturing

onto effective stiffness (E) of the scaffold made from PGA/PLLA). The cells were seeded on

the composite scaffold for three weeks in vitro either in a static condition (static group) or a

dynamic condition (flex group). The results showed that the flex group (E) improved by 429%,

and cellular infiltration and collagen expression increased along with a decrease in cellular

necrosis. The study on cultivation methods (static or dynamic) on a polyurethane (PU) scaffold

by Aleksieva et al. (2012) also showed that dynamic cell culturing in the bioreactor improved

cell distribution, behaviour and resulted in a higher expression of the extracellular matrix.

Sutherland et al. (2005) seeded the (PGA/PLLA) scaffold with ovine bone marrow cells in vitro

and then implanted this into the pulmonary position of sheep on the cardiopulmonary bypass.

The echocardiography after four months showed mild regurgitation and a histology study

showed that fibrosa, spongiosa and ventricular layers formed similarly to a native heart valve.

Non-woven PGA coated with P4HB polymer has also been used as the scaffold for

TEHV in a number of studies. Perry et al. (2003) seeded bone marrow cells onto the scaffold.

Analyses revealed that the cusps were coated uniformly by the cells, and the stiffness of the

leaflets was similar to native ones. Furthermore, the cell distribution through the full thickness

of the cusps was acceptable, but the scaffold did not degrade completely; even at week three,

residual polymer fibres were traceable. Kadner et al. (2002) seeded the scaffold with human

umbilical cord cells (UCC) for 21 days. They evaluated the constructed valve by uniaxial stress

18

testing, and found that uniaxial stress response of the leaflets was similar to a native pulmonary

valve, but it was less pliable and distensible. Hoerstrup et al. (2002) cultured the scaffold with

human marrow stromal cells for seven days in vitro. The valve was tested in a bioreactor, and

synchronous opening and closing was observed. They also mentioned that the histology of the

TEHV showed viable extracellular matrix (ECM) formation. Furthermore, the mechanical

properties of the fabricated TEHV leaflets were comparable to the native tissue. Dvorin et al.

(2003) seeded the scaffold with valvular endothelial cells (VECs) and circulated endothelial

progenitor cells for eight days in static culture in vitro. They claimed that cell proliferation

increased, but a degradation performance of the scaffold was not reported. Balguid et al. (2007)

examined the relationship between collagen content, collagen cross-link and biomechanical

behaviour in the main loading direction (circumferential) for PGA coated with thin layer of

P4HB. The scaffold was seeded with human venous myofibroblasts. The tissue engineered

valves divided into two batches, static group (without external load), and Dynamic group (with

external loads). The finding showed dynamic loads improve collagen cross-link concentration

and the mechanical behaviour.

Poly(vinyl alcohol) (PVA) with grafted PLA side chains was studied by Nuttelman et al.

(2002). The results showed that this material had great potential for tissue engineering due to

superior cell attachment to the scaffolds and the ability to control the degradation rate.

The electrospinning technique has also been used to construct the scaffold due to its

capability of produce fibres in nanometre scale (Kim et al., 2004, Shin et al., 2004) or

micrometer scale (Mitchell and Sanders, 2006). Furthermore, the electrospinning technique can

be used in conjunction with other rapid prototyping methods. For instance, Chen et al. (2009)

combined electrospinning and fuse deposition modelling (FDM) techniques to construct the

scaffold and the aligned nanofibrous leaflets that were made from the electrospinning machine

were mounted on the stent made by the FDM machine. The structural and functional effects of

electrospun-based PLLA, PLA75GA25+PEG-PLA and PLA10GA90+PLLA scaffolds on the

growth and attachment of cardiac myocytes cells (CMs) to form heart tissues were examined by

Zong et al. (2005). The porosity ranges of the scaffolds achieved was 71% for PLLA to 78%

for PLA75GA25+PEG-PLA. In this study, the hydrophilic surface of PLGA and PEG-PLA had

an adverse effect on cell proliferation, producing clumps which compromised the cells. The

most hydrophobic scaffold was the PLLA scaffold which had the best support for CM

attachment and structural development. It was also confirmed that the faster degradation rate of

the scaffold negatively affected the density of cardiomyocytes cells by losing spatial

19

organization and cluster together. It was concluded that the main disadvantages of using this

technique are poor cell penetration and attachment.

The limited number of conventional techniques in the field of tissue engineering led to

the emergence a new set of manufacturing techniques known as advanced manufacturing

techniques or rapid prototyping (RP) techniques, such as fused deposition modelling (FDM),

stereolithography, and 3D printing. Implementing RP techniques in tissue engineering can

potentially provide a 3D scaffold with a fully interconnected pore network with the ability to

regulate the porosity across the scaffold. Furthermore, scaffolds with a complex geometry such

as heart valves can be fabricated with high precision from the data collected from patients’ MRI

or CT scans. RP techniques can also be combined with other techniques such as molding to

form and manufacture the scaffold. Schaefermeier et al. (2009) molded the scaffold by

enhancing the rapid prototyping tools. The CT scan was obtained from an aortic homograft and

the image was processed to a 3D image of the aortic valve. An established 3D image was

converted to a stereolithographic (STL) model and fed into the FDM3000 stereolithography

machine. The machine fabricated the STL valve model and the negative cast of the ventricular

side of the prototype. This cast was then used to form the P4HB scaffold by pressing the

polymer into the cast and using the thermal processing technique. The scaffold was tested in a

pulsatile flow bioreactor and synchronous opening and closure was observed under normal,

supranormal flow and pressure conditions (maximum pressure gradient of 10 mmHg).

However, mild stenosis and regurgitation were noticed.

2.3.1.2 Overview of Biological Scaffold (Decellularization Approach)

Biological scaffolds used in tissue engineering from natural materials including fibrin,

collagen and chitin showed poor mechanical properties as well as a high degree of shrinkage

(Ye et al., 2000, Jockenhoevel et al., 2001, Yang et al., 2001). In addition, natural materials

vary from batch to batch, and they are not suitable for large fabrication (Yang et al., 2001). The

bulk of the research on TEHV using a biological scaffold has focused on the scaffolds obtained

from the decellularization process.

In this approach (decellularization) donor or animal-derived valves (allogenic or

xenogenic) are depleted of cellular antigens, which make them less immunogenic. The resulting

extracellular matrix (ECM) proteins were then used as a native template or scaffold to guide the

cells growth and generate the tissue.

20

Generally, the acellularization of the valve involves the use of trypsin/

ethylenediaminetetraacetic acid (EDTA), followed by sodium dodecyl sulphate (SDS) washing.

The success of the decellularization approach mainly depends on two factors: the preservation

of the ECM organization of native valves to provide sufficient support during the tissue

generation phase, and complete removal of all cytoplasmic elements from the native valve. The

tradeoff of this process is that treatments of the valve to remove the cells also cause damage to

the ECM of the valve. The main challenge is to find the optimum treatment process to remove

the cellular debris while the ECM architecture was preserved effectively. Numerous studies

have been carried out to evaluate the effect of different treatment techniques on the valve as

well as investigating the possibility of regenerating a tissue for the heart valve. A selected

number of these approaches are presented below:

Steinhoff et al. (2000) used decellularized ovine (sheep) valves for in vivo tissue

regeneration. The ECMs were obtained by immersing the valves into a solution of trypsin, and

EDTA in controlled ambient parameters under constant shaking. The histology analysis of the

acellularization procedure revealed a patchy incomplete seeding of endothelial and

myofibroblast cells on the surface of the valves, but after the implantation of the valves, the

confluent layer of the endothelial cells formed on all valves after 12 weeks. Microscopic valve

morphology observation of valves showed a different degree of subvalvular calcification on all

valves. However, the extracellular matrix of the decellularized valve was preserved, which was

the main advantage of this approach. Trypsin/EDTA treatment was also used by Schenke-

Layland et al. (2004) in their study to compare the properties of ECM obtained from a

generated tissue valve and a porcine valve. The results showed the structural similarity between

the native valve and the tissue-engineered valve. However, the valvular cell phenotype was not

replicated completely.

Furthermore, Zeltinger et al. (2001) developed a TEHV by seeding cells onto a

decellularized porcine heart valve. The native valve was treated with Tris-Buffer and

phenylmethylsulfonyl fluoride (PMSF) to break the native cells, followed by repeated treatment

of the valve with DNase, RNase, Phospholipases, and Trypsin protease. Two types of samples

(whole valve and leaflet) were seeded, and cultured in a pneumatic bioreactor (PB) for up to 8

weeks. The results revealed that the cells attached to the surface of decellularized porcine

matrix from day one through to week 8 and the recellularization density reached 45% of the

native porcine leaflets after eight weeks. However, disruption of cells on the valve surface was

21

observed in the corrugation regions. Furthermore, cells did not attach to the cusp surface in the

commissures region.

Dohmen et al. (2003) used a decellularized porcine scaffold to examine morphological

and histological alterations in a tissue-engineered heart valve. The autologous vascular

endothelial cells (AVEC) were seeded onto decellularized porcine pulmonary valves. They

used 0.1% deoxycholic acid in the decellularization process. The tissue-engineered valves were

implanted in sheep for a period of up to six months. The results showed no cusp calcification

for explanted tissue-engineered valves, however, endothelial cells were only partially

developed without any cells at the free edge.

It is known that scaffolds made from the decellularization of xenograft are still

immunogenically active and potentially can transmit disease from donor to host (Nakamura,

2003, Lynn et al., 2004). Also, the porcine endogenous retrovirus (ERV) is capable of infecting

human cell lines in vitro. Leyh et al. (2003) investigated the risk of cross-species transmission

of the porcine ERV. In this study, the porcine aortic valve was decellularized by trypsin/EDTA

detergent then seeded with ovine myofibroblasts and coated with endothelial cells. An analyses

of the harvested valves after being implanted in sheep for 6 months showed that even after the

decellularization of heart valve, 2% of native DNA was still detectable, but after 6 months of

implantation no sign of porcine ERV was detected, which indicates that chemical treatment

with trypsin/EDTA was sufficient to prevent the transmission of porcine ERV. This finding

supports the hypothesis that acellularized porcine heart valves do not transmit porcine retrovirus

to recipients.

Later Lichtenberg et al. (2006) decellularized an ovine pulmonary valve using sodium

deoxycholate (NaDC) and sodium dodecyl sulphate (SDS) and seeded it with endothelial cells

(ECs). In this study, three pulmonary valve models were examined for morphology and

viability of cells. The findings indicated that a monolayer of ECs covered the luminal surface of

the conduit of the valve and both sides of the valve cusps. Moreover, the tissue matrix showed

comparable values of collagen, elastic fibre, and glycosaminoglycan (GAG) to the native valve.

Furthermore, Scanning Electron Microscope (SEM) observations indicated that ECM preserved

a 3D structure network and completely maintained the basement membrane in the inner surface

of the pulmonary wall as well as both sides of the valve leaflets. Also, sufficient cell attachment

and stability were observed. The author emphasised the importance of maintaining and

monitoring the correct cell culture parameters such as temperature, nutrition, O2, CO2 and PH to

ensure the generation of a stable cell matrix and cell connectivity.

22

Moreover, Tudorache et al. (2007) examined the effect of three different

decellularization protocols on the structural integrity and surface morphology of the porcine

pulmonary valve. The cells were removed from the porcine valve by SD, SDS, and

trypsin/EDTA techniques. The findings indicate that both detergent-treated valves appeared to

preserve ECM, and all cells completely detached. Enzymatically treated valves, on the other

hand, had ECM disruption. Later Liao et al. (2008) also investigated the effect of

decellularization on the mechanical properties of a porcine heart valve. In this study, different

types of detergents and enzymatic treatments, namely SDS RNase and DNase, trypsin/EDTA

with RNase, as well as Triton x-100 with DNase was used to decellularize porcine aortic types

of valves. These findings were in line with those reported in Tudorache et al. (2007) study,

concluding that the valves treated by SDS resembled native valves, whereas treatment by Triton

X-100 showed disruption and little damage to ECM.

Composite materials have also been investigated to improve the structural integrity of

the decellularized valve and reduce antibody reactions. Stamm et al. (2004) deep-coated

decellularized porcine valves with poly(4-hydroxybutyrate) (P4HB), Poly(3-hydroxybutrate)

(P3HB), and poly(3-hydoxybutrate-co-4-hydoxybutrate) polymers. The decellularized heart

valves were implanted in a lamb model in pulmonary and aortic positions. The results of the

study showed that residual antigenicity related to the xenograft valve can be overcome by pre-

treatment (coating) with a biodegradable polymer. Furthermore, evaluations of the constructed

valved showed excellent biologic and biomechanical characteristics of matrix/polymer hybrid

valve, which can be described as a promising development for valve replacement.

Hong et al. (2009) coated the decellularized porcine aortic heart valve scaffold with

basic fibroblast growth factor (bFGF)/chitosan/poly-4-hydroxybutyrate(P4HB). Subsequently,

the hybrid valve was seeded with mesenchymal stem cells (MSCs). The hybrid valve showed

good cell attachment, growth, and adequate mechanical strength.

More recently, Deng et al. (2011) compared the mechanical properties of

decellularized valves with modified valves with PEG and TGF-β1. In this study, the

decellularized scaffolds were named “simple scaffolds” and were obtained by treating porcine

aortic leaflets with trypsin/EDTA, followed by Triton X-100, RNase, and DNase. The leaflets

that were combined with poly (ethylene glycol) (PEG) nanoparticle via a coupling reagent,

carbodiimide, were named ” Modified Scaffolds”, and the ones that were loaded with TGF-β1

were named “Delivery Scaffolds”. In general, the results showed that the ECM preserved better

on “Delivery Scaffolds”, with clear evidence of the confluence layers of cells forming on the

23

surface of the scaffolds. Importantly, the biocompatibility and biomechanical properties of

Delivery and Modified Scaffolds were significantly improved which is beneficial for heart valve

tissue-engineering.

2.3.2 Polymeric Heart Valves

Polymeric valves (PVs) have been researched since the 1950s (Roe and Moore, 1958,

Ten Berge, 1958, Akutsu et al., 1959, Braunwald et al., 1960), which led to the first PVs being

implanted in human mitral (Braunwald et al., 1960) and aortic (Roe et al., 1966) positions in the

1960s. However, the clinical outcomes of these initial trials were not successful as the available

polymers at the time did not provide sufficient biostability and durability. Currently, there are

no clinically approved PVs except those used in artificial hearts for the short term. However,

advances in material sciences and the development of super biostable polymers may meet the

clinical requirements of PVs. The choice of material is a crucial factor in the fabrication of

polymeric heart valves. The chosen polymer should be biocompatible, biostable, anti-

thrombogenic, and provide sufficient mechanical integrity to withstand the loads. Hence,

several new or improved polymers are being investigated such as polysiloxanes,

polytetrafluoroethylene, polyurethane (PUI), poly (styrene-b-isobutylene-b-styrene), and

polyurethane with poly (dimethylsiloxane) soft segment (Elast-Eon). In general, the

manufacturing method strongly depends on the polymer type; hence, the literature review is

categorised based on the scaffold material as described as follows.

2.3.2.1 Polysiloxane (Silicone) valves

Polymerized siloxanes or polysiloxanes, which are known more commonly as silicones

are polymers from mixing inorganic and organic polymers. The chemical formula is [R2SiO] n,

where R can contain a variety of pendant organic groups such as methyl, phenyl, and ethyl i.e.

R is CH3 in polydimethylsiloxane (PDMS). The inorganic side of the polymer consists of a

silicon and oxygen backbone (…..Si-O-Si-O-…). Silicones can be synthesized with a broad

range of properties by varying side groups and the -Si-O- chain length.

Silicone polymers can also be transformed into silicone elastomers with a three-

dimensional network by mainly crosslinking with radicals, crosslinking by condensation, and

crosslinking by additional reactions. Silicon elastomer materials have been used in a wide range

of medical devices due to their characteristics regarding biostability, durability, and flexibility.

In the 1950s and 1960s, silicone gained attention as a material to construct a polymeric heart

24

valve due to its great flexibility and biocompatibility properties. One of the first flexible tri-

leaflet valves from silicone polymers (Silastic 50 from Ellay Rubber Company) was developed

by Roe and Moore (1958) in the late 1950s. The constructed valve with 380 µm leaflet

thickness was evaluated in an acute ascending aorta of a dog, which demonstrated satisfactory

results. However, a long-term evaluation in a subsequent sub-coronary model (Roe et al., 1960)

showed survival could be achieved. Later, Roe et al. (1966) carried out clinical trials with 18

selected patients between 1960 and 1962 (Roe, 1969). The constructed valve contained a

slightly thicker leaflet range between 430 and 500 µm from the different types of silicone

(General Electric SE-555). The clinical trials were interrupted due to the high mortality rate.

However, the author claimed that the mortality rate was related to surgical complications and

was not due to the malfunctioning of the implanted prosthetic heart valve.

Mori et al. (1973) later investigated various leaflet thicknesses from 225 to 510 µm

from different silicone formulations. This study showed that the mechanical properties of the

valve depended on the design of the valve. Furthermore, poor durability was observed for

dome-shaped valves, whereas valves with a triangular leaflet were demonstrated to function for

between 17.7 to 23.8 years. However, raw material inconsistency affected the outcome as

valves made from a different batch of the same material showed different results. The Oxford

valves constructed by Gerring et al. (1974) from DC silastic 5505 silicone coated with terylene

fabric with 120 µm thickness were evaluated in vivo. The valves were implanted in the

pulmonary position in calves and the survival animal up to 30 months showed 2 out of 7 calves

had died from thromboembolic issue.

These aforementioned clinical investigations and trials show that silicone valves

increase the risk of thrombosis in some cases, and also valve thickening was observed. As a

result of these issue, along with the reported incident of structural failure caused silicone valves

to be abandoned as a potential replacement material for polymeric prosthetic heart valves.

2.3.2.3 Polytetrafluoroethylene (PTFE) valves

Polytetrafluoroethylene (PTFE), which is well known by its brand name Teflon, is a

synthetic fluorinated polymer of tetrafluoroethylene. PTFE is a fluorocarbon with the chemical

formula of [C2F4]n. It is well known for its hydrophobic characteristic, very small coefficients

of friction, and chemical inertness.

The first clinical trials using flexible tricuspid PTFE replacement for aortic heart

valves were carried out by Braunwald and Morrow (1965) with 23 patients between 1962 and

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1963. Three designs were used, single Bahnson leaflets of Jersey-Knit PTFE, and the

combination of plain PTFE fabric valves and PTFE fabric valve with PTFE dispersion.

Prosthetic PTFE valves were removed and subsequently examined. The outcome showed that

the valves stiffened with mild calcification; it was also noted that the removed valves had holes

on the leaflets, tears on the leaflets and disruption to the valve integrity.

In another in vivo study by Nistal et al. (1990), twelve prosthetic PTFE tricuspid valves (eight

23 mm in size, and four 25 mm in size) were implanted in the aortic position in sheep aged

between 3 and 4 months. Ten out of twelve animals survived this experiment, and the survivors

were slaughtered stepwise to observe the mineralization profile of the valves. The results

showed no evidence of pulmonary thromboembolism in all twelve animals with one episode of

acute thrombosis. In six animals, one or more cusps were stiffened, and in all animals, the

leaflets became thinner and unretracted. Microscopic studies detected evidence of calcification

in seven animals, mostly in commissural areas. Radiologic studies also confirmed the calcium

deposition on the valves but showed one valve only suffered from severe calcification and

diffused mineralization. The analyses of the valves made of compact PTFE with light

microscopy revealed the lack of cell infiltration within the cuspal material. However, the valves

made of expanded PTFE did show infiltration by the host cells and calcium, where the fibrin

and fibroelastic host tissue accumulated in the inflow of the commissural region. It is

concluded that the PTFE valve had a moderate calcification rate which mostly appeared in the

commissural region. Furthermore, Ando and Takahashi (2009) investigated the use of

handmade PTFE trileaflet conduits (shown in Figure 2.1) implanted in the pulmonary position

for 139 patients, of which 21 conduits were implanted using the Ross procedure, and 108

conduits were used to repair complex congenital heart disease. It was reported that three

patients died in hospital, and one died later, four patients were needed to have the conduit

removed due to pulmonary artery distortion at a distal anastomotic site. In this study, the PTFE

conduit valves function were investigated by a series of echocardiographic studies, and the

authors claimed that PTFE conduit valves were a valid and reliable replacement option to

homograft and xenograft valves for pulmonary reconstruction purposes.

Although the good hemodynamic properties of PTFE or Teflon attracted researchers,

evidence of low resistance to thromboembolism, leaflet stiffening, and calcification issues in

clinical trials restricted the further development and study of PTFE valves.

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Figure 2.1. Instructions on fixing the valve inside the conduit. A) The constructed valve is pushed inside the conduit; B) The valve is sutured onto the Dacron conduit at the top and bottom ends; C) Commissural sutures are placed at a 1-mm distance from the commissure (arrow in C), D) The outer layer of the polytetrafluoroethylene valve is sutured to the conduit at the midpoint of the sinus (Ando and Takahashi, 2009).

2.3.2.4 Polyurethane (PU) valves

Polyurethane (PU) is a polymer which can be manufactured in a wide range of

properties depending on the chemistries involved in the polymer chain. PU is composed of

carbamate (Urethane) links attached to a chain of an organic unit. Polyurethane products mostly

have a complicated formula which may contain several different types of bonds. It is produced

from a reaction between isocyanate (R-(N=C=O) n ≥ 2) with a polyol (an alcohol functionalized

with low molecular weight polymer) (R'-(OH) n ≥ 2) containing two or more hydroxyl group per

molecule in the presence of a catalyst. Properties of PU polymers can be controlled by adjusting

the composition of each component. The polyol component contributes to the flexibility

property of the polymer and results in an elastic polymer, and a large amount of crosslink

contributes to the rigidity property of the polymer.

27

The first use of a polyurethane-based polymeric heart valve was reported in the late

1950s (Akutsu et al., 1959). These polyether urethane (PEU) valves of 130 to 180 µm thickness

in mitral were implanted in the aortic position in dogs. A high mortality rate was reported and

there were also signs of emboli and stenosis due to fibrin deposition on the valves.

Hilbert et al. (1987) constructed eight prototypes of trileaflet valves from polyurethane

material and implanted them in juvenile sheep for 17 to 21 weeks in the mitral position. The

morphologic study revealed calcium deposition on the PU leaflet surface with two distinct types

of calcifications: one was associated with degenerated cells within fibrous sheath, and the other

was associated with the interface between the fibrous sheath and the leaflet. Both stenosis and

regurgitate issues were reported in the hemodynamic study. These findings were in line with the

previous research carried out by Wisman et al. (1982) in bovines in the aortic and mitral

positions.

Jansen and Reul (1992) investigated a new design of prosthetic trileaflet heart valve

with the aim of reducing the mechanical stress imposed on the leaflets and calcification

tendencies while increasing durability. The new design (the J-3) of the PU-based (an aliphatic

PCU; ENKA 1025/1; ENKA/AKZO) prosthetic valve was manufactured in a medium open,

and almost flat-shaped position with the expanded stent using a cone-shaped mold. The

hydrodynamic evaluation showed minimum pressure drop and very small energy losses with

stable closure and opening of the leaflet. Laser Doppler anemometry also showed very low

shear stresses in the downstream flow field of the valve. In the durability test, the prototypes’

lifespan reached 400~648 million cycles, which is equivalent to 7~11 years in accelerated tests.

However, in vivo biocompatibility and durability tests showed calcium deposits on the cusps

which seemed to be associated with surface roughness.

The low elastic modulus polyurethane (Eurothane 2003) material was used by Leat

and Fisher (1994) to investigate hydrodynamic performance and the leaflets’ opening

characteristics of a newly proposed design (alpharabola design) and compare it to a valve with

spherical leaflet geometry. The valve frames were made of PEEK material and were dip-coated

with polyurethane. The leaflets were fabricated from solvent cast flat films with a constant

thickness of between 150 to 210 µm, then bonded to the outside of the frames. Both valves

underwent steady and pulsatile flow tests in vitro condition. The finite element analyses

revealed that principal tensile stress reduced by 60% in alpharabola design compared to

spherical leaflet valve. A short-term durability test of 100 million cycles was undertaken and

the alpharabola valves showed an improvement to the opening characteristics compared to the

28

spherical leaflet and noted that leaflet thickness contributed to increasing the opening pressure.

In addition, this design (alpharabola) was used to investigate the influence of two

manufacturing techniques, thermoforming and dip casting on the hydrodynamic function of

synthetic valves made of IT C34 polyurethane material. While both valves had similar

hydrodynamic performance, the dip cast valves had superior structural durability over thermally

formed fabricated leaflet valves.

Bernacca et al. (1995) investigated calcification and fatigue failure in PU prosthetic

heart valves. The prosthetic valves were constructed from a PU with a 4,4'-diphenylmethane

diisocyanate in the hard segment, and chain-extended with butanediol and a polyether in the

soft segment. The results showed that the rate of calcification of the PU prosthetic valves was

significantly slower in the in vitro test compared to similar currently available bioprosthetic

heart valves. It is also noted that calcium deposits were only accumulated at the region of

material failure. However, Fourier transform infrared (FTIR) spectroscopy analyses revealed

that the calcification process was in direct relationship with the polyether soft segment of the

polymer.

A new polymeric prosthetic tri-leaflet valve design was developed by Mackay et al.

(1996) made entirely from polyurethane. Six valves comprising three leaflets with an

approximately 100-micron thickness were constructed from PU material which was fused with

their stents in a single dip-coating process. The closed leaflet geometry was hyperbolic in the

circumferential direction and elliptical in the radial direction. The hydrodynamic analysis

revealed that the valves had similar pressure gradients to (St Jude Bioimplant) prosthetic valves

with a lower level of regurgitation. The in vitro durability test for all valves also showed that

the valves could function up to 10 years without any failure.

Leaflet thickness and material type both have significant effects on the hydrodynamic

functions of a prosthetic heart valve, hence, the same group, Bernacca et al. (1997a)

investigated the contribution of leaflet thickness and material to the durability of PU-based

PHVs. In this study, 22 valves made of a polyether urethane (PEU), and 9 valves made of a

polyether urethane urea (PEUE) in varying thicknesses (60 to 200 microns) were examined in

the accelerated fatigue test. It was reported that the leaflet thickness made no significant

contribution to the durability of the PEU valve which was less than 400 million cycles.

However, PEUE leaflet thickness had a direct relationship with the durability of the valves, and

the best performance was obtained with a leaflet thickness of 150 microns with a durability of

29

more than 800 million cycles. The hydrodynamic functions of both valves were studied

(Bernacca et al., 1996) which showed similar performance to the porcine aortic valve.

The study carried out by Bernacca et al. (1997a) on the calcification progress of PHVs

made from PEUE and PEU polymers showed localized calcium deposits for both valves.

Young’s modulus and leaflet thickness were also regarded as having an influence on the

hydrodynamic function of PHVs. Low modulus polymers are more beneficial to achieve the

desired hydrodynamic function; however, they have high strain accumulation issues and lower

durability compared to higher modulus polymers. On the other hand, higher modulus polymers

suffer from a poor hydrodynamic function. Hence, Bernacca et al. (2002) investigated the

hydrodynamic function of PU PHVs with different Young’s modulus (ranging from 5 to 63.6

MPa), and leaflet thickness of 48 to 238 microns. All valves examined in the cardiac system

with an output range of 3.6, 4.9, 6.4, 8.00, and 9.61 lit/min, and three parameters including the

mean pressure gradient, energy losses and regurgitation were measured. This study showed that

leaflet thickness significantly correlated with two parameters (mean pressure gradient and

energy loss) in all cardiac output, whereas modulus was not significantly correlated with any of

the three parameters and only at 9.61 lit/min flow was the modulus affected by the mean

pressure gradient. It was also suggested that an elastomer with up to Young’s modulus of

32.5 MPa may have a desirable hydrodynamic function with an acceptable lifetime. The

hydrodynamic function of PU valves was compared to the well-established mechanical and

bioprosthetic valves and demonstrated superior performance (Wheatley et al., 2000). In this

experiment, fourteen PU valves with a polyetheretherketone (PEEK) stent, twelve Carpentier-

Edwards supra-annular porcine aortic valves, and thirteen ATS bileaflets mechanical valves

were implanted in growing sheep to assess the in vivo hydrodynamic function. After six-

months, the PU valves showed a low level of platelet aggregation, a small level of fibrin

attachment to leaflet surface, no evidence of pannus overgrowth and a small change in

haemodynamic performance without any proof of thromboembolism. The PU valves

demonstrated a lower level of platelet aggregation compared to the mechanical valves, and

lower pannus overgrowth compared to the bioprosthetic valves. These findings were in line

with results retrieved by light and electron microscopy of implanted PU valves in growing

sheep in the mitral position, which showed improved blood compatibility and unimpaired valve

function.

Later, Adiam Life Sciences, Erkelnz in Germany developed a prosthetic heart valve

for both aortic and mitral positions entirely from polycarbonate-urethane (PCU). Deabritz et al.

30

carried out studies (Daebritz et al., 2004a, Daebritz et al., 2004b, Daebritz et al., 2003) to

evaluate the long-term hydrodynamic function of both valves using in vitro testing and in vivo

testing with a comparison of two well-established bioprosthetic mitral and aortic valves. A

specially designed bileaflets (PCU) valve for the mitral position (shown in Figure 2.2) was

used, and the in vitro durability test showed that the valve had a lifespan of more than 15 years.

Seven fabricated PCU valves and seven commercially available bioprostheses (n=4 Perimount,

n=3 Mosaic) valves were implanted in the mitral position into growing calves (Daebritz et al.,

2003). 2D echocardiography results obtained after implantation and before sacrification showed

mild leaflet thickening with trivial regurgitation. Mild calcification with no structural

degeneration was observed for PCU valves, whereas all perimount bioprostheses valves were

significantly calcified and degenerated, one mosaic bioprosthetic valve had a thrombosis issue,

and two valves showed moderate and severe degeneration. In comparison with the PCU mitral

valve, and the commercial bioprosthetic (Perimount and Mosaic) valves, the proposed PCU

prosthesis valve designed specifically for the mitral position showed superior hemodynamic

performance with 15 years’ proven durability in the in vitro testing condition with less

calcification issues and structural changes compared to the bioprosthetic valves.

Figure 2.2. The ADIAM polyurethane (PU) valve for the mitral position (Daebritz et al., 2003).

31

Figure 2.3. The ADIAM polyurethane valve for the aortic position (Daebritz et al., 2004b).

In another study by the same group (Daebritz et al., 2004b), the specially designed

trileaflet PCU valves (n=7) (shown in Figure 2.3) were implanted in growing calves for in vivo

testing and were compared to commercial bioprosthetic valves. The five calves with the

implanted PCU valves experienced a good clinical course while two animals died at 27 and 77

days after the implantation due to an overgrowth of pannus without degeneration of the valves.

The PCU valves had a variable level of calcification with mild degeneration and no increase in

thrombogenicity compared to the bioprosthetic valves. However, both the animals with the

commercial bioprosthetic valves had to be sacrificed due to structural degeneration of the

valves causing congestive heart failure after 10 and 30 days of implantation.

High silicon content polyurethane copolymer (Elast-EonTM) trileafelts valves provided

by AorTech Europe were studied by Leo et al. (2005a), Leo et al. (2006). Three different

designs (open, semi-open, closed commissural as shown in Figure 2.4) of polymeric prototype

valves underwent in vitro studies to characterize the high blood velocity, and Reynolds shear

stress (RSS) inside and downstream of the valves. They reported that the design parameters,

including leaflet thickness and commissural design had a significant effect on the flow structure

downstream of the valves. The valves with a thinner leaflet showed better performance in

minimizing the back flow issue. It was also noted that none of the proposed design for the

32

commissural were able to provide sufficient washout inside the valve in systolic phase. In

addition, high shear stress along the edge of the central orifice during systole, and split flow

inside the valve were observed which possibly contributed to blood clot formation.

Figure 2.4. A) Polyurethane copolymer (Elast-EonTM) trileaflet prototype valves with a closed commissural design, B) polyurethane copolymer (Elast-EonTM) trileaflet prototype valves with an open commissural design (Leo et al., 2005a).

The calcification property and the mechanical integrity of a new nanocomposite

polyurethane material, namely polyhedral oligomeric silsesquioxane poly (carbonate-urea)

urethane (POSS-PCU) was investigated in an in vitro accelerated test to assess its potential use

in polymeric heart valves (Ghanbari et al., 2010). POSS-PCU valves (see Figure 2.5)

demonstrated significant resistance to calcification compared to bovine pericardium (BP), and

polyurethane (PU) valves with no sign of deterioration, unlike the PU valves. Furthermore, the

POSS-PCU valve surface remained intact during the test with significantly less platelet

adhesion compared to the PU valves. A prototype of the heart valve from the POSS-PCU

material was also made with a semi-stented surgical aortic valve (SSAV) design with leaflet

thickness of between 150 to 200 micron, and was compared to a commercially available

porcine bioprosthetic valve (EpicTM, St. Jude Medical, MN, USA) as a control model (Rahmani

et al., 2012). The SSAV valves were assessed using a hydro-mechanical cardiovascular pulse

duplicator system in vitro. The analyses revealed that SSAVs had a significantly lower

transvalvular pressure drop, energy loss, and regurgitation compared to the control valve while

the associated effective orifice area (EOA) was significantly higher over the control valve.

33

Figure 2.5. A) Schematic representation of the valve design B) The trileaflet prototype made of a POSS-PCU material with a suture ring (Ghanbari et al., 2010).

2.3.2.5 Poly (styrene-b-isobutylene-b-styrene) (SIBS) valves

Thermoplastic elastomers (TPEs) such as triblock Poly (styrene-b-isobutylene-b-

styrene) or SIBS are composed of the glossy outer block and rubbery inner blocks. The triblock

copolymer is based on polyisobutylene (PIB) for the inner block, and polystyrene (PS) for the

outer block. The fully saturated PIB exhibits thermal properties and oxidative stability (Storey

and Baugh Iii, 2000). A superior inertness property, combined with the thermoplastic, biostable,

and rubbery characteristics of SIBS (Pinchuk et al., 2008) make it a suitable choice of material

for medical applications such as PHVs. However, the potential for thrombogenic complication

of the heart valves made of the newly developed SIBS material was addressed by Yin et al.

(2005). In this study, the platelet activity state (PAS) was measured for SIBS trileaflet, St. Jude

Medical bileaflets MHV, and St. Jude tissue valve to investigate the thrombogenic potential of

SIBS valves compared to the current pervasive mechanical and tissue valves. Tested SIBS

valves showed similar platelet activation to the tissue valves (see Figure 2.6), which was lower

than the mechanical valves (see Figure 2.7) after normalizing to their effective orifice area.

PAS measurements of the Innovia SIBS polymeric heart valves were also compared to the

commercially available Carpentier-Edwards Perimount Magna aortic bioprosthetic valve, as

shown in Figure 2.6. The SIBS valve, in this study, demonstrated a significantly lower

thrombogenic potential compared with the commercially available, FDA approved Edwards’s

tissue valves. As there was no need for anticoagulation for the Edward’s tissue valve in the

majority of patients, polymeric heart valves may not require anticoagulation.

34

Figure 2.6. PAS measurements of the St. Jude tissue valve and SIBS trileaflet heart valve (Claiborne et al., 2011).

Figure 2.7. PAS measurements of the St. Jude bileaflet mechanical valve and SIBS trileaflet heart valve (Claiborne et al., 2011).

In 2009, xSIBS which is an improved version of SIBS, was developed by Innovia

(Pinchuk and Zhou, 2009) with the aim of eliminating the dynamic creeping issue associated

with thermoplastic SIBS. Claiborne et al. (2013) fabricated PHV from xSIBS material as shown

35

in Figure 2.8b and optimised the design to reduce the stresses, thrombogenicity, and improve

hemodynamic performance using their device thrombogenicity emulation (DTE) methodology

(Xenos et al., 2010). The results obtained from the hydrodynamic performance and platelet

activation measurement for the optimized design of the valve prototype was compared to the

commercially available Edward’s Perimount Magna bioprosthesis. xSIBS valves exercised

under maximum 120 BPM, and 11.4 l/min in the left heart simulator (LHS), at 4-6 l/min

optimized xSIBS valves and the benchmark tissue valve showed similar transvalvular energy

loss, but at a higher flow rate, xSIBS valves showed more transvalvular energy loss. xSIBS

valves showed less backflow compared to the tissue valve but exhibited smaller effective

orifice area (EOA) which lead to a 15% increase in velocity peak for xSIBS valves. Bulk

Human Platelet Activation studies of xSIBS valves revealed that platelet activation rate (PAR)

of the xSIBS valves was similar to the PAR of the tissue valve, however the PAR trend of the

xSIBS valve was slightly higher.

Figure 2.8. A) The compression mold used to fabricate the optimized valve, and (b) the optimised xSIBS valve (Claiborne et al., 2013).

2.4 Manufacturing techniques of polymeric valves

The selection of a suitable manufacturing technique to form polymeric material into a

heart valve shape depends strongly on the type of polymer and its nature. For example,

compression molding is a common manufacturing technique to shape thermosetting polymers

whereas it is seldom to be used for forming thermoplastic polymers. Hence, different

36

manufacturing techniques are discussed as follows for each type of polymer which have been

used for polymeric heart valve construction.

2.4.1 Polysiloxane (Silicone) valve manufacturing technique

Roe et al. (1966), Roe and Moore (1958) fabricated a precision molded, single unit

tricuspid silicon valve. The valve was cast in one single unit by compressing the heated molds

at 180 °C under high pressure and was then cured for 4 hours at 200 °C. Mori et al. (1973) also

used a similar technique for a tricuspid valve by injecting silicon into a three-piece metal mold

(highly polished). Filling cavities of the mold with silicon using centrifugation and or

evacuation technique was also undertaken by Chetta and Lloyd (1980). However, using multi-

piece molds for injection into the mold of a silicon valve may result in an unexpected thickness

variation (Sacristan et al., 2003) which could lead to the partial opening of the valve and could

have an adverse effect on the hemodynamic performance of the valve. Nevertheless, the study

by Escobedo et al. (2006) on the hemodynamic effects of the partial opening of a trileaflet valve

constructed with a similar injection molding process showed thickness variation of the leaflet

does not significantly affect ventricular assist devices (VAD).

Figure 2.9. A silicon valve, A) The upper picture shows the whole valve, B) Cross-section of one leaflet from the top (Escobedo et al., 2006).

37

2.4.2 Polytetrafluoroethylene (PTFE) valve manufacturing technique

Rheological properties of PTFE are not like usual thermoplastic polymers and

common techniques of melt processing, such as extrusion or injection molding, are impractical.

Hence, a series of processing techniques have been developed to form PTFE polymers into a

tricuspid prosthetic valve, which are unique to the PTFE industry (Rubin, 1990). In 1977,

Imamura and Kaye (1977) constructed a stent-mount PTFE cardiac valve in which the valve

leaflets were fabricated from laminating 4 to 15 layers of 0.003 mm films of expanded PTFE

(ePTFE, or Gore-Tex®) in a multi-direction to achieve the desire tensile strength (equivalent to

20 times of conventional PTFE). Nistal et al. (1990) used a combination of PTFE and ePTFE

sheets to construct the valve. ePTFE sheets were used to cover the valve which comprised

compact PTFE leaflets in a valve frame.

Ando and Takahashi (2009) introduced a simple and innovative manufacturing

technique. They used ePTFE sheets to construct the valve in three simple steps. 0.1 mm PTFE

membrane (Gore-Tex; W.L. Gore & Associates, Inc. Newark, Del) was cut in a rectangular

shape, then folded in half along the long edge, and the folded membrane was stitched to make

three pockets, and was then sewn to form a cylindrical shape. The cylinder then was sewn into a

Dacron conduit (Hemashield; Boston Scientific Corp, Natick, Mass) of 12 to 28 mm diameter

size, as demonstrated in Figure 2.10.

Figure 2.10. Schematic drawing of heart valve construction fixed in a Dacron conduit.

Step 1. PTFE sheet marked with the

positions of the leaflets and folded at

valve height.

Step 2. The cylinder is fixed inside the

conduit by stitching the top (1) and

bottom (2) ends, and then each valve is

stitched together at a point 1 mm from

each commissure (3), (4) the outer layer

of PTFE valve is then stitched to avoid

free floating (Ando and Takahashi, 2009).

38

2.4.3 Polyurethane (PU) valves manufacturing technique

Polyurethane (PU) is one of the most important classes of polymers, and has been used

widely in the medical industry. In general, depending on the nature of the PU polymer, it can be

categorised as either thermoplastic polyurethane (TPU) or thermoset polyurethane. Each has a

different manufacturing technique by which to process PU polymers. TPU can be processed by

any standard manufacturing method for thermoplastic polymers such as injection molding,

compression, and extrusion. Thermoset PU polymers, in general, are categorised into seven

groups, namely PU elastomer, foam (flexible, rigid, and RIM), millable, adhesive, coating,

sealant, and fibres, and each is treated differently. In this section, the manufacturing techniques

for PU polymers used to construct heart valves are described.

Jansen and Reul (1992) constructed the valves by dip coating the metal molds in a

PCU solution and then tumbling the mold in a motion-controlled system for the drying phase to

eliminate the leaflet thickness variation and to ensure an even thickness.

ADIAM Life Science in Germany developed prosthetic heart valves for both aortic

and mitral positions by combining dip and dropping coating techniques. In this approach, PCU

(PCU, ADIAMat®) with two different harnesses were used, where the outer layer had soft

hardness, and the core had medium hardness. Dropping the PCU solution was performed by the

robotic droplet deposition technique to control the leaflet thickness in different positions (leaflet

thickness variation ranged from 80 to 200 µm).

Mackay et al. (1996) constructed a trileaflet valve entirely from PU, using a

combination of injection molding and solution casting. Injection molding was used to construct

the stent, and then the stent was assembled onto the metal mandrel (named former). The whole

assembly (stent and former) was dipped into the polyurethane concentration (35-45 %w/v), and

it was dried in a downward position. As the solvent evaporated, a thin layer of PU remained

which wrapped the frame. A combination of manufacturing techniques was also used by Leat

and Fisher (1994). They used PU dip-coated (250 µm thickness) polyetheretherketone (PEEK)

for the frame. The leaflets were manufactured from the solvent cast of the flat film of low

elastic modulus PU (Eurothane 2003). Each leaflet was cut out from the flat film, and then the

solvent bonded to the outer side of the PU-coated PEEK frame. In the final step, the leaflets

were thermally formed into the designated geometry with a mold.

39

More recently, a tricuspid valve from a nanocomposite of polyurethane POSS-PU or

UCL-NanoTM was constructed with an automated dip coating technique (Rahmani et al., 2012).

A stainless steel mandrel was dipped into polymer solution (18% w/v), then the mandrel was

removed from the solution at a controlled rate and was placed in an air circulating oven for 1

hour at 60 ° C to allow the solvent (dimethylacetamide) to evaporate. The results showed that a

thin film remained on the mandrel and by repeating the same procedure, the desired thickness

for the leaflet was obtained.

2.4.4 Poly (styrene-block-isobutylene-block-styrene) (SIBS) valve manufacturing

technique

In the study carried out by Claiborne et al. (2009) a catheter-based polymeric heart

valve was manufactured from SIBS polymer. To process SIBS polymer and form it into a

tricuspid valve, SIBS (Innovia, LLC, Miami, FL, USA) was dissolved in toluene (15% SIBS

m/m) and poured onto the Dacron (CR Bard, Covington, GA, USA) sheet fixed onto an

aluminium drying plate. After the composite dried and attached to the proximal stent, the

leaflets were annealed into a semilunar shape using three 9.525 mm stainless steel ball bearings

and a 19 mm diameter aluminium cylinder, as shown in Figure 2.11

Figure 2.11. The modified Edward’s Life Sciences Cribier-Sapien stent is shown with composite material, and three stainless steel ball bearings used to shape the leaflet into a semilunar shape (Claiborne et al., 2009).

40

The aforementioned approaches are mainly carried out to investigate the feasibility of

the proposed approach to developing an alternative PHV. However, the hemodynamic

performance of the PHVs is also significantly affected by the valve design itself. In general, an

optimum design of PHVs must satisfy the following requirements:

- A minimum pressure drop to open the leaflets (Ghista, 1976, Leat and Fisher, 1994)

- Minimum stress and stress concentration on the cusp membranes (Leat and Fisher,

1994)

- The leaflet shape must provide a smooth wash out (Leat and Fisher, 1994)

- Minimum blood regurgitation

- Minimum blood disturbance and associated thrombogenicity risk

- Maximum effective orifice area (EOA)

Hence, the design of the valve has a crucial role in the success of PHVs. A brief literature

review of the current designs is provided in Chapter 3.

2.5 Summary of findings

Based on the literature review, two alternative types of prosthetic valves, tissue-

engineered and polymeric heart valves were investigated to overcome the drawbacks of current

PHVs substitutes. Despite the great potential of TEHV, important barriers still persist in terms

of achieving the desired cell adherence, proliferation, scaffold heterogeneity, degradation rate,

mechanical properties, microstructure and porosity. In addition, the need for cell harvesting,

scaffold seeding, and a bioreactor culture for this approach were sufficiently substantial to

make the clinical application unrealistic (Mack, 2014).

In contrast, polymeric valves (PVs) can potentially address the limitations associated

with current Mechanical and Tissue valves. PVs ideally have flexible leaflets similar to tissue

valves that enhance blood flow and improve blood disruption, as well as lifelong biostability

and durability. In addition, advances in material sciences and new developments in super

biostable polymers may fulfil the clinical requirements of PVs, and make it more reachable in

the near future. However, the development of PVs is still under investigation, and there is no

clinically available polymeric valve substitute. The literature showed that the proposed valve

designs and approaches to developing PVs still suffer from impaired haemodynamic

performance compared to native valves. Therefore, this research aims to develop a parametric

design of a high performance polymeric aortic valve as well as developing a numerical

41

technique to evaluate the valve performance. A testing machine, namely the Pulse Duplicator

machine, is also designed and manufactured to validate the numerical model.

42

3 Chapter 3 Design procedure

3.1 Introduction

Currently, commercially available prosthetic heart valves (PHVs) including

bioprosthetic and mechanical heart valves (MHV) impose neo-diseases with health risk

complications. Patients who have received an MHV still need to take lifelong anticoagulant

medication which elevates the risk of haemorrhagic complication. Even the newer generation

of MHVs, including the third generation of bi-leaflet valves, still suffer from a high degree of

turbulence fluctuation, and high shear stresses that induce platelet activation, aggregation, and

deposition (Bluestein et al., 2004, Yin et al., 2004). In contrast, current tissue valves have less

structural reliability. In general, the lifespan of a tissue valve is shorter due to its progressive

tissue deterioration and most patients require another operation. However, a 20-year post-

operation follow up on 2,533 patients aged 18 years or older who had received either a tissue or

a mechanical valve conducted by Khan et al. (2001) showed that there were no overall

differences in the survival rate for both types of valves. It is evident that both types of PHVs

still suffer from a number of drawbacks, and an ideal PHV with lifelong durability without

thrombotic complication is yet to be developed. In contrast, polymeric heart valves ideally have

flexible leaflets similar to tissue valves, which enhance blood flow, and improve blood

disruption with lifelong biostability and durability. Hence, a prosthetic valve is designed

according to the valve material and its function.

3.2 The design parameters

The design and development of a prosthetic valve requires a thorough understanding

of the physiological loads applied to the native valve, its mechanism to respond to this

haemodynamic load, and the resultant blood flow profile. It should be taken into account that

the valve opens and closes approximately every 0.8 seconds in each cardiac cycle. Hence, the

prosthetic valve must survive at least over 400 million cyclic loads, corresponding to

approximately ten years of use. Such cyclic loadings impose harsh oscillating mechanical

stresses on the valve. In this working environment, the fatigue life of polymeric valves must be

taken into consideration. It is widely accepted that the stress concentration in the leaflets is

associated with leaflet tearing and prolapse (Claiborne et al., 2012). In addition, calcification is

43

reported as one of the causes of the clinical failure of PVs (Claiborne et al., 2012). Although the

exact mechanism of calcification remains unclear, studies (Levy et al., 1991, Vyavahare et al.,

1997) show that calcium deposition often occurs at the region of stress concentration. In this

context, wall shear stress (WSS) and platelet exposure time to the stress are known to induce

platelet activation and thrombus formation (Ramstack et al., 1979, Holme et al., 1997).

Consequently, the valve design must be optimized from the hydrodynamic and structural point

of view. Hydrodynamic performance of the valve is frequently evaluated by measuring the

effective orifice area (EOA) and pressure drop across the valve. In fact, the EOA of the

prosthetic valve is one of the major parameters associated with patient valve mismatch

complications (Marquez et al., 2001). EOA is defined as the cross-sectional area of vena

contracta (VC) in the left ventricular outflow tract (LVOT), which is inversely proportional to

the pressure drop (Garcia and Kadem, 2006).

EOA can be calculated from either the Gorlin equation ( ) or continuity

equation ( ). The Gorlin equation is originally based on the Bernoulli equation and

conservation of flow energy for the purpose of calculating the aortic valve area (AVA). The

Gorlin equation is a function of the mean systolic flow rate (Q) and TPG with a standard

clinical unit of mmHg and ml/s respectively as described as follows:

Equation 3.1. Gorlin equation (Garcia and Kadem, 2006).

√

Theoretically, EOA can be obtained from the Gorlin equation when the maximum value of TPG

obtained from the pressure measurement within the vena contracta is applied in the Gorlin

equation. However, the modified version of Equation 3.1 is more frequently used and can be

written as:

Equation 3.2. Modified Gorlin equation (Dasi et al., 2009).

√

where Qrms is the root mean square systolic/diastolic flow rate (cm3/s) and Δp is the mean

systolic/diastolic pressure drop (mmHg).

44

The other method to calculate AVA is based on continuum mechanics principles, where

continuity equation describes that the flow rate in the VC is equal to the flow rate in LVOT.

Thus, EOAKont can be written as:

Equation 3.3. EOA calculated from the continuity equation (Garcia and Kadem, 2006).

where ALVOT is the area of the left ventricular outflow tract (LVOT) cross-section, VTILVOT is

the blood velocity time integral at LVOT cross-section, and VTIVC is the velocity time integral

at the VC cross-section.

Although both methods to calculate the EOA are common, it should be noted that the

comparison studies carried out by Rudolph et al. (2002), Garcia and Kadem (2006) showed

discrepancies between the value of EOA obtained by the Gorlin and continuity equations. In

general, the Gorlin equation produced a higher value compared to the other method.

Furthermore, the flow dynamics of the generated blood stream also has an important

influence on the valve hydrodynamic performance. Elevated shear stress regions and high

turbulence fluctuations in the blood stream have been found to be responsible for damaging red

blood cells (RBC) and initiating platelet activation causing thromboembolic complications

(Dasi et al., 2009). It is reported by Wurzinger et al. (1985) that the threshold of turbulence

stress level to initiate platelet activation is between 10 to 100 Pa. However, taking stress level

alone into account is not sufficient, and it is necessary to measure both stress level and the time

duration of blood cell exposure to the elevated stress (Hellums et al., 1987). In this respect, a

more accurate threshold known as Hellmus criteria (3.5 Pa.s) is proposed which describes the

behaviour of platelet activation more precisely.

In diastolic phase, the valve regurgitation volume or the total blood volume that

returns back after valve closure is accountable for the valve performance. The valve geometry

determines the valve response to haemodynamic loads and closure dynamics. In the case of

good leaflet coaptation and rapid response, the regurgitation will be in an acceptable range.

However, a poorly designed prosthetic valve will result in high leakage which imposes

unnecessary pressure on the heart to compensate for the shortfall of net cardiac output.

45

In addition to the aforementioned hydrodynamic standards, the structural properties of

the valve also have a significant effect on the valve performance. The desired valve should

provide sufficient mechanical properties to withstand cyclic loads, ideally for the patient’s life

span or an acceptable life span of 12 to 24 years (Ghista, 1976).

The above-mentioned standards are related to the actual design of PHVs. Accepting

these requirements, various designs for polymeric valves have been proposed (Mercer et al.,

1973, Ghista, 1976, Reul, 1981, Herold et al., 1987, Leat and Fisher, 1994, Mackay et al., 1996,

Jiang et al., 2004, Burriesci et al., 2010, Kouhi and Morsi, 2013) with the aim of improving the

hemodynamic performance. However, there is no standard method to design the leaflet shape,

and researchers have used different approaches to define the valve geometry. Major techniques

and approaches which have been previously carried out to parameterise the leaflet geometry are

detailed in the following sections.

3.3 Approaches to parameterise the leaflet geometry

Early attempts to design an aortic valve (AV) were initiated by extracting the native

AV geometry, and by measuring a pig’s frozen aortic valve (Wood et al., 1963) and by

measuring a constructed mold from a human AV (Mercer et al., 1973, Swanson and Clark,

1974). In particular, Swanson and Clark (1974) introduced a dimensionless model of an AV by

normalizing the valve dimensions by the aortic diameter do, as shown in Figure 3.1

Figure 3.1. Dimensionless configuration of AV (Swanson and Clark, 1974).

46

Leat and Fisher (1994) designed a valve by utilizing an Alpharabola equation (see

Equation 3.4), in which the radius of the leaflet curvature increased from the centre of the valve

toward the base and stent post.

Equation 3.4. Alpharabola equation of the leaflet (Leat and Fisher, 1994).

where the leaflet-free edge in the circumferential direction lies in an x-y plane, and z-

axis is the flow direction. RL is the minimum radius of the leaflet-free edge at the centre of the

leaflet, and g is the small offset in x direction. α (0 ≤ α ≤ 1) is a parameter to control the rate of

increase of the leaflet curvature, where α=0 produces a paraboloid of revolution and α=1 results

a spherical leaflet with a constant radius of curvature. Two types of valves, alpharabola and

spherical, were constructed from polyurethane (PU), and their hydrodynamic performance was

evaluated under steady state and pulsatile flow in vitro. The results showed that the spherical

leaflet valve required more inflow pressure to open compared to the alpharabola leaflets valves.

However, the pressure drop across both valves was lower than the bioprosthetic model

(Hancock II). It is also noted that this design has a large central opening in the closed position,

which may have an adverse effect on valve performance in diastolic phase.

Mackay et al. (1996) utilized two sets of equations to describe a leaflet in the closed

position. It is stated that when the leaflet-free edge is located in the x-y plane (z is the flow

axis), the elliptical equation for the radial direction is expressed as:

Equation 3.5. Elliptical equation for the radial direction of the leaflet (Mackay et al., 1996).

[ ] [ ]

and the circumferential direction was described with a hyperbolic equation (Mackay et al.,

1996) as:

47

Equation 3.6. Hyperbolic equation for the circumferential direction of the leaflet.

[ ] [ ]

where E0 and H0 are offset from x-axis, and Emajor, Eminor, Hmajor and Hminor are the major and

minor axes of the respective conics, and Hmajor is:

Equation 3.7. The hyperbolic curve major axis length (Mackay et al., 1996).

( [ ]

)

and Hminor axis is:

Equation 3.8. The hyperbolic curve minor axis length (Mackay et al., 1996).

Their experimental findings showed that the valve had lower blood regurgitation

compared to the St. Jude mechanical valve and the bioprosthetic valve with lesser overall

energy loss at low flow rate.

Jiang et al. (2004) incorporated a hyperbolic of revolution to describe the leaflet

geometry as follows:

Equation 3.9. The hyperbolic equation of the leaflet (Jiang et al., 2004).

where the value of b determines the distance between the centre of the curve and the valve

centre, and x are the asymptotes, as shown in Figure 3.2.

48

Figure 3.2. Configuration of leaflet-free edge using a hyperbola (Jiang et al., 2004).

The value of

√

was selected based on the fact that each of the three leaflets

occupies one third of the stent area resulting in an angle of 120° between the asymptotes.

Obviously, angles greater than 120° result in the intersection of the free edge and angles smaller

than 120° result in a large central opening area. However, in the case of an asymptote having an

angle of 120°, the gap between the adjacent two hyperbolas with a common asymptote is equal

to 2gsin60˚. g in Figure 3.2 is the distance of the free edge distal point to the adjacent

asymptote and can be calculated as:

Equation 3.10. Distance of the leaflet free edge distal point from the adjacent asymptote (Jiang et al., 2004).

√

where B represents the stent orifice diameter. The leaflet-free edge is then transferred toward

the centre of the stent orifice by the value of g to minimize the central opening area A0. The

value of b determines the distance from the centre of hyperbola curve to the centre of the stent

orifice. Thus, this value was chosen (b=2 mm) based on the minimal central opening area and

also the moderate curvature of the leaflet free edge in the closed position. The MNL area

(shaded area in Figure 3.2) shows one-sixth of the total central opening area in the closed

position of the valve and can be calculated as:

49

Equation 3.11. The area of central opening (Jiang et al., 2004).

[√

(

)

]

Jiang et al. (2004) also used a technique called “revolved arc subtending two straight

lines” to have more control over minimizing the central opening area A0. The leaflet-free edge

curve was then defined as the two straight lines (SM and TN) lie on the asymptotes (120° from

each other) joined by the arc MN (see Figure 3.3).

Figure 3.3. Configuration of the leaflet-free edge using two straight lines (Jiang et al., 2004).

In this method, revolving the free edge curve about the ST axis generated the leaflet

surface. The central opening area A0 (which is proportional to the radius of the MN arc) can be

expressed as:

Equation 3.12. The central opening area in the revolved arc technique (Jiang et al., 2004).

(

)

The valve prototypes constructed by Jiang et al. (2004), as previously mentioned,

showed the successful opening and closing in a cyclic flow tester, however, no evidence of

50

pressure drop across the valve or wall shear stress were reported in this study. It was also noted

that the valve constructed by the “revolved arc subtending two straight lines” techniques had

lower regurgitation and a better response to haemodynamic loads.

In another study by the same group (Jiang et al., 2005b), a mathematical equation of

one leaflet of the Baxter Carpentier-Edward ® pericardial heart valve was obtained. In this

technique, a laser digitizer was used to collect the leaflet geometry profile. The collected data

was from cloud points representing the leaflet geometry profile. Subsequently, a quadric

surface was fitted to the cloud points using the least squares fit algorithm resulting in an

elliptical hyperboloid equation as:

Equation 3.13. Elliptical hyperboloid equation of Baxter Carpentier-Edward (Jiang et al., 2005b).

The equation was also simplified to a hyperbolic equation in the circumferential direction, and

radial direction as shown in Equation 3.14 and Equation 3.15, respectively.

Equation 3.14. The leaflet constructive curve in the circumferential direction (Jiang et al., 2005b).

Equation 3.15. The leaflet constructive curve in the radial direction (Jiang et al., 2005b).

Labrosse et al. (2006) conducted a study to investigate how much the dimension of the

aortic valve can vary before it affects valve functionality. In this study, they introduced

analytical equations to describe the geometry of the AV in open and closed positions. It was

51

assumed that three leaflets were isometric, and each leaflet occupied exactly one-third of the

valve (120o from each other) to simplify the complex structure. In this approach, two sets of

parameters were defined as primary and secondary parameters on the cross-section of the aortic

root and leaflet, as shown in Figure 3.4 and Figure 3.5, respectively.

Figure 3.4. Schematic view of a longitudinal cross-section of the aortic valve in close position (Labrosse et al., 2006).

Figure 3.5. Schematic view of one leaflet in both the open and closed positions (Labrosse et al., 2006).

where the parameters in the above two figures are as follows:

Db : base diameter, Dc : The commissure diameter, H : Valve height, Lf Leaflet free edge length,

Lh : Leaflet height. Xs Coaptation height in the center of the valve. α (resp. β): angle of the

52

closed leaflet, Hs: height of the commissures, and Ω: angle of the leaflet free-edge in the open

position.

Given the primary and secondary parameters, the analytical equations are described as:

In the open position, the leaflet-free edge Lf (shown in Figure 3.4) is obtained as:

Equation 3.16. Length of the leaflet-free edge (Lf) (Labrosse et al., 2006).

√

(

√

)

√

√

{ (

√

)}

√

where d is the radial location of the centre of the arc spanned by Lf with respect to the middle of

commissure.

By solving Equation 3.16 numerically for d, the radius of the arc R spanned by Lf is obtained

as:

Equation 3.17. Radius of the arc spanned by Lf (Labrosse et al., 2006).

√

Moreover, the parameter (angle of the leaflet free edge as shown in Figure 3.5) described as:

Equation 3.18. Angle of the leaflet free edge in the open position (Labrosse et al., 2006).

{

[(

)

]

√(

)

}

{

}

53

where:

√

√

The parameter β (angle of the leaflet in the open position to the centerline of the valve, as

shown in Figure 3.5) is described as:

Equation 3.19. Angle of the opened leaflet to the valve centerline (Labrosse et al., 2006).

{ (

)

}

In the closed position, the leaflet-free edge length and height can be expressed in a set of

nonlinear equations as:

Equation 3.20. Lf leaflet- free edge length, Lh leaflet height in the closed position (Labrosse et al., 2006).

{

[ ]

The commissure height ( ) is then calculated for two cases as follows:

In the case where the commissures run parallel to the valve centerline:

Equation 3.21. Commissure height (Labrosse et al., 2006).

(

) [

(

)]

In the case where the commissures lie on the frustum of a cone extending between the diameter

of the base of the valve and the diameter of the commissure:

54

Equation 3.22. Commissure height (Labrosse et al., 2006).

(

) [

(

)]

(

) [

(

)]

In general, the techniques to parametrise the leaflet geometry, including mathematical

equations and analytical formula as outlined above, can potentially be used to optimize the

current designs or to develop a new parametric design. Such a design is crucial for modelling

and optimizing the valve.

3.4 Polymeric aortic valve design

Polymeric valves (PVs) have been researched since the 1950s (Ten Berge, 1958, Roe

and Moore, 1958, Akutsu et al., 1959, Braunwald et al., 1960, Roe et al., 1966, Mori et al.,

1973, Chetta and Lloyd, 1980, Wisman et al., 1982, Jansen and Reul, 1992, Bernacca et al.,

1997b, Sachweh and Daebritz, 2006, Ando and Takahashi, 2009, Ding et al., 2009, Kutting et

al., 2011, Rahmani et al., 2012, Claiborne et al., 2013) and the first PVs were implanted in

human mitral (Braunwald et al., 1960) and aortic (Roe et al., 1966) positions in the 1960s.

However, the clinical outcomes of these initial trials were not successful as the available

polymers at the time did not provide sufficient biostability and durability. Currently, there are

no clinically approved PVs, however advances in material sciences and the recent new

development of super biostable polymers such as a new generation of polyurethane urea

(Thomas and Jayabalan, 2009), polytetrafluoroethylene (Nistal et al., 1990), poly (styrene-b-

isobutylene-b-styrene) (SIBS) (Pinchuk et al., 2008), polyurethane with a poly

(dimethylsiloxane) soft segment (Elast-Eon) (Kidane et al., 2009), and bionate polycarbonate

urethane (PCU) (Dempsey et al., 2014) may fulfil the clinical requirements of PVs. The choice

of material is a crucial factor in the fabrication of polymeric heart valves. The chosen polymer

should be biocompatible, biostable, anti-thrombogenic, and provide sufficient mechanical

integrity to withstand the load. In addition to material selection, the hemodynamic performance

of the PVs is another challenging area that is yet to be fully addressed and optimized.

Generally, an optimum design must satisfy the following haemodynamic and structural

requirements of a PV:

55

Provide sufficient mechanical properties to withstand cyclic loads, ideally for a patient’s

lifespan or an acceptable lifespan of 12 to 24 years (Ghista, 1976)

Minimum mean systolic Transvalvular Pressure Drop (TPG)

Minimum stress concentration in the cusps’ membrane to increase fatigue strength

Minimum blood regurgitation

Minimum blood disturbance, damage to blood cells and associated thrombogenicity risk

Large effective orifice area (EOA)

Accepting these requirements, various designs for PVs have been proposed (Mercer et

al., 1973, Ghista, 1976, Reul, 1981, Herold et al., 1987, Leat and Fisher, 1994, Mackay et al.,

1996, Jiang et al., 2004, Jiang et al., 2005a, Burriesci et al., 2010, Kouhi and Morsi, 2013).

However, there is no standard method to design the leaflet shape, and researchers have used

different approaches to define the geometry of the cusps. Leat and Fisher (1994) designed the

valve by utilizing an Alpharabola equation, in which the radius of leaflet curvature increased

from the centre of the valve toward the base and stent post. This design showed acceptable

opening performance, but it had a great regurgitation volume due to its large central opening

area when the valve is closed.

The incremental revolution of the leaflet curve in a circumferential or radial direction

about a parallel axis has also been used to describe the leaflet shape. However, this method has

numerous limitations. A paraboloid of revolution with its focus at the base of the valve (Mercer

et al., 1973) was unacceptable as the cusp cross-section decreases toward the base.

Incorporating the ellipsoid of revolution is also not practical as ellipsoid eccentricity is

restricted by valve height (Leat and Fisher, 1994). A hyperboloid revolution introduced by

Jiang et al. (2004) showed successful opening and closing in a cyclic flow tester. However, this

method imposed geometrical constraints on the valve design as the valve height and shape of

the cusp were correlated with the position of the revolution axis simultaneously.

In contrast, defining the leaflet geometry in radial and circumferential directions can

potentially provide better control over the design parameters. Mackay et al. (1996) designed

the valve with an elliptical hyperbolic conicoid (elliptical in the radial, and hyperbolic in the

circumferential direction). Their experimental findings showed that the valve had lower blood

regurgitation compared to the St. Jude mechanical valve and bioprosthetic valve with lesser

overall energy loss at low flow rate. (Kouhi and Morsi, 2013) also used the same method to

design the constructive curves, where an elliptical, hyperbolic curve was adapted for both the

56

circumferential and radial direction of the cusp. However, defining the leaflet geometry by

solely mathematical equations is not necessarily the best engineering approach. A method such

as fitting a curve using the least square fit algorithm as incorporated in Jiang et al. (2005a)

study may result in a too simplified geometry and limited control to alter the shape. A more

appropriate engineering approach could be to design the valve based on engineering principles

and then optimize it to achieve maximum performance (Thubrikar et al., 1991, Burriesci et al.,

2010, Claiborne et al., 2013). In particular, Burriesci et al. (2010) introduced a parametric

design for a tri-leaflet PHV and succeeded to optimize the design variables such as valve

height, leaflet angle, and commissure distance. Various valve designs were modelled in Ansys

LS-DYNA to find the optimum value of the design parameters. Nonetheless, it was assumed

that the leaflets were constructed only by straight lines in the radial direction. The importance

of optimizing the valve was also noted in Claiborne et al. (2013) study in which the original

Innovia SIBS-Dacron polymeric valve design was modified to have a variable thickness leaflet

to optimize the stress distribution. The finite element analysis showed that the proposed valve

had less damaging stress concentration compared to the Carpentier-Edwards Perimount Magna

bovine tissue PHV. Moreover, previous studies (Luo et al., 2003, Kouhi, 2012) also

demonstrated that the design of the valve with multi-thickness leaflets could improve the stress

level in the leaflet. However, it is a very challenging task to construct such a leaflet as the

required manufacturing tolerance is approximately 50 µm. The measurement of 12

consecutively polyurethane valves with uniform valve thickness which were fabricated by

combinations of solution casting and injection molding techniques showed variations of up to

160 µm in the leaflets thicknesses (Mackay et al., 1996). The variations in the thicknesses of

the leaflets were approximately three times greater than the required manufacturing tolerance,

which indicates that it is impractical to construct a PHV with a multi-thickness design of the

leaflets on a commercial scale.

In addition, none of the mentioned studies investigated the effect of varying degrees of

leaflet curvature in the circumferential direction on the stress distribution in the cusps. In the

present study, a parametric design of a tri-leaflet prosthetic aortic valve is introduced, based on

the assumption that the leaflets were constructed by a circumferential curve and a radial curve.

The leaflets were assumed to have a uniform thickness to enhance the manufacturing process.

In this regard, the initial design strategy aimed at reducing the valve central opening area when

the valve is closed as well as maximizing the effective orifice area (EOA). Subsequently, the

initial design was then optimized to improve the durability of the valve. Moreover, a strongly

coupled FSI simulation was developed as a tool to evaluate the varying designs.

57

3.5 Proposed Design

In the current study, the prosthetic valve is designed by taking the following two major

steps: 1) initially, the valve is designed to possess high haemodynamic performance, 2) the

initial design is then optimised in the series of FSI simulations to obtain an optimum design as

described below. Note that most of the following sections have already been published by the

author (Gharaie and Morsi, 2015).

3.5.1 Initial design

The valve design consists of three symmetrical leaflets attached to a supporting frame (stent).

The leaflet geometry was defined in the closed position by sweeping the constructive curve of

the cusp in the circumferential direction (lc) through the radial curve (lr) as shown in

Figure 3.6.

Figure 3.6. Schematic view of generated 3D surface of the leaflet.

The generated leaflet surface was trimmed to the stent size by cutting a portion of the leaflet,

which was outside of the stent orifice as shown in Figure 3.7.

58

Figure 3.7. Trimmed leaflet surface to the stent size.

In the final step, the leaflet geometry was patterned abound the z-axis and assembled onto the

stent as shown in Figure 3.8.

Figure 3.8. 3D representation of the assembled tri-leaflets valve.

3.5.1.1 Constructive curve in the circumferential direction (lc)

The geometry of lc curve was defined initially by using a hyperbola equation as

suggested by Jiang et al. (2004).

59

Equation 3.23. Hyperbolic equation suggested by Jiang et al. (2004).

where b is the distance of the hyperbola vertices to the origin, and y= x are the

asymptotes (see Figure 3.9a). At the valve closed position, the smallest central opening area A0

(blue area in Figure 3.9b) is desired to prevent blood backflow. Thus, the gap between the

hyperbola arm and the asymptotes (g represents this gap in Figure 3.9a) was eliminated by

moving the curve vertices toward the centre of the hyperbola, as shown in Figure 3.9b.

Figure 3.9. Configuration of the leaflet constructive curve in a circumferential direction. (a) The blue area shows the central opening area for one leaflet; (b) The central opening area after transferring the hyperbolic curve.

60

A0 could be further reduced by decreasing the value of b to nearly zero. However, this

can cause stress concentrations which have an adverse effect on the valve durability (Jiang et

al., 2004). In this research, b=1 mm was selected as it showed acceptable A0, and a reasonable

degree of curvature in the centre of the curve. The optimum value of b could be obtained from

further research; however, it is out of the scope of this study. In the hyperboloid design

proposed by Jiang et al. (2004), the value of

√

was selected based on the fact that each of

the three leaflets occupies one third of the stent area resulting in an angle of 120° between the

asymptotes. However, the effect of varying angles of the asymptotes on A0 has not been

investigated. Table 3.1 shows the calculated A0 (after eliminating the gap between the

hyperbolic curve arm and asymptote) for the selected value of this angle from 117° to 120°.

Table 3.1. A0 computed by various asymptotes of the hyperbolic curve.

It was noted that an angle smaller than 118° resulted in the hyperbolic curves

diverging at the commissures (Figure 3.10a) and forming a gap. Therefore, the angle of 118°

was selected as it provided parallel-free edge contact at the commissural area (Figure 3.10b) to

improve the leaflet coaptation, and it also had a small central orifice area A0 (Table 3.1). The

geometry of lc after optimization can be written as follows:

Equation 3.24. The optimum hyperbolic curve.

Stent internal diameter = 23 mm

Asymptotes subtending

angle

a (mm) b (mm) g (mm) A0 (mm2)

120° 1.732 1 0.0712 11.49

119° 1.697 1 0.1505 9.51

118° 1.69 1 0.17 7.14

117° 1.63 1 0.3232 5.94

61

Figure 3.10. Configuration of the leaflet-free edge defined by the hyperbolic curve with asymptote subtending angle of (a) 117° and (b) 118°.

(a)

(b)

62

3.5.1.2 Constructive curve of the leaflet in radial direction (lr)

It should be noted that the degree of the leaflet curvature in the radial direction has a

great influence on the valve performance in both the opening and closing phases. A curvature

degree which is too high results in the cusps entering into the SOV region and interfering with

the flow vortex inside the SOV, and also has an adverse effect on the closing performance of

the valve. Conversely, a curvature degree which is too low limits the leaflet displacement,

resulting in a small geometric orifice area (GOA). The GOA is the maximum opening area of

the valve and is directly correlated to EOA. It was demonstrated by Sauter (2010) that the GOA

and the space efficiency of the valve (ratio of the GOA to the overall space occupied by the

valve) are two alternative parameters to EOA that can be used by a surgeon to find the valve

that resembles most closely the flow of a native healthy valve. In addition, the valve height

should be adapted according to the geometry of the SOV, as reported by Bellhouse and Talbot

(1969). The author demonstrated that the gap between the leaflets (when they are widely

opened) and the ridge of the SOV determines the flow vortex pattern in SOV, in which the

generated vortex helps the leaflet to close slowly and evenly. Hence, it is necessary to design

the valve according to a patient’s SOV geometry. In this respect, the valve height and the

geometry of the SOV were retrieved from the data collected by Book (2010) for an average

patient under 50 years of age as shown in Table 3.2 for the purpose of this research as a guide

(see Figure 3.11a). Subsequently, the design criteria of lr were defined to have maximum GOA

and space efficiency without interfering with the flow vortex in a patient-specific SOV.

Valve height (mm) Annulus radius

(mm)

Aorta radius

(mm)

la (mm) lb (mm) ld (mm)

8.5 12.5 15 24 12 34

Table 3.2. Valve height and SOV measurements (data is rounded).

(a)

63

(a)

Figure 3.11. (a) Representation of a patient’s SOV and the leaflet radial curve in zy-plane. (b) Configuration of

lr in zy-plane, where dni is the distance of point ni to plane (d) in y direction, and dnꞌi is the

distance of point nꞌi to plane (d) in y direction. The lr curve was defined using the illustrated

parameters; Plane (e) was defined to separate the SOV region from the main stream, plane (d)

passes through leaflet distal points in the xy-plane (see Fig 3.8) and the centre of the stent ring

cross-section in zy-plane.

(b)

64

It was assumed that the displacement of the leaflet was limited by plane (d) as shown

in Figure 3.11b. Therefore, the designated distance of each given point (ni) (denoted dni in

Figure 3.11b) on lr to plane (d) determined the opening characteristics of the leaflet. In

addition, for each ni point, a peer nꞌi point was defined on the plane (e) (see Figure 3.11b) as

the maximum tolerated displacement of point ni. Moreover, the distance of point ni and nꞌi to

plane (d) were denoted as dni and dnꞌi, respectively (Figure 3.11b). The value of dni should not

exceed the value of dnꞌi as it elevates the risk of leaflets interfering with SOV vortex.

Additionally, selecting d < resulted in a reduction of the maximum GOA of the valve.

Consequently, dni = dnꞌi was chosen based on the maximum GOA and also stopping the leaflet

from entering into the SOV region. The radial curve lr was then defined by finding the best

fitted Spline curve passing through ni points. Subsequently, a polynomial equation fitted to the

2D model of lr was found in MATLAB. The quartic polynomial equation showed a perfect

match to the 2D geometry of lr, and can be written as Equation 3.25 after transferring the origin

to the centre of the stent ring cross-section (Figure 3.11b):

Equation 3.25. Equation of lr in zy-plane.

3.5.2 Design optimization

The design parameters described in section 3.5.1.1 and 3.5.1.2 mainly focused on

maximizing GOA and minimizing regurgitation. However, the durability of this class of PHVs

also has a substantial effect on the valve performance. In the previous designs, such as

(Burriesci et al., 2010, Claiborne et al., 2013), stress localizations were noted and the maximum

stress was mainly located where the leaflets attached to the stent proximately near the leaflet

commissure area. Hence, the leaflets are subjected to repeated cyclic load; the stress

concentration will promote fatigue failure of the valve more aggressively. This could be

improved by altering the valve design to have a better stress distribution in the leaflets. In order

to optimize the valve design, an additional circumferential curve (lꞌc) was incorporated in the

design in which the leaflet surface was generated by the sweep blending of two circumferential

curves (lc, and lꞌc) through the radial curve (lr) as illustrated in Figure 3.12 and the excess

material was trimmed as described in Figure 3.7.

65

The Hyperbolic Equation 3.23 was used to define the geometry of lꞌc. It was assumed

that b=1 mm, then varying values of a corresponding to the asymptote angles of ranging from

120° to 125° were examined in the series of FSI simulation.

Figure 3.12. Schematic view of the optimized leaflet geometry. The vertices of hyperbolic

curve (lꞌc) is located on the radial curve. The distance from the xy-plane is half of the valve height.

3.6 Reference Valve design

The trileaflet valve developed by Aortech Europe Ltd (Wheatley et al., 1998) showed

acceptable hydrodynamic performance and durability in the literature (Mackay et al., 1996,

Bernacca et al., 1997a, Butterfield et al., 2001). In addition, the same valve was used as a

reference valve in the study carried out by Burriesci et al. (2010) to verify the validity of the

proposed optimized valve. Therefore, this valve was selected as the reference valve in the

present study. The valve was designed by tangentially joining a truncated spherical surface to a

truncated conical surface according to the design parameters provided in (Wheatley et al., 1998)

as shown in Figure 3.13. The leaflets were attached to a cylindrical support with a 23 mm

internal diameter and thickness of 0.75 mm. The valve height was assumed to be 15 mm to be

consistent with the previous study (Burriesci et al., 2010).

66

Figure 3.13. Schematic view of the reference valve.

3.7 Summary

In this chapter, a literature review of the existing studies on the techniques to find the

mathematical equation of the leaflet geometry is provided, which advances the knowledge

about the influence of the various designs on valve performance. Consequently, a new design

for the prosthetic valve was proposed for a stented polymeric valve in which the valve design

was parameterised in circumferential and radial directions to have maximum control over the

design parameters. The initial design was then optimised in the series of the FSI simulations as

described in chapter 4. Moreover, the rationale for choosing the reference valve and its design

were provided.

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4 Chapter 4 Numerical simulation theory and boundary condition

4.1 Fluid Structure Interaction (FSI) analyses

The interaction between the heart valve and blood in a native heart imposes stress onto

the valve, which causes deformation in the valve. This deformation may also alter the blood

flow itself. This type of problem is classified as a multiphysics problem. The solution for such a

problem can be calculated using the relations of continuum mechanics which are mostly solved

with numerical methods such as the finite element method (FEM). It would be near impossible

to obtain an analytical solution for this kind of complex interaction between solids and fluids

(Hou et al., 2012). In this context, FSI simulations are categorised into two main modelling

strategies, monolithic and partitioned methods (Heil et al., 2008, Ryzhakov et al., 2010). In the

partitioned method, fluids and solids are coupled either in the one-way (weakly coupled) or

two-way (Strongly coupled) method. The difference between weakly and strongly coupled

approaches can be found in a study carried out by Vaassen et al. (2010). In this chapter, the

developments and limitations of the FSI methods (both one-way and two-way) that have been

used as part of the valve design verification or optimization processes are discussed.

Consequently, the theory of the chosen FSI method is given in detail as well as the boundary

condition.

4.2 One way FSI evaluation

The evaluation of one-way coupling PHVs, also known as weakly coupled FSI, is

based on the physical properties obtained from a CFD model which is purely mapped to

structural FE model. This type of analysis is more appropriate when the mesh deformation of

the solid domain is small enough to have a negligible effect on the fluid domain. However, a

weakly coupled FSI has been used for the analysis of PHVs with the aim of reducing

computational effort.

In this context, Peskin (1972) simulated the flow pattern around the natural mitral

valve and also the prosthetics aortic valve by using the immersed boundary technique.

Visualizing the flow pattern was continued by weakly coupling FSI of ball disc and tilting disc

PHVs by Greenfield and Au (1976). In this study, the flow velocities, vorticity, pressure and

68

stress value were successfully calculated from the simulation. The turbulent flow past through a

fully open cage ball (Starr-Edwards) PHV was also simulated by Thalassoudis et al. (1987), in

which the governing equations were described by partial differentiation Navier-Stokes

equations. The numerical method used to solve the problem also revealed a simple power-law

relationship between the steady flow rate and the generated turbulent shear stress. The

maximum turbulent shear stress location was successfully located near the sewing ring tip. The

vortex flow through a tilting disc was also simulated in three dimensions using the partitioned

FE scheme proposed by Shim and Chang (1994). The 3D simulation was continued by King et

al. (1996) and the results compared with experimental data. In this work, the flow past the bi-

leaflet mechanical valve for the first half of systolic was predicted using computational fluid

dynamics (CFD). Both the LDA technique and flow visualization were performed to validate

the CFD results. Flow visualization showed a similarity to the predicted flow by CFD. The

LDA measurements were also found to be in reasonable agreement with CFD predictions.

The calculation of the structure side (solid domain) is mostly based on the impulse

conservation (Benra et al., 2011). However, other methods have been used as well, such as the

Newton-Euler method (NEM) and the Lattice Boltzmann method. In the NEM, Newton-Euler

equations are used to describe the combined rotational and transitional dynamics of the valve.

The Newton-Euler method was employed by Gardner et al. (1995) in one-way coupling FSI to

simulate the dynamic motion of a tilting disk valve. The pressure distribution on the solid-fluid

interface in the fluid domain was mapped onto the solid-fluid interface in the solid domain (disk

surface). Consequently, the disk motion and stress distribution in the solid domain were

calculated by the Newton-Euler method. However, the accuracy of the results was adversely

affected by the absence of updating mesh in the solid domain. The Lattice Boltzmann (LB)

method with the incompressible Bhatnagar-Gross-Krook (LBGK) model was used by

(Krafczyk et al.) to simulate the 2D flow through a bileaflet mechanical valve instead of solving

the Navier-Stokes equations. It was found that the LB method could predict reasonable results

for the velocity and stress field. However, the method could be more suitable for semi-

turbulence flow regimes and structurally easier problems such as stenosis blood flow dynamics.

As previously mentioned, one of the disadvantages of the mechanical valve is high

shear stresses which can initiate platelet activation and thrombus formation. In this context,

Leat and Fisher (1995) performed two-dimensional quasi-state numerical simulations for

backflow through central clearance of an Edwards-Duromedics bileaflet mechanical valve at

the instant of closure. The results showed that average wall shear stress (WSS) was an order of

69

magnitude larger than turbulent shear stress during the opening. These findings suggested that

elevated WSS during backflow through clearance at closure could cause haemolysis and

thrombosis in mechanical valves.

The commercial CFD code, Fluent, also attracted lots of attention to tackle this kind of

FSI problem. Dumont et al. (2004) carried out a study to validate the FSI model of a PHV using

Fluent. In this study, Fluent was weakly coupled with a user-defined function (UDF) of valve

motion. In addition, the Arbitrary Lagrangian-Eulerian (ALE) framework was used by

employing the dynamic re-meshing feature in Fluent (information on the ALE method is

provided in Section 2.5.2.2). The 2D FSI model of the valve was validated by comparing the

predictions to those obtained from the experimental data in which the CFD results were in good

agreement with the experimental observations. Similarly, Morsi et al. (2007) used the weak

coupling of ALE-based Fluent with FE solver in ANSYS software. In this study, a 2D model of

one leaflet of the aortic valve was modelled in various Reynolds numbers. It was well

demonstrated that the FSI method can predict the flow characteristics and calculate the wall

shear stress (WSS) on the leaflet, however, this study only focused on the initial opening stage

of the valve leaflets.

Even though a one-way simulation could enhance a certain type of analyses that

focuses on the specified position of the valve (Leat and Fisher, 1995), a weakly coupled FSI is

only valid if the deformation of the solid domain has a negligible effect on the fluid domain. In

a weakly coupled FSI of PHVs, it is assumed that the moving valve part has a negligible effect

on the fluid domain to reduce the computational process. Nevertheless, a two-way FSI

simulation is required to explain the phenomena completely. In this respect, numerous studies

have been carried out to evaluate valve performance in strongly coupled FSI schemes, as

discussed in the following.

4.3 Two-way FSI evaluation

In general, the two-way coupling (also known as strongly coupled) FSI evaluation of

PHVs can be described as the physical properties obtained from a CFD solver mapped to a

structural FE solver where these results are then mapped back to the CFD solver in an iterative

loop until all solutions converge to a specific value. The two-way coupling method guarantees

energy conservation at the fluid-solid interface whereas one-way coupling does not (Benra et

al., 2011). However, implementation of the two-way coupling method for simulating such a

complex biofluid flow past PHVs with flexible leaflets is a challenging task. In this context,

70

various FSI algorithms have been developed such as immersed boundary (IB) and fictitious

domains methods. In addition, different computational coordinate systems such as Arbitrary-

Lagrangian-Eulerian (ALE) and Eulerian-Lagrangian based FSI models have been investigated.

In the most convenient terms, an FSI model is commonly described by the Eulerian-

Lagrangian framework. In this method, the fluid is represented in Eulerian coordinates and the

structure is described in Lagrangian coordinates. This means that the computational mesh in the

fluid domain is fixed and the material (fluid) moves with respect to the grid, whereas in the

solid domain, each node of the computational mesh follows the material in its motion (Donea et

al., 2004). However, these formulations are incompatible with each other. Hence, the ALE

formulation, which effectively combines these two formulations, is mostly used to continuously

adapt the mesh without changing the mesh topology. In an FSI simulation of PHV, it is a

difficult task to adapt the mesh and maintain the mesh quality due to the large deformation of a

thin leaflet. One strategy to solve such a problem is to re-mesh the mesh with exceeded

degenerated quality by using a Lagrangian formulation or with an ALE formulation. More

recently, the dynamic mesh method has been integrated into Fluent software which results in an

ALE method and local re-meshing approach being used in FSI problems. Basically, in the ALE

method, the grid inside the fluid domain can arbitrarily move to optimize the mesh elements

and the mesh in the boundaries and solid-fluid interfaces can move with solid material motion.

This method can potentially reduce the associated drawbacks to the classical Lagrangian-

Eulerian FSI simulation. Detailed information on ALE and its advantages can be found in the

study conducted by Donea et al. (2004). The reliability of this method in FSI analysis of PHVs

is also investigated by Dumont et al. (2004). In this context, the commercial CFD code, Fluent,

has been widely used in FSI analyses. In this approach, the Fluent solution is either coupled

with a commercial FE structural solver or a user coded structural solver with the Lagrangian

algorithm. Nevertheless, the user-defined structural solver is more applicable in MHVs FSI

simulations as it is a complicated tax to define a code for flexible leaflets PHVs. However, of

particular interest in an innovative algorithm, an in-house coded structural solver is strongly

coupled with a commercial CFD package Fluent to model a flexible heart valve (Vierendeels et

al., 2008). The structural solver is defined based on the previous studies by Horsten (1990) and

David (2000) for a 2D model of the flexible aortic valve in systolic and diastolic phase. In this

study, a fully implicit FSI scheme is developed which also had the potential to calculate the

shear stress on the leaflet.

71

Nobili et al. (2007) carried out a comparative study to investigate the influence of

using different types of coupling methods. In this study, the Fluent solutions were coupled

weakly and strongly with an in-house coded structural solver for the 3D ALE-based FSI

analysis of the St. Jude mechanical valve during the opening phase. The comparative study

showed that both coupling methods had similar angle/velocity evolutions, but the strong

coupling scheme performed better at the starting phase by suppressing the numerical time delay

(order 10-3 sec, i.e. milliseconds) between external momentum and angular acceleration. It is

also noted that the weak coupling model introduced an inaccurate physical description of the

interaction at a small scale feature such as stress near geometrical singularities, whereas the

strong coupling model provided more consistent results. Furthermore, the numerical results

compared to the experimental study showed discrepancies in terms of opening time delay

(15%) and peak velocity (8% underestimation). This study was carried out only in the opening

phase. However, it was extended to modelling the valve for both the opening and closure by

using a fully implicit FSI method (Nobili et al., 2008). The quantitative comparison showed that

using a new coupling scheme could improve the simulation predictions. These findings also

suggested that ALE-based FSI simulation is a reliable engineering tool to optimize PHVs

designs and provide key information to surgeons.

However, the dynamic re-meshing strategy in the ALE-based FSI simulation imposes

an expensive and heavy computational load. An alternative approach to avoid re-meshing is the

Fictitious Domain (FD) method proposed by Peskin (1972). In this method, the flow

computation is solved on a fixed grid which contains moving rigid bodies and the presence of

the solid bodies are defined by Lagrange multipliers on the region occupied by the solid bodies

to match the fluid flow and the rigid body motion velocities over these regions (Glowinski et

al., 2001). The FD method was initially used by (De Hart et al., 2000) in 2D FSI study of the

aortic valve with flexible leaflets and validated experimentally using LDA measurements and

visualization by high-speed camera. In this approach, the Reynolds numbers were within the

physiological range and a Lagrangian multiplier was used to couple the fluid and solid phases.

The extension of this study to the 3D model of the aortic valve was further carried out by De

Hart et al. (2003). This method was based on applying kinematic constraints by using a

Lagrangian multiplier with a no-slip condition along the FSI. The computational domains were

discretised independently which means that the presence of a rigid body did not interrupt or

change the computational mesh in the fluid. The predicted results showed that the fluid motion

governed the valve leaflets displacements in a kinematical process. In addition, the detailed

description of the flow development and the accurate prediction of the flow near the leaflets

72

were provided by this model. However, it was assumed that the leaflets were identical, and

only one-sixth of the valve was modelled, while this assumption may adversely affect the

predicted results for the simulated 3D flow patterns and magnitude of stress imposed onto the

valve. The FD-method was also evaluated for the dynamic response of the MHV for several

Reynolds and Strouhal numbers by Stijnen et al. (2004). In this study, the FSI predictions and

experimental results obtained by PIV method were in satisfactory agreement. Although FD-

method has the advantage of less computational load compared to ALE method, the accuracy of

predicted pressure and shear stress in the vicinity of the rigid body is poor.

An alternative strategy for the FD method is the Immersed Boundary (IB) method

which is a powerful simulation tool to solve such a complex flow past PHVs due to its ability to

handle arbitrarily complex bodies (Sotiropoulos and Yang, 2014). The IB formulation in the

FSI problem is based on the fluid represented by the Eulerian coordinate and the solid

represented in the Lagrangian coordinate in which the two phases are linked by the Dirac delta

function which is broadly categorised as a diffused and sharp interface method. The detailed

description can be found in (Peskin, 2002, Uhlmann, 2005). In this context, Watton et al. (2004)

used the IB method in modelling a heart valve. A native mitral valve and a prosthetic aortic

valve were modelled and the predicted results were compared to those obtained from the

commercial package ANSYS and experimental measurements. The comparative study showed

qualitative agreement with some discrepancies due to the incapability of the IB method to

model bending and shear behaviour. An extension of this study was performed by means of the

dynamic modelling of the prosthetic mitral valve through a fully coupled FSI analysis (Watton

et al., 2007). The IB method is validated by comparing the predicted displacements to those

obtained from ANSYS simulations and experimental measurements, in which the predicted

results were in good quantitative agreement with those obtained from the ANSYS solver in

terms of flow pattern and leaflet deformation.

The curvilinear IB method was used by Borazjani et al. (2008) to perform a 3D FSI

simulation of a bileaflet mechanical heart valve under physiological conditions. The

simulations were carried out for both loose and strong coupling strategies. The FSI approach

was validated by comparing the results with those obtained from benchmark simulations and

experimental data, where the results showed excellent agreement. However, it was noted that

under certain conditions the FSI simulation became unstable even when a strong coupling

scheme was employed. It was also suggested that for such a case, the instability problem can be

effectively improved by a combination of strong coupling with under relaxation and with

73

Aitken’s acceleration technique. This framework was further extended by (Borazjani, 2013) to

simulate a flexible leaflet heart valve under a physiological condition. The FSI solver was also

verified against experimental data as well as benchmark numerical data which showed a good

qualitative agreement.

In conclusion, each of the mentioned methods has been extended to three dimensions

of FSI simulations of PHVs with flexible leaflets. However, ALE approaches with a dynamic

re-meshing method showed superior performance which has been extensively and successfully

used for FSI problems. The main disadvantage associated with this technique is the need for the

expensive re-meshing method and computational cost. However, the effect of this drawback has

been reduced with current developments and advancements in the field of computational

hardware. Hence, in the current study, the proposed design of the valve was modelled in a

strongly coupled FSI scheme using the dynamic re-meshing method as described in the

following sections.

4.4 FSI Method

The FSI analysis was carried out by strongly coupling ANSYS Fluent (Participant 1)

to ANSYS dynamic structural (Participant 2) in an iterative sequential algorithm which was

managed by the system coupling component in ANSYS. The arbitrary Lagrangian-Eulerian

(ALE) method was used by means of the dynamic mesh model in Fluent to model the blood

flow past the valve. In the two-way coupled FSI, the source and target regions were defined on

both participants and data was transferred in both directions between the participants, in which

the solid-fluid interface region in the Fluent system was the source region for the transfer of

force, and the target region for the transfer of displacement. Similarly, the solid-fluid interface

in the dynamic structural system was the source region for the transfer of displacement and the

target for the transfer force. At the first coupling time step, boundary conditions were applied to

the Fluid domain (source), then calculated forces acting on the solid-fluid interface region were

mapped and interpolated to the structural mesh (target). Subsequently, imported forces into the

structural solver were set as a new boundary condition for the structural solver. Then, the

calculated mesh deformations and displacements in the structural solver (source) were mapped

and interpolated to the fluid mesh (target). Data transfers in system coupling used profile-

preserving data transfer algorithm when transferring a non-conserved quantity (displacement)

and the conservative profile preservative data transfer algorithm when transferring a conserved

quantity (Force). For the first data transfer algorithm, mapping weights are generated by the

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Bucket Surface mapping algorithm. As illustrated in Figure 4.1, the target side mesh nodes are

mapped onto the mesh element on the source side. The final data applied on the target side of

the interface is evaluated by a standard, weight based interpolation and subsequent under-

relaxation.

Figure 4.1. Mapping target node to source element, values are the result of the interpolation (ANSYS System coupling User's Guide, 2013).

For the latter data transfer algorithm, the mapping weights are generated by the

General Grid Interface (GGI) mapping algorithm as explained in the ANSYS coupling system

user guide (2013).

The data transfer algorithms noted above have the following components:

- Data pre-processing: This encompasses the formation of the supplemental data on mesh

locations needed by mapping and interpolation algorithms.

- Mapping: In this process, the weights are generated by the pairing of a source and a

target location (e.g., displacements in a fluid-solid interaction problem are received by

mapping a fluid node to a solid element). Equally, a Gauss point (solid node) in a solid

element must be mapped to a fluid element to receive the stress.

- Interpolation: The generated weights are used or reused to project source data onto a

target location.

- Interpolated Data Post-Processing: This encompasses explicit under-relaxation, clipping

and ramping of the target data. It also involves the creation of supplemental data on

mesh location required by the consumer of the interpolated target data.

The interpolation algorithm is responsible for providing target node values using the

source data and mapping weights that were generated by the mapping algorithm. The mapping

weights are applied in Equation 4.1 to evaluate , which is the target node, or iteration point

(IP) face value.

75

Equation 4.1. Interpolation algorithm.

∑

where

value at the source node

d associated weight

is dependent on the type of mapping algorithm used. For the surface mapping algorithm and

weights obtained via GGI mapping, it is the number of nodes in the source element or the

number of areas acquired due to the intersection of the sender and receiver faces on the control

surface, respectively. For situations in which the number of coupling iterations is greater than

one within a coupling step, post-processing of the interpolated data is required before being

exposed to the data transfer target participant. The main options that can be applied to the target

data generated during the interpolation are ramping and under-relaxation. However, the

mentioned optional algorithms are not used in the current simulation.

4.4.1 Coupling Management

System Coupling primarily manages the coupled analysis. This involves three aspects:

- Inter-Process Communication

- Process Synchronization and Analysis Evolution

- Convergence Management

4.4.1.1 Inter-Process Communication

This aspect is employed when the coupling service and participants are executed as

independent computational processes. This is actualized by the use of a proprietary,

lightweight, TCP/IP based client-server infrastructure in order to avoid interaction with other

communication mechanisms e.g. Message Passing Interface (MPI). The necessary high-level

communication required for process synchronization, managing convergence and brokering

data transfers between the coupling service and participants are defined in terms of APIs

(Application Programing Interface). The APIs make use of the low-level IPC infrastructure.

76

4.4.1.2 Process Synchronization and Analysis Evolution

There is synchronization between the coupling service and participants and thus, they

advance together throughout the coupled analysis. Synchronization points are used to manage

high-level synchronization while low-level synchronization is managed by the use of the token-

based protocol. In Figure 4.2, the synchronization points in bold typeface denote a gateway.

Note that no particular process advances past the gateway until all other processes are present.

Figure 4.2. Execution sequence of the coupling service (ANSYS System coupling User's Guide, 2013).

77

Figure 4.3. Processing detail of the coupling system (ANSYS System coupling User's Guide, 2013).

From the information provided in Figure 4.2 and Figure 4.3, it is worth noting that all

the participants traverse the whole coupling step during the coupling iteration. They can also

traverse the coupling step duration in more than one solver step, which may contain one or

several iterations. Sub-stepping occurs when many solver steps are used within one coupling

step. This is also called sub-cycling.

4.4.1.3 Evaluating Convergence of Data Transfers

The iterations are measured against each other, i.e. each iteration is measured against

the previous iteration in order to evaluate data transfer convergence by which the changes of all

data transfer values are normalized. If the normalized value received is under the set target for

convergence, then the data transferred is converged.

The global measures of convergence calculated are:

Root Mean Square (RMS)

78

This is the default measure employed in determining convergence. At the end of each

coupling iteration, the current coupling step convergence is evaluated. The iteration is such that

if there is no convergence, a new coupling iteration is started, and if there is convergence, a

new coupling step is started.

Equation 4.2. RMS formula.

√

where

= Normalized change in the data transfer value.

Equation 4.3. Normalized change in the data transfer.

| | | | | |

where

is the data transfer value.

l is the location of the data transfer on the coupling interface.

The denominator in the above equation is the normalization factor and is equal to the average of

the range and mean of the magnitude of data transfer values over all locations for the current

iteration in the transient coupling case.

In Equation 4.3, the numerator, is the un-normalized change between successive iterations,

and is expressed as:

Equation 4.4. The un-normalized change between successive iterations.

where

____ and

___ correspond to the current and the previous iterations respectively

_is the under-relaxation factor applied in forming the final value applied during the current

iteration.

79

In the first coupling iteration of every coupling step, is assumed to be unity.

When there is no change in data transfer values, the default for RMS/MAX is 1.0e-014.

Figure 4.4. Schematic view of the two-way strongly coupling FSI flow chart.

4.5 Material properties and effect of nonlinearity

As discussed in Chapter 2, various synthetic polymers have been investigated in

experimental and numerical studies for use in PHVs. Biomedical grade PU-based polymers

demonstrated good qualities in terms of biostability, biocompatibility, fatigue and flexibility in

which the thermoplastic polycarbonate urethane known as Bionate® is among the most

extensively tested biomaterial and is backed by a comprehensive FDA master file such as

master file MAF844. Bionate® polymer is capable of large deformations, and it is classified as

an isotropic incompressible hyperelastic material (Nic An Ghaill and Little, 2008). Malvern

(1969) showed that for hyperelastic material, the recoverable strain energy density with respect

to the initial configuration can be described as a function of the principal invariants of the

80

Cauchy-Green deformation tensor. In this respect, there are a number of strain energy density

functions that ANSYS (by release 15) supports, such as Mooney-Rivlin, Yeoh, and Ogden

material models. It has been previously shown (Nic An Ghaill and Little, 2008) that the

experimental uniaxial and biaxial data curve of Bionate® 80A fits very closely to the three-

parameter Monney-Rivlin model with material constant of = -3.63 MPa, =7.32 MPa,

and =-5.23 MPa. Hence, the mentioned strain energy density function and material constants

are used in the present study as the structural material of the leaflets and the density is assumed

to be 1190 kg/ .The strain energy density function W is:

Equation 4.5. Strain energy density function in the three-parameter Mooney-Rivlin formula.

( ) ( ) ( ) + D

where

, and are three material constants,

and are the invariants of the Cauchy–Green deformation tensor

D is incompressibility parameter (the value of D was assumed 0 in respect to the material

volumetric response)

The polyether ether ketone (PEEK) polymer has been used in a number of studies on stents and

showed good mechanical properties to withstand the cyclic load (Leat and Fisher, 1994,

Wheatley et al., 2000). Hence, 450G polymer material is defined for the valve stent with

density of 1320 kg/ , Young’s modulus of 4.6 GPa, and Poisson’s ratio of 0.38 (Rae et al.,

2007).

81

4.6 Boundary Conditions

4.6.1 Fluid domain

Fluid (blood) is assumed to be incompressible and Newtonian with a constant viscosity

of 0.004 kg/m-s and a density of 1060 kg/m3. The Newtonian rheology assumption for this type

of simulation is a valid approach as there is no significant difference between shear stress

calculated from non-Newtonian and Newtonian simulation (Vasava et al., 2012). In order to

apply the boundary conditions, the Wiggers diagram (Figure 4.5) was used to determine the

functions of the aortic and left ventricular pressure. Note that the data presented is based on 60

beats/min heart rate and mean flow rate of 5 l/min.

Figure 4.5. The Wiggers diagram showing two cardiac cycle events occurring in the left

ventricle (Franzone et al., 2012).

82

The Wiggers diagram was first imported into AutoCAD in order to add the x-axis

(time scale) and y-axis (pressure scale) to the figure accordingly. The modified figure then was

imported into MATLAB to extract the data and perform the curve-fitting analysis. Figure 4.6

shows the AP and VP curves obtained from the curve fitting analysis overlaid on the AP, and

the VP curves of the original Wiggers diagram. Note that VP was assumed to be zero after is

volumetric relaxation as the original VP for this period is nearly zero and the difference is

negligible. The ventricular pressure curve from the Wiggers diagram was divided into two

sections in order to obtain the best possible fitted curve as follows:

Equation 4.6. VP function in mmHg unit.

{

The VP function was then adapted for the Pascal unit and applied into the inlet region for the

simulation.

Equation 4.7. VP function in the Pascal unit.

{

Similarly, the AP curve from the Wiggers diagram was divided into four sections and the

functions obtained from the curve fitting analysis are as follows:

Equation 4.8. AP function in the mmHg unit.

{

83

Equation 4.9. AP function in the Pascal unit.

{

Subsequently, AP (Equation 4.9) was applied on the aortic side of the valve for the simulation.

Figure 4.6. Curve fitting to the Wiggers diagram.

84

4.6.2 Solid domain

Arteries and sinus of valsalva walls were assumed to be rigid with no slip condition.

The ventricular side of the stent was fixed for both references and the proposed prosthetic heart

valves. As previously discussed, contact regions were assigned by contact elements between the

leaflets themselves and between the leaflets and the stent. In this respect, the frictionless contact

condition was applied to the ventricular side of the adjacent leaflets, and the bonded contact

type was assigned between the leaflet and the stent for all valves. These sections are

characterized by restricting interpenetrations between the surfaces, together with an allowance

of transferring comprehensive normal and tangential friction forces. The contact type is the

main determinant of how the contacting bodies move about one another. It is the most

important parameter in the contact definition. This type models the gaps, and it models more

precisely the true area of contact. When contact and the target surface are constrained from

penetrating into each other, the symmetrical behaviour is presumed.

In the subsequent stages, the contact formulation is defined, with respect to the physics

of the problem and surface material. Contact algorithms available in the ANSYS structural

analyser include:

- Pure Penalty

- Augmented Lagrange

- Normal Lagrange, and

- Multi-Point Constraint (MPC)

The Pure Penalty method is used for nonlinear contact surfaces. In this case, the contact force is

evaluated based on the elastic spring, as follows:

F normal = k normal × X penetration.

where

k normal = Normal contact stiffness

X penetration= Amount of penetration

The rate of convergence of the solution and the accuracy of the contact force are influenced by

the normal stiffness factor. However, the surfaces bounce off each other due to oscillation thus

affecting solution convergence. It is highly recommended that the value of the normal stiffness

85

factor should be selected within the range of 0.01 up to 0.1 for bending dominant problems.

Hence, the manual contact stiffness factor is initially presumed to be 0.1 for all the contact

surfaces with an automatic update at all equilibrium iterations.

The implementation and updating of the Pure Penalty algorithm on different nodes is

done while the leaflets are displaced dynamically. Checking contact detected points and target

area movement is essential during the solution process. Contact formulation was reached due to

the closeness of surfaces compared to pinball. It should also be noted that the pinball region is

the sphere that surrounds the contact nodes and the target surface. Table 4.1 and Table 4.2 show

a summary of the contact status and detected contact points after applying the optimum settings

to the leaflets and the stent regions.

Table 4.1. Summary of initial contact status and contact detection for the proposed PHV.

Name Contact

Side Type Status

Penetration

(mm)

Gap

(mm)

Geometric

Penetration

(mm)

Geometric

Gap (mm)

Resulting

Pinball

(mm)

Leaflet (1) to

Leaflet (2) Contact Frictionless

Near

Open 0. 0.12294 0 0.12294 0.24582

Leaflet (1) to

Leaflet (3) Contact Frictionless

Near

Open 0. 0.12296 0. 0.12296 0.24587

Leaflet (2) to

Leaflet (3) Contact Frictionless

Near

Open 0. 0.12297 0. 0.12297 0.24587

Leaflet 1

(attachment

surface) to Stent

Contact Bonded Closed 7.4088e-015 0. 2.8478e-004 3.4275e-004 6.6356e-002

Leaflet 2

(attachment

surface) to Stent

Contact Bonded Closed 7.5339e-015 0. 3.4081e-004 3.3201e-004 6.6361e-002

Leaflet 3

(attachment

surface) to Stent

Contact Bonded Closed 6.2761e-005 0. 3.5401e-004 3.4531e-004 6.6362e-002

86

Table 4.2. Summary of initial contact status and contact detection for the reference valve.

Name Contact

Side Type Status Penetration(mm) Gap(mm)

Geometric

Penetration(mm)

Geometric

Gap(mm)

Resulting

Pinball(mm)

Leaflet (1) to

Leaflet (2) Contact Frictionless Near Open 0. 4.4704e-002 0. 4.4704e-002 0.23938

Leaflet (1) to

Leaflet (3) Contact Frictionless Near Open 0. 4.4841e-002 0. 4.4841e-002 0.23916

Leaflet (2) to

Leaflet (2) Contact Frictionless Near Open 0. 0. 4.4702e-002 4.4702e-002 0.23954

Leaflet 1

(attachment

surface) to

Stent

Contact Bonded Closed 4.7403e-005 0. 7.447e-00 1.3416e-004 0.11352

Leaflet 2

(attachment

surface) to

Stent

Contact Bonded Inactive 3.8321e-005 0. 7.4472e-005 1.3416e-004 0.11325

Leaflet 3

(attachment

surface) to

Stent

Contact Bonded Closed 3.8483e-005 0. 7.447e005 1.3416e-004 0.11325

4.7 Governing Equations

In the following section, the governing equations of the fluid and solid domains are

explained as it is necessary to understand the physics of the problem in order to choose the

correct solver and setting. This section explains the following:

- The instantaneous equations solved in the fluid-structure interaction (FSI) analysis of

the prosthesis

- The governing equations for each solver;

- The algorithm for the synchronization at the interface

- The complementary assumptions described as solver key parameter settings to ensure

the accuracy of the simulation and the validation of results.

It is noteworthy to indicate that the source of information used in this section is

derived from the ANSYS CFX Theory Manual with major references for Sections 4.5.1 being

the ANSYS Mechanical APDL Theory Manual and the published work presented by Renaud

(Renaud, Cros et al. 2009) and Feng (Feng, Peyraut et al. 2003). Previous discussions have

87

explained the structural analysis of the heart being undertaken within the finite element

framework in the ANSYS mechanical module. Discretization of the large displacement and

deformation of the leaflets was done using the Lagrangian Multiplier Method. The contact

analysis, on the other hand, was done using the Pure Penalty formulation. The governing

equations were divided into two sections, the Fluid domain and the Solid domain, for a better

understanding as detailed in the following sections.

4.7.1 Fluid Domain Governing Equations

The pressure-based coupled algorithm (Figure 4.7) is used to solve a system of

momentum and pressure-based continuity equations simultaneously as it produces a more

robust and accurate solution.

Figure 4.7. Overview of the pressure-based coupled algorithm.

Fluent solves the Navier-Stokes equations (Equation 4.10) for the transport of mass,

momentum, species and energy when the flow is laminar. In the case of turbulent flow,

additional transport equations are solved such as Reynolds Averaged Navier-Stokes (RANS)

with the realizable k-

88

Equation 4.10. Transport equations.

{

∑

where

is fluid density,

U denotes fluid velocity,

F represents external body force,

is stress tensor,

is the effective conductivity

(k+ , where is defined according to the chosen turbulent model),

is the diffusion flux of species j,

represents the heat of chemical reaction or any kind of heat source,

E calculated as

, and sensible enthalpy h for incompressible flow calculated as

∑

is the mass fraction of species j and

∫

).

89

ANSYS Fluent uses the finite volume (FV) numerical technique to solve the governing

equation by the volumetric division of the computational domain and converting the general

form of the scalar transport equation into an algebraic system that can be solved numerically.

The transport equations for each control volume yield to a discrete equation, which is based on

the conservation law on the controlled volume. Discretization of the governing equations can be

illustrated most easily by considering the unsteady conservation equation for transport of a

scalar quantity . This is demonstrated by the following equation written in integral form for an

arbitrary control volume V as in equation 4.11 where the left-hand side contains the rate of

change and convective terms and the right-hand side contains the diffusive and source terms.

Equation 4.11. Discretization of the governing equations.

∫

∮

∮ ∫

where

is density

is surface area vector,

is diffusion coefficient for ,

is source of per unit volume,

is gradient of ,

is velocity vector.

With respect to the dynamic mesh incorporated in the current simulation, for a general scalar ,

an arbitrary control volume, V, whose boundary is moving can be written as follows:

Equation 4.12. Discretization of the governing equations with respect to dynamic mesh.

∫

∫

( ) ∫

∫

It is noted that in the above equation, represents the boundary of the control volume V.

When equation 4.12 is applied to each cell in the fluid domain, the discretization of this

equation on a given triangular cell would yield:

90

Equation 4.13. Discretization of equation 4.12 on a triangular cell in 2D.

∑

∑

where

is number of faces enclosing cell,

is value of convected through face f,

is mass flux through the face,

is area of face f,

is gradient of at face f,

V is cell volume.

It should be noted that

is defined in temporal discretization.

As the simulation is transient, it is necessary to discretise the governing equation both in space

and time. For the spatial discretization, the discrete value of the scalar is stored at the centre

of the cell. Nonetheless, Equation 4.13 involves which must be interpolated from cell centre

values as shown as follows:

Equation 4.14. Second-Order Upwind scheme.

where

and and are the cell-centred values,

is the displacement vector in respect to upstream cell centroid to the face centroid.

The gradient of the scalar in each cell is calculated based on Green-Gauss theorem at the cell

centre as follows:

91

Equation 4.15. Gradient of at the cell center.

∑

For temporal discretization, every term is integrated into the differential equation over a time

step t. The transient terms are integrated as shown as follows:

Equation 4.16. Transient term integration.

Here, the time derivative is discretized using second order backward differences is:

Equation 4.17. Second order derivative.

where

t+

The choice for evaluating still remains after discretization of the time step. A choice has to be

made regarding the time level values of to be used for computing F. In the current simulation,

implicit time integration is used to evaluate ) as follows:

Equation 4.18. Implicit time integration.

This is referred to as “implicit” integration since in a given cell is related to in

neighboring cells through :

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Equation 4.19. Implicit time integration.

This implicit equation can be solved iteratively at each time level before moving to the

next time step. The advantage of the fully implicit scheme is that it is unconditionally stable

with respect to time step size.

Although turbulence flow can be modelled by the Navier-Stokes equation by taking

turbulence into account, in this simulation, Reynolds Averaged Navier-Stokes (RANS) with the

realizable k- is incorporated as it is a reliable turbulence model for this type of simulation

(Scott et al., 2013). It holds two additional transport equations where turbulence kinetic energy

(k) and turbulence dissipation rate ( ) were solved to model the turbulence flow. The transport

equation for (k) and ( ) are as follows:

Equation 4.20. The epsilon equation.

( )

[

]

and

Equation 4.21. The K equation.

( )

[

]

√

Where [

] ,

, √ ,

,

,

, √

,

In the above equations,

and are constant,

and are the turbulent Prandtl numbers for K and respectively.

T is the absolute temperature,

is the adiabatic index,

R is the Molar gas number,

and are the user-defined source term,

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indicates the generation of turbulence kinetic energy due to the mean velocity gradient,

is the generated kinetic energy due to buoyancy

4.7.2 Solid Domain Governing Equation

Since the structural domain is fully coupled with the transient fluid forces, the FE

semi-discrete equation of motion can be described as follow:

Equation 4.22 Equation of motion for non-linear structural analysis

[ ]{ } [ ]{ } [ ]{ } { }

Where [M] is structural mass matrix, [C] is structural damping matrix, is internal load

vector, { } is nodal acceleration vector, { } is nodal velocity vector, { } is nodal displacement

vector, and { } is applied load vector.

ANSYS Mechanical provides three methods of numerical integration for solving Equation 4.22:

Central difference time integration method which is for explicit transient analyses only.

Newmark time integration method

Hilber-Hughes-Taylor (HHT) time integration method, this method is an extension of

the Newmark time integration method.

Both of Newmark and HHT methods are suitable for implicit transient analyses,

however, HHT method allows second order accuracy which is not possible with the Newmark

method. Hence, HHT method is used in the current study. In addition, this method showed

previously (Kouhi, 2012) to provide robust simulation of large deformation. For more

information, refer to the ANSYS mechanical APDL Theory Reference (ANSYS Mechanical

APDL Theory Reference, 2013).

94

4.8 Theory of elements

As mentioned in section 4.7, the ANSYS Fluent was used to mesh the fluid domains,

using the element-based finite volume method, where the spatial domain is discretised using a

mesh to construct finite volumes. The mesh can be created with four different element types,

namely Tetrahedron, Hexahedral, Pyramid, and Wedges elements in the 3D model as shown in

Figure 4.8. In general, the selection of the mesh type is highly dependent on the application in

addition to setup time, computational effort and numerical diffusion. The proposed valve and

also the reference valve both exhibit complex geometries. Subsequently, creating a structured

mesh with quadrilateral or hexahedral elements for such geometries is extremely time-

consuming. However, excellent mesh quality can be achieved as described in section 4.7 by

using unstructured grids employing tetrahedral elements. It should be noted that a complex

geometry can be meshed using a tetrahedral element with significantly fewer cells compared

with the equivalent mesh consisting of hexahedral elements which could result in less

computational effort. Numerical diffusion can be minimized when the flow is aligned with the

mesh, but in the case of using tetrahedral mesh, it is impossible to align the flow with the grid.

However, for such a complex flow past through the valves, even structured hexahedral mesh

can never be aligned with the flow. Hence, unstructured four node-tetrahedral elements were

selected for both the fluid domains.

Figure 4.8. Schematic of element types.

95

According to the Mechanical APDL user guide, SOLID185 (3D 8 node structural

solid, DOF: UX,UY,UZ), SOLID186 (3D 20 node structural solid, DOF: UX,UY,UZ),

SOLID272 (4 to 48 node axisymmetric solid, DOF: UX,UY,UZ), Solid273 (8 to 96 node

axisymmetric, DOF: UX,UY,UZ), and SOLID285 (3D 4 node Tetrahedral structural solid,

DOF: UX,UY,UZ, Nodal hydrostatic pressure) can be used for hyperelastic materials.

However, due to the geometry complexities of the valves, a good quality grid could not be

achieved by the brick elements (SOLID185, and SOLID186), and the axisymmetric elements

(SOLID272, and SOLID273). Similarly, meshing the solid domains associated with the stent

geometries using SOLID285 elements showed a better mesh quality. The disadvantage of using

four node elements could be inadequate accuracy for the bending domain; however, this issue is

addressed by incorporating high mesh density in high bending regions. The statistical analysis

of the mesh quality for the both solid domains is given in Figure 4.12, and Figure 4.13.

Consequently, SOLID285 was used to mesh the solid domains. The SOLID285 element is

defined by four nodes, each of which has four degrees of freedom: three translation degrees of

freedom (x, y, and z directions), and one nodal hydrostatic pressure (HDSP) for all materials. In

the case of nearly incompressible hyperelastic material, the volume change rate is used instead

of hydrostatic pressure. In addition, this element has plasticity, hyperelasticity, creep, stress

stiffening, large deflection and large strain capabilities. The CONTA173 element was used

along with TARGET170 target surface element to define the contact between surfaces that

could be in contact during the simulation. The CONTA173 element has three translation

degrees of freedom (UX, UY, UZ) and it had the same geometric characteristic as the

underlying element (SOLID285 in the current simulation). A set of target segment elements

(TARGET170) was used to discretise the target surface that is paired with the contact surface

by a shared real constant set. The detail of the contact settings and the configuration of the

contact regions is given in the following section.

4.8.1 Meshing and element configurations

It is well known that mesh quality plays a crucial role in FE/FV applications as it has a

significant effect on the solution accuracy as well as the efficiency of the simulation and

computational effort. Hence, the solid and fluid domains must be discretised cautiously

according to the physics of the problem. The following sections provide specific details of the

discretisation process for each of the solid and the fluid domains.

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(a) (b)

4.8.1.1 Fluid domain, meshing strategies, and mesh independence study

The fluid domain is defined according to a patient’s SOV from the measurements

provided in Table 3.2 The generated fluid domain was then altered for each of the proposed

PHV and the reference valves, and is named Fluid PHV and Fluid Ref, respectively. FluidPHV and

Fluid Ref were constructed by subtracting the geometries of the proposed PHV and the reference

valve accordingly from the initial fluid domain.

It is well known that the accuracy of the CFD solver is highly dependent on the quality

of the mesh introduced to the computational domain. In general, based on the aspect ratio,

skewness, and smoothness of the grid, the suitability of the mesh can be determined.

The process of meshing for both fluid domains was commenced by categorising each

of the FluidPHV and Fluid Ref domains into five distinct regions: inlet, outlet, SOV walls, stent

walls, and the leaflets (see Figure 4.9) in order to apply different mesh densities and boundary

conditions. Basically, a high density mesh is required in the region of interest to capture all the

flow features. However, excessive mesh refinement could lead to unnecessary computational

time. It is a challenging task to obtain an optimum mesh density which will result in an accurate

solution. In this respect, it is a common practice to perform a mesh independence study to

obtain a numerical solution which is invariant with the finer mesh.

Figure 4.9. Sectional view of the fluid domains (a) FluidRef, and (b) FluidPHV.

97

As described in the FSI method, the displacement of the structure was mapped and

interpolated into the fluid mesh in all coupling iterations. Hence, this displacement is large

compared to the local cell sizes and the call quality would deteriorate or degenerate. This could

result in invalidating the mesh and cause convergence issues when the solution is updated to the

next step. To address this problem, the dynamic mesh function with a local re-meshing method

was selected in Fluent. In this method, cell skewness and minimum or maximum length scales

of each cell were marked for re-meshing if they did not meet one or any combination of the

following criteria:

- The cell skewness becomes greater than a specified maximum skewness

- The cell is smaller than a specified minimum length scale

- The cell is larger than a specified maximum length scale

- The cell height does not meet the specified length scale

The optimum mesh density and element quality were determined by performing a

mesh independence study as well as statistically analysing the element quality, aspect ratio and

skewness of the grid. Mesh independence studies were conducted for both domains with

varying element sizes for one cardiac cycle, as demonstrated in Table 4.3 and Table 4.4, where

higher mesh density was selected for the region of interest (solid-fluid interface) and local mesh

refinement was conducted to achieve high mesh quality. Consequently, the model that had less

than 5% variation (see Equation 4.27) in the calculated maximum WSS in the Fluid-Solid

interface was selected to be used in the FSI simulation. Consequently, the FluidPHV domain was

modelled with 1,074,418 elements (See Figure 4.10), and the FluidRef domain was modelled

with 1, 160, 661 elements, as shown in Figure 4.11.

Equation 4.23. Variation percentage of WSS.

where n is the simulation number and τ denotes the maximum WSS.

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Figure 4.10. FluidPHV domain discretization with tetrahedral elements. (a) Side view of the fluid domain with positions of inlet and outlet, (lv =16 mm, and lo=57 mm) (b) Top view (downstream) of the fluid domain.

Figure 4.11. FluidRef domain discretization with tetrahedral elements. (a) Side view of the fluid domain with positions of inlet and outlet, (lv =16 mm, and lo=57 mm) (b) Top view (downstream) of the fluid domain.

(a) (b)

(a) (b)

99

Table 4.3. Mesh independence study of the Fluid PHV domain.

Table 4.4. Mesh independence study of the fluid domain Fluid Ref domain.

Simulation

Number

Main body

min-max

size(mm)

Solid-Fluid

Interface

Min-Max

size (mm)

Total

elements

Maximum Wall

shear stress in the

interface

Variation

in (%)

Case 1 0.188-4.41 0.01724-0.75 441,061 165 10.56

Case 2 0.01724- 4.41 0.01724-0.5 526,162 159.36 6.7

Case 3 0.011-1 0.011-0.5 588,284 151.69 1.64

Case 4 0.011-1 0.011-0.25 1,160,666 149.343 0.07

Case 4 0.011-1 0.011-0.2 1,602,291 149.343 -

Simulation

Number

Main body

min-max

size (mm)

Solid-Fluid

Interface

Min-Max size

(mm)

Total

elements

Maximum Wall

shear stress in the

interface

Variation in

(%)

Case 1 0.188-3.00 0.188-0.4 160,758 165 10.56

Case 2 0.188-2.00 0.188-0.2 212,661 159.36 6.7

Case 3 0.0188-1.00 0.0188-0.1 1,074,428 151.69 1.64

Case 4 0.0188-0.9 0.0188-0.05 1,180,560 149.343 0.07

Case 5 0.0188-0.8 0.0188-0.025 1,443,515 149.23 -

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Furthermore, mesh quality was examined for each of the mesh independence studies.

Figure 4.12 and Figure 4.13 show the statistical analyses of the selected meshes for Fluid PHV

and Fluid Ref domains, respectively. As shown in Figure 4.12a, an element quality ranging

between 0.142 and 0.99 with an average of 0.886 was achieved. The element quality metric

represents the ratio of the element volume to its edge length, where the value of 1 indicates a

perfect triangle shape while the value of 0 indicates that the element has a zero or negative

volume. The low magnitude of standard deviation (0.088) also shows minimized variations in

the element quality of cells from the average element quality. Similarly, a high element quality

ranging between 0.419 and 0.99 with an average of 0.8310 and a standard deviation of 0.0926

was achieved for the Fluid Ref domain (see Figure 4.13a). Aspect ratio is another indicator of

mesh quality which is a measure of the stretching of a cell. It is calculated as the ratio of the

longest element edge to the shortest element edge, and the best possible triangle aspect ratio is 1

for an equilateral triangle. In general, it must be less than 100 and a higher aspect ratio could

result in convergence issues. The average aspect ratio of FluidPHV mesh was reported as 1.691

with a standard deviation of 0.324 (Figure 4.12b) and average aspect ratio of 1.867, and a

standard deviation of 0.488 was achieved for the Fluidref mesh (see Figure 4.13b). Importantly,

the skewness of the mesh element was examined for the both domains. It is one of the primary

measures of mesh quality and shows how close the mesh cells are to ideal. Skewness of the

tetrahedral element is defined as:

Equation 4.24. Equilateral-Volume-based skewness.

where the optimal cell size is defined as the size of an equilateral cell with the same

circumradius. According to the ANSYS® mesh user guide, mesh with a skewness value of less

than 0.4 is assumed to be a quality grid, and skewness of less than 0.25 indicates an excellent

quality grid. The average skewness of 0.138 with a standard deviation of 0.13 was reported for

FluidPHV mesh, as shown in Figure 4.12c. A low average skewness of 0.23 with a standard

deviation of 0.123 was also reported for FluidRef mesh (see Figure 4.13c). As the above

statistical analysis of the mesh quality showed excellent results for each of the quality

measures, it is determined that acceptable mesh quality was achieved for both fluid domains.

101

(a)

(b)

102

Figure 4.12. Mesh statistics for the FluidPHV domain (a) quality, (b) aspect ratio and (c) skewness.

(c)

(a)

103

(b)

(c)

Figure 4.13. Mesh statistics for the FluidRef domain (a) quality, (b) aspect ratio and (c) skewness.

104

4.8.1.2 Structural domain and mesh independence study

The reference valve and the proposed PHV were modelled in Solidworks® and

imported into the ANSYS ® transient structural component. Bionate® and PEEK polymers

were defined as the leaflets and the stent materials. All faces of the leaflets (except where the

leaflets attached to the stent) were categorised as an interface region, and a solid-fluid interface

element type was applied. In addition, the frictionless contact condition was applied to the

ventricular side of the adjacent leaflets and the bonded contact type was assigned between the

leaflet and the stent for all valves. The tetrahedron element was used to discretise the solid

domains. Similarly, the mesh independence studies were conducted for both valves, as shown

in Table 4.5 and Table 4.6, and the model that had less than 5% variation in the calculated

maximum Von Mises stress in the leaflets was selected to be used in the FSI simulation.

Consequently, the proposed PHV and the reference valve were modelled with 30,895, and

22,453 elements, respectively as shown in Figure 4.14. Similarly, the quality of the meshes was

statistically analysed, as shown in Figure 4.15 and Figure 4.16. All the quality measures

(element quality, aspect ratio, and skewness) had excellent values. These results confirmed the

mesh strategy was suitable and showed that the solid domains had acceptable mesh quality.

Table 4.5. Mesh independence study of the reference valve.

Simulation

Number

Leaflet

Element

size (mm)

Stent

element

size (mm)

Total

elements

Maximum

stress in

diastole

(MPa)

Variation in

percentage

(%)

Case 1 1 1 7,809 7.63 7.49

Case 2 0.75 0.75 15,747 7.51 5.80

Case 3 0.60 0.60 30,895 7.49 3.9

Case 4 0.5 0.5 51,794 7.102 0.05

Case 5 0.4 0.4 105,094 7.098 -

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Table 4.6. Mesh independence study of the optimized valve.

Simulation

Number

Leaflet

Element

size(mm)

Stent

element

size

(mm)

Total

elements

Maximum

stress in

diastole

(MPa)

Variation in

percentage

(%)

Case 1 1 1 6,009 5.81 9.3

Case 2 0.75 0.75 11,095 5.675 6.79

Case 3 0.60 0.60 22,453 5.575 4.9

Case 4 0.5 0.5 36,253 5.321 0.13

Case 5 0.4 0.4 76,450 5.314 -

Figure 4.14. Discretization of (a) the optimized valve, and (b) the reference valve.

(a) (b)

106

(a)

(b)

107

Figure 4.15. Mesh statistics for the optimized valve (a) quality, (b) aspect ratio and (c)

skewness.

(c)

(a)

108

Figure 4.16. Mesh statistics for the reference valve (a) quality, (b) aspect ratio and (c) skewness.

(b)

(c)

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4.9 Hydrodynamic evaluation methods

As blood passes through the valve orifice area, the flow stream starts necking down or

contracting just downstream of the geometric orifice area (GOA). The contraction of the flow

stream continued to reach its minimum at a point called vena contracta (VC), and further

downstream of VC, the flow starts expanding to the outlet size. EOA is defined as the cross-

sectional area of VC as shown in Figure 4.17.

Figure 4.17. Schematic representation of EOA and GOA.

Theoretically, EOA can be calculated from either the Gorlin formula ( ) or

continuity equation ( ). However, a comparative study showed discrepancy in the

calculated EOA using these methods (Rudolph et al., 2002). Alternatively, the EOA or VC

cross-sectional area of the left ventricular outflow tract (LVOT) can be measured in the FSI

simulation. When the GOA of the valve reached its maximum, the location of the VC was

accurately determined in the Fluent software. Subsequently, EOA was calculated by measuring

the area of the VC cross-section at peak systole.

The difference between the mean pressure at VC and LVOT during systole was considered as

the transvalvular pressure drop ( ) (Kouhi, 2012). was calculated from Equation 4.28

based on the law of conservation of energy.

Equation 4.25. Transvalvular Pressure drop.

)

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where 𝝆 is blood density and and are the mean blood velocity at the inlet and at VC,

respectively. Note that Equation 4.28 is derived from the Bernoulli equation with the

assumption that the viscous effect of blood is negligible. This assumption does not alter the

result as the boundary formation is only considered at the vicinity of the wall (Vandervoort et

al., 1995). Furthermore, the left ventricular energy loss during systole was calculated as the

time integral of the product of the mean pressure drop and left ventricular outflow (Akins et al.,

2008) as follows:

Equation 4.26. Left ventricular energy loss.

∫

4.10 Optimization Process

As described in section 3.5.2, an additional circumferential curve (lꞌc) was

incorporated in the design. It was assumed that b=1mm and then varying values of a

corresponding to the asymptote angles ranging from 120° to 125° were examined in the FSI

simulation. Consequently, six valves were modelled to be analysed. It should be noted that

further increasing the asymptote angle was not considered due to geometrical constraints.

Figure 4.18 shows the flow chart of the optimization process.

Figure 4.18. The optimization process diagram.

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5 Chapter 5 The valve construction and experimental setup

5.1 Overview This chapter provides information about the experimental equipment and procedures

used to collect the data presented in this dissertation. In addition, a new advanced

manufacturing technique is introduced to construct the valve. The aim of this chapter is to

define the most suitable technique to validate the numerical results, taking into account the

constraints related to infrastructure available at the Swinburne University of Technology.

5.2 Introduction Experimental approaches: Developments and Limitations

In developing a bioprosthetic heart valve, an evaluation of the haemodynamic and

structural performance of the valve should be undertaken as part of the design verification

process. The key factors including pressure drop across the valve, EOA, blood jet stream

profile, flow turbulence, thrombosis, haemolysis and the durability of the valve must be

evaluated thoroughly before the clinical trial. In addition, studies on thromboembolic

complication associated with PHVs showed physical forces (shear stresses) applied on the

blood platelet cells will initiate the platelet activation, aggregation, and activate coagulation

cascade leading to thrombus formation. It is suggested by Brown et al. (1975) that the

platelets are extremely sensitive to shear stress; even low shear stress of 5 Pa could initiate

platelet activation. However, a more accurate threshold of 3.5 Pa.s known as Hellums criteria

(Hellums et al., 1987) suggests that platelet exposure time to the stress as well as shear stress

level could initiate platelet activation. Based on these suggestions, numerous research was

performed to develop accurate methods to evaluate PHVs either in vitro or in vivo. Note that

in this section a brief review of the in vitro approach is provided. However the in vivo

method is out of the scope of this study.

One of the earliest in vitro experimental attempts was carried out by Yoganathan et

al. (1984) to evaluate the hydrodynamic performance of the Starr-Edwards ball valve. The

flow profile was characterized using Laser Doppler anemometer (LDA) technique under a

steady flow condition. The results highlighted major fluid dynamic drawbacks including

high-pressure drop (17.3 to 31 mmHg at 417 cm3/sec), flow stagnation at the apex of the

112

cage, high wall shear stress (50 to 200 Pa), and bulk turbulence shear stress (10 to 500 Pa) in

the immediate vicinity of the valve. The St. Jude cardiac prosthetic aortic valve was also

evaluated by Gray et al. (1984) using the LDA technique under the same boundary conditions

in vitro. A relatively low wall shear stress of 60 Pa, and pressure gradient of 5.2 +/- 1 were

measured along with low turbulence. However, in the in vitro part of the study, the pressure

drop across the valve was measured 3.3 +/- 1.9 mmHg at 249 +/- 96 ml/sec. In contrast, the

shear stress measurement of the St. Jude valve using two-dimensional LDA by Woo and

Yoganathan (1986b) showed a higher shear stress of 200 Pa. Later the performance of a

polymeric PHV called the Abiomed valve was compared with Carpentier-Edwards and

Lonescu-Shiley tissue valves. Steady and pulsatile flow velocities were characterized with an

LDA. A jet-like and turbulent flow was observed with axial velocity fluctuations of 55 and 83

cm/s. The turbulent shear stress was measured for 25 and 21 mm valves and maximum shear

stresses of 220 and 450 Pa respectively were observed in the immediate vicinity of the valves

(Woo et al., 1983).

A more accurate technique to evaluate the hydrodynamic performance of the valve

called the colour Doppler mapping technique was introduced by Kapur et al. (1989). This

technique provides a reliable tool to assess the high flow velocity field. In addition, it is

demonstrated by Cape et al. (1991) that this technique is able to detect PHV insufficiency and

measure the regurgitation volume. However, Bargiggia et al. (1989) extended this technique

and proposed the continuous-wave Doppler technique to improve the accuracy of measuring

the EOA in turbulence flow regimes.

A two-dimensional LDA was also used to measure mean velocity and Reynolds

stress within the backflow jet produced by tilting disk valves (Baldwin et al., 1991).

However, a comparative study using 2D and 3D LDA analysis of three prosthetic valves (St.

Jude bileaflet, Bjork-Shiley, Starr-Edwards) showed a discrepancy in the results,

demonstrating that 2D LDA underestimates the largest normal stresses by 10% to 15%. The

LDA technique was also used in our laboratory at Swinburne University to characterize the

flow velocity past the Jellyfish (JF) valve and measure the elevated shear stress in the mitral

position of a ventricular assist device (Morsi et al., 1999a). The results obtained from the

LDA data showed a disturbed flow field along with high shear stress in the immediate

vicinity and up to 1D (diameter of valve ring). The results were compared with the Bjork-

Shiley mono strut valve (BSM) data and the comparison indicated that the flow turbulence

generated from both valves was capable of lethal damage to blood cells. In another study by

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Morsi et al. (1999b), the blood damage index was measured with the assistance of the LDA

technique for both valves under a pulsatile flow condition. The elevated shear stresses data

was used to compute the relative release of haemoglobin by damaged RBCs and of lactate

dehydrogenase by platelets with the aid of a mathematical model. The results showed that the

Jelly fish (JF) valve was less thrombogenic with a relative blood damage index of 0.27

compared to 0.47 for BSM valve.

Although the LDA technique provides point-to-point velocity measurements which

are sufficient for temporal variations of flow velocity, this data acquisition is very time-

consuming. In contrast, particle image velocimetry (PIV) is able to measure the entire flow

field in a plane at a given instant. Kini et al. (2001) carried out a comparative study to

measure the backflow volume of the Bjork –Shiley mono strut (BSM) valve using PIV and

LDA techniques in vitro. The PIV technique allowed two velocity components in a plane

simultaneously which provided a different insight into the flow field. It was demonstrated

that incorporating both techniques could provide more insight into the complex flow by

combining the advantage of planar visualization of PIV method with the detailed temporal

variations and trend data of the LDA technique (Kini et al., 2001). Moreover, the advantage

of the PIV technique over traditional methods such as ultrasound techniques and LDA is

emphasized by Manning et al. (2003). In this study, the relationship between the particular

regurgitant flow field characteristics of the St. Jude bileaflet valve to the tendency for

cavitation was assessed using the PIV technique under pulsatile flow condition. Data was

collected prior and after valve closure and the results showed a strong regurgitant jet along

with two vortices close to the leaflets. It is also noted that the vortex motion around the

occluder tips provided a low-pressure environment for cavitation (Manning et al., 2003).

The LDA and PIV techniques are the most frequently used method to evaluate valve

performance in vitro, however they are relatively expensive and required a trained operator to

perform the test. Hence, in recent years, commercially available pulse duplicator systems

with integrated software have been used to collect the data. Claiborne et al. (2013) used the

Vivitro left heart simulator (LHS) for in vitro hydrodynamic testing of the proposed xSIBS

polymeric valve and undertook a comparative study with the Carpentier-Edwards

bioprosthetic valve. Vivitest software was also used to collect and process the data to

compute the transvalvular pressure gradient, regurgitation, energy loss, and EOA for each

valve. It was demonstrated that the proposed optimized xSIBS valve had lower regurgitation

volume compared to the benchmark tissue valve. Similar transvalvular energy loss was

measured for both valves in 4- 6 l/min cardiac output while for the higher flow rate, xSIBS

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energy loss exceeded that of the tissue valve. Notably, the EOA of xSIBS was smaller than

the tissue valve, resulting in a higher transvalvular pressure gradient (TPG) for xSIBS

compared to the tissue valve.

These experimental methods to evaluate PHV performance are a vital part of design

verification. However, these techniques are still a very time-consuming practice which

requires expensive laboratory equipment. In this regard, an alternative low-cost approach,

computer modelling of the valve using the Finite Element/Finite Volume methods, has

become increasingly popular where the numerical modelling of the valve via user-designed

functions or commercial fluid-structure interaction (FSI) packages is a common practice to

analyse valve performance. Numerical methods and available commercial FSI packages

could provide more quantitative and qualitative data, such as the visualization of the three-

dimensional blood flow field within the valve and stress data. In the current study, the valve

is modelled using two-way FSI simulation as explained in detail in Chapter 4. However, it is

crucial to validate the predicted results. In the literature, numerous methods (De Hart et al.,

2000, De Hart et al., 2003, Carmody et al., 2006, Nobili et al., 2008, Guivier-Curien et al.,

2009, Kanyanta et al., 2009, Kouhi and Morsi, 2010, Borazjani et al., 2010, Becker et al.,

2011, Falahatpisheh and Kheradvar, 2012, Griffith, 2012, Chandra et al., 2012, Marom et al.,

2012) have been used to validate FSI results, in which the leaflet kinematics (De Hart et al.,

2003, Carmody et al., 2006, Griffith, 2012) and visualization of the fluid flow field using

particle image velocimetry (PIV) (Guivier-Curien et al., 2009, Falahatpisheh and Kheradvar,

2012) or Laser Doppler anemometry (LDA) (De Hart et al., 2000) are the most common

practices. Although it was initially planned to use the LDA technique to compare the

predicted fluid velocity profile with the experimental measurements as part of the validation

process, the laser machine broke down unexpectedly and the repair time was beyond the time

constraints of the Ph.D. candidature. Consequently, the following approaches were carried

out to validate the simulation.

1) Numerical method: by modelling a reference valve and comparing the predicted results

with the previously published data (see Chapter 6)

2) In vitro validation: Comparing the numerical predictions of the leaflet displacement to the

in vitro experimental measurements, which is known as the leaflet kinematics approach as

discussed in Chapter 6.

115

In this chapter, the experimental setup, including the testing machine design and the valve

construction procedures are described in detail.

5.3 Pulse duplicator machine design The testing machine (pulse duplicator machine) is manufactured to simulate the

hemodynamic loads that the native heart valve endures during a cardiac cycle. In order to

design the testing machine, the following five criteria are assumed to cover all the

requirements.

1) to ensure that the valve is exposed to similar hemodynamic condition in vivo including

similar aortic pressure and pulsatile forces;

2) to allow full control over flow rate, stroke volume, stroke rate, and flow waveform;

3) to use transparent material to ensure maximum visibility;

4) to allow the mounting of different sized prosthetic valves;

5) to ensure that the system is capable of working for a long period of time and the process is

repeatable every time.

The pulse duplicator machine (PDM) consists of the following components in addition to the

motion controller unit and motor (see Figure 5.2)

1) Connection Rod

2) Piston

3) Cylinder

4) Drain valve

5) PVC Pipes

6) Check Valve

7) Valve mounting module (location of the testing valve)

8) Acrylic unit (Testing chamber)

9) Compliance Chamber

10) Air valve and pressure sensor

11) Solenoid valve 1 (normally closed)

12) Ring to control the flow

13) Reservoir Chamber

116

14) Closed PVC tube with a number of holes. This feature together with #12 (ring)

controls the outflow resistance.

15) Solenoid Valve 2 (normally closed)

These items are identified by their reference number in Figure 5.1.

Figure 5.1. Schematic view of the pulse duplicator machine (the motor and controller unit is not shown).

The heart valve prototype can be tightly positioned between the fixation ring and the

two flanges (#7 in Figure 5.1). A pressurized chamber (#9 in Figure 5.1) is used as a

compliance chamber and mimics the elastic function of large arteries. This chamber is

pressurized to 100 mmHg to represent the aortic pressure (AP in Figure 4.5) by pumping in

air through the air valve (#10 in Figure 5.1). The resistance module consists of a blocked

PVC pipe with a number of holes at the end (#14 in Figure 5.1) and a stainless tell ring (#12

in Figure 5.1). The flow resistance is adjusted by sliding up and down the ring. The

connection rod (#1 in Figure 5.1) is attached to a piston from one end as shown in Figure 5.1,

117

and the other end is attached to a crank connected to the shaft of a DC electric motor

(supplied by Sanyo Denki Co Ltd, Tokyo, Japan). The rotation speed of the motor shaft is

controlled by the RTA Plus K5 motion controller (supplied by RTA Srl, Marcignag, Italy).

Figure 5.2. Picture of the pulse duplicator machine, including the motor and motion

controller.

5.4 Valve construction A solution cast film of Bionate ® Thermoplastic Polycarbonate urethane (PCU) with

a 5 mil thickness (supplied by DSM, Exton, PA, USA) is used to construct the leaflet. Its

special mechanical properties, such as its exceptional load bearing capability and biostability

has resulted in Bionate being used in a wide range of application, such as vascular, artificial

heart, hip, knee and spinal motion preservation devices (Zdrahala and Zdrahala, 1999).

Bionate is chosen for this study due to its high tensile strength, biostability, biocompatibility

and flexibility (Claiborne et al., 2013).

The Bionate ® sheets were formed into the designated leaflet geometry using the

thermoforming manufacturing technique. In this method, the polymer film is sandwiched

between the two molds (see Figure 5.3) for 125 minutes at 170 degrees Celsius under 50 N

force. Initially, the molds were manufactured by CNC 3D drill milling of two aluminium rods

118

(one for each of the male and female molds). However, the machining process became

extremely difficult due to the complexity of the leaflet geometry, especially near the

commissure in the female mold. Alternatively, the molds were constructed using the Electron

beam melting (EBM) technique from Ti6Al4V material (provided by Lab 22, CSIRO).

Figure 5.3. Molds constructed by EBM technique to form the polymer films into the leaflet geometry.

The supporting frame (stent) of the leaflets must be constructed according to the

leaflet geometry in order to provide optimum support as well as complying with the FSI

setup. Hence, the 3D printing manufacturing technique was chosen to construct the stent with

high precision and in a timely manner.

The stent was built from ZP150 composite polymer powder (see Figure 5.4). The

printed stent was infiltrated by Z90 super glue and baked in the oven for 2 hours at 75

degrees Celsius to maximize the mechanical properties of the stent, as described previously

(Gharaie et al., 2013). Ultimately, the valve prototype was constructed by mounting the

thermoformed leaflets onto the stent by Z90 super glue, as shown in Figure 5.5.

119

Figure 5.4. 3D printed stent (supporting frame)

Figure 5.5. Polymeric leaflets attached to the stent.

120

5.5 Flow in the Pulse Duplicator Machine The valve prototype was mounted onto the designated location (#7 in Figure 5.1).

The same stroke volume produced by a native heart (see ventricular volume profile in Figure

4.5) was generated by the controlled displacement of the piston from position 1 (see Figure

5.1) to position 2 (see Figure 5.6). In this step (systole), solenoid valve 1 (#11 in Figure 5.6)

is opened and solenoid valve 2 (#15 in Figure 5.6) remained closed to permit the fluid flow

into the reservoir chamber (the red arrows in Figure 5.6 show the fluid flow direction). The

resistance module regulated the outflow rate from the compliance chamber. The flow

resistance was determined by adjusting the position of the ring (#12 in Figure 5.6) and

increasing or decreasing the number of outlets (#14 in Figure 5.6).

Figure 5.6. Systolic flow direction in the pulse duplicator machine.

121

In the diastolic phase, the solenoid valve 1 (#11 in Figure 5.7) remained closed to

prevent the fluid flowing through the valve. This is to ensure the aortic pressure is the only

acting pressure on the valve. The piston returned to its original position, and at the same time,

solenoid valve 2 (#15 in Figure 5.7) is opened, resulting in the one-way tilting valve (#6 in

Figure 5.7) opening. Consequently, the fluid flowed from the reservoir into the PVC pipe

adjacent to the cylinder.

Figure 5.7. Diastolic flow direction (red arrows) in the pulse duplicator machine.

122

5.6 Flow rate The purpose of testing the valve in vitro is to validate the numerical simulation.

Hence, the same boundary conditions applied on the valve in the FSI simulation must be

applied on the valve in the experiment. As explained in Chapter 4 (see section 4.4 boundary

conditions), aortic and ventricular pressures derived from the Wiggers diagram were applied

on the aortic (outlet) and ventricular (inlet) side of the valve as the boundary conditions.

Therefore, the differential pressure at each given time generated the outlet flow in the FSI

simulation which resembled most closely the native physiological loads. Nevertheless,

applying such a complex pressure profile on each side of the valve was substantially difficult.

It was more practical to control the flow rate passing through the valve. Hence, the aortic

valve flow rate data (see Figure 5.8) was retrieved from the simulation and used to program

the controller unit (RTA Plus K5 motion controller supplied by RTA Srl, Marcignago, Italy).

Figure 5.8. Aortic valve flow rate in a full cardiac cycle.

123

As the internal diameter of the cylinder is constant, the forward traveling speed of

the piston from position 1 (see Figure 5.6) to position 2 (see Figure 5.7) can be calculated by

dividing the flow rate data by the area of the internal cylinder. Consequently, the travelling

speed of the piston in systolic phase can be expressed as shown in Figure 5.9.

Figure 5.9. Piston speed in forward travel (systole).

From the linear speed of the piston (see Figure 5.9), the angular speed of the motor shaft can

be calculated as follows:

Figure 5.10 shows the piston motion with respect to the crankshaft angular position ( . As

the crankshaft rotates (from point A to point B), the piston displacement can be described as

follows:

Equation 5.1. Displacement of the piston along the x-axis at a given ti time.

Piston displacement= OX(ti)+ X(ti)C

124

from triangle relation:

Equation 5.2. Displacement of the piston with respect to crank angle.

Piston displacement = √

as then

Equation 5.3. Displacement of the piston with respect to the angular velocity of the crankshaft.

Piston displacement = √

The piston velocity function can be found by differentiating Equation 5.3:

Equation 5.4. Velocity equation of the piston with respect to the crankshaft angular velocity.

√

Figure 5.10. Piston movement by circular motion of the crankshaft. Note that crankshaft size is exaggerated to show the detail.

125

In the above equations, r is the length of the crank (a distance of crank pin to centre

of the crankshaft), and l is the length of the connection rod, as shown in Figure 5.10.

Consequently, by knowing the piston velocity (see Equation 5.4), it was possible to calculate

the required angular velocity of the crankshaft ( ) during the systole, as presented in Figure

5.11. Hence, data provided in Figure 5.11 was used to program the motor. In addition, the

rotation of the crankshaft was captured by a high-speed camera and the position and rotation

speed ( ) of the crankshaft at each given time was compared to the input data (presented in

Figure 5.11) in order to validate the motor performance. The comparative study confirmed

the performance of the motor.

Figure 5.11. Systolic angular velocity of the crankshaft.

Note that the negative values of the flow rate (see Figure 5.12) indicate valve leakage;

therefore, the motor has been programmed to produce only positive values (forward flow

rate).

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350

Cra

nks

haf

t an

gula

r ve

loci

ty (

rad

/se

c)

Time (ms)

126

5.7 Data acquisition In the interest of performing quantitative data analysis to validate the FSI simulation,

the valve opening and closing mechanism is visualized using a high-speed camera with a

shutter speed of 300 per second. The camera is equipped with a long-distance microscope

lens (1030 mm focal length) and is positioned on top of the compliance chamber (see Figure

5.12). The camera captures 2D images of the leaflet kinematics from the downstream

direction. The data was downloaded into a computer as a collection of consecutive frames.

Hence, the correlation of each frame to its FSI prediction is determined by knowing that the

time interval between each frame is 1/300 second.

Figure 5.12. Configuration of the high-speed camera in the experimental test.

127

5.8 Summary and limitations In this chapter, a full description of the experimental setup is proved including the

valve construction procedure and the design of the pulse duplicator machine. In the current

study, advanced manufacturing techniques such as electron beam melting (EBM) and 3D

printing methods were used to construct the valve. To the best of our knowledge, this is the

first time that these techniques have been combined to construct a prosthetic valve. The lead

manufacturing time of the proposed technique for a customised prosthetic valve (patient

match implant) was estimated to be less than 4 hours. Note that the 3D printing of the stent

and adhesion method (using glue) to attach the leaflet to the stent used in this study were not

biocompatible. Such techniques were used to construct the valve to demonstrate the

feasibility of using advanced manufacturing techniques. Further studies are required in order

to construct a fully biocompatible and biostable prosthetic valve, however, it was out of the

scope of the current study.

In addition, the pulse duplicator machine was designed and manufactured to

simulate the haemodynamic loads applied to the valve in the FSI simulation. The aortic flow

rate data for the systole was retrieved for the simulation. The motor of the pulse duplicator

machine was then programmed to produce such a flow rate. Note that in the FSI simulation,

the aortic and ventricular pressure was applied as boundary conditions, while in the

experiment, the generated flow rate (resulting from the differential pressure) was used in

systole. Furthermore, the machine was designed to apply 100 mmHg aortic pressure on the

valve prototype during diastole. This pressure is considered as the average aortic pressure

applied on the valve during the numerical simulation.

The experiment ran for several days in order to test the integrity of the valve

structure. For the purpose of validating the FSI results, ten consecutive cardiac cycles were

considered in which the leaflet kinematics were captured from the downstream direction.

128

6 Chapter 6 Results and discussion

Overview 6.1.In this chapter, the results obtained from the FSI simulations and in vitro testing of

the proposed valve are presented. The hydrodynamic performance of the valve is evaluated

and compared to previously published data. The hydrodynamic quantities of the proposed and

reference valves, including effective orifice area (EOA), geometric orifice area (GOA),

transvalvular pressure gradient (TPG), leakage volume, and maximum Von Mises stress are

computed and compared to previously published data. The complex flow regime past the

optimized valve is thoroughly analysed during systole in order to characterize regions of high

turbulence as well as flow separation with eddy formation and stagnation point. In addition,

the shear stress distribution in the leaflet and flow field are investigated to determine in which

degree the proposed valve will damage blood components. Importantly, the predicted

deformation of the leaflets in the FSI simulation is compared to the in vitro experimental

values as part of the validation of the simulation.

Velocity distribution 6.2.As mentioned in the literature, patients who received PHVs often have subsequent

health complications which are related to the haemodynamic characteristics of the blood past

the implanted PHV. These complications may derive from elevated turbulence shear stress

and impaired blood flow patterns (Kozerke et al., 2001). Previous studies (Woo and

Yoganathan, 1986a, Nygaard et al., 1992) have shown that locations of turbulence shear

stress are linked to regions of high velocity gradients which mostly occur in systole.

Consequently, mapping the velocity gradients during systole is useful to estimate the

complicity of the flow field as well as identifying the region of flow field prone to high shear

stress. However, this analysis requires breaking down the complex 3D velocity profile into

planar 2D velocity streamlines. Hence, two main reference planes are assumed in Cartesian

coordinates which intersect the proposed valve as shown in Figure 6.1 and the velocity

129

profile is analysed in three time steps related to early systole (t=20 ms), mid systole

(t=84.25 ms), and peak systole (t=168.5 ms).

Figure 6.1. 2D reference planes (a) asymmetrical YZ plane (b) Cross-sectional XY plane.

(a) (b)

130

Asymmetrical velocity profiles on YZ plane 6.6.1.The 3D velocity profile is mapped in a series of 2D asymmetrical planes, as shown

in Figure 6.2. The first plane is defined on the YZ plane at the coordination system, and six

planes are defined on each side of the X-axis (2 mm gap between each of the planes). Note

that the asymmetrical term is chosen for these planes, as the planes defined on each side of X-

axis are not identical.

Figure 6.2. Schematic view of asymmetrical planes from sinus cavity to the commissural

end.

131

In early systole, the flow quantification showed that the boundary layer has

separated from the leaflets wall (aorta side) and forms an eddy in the region between the

leaflets and SOV cavities since early systole (see Figure 6.3). At an early stage of the valve

opening (t=20 ms), peak velocities of up to 0.975 m/s are recorded near the leaflet distal end.

The blood flow accelerated in the axial direction and developed a central jet in which the

velocity magnitude decreased gradually from the axial jet towards the recirculation regions

inside the sinus cavities. Flow constriction is noted where the maximum constriction of the

central jet occurred 0.45D to 0.50D (D = diameter of the stent) downstream from the stent

ring. However, the axial jet fanned out further downstream at 0.85D to 0.90D. Antegrade and

retrograde flow were observed in the regions between the leaflets (aortic side) and sinus

cavities, in which the recirculation flow pushed away from the main tract toward the sinus

cavity as flow accelerated during systole (see Figure 6.4 and Figure 6.5). The boundary

regions between the axial jet and the recirculating region in the sinus cavities can be clearly

observed in this time step.

Figure 6.3. Asymmetrical 2D velocity profile on YZ plane at t=20 ms.

132

After 84.25 ms of the valve opening (mid-acceleration phase), the acceleration of the

flow can still be observed where the peak velocities reached up to 1.395 m/s (see Figure 6.4).

The central jet showed more uniform velocity components along the axial direction compared

to early systole, resulting in less flow expansion further downstream.

Figure 6.4. Asymmetrical 2D velocity profile on YZ plane at t=84.25 ms.

133

At peak systole, after 168.5 ms opening of the valve, the acceleration of the flow is

diminished, and the development of more uniform velocity components are observed along

the axial direction (see Figure 6.5). The peak velocities of up to 1.55 m/s are detected away

from the axial jet towards the leaflet distal end near the stent posts. Furthermore, flow

expansion is less pronounced in this time step. In general, the velocity profiles are more

uniform in nature. Importantly, the development of a uniform central jet flow during peak

flow (Figure 6.5) as a result of incorporating the proposed PV in this study is in good

qualitative agreement with the flow past a native aortic valve (Markl et al., 2004).

Figure 6.5. Asymmetrical 2D velocity profile on YZ plane at t=168.5 ms.

134

Cross-sectional velocity profile on XY plane 6.6.2.The 3D velocity profile is mapped in a series of 2D longitudinal planes (see Figure

6.6) in order to analyse the cross-sectional velocity profile of the blood flow. The reference

plane is located at the leaflet-free edge level (Z=0 mm), and two sets of auxiliary XY planes

are defined towards the ascending aorta and ventricular side of the leaflets at Z=2 mm,

Z=4 mm, Z= 8 mm and Z=12 mm. Note that the locations of the reference planes are chosen

to provide the flow characteristics from the left ventricle (Z=-12 mm) towards the ascending

aorta at 0.2D (Z=-4mm), 0.25D (Z=-2mm), 0.35D (Z=0mm), 0.45D (Z=2mm), 0.5D

(Z=4mm), 0.7D (Z=8mm), 0.85D (Z=12mm) where D is the internal diameter of the valve.

Figure 6.6. Schematic view of cross-sectional planes from the valve inlet to outlet.

135

At early systole (t=20 ms), a fully developed forward fellow is observed at the aortic

root as shown in the Cross-sectional 2D velocity profile on YZ plane at t= 20 ms(Z=-12 mm)

with a mean velocity of 0.057 m/s. As the flow moved towards the ascending aorta, the mean

velocity has increased as the orifice area is decreased. Observation of the velocity gradient in

each cross-sectional plane shows that at Z=0 mm, the maximum velocity is located near the

leaflet commissure area close to the stent posts. Similarly, in the mid-acceleration phase

(Figure 6.8) and peak systole (Figure 6.9), the maximum velocity is observed in the same

regions, at 1.39 m/s and 1.55 m/s respectively. It is noted that the velocity distribution

becomes more uniform as the flow develops towards downstream in all cases. As observed in

the previous section (see Section 6.6.1), the flow vortices that are generated in the sinus

regions are dissipated as flow develops further downstream, resulting in a uniform central jet

(see planes Z=8 mm, and Z=12 mm in the Cross-sectional 2D velocity profile on YZ plane at

t= 20 ms in Figure 6.8 and Figure 6.9). However, analyses of the velocity distributions in the

cross-sectional planes shows high-velocity gradients in the vicinity of the leaflets. These

velocity gradients are proportional to shear stress and may cause mechanical damage to red

blood cells and the leaflet surfaces. Hence, measurements of shear stresses are provided in

section 6.3 for diagnosis of suspected complications.

Figure 6.7. Cross-sectional 2D velocity profile on YZ plane at t= 20 ms.

136

Figure 6.8. Cross-sectional 2D velocity profile on YZ plane at t= 84.25 ms.

Figure 6.9. Cross-sectional 2D velocity profile on YZ plane at t= 168.5 ms.

137

Red blood cell damage 6.3.It is widely accepted that both the magnitude of the shear stress and exposure time of

blood cells to the exerted forces influence the onset and severity of blood element damage.

Previous studies (Leverett et al., 1972, Dasi et al., 2009) showed that high shear stress levels

have an adverse effect on erythrocytes and may cause platelet activation (Sheriff et al., 2013)

and thrombus formation (Nesbitt et al., 2009). Hence, it is essential to investigate the

possibility of red blood cell (RBC) damage, platelet activation, and thrombus formation due

to implanting the proposed valve.

As described in Section 6.2, the regions suspected to be associated with the highest

shear stress were identified in the vicinity of the leaflets. This type of shear stress is known as

wall shear stress (WSS), which is computed by measuring viscous shear stress near the

leaflet. However, the total shear stress at any point consists of both viscous shear stress and

turbulent shear stress where the viscous shear stress is applicable only near the boundary

(Bansal, 2010). Hence, the turbulent flow regime is also quantified by Reynolds shear stress

(RSS) tensor, and both WSS and RSS data are used to evaluate the proposed valve design.

Previous studies (Leverett et al., 1972, Hung et al., 1976, Kouhi, 2012) showed RBC

damage and thrombus formation are mainly caused by the blood contacting the valve surfaces

and by WSS generated in the region of the implanted valve. WSS on the leaflets is analysed

by extracting the WSS exerted on each node of the leaflets and stent surfaces in the

acceleration period. Note that the maximum shear stresses are generated in this phase (Lim et

al., 2001, Claiborne, 2012, Kouhi, 2012). Figure 6.12 depicts temporal variations of the

recorded maximum WSS (WSSmax) on the prosthetic surfaces over the acceleration period. It

is noted that the magnitude of WSSmax fluctuated dramatically which is due to the rapid

response of the leaflets to the variations of the blood inflow rate. The phenomena of

fluctuating WSS over the acceleration phase and location of WSSmax (see Figure 6.10) are in

line with the previous FSI study carried out by our group (Kouhi, 2012). The highest value of

WSSmax is recorded as 137.703 Pa after 69 ms of the valve opening, Figure 6.11 gives details

of nodal distribution of WSS at this time step.

138

Figure 6.10. 3D presentation of WSS distribution on the leaflets at t=69 ms.

Figure 6.11. Nodal distribution of WSS at time step=69 ms (peak WSS).

139

Figure 6.12. Temporal distribution of WSSmax over the acceleration phase.

On the other hand, turbulent flow was observed in the wake of the valve (see

Figure 6.3, Figure 6.4 and Figure 6.5). This is known to be responsible for generating a high

level of shear stress further downstream. In this regard, a 3D turbulence shear stress analysis

was performed over the cardiac cycle in order to identify regions of elevated shear stresses.

An analysis of RSS revealed that the maximum RSS occurred at a time step 168.5 ms (peak

systole) as shown in Figure 6.13. Hence, the total shear stresses experienced by the blood

elements at time steps 69 ms and 168.5 ms have the highest possibility of causing RBC

damage. Table 6.1 gives a comparison of the WSSmax, and peak Reynolds shear stresses

( , , ), normal axial ( ), and transverse stresses ( , ) recorded for these critical

time steps.

Table 6.1. Maximum Reynolds and WSS stresses recorded for the proposed valve at the critical time steps.

Time (ms) after the

valve opening

Max. Reynolds shear stress (Pa) WSSmax

(Pa)

69

137.367 4.579 3.458 3.573 1.872 1.452 1.089

168.5 7.226 6.786 6.872 4.910 3.232 2.112 60.69

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80 90 100110120130140150160170180190200

She

ar S

tre

ss (

Pa)

Time (ms)

Maximum WSS

140

Figure 6.13. Distribution of max. Reynolds stresses mapping on the reference ZY plane at

X=0 mm at t=168.5 ms (Peak systole).

𝜏𝑧𝑧

(a)

𝜏𝑦𝑦

(b)

𝜏𝑥𝑥

(c)

𝜏𝑦𝑧

(d) 𝜏𝑥𝑦

(e)

𝜏𝑥𝑧

(f)

141

The highest RSS (see Figure 6.13d) of 4.910 Pa was recorded at 0.5D to 0.7D

downstream from the stent ring and 14 mm away from the valve centerline towards the right

aortic wall. However, this magnitude of shear stress can be considered to have negligible

effects on RBCs. Studies show that blood elements can tolerate a stress level of 150 Pa

without significant RBC damage (Leverett et al., 1972). Furthermore, a shear stress of less

than 10 Pa is accepted as a safe limit for platelet lysis (Hwang and Normann, 1977). The low

level of RSS recorded in the current study is in line with the previous study carried out by our

group (Kouhi, 2012). Therefore, blood element damage caused by WSS has been analysed in

order to evaluate to which degree the proposed PHV will damage blood components. The

temporal distribution of WSSmax (see Figure 6.12) was retrieved from the simulation for

further analyses. Figure 6.12 shows that the maximum WSS occurred at 69 ms after the valve

opening; hence, the possibility of blood damage at this instance was investigated. The

movements of 6 particles (A, B, C, D, E, F) which passed across the elevated shear stress

zones at t=69 ms were traced (see Figure 6.14). Subsequently, the shear stress histories of the

particles as they traverse the leaflets were extracted from the simulation, as shown in Figure

6.15 in order to calculate the blood damage indices (BDIs). In general, the following

mathematical models established by Giersiepen et al. (1990) are widely used to classify the

blood damage potential of artificial organs.

Equation 6.1. Percentage of Hb released by RBC as a function of shear stress and exposure

time.

Equation 6.2. Percentage of cytoplasm enzyme (LDH) released by platelets (PLs) as a

function of exposure time and shear stress.

where the effective exposure time in second (s), is shear stress of N/m2 (Pa), and

c1,a1,b1, c2,a2,b2 are constant values proposed by Giersiepen et al. (1990) (see Table 6.2).

142

Table 6.2. Constant values of power law equations proposed by (Giersiepen et al., 1990).

Figure 6.14. Presentation of streamlines and sample particles on the leaflet.

c1 a1 b1 c2 a2 b2

143

Figure 6.15. Exposure time history of sample particles passing the peak shear stress at 69 ms after the valve opening.

0

50

100

150

0 1 2 3

She

ar S

tre

ss (

Pa)

Timeexp (ms)

Particle "A"

0

50

100

150

0 1 2 3 4

She

ar s

tre

ss (

Pa)

Timeexp (ms)

Particle "B"

0

20

40

60

80

0 2 4 6 8

She

ar S

tre

ss (

Pa)

Timeexp (ms)

Particle "C"

0

20

40

60

0 2 4 6 8

She

ar s

tre

ss (

pa)

Timeexp (ms)

Particle "D"

0

20

40

60

80

0 2 4 6 8

She

ar s

tre

ss (

Pa)

Timeexp (ms)

Particle "F"

0

10

20

30

40

50

0 5 10

She

ar s

tre

ss (

Pa)

Timeexp (ms)

Particle "E"

(a) (b)

(c) (d)

(e) (f)

144

It is shown by Giersiepen et al. (1990) that the BDIs obtained by applying these

equations are in good agreement with the clinical results. However, in their study, the laser

Doppler anemometry (LDA) technique was used which is based on the point measurement

technique. The disadvantage of this method is that LDA does not provide information on both

time and space. To address this issue, Lim et al. (2001) incorporated the particle image

velocimetry (PIV) technique in order to compute the exposure time based on the velocity of

the individual particle as it passes through the elevated shear stress zone. The estimation of

exposure time was based on 40 ms exposure time of a 2D PIV image frame, and the

movement of the particle was based on the mean velocity vector. In this study, the average

shear stress was considered to calculate the BDIs for the exposure time ranging from 1 ms to

10 ms. Similarly, Kouhi (2012) followed the same principles and calculated the BDIs for an

exposure time ranging from 5 ms to 80 ms. The mathematical method (named the Average

Shear Stress method) used in Kouhi (2012)’s and Lim et al. (2001)’s studies can be written

as:

Equation 6.3. Percentage of Hb released by RBCs as a function of mean shear stress and exposure time.

Equation 6.4. Percentage of cytoplasm enzyme (LDH) released by platelets (PLs) as a function of mean shear stress and effective exposure time.

where is the average shear stress experienced by the particle as it moves across the

leaflets.

However, the 3D FSI simulation presented in the current study provides more accurate

information for real-time movements of sample particles and their shear stresses, as shown in

Figure 6.15. Thus, the exact exposure time of each particle as it traverses the leaflets and the

average shear stresses were retrieved from the simulation (see Table 6.3). Consequently,

these values were applied to Equation 6.3 and Equation 6.4 to compute the BDIs. Figure 6.16

gives a comparison of the computed percentage of LRBC and LPL for the sample particles by

incorporating the average shear stress method.

145

Table 6.3 Average shear stresses and exposure times calculated for the sample particles.

Figure 6.16. Calculated BDI values using the average shear stress method.

Particle ID A B C D E F

Average shear stress (Pa) 50.519 47.10

4

33.24

1 30.498

18.20

5 38.775

Exposure time (ms) 2.47 3.21 6.19 7.06 8.12 5.89

A B C D E F

LRBC 4.24E-03 4.40E-03 3.17E-03 2.86E-03 9.07E-04 4.43E-03

LPL 5.63E-03 5.55E-03 3.15E-03 2.68E-03 6.01E-04 4.87E-03

0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

6.00E-03

Pe

rce

nta

ge

146

As depicted in Figure 6.16, the peak of total blood damage percentage (LRBC and

LPL) occurred in the vicinity of the leaflet-free edge distal end, where particles A and B

passed across the leaflet. It is noted that particle A also experienced the highest platelet lysis

corresponding to LPL index of 5.63 x 10-3 %, and particle F encountered the highest RBC

damage with LRBC index of 4.40 x 10-3 %. It is interesting to note that the LRBC index of

particle F was 4.4% greater compared to LRBC index of particle A. As the average shear

stress endured by particle F was 23.24% smaller that particle A, a higher value of the LRBC

index calculated for particle F compared to particle A indicates that blood elements are more

vulnerable to prolonged exposure time than the magnitude of shear stress. However, it should

be noted that shear stress of above 150 Pa is suggested to be sufficient to cause extensive

blood damage, directly due to shear stress (Leverett et al., 1972). A similar response of blood

elements to the exerted shear stress and exposure time is also reported in an experimental

study of blood damage passing the St. Vincent’s porcine aortic valve (Lim et al., 2001). On

the contrary, the analysis of LRBC and LPL indices of the blood particles show that in the case

of particles C, D and E, RBCs were more vulnerable than platelets to shear stresses. This

suggests that there is a threshold of shear loads (named for each given exposure time

where RBCs become more vulnerable than platelets to shear stresses. For instance, at

exposure time of 6.19 ms corresponding to particle C, the threshold can be calculated as

follows:

From Equation 6.1, and Equation 6.2

Replacing by its value (6.19 x10-3 s), then calculated as 33.588 Pa. As the average

shear stress of particle C ( Pa) is below the , subsequently the platelets

showed more resistance than the RBCs to the shear stress.

Nevertheless, this contradicts the known fact that RBCs are more resistant than PLs

to shear stress (Giersiepen et al., 1990). The source of error in the above calculations could be

the assumption of the average shear stress as the acting load on the particle over the given

exposure time. In this approach, the effect of the accumulation of damage endured by the

particle is neglected. It is has been found in various references (De Wachter et al., 1996,

Grigioni et al., 2002, De Wachter and Verdonck, 2002) that in order to determine the onset

and severity of blood damage, it is necessary to consider the accumulation of damage. In this

147

regard, the LPL and LRBC indices can be calculated numerically by the summation of the

damage along the path line as described by (Grigioni et al., 2004):

Equation 6.5. Accumulated RBC damage (%) along the path line.

∑

Equation 6.6. Accumulated platelet damage (%) along the path line.

∑

where is the time duration of the particle to reach ith observation point, is observation

interval, and is the shear stress endured by the particle during the ith observation interval

.

Equation 6.5 and Equation 6.6 are derived from the differential quotient of Equation

6.1, and Equation 6.2 with respect to time (t) as the independent variable. This temporal

differential method has been widely used to assess the hemolytic potential of PHVs (Grigioni

et al., 2002, Zimmer et al., 2000). Hence, the results obtained from the time histories of the

particles traversing the leaflet (see Figure 6.15) are linked to the temporal differential

equations (time interval ( ) assumed as 0.1 ms) in order to calculate the summation of

blood damage. Figure 6.17 provides the calculated percentage of the BDIs (LRBC and LPL)

using the temporal differential method.

148

Figure 6.17. Calculated BDI values using the Temporal Differential Method.

The results obtained from the temporal differential method are more consistent with

the accumulation of damage hypothesis (fatigue phenomena) compared to those calculated

from the average shear stress method. This is due to the fact that in this method, the history of

the acting shear stress on the blood elements is considered. Overall, LRBC and LPL indices

obtained by incorporating the temporal differential method showed considerable increases in

all cases compared to those values calculated from the average shear stress method (see

Figure 6.18).

A B C D E F

LRBC 7.70E-03 7.65E-03 4.08E-03 3.67E-03 1.29E-03 5.46E-03

LPL 1.56E-02 1.45E-02 5.07E-03 4.31E-03 1.23E-03 7.32E-03

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

1.40E-02

1.60E-02

1.80E-02

Pe

rce

nta

ge

149

Figure 6.18. BDI values calculated from the Average Shear Stress and Temporal Differential

methods.

However, BDI values of particle E were still questionable as the LPL index was

smaller than the LRBC index. This calculation error could be caused due to the fact that the

effect of acting loads was neglected in the proposed differential equations. It should be noted

that based on the analytical Lagrangian description, when the trajectory of the particle is

known (predicted by the FSI simulation in this study), then the damage experienced by the

particle during its motion is a function of both the run time (t) and the acting load

(Grigioni et al., 2004).

Another mathematical method, the total differential method, was introduced by

Grigioni et al. (2004) using a differential quotient for Equation 6.1 with respect to both time

(t) and shear stress ( ) as follows:

AverageShearStress

Method

Temporal

Differential

Method

AverageShearStress

Method

Temporal

Differential

Method

AverageShearStress

Method

Temporal

Differential

Method

AverageShearStress

Method

Temporal

Differential

Method

AverageShearStress

Method

Temporal

Differential

Method

AverageShearStress

Method

Temporal

Differential

Method

Particle A Particle B Particle C Particle D Particle E Particle F

LRBC 4.24E-03 7.70E-03 4.40E-03 7.65E-03 3.17E-03 4.08E-03 2.86E-03 3.67E-03 9.07E-04 1.29E-03 4.43E-03 5.46E-03

LPL 5.63E-03 1.56E-02 5.55E-03 1.45E-02 3.15E-03 5.07E-03 2.68E-03 4.31E-03 6.01E-04 1.23E-03 4.87E-03 7.32E-03

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

1.40E-02

1.60E-02

1.80E-02

Pe

rce

nta

ge

150

Equation 6.7. Total differential quotient of RBC damage index in respect to time and shear stress.

In discrete form, this can be expressed as:

Equation 6.8. Discrete form of total differential quotient of RBC damage index.

Similarly, Equation 6.2 can be written as:

Equation 6.9. Total differential quotient of platelet damage index with respect to time and shear stress.

In discrete form, this can be expressed as:

Equation 6.10. Discrete form of total differential quotient of platelet damage index

Grigioni et al. (2004) used the above method to investigate the effect of loading

history when the shear stress is fluctuating along the path travelled by the blood elements. In

this study, it is noted that when is a decreasing function, the second term on the right-hand

side of Equation 6.8 has a negative algebraic sign, therefore it becomes a subtracting term to

BDI. This means that if the shear stress decreases over time, then the effect of acting shear

stress is decremental, which is in opposition to the princple of causality. Considering the fact

151

that the second term in the equations represents sublethal damage to blood corpuscles due to

the effect of different shear stresses ( , therefore, under accumulation of

damage hypothesis, it can be assumed that only is valid as the acting load on the

particle during the time it takes to reach ith observation piont. shows that the shear

stress exerted on the blood elements at ith observation point is less than the previous step, so

as the particle experienced less stress compared to the previous step, and there is no sublethal

damage due to different shear stress. In this situation, when , only the shear stress

acting on the blood corpuscles at ith observation point over can be considered

as the acting load. Consequently, in such a situation (when the value of becomes

negative), it is assumed that only the first term of Equation 6.8 and Equation 6.8 are valid. In

order to calculate the RBC and PL damage endured by the particle passing across the

elevated shear stress, the summation of accumulated blood damage over the corresponding

exposure time should be computed. This accumulated damage can be calculated by the

integral sum of Equation 6.8 and Equation 6.10 as follows:

Equation 6.11. Accumulated red blood damage.

∫ ∫

Equation 6.12. Accumulated platelet damage.

∫ ∫

152

Figure 6.19. Fitted curves (red lines) on the shear stress curves extracted from the FSI

simulation.

R² = 0.9968

0

20

40

60

80

100

120

140

0 1 2 3

She

ar S

tre

ss (

Pa)

Timeexp (ms)

Particle "A"

R² = 0.9958

0

20

40

60

80

100

120

0 2 4

She

ar s

tre

ss (

Pa)

Timeexp (ms)

Particle "B"

R² = 0.9927

0

10

20

30

40

50

60

70

0 2 4 6 8

She

ar S

tre

ss (

Pa)

Timeexp (ms)

Particle "C"

R² = 0.9954

0

10

20

30

40

50

60

0 2 4 6 8

She

ar s

tre

ss (

pa)

Timeexp (ms)

Particle "D"

R² = 0.9972

0

10

20

30

40

50

60

70

80

0 5 10

She

ar s

tre

ss (

Pa)

Timeexp (ms)

Particle "F"

0

10

20

30

40

50

0 5 10

She

ar s

tre

ss (

Pa)

Timeexp(ms)

Particle "E"

153

However, in order to solve Equation 6.11, and Equation 6.12, it is necessary to find

the analytic expression of the shear stress acting on the blood particle. In this regard, data

provided in Figure 6.15 was imported into MATLAB to perform the curve-fitting analysis.

Figure 6.19 shows the best-fitted curves computed in MATLAB overlaid on the shear stress

history of the particles. The shear stress functions, , are then computed for each particle

from the curve-fitting analysis as follows:

Equation 6.13. Shear Stress Function of Particle A.

Equation 6.14. Shear Stress Function of Particle B.

Equation 6.15. Shear Stress Function of Particle C.

Equation 6.16. Shear Stress Function of Particle D.

154

Equation 6.17. Shear Stress Function of Particle E.

{

Equation 6.18. Shear Stress Function of Particle F.

Accordingly, the BDIs values of the particles as they travelled across the leaflets are

calculated using Equation 6.11 and Equation 6.12. In general, the BDIs calculated using the

total differential method showed significant rises compared to those obtained from the

temporal differential method, as depicted in Figure 6.20.

Figure 6.20. BDI values calculated from Average Shear Stress, Temporal Differential and

Total Differential methods.

TotalDifferential

Method

TemporalDifferential

Method

TotalDifferential

Method

TemporalDifferential

Method

TotalDifferential

Method

TemporalDifferential

Method

TotalDifferential

Method

TemporalDifferential

Method

TotalDifferential

Method

TemporalDifferential

Method

TotalDifferential

Method

TemporalDifferential

Method

Particle A Particle B Particle C Particle D Particle E Particle F

LRBC 3.67E-02 7.70E-03 3.78E-02 7.65E-03 1.29E-02 4.08E-03 1.16E-02 3.67E-03 8.95E-03 1.29E-03 1.66E-02 5.46E-03

LPL 8.84E-02 1.56E-02 8.61E-02 1.45E-02 1.88E-02 5.07E-03 1.60E-02 4.31E-03 1.12E-02 1.23E-03 2.61E-02 7.32E-03

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

8.00E-02

9.00E-02

1.00E-01

Pe

rce

nta

ge

155

Importantly, it is also noted that the LRBC index is smaller than the LPL index in all

cases, which is consistent with the known fact that red blood cells are more resistant to shear

stress than platelets (Lim et al., 2001). This finding indicates that the total differential method

presented here is the suitable choice for assessing the potential blood trauma in such a

complex flow field. The highest values of BDI were associated with particle A and particle B

as the particles passed through the small gap between the leaflets’ distal end. These peak

values of BDI are still very low, which suggests that the generated shear stress as a result of

implanting the proposed PHV was insufficient to cause blood damage. However, it should be

noted that the calculated BDIs in this study are intended to be indicative than definitive. This

is due to the fact that there is still no comparable experimental data available to verify the

proposed mathematical methods. Previous studies (Richardson, 1975, Schima et al., 1993, De

Wachter and Verdonck, 2002) to assess the sublethal blood trauma carried out under the

assumption of simple loading conditions (e.g. uniform or laminar flow) is fundamentally

different to such a complex flow field as the one presented in this study. However, any

attempt to explain the rationale of various mathematical methods of estimating blood damage

trauma and to account for understanding the difference between the results could be useful in

assessing the performance of the valve.

Stress distribution in the leaflets 6.4.

Following the optimization process, the effect of decreasing the curvature degree of

lc on the stress distribution in the leaflet was examined in the series of FSI models.

Subsequently, lc with an asymptote angle of 125° was chosen as it showed minimum stress

concentration in the leaflet (Figure 6.21c). It was noted that further increasing the asymptote

angle resulted in an unrealistic shape for the leaflets.

The geometry of lc with an optimum value of a can be written as:

Equation 6.19. Second circumferential curve (optimized curve).

The stress distribution in the leaflets was quantified by equivalent Von Mises

stresses. The Von Mises model was chosen as the yield stress of polymers is commonly

described by modified Von Mises yield criteria (Christiansen et al., 1971, Burriesci et al.,

2010). The stress distribution in the leaflets and the value of the stress was closely examined

156

in the sequences of the opening and closing of one cardiac cycle. The maximum stress level

was observed at the end of the diastole for all valves in which the reference valve was

subjected to a maximum stress level of 7.10 N mm-2 near the commissures (red circles

highlight these regions in Figure 6.21a). A similar finding was reported in the numerical

study previously done for the same valve (Burriesci et al., 2010). In the case of the initial

design and optimized valve, the peak of the stress level was detected as 6.10 N mm-2 and 5.32

N mm-2, respectively.

Figure 6.21. Stress distribution in the leaflet of (a) the reference valve, (b) the initial design,

(c) the optimized valve at t=0.8 s (end of diastolic phase).

(c)

(b)

(a)

157

Although the proposed method of design showed superior control over the design

parameters in terms of the hydrodynamic performance of the valve, finite element (FE)

analysis of the initial valve showed stress localizations along the leaflet attachment line to the

stent (Figure 6.21b). Similarly, a high-stress concentration was observed in the analysis of the

reference valve (Figure 6.21a). In addition, both the reference and initial valve had patchy

stress distribution along the attachment line. The prosthetic valve must survive over 400

million cyclic loads corresponding to approximately ten years of use. Such cyclic loading

imposes harsh oscillating mechanical stresses on the valve. In this working environment, the

fatigue life of polymeric valves must be taken into consideration. It is widely accepted that

stress concentration in the leaflets is associated with leaflet tearing and prolapse (Leo et al.,

2005b, Lynn Gallocher, 2007, Claiborne et al., 2012).

Moreover, calcification is reported as one of the causes of the clinical failure of PVs

(Claiborne, 2012). Although the exact mechanism of calcification remains unclear, studies

(Levy et al., 1991, Vyavahare et al., 1997) show that calcium deposition often occurs at the

region of stress concentration. Previous studies (Mercer et al., 1973, Luo et al., 2003, Kouhi,

2012, Claiborne et al., 2013) showed that a multi-thickness design of leaflets could improve

the stress concentration and reduce the stress level in the leaflet. However, it should be noted

that incorporating such a design to construct the valve requires a manufacturing tolerance of

approximately 1µm, which is a very challenging task from a manufacturing point of view.

In this respect, the measurements of 12 consecutive polyurethane valves with a uniform valve

thickness which were fabricated by combinations of solution casting and injection molding

techniques showed variations of up to 160 µm in the leaflet thicknesses (Mackay et al.,

1996). In fact, the variations in the thickness of the leaflets were substantially greater than the

required manufacturing tolerance which indicates that it is impractical to construct a multi-

thickness design PHV on a commercial scale. Taking this issue into account, the leaflet was

designed with uniform thickness. Subsequently, a novel optimization method was performed

as described in section 4.10 to improve the stress distribution.

In general, the stress distribution analyses showed that the transition from the

regions with a high stress level to the adjacent regions was smoother in the case of the

optimized valve (Figure 6.21c) compared to the initial valve (Figure 6.21b). Note that the

difference between the maximum and minimum stress level along the attachment line was

lower in the case of the optimized valve (2.2 N mm-2) compared to the initial design (4.49 N

mm-2). As shown in Figure 6.21b, the stress levels along the leaflet attachment line varied

158

from 6.10 N mm-2 to 1.61 N mm2 and the stress distribution was erratic. In contrast, the

transition of the maximum stress (5.32 N mm-2) to minimum stress (3.12 N mm-2) was

smoother in the case of the optimized valve. The improvement of stress distribution and

reduction of maximum stress level achieved in the present study can potentially increase the

durability of the valve (Lynn Gallocher, 2007).

Furthermore, the observations showed that the optimized valve opened and closed

synchronously without a sign of significant stress concentration in the entire cycle (Figure

6.21c, and Figure 6.22). Figure 6.22 shows the stress distribution in the optimized leaflets

during the systolic phase until the valve closed. In the early stage of the valve opening (t=20

ms), it was noted that the tensile stresses were more dominantly located in the tip of the

leaflet on the aortic side. This was caused by the relatively low degree of the curvature in the

radial curve (lr). The valve reached its maximum GOA at t=168.5 ms before mid systole. The

early systolic closure (ESC) of the valve was then begun at t=168.5 ms and the closure

continued gradually until the valve closed completely at t=370 ms. The valve closure

mechanism was in good qualitative agreement with the previous study carried out by Sakurai

et al. (Sakurai and Tanaka, 1986) in the temporal relationship between ESC and aortic flow.

Moreover, the maximum value of the stress level in the leaflets of the optimized valve was

significantly lower than the yield tensile strength of biocompatible polymers (i.e.

Bionate=57.4 N mm-2 , Elast-Eon=21~60 N mm-2) which confirmed that the structural

capacity of the valve was beyond the expected hydrodynamic load.

159

Figure 6.22. Equivalent Von Mises stress distribution in the leaflets during systole.

160

Hydrodynamic performance 6.5.Generally, in the case of similar PHVs in terms of durability and thrombogenicity,

the one that provides the largest EOA is preferable (Pibarot and Dumesnil, 2009). EOA of the

prosthetic valve is one of the major parameters associated with prosthetic patient mismatch

(PPM) complications (Marquez et al., 2001). To this effect, measurement of the maximum

EOA of the proposed valve is necessary for the assessment of the valve performance. As

mentioned in section 4.8, traditionally EOA can be calculated either from the Gorlin formula

( ) or continuity equation ( ). Despite the popularity of these two methods,

comparative studies showed discrepancy in the EOA calculated from these methods where it

is noted that systematically underestimated (Rudolph et al., 2002).

However, as EOA is defined as the vena contracta (VC) cross-sectional area of the left

ventricular outflow tract (LVOT), EOA can be accurately measured in the FSI simulation.

Hencehe exact position of the VC (Section A-A in Fig 12) of the LVOT at peak systole was

visualised in the Fluent software for both prototypes (the optimized valve and the reference

valve). Thereby, the EOA of the valves were calculated by measuring the VC cross-sectional

area as 3.05 cm2 and 3.22 cm2 for the reference valve and optimized valve respectively.

Figure 6.23. Predicted blood stream at peak systolic flow rate (t=168.5 ms) passing through

(a) the optimized valve, (b) the reference valve. The solid area represents the

calculated cross-sectional area of the VC (red area in (a), and blue area in (b)).

(a) (b)

161

This is the maximum EOA that the valve can potentially provide which is correlated

to the pressure drop across the valve. It should be noted that pressure drop across the valve or

transvalvular pressure gradient (TPG) is an important parameter by which to assess valve

performance. The small EOA is usually associated with higher blood pressure loss across the

valve and resulting excessive workload for the heart to pump the blood. Hence, evaluating the

systolic TPG is a common practice to characterize valve performance (Grigioni et al., 2000).

Thereby, TPG of the reference and optimized values were calculated during the systole from

Equation 4.28 determining the mean transvalvular systolic pressure drops and systolic energy

loss (Equation 4.29). The regurgitations of the valves were also characterized for the closing

volume (leakage volume associated with the valve closure dynamics) and the leakage volume

(leakage volume through the closed valve). Table 6.4 provides the key hydrodynamic

performance of the reference and optimized valves.

Table 6.4 Hydrodynamic quantities of the reference and optimized valve.

Quantity Reference Valve Optimized valve Transvalvular Systolic pressure

drop (mmHg) 3.94 3.52

Closing volume in one cycle(ml) 2.949 4.2 Leakage Volume in one cycle(ml) 7.84 2.6 Total leakage rate (ml s-1) 13.486 8.5 Effective Orifice area (cm2) 3.05 3.22 GOA space efficiency (% of inner

stent area) 74.53 77.7

Maximum Von Mises stress (N

mm-2) 7.1 5.32

Total energy loss during the

systole (j/beat)

0.0574 0.0507

Overall, the hydrodynamic performance of the valves was evaluated by means of a

3D two-way FSI simulation. As a result, the optimized valve demonstrated 4.25% increase in

EOA, 10.65% and 11.6% reductions of and total systolic energy loss respectively

compared to the reference valve. It should be noted that TPG and the energy loss reductions

that are achieved in the present study could reduce left ventricle hypertrophy which is

suggested to improve long-term survival (Marquez et al., 2001).

162

The regurgitation of the valves was characterized for the closing volume and the

leakage volume in which the optimized valve produced lower leakage volume due to its

smaller commissural gap. However, the reference valve had slightly lower closing

regurgitation volume. In general, the optimized valve showed 36.97% reduction of total

leakage rate per cycle over the reference valve (Table 6.4) Note that the valve leakage

implicates increases of overall volume work for the heart, which leads to heart failure (Claiborne,

2012). Hence, the improved regurgitation volume obtained for the optimized valve could also

increase the success rate of the proposed valve.

As mentioned in section 3.6, the reference valve in the present study showed

acceptable haemodynamic performance in the literature. Therefore, the hydrodynamic

performance of the optimized valve compared to the reference valve. Moreover, the key

hydrodynamic performance (TPG and EOA) of the proposed valve and commercially

available PHVs tabulated in Table 6.5 and Table 6.6 demonstrate how the proposed valve

would perform compared to available PHVs (6 bio-prostheses and three mechanical

prostheses that had acceptable hydrodynamic performance). A comparison of similar valves

or the one with the lower performance was excluded in the comparative study. However, it

should be noted that the EOA and TPG of available PHVs were calculated via a different

setup e.g. in vitro testing. Hence, the comparative study is much more indicative rather than

definitive.

Table 6.5. Systolic pressure drop caused by the proposed valve compared to aortic PHVs. Data for PHVs were collected from the Textbook of Clinical Echocardiography (Otto, 2013)

ProposedPolymeric

Valve

Carbomedics(bileaflets)

St.JudeMedical

(bileaflet)

Medtronic-Hall (tilting

Disk)

Carpentier-Edwards(Ste

ntedbioprosthesi

s)

Carpentier-Edwards

Pericardial(Stented

bioprosthesis)

CryoLife-O'Brien

(stentlessBioprosthesi

s)

EdwardsPrima

(stentlessBioprosthesi

s)

MedtronicFreestyle(stentless

Bioprosthesis)

MedtronicMosaicPorcine(stened

Bioprosthesis)

Average 3.52 12.25 14.96 14.1 16.49 18.56 10.33 16.36 7.66 12.5

High 3.52 16.97 21.49 20.03 23.49 29.38 12.33 27.72 10.59 19.87

Low 3.52 7.53 8.44 8.17 9.49 7.74 8.33 5 4.74 5.13

0

5

10

15

20

25

30

Pre

ssu

re D

rop

(m

mH

G)

Systolic Pressure Drop

163

Table 6.6. EOA of the proposed valve compared to aortic PHVs. Data for PHVs were collected from

Textbook of Clinical Echocardiography (Otto, 2013)

As depicted in Table 6.5 and Table 6.6, the proposed valve had the highest EOA and

respectively the lowest systolic TPG compared to the currently available prostheses. This

suggests that the proposed valve can be implanted in most patients without the occurence of

prosthesis/patient mismatch (PPM). PPM occurs when the EOA of the prosthesis is less than

that of a normal valve (Rahimtoola, 1978). PPM occurs when the EOA of the implanted

valve is relatively small compared to a patient’s body surface area (BSA) (Rahimtoola, 1978,

Dumesnil et al., 1990, Pibarot and Dumesnil, 2006). Hence, the EOA of a prosthetic valve

divided by the patient’s BSA is defined as the EOA Index (Pibarot and Dumesnil, 2006) in

which the EOA index 0.85 cm2/m2 is considered as the threshold for PPM in the aortic

position, while 0.65 cm2/m2 0.85 cm2/m2 and 0.65 are

regarded as moderate and severe PPM, respectively (Pibarot and Dumesnil, 2000, Dumesnil

and Yoganathan, 1992, Pibarot and Dumesnil, 2006). Table 6.7 shows the EOA index of the

proposed valve and available PHVs for varying the BSA.

ProposedPolymeric

Valve

Carbomedics

(bileaflets)

St.JudeMedical

(bileaflet)

Medtronic-Hall (tilting

Disk)

Carpentier-Edwards(St

entedbioprosthes

is)

Carpentier-Edwards

Pericardial(Stented

bioprosthesis)

CryoLife-O'Brien

(stentlessBioprosthes

is)

EdwardsPrima

(stentlessBioprosthes

is)

MedtronicFreestyle(stentless

Bioprosthesis)

MedtronicMosaicPorcine(stened

Bioprosthesis)

Average 3.22 1.52 1.51 1.33 1.66 1.57 1.58 1.455 1.84 2.1

High 3.22 1.98 2.03 1.75 2.14 2.03 2.2 1.95 2.4 2.9

Low 3.22 1.06 1.01 0.91 1.18 1.11 0.97 0.96 1.28 1.3

0

0.5

1

1.5

2

2.5

3

3.5

Squ

are

d c

m

Effective Orifice Area (EOA)

164

Table 6.7. EOA index of the proposed valve compared to the EOA index of aortic PHVs.

Indexed EOA

Valve

Name

Proposed valve

Carbom

edics (bileaflets)

St.Jude Medical (bileaflet)

Medtronic-H

all (tilting Disk)

Carpentier-Edw

ards

(Stented bioprosthesis)

Carpentier-Edw

ards Pericardial

(Stented bioprosthesis)

CryoLife-O

'Brien

(Stentless Bioprosthesis)

Edwards Prim

a (Stentless

Bioprosthesis)

Medtronic

Freestyle

(Stentless Bioprosthesis)

Medtronic M

osaic Porcine

(stented Bioprosthesis)

EOA(cm2)

BSA 3.22 1.52 1.51 1.33 1.66 1.57 1.58 1.455 1.84 2.1

0.6 5.36 2.53 2.51 2.21 2.76 2.62 2.63 2.43 3.07 3.50

0.7 4.6 2.17 2.15 1.9 2.37 2.24 2.26 2.08 2.63 3.00

0.8 4.02 1.90 1.88 1.66 2.0 1.96 1.98 1.82 2.30 2.63

0.9 3.5 1.69 1.67 1.47 1.8 1.74 1.76 1.62 2.04 2.33

1.0 3.22 1.52 1.51 1.33 1.66 1.57 1.58 1.46 1.84 2.10

1.1 2.92 1.38 1.37 1.2 1.50 1.43 1.44 1.32 1.67 1.91

1.2 2.68 1.27 1.25 1.1 1.38 1.31 1.32 1.21 1.53 1.75

1.3 2.3 1.17 1.16 1. 1.27 1.21 1.22 1.12 1.42 1.62

1.4 2.15 1.09 1.07 0.95 1.18 1.12 1.13 1.04 1.31 1.50

1.5 2.14 1.01 1.0 0.88 1.10 1.05 1.05 0.97 1.23 1.40

1.6 2.01 0.95 0.94 0.83 1.03 0.98 0.99 0.91 1.15 1.31

1.7 1.89 0.89 0.88 0.78 0.97 0.92 0.93 0.86 1.08 1.24

1.8 1.78 0.84 0.8 0.73 0.92 0.87 0.88 0.81 1.02 1.17

1.9 1.69 0.80 0.79 0.7 0.87 0.83 0.83 0.77 0.97 1.11

2 1.61 0.76 0.75 0.66 0.83 0.79 0.79 0.73 0.92 1.05

2.1 1.53 0.72 0.71 0.63 0.79 0.75 0.75 0.69 0.88 1.00

2.2 1.46 0.69 0.68 0.6 0.75 0.71 0.72 0.66 0.84 0.95

2.3 1.4 0.66 0.65 0.57 0.72 0.68 0.69 0.63 0.80 0.91

2.4 1.34 0.63 0.62 0.55 0.69 0.65 0.66 0.61 0.77 0.88

2.5 1.28 0.61 0.6 0.53 0.66 0.63 0.63 0.58 0.74 0.84

165

In Table 6.7, the calculated EOA index of the valves is highlighted in green, yellow

and red representing no PPM, moderate risk of PPM and severe risk of PPM, respectively. in

the table shows the proposed valve avoids PPM where moderate PPM occurs for most of

other PHVs starting from BSA of 2. In fact, the proposed valve can be used for patients up to

BSA of 3.78 without the presence of PPM which shows that the proposed valve can be used

for a wide range of patients, including obese patients.

Validation of the FSI simulation 6.6.The FSI simulation of the proposed valve was validated by comparing the predicted

results with the previously published data and in vitro experimental measurements as

described in the following.

Computational validation 6.6.1.The results obtained from the FSI analyses of the reference valve were compared to

those obtained from in vitro hydrodynamic testing of the same design and boundary

conditions (Burriesci et al., 2010). The comparative study showed small deviations in the

results (see Table 6.8) which support the validity of the FSI model used in the present study.

In general, the predicted kinematics, mechanics, and hydrodynamic of the reference valve

were in good agreement with the numerical and experimental study previously done which

support the validity of the predicted results for both the optimized and reference valve

(Burriesci et al., 2010). It should be noted, however, in the present study, we used the FSI

model as a tool to evaluate varying valve designs, and analysing the effect of varying design

parameters on the durability and hydrodynamic performance of the valve rather than an

approximation of the physiological situation.

166

Table 6.8. Comparison of the experimental results with the predicted results.

In Vitro validation 6.6.2.The simulation results of the proposed valve were compared to the 2D deformation

of the leaflets (optimized valve) captured by the high-speed camera positioned in the

upstream direction during the cardiac cycle of the in vitro experiments. Figure 6.24 shows

the results at six major time intervals as follows: a) early systole, b) mid- systole, c) peak

systole, d) early diastole, e) mid-diastole f) end diastole. A comparison of the experimental

results (provided in the left column) with the FE results (the right column) show that the

predicted kinematics of the leaflets were in good qualitative agreements with the

experimental results. Similar opening and closing features were noted in both the predicted

and experimental results. In this sense, it is observed that the gap between the leaflet-free

edge near the stent post tended to widen from early systole and form a concave shape in these

regions. This characteristic of the leaflet opening shape lasted until peak systole. In addition,

both predicted and experimental results show that the leaflets started to close by reducing the

gap between the leaflets near the stent post. However, it is noted that starting from mid-

diastole towards the end of diastole, the leaflets began to close abruptly and unevenly as

shown in Figure 6.24e. The abrupt closure of the valve observed in the in vitro experiment

Quantity

Experimental

Results

Predicted

Results

Reference Valve Reference

valve

Percentage of

error (%)

Transvalvular pressure drop (mmHg) 4.0 3.94 1.5

Closing volume in one cycle(ml) 3.0 2.949 1.7

Leakage Volume in one cycle(ml) 8.0 7.84 2

Total leakage rate (ml s-1) 15.7 13.486 14.14

Effective Orifice area (cm2) 3.02 3.05 1

GOA space efficiency (% of inner stent area) 73.7 74.53 1.12

Maximum Von Mises stress (N mm-2) 6.9 7.1 2.89

167

could be due to the absence of the SOV cavities. It is shown that the generated vortices in the

SOV cavities facilitate the smooth and gradual closure of the valve (Katayama et al., 2008).

Figure 6.24. Comparison of the FE structural model with in vitro leaflet motion.

168

Furthermore, in order to provide quantitative verification of the FE results, three

deformation measures were defined in this study, as illustrated in Figure 6.25. The three

metrics (D1, D2, D3) are the distance between the centre of PHV and the point on the tip of

the leaflet edges at each time interval. The 2D images recorded by the high-speed camera

were processed and then the rates of change of these metrics were compared to those

obtained from the simulation as depicted in Figure 6.26. The proposed verification method

was used previously by Haj-Ali et al. (2008). In the case of the simulation, only one metric

was used (D1) in the comparative study, as the displacement of the leaflets were almost

symmetrical.

Figure 6.25. Proposed deformation measures on a) the actual valve in vitro and b) the

optimized valve in the FSI simulation.

The image processing of the 2D deformation of the proposed PHV revealed that the

FSI simulation predicted relatively accurate results for the overall structural responses. The

maximum errors of 15%, 8%, and 11% were recorded for D1, D2, and D3 respectively. As

previously mentioned, the EOA of the valve is one of the major key performances of the

valve, which is directly correlated to the GOA of the valve. Hence, the GOA of the valve at

peak systole is also measured in the in vitro experiment and compared to the predicted results

as shown in Figure 6.27 The GOA calculated from the FSI simulation and image processing

of the 2D deformation of the valve in the in vitro experiments is 3.31 cm2 and 3.13 cm2,

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respectively. These results also can only add to the confidence in the accuracy of the

predicted leaflet deformation as the 5.7% error in the calculated GOA is relatively small.

Figure 6.26. Comparing the FE predictions with the experimental values.

Figure 6.27. Maximum GOA at peak systole for a) the actual valve b) FE structural model.

-1

0

1

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1

Dis

tan

ce (

mm

)

Time (s)

Experimental data (D1)

Experimental data (D2)

Experimental data (D3)

FSI data (D1)

GOA experimental

(cm2)

Predicted GOA

(cm2)

Percentage error (%)

3.13 3.31 5.7

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7 Chapter 7

7.1 Overall conclusion In this research, an extensive literature review was undertaken on the previous

studies to develop a prosthetic aortic heart valve. The literature review covered the limitations

of commercially available prosthetic heart valves (PHVs) and approaches to develop an

alternative PHV including the valve deign procedures, and validation techniques. These

limitations are mainly the poor structural reliability of the bioprosthetic valve, and the

impaired haemodynamic compatibility of the mechanical heart valve. Hence, the motivation

of this research was to design a PHV that has lifelong durability with a similar hemodynamic

performance to a native valve. Prosthetic heart valves made of biocompatible and biostable

polymers can ideally fulfil these requirements. However, the literature review showed that

despite the advancements in the development of biostable and biocompatible polymers,

current designs still suffer from impaired haemodynamic performance. Moreover, the FSI

models incorporated in these methods are seriously questionable in terms of the reliability of

the FSI results and the validation process. Hence, the achievements of this study can be

highlighted as the development of a reliable FSI model and an optimized polymeric aortic

valve that is capable of providing a similar hemodynamic performance to a native valve.

A novel parametric design for a polymeric stented heart valve was proposed. The

design of the valve was characterized by two curves (circumferential and radial), which were

optimized in the series of FSI simulations to have maximum GOA, minimum regurgitation

and less damaging stress concentration in the leaflets. A two-way coupling FSI simulation

was chosen for the evaluation of the valve performance as it has been shown in the literature

that this type of simulation produces more accurate solutions compared to one-way, in fact, it

can be of second-order time accuracy. Furthermore, the two-way coupling method guarantees

energy conservation at the fluid-solid interface whereas one-way coupling does not.

However, the implementation of the two-way coupling method to simulate such a complex

biofluid flow past PHVs with flexible leaflets is a challenging task. Various FSI algorithms

have been developed such as immersed boundary (IB) and fictitious domains methods. In

addition, different computational coordinate systems such as Arbitrary-Lagrangian-Eulerian

(ALE) and Eulerian-Lagrangian based FSI models have been investigated. The literature

shows that each of these methods has been extended to three dimensions of FSI simulation of

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PHVs with flexible leaflets. However, ALE approaches with the dynamic re-meshing method

showed superior performance which has been extensively and successfully used for FSI

problems. The main disadvantage associated with this technique is the need for the expensive

re-meshing method.

Consequently, FSI analysis was carried out by strongly coupling

(two-way coupling) ANSYS Fluent (Participant 1) to ANSYS dynamic structural (Participant

2) in an iterative sequential algorithm which was managed by the system coupling component

in ANSYS. The arbitrary Lagrangian-Eulerian (ALE) method was used by means of the

dynamic mesh model in Fluent to model the blood flow past the valve. The experimental

uniaxial and biaxial data curve of Bionate® 80A were fitted to the three-parameter Mooney-

Rivlin model in order to model the non-linear characteristic of the hyperplastic polymer.

Importantly, the numerical simulation carried out in this research was validated by

means of the numerical method and in vitro leaflet kinematic method. In the first method, a

polymeric valve that was shown in the literature to possess acceptable haemodynamic

performance is chosen as a reference valve. A simulation that used the same reference valve

and was validated by extensive in vitro evaluation was selected as a reference study.

Consequently, the reference valve was successfully modelled and simulated with the exact

boundary conditions as the reference study. Finally, the FSI simulation was validated by

comparing the predicted results to those in the previously published literature. The

comparative study showed small deviations in the results which support the validity of the

FSI model used in the present study. In general, the predicted kinematics, mechanics and

hydrodynamic of the reference valve were in good agreement with the numerical and

experimental studies previously conducted which supports the validity of the predicted results

for both the optimized and reference valve.

In the in vitro validation method, the simulation results of the proposed valve were

compared to the 2D deformation of the leaflets (optimized valve). The experimental results

were taken at six major time intervals: a) early systole, b) mid-systole, c) peak systole, d)

early diastole, e) mid-diastole f) end diastole. A comparison of the experimental results to the

FSI results showed that the predicted kinematics of the leaflets were in good qualitative

agreement with the experimental results. Similar opening and closing features were noted in

both the predicted and experimental results. It is observed that the gap between the leaflet-

free edge near the stent post tended to widen from early systole and form a concave shape in

these regions. This characteristic of the leaflet opening shape lasted until peak systole. In

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addition, both the predicted and experimental results showed that the leaflets started to close

by reducing the gap between the leaflets near the stent post.

Furthermore, in order to provide a quantitative verification of the FSI results, three

deformation measures were defined in this study. The three metrics (D1, D2, D3) were

defined to measure the displacement of the leaflet tip during the experiment as well as FSI

simulation. The 2D images recorded by the high-speed camera were processed, and then the

rates of change of these metrics were compared to those obtained from the simulation. The

comparative study showed a maximum error of 15%, 8%, and 11% for D1, D2, and D3

respectively. The geometric orifice area (GOA) of the optimized valve was 5.7% smaller in

the experiment (at peak systole) compared to the predicted GOA. Overall, these quantitative

comparisons can only add to the confidence in the accuracy of the numerical simulation.

In order to implement the in vitro validation technique, the pulse duplicator machine

was designed and manufactured to simulate the haemodynamic loads applied to the valve in

the FSI simulation. A prototype of the optimized valve was constructed from the Bionate®

polymer using advanced manufacturing techniques, including electron beam melting (EBM)

and 3D printing methods to construct the valve. To the best of our knowledge, this is the first

time that such techniques have been combined to construct a prosthetic valve. The lead

manufacturing time of the proposed technique for a customised prosthetic valve (patient

match implant) was estimated to be less than 4 hours. This means that in the future,

hypothetically, a patient can walk into a hospital and have heart valve replacement surgery

the very next day.

The performance of the optimised valve was evaluated thoroughly with respect to

both structural and haemodynamic performance. The structural performance of the valve was

determined by analysing the stress distribution in the leaflets. The stress distribution and its

magnitude were quantified by equivalent Von Mises stresses. In general, the analyses showed

that transition from the regions with high stress level to the adjacent regions was smoother in

the case of the optimized valve compared to the initial valve. Furthermore, the observations

showed that the optimized valve opened and closed synchronously without a sign of

significant stress concentration in the entire cycle. The maximum value of the stress level in

the leaflets of the optimized valve was significantly lower than the yield tensile strength of

biocompatible polymers (i.e. Bionate=57.4 N mm-2 , Elast-Eon=21~60 N mm-2) which

confirmed that the structural capacity of the valve was beyond the expected hydrodynamic

173

load. The improvement of stress distribution and reduction of maximum stress level achieved

in the present study can potentially increase the durability of the valve.

The haemodynamic performance of the valve is evaluated through the analysis of the

velocity streamline on series of 2D planar locations, where the analyses of the velocity

distributions in the cross-sectional planes showed high-velocity gradients in the vicinity of

the leaflets. These velocity gradients are proportional to shear stress and may cause

mechanical damage to red blood cells and the leaflet surfaces. Hence, the turbulent flow

regime is quantified by Reynolds shear stress (RSS) tensor, and wall shear stress (WSS) to

evaluate the proposed valve design. The highest RSS of 4.910 Pa was recorded at 0.5D to

0.7D downstream from the stent ring and 14 mm away from the valve centerline towards the

right aortic wall. This magnitude of shear stress can be considered to have a negligible effect

on RBC damage. Therefore, blood element damage caused by WSS was analyzed in order to

evaluate to which degree the proposed PHV will damage blood components. In this regard,

the movements of 6 blood particles passing across the elevated shear stress zones were

traced. Subsequently, the shear stress histories of the particles as they traversed the leaflets

were extracted. The BDIs were calculated from the mathematical model that was introduced

in this study, namely, the total differential method. It is noted that the highest values of BDI

were associated with the particles passing through the small gap between the leaflet distal

end. However, these peak values of BDIs (LRBC=3.78e-3, LPL=8.61e-2) were still very low,

which suggested that the shear stress generated as a result of implanting the proposed PHV

was insufficient to cause blood damage.

The key hydrodynamic performance criteria of the valve in terms of the EOA and

transvalvular pressure drop were calculated as 3.22 cm2 and 3.52 mmHg respectively. The

optimized valve demonstrated 4.25% increase in EOA, 10.65% and 11.6% reductions of

and total systolic energy loss respectively compared to the reference valve. It should be

noted that TPG and the energy loss reductions that are achieved in the present study could

reduce left ventricle hypertrophy which is suggested to improve long-term survival.

Furthermore, the optimized valve showed a 36.97% reduction in the total leakage rate per

cycle over the reference valve. Note that valve leakage implicates an overall increase in the

volume of work for the heart, which leads to heart failure. Hence, improved regurgitation

volume obtained for the optimized valve could also increase the success rate of the proposed

valve.

174

7.2 Limitations There are a number of limitations in this research. In this study, the numerical

simulation is validated by comparing the predicted results with the previously published data.

However, there was no validation of the velocity profile of the flow passing through the

optimised valve. It was initially planned to use the laser Doppler anemometry (LDA)

technique to compare the predicted fluid velocity profile with experimental measurements as

part of the validation process. However, the laser machine broken down unexpectedly and the

repair time was beyond the time constraints of the Ph.D. candidature.

It is noted in the experimental results that starting from mid-diastole towards the end

of diastole, the leaflets began to close abruptly and unevenly. The abrupt closure of the valve

that was observed could be caused due to the absence of similar sinus of Valsalva (SOV)

cavities in the pulse duplicator machine.

Furthermore, the 3D printing of the stent and adhesion method (using glue) to attach

the leaflet to a stent that is used in this study were not biocompatible. Such techniques are

used to construct the valve to demonstrate the feasibility of using advanced manufacturing

techniques. Further studies are required in order to construct a fully biocompatible and bio-

stable prosthetic valve, however, this was out of the scope of the current study.

7.3 Future research and recommendations The advanced design and numerical simulation presented in this study is the first

fundamental step towards the development of the polymeric PHV. However, further research

is needed in both computational simulation and experimental examinations as follows:

7.3.1 Computational research requirements The advanced numerical simulation introduced in this research required both solid

and fluid domains to be resolved in a very fine discretization scheme. Therefore, the

computational cost of such a simulation was subnational. Furthermore, the deformation of

each mesh (in moving regions) in relation to the adjacent cell was too large, causing mesh

distortion. Consequently, a mesh adaption technique such as dynamic re-meshing was used

combined with the user-defined subroutine. However, setting up the FSI model to simulate

the cardiac cycle as a dynamic event was seriously challenging. In this regard, further

research is still needed to improve the numerical algorithms in such a multi-domain

simulation.

175

In addition, in the present simulation, the aortic roots were modelled as rigid walls

with a no slip condition. As previously mentioned, this is common practice for this type of

simulation; furthermore, this was necessary in order to have the same boundary conditions

apply on the valve in the pulse duplicator machine. However, further study can be performed

to investigate the effects of implanting such a polymeric valve on the native site with flexible

aortic roots.

7.3.2 Future experimental requirements The advanced manufacturing techniques described in this study can be used to

construct primitive prototypes. However, stent material and the adhesion method to attach the

polymeric cusps to a stent must be adopted to be biocompatible and biostable. Hence, further

research is required in this respect.

Further in vitro studies should be carried out to fully characterise the flow past the

valve using the LDA technique. In addition, the durability and fatigue life of the valve must

be tested to evaluate the continued function of the valve. Note that FDA requires the valve to

remain functional for 600 million cycles, and such a test often runs at a rate of 900 to 1500

beat per second which is referred to as an accelerated test. Creep characterization of the

polymeric valve also should be performed to evaluate the potential creep deformation of the

polymeric stent. On the success of these in vitro examinations, this work can be extended to

in vitro trials on animals.

176

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