dynamic modelling and analysis of hydraulic forces in...
TRANSCRIPT
Ana Rita Pires Quintas
Dynamic modelling and analysis ofhydraulic forces in radial blood pumps
Ana
Rita
Pire
s Qu
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s
October 2015UMin
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201
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Universidade do MinhoEscola de Engenharia
October 2015
M.Sc. DissertationIntegrated Master in Biomedical EngineeringBiomaterials, Biomechanics and Rehabilitation
Dissertation done under the supervision ofProfessor Doutor João Paulo Flores Fernandes
Ana Rita Pires Quintas
Dynamic modelling and analysis ofhydraulic forces in radial blood pumps
Universidade do MinhoEscola de Engenharia
Acknowledgments
Developing this dissertation was one of the most challenging endeavours of my life. For this
reason, the support I received from an amazing set of people during this period was invaluable for
me. Therefore, I would like to extend a deep thank you:
To Professor Paulo Flores, for his end-to-end guidance, from helping me to choose my
dissertation topic and for all the advice on the development of my dissertation.
To the Department of Mechanism Theory and Dynamics of Machines of the RWTH Aachen,
for the incredibly warm welcome I received. I am grateful to them for accepting my request to
develop my investigation in the institute and for making me feel at home from day one. In particular,
I want to thank Ferdinand Schwarzfischer, my orientator, for helping me to overcome all the
obstacles I faced, and for teaching me how to structure my approach to this investigation.
To ReinVAD GmbH, for their receptiveness and for letting me contribute to their project. In
particular, I wanted to thank Hongyu Deng for always having the patience to shed light into all my
doubts. Finally, I wanted to extend my deepest gratitude to Roland Graefe. For providing me with
all the data and relevant materials I needed, for thoroughly explaining me how the ReinVAD LVAD
worked and for saying “now this becomes interesting” whenever something unexpected happened
to my research and I got worried.
To my friends in Portugal and in Germany who always told me to believe in myself and gave
me support when I needed it. In special, I am grateful to my roommates in Aachen, Joana and
Ana, for being my second family when I was away from home.
And last but must important, to my family, for all the support. Throughout my life they have
been the pillar that supported me, and everything I ever achieved, I owe it to them. In particular I
must deeply thank my mother, for always listening to me and putting a smile on my face when I
needed it the most. I also want to give my deepest thanks to Tiago. Words cannot express how
grateful I am for him being in my life and how much his help and support made this work easier.
1
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Abstract
Dynamic modelling and analysis of hydraulic forces in radial blood pumps.
Cardiovascular diseases are the most frequent cause of death worldwide and one of the
most important challenges that health systems across the world have to face.
Despite all their merits, conventional medication therapy and heart transplants present,
respectively, important limitations of effectiveness and availability. As a result, cardiac mechanical
assist devices have become a crucial and widely accepted option. The last decades witnessed the
proliferation of a wide range of such devices, including the ReinVAD LVAD, which is a third
generation blood pump currently under development by the Helmholtz-Institute for Biomedical
Engineering and ReinVAD GmbH.
The present work focused on the dynamic analysis of the hydraulic forces acting on
impellers of radial blood pumps. This approach was tailored to the ReinVAD LVAD, aiming to
support its development. An analytical model of the axial hydraulic forces acting on this pump was
developed and implemented in MATLAB® and SIMULINK®, allowing for the estimation of these
forces under different scenarios and pump designs. As for the radial hydraulic force, a quick
estimation methodology was adopted, which validated the initial assumption that the magnitude of
this force would not be very relevant when compared to the one of the axial hydraulic force.
Applying this axial hydraulic force model, the two major variables of the pump operation -
flow rate and rotation speed - were tested. The resultant axial hydraulic force magnitude was
estimated, and its behaviour with changing conditions was discussed. Under a normal operating
context, the magnitude of this force was estimated to be in the order of 0 to 1 N. Moreover, it was
concluded that this force decreased in magnitude with increasing flows, while it increased in
magnitude with increasing rotation speeds. To understand these results, the individual effects that
affected the different components of the axial hydraulic resultant force were analysed in detail.
The conclusions of this study were found to match the existing literature on similar pumps.
An additional validation of the model was performed, comparing its results with available CFD
simulations of the ReinVAD LVAD. The predictions of the model and of the CFD simulations
regarding the tendencies of the forces were found to be consistent in both simulations.
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Resumo
Análise e modelação dinâmica das forças hidráulicas em bombas cardíacas
radiais.
As doenças cardiovasculares constituem a principal causa de morte no mundo,
apresentando-se como um dos mais críticos desafios enfrentados pelos sistemas de saúde.
Apesar de todos os seus méritos, a medicação convencional e os transplantes cardíacos
apresentam importantes limitações, respetivamente de eficácia e disponibilidade. Estas razões
levaram a que as bombas cardíacas se tenham tornado uma opção clínica amplamente aceite e
crucialmente importante. Assim, as últimas décadas testemunharam a proliferação de um leque
diversificado destes dispositivos, incluindo o ReinVAD LVAD, um dispositivo de terceira geração em
desenvolvimento pelo Helmholtz-Institute for Biomedical Engineering e pela ReinVAD GmbH.
A presente investigação focou-se numa análise dinâmica das forças hidráulicas que atuam
em bombas cardíacas radiais. Esta abordagem foi adaptada ao caso específico do ReinVAD LVAD,
de forma a apoiar o seu desenvolvimento. Um modelo analítico das forças axiais hidráulicas que
atuam nesta bomba foi assim desenvolvido e implementado em MATLAB® e SIMULINK®,
permitindo estimar estas forças em diferentes cenários. Já a força radial hidráulica foi estimada
de acordo com uma abordagem simplificada, validando a hipótese de que a sua magnitude é
pouco relevante quando comparada com a da força axial hidráulica.
Aplicando o modelo desenvolvido para as forças axiais hidráulicas, foram testadas as duas
principais variáveis do funcionamento da bomba – fluxo e velocidade de rotação. Estas simulações
permitiram estudar a forma como as forças axiais hidráulicas reagem a alterações nestas duas
variáveis. Concluiu-se que a magnitude da força resultante aumenta com reduções do fluxo e com
aumentos da velocidade de rotação. Adicionalmente, estimou-se que esta magnitude esteja
compreendida, para condições normais de funcionamento da bomba, entre 0 e 1 N. Os efeitos
individuais e as diferentes componentes da força resultante foram analisados detalhadamente, e
as conclusões deste estudo mostraram-se coerentes com a literatura existente.
Por último, o modelo foi validado através da comparação dos seus resultados com dados
de CFD da ReinVAD LVAD, tendo-se concluído que os resultados eram coerentes em ambas as
simulações.
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Contents
Abstract ................................................................................................................... v
Resumo .................................................................................................................. vii
Contents ................................................................................................................. ix
List of Abbreviations .............................................................................................. xiii
List of Symbols ....................................................................................................... xiv
List of Figures ....................................................................................................... xvii
List of Tables .......................................................................................................... xxi
Chapter 1 - Introduction ........................................................................................... 1
1.1 Motivation ................................................................................................................. 1
1.2 Scope and Objectives ................................................................................................ 2
1.3 Literature Review ....................................................................................................... 3
1.4 Dissertation Overview ................................................................................................ 8
Chapter 2 - Human Cardiovascular System and Cardiac Assist Devices .................... 9
2.1 The Heart ................................................................................................................ 10
2.2 The Blood ............................................................................................................... 11
2.2.1 Composition of Blood ............................................................................................... 11
2.2.2 Macroscopic Rheological Properties of Blood ............................................................ 13
2.2.3 Hemolysis and Thrombosis ...................................................................................... 15
2.3 Heart Failure ........................................................................................................... 16
2.4 Cardiac Assist Devices ............................................................................................. 18
2.4.1 Types of Cardiac Assist Devices ............................................................................... 19
2.4.2 Hydrodynamic and Electromagnetic Bearings in Third Generation Blood Pumps ........ 23
2.5 Summary and Discussion ........................................................................................ 25
x
Chapter 3 - Dynamic Modelling and Analysis of ReinVAD LVAD .............................. 27
3.1 The ReinVAD LVAD .................................................................................................. 27
3.1.1 ReinVAD LVAD Description ....................................................................................... 28
3.1.2 Blood Flow in ReinVAD LVAD .................................................................................... 31
3.2 Identification of Forces Acting on the Pump.............................................................. 32
3.3 Axial Hydraulic Force Model ..................................................................................... 34
3.3.1 MATLAB and SIMULINK Implementation .................................................................. 42
3.4 Radial Hydraulic Force ............................................................................................. 43
3.4.1 Estimation of the Radial Force .................................................................................. 45
3.5 Summary and Discussion ........................................................................................ 47
Chapter 4 - Results and Discussion ........................................................................ 49
4.1 Scenario of Simulation ............................................................................................. 49
4.1.1 Simulation Conditions - Physiological Variables ......................................................... 49
4.1.2 Simulation Conditions – Pump Design and Dimensions ............................................ 50
4.1.3 Simulation Conditions – Additional CFD Data ............................................................ 51
4.1.4 Description of the Simulations .................................................................................. 52
4.2 Analysis of Results ................................................................................................... 53
4.2.1 Simulation with Variable Flow ................................................................................... 53
4.2.2 Simulation with Variable Rotation Speed ................................................................... 60
4.3 Comparison with Available Data ............................................................................... 65
4.4 Summary and Discussion ........................................................................................ 66
Chapter 5 - Conclusions and Future Developments ................................................ 67
5.1 Conclusions ............................................................................................................ 67
5.2 Future Developments .............................................................................................. 69
References ............................................................................................................. 71
xi
Appendix I - Auxiliary Calculation of Radial Hydraulic Force ................................... 79
Appendix II – SIMULINK® and MATLAB® Code...................................................... 81
Appendix II.I – MATLAB ® Code ........................................................................................ 81
Appendix II.II – SIMULINK ® Blocks ................................................................................... 85
Appendix III - Additionally CFD Data ....................................................................... 89
xii
xiii
List of Abbreviations
AMB - Active magnetic bearing
BiVAD - Biventricular assist device
CFD - Computational fluid dynamics
DOF - Degree of freedom
HF - Heart failure
IABP - Intraaortic balloon pump
LVAD - Left ventricular assist device
PID - Proportional integral derivative
PMB - Passive magnetic bearing
RBC - Red blood cell
RBP - Rotary blood pump
RVAD - Right ventricular assist device
TAH - Total artificial heart
xiv
List of Symbols
Symbol Description Unit
b1 Blade inlet width m
b2 Blade outlet width m
b3 Volute inlet width m
b4 Blade inlet width with shrouds m
C Radial force coefficient -
c Absolute velocity m/s
c1m Meridional component of velocity in the impeller inlet m/s
c2m Meridional component of velocity in the impeller outlet m/s
cax_FS Axial distance between casing inlet and front casing wall (sax_FS + oax1) m
cax_RS Axial distance between casing inlet and rear casing wall (sax_RS + oax2) m
cu Absolute circumferential velocity m
dFS Diameter at front shroud m
dI Diameter at impeller m
dRS Diameter at rear shroud m
dV Diameter at volute m
f Frequency of the AC supply current Hz
Fax Axial hydraulic force N
Fb Buoyancy force N
FFS Axial hydraulic force on front shroud N
Fg Gravity force N
FG Gyroscopic force N
FH Hydraulic force N
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FHS Axial hydraulic force on shroud N
FI Inertial force N
FM Magnetic force N
Fm Momentum force N
FRS Axial hydraulic force on rear shrouds N
g Gravity acceleration ( g=9.8 m/s2) m/s2
H Pressure Head m
k̅ Mean rotation factor -
kWF Rotation coefficient of the fluid without flow through impeller sidewall clearances
-
k̅FS Mean rotation factor at front shroud gap -
k̅RS Mean rotation factor at rear shroud gap -
mb Buoyancy mass kg
mR Rotor mass kg
Ns Synchronous speed rad/s
oax1 overlap between the volute and the impeller at front side m
oax2 overlap between the volute and the impeller at rear side m
P number of poles of the rotor -
p1 Pressure at impeller inlet Pa
p2 Pressure at impeller outlet Pa
Q Flow rate m3/s
q* Flow rate ratio -
QBEP Flow rate at best efficient point m3/s
Qlf Leakage flow m3/s
Qlf_FS Leakage flow in front shroud m3/s
xvi
Qlf_RS Leakage flow in front shroud m3/s
r Radius m
Re Reynolds number -
rFS Radius at front shroud m
rI Radius at impeller m
rRS Radius at rear shroud m
rV Radius at volute m
sax_FS Axial distance between impeller front shroud and volute m
sax_RS Axial distance between impeller rear shroud and volute m
u Circumferential velocity m/s
u2 Circumferential velocity at the impeller outlet m/s
xFS Ratio of front shroud diameter and the impeller diameter ( dFS/dI) -
xRS Ratio of rear shroud diameter and the impeller diameter ( dRS/dI) -
β Angular velocity pf the fluid in the impeller sidewall clearances rad/s
ΔPim Static pressure rise in impeller (above impeller inlet) Pa
ε2 Angle between mean streamline and impeller axis at impeller outlet deg
μ Dynamic viscosity Pa.s
ν Kinematic viscosity (μ = ρ x ν) m2/s
ρ Density kg/m3
φlf Leakage flow coefficient -
ω Angular rotor velocity rad/s
xvii
List of Figures
Chapter 1
Figure 1.1 - Model II of the heart-lung machine used by Dr. John H. Gibbon in his first successful
heart operation on May 6, 1953 (Hill 1982). ............................................................................. 3
Figure 1.2 - Second generation pumps with successful application and implementation: (a)
DeBakey VAD (Noon & Loebe 2010); (b) Jarvik 2000 (Jarvik Heart Inc. 2009); and (c) HeartMate
II (Thoratec Corporation 2008). ................................................................................................. 4
Figure 1.3 - Third generation pumps with successful application and implementation: (a)
VentrAssist LVAD (Jayanthkumar et al. 2013); (b) Berlin Heart INCOR (Berlin Heart GmbH 2009);
(c) HeartMate III (Thoratec Corporation 2014) ;and (d) Levitronix CentriMag (Thoratec Corporation
2011). ...................................................................................................................................... 5
Chapter 2
Figure 2.1 - An overview of the cardiovascular system and both systemic and pulmonary circulation.
The blood is shown in blue when it deoxygenated and red when fully oxygenated; adapted
from Whittemore (2009). .......................................................................................................... 9
Figure 2.2 - Structure of the heart, and course of blood flow through the heart chambers; adapted
from Guyton & Hall (2006)...................................................................................................... 10
Figure 2.3 - Viscoelastic profile dependent of shear rate of normal human blood. Measurements
were made at 2 Hz and 22 °C in an oscillating flow. In the bottom of the picture an illustration of
the arrangement of RBC in each region is represented (Kowalewski 2005). ............................. 13
Figure 2.4 - Prevalence of heart failure by sex and age; adapted from Lloyd-Jones et al. (2009).
.............................................................................................................................................. 16
Figure 2.5 - Diagram of current solutions of cardiac assist devices; adapted from Reul & Akdis
(2000). ................................................................................................................................... 20
xviii
Chapter 3
Figure 3.1 – (a) Exploded view of the ReinVAD LVAD; (b) Assembled view of the ReinVAD LVAD;
adapted from Graefe & Deng (2015). ...................................................................................... 28
Figure 3.2 - Scheme of the single volute configuration: (a) Volute front view, with representation of
volute throat and diffuser; (b) Volute cross section; adapted from Lazarkiewicz, Stephen
Troskolanski (1965). ............................................................................................................... 29
Figure 3.3 - 3D CAD illustration, with different materials represented of the internal elements of the
pump: AMB; rotor/impeller; and motor stator; adapted from Graefe & Deng (2015)................. 29
Figure 3.4 - Illustration of the impeller: (a) Closed impeller design; adapted from Lazarkiewicz,
Stephen Troskolanski (1965) and (b) Meridional section of the ReinVAD LVAD impeller and volute
casing. ................................................................................................................................... 30
Figure 3.5 - Meridional section of the impeller and volute casing, presenting the pressure
distribution and axial hydraulic forces. ..................................................................................... 35
Figure 3.6 -Meridional section of the impeller and volute casing, presenting the main geometric
variables. ................................................................................................................................ 36
Figure 3.7 - Main blocks of the resultant hydraulic force: axial hydraulic force on impeller shrouds
and momentum force. ............................................................................................................ 43
Figure 3.8 - Uniform pressure distribution around the impeller; adapted from Lazarkiewicz,
S.Troskolanski (1965). ............................................................................................................ 43
Figure 3.9 - Radial force for (a) low flow rates (q*<<1); and (b) high flow rates (q*>>1); ; adapted
from Guelich et al. (1987). ...................................................................................................... 45
Chapter 4
Figure 4.1 - CFD simulations: (a) Graph presenting the relationship between the pressure rise in
impeller (mmHg) and the flow rate (l/min);(b) Graph presenting the relationship between the
leakage flow (l/min) in each shroud and the flow rate (l/min): leakage flow in front shroud – red;
leakage flow in rear shroud – blue. ......................................................................................... 51
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Figure 4.2 - CFD simulations: (a) Graph presenting the relationship between the pressure rise in
impeller (mmHg) and the rotation speed (rpm);(b) Graph presenting the relationship between the
leakage flow (l/min) in each shroud and the rotation speed (rpm): leakage flow in front shroud –
red; leakage flow in rear shroud – blue. .................................................................................. 52
Figure 4.3 - Graph presenting the relationship between the axial hydraulic force (N) and the flow
rate (l/min), based on the analytical model. ............................................................................ 53
Figure 4.4 - Graph presenting the relationship between each component of the axial hydraulic force
and the flow rate (l/min): momentum force - red (N) and the resultant force acting in the shrouds
- blue (N), based on the analytical model. ................................................................................ 55
Figure 4.5 - Graph presenting the relationship between each component of the resultant axial
hydraulic force acting on the shrouds and the flow rate (l/min): Force acting on the rear shroud -
blue (N) and force acting on the front shroud - red (N), based on the analytical model. ............. 56
Figure 4.6 - Graph representing the local rotation factors along each radius ratio for the front
shroud, for each flow rate – 1l/min (blue), 3l/min (red), 5l/min (black), 7l/min (blue dotted) and
9l/min (red dotted). ................................................................................................................ 58
Figure 4.7 - Graph representing the local rotation factors along each radius ratio for the rear shroud,
for each flow rate – 1l/min (blue), 3l/min (red), 5l/min (black), 7l/min (blue dotted) and 9l/min
(red dotted). ........................................................................................................................... 58
Figure 4.8 - Graph presenting the relationship between the axial hydraulic force (N) and the rotation
speed (rpm), based on the analytical model. ........................................................................... 60
Figure 4.9 - Graph presenting the relationship between each component of the axial hydraulic force
and the rotation speed (rpm): momentum force - red (N) and the resultant force acting in the
shrouds - blue (N), based on the analytical model. ................................................................... 61
Figure 4.10 - Graph presenting the relationship between each component of the resultant axial
hydraulic force acting on the shrouds and the rotation speed (rpm): Force acting on the rear shroud
- blue (N) and force acting on the front shroud - red (N), based on the analytical model. ........... 62
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Figure 4.11 - Graph representing the local rotation factors along each radius ratio for the front
shroud, for each rotation speed of the impeller– 1800 rpm (blue), 2100 rpm (black), 2400 rpm
(red), 2700 rpm (blue dotted) and 3000 rpm (red dotted). ...................................................... 63
Figure 4.12 - Graph representing the local rotation factors along each radius ratio for the rear
shroud, for each rotation speed of the impeller– 1800 rpm (blue), 2100 rpm (black), 2400 rpm
(red), 2700 rpm (blue dotted) and 3000 rpm (red dotted). ...................................................... 64
Figure 4.13 - Graph presenting the relationship between the axial hydraulic force (N) and the flow
rate (l/min) by the mathematical model developed – blue and the CFD data available for the
ReinVAD pump – red. ............................................................................................................. 65
Figure 4.14 - Graph presenting the relationship between the axial hydraulic force (N) and the
rotation speed (rpm) by the mathematical model developed – blue and the CFD data available for
the ReinVAD pump – red. ....................................................................................................... 66
Appendices
Figure AII.1 - Main blocks of the resultant hydraulic force: axial hydraulic force on impeller shrouds
and momentum force. ............................................................................................................ 85
Figure AII.2 - “Momentum Force” subsystem block. ................................................................ 86
Figure AII.3 - “Resultant force in the shrouds” subsystem block. .............................................. 86
Figure AII.4 - “Axial hydraulic force on front shroud” subsystem block...................................... 87
Figure AII.5 - “Pressure component” subsystem block. ............................................................ 87
Figure AII.6 - “Rotation component” subsystem block. ............................................................. 87
xxi
List of Tables
Chapter 2
Table 2.1 - The constituents of human whole blood; adapted from (Bitsch 2002). .................... 12
Table 2.2 - Application of mechanical circulatory support devices under different clinical scenarios.
.............................................................................................................................................. 19
Chapter 3
Table 3.1 - Results of radial force (N) vs flow rate (l/min). ....................................................... 46
Chapter 4
Table 4.1 - Rheological proprieties of the blood used for all simulations (Timms 2005; Fung 1993).
.............................................................................................................................................. 50
Table 4.2 - Dimension of the pump, according to Figure 3.6, in millimetres (mm) (Graefe & Deng
2015). .................................................................................................................................... 50
Table 4.3 - Description of each simulation. .............................................................................. 52
Appendices
Table AI.1 - Dimension of the pump, according with Figure 3.6, in millimetres (mm). ............... 79
Table AI.2 - CFD data static pressure rise in the pump (mmHg) for different flow rates in the pump
(l/min). .................................................................................................................................. 80
Table AIII.1 - CFD data for leakage flow in rear and front shroud (l/min), and static pressure rise in
the impeller (mmHg) for different flow rates in the pump (l/min). ............................................ 89
Table AIII.2 - CFD data for leakage flow in rear and front shroud (l/min), and static pressure rise in
the impeller (mmHg) for different rotation speeds of the impeller pump (l/min). ...................... 89
Table AIII.3 - CFD data of axial hydraulic force (N) for different axial positions (mm). ................ 90
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1
Chapter 1
Introduction
1.1 Motivation
Cardiovascular diseases (CVD) are the number one cause of death in the world, according
to the World Health Organization (2014), being responsible for approximately 31% of all global
deaths. In the particular case of heart failure (HF), it is estimated that approximately 23 million
people in the world present this chronic conditions (Westaby & Frazier 2012). HF is a common
clinical syndrome that affects the chambers of the heart, involving severe ventricular dysfunction,
and ultimately leads to a reduction in cardiac output (Song et al. 2004; Couper 2001).
Cardiac medications used for conventional medical therapy for HF are frequently not
sufficient, and, at any time, there is a limited number of donor hearts available. Against this
background, mechanical cardiac assist devices (MCAD) are fast becoming an important accepted
treatment strategy, often used as a bridge to transplantation and even as a long-term therapy
(Bonow et al. 1980; Timms 2011; Song et al. 2004). The development of adequate and affordable
MCAD is nowadays a major challenge for both academic researchers and companies.
The ReinVAD GmbH, in cooperation with RWTH Aachen University, is developing the
ReinVAD Left Ventricular Assist Device (LVAD). The ReinVAD LVAD is a small, inexpensive,
intelligently controlled radial ventricular assist device of the latest generation, which ensures stable
and reliable circulatory support. At the present time, the LVAD is in prototype stage, and is expected
to reach the market in 2018 (Graefe & Deng 2015).
In order to ensure optimal functioning of the ReinVAD LVAD, hydraulic forces acting on the
rotor of the pump must be known and understood. A computational fluid dynamics (CFD) model
has previously been prepared, which details the fluid dynamics of blood flow. However, despite
being central for the development and functioning of the pump, this model presents some relevant
limitations. Firstly, it does not detail the behaviour of each component of the hydraulic force
separately. In fact, the CFD outputs a final resultant force, but does not detail a mathematical
framework which explains how the change in each variable affects the final result, making it hard
to predict how the resultant force will react to changes in relevant internal and external parameters.
2
Second, the CFD model is not capable of being integrated in the PID (proportional integral
derivative) controller that has been developed for the pump in MATLAB®/SIMULINK®. Finally, the
complexity of this model makes it unsuitable for the development of quick simulations, which are
relevant when trying to test how the pump might react to a multitude of different scenarios.
The opportunity to develop a model that addresses the limitations of the CFD simulations,
complementing them, motivates the present dissertation.
1.2 Scope and Objectives
The scope of the dissertation is the study of hydraulic forces acting on impellers of radial
blood pumps. Thus, the major goal of this work is to develop a dynamic model of these hydraulic
forces, and to apply it in the analysis of ReinVAD LVAD, in order to support the development of this
device. To fulfil the purpose of this research, five objectives were outlined:
i. Develop a robust and flexible model of the axial hydraulic forces acting on the
ReinVAD LVAD; by creating a flexible model that allows for quick simulations, yields results
both for the resultant force and for each of the individual forces, and gives insight into the
mechanisms that influence their behaviour. This research aims at creating an analytical tool
that gives researchers the ability to quickly estimate how the axial hydraulic forces behave under
different design and operation conditions of the pump.
ii. Analyse and discuss the behaviour of the axial hydraulic forces for the pump
current design; by simulating the response of each component of the axial hydraulic force to
changes in the two major variables of the pump operation (flow rate and rotation speed) and
analysing the results. With this objective, this research aims at understanding and explaining
the mechanisms that lead to the changes in the resultant force;
iii. Support the development of the pump controller; by implementing the model in
MATLAB® and SIMULINK®, in order to integrate it in the pump controller in the near future;
iv. Validate the developed model; by comparing the model results with available CFD
simulation data;
v. Assess if the hydraulic radial force is relevant for the ReinVAD LVAD; by evaluating
the hypothesis, suggested by the reviewed literature, that this force would not be relevant.
3
1.3 Literature Review
In the last decades, mechanical cardiac assist devices have gained widespread acceptance
as therapeutic instruments for the treatment of heart failure (Reul & Akdis 2000).
The first milestone in the field of mechanical cardiac assist devices occurred in the mid-
twentieth century, with the development of the heart-lung machine by Gibbon J., Lillehei C., Kirklin
J. and other investigators, Figure 1.1 (Hill 1982). The first clinical use of this technology, by Gibbon
in 1953, successfully allowed for the correction of an atrial septal defect, by temporarily replacing
the native heart while it underwent surgery (Argenziano et al. 1997; Bonow et al. 1980).
Figure 1.1 - Model II of the heart-lung machine used by Dr. John H. Gibbon in his first successful heart operation on
May 6, 1953 (Hill 1982).
The next major progress was the intraaortic balloon pump (IABP), developed by Moulopoulos
et al. (1962). This device was first applied surgically in 1967, in a patient with cardiogenic shock.
Afterwards the IABP became widely used due to their usefulness in patients with reversible
cardiogenic shock and as a bridge to transplantation (Argenziano et al. 1997; Bonow et al. 1980).
The first successful clinical use of a left ventricular assist device (LVAD), the class of device
this investigation will address, was achieved by DeBakey et al. (1966). A patient with
postcardiotomy syndrome was supported by an extra thoracic left heart bypass system for 10 days,
after which the device was removed, and the patient survived (Argenziano et al. 1997; Bonow et
al. 1980; Liotta 2002).
4
Meanwhile, several efforts to develop left ventricular assist devices (LVADs) were achieved.
Initially, these devices were focused on reproducing the pulsatile outflow delivered by the native
heart. These pumps, classified as first generation, presented reliability problems, by virtue of their
mode of operation. In order to try to overcome these issues, continuous flow devices were
developed, also called second generation pumps (Timms 2011).
Saxton & Andrews (1960) published the first article describing a continuous flow pump,
presenting several potential advantages of the continuous flow blood pump over the positive
displacement pumps. The authors referred as advantages the smaller size of the pumps, the lower
power requirements, the minimum number moving parts and the extinction of valves. After that,
several studies with continuous flow pumps were performed. Rafferty et al. (1968) developed a
continuous flow blood pump, known as BioPump, with extremely low hemolysis rates,
commercialized in 1976. Bernstein et al. (1974) published the results of a continuous flow
ventricular bypass successfully implanted in a calf for 24h. Golding et al. (1979) reported
favourable clinical results with the Medtronic pump (continuous flow pump) (Olsen 2000).
Since 1980, the progress of continuous flow blood pumps was so notary that several
companies started the development of VADs. As a result, second-generation blood pumps as the
DeBakey VAD (MicroMed), the Jarvik 2000 FlowMaker (Jarvik Heart), and the HeartMate II
(Thoratec) have been implanted in selected patients for both bridge to transplantation and for
destination therapy, Figure 1.2 (Reul & Akdis 2000).
(a)
(b)
(c)
Figure 1.2 - Second generation pumps with successful application and implementation: (a) DeBakey VAD (Noon &
Loebe 2010); (b) Jarvik 2000 (Jarvik Heart Inc. 2009); and (c) HeartMate II (Thoratec Corporation 2008).
Literature reports of the successful use of continuous flow blood pumps encouraged
investigators to develop a variety of pumps of this category (Olsen 2000). The third generation
blood pumps resulted from additional investigation. These pumps eliminated wear by allowing the
5
suspension of the rotor without any mechanical contact. The earliest article describing a
magnetically suspended impeller blood pump was published by Olsen et al. (1981). Akamatsu et
al. (1992) also reported a magnetic suspended impeller pump that was in 1995 acquired by the
Terumo Corporation. In 2001 the spin-off company Terumo Heart was created, in order to continue
the development process, creating the DuraHeart VAD (Hoshi et al. 2006).
Many systems followed the successful application and implementation of the third
generation pumps, including the VentrAssist LVAD (Ventracor), the MiTiHeart (MiTi Heart), the
INCOR system (BerlinHeart), the MedQuest Heartquest (WorldHeart), the HeartMate III (Thoratec),
and the Levitronix CentriMag (Thoratec), Figure 1.3 (Reul & Akdis 2000).
(a)
(b)
(c)
(d)
Figure 1.3 - Third generation pumps with successful application and implementation: (a) VentrAssist LVAD
(Jayanthkumar et al. 2013); (b) Berlin Heart INCOR (Berlin Heart GmbH 2009); (c) HeartMate III (Thoratec
Corporation 2014) ;and (d) Levitronix CentriMag (Thoratec Corporation 2011).
In magnetically suspended impeller blood pumps, the hydraulic forces need to be studied in
order to support the design and operation of the magnetic levitation system (Japikse et al. 1997).
The study of the hydraulic forces acting on the impeller includes the axial and the radial hydraulic
forces, which are the subject of this investigation. Below several major studies of this subject are
outlined.
6
Takami et al. (1997) investigated the axial force on the GYRO blood pump. The pump
presented significant axial forces, due to the pump semi-open impeller, which created an
asymmetric pressure distribution.
Allaire et al. (1996) described the development of a VAD prototype supported by an active
magnetic bearing system. In the study the radial forces, including non-hydraulic ones (unbalanced
forces, motor eccentricity magnetic forces, and others) were measured, reaching a maximum
resultant radial force of 1.5 N.
Curtas et al. (2002) performed a CFD investigation of the axial forces acting on the
HeartQuest LVAD. The axial force was simulated for two different impellers (CF3 and CF4). It was
concluded that much more force acted on CF3, due to the fact that it produced more pressure and
was larger, presenting more area on which the pressure could act.
Song & Wood (2004) performed a CFD study determining the axial and radial forces acting
in a blood pump impeller. They concluded that the radial forces were small and negligible, contrarily
to the axial force, which was revealed to be a critical parameter for magnetic suspension design.
The tendency of the axial forces with the flow rate and rotation speed was also evaluated by Song
& Wood (2004), which concluded that decreases of flow rate or increases in rotation speed led to
increases in the magnitude of the axial force.
Untaroiu et al. (2005) compared measurements of the axial forces acting on an axial blood
pump with CFD predictions, and found the CFD predictions to be accurate. The CFD model
predicted that the axial force increased with the increase of rotation speed on the pump. The radial
forces were found to be on the order of 10–3 N, and thus virtually insignificant.
Recently, Boehning et al. (2011) evaluated and discussed the dependency of the hydraulic
radial forces and the volute type. The experimental tests concluded that the single volute had the
lowest radial force (∼0 N), the circular volute yielded the highest force (∼2 N), and the double
volute possessed a force of approx. 0.5 N.
Even with the successful application of blood pumps, there are still relatively few theoretical
models for the hydraulic forces acting on the impeller, and most design improvements were
developed through experimentation and practical experience. Therefore, for an improved literature
review in this area, the behaviour of hydraulic forces in general radial pumps was also reviewed.
7
Many authors contributed to the research of the axial hydraulic force in radial pumps.
Kazakov & Pelinskii (1970) evaluated the relationship between the axial force and the clearances.
The study demonstrated that the axial force increased with an increase of the seal clearances,
however it also concluded that in open impellers the increase of the axial force is several times
faster than in pumps with closed impellers. Most recently, Gantar et al. (2002) performed a
numerical flow analysis method to investigate the axial hydraulic force after the implementation of
some pump design changes (wear rings). Comparisons of the original and modified design
concluded that the generated forces under the new design were smaller.
As for the analytical approach to studying these forces, Lazarkiewicz, Stephen Troskolanski
(1965), Lobanoff & Ross (1992) and ANSI/HI (1994) defined mathematical methods to predict
axial forces. Most recently Gülich (2010) also defined a mathematical method to predict axial forces
in radial pumps. This method of axial calculation accounts for the contribution of fluid momentum,
and pressure distribution underneath and above the impeller.
The radial hydraulic forces were also studied by many authors. Flack & Allaire (1984)
published a literature review of the measurement of both static and dynamic radial thrust and
Guelich et al. (1987) provided an overview of the physical mechanisms that cause radial forces on
an impeller, and also a review of the available techniques to measure them.
Adkins & Brennen (1988) investigated the radial forces that act on the impeller due to its
interaction with the volute casing. The developed model requires a knowledge of the dimensions
of the volute and impeller, and the total head rise across the entire pump. Comparisons between
the predicted model and the experimental results were performed allowing the model to be
validated.
Most recently, Baun & Flack (2003) performed a series of experiments in order to determine
the effect of various impeller (four-blade and five-blade) and volute (spiral volute, concentric volute
and double volute) combinations on radial force. The study concluded that the difference in the
magnitude forces for the two different impeller in the same volutes was not significant. In the case
of different volutes for the same impeller, the spiral volute presented the smallest magnitudes of
the force, while the double volute presented the biggest magnitudes.
As for the analytical approach to calculate these forces, Stepanoff (1957) devised a method
which enabled the pump designers to estimate the radial force on a radial pump. Biheller (1971),
8
Chamieh et al. (1985), Agostinelli et al. (1960), and Iversen et al. (1960) used this methodology,
in order to compare the steady hydrodynamic forces on a radial pump impeller with empirical
measurements and concluded that the model performed satisfactorily.
1.4 Dissertation Overview
This dissertation is divided in five chapters, addressing the scope and objectives outlined
above.
The motivation for the dissertation is presented in chapter 1, together with the scope and
objectives of the project. Moreover, the major literature on blood pumps and hydraulic forces acting
on them are reviewed.
The background of the dissertation is outlined in chapter 2, where the human
cardiovascular system, cardiac diseases and current blood pump solutions are discussed.
With this context in mind, chapter 3 details the previous developments of the ReinVAD
LVAD, the technical elements of the device and the different forces acting on the pump. Having
established this framing, a mathematical model of the axial hydraulic forces acting on the device
is defined and implemented in MATLAB®/SIMULINK®. Furthermore, the radial hydraulic force
acting on the pump is investigated and a simple estimation approach is implemented.
The results of the developed analytical model for the axial hydraulic force are presented in
chapter 4, which is divided into three main sections. The first section describes each simulation
and associated conditions (physiologic, design and dimensions). The second section analyses and
discusses the performed simulations. Finally, the last section compares the developed
mathematical model with available CFD data of the ReinVAD LVAD.
Finally, the conclusions of the dissertation are discussed in the chapter 5, and future
developments are proposed.
9
Chapter 2
Human Cardiovascular System and Cardiac
Assist Devices
The cardiovascular system is comprised of four major components: blood, blood vessels,
the heart, and the lymphatic system. Fundamentally, the function of the cardiovascular system is
to service the needs of the body tissues; to circulate and transport nutrients, oxygen, hormones to
the body tissues; and to transport waste products away from them. In short, to maintain an
appropriate environment in all the body tissues for optimal survival and functioning of the cells
(Zaret et al. 1992; Klabunde 2005).
The cardiac circulation is divided into the systemic circulation and the pulmonary circulation,
shown in Figure 2.1. The systemic circulation is responsible for transporting oxygenated blood from
the left ventricle to the rest of the body (except the lungs), and returning deoxygenated blood back
to the heart. Conversely, the pulmonary circulation transports deoxygenated blood away from the
heart into the lungs, and returns oxygen-rich blood back to the heart (Iaizzo 2005; Zaret et al. 1992;
Klabunde 2005).
Figure 2.1 - An overview of the cardiovascular system and both systemic and pulmonary circulation. The blood is
shown in blue when it deoxygenated and red when fully oxygenated; adapted from Whittemore (2009).
10
2.1 The Heart
The heart is a muscular pump that has two main functions: to collect blood from all the body
tissues and to pump it to the lungs; and to pump the blood collected from the lungs to all tissues
of the body.
The human heart, as is possible to see in Figure 2.2, is constituted of four heart chambers,
each composed of cardiac muscle: two atria in the upper half of the heart; and two ventricles in
the lower half. The ventricles pumps blood to all the organs and tissues and the atria receive blood
as it circulates back from the rest of the body. Completing and separating the four chambers, the
heart also presents a set of four valves. These valves are responsible for maintaining a one-way
flow of blood through the heart. The atrioventricular valves (tricuspid and mitral) force blood to flow
only from atria to ventricles. The semilunar valves (pulmonary and aortic) force blood to flow only
from the ventricles out of the heart and through the great arteries (Guyton & Hall 2006; Zaret et
al. 1992).
Figure 2.2 - Structure of the heart, and course of blood flow through the heart chambers; adapted from Guyton &
Hall (2006).
The cardiac events that occur in a complete heartbeat from its generation to the beginning
of the next beat are called the cardiac cycle. Each cycle includes a period of relaxation called
diastole, followed by a period of contraction called systole. The rhythmic contraction and relaxation
11
of the chambers of the heart are controlled by electrical activity of the cells in the heart muscle
(myocardium)(Guyton & Hall 2006; Zaret et al. 1992).
Diastole is the longer phase of the cycle, taking up approximately two-thirds of its duration.
During this phase the tricuspid and mitral valves are open, and the pressures in the ventricles fall
below those in the atria, propelling the blood from the atria into the relaxed ventricles. Note that,
during the diastole, the aortic and pulmonary valves are closed since the interventricular pressure
is lower than in the arterials (aorta and pulmonary artery) (Zaret et al. 1992; Klabunde 2005; Iaizzo
2005).
During systole, as soon as the ventricles fill in, the pressure inside them is larger than in the
atria, hence the tricuspid and mitral valves close. As a result, the intraventricular pressure rises
enough to force the pulmonary and aortic valves to open, and blood is forced out of the given
ventricular chamber to the arteries (Zaret et al. 1992; Klabunde 2005; Iaizzo 2005).
In order to maintain the efficiency of the heart, contractions must occur at regular intervals
and be synchronized; the valves must fully open and must not leak; ventricular contractions must
be forceful (not failing); and the ventricles must fill adequately during diastole (Iaizzo 2005).
2.2 The Blood
2.2.1 Composition of Blood
Blood is a complex fluid that provides necessary substances, such as nutrients and oxygen
to all of the body cells and removes metabolic waste products from them. The human blood mainly
consists of a suspension of blood cells in plasma (Stoltz, J. F., Singh, Megha, Riha 1999). Table
2.1 shows the different constituents of blood and their respective concentrations.
The plasma is constituted by approximately 90% (w/w) water, containing 7 % (w/w) plasma
proteins. Furthermore, it is widely considered to behave like a Newtonian (constant viscosity) fluid
with a coefficient of viscosity about 1.2x10−3 Pa.s (Bitsch 2002; Fung 1993).
The blood cells include erythrocytes, leucocytes and platelets, all formed in bone marrow
from a common stem cell, and each one contributes directly to blood viscosity. The erythrocytes,
commonly named red blood cells (RBCs), are the blood cells with the most influence on blood
viscosity. RBCs are disk shaped, with an average diameter of 7.6 µm and thickness 2.8 µm. These
12
cells have a primary role in the transportation of the oxygen in blood, since they carry haemoglobin.
This protein allows blood to transport 40 to 50 times the amount of oxygen that plasma alone could
carry. The leucocytes are required for the immune process to protect against infections and
cancers, while the platelets play a determinant role in blood clotting (Iaizzo 2005; Fung 1993).
In an average-sized, healthy individual of 70 kg, the total volume of blood is approximately
5.5 L, while the haematocrit level (percentage of blood volume occupied by the RBCs) is 40−52%
for men, and 35−47% for women. The high concentration of these cells in the blood, combined
with their flexibility gives to blood an important non-Newtonian property (shear-thinning1) (Iaizzo
2005; Bitsch 2002; Fung 1993).
Table 2.1 - The constituents of human whole blood; adapted from (Bitsch 2002).
Composition Concentration
Plasma Water 90% (w/w)
Proteins 7 % (w/w)
Albumins
Globulins
Fibrinogen
4.5 – 5.7 x 10-5 µL-1
1.3 – 2.5 x 10-5 µL-1
1.3 – 2.5 x 10-5 µL-1
Salts,
dissolved gases,
glucose,
metabolites,
nutrients
Cellular Components
Red blood cells (7µm)
White blood cells (8 - 20 µm)
Platelets ( 1- 2 µm)
3.6 – 5.4 x 106 µL-1
5 – 10 x 103 µL-1
1.5 – 4 x 105 µL-1
1 The viscosity of the fluid decreases with an increasing rate of shear stress.
13
2.2.2 Macroscopic Rheological Properties of Blood
Rheology is the science that studies deformation and flow of materials under applied
forces. Thus, rheological properties are the properties that affect the deformation and flow of a
material (Stoltz, J. F., Singh, Megha, Riha 1999; Tanner 2000).
Viscosity is one of the most relevant properties when discussing flowing fluids. From the
macroscopic point of view, the viscosity of a fluid is a measure of its resistance to gradual
deformation by shear or tensile stress (Stoltz, J. F., Singh, Megha, Riha 1999; Kowalewski 2005).
The shear rate, which is a measure of the deformation of the liquid, is defined according to
Equation (2.1), where, vi is the velocity in the xi direction.
Blood is a viscoelastic fluid and Figure 2.3 shown that the viscoelastic behaviour of normal
human blood can be divided into three regions, according to the shear rate: Region 1 – Low Shear
Rates, Region 2 – Mid-Shear Rates and Region 3 – High Shear Rates. As it can be seen in Figure
2.3 the arrangement, orientation and stretching of the RBCs are responsible for changes in blood
viscosity (Fung 1993; Bitsch 2002).
Figure 2.3 - Viscoelastic profile dependent of shear rate of normal human blood. Measurements were made at 2 Hz
and 22 °C in an oscillating flow. In the bottom of the picture an illustration of the arrangement of RBC in each region
is represented (Kowalewski 2005).
γ̇ = dvi
dxj +
dvj
dxi (2.1)
14
Region 1 – Low Shear Rates
In the first region, the viscosity presents higher values and is approximately constant. At low
shear rates, normal RBCs tend to aggregate in a space efficient manner, generating large
aggregates of cells. These large agglomerates of blood cells cause disturbances in the laminar flow
profile of the plasma. The aggregation properties of the RBCs control the viscoelasticity of the blood
in this region, while the deformability is less relevant (Bitsch 2002; Olesen 2003).
Region 2 – Mid-Shear Rates
In this region, the viscosity of blood is a decreasing function of the shear rate – the fluid
displays shear thinning. This property is a result of the breakage of aggregates and a cell layering
of the RBCs. The internal stress due to the pressure is enough to separate aggregated cells and,
with the increase of the shear rate, the cells are oriented in the direction of flow. As result of the
internal organization of the RBCs, friction reduces. In this region, red cell deformability influence
overcomes influence of the aggregation properties in the control of viscoelasticity (Fung 1993;
Bitsch 2002; Olesen 2003).
Region 3 – High Shear Rates
At shear rates above about 100 s−1, blood viscosity is reported to be a constant value, 3 x
10−3 – 4 x 10−3 Pa.s. With increasing shear, RBCs stretch or deform and align with the flow, which
decreases the viscosity. For this reason, in this region, the viscoelasticity is controlled by the
deformability of the RBCs. Due to the characteristics of this region, the blood is commonly
approximated to a Newtonian fluid in shear rates over than 100 s−1(Fung 1993; Bitsch 2002;
Olesen 2003).
Note that, viscosity is influenced by several factors besides shear stress, including the
haematocrit (viscosity increases with increasing haematocrit levels), temperature (viscosity
decreases with increasing temperatures) and some diseases (Fung 1993; Olesen 2003; Bitsch
2002; Stoltz, J. F., Singh, Megha, Riha 1999).
15
2.2.3 Hemolysis and Thrombosis
Hemolysis is the premature destruction of RBCs. RBCs normally live for approximately 115
days, afterwards naturally breaking down and being removed from the circulation (Franco 2012).
However, some conditions cause their early destruction.
One of these conditions is the exposure to high shear rates for a prolonged period of time.
Note, however, that since RBCs have a viscoelastic behaviour they can support high stresses for
short exposure times without hemolysis (Leverett et al. 1972). Furthermore, hemolysis can also be
caused by some diseases or be influence for some interaction of the cells with different surfaces
(Sowemimo-Coker 2002).
The breakage of RBCs causes the release of haemoglobin and other internal components.
As result, hemolysis can be experimentally monitored by measuring the concentration of
haemoglobin released to the extracellular medium (Deutsch et al. 2006).
A different condition is thrombosis, consisting in the formation of a blood clot, generally
called thrombus. Typically, the blood clots are formed on an injured inner wall of a blood vessel
and on contact with the surfaces of medical devices. The clot formation involves a complex cascade
of enzymatic reactions (Fung 1993).
When blood contact with an injured vessel occurs, platelets adhere to its surface forming a
larger aggregation. Afterwards, thrombin, the bottom enzyme of the coagulation cascade, converts
fibrinogen (a blood protein) into fibrin, which in turn stabilizes the adhered platelets and forms a
blood clot (Fung 1993; Galdi et al. 2008; Schima et al. 2008).
The formation of a thrombus and hemolysis are both frequent occurrences in blood pumps
that should be avoided in order to ensure the success of the pump therapy. Thus, when designing
a blood pump, the main factors that influence these two phenomena must be considered: the
blood material interface, the surface topography, and the fluid mechanics. (Deutsch et al. 2006;
Schima et al. 2008; Song et al. 2003).
16
2.3 Heart Failure
The heart is an efficient and durable pump. However, as any other electromechanical device,
it can become less efficient or break down.
Heart failure (HF) is a major public health issue with a current prevalence of over 23 million
worldwide (Westaby & Frazier 2012; Bui et al. 2011). The incidence of this condition has increased
during the last decades and is expected to continue to grow. Projections estimate that by 2030,
the prevalence of HF will increase 25% from 2013 estimates (Lloyd-Jones et al. 2009).
The main reason for this growth is the general aging of the population, since HF is age
related. Figure 2.4 shows that the prevalence of HF increases with age, with approximately 13% of
the American population over 80 years having HF (Lloyd-Jones et al. 2009).
Figure 2.4 - Prevalence of heart failure by sex and age in the USA in 2009 ; adapted from Lloyd-Jones et al. (2009).
HF imposes a huge global economic burden with direct costs to countries healthcare
systems and indirect costs to society (through morbidity, unpaid care costs, premature mortality
and lost productivity). In 2012, the total costs are estimated at approximate $108 billion (with
direct costs accounting for approximately 60% of the overall spend and indirect costs for the
remaining 40%) (Cook et al. 2014).
Fundamentally, HF is a condition in which the heart has a reduced ability to pump enough
blood to satisfy the needs of the body. Most commonly, HF involves the left ventricle, with right
ventricular failure normally occurring secondary to left ventricular failure. In rare instances,
0,1
2,2
9,3
13,8
0,21,2
4,8
12,2
0
2
4
6
8
10
12
14
16
20-39 40-59 60-79 80+
Perc
ent o
f pop
ulat
ion
(%)
Age group (years)Men Women
17
however, the right side might fail on its own or in association with pulmonary disease (Guyton &
Hall 2006; Klabunde 2005; Zaret et al. 1992).
Normally HF is classified according to the affected heart function, with the main types
being systolic heart failure and diastolic heart failure. Frequently, patients present a combination
of both systolic and diastolic dysfunctions. In case of systolic heart failure, the ventricles do not
contract properly during each heartbeat, resulting in blood not being adequately pumped out of the
heart. This dysfunction is characterised by a drop in cardiac output due to decreased contractility.
Diastolic heart failure, on the other hand, is characterized by an impaired ventricular filling between
each heartbeat (Klabunde 2005).
The most common symptoms of these conditions are shortness of breath, fatigue and
swelling in the ankles, feet, legs and abdomen. In the early stage of the disease, patients start
feeling tired and short of breath, while and after doing physical activities. In more severe stages, a
patient may experience breathlessness even while at rest. Furthermore, the patient are likely to
have significant pulmonary edema (a condition in which too much fluid builds up in the lungs).
(Zaret et al. 1992; NHLBI Health Topics 2013).
Heart failure is usually a slow process, which can have several causes. The two major ones
are: coronary artery disease and myocardial infarction (Klabunde 2005; Zaret et al. 1992).
The first one is responsible for a reduction in the coronary blood flow, which is the
circulation of blood in the blood vessels of the heart muscle (myocardium). This reduction, in turn,
leads to decreased contractility of the myocardium, since with a reduction in this blood flow, the
levels of oxygen in the myocardium reduce too, causing myocardial hypoxia and impaired function
(Guyton & Hall 2006; Klabunde 2005). The second, consisting of the partial death of heart tissue,
reduces the efficiency of the heart, since the infarcted tissue does not contribute to the generation
of mechanical activity of the heart. For this reason, the non-infarcted regions of the heart have to
compensate for this loss of function, and with time the over-work demanded from these regions
leads to a heart failure (Guyton & Hall 2006; Zaret et al. 1992).
Besides these main causes, heart failure can also be caused by valvular disease, long-
standing hypertension, vitamin B deficiency, viral infections, congenital defects, chronic
18
arrhythmias, or any other abnormality that turns the heart into a hypoeffective pump (Klabunde
2005; Zaret et al. 1992).
The treatment for HF has mainly been aimed at improving quality of life of the patients,
reducing the symptoms. Patients with this condition follow a significant regimen of cardiac
medications, a therapy that sometimes is inefficient and fails. In fact, some patients become
tolerant or develop side effects that prevent drug use. Moreover, in end-stage HF, the drug therapy
is not enough, with these cases requiring a heart transplantation (Bonow et al. 1980; Song et al.
2004; Timms 2011). The International Society for Heart and Lung Transplantation estimates that,
annually, the lives of approximately 50 000 persons in the world would improve with heart
transplantation. Nevertheless, the number of available donor hearts only reaches 12% of the total
needed amount, approximately 6 000 annually (Lund et al. 2014).
Considering the scarcity of donor hearts associated to the increase of HF cases, a necessity
arose to explore alternative options. Hence, cardiac assist devices have become a promising
alternative for the patients with HF. These devices can be employed to bridge a patient to heart
transplant, to recovery, or indeed as a destination alternative (Park et al. 2005).
2.4 Cardiac Assist Devices
There are a large number of different mechanical devices to treat end-stage heart failure,
appropriate for use in a number of different clinical scenarios. These devices can be categorized
in four groups, depending on their main function: left ventricular assist device (LVAD); right
ventricular assist device (RVAD); biventricular assist device (BiVAD) and total artificial heart (TAH).
Given the higher prevalence of left ventricle failure, the LVAD became the most common
type of mechanical support device, being surgically implanted between the left ventricle and aorta.
The blood flows from the ventricles into the LVAD and afterwards it is pumped out to the aorta.
Note that this device does not substitute the left ventricle, and instead supports its functioning
(Lund et al. 2014; Reul & Akdis 2000).
The RVAD works similarly to the LVAD, but is applied to the right ventricle, helping it to pump
blood to the pulmonary artery. The implantation of this device is normally applied after LVAD
surgery or other heart surgery (Couper 2001; Lund et al. 2014; Reul & Akdis 2000).
19
BiVAD and TAH are both used for biventricular heart failure. The first one provides circulating
support to both of ventricles, while the second one consists of two mechanical pumps that replace
both failing ventricles. In cases with reversible or acute HF, BiVAD are normally used, since the
natural heart continues to work in parallel with the device. However, in chronic HF and very limited
natural cardiac outputs, the TAH is normally applied. (Lund et al. 2014; Reul & Akdis 2000).
Furthermore, the selection and use of a mechanical circulatory support devices depends on
the clinical scenario(Hoshi et al. 2005; Greatrex 2010):
1. Bridge to Transplant - Patients awaiting cardiac transplant can be implanted with a VAD
to support the diseased heart until a donor organ is available.
2. Bridge to Recovery - Patients with reversible forms of cardiac disease can be implanted
with a VAD, used in conjunction with regenerative medicine.
3. Destination Therapy - Patients with irreversible cardiac disease who are ineligible for
transplant can be implanted with a VAD or TAH that is aimed at long-term out-of-hospital use.
Table 2.2 summarizes the relation between the implanted device used and the clinical
scenario of the patient.
Table 2.2 - Application of mechanical circulatory support devices under different clinical scenarios.
Bridge To Transplant
Bridge to Recovery
Destination Therapy
LVAD X X X
RVAD X X
BiVAD X X
TAH X X
2.4.1 Types of Cardiac Assist Devices
Mechanical cardiac assist devices (MCAD) are typically classified into two groups, according
to their characteristic outflow: displacement blood pumps and rotary blood pumps. A summary of
the different types of blood pumps is shown in Figure 2.5.
20
Figure 2.5 - Diagram of current solutions of cardiac assist devices; adapted from Reul & Akdis (2000).
2.4.1.1 Displacement Blood Pumps
Displacement blood pumps, the first generation of pumps, were initially developed with the
aim of reproducing the pulsatile outflow delivered by the natural heart (Reul & Akdis 2000). As a
result, the energy transfer in displacement pumps is characterized by periodic changes of a working
space (Reul & Akdis 2000).
Normally, these type of pumps have an inherently large tissue and blood contacting surface.
Furthermore, they have multiple moving mechanical parts, incorporating different valves, devices
with flexible membranes, pneumatically or electrically actuated sacs and diaphragms or pusher
plates (Timms 2011; Song et al. 2004).
Despite the simplicity of operation and the improved one-year survival observed in patients
treated with these devices vs. optimal medical therapy, displacement blood pumps are often flawed
with reliability and durability problems, by virtue of their mode of operation (Timms 2011; Reul &
Akdis 2000).
The complexity and variety of displacement pumps components promote numerous
mechanical failures due to wear, two or three years after the implantation in the patients. Moreover,
the elevated contact with tissues and the formation of particle spallation (process in which
fragments of material are ejected from a body due to impact), resulting from wear components,
causes an inherent risk of infection, thrombus formation and blood trauma (Timms 2011).
Additionally, the patients have very little mobility due to the bulky driving consoles (Reul & Akdis
2000).
TAH, LVDA, RVAD and BiVAD
Displacement Blood Pumps
Rotory Blood Pumps
Axial Pumps
Radial Pumps
Diagonal Pumps
21
2.4.1.2 Rotary Blood Pumps
The numerous disadvantages presented by displacement blood pumps led to an effort to
develop continuous flow devices based on a rotating impeller. As resulted, rotary blood pumps
(RBPs) have become a common clinical therapy and an important alternative to displacement blood
pumps, due to the improved outcomes for patients treated with these devices (Vollkron et al. 2004).
RBPs are constituted by a rotating impeller housed within a small pump chamber (without need of
directional valves). (Timms 2011; Park et al. 2005).
The original rotary blood pumps were the second generation of pumps, which are
characterized by contact shaft/roller bearing or a blood immersed (pivot) bearing impeller support
mechanism. Despite the good results of these pumps, the mechanical contact continues to pose
a severe contraindication for long-term use (more than five years). Aiming to solve this problem,
many solutions have been proposed, resulting in the third generation of blood pumps. These new
pumps utilize contactless suspension mechanisms (magnetic or hydrodynamic forces) to eliminate
mechanical contact and, consequently, wear (Timms 2011; Olsen 2000; Hoshi et al. 2006).
RBPs have distinct physiological and technological advantages in comparison with first
generations blood pumps. In fact, they are smaller in size, which is an important characteristic
both in terms of level of implantability as well in terms of level of transportability and integration
into more complex devices. Furthermore, they require much less power, with a minimum of moving
parts and no valves or flexing plastic chambers being needed. Therefore, this type of blood pumps
results in lower blood damage, lower filling volume and absence of spallation. Furthermore, the
lower pulsatility that results from the continuous transport mechanism, which was expected to be
a disadvantage, has proven its suitability for patient recovery and rehabilitation (Reul & Akdis 2000;
Vollkron et al. 2004).
Although RBPs present a series of advantages that are distinctive, they also present two
primary disadvantages. One of them is the unknown shear stresses within the pumping chamber
that could result in blood cell damage. It is important to refer that excessive blood cell injury caused
by high shear stress could result in hemolysis. The second disadvantage is that continuous flow
requires higher blood output volumes than pulsatile flow (Olsen 2000).
22
Depending on impeller geometry and the direction in which the blood enters and leaves the
impeller, the rotary blood pumps can be classified into three main categories: axial, radial
(centrifugal) and diagonal (mixed flow) pumps (Timms 2011).
Axial flow pumps
Axial flow pumps have a tubular configuration and they are smaller and lighter than radial
pumps. Despite these advantages, and as result of their size, this type of pump normally uses
second generation technology (even so, third generation pumps have also been utilized) (Fraser et
al. 2011; Timms 2011).
Compared to other rotary type devices, axial pumps require much faster rotation speeds
since they produce higher flows with lower pressure rises. In face of their higher velocity
requirements, there is a relatively higher shear stress, which when combined with stationary guide
vanes and contact impeller suspension may lead to hemolysis or thrombosis. (Timms 2011; Reul
& Akdis 2000).
The excepted lifespan of axial pumps is around five years (however, there are cases in
which they outlast this period). This limited lifespan is mainly due to the combination of high
rotation speed and contact bearing mechanism (Timms 2011).
Currently, there are some axial flow devices that are commonly used clinically, such as:
DeBakey, Jarvik 2000 and HeartMate II (Reul & Akdis 2000).
Radial /Centrifugal flow pumps
Radial pumps convert the axial flow, entering the inlet of the pump, into a radial flow,
exiting the outlet. This type of pumps are the most capable of producing higher pressures at lower
flow rates (Reul & Akdis 2000; Fraser et al. 2011).
Generally, radial pumps are used for long term cardiac assistance due to their lower
corresponding rotation speed and higher hydraulic efficiency (Reul & Akdis 2000).
Furthermore, and despite being wider in diameter than axial pumps, these pumps are
pancake-shaped (they are flatter), which is a more suitable shape for anatomical fitting. They are
often used with third generation bearing technology. For this reason, the component of wear is
completely eliminated, since the impeller is completely suspended using hydrodynamic or
magnetic bearing forces (Timms 2011).
23
In general, radial pumps appear to have better results than other type of rotary blood pumps
and, due to their particular characteristics, show a longer lifespan, of roughly ten years (Timms
2011).
Radial flow devices are commonly clinically accepted, with some examples of these devices
being the HeartMate III, HeartWare and DuraHeart (Reul & Akdis 2000).
Diagonal (Mixed) flow pumps
This type of pumps is a combination of axial and radial flow pumps, and, for this reason,
they tend to have the capability of generating high pressures and high flows. Normally, these
diagonal pumps are associated with second generation techniques due to the difficulty of
completely suspending the impeller (Reul & Akdis 2000; Timms 2011).
In clinical practice, some commonly used diagonal flow devices are: VentrAssist and
HeartQuest (Reul & Akdis 2000).
Despite initial scepticism within the medical community, the number of patients ultimately
supported with continuous flow type devices is increasing. For this reason cardiovascular device
manufacturers are more and more interested in investing in the development of this type of devices
(Timms 2011).
2.4.2 Hydrodynamic and Electromagnetic Bearings in Third Generation Blood
Pumps
As previously mentioned, third generation blood pumps use hydrodynamic and
electromagnetic bearing technology to suspend the impellers without contact. The most significant
advantage of a levitated impeller is the improved life expectancy of the device.
Hydrodynamic Bearings
A hydrodynamic bearing uses a thin layer of fluid to separate two objects that are in relative
motion to each other. As such, the use of hydrodynamic bearings to support the pump rotor is
based on the formation of a thin fluid film of blood between the rotor and the stator. This blood
fluid film supports the rotor loads, without any contact. The working principle is based on the
hydrodynamic pressure generation in the fluid (Eling et al. 2013).
24
This type of support presents two main disadvantages: it requires particular operating
conditions, such as a minimum and maximum rotation speed or pump flow conditions; and the
bearing clearances may cause shear damage to red blood cells and lead to hemolysis (Greatrex
2010).
Magnetic Bearings
A magnetic bearing system supports a load using magnetic levitation. The interaction
between magnetic fields generates a lifting force that suspends the rotor. Once again, this type of
suspension avoids any type of physical contact. Compared to the hydrodynamic bearings, the
magnetic bearings can be designed to operate with a larger clearance gap and can achieve a stable
levitation at almost all operation conditions (Maslen & Schweitzer 2009).
The magnetic bearings can be divided in two groups: passive magnetic bearings (PMB) and
active magnetic bearings (AMB).
PMB achieve contact-free levitation of an object through magnetic fields generated by static
sources such as permanent magnets. PMB can be used to create an attractive or repulsive force.
By placing same-pole magnets in juxtaposition, it is possible create a repulsive force. Conversely,
by placing opposite pole magnets pairs near each other, an attractive force is generated. Depending
on the configuration, stabilization in both the radial and axial directions are possible. However, it is
not possible to stabilize all degrees of freedom of a body by passive magnetic levitation alone. The
main advantage of these magnetic bearings is mechanical simplicity, since they do not use any
active component (Greatrex 2010; Maslen & Schweitzer 2009).
AMB use electromagnetic actuators in order to control the position of the levitated object. In
contrast to PMB, a stable levitation is possible using only AMBs, since any degree of freedom can
be stabilized. However, AMBs are an unstable system, therefore they require an electronic control
system. Though this control system introduces a degree of complexity in AMB systems, it allows to
adjust and control the bearing performance in real-time (Maslen & Schweitzer 2009).
25
2.5 Summary and Discussion
The chapter started with a brief overview of the cardiovascular system and its importance,
with particular emphasis on the blood, and its most relevant characteristics to the dissertation. It
was emphasized that, for high shear rates, blood acts as a Newtonian fluid, which will be an
important consideration for the development of an analytical approach to the hydraulic forces in
section 3.3.
Next, it was discussed the prevalence of heart diseases and how the limitations of
conventional therapy and scarcity of transplant hearts led to mechanical cardiac assist devices
becoming a widely used treatment option.
These mechanical devices were afterwards categorized in four groups: left ventricular assist
device (LVAD); right ventricular assist device (RVAD); biventricular assist device (BiVAD) and total
artificial heart (TAH). Since the left ventricle failure is the most common cause for HF, the LVAD
was concluded to be the most common type of mechanical support device.
Finally, these different types of mechanical cardiac assist devices were briefly reviewed,
according to their characteristic outflow, from displacement devices to rotary devices. It was
concluded that rotary blood pumps are the most common clinically mechanical device used in
heart failure, due to the improvement outcomes for patients treated with these devices. Moreover,
it was concluded that rotary devices with electromagnetic bearing technology to suspend the
impellers without contact, such as the ReinVAD LVAD, present important advantages, at the level
of durability and efficiency.
26
27
Chapter 3
Dynamic Modelling and Analysis of ReinVAD
LVAD
In this chapter, an analytical framework will be outlined and applied to the ReinVAD LVAD,
in order to model and analyse the hydraulic forces in action.
In the first place, the pump and its major functional components will be studied, in order to
develop a solid understanding of their functioning. The various forces acting upon the pump will
also be explored.
With this context in mind, a robust mathematical model for the axial hydraulic force will be
developed, and its implementation in MATLAB ® and SIMULINK ® will be detailed. This work will
outline the major axial hydraulic forces during operation, and how they are influenced by different
variables, both internal and external to the pump. As for the hydraulic radial force, it will be studied
using a simple approximation, since the reviewed literature overwhelmingly suggests that its
magnitude would not be relevant in the ReinVAD LVAD.
3.1 The ReinVAD LVAD
The Department of Cardiovascular Engineering of the Helmholtz-Institute for Biomedical
Engineering of the RWTH Aachen University is engaged in the development of different
cardiovascular devices. In particular, it is in the process of developing the ReinVAD Left Ventricular
Assist Device (LVAD), a fully implantable pump system of the latest generation, which ensures
stable and reliable circulatory support. Aiming to be a cost efficient miniaturized device with an
intelligent controller, the ReinVAD LVAD is also being designed to be highly biocompatible with
human blood and tissues, through its surface material and to its form of functioning, which only
imposes low mechanical stress on blood cells (ReinVAD GmbH 2014).
At the present time, the device is in a prototype phase, having already been tested
successfully in acute animal trials (Graefe & Deng 2015). With the aim of continuing to develop
this device, and successfully commercializing it, ReinVAD GmbH was created in 2013 (ReinVAD
GmbH 2014).
28
3.1.1 ReinVAD LVAD Description
The ReinVAD LVAD is a fully implantable magnetically levitated radial blood pump, in which
active and passive magnetic bearings are integrated to construct a durable ventricular assist device.
The design of the current prototype of the ReinVAD LVAD is shown in Figure 3.1. In
fundamental terms, the pump presents a volute casing and internal elements, surrounded by it
(Pohlmann et al. 2011).
(a) (b)
Figure 3.1 – (a) Exploded view of the ReinVAD LVAD; (b) Assembled view of the ReinVAD LVAD; adapted from Graefe
& Deng (2015).
Regarding the volute casing, ReinVAD LVAD uses a single volute casing, which presents a
spiral shaped flow passage (Figure 3.2a) and a trapezoidal cross section (Figure 3.2b). This volute
casing has two basic functions: to collect and discharge the fluid through the outlet and to convert
the fluid kinetic energy to pressure energy. Downstream of the volute, from the volute throat to the
delivery pipe, a diffuser is used to convert the remaining amount of kinetic energy into pressure
(Gülich 2010).
29
(a) (b)
Figure 3.2 - Scheme of the single volute configuration: (a) Volute front view, with representation of volute throat and
diffuser; (b) Volute cross section; adapted from Lazarkiewicz, Stephen Troskolanski (1965).
Regarding the internal elements of the pump, Figure 3.3 shows a 3D CAD illustration of
these elements and the different materials that compose them.
Figure 3.3 - 3D CAD illustration, with different materials represented of the internal elements of the pump: AMB;
rotor/impeller; and motor stator; adapted from Graefe & Deng (2015).
The three main sections shown in Figure 3.3 are: the active magnetic bearing stator (on the
top of the Figure 3.3); the rotor with an impeller (on the middle of the Figure 3.3) and the motor
stator (lower section of the Figure 3.3). It should be noted that the active magnetic bearing (AMB)
comprises the AMB stator and the rotor, while the motor of the pump includes the motor stator
and the rotor.
30
Firstly, the active magnetic bearing stator, which characterizes the ReinVAD LVAD prototype,
is constituted of a ferromagnetic core, which carries electromagnets as well as permanent
magnets. The function of the electromagnets of the active magnetic bearing (AMB) is to generate
a variable magnetic field, which in turn creates an attractive force effect on the rotor. This way, the
pump controller can counterbalance forces acting upon the rotor in order to stabilize it, by
controlling the magnetic field of the AMB. By changing the electric current in the copper windings
of the electromagnets, the resulting magnetic field can be changed, thus also altering the passive
magnetic field of the permanent magnets of the rotor. As for the permanent magnets of the AMB
stator, their role is to stabilize the rotor in the radial direction (Graefe & Deng 2015).
Secondly, the rotor is the part of the motor which rotates the impeller. The ReinVAD LVAD
incorporates a closed impeller, presented in Figure 3.4a. The main task of the impeller is to transfer
the necessary energy to transport and accelerate the blood, and it is composed of a rear shroud,
a set of blades transferring energy to the fluid and a front shroud, Figure 3.4b (Graefe & Deng
2015; Gülich 2010).
(a) (b)
Figure 3.4 - Illustration of the impeller: (a) Closed impeller design; adapted from Lazarkiewicz, Stephen Troskolanski
(1965) and (b) Meridional section of the ReinVAD LVAD impeller and volute casing.
Third, the motor stator is the second part of the motor of the pump, together with the rotor
mentioned above, and constitutes the static part of the motor (Graefe & Deng 2015).
This motor has the function of producing the driving torque that rotates the impeller, and
has the working principle of a synchronous motor, which means it is capable of running at a
constant speed. This characteristic of constant speed is achieved by an interaction between a
31
constant magnetic field, created by the rotor, and a rotating magnetic field, created by the stator.
This way, the opposite poles of the rotor and the stator attract each other, locking magnetically.
This means that the rotor rotates at same speed of the revolving magnetic field produced by the
stator. The synchronous speed, Ns, can be derived as follows: Ns = 4πf/P, where f is the frequency
and P the number of poles of the rotor (Pohlmann et al. 2011; Graefe & Deng 2015).
As previously mentioned, the materials that make up the pump are presented in Figure
3.3. Note that the parts of the pump that are in direct contact with blood are made of paramagnetic
materials such as titanium or ceramic, two materials which present good hemocompatibility, thus
avoiding the phenomena of hemolysis and thrombosis referred to in section 2.2.3. Regarding the
magnetic core of the stators, it is composed of ferromagnetic material ideally laminated in order to
avoid eddy current losses(Graefe & Deng 2015).
3.1.2 Blood Flow in ReinVAD LVAD
The ReinVAD LVAD is designed to support the body at its normal hemodynamic levels, at
the operating speed of 2400 rpm and a flow of 5 l/min (Graefe & Deng 2015).
This device is connected to the native heart by an inflow and an outflow cannula. The inflow
cannula links the inlet of the blood pump to the lowest part of the left ventricle called the apex of
the heart. As for the outflow cannula, it links the outlet of the ReinVAD LVAD to the ascending aorta
(Jansen-Park et al. 2014). The circulation of the blood through the pump is parallel to the natural
circulation from the left ventricle to the aorta, while the aortic valve is open and blood is being
ejected. Thus, the oxygenated blood circulates from the bottom of the left ventricle into the pump
chamber (Graefe & Deng 2015).
Once inside the pump, the blood flows from the pump inlet towards the inlet edge of the
impeller blades. The impeller transfers the necessary energy to transport the blood, and accelerates
it in the circumferential direction. The fluid exiting the impeller is then decelerated in the outlet
diffuser, in order to utilize the greatest possible amount of the kinetic energy at the impeller outlet
for increasing the static pressure (Gülich 2010). After exiting through the discharge, the blood is
fed to the systemic circulation again by an aortic connection (Jansen-Park et al. 2014).
In addition to the main flow, there is also a leakage flow from the impeller discharge to the
inlet. For reasons of mechanical design, axial clearances are required between the shrouds of the
32
closed impeller and the volute casing (these clearances are called “impeller sidewall gaps”).
Because of this, after the acceleration by the impeller, a small amount of blood flows through the
clearances between the impeller and the casing (Gülich 2010). Further analysis of this
phenomenon is detailed in section 3.2.
3.2 Identification of Forces Acting on the Pump
The ReinVAD LVAD features a magnetic bearing suspension system that promotes a
suspension of rotor allowing a contact-free operation. In order to suspend the rotor, the forces
acting on the rotor must be balanced by the magnetic bearing. Hence, several conditions that can
drastically affect the magnitude and direction of the forces in the rotor should be considered. In
particular, the hydraulic forces from the fluid pressure distributions can produce large resultant
forces on the rotor, which must be balanced against the magnetic forces.
A brief description of the major forces that act in the device will be presented in this chapter.
Gravity and Buoyancy – Fg ,Fb : These two opposite forces act on the rotor. On the one
hand, gravity attracts it towards the center of the earth, proportionally to its mass. On the other
hand, and because the rotor is immersed in blood, buoyancy opposes the body weight (Bearnson
et al. 2002).
The amplitude of the gravitational force, Fg, acting on the rotor is calculated from Equation
(3.1), representing the product of the gravitational acceleration g and the mass of the rotor, mR
(Moran 2011).
The prototype rotor used in this study has a free mass of 0.080 kg, thus a gravitational force
of 0.784N acts on the rotor.
In the case of the buoyancy force, the amplitude of the buoyant force is equal to the weight
of the blood displaced by the rotor, Equation (3.2) (Moran 2011).
Fg = mR .g (3.1)
Fb = mb .g (3.2)
33
The prototype rotor has a volume of 6.785x10-6 m3, and the blood density of 1060kg/m-3
giving it at buoyant mass of 0.00719 kg and a buoyancy force of 0.0705N (Fung 1993). Given that
these forces act in opposite direction, the resultant force on the rotor due to gravity and buoyancy
is 0.714N.
The directions of both forces relative to the rotor cannot be predicted, since they are
dependent on the orientation of the rotor, which varies due to the movement of the patient.
Therefore, it can be assumed that gravity and buoyancy are opposite forces that act on the rotor
with a known magnitude and an unpredictable direction.
Inertia - FI : The rotor is exposed to inertial effects when it alters its stage of motion, due
to the acting external forces or momentums, for example when the patient moves. When such a
change in the stage of motion occurs, and the rotor is accelerated/decelerated, an inertial force
acts upon the rotor, with a direction contrary to the initial force (Greatrex 2010).
Gyroscopic Force - FG : Gyroscopic forces, as inertial forces, manifest themselves upon
the rotor when a patient or the pump bends or turns. The magnitude of these forces depends on
the impeller operating rotation speed, impeller moment of inertia and rate of turn/bend (Greatrex
2010).
Magnetic Forces - FM : Magnetic forces acting on the rotor are caused by the active
magnetic bearing and by the motor stator. Both of these magnetic elements generate a passive
magnetic field, due to the permanent magnets that they contain. This magnetic field can be
modified by electromagnets to vary the magnetic forces as well as to provide rotation torque to the
rotor. It is important to control the magnetic forces by the active magnetic bearing in order to have
a great effect in the magnetic levitation system. However, the controllability and the performance
of this system is hampered by some factors as the magnetic saturation effects, magnetic stray
fields, electrical considerations (Maslen & Schweitzer 2009; Graefe & Deng 2015; Greatrex 2010).
Damping Force - FD : As the rotor is immersed in the blood fluid, a damping force acts on
the rotor. The damping is primarily a function of the fluid viscosity and rotor movement velocity,
and its amplitude increases in proportion to the speed of the rotor. The direction of the damping
force is opposite to the direction of the velocity of the rotor, slowing its movement (Greatrex 2010).
34
Hydraulic Forces- FH : The hydraulic forces are generated by the pressure rise in the
impeller and act in both radial (perpendicular to axis of rotation) and axial (parallel to axis of
rotation) direction. In particular, radial forces are determined by the non-uniform fluid pressure
distribution around the impeller circumference caused by asymmetric flow. As for the axial
hydraulic force, it is governed by the flow through the impeller sidewall gaps and the resulting
pressure distributions on the shrouds. The hydraulic forces are highly dependent on pump design
and the operating conditions, such as rotor speed, inlet and outlet pressures and leakage flow
(Gülich 2010; Girdhar & Moniz 2005).
The study of these forces is important both for the sizing of the pump and for the
improvement of the magnetic suspension system. The magnetic suspension system must suspend
the impeller against the changes of the hydraulic force. Note that the radial hydraulic force is less
relevant for the ReinVAD LVAD than the axial hydraulic force, since the first can be balanced by the
passive magnetic forces of the AMB and the motor. Furthermore, the reviewed literature suggests
that the magnitude of the radial hydraulic force would be much less relevant than the one of the
axial hydraulic force (Untaroiu, Throckmorton, et al. 2005).
The focus of this dissertation is the study of these hydraulic forces. Over the next sections,
a detailed discussion of these forces will be carried out.
3.3 Axial Hydraulic Force Model
Significant axial hydraulic forces are generated in the pump. Since third generation pumps
incorporate magnetic levitation systems to suspend the rotor, the axial hydraulic forces acting upon
these pumps must be balanced through the action of the controller and the AMB, in order to ensure
there is no touchdown of the rotor (Girdhar & Moniz Lobanoff & Ross 1992; Gülich 2010).
Axial hydraulic forces in a radial pump mainly result from internal pressures acting on the
exposed areas of the rotor. Therefore, the magnitude and direction of these axial hydraulic forces
change during the pump operation. These changes are governed by different factors, including the
variation on the flow conditions in gaps between the impeller shrouds and the volute casing, and
the resulting pressure distributions on the impeller shrouds (Girdhar & Moniz 2005; Bloch & Budris
2015).
35
The methodology adopted to model the axial hydraulic force on the ReinVAD LVAD was
based on Gülich (2010) work. Accordingly, the resultant force in this model comprises, as per
Equation (3.3): the resultant force in the shrouds, FHS, caused by the pressure distributions acting
on the impeller rear and front shroud (FRS, FFS); and a momentum force, Fm . Note that the
unbalanced axial hydraulic forces acting on the shaft, referred to by Gülich (2010), are not
considered in this case since the ReinVAD LVAD does not present any shaft (the rotor is
suspended).
Given that the resultant force in the shrouds corresponds to the difference between the
forces in the front and rear shrouds, Equation (3.3) can be rewritten as, Equation (3.4) :
These different components of the axial hydraulic force, their relative directions and the
relevant pressure distributions, p(r), are shown in Figure 3.5, which represents a schematic
meridional section of the impeller. It is important to mention that the signs in the Equation (3.4)
indicate the direction of the force, in accordance to the positive direction (z+) defined in Figure 3.5.
Figure 3.5 - Meridional section of the impeller and volute casing, presenting the pressure distribution and axial
hydraulic forces.
Fax = FHS − Fm (3.3)
Fax = (FRS − FFS) − Fm (3.4)
36
The key geometric variables for the study of these forces in the developed analytical model
are represented in Figure 3.6.
Figure 3.6 -Meridional section of the impeller and volute casing, presenting the main geometric variables.
A final consideration for the development of this model is that the rotor was assumed to be
centred in the volute casing. This assumption was motivated by two reasons: firstly, the movements
of the rotor, except for its rotation around the z-axis, are constrained by the permanent and active
magnetic bearings that stabilize the entire rotor. Secondly, CFD data suggests that even if
temporary variations in the position of the rotor occur, their impact in the axial hydraulic force is
not very significant (even the movement of the rotor to extreme positions only resulted in a change
of 0.07 N in the magnitude of the force – Appendix III).
In the next sub-sections, each of the two main components of the axial hydraulic force will
be detailed: the force acting on the impeller shrouds and the momentum force.
Force acting on the impeller shrouds
For reasons of mechanical design, the pump requires axial clearances, commonly named
impeller sidewall gaps, between the shrouds of a closed impeller and the volute casing. This design
leads to the formation of a leakage flow in the clearances. The rotation of the fluid, imparted by the
rotation of the impeller, generates a variable pressure distribution along the radius of the shroud.
37
The resulting pressure distribution from this leakage flow acting on the shrouds generates an axial
hydraulic force (IMechE 2014).
In order to describe the leakage flow, an approach based on a flow model with separate
boundary layers was adopted. This flow model presents three different regions: A rotating boundary
layer, immediately at the shroud, a stationary boundary layer next to the volute casing, and a core
region between them.
Immediately at the shroud, the fluid adheres to the rotating wall, and thus has the velocity
cu=ω.r. Moving away from the shroud, a rotating boundary layer is formed, with decreasing
tangential velocity. Finally, the stationary boundary layer presents the inverse behaviour, with a
velocity that reaches zero when the fluid adheres to the casing wall, cu=0 m/s, and increases when
moving away from it.
The centrifugal forces in the rotating boundary layer induce the movement of the fluid
radially outwards. Consequently, for reasons of continuity, the fluid flows back radially inwards
along the volute casing wall, as shown in Figure 3.5. Due to the connection between the sidewall
gaps and the pump inlet, the flow through the impeller sidewall gaps is imposed on the circulating
flow. This phenomenon is crucial in a blood pump since blood must never be stationary in the
sidewall gaps.
In order to calculate the axial hydraulic force in the shrouds, the fluid rotation on the shrouds,
which influences the pressure distributions, must be analysed. An exact analytical calculation the
fluid rotation is complex, since the tangential velocity cu of the fluid contained in the sidewall gaps
results from a balance of all momentums acting on the fluid. In practice, empirical coefficients and
procedures are employed, which describe the flow by rotation factors, k. In this model, the rotation
factor is defined as the ratio of the tangential fluid velocity cu= β.r to the circumferential velocity
u=ω.r (β is the angular velocity of the fluid in the core flow), Equation (3.5).
The rotation factor is a function of the radius of the sidewall gap, k(r).
The calculation of the rotation factor function k(r) is based on a step-wise procedure
developed by Gülich (2010), derived from the balance of momentums acting on a fluid element in
k =cu
u=
β
ω (3.5)
38
the sidewall gaps. This calculation needs to be performed separately for each shroud, resulting in
kRS(r) and kFS(r) (rear shroud and front shroud respectively), following the same procedure but
adjusting the relevant variables for each case. The general procedure comprises the following
steps:
1. Calculate the flow coefficient, φlf, and the Reynolds number, Re, by Equation (3.6), and
Equation (3.7), respectively. The flow coefficient needs to be calculated separately for each
shrouds, since Qlf,,RS and Qlf,FS are different.
2. Determine the parameter k WF, which represents the rotation of the fluid without flow through
the impeller sidewall gaps (for φlf = 0), using Equation (3.8). Note that k WF depends only on
the dimensions of the pump.
Note that this rotation factor needs to be calculated separately for the front shroud (kWF,FS)
and for the rear shroud (kWF,RS), with cax being different in each case. Note that cax =sax + oax.
3. Calculate the rotation factors k(x) in each impeller sidewall gap from Equation (3.9) and
Equation (3.10). Note that x represents the ratio of each of the radii to the outer impeller radius,
x =r/rI.
φlf=Qlf
π ri2u2
(3.6)
Re =u2 rI
ν (3.7)
kWF =1
1+ (rvrI
)2
√(rvrI
+ 5 caxrI
)
(3.8)
dkdx
=0.079 xn
1.6
φlf Re0.2 {(1 − kWF
kWFkn)
1.75
− |1 − kn|1.75} − 2kn
xn (3.9)
kn +1 = kndkdx
(xn +1 − xn) (3.10)
39
3.1 Select an appropriate starting point for the integration. In this investigation, it was
assumed that the leakage flow is directed radially inwards in both shrouds (according
to the prediction of previous CFD simulations on ReinVAD LVAD)(Graefe & Deng 2015).
As such, the calculation followed the flow direction from outside to inside. Taking this
into consideration, and since the tangential velocity cuE at the entry of each impeller
sidewall gap has a strong impact on fluid rotation, kE (kE_FS and kE_RS depending on the
shroud) 2 was defined as starting point for the integration, Figure 3.5.
3.2 Define the number of partitions, n, between rFS or the rRS (for front shroud or for rear
shroud respectively) and rI, for which rotation factors was calculated. The number of
partitions should be large enough so that increasing it will not change the mean value
of k(x).
3.3 Calculate each individual rotation factor k(x) between x=1 (for r =rI) and x = rFS|RS /rI
(for r =rFS|RS ); based on the step-wise procedure explained above, Equation (3.9) and
Equation (3.10).
It is important to note that this calculation is sensitive to two factors: the value of kWF, which
depends on geometric parameters; and the value of kE used as a boundary condition for the step-
wise calculation.
Having obtained the rotating factors for each shroud, which describe the leakage flow, it is
now possible to calculate the axial hydraulic forces acting on the shrouds. For this, the mean of
the rotation factors,k̅ , will have to be calculated for each shroud, according to Equation (3.11) .
Note that n is defined as the number of partitions between rFS or the rRS and rI.
The axial hydraulic forces acting on the shrouds can be represented by the integral shown
in Equation (3.12) , over the pressure distribution given by Equation (3.13). This integration must
be performed separately for each shroud. In the case of the front shroud it is done from rFS to rI ;
2 Note that kE represent k for x=1 and is the starting point of the integration, whereas k WF is a fixed parameter representing the rotation of the fluid without flow through the impeller sidewall gaps.
k̅=1
n∑ kn
n
n=0
(3.11)
40
while in the case of rear shroud it is done from rRS to rI. Likewise, the mean rotation factor in each
shroud is also different: k̅FS for the front shroud and k̅RS for the rear shroud. Note that the differences
in these two values can be explained by the different dimensions of the sidewall gaps and the
differences in leakage flow in each gap.
Equation (3.13) can be deduced by integrating the general motion equation of a fluid particle
on a 3-dimensional curved streamline, Equation (3.14), with c=ω.k.r. (Gülich 2010).
Solving the integral of the Equation (3.12), the forces acting on front shroud and rear shroud
are represented in Equation (3.15) and Equation (3.16), respectively:
Set xFS = dFS/dI for the front shroud and xRS = dRS/dI for the rear shroud.
Finally, the resultant axial hydraulic force acting on the impeller shrouds is given by the
difference between the forces acting on rear and front shrouds FHS= FRS - FFS, Equation (3.17).
FFS|RS = 2π ∫ p . r .dr (3.12)
p = p2 −ρ
2 u2
2 k̅ 2(1 −
r 2
rI 2) (3.13)
dpdr
=ρc 2
r (3.14)
FFS = π rI 2 {(1 − xFS
2)Δpim −ρ
4u2
2 kFS̅̅̅̅ 2(1 − xFS
2)2} (3.15)
FRS = π rI 2 {(1 − xRS
2)Δpim −ρ
4u2
2kRS̅̅̅̅ 2(1 − xRS
2)2} (3.16)
FHS = π rI 2 {Δpim(xFS
2 − xRS2) −
ρ
4u2
2 [kRS̅̅̅̅ 2(1 − xRS
2)2 − kFS̅̅̅̅ 2(1 − xFS
2)2]} (3.17)
41
Momentum Force
The force associated with the change in the momentum of incoming flow also needs to
be considered (Godbole et al. 2012). In fact, the conservation of momentum states that the amount
of momentum ( ρ .Q .c ) remains constant in a closed system. Consequently, changes in the
momentum of the fluid are necessarily associated with a force (Gülich 2010).
This force is called the momentum force and can be represented by Equation (3.18),
Since the axial direction is investigated, the velocity component for the momentum force
must also be in the axial direction. Thus, c1m and c2m are the meridional component of velocity in
the inlet and outlet edge of the impeller blade, respectively. The factor cos ε2 is added in order to
isolate the axial component of the velocity.
Note that ε2 is the angle between the mean streamline at the impeller outlet and the rotor
axis, represented in Figure 3.6. In the particular case of the ReinVAD LVAD, the impeller is radial
and so ε2= 90°. Additionally, the meridional component of velocity at the inlet edge of impeller is
defined as c1m= QAim
; where Ain=π .dFS .b 1. Applying these expressions, Equation (3.18) can be
rewritten as,
Equation (3.19) implies that, as Q increases, Fm increases since it is directly proportional to
the square of the flow in the impeller inlet.
Fm = ρ Q (c1m − c2m cos ε2) (3.18)
Fm =ρ. Q 2
π .dFS .b1 (3.19)
42
3.3.1 MATLAB and SIMULINK Implementation
After being defined, the theoretical framework to analyse the axial hydraulic force was
implemented in MATLAB® and SIMULINK®, Appendix II, in order to obtain numerical results for
different scenarios. The mathematical model was implemented in SIMULINK® and the pre and
post processing of the values and results was performed in MATLAB®.
As discussed in the section 1.2, this investigation aimed to support the design of the ReinVAD
LVAD and create the basis for a model to be integrated in the controller of the pump. Implementing
the developed model in MATLAB® and SIMULINK® was decided to be the best way to achieve
these goals. On the one hand, this approach was considered to be a user-friendly solution, thus
better supporting the design of the pump. In fact, it allows for easy adaptations and modifications
by the ReinVAD GmbH researchers, should any changes be required in one of the fixed parameters
or variable inputs. On the other hand, the pump controller is being developed using SIMULINK®,
so this approach facilitates an easier integration with the work that has been developed so far.
To enable the exhaustive study of the hydraulic forces, the model generates a “results table”
presenting the results of each one of the components of the axial hydraulic force (momentum force,
axial hydraulic force acting on front shroud; axial hydraulic force acting on rear shroud) and the
resultant axial hydraulic force for all possible combinations of the 5 variable inputs (the rotation
speed – rotation_speed; the flow rate – Q; the pressure rise in the impeller - delta_p_im; the
leakage flow in front shroud -Q_lf_FS; and the leakage flow in rear shroud - Q_lf_RS).
To reach these results, two scripts were created in MATLAB®: one script for initializing the
SIMULINK® model and another with the variables to be tested. The first script contains all the
fixed input parameters required for the simulation. The second one uses five for –loops to call the
SIMULINK® model (Hydraulic_axial_force_model) various times to calculate all possible
combinations of the variable inputs and fill in the results table.
In SIMULINK® two main blocks were created, each one presenting one component of the
axial hydraulic force, Figure 3.7. Using mathematical operation blocks, the equations defined in
section 3.2 were implemented in each block of the SIMULINK® model. Note that, on the “Resultant
force in the shrouds” block, a mathematical function block was used, allowing for the addition of
a MATLAB® function in the SIMULINK® model. This function was necessary for the calculation of
the rotation factor in each shroud through a step-wise procedure, as defined in section 3.2.
43
Figure 3.7 - Main blocks of the resultant hydraulic force: axial hydraulic force on impeller shrouds and momentum
force.
3.4 Radial Hydraulic Force
The steady radial force results from the non-uniform fluid pressure distribution around the
impeller circumference (Sulzer Pumps 1998; Gülich 2010). Several physical effects directly
influence this steady radial force on the impeller, such as:
1. Non-uniform flow in the collector, acting on the impeller outlet width;
2. Non-uniformities of the flow in the impeller sidewall gaps, which can be created by the
pressure distribution in the collector;
3. Non-uniform flow distribution at the impeller inlet.
Typically, the volutes are designed in order to provide a uniform impeller discharge at the
best efficient point (BEP) of the pump, which generates constant pressures around the impeller,
like in the schematic representation in Figure 3.8. However, for other non-optimal pump conditions,
the discharge flow becomes asymmetric.
Figure 3.8 - Uniform pressure distribution around the impeller; adapted from Lazarkiewicz, S.Troskolanski (1965).
44
Three different pump conditions must be considered in order to better understand the
occurrence of the radial hydraulic force: the best efficient point (q*=1); low flow rates (q*<<1) and
high flow rates (q* >>1). Note that, the flow rate ration, q*, is represented by Equation (3.20).
The radial force for the three pump conditions will be discussed for the case of a single
volute, the volute type of the ReinVAD pump (different volutes present different phenomena).
Best efficient point
Near the best efficiency point, the pressure distribution is nearly uniform around the volute
cross sections. Hence, the pressure distribution integration results in a negligible resultant radial
force. The uniform pressure is a consequence of the uniform flow around the volute. As the flow
angle at the impeller outlet matches the tongue angle, no-perturbations act on the flow path. As
such, the flow velocity along the volute follows the conservation of momentum (section 3.2 describe
the conservation of momentum). This force would be theoretically zero at the best efficiency point
with an infinitely thin tongue (Guelich et al. 1987; Gülich 2010).
Low flow rates
In contrast, at low flow rates, due to non-uniform flow, the variation of the static pressure
over the volute casing induces a radial force on the impeller.
In fact, at low flow rates (q*<<1), the flow angle is smaller than the geometric angle of the
tongue, and consequently flow separation occurs downstream of the tongue, as represented in
Figure 3.9a. This, in combination with the operation at low flow rates, results in the radial force
being directed towards this region (pressure minimum)(Guelich et al. 1987; Gülich 2010).
High flow rates
At high flow rates (q*>>1), a variation of the static pressure over the volute casing also
occurs.
The flow angle leaving the impeller is, in these flow conditions, larger than the geometric
angle of the tongue, generating a flow separation in the diffuser, Figure 3.9b.
q*=Q
QBEP (3.20)
45
Additionally, there is a pressure build-up downstream of the tongue (reaching a pressure
maximum), due to a stagnation point in this area. Thus, the radial force is directed away from that
pressure maximum (Gülich 2010; Guelich et al. 1987).
(a) (b)
Figure 3.9 - Radial force for (a) low flow rates (q*<<1); and (b) high flow rates (q*>>1); ; adapted from Guelich et al.
(1987).
3.4.1 Estimation of the Radial Force
The discussed effects, and consequently the radial force encountered by the impeller of a
radial pump, are not subject to a simple exact theoretical prediction (which would require modelling
the three-dimensional flows in impeller and volute). Therefore, many authors have derived empirical
coefficients for estimating the radial force (based on experimental data).
From literature, section 1.3, the radial force in the case of ReinVAD LVAD was expected to
be small. As such, in this investigation, a simple estimation of the magnitude of the force was
performed, in order to validate that this force would not be relevant compared to the axial hydraulic
force and consequently did not warrant the application of a more complex model.
In order to estimate the static radial force, the equation derived by Stepanoff (1957) was
used, given by Equation (3.21).
FR =C. H.dV . b4
2.31 (3.21)
46
The coefficient C is a function of flow and changes for each volute type. In the case of single
volute (as the one being studied) the coefficient C is calculated in accordance with Equation (3.22).
The results of the magnitude of the radial force on the impeller of the ReinVAD pump are
presented on Table 3.1. In Appendix I, the calculation process to reach these results is detailed.
Table 3.1 - Results of radial force (N) vs flow rate (l/min).
Flow - l/min Radial Force - N
1 8.76 x 10-5
3 5.72 x10-5
5 0
7 6.47 x10-5
9 1.07 x 10-4
Analysing the results presented in Table 3.1, it can be concluded the radial forces exerted
on the impeller present very low magnitudes (in order of 10-4 or 10-5 N) for the simulated flow rates.
Though this methodology presents some limitations, such as not accounting for variations
resulting from pump-specific speed, it is expected that the real values of the radial force will not
differ significantly from this results.
In conclusion, this methodology indicates that, as expected from the literature review in
section 1.3, the radial force is not very relevant in the context of the ReinVAD LVAD and, as such,
this investigation does not require the development of a more complex model to analyse it. The
fact that this radial hydraulic force can be partially managed by passive magnetic bearings, which
do not depend on the responses of the controller, reinforces the notion that the development of a
dynamic model for this force is less relevant than for the axial hydraulic force.
C = 0.36 (1 − (Q
QBEP)
2
) (3.22)
47
3.5 Summary and Discussion
This chapter started with a detailed description of the ReinVAD LVAD device and its mode of
operation. The main components of the pump were detailed, including the active magnetic
bearings, the rotor and impeller and the motor stator. The use of a magnetic bearing system to
stabilize the impeller within the pump volute was also explained. In addition to the design of the
pump, the flow conditions in the ReinVAD LVAD were described, explaining that the circulation of
the blood through the pump is parallel to the natural circulation and that, due the mechanical
design, a leakage flow occurs within the pump.
This chapter then advanced to the identification of the forces acting on the rotor, in order
to develop a comprehensive understanding of the system of forces affecting the pump. In particular
it was explained how hydraulic forces develop from the fluid pressure distributions and flows within
the pump casing.
After identifying all the forces acting on the rotor, a mathematical model of the axial hydraulic
forces acting on the rotor was developed, with two key components: a resultant force acting on the
shrouds (which is itself comprised of a force acting on the front shroud and one in the rear shroud)
and a momentum force. The major variables that affect each one of these forces were described,
in order to build a better understanding of their behaviour. Moreover, a detailed implementation of
this model in MATLAB®/SIMULINK® was presented.
Finally, a simplified approach estimating the radial force was described and implemented,
which allowed to conclude that this force is less important for the ReinVAD LVAD case.
48
49
Chapter 4
Results and Discussion
In this chapter, the results of the analytical model for the axial hydraulic force will be
presented. In order to achieve this, the scenarios of the simulations and key inputs will be detailed.
Two simulations will be implemented based on these conditions, analyzing the response of the
axial hydraulic force components to changes in the flow rate and the rotation speed. The results
will be discussed and analysed in depth, in order to understand the underlying effects that influence
them. Moreover, the results will be evaluated in the light of the relevant literature, in order to
understand if they are consistent with previous investigations; and compared to existing CFD data,
in order to perform an additional validation of the model.
4.1 Scenario of Simulation
In order to evaluate the developed analytical model, the behaviour of the axial hydraulic force
was analysed under two distinct simulations: variable flow and variable rotation speed. Each one
of the simulation results was obtained from the overall table results discussed in the section 3.3.1,
using different combinations of the variable inputs. In this section, the initial conditions of each
simulation will be presented, including: assumptions about physiological conditions, the design and
dimensions of the pump and additional CFD data.
4.1.1 Simulation Conditions - Physiological Variables
To develop a robust simulation of the axial hydraulic forces, the rheological properties of the
fluid that circulates the pump must be defined. As discussed in section 2.2.2, blood properties are
strongly dependent on shear rate, temperature and haematocrit. For the theoretical analysis, it was
assumed that the pump would operate in a man with a body weight of 70Kg, a blood-temperature
of 36º (physiological temperature of the human body), a haematocrit level of 45% and with no
health issues that could influence the normal properties of blood.
Blood was assumed to behave as a Newtonian fluid, presenting a constant viscosity, since
under normal functioning of the pump, the shear rates are substantially above 100 s-1 (which
causes the blood act as an almost perfect Newtonian fluid, as discussed in section 2.2.2).
50
Table 4.1 presents the density and viscosity of the blood under these conditions.
Table 4.1 - Rheological proprieties of the blood used for all simulations (Timms 2005; Fung 1993).
Properties Value
Blood Density (ρ) 1.06 x 103 Kg/m3
High shear-rate blood viscosity (η) 3.50 x 10-3 Pa.s
Kinematic viscosity (ν) 3.30 x 10-6 m2/s
4.1.2 Simulation Conditions – Pump Design and Dimensions
For the analysis, the geometry and design of the current ReinVAD LVAD prototype is
presented in Table 4.2, following the nomenclature defined and presented in Figure 3.6.
Table 4.2 - Dimension of the pump, according to Figure 3.6, in millimetres (mm) (Graefe & Deng 2015).
Variable Value (mm)
b 1 5
b 2 4
b 3 6
dFS 14
dRS 10
dR 38
dV 38.5
sax_FS 0.15
sax_RS 0.15
oax 1 2
oax 2 2
51
4.1.3 Simulation Conditions – Additional CFD Data
In order to undertake the proposed simulations, the responses of the pressure rise in the
impeller (ΔPim) and of the leakage flow in both clearances (Qlf_RS, Qlf_FS) to changes in the variables
under analysis in each simulation were obtained by CFD simulations of the ReinVAD LVAD. These
relationships are presented in Figure 4.1 and Figure 4.2, while the relevant raw data from the CFD
simulations can be found in Appendix III.
Figure 4.1 illustrates that both the pressure rise in the impeller and the leakage flows (in the
front and rear shroud) reduce with increasing flow rates. It should be noted that the leakage flows
tendency is not very pronounced, especially for the front shroud.
(a) (b)
Figure 4.1 - CFD simulations: (a) Graph presenting the relationship between the pressure rise in impeller (mmHg)
and the flow rate (l/min);(b) Graph presenting the relationship between the leakage flow (l/min) in each shroud and
the flow rate (l/min): leakage flow in front shroud – red; leakage flow in rear shroud – blue.
Figure 4.2 illustrates that both the pressure rise in the impeller and the leakage flows (in the
front and rear shroud) increase with increasing rotation speeds. It should be noted that in this case
there is a very substantial variation in the leakage flows for both shrouds, which will be discussed
in section 4.2.2.
50
65
80
95
0 3 6 9
Pres
sure
rise
in im
pelle
r [m
mH
g]
Flow rate [l/min]
0,05
0,15
0,25
0,35
0,45
0 3 6 9
Leak
age
Flow
[l/m
in]
Flow rate [l/min]
Leakage flow in rear shroud
Leakage flow in front shroud
52
(a) (b)
Figure 4.2 - CFD simulations: (a) Graph presenting the relationship between the pressure rise in impeller (mmHg)
and the rotation speed (rpm);(b) Graph presenting the relationship between the leakage flow (l/min) in each shroud
and the rotation speed (rpm): leakage flow in front shroud – red; leakage flow in rear shroud – blue.
4.1.4 Description of the Simulations
Using the developed model, two different simulations were performed, each of them
simulating the response of the hydraulic force to changes a key variable, as outlined in Table 4.3:
1. Simulation with variable flow (assuming a rotation speed of 2400 rpm);
2. Simulation with variable rotation speed (assuming a flow of 5 l/min);
Table 4.3 - Description of each simulation.
Simulation Flow (l/min) Rotation Speed (rpm)
1 1-9 - Variable 2400
2 5 1800-3000 - Variable
In the first simulation, the relationship between the flow rate and the axial hydraulic force
was analysed. To this end, the axial hydraulic force was calculated for five different flows between
1l/min and 9l/min. The limits of the range of values for the pump flow were defined according to
the cardiac flow of a failing heart (bottom limit: 1 l/min) and in physical exercise conditions (upper
limit – 9 l/min). Endo et al., (2002) recommend values of 0.5-2 l/min for simulating a failing heart,
30,0
50,0
70,0
90,0
110,0
130,0
1800 2100 2400 2700 3000
Pres
sure
rise
in im
pelle
r [m
mH
g]
Rotation Speed [rpm]
0,05
0,15
0,25
0,35
0,45
1800 2100 2400 2700 3000
Leak
age
Flow
[l/m
in]
Rotation Seed [rpm]
Leakage flow in rear shroud
Leakage fow in front shroud
53
and Golding & Smith, (1996) proposed that for an healthy heart, cardiac flow was expected to be
between 4-6 l/min at rest, and 7-10 l/min under moderate activity. In this simulation, it was
assumed that the rotation speed was constant, at 2400 rpm. This particular rotation speed allows
the pump to meet its design conditions, achieving its maximum efficiency at 5 l/min (cardiac output
of a healthy heart at rest).
In the second simulation, the axial hydraulic force was simulated for different rotation speeds
of the pump. To this end, a range of five different rotation speeds between 1800 rpm and 3000
rpm was defined, based on the best efficiency point for a normal cardiac flow of 2400 rpm and a
range of [+25%;-25%]. This range covers most of the operating conditions of the pump, with the
bottom limit meeting the requirements for partial support (in case of a recovering heart), and the
upper limit meeting the requirements for full support (in combination with physical activity) (Timms
2005). To implement the simulation, the flow rate was fixed at 5 l/min, which, as already
mentioned, corresponds to the cardiac output of a healthy heart in rest.
4.2 Analysis of Results
The results for each one of the simulations is presented and discussed in this section.
4.2.1 Simulation with Variable Flow
The behaviour of the axial hydraulic force in relation to the flow rate (results from the first
simulation described in section 4.1.4) is presented in Figure 4.3.
Figure 4.3 - Graph presenting the relationship between the axial hydraulic force (N) and the flow rate (l/min), based
on the analytical model.
-0,60
-0,50
-0,40
-0,30
-0,20
-0,10
1 3 5 7 9
Axia
l Hyd
raul
ic F
orce
[N]
Flow rate [l/min]
54
In order to properly analyse the behaviour of the axial hydraulic force, three main aspects
need to be considered: its direction, its magnitude and its tendency in relation to variations in the
flow rate.
Starting with the first characteristic, for all simulated flows the resultant axial hydraulic force
acts in the negative direction – from the front side to the rear side of the impeller (according with
the positive direction defined in Figure 3.5, in section 3.3). This direction of the resultant force
indicates that the forces acting on the front side of the impeller (the axial hydraulic force on the
front shroud and the momentum force) display a higher magnitude than the force acting on the
rear side (the axial hydraulic force acting on the rear shroud).
As for the magnitude of the axial hydraulic force, it displays values in the order of 10-1N,
reaching a maximum of 0.57N at the lowest simulated flow rate (1l/min) and a minimum of 0.29N
at the highest (9l/min). These extremes values of the curve correspond, respectively, to the highest
and lowest values of pressure distribution around the impeller, Figure 4.1 section 4.1.3. This
behaviour was expected given the dependency between the pressure distribution and the hydraulic
force on the impeller - the pressure rise in the impeller decreases with the flow rate, which in turn
leads to a decrease in force.
These magnitudes are relatively small, which was expected since the ReinVAD LVAD has a
closed impeller, a design which produces minimal axial hydraulic forces due to the rear shroud
pressure being countered by the front shroud pressure (Bloch & Budris 2015). As a final note, it is
important to mention that the relatively low magnitude of the resultant axial hydraulic forces does
not imply that the individual forces acting on the impeller are irrelevant. On the contrary, each
component of axial hydraulic force has a significantly larger magnitude, as it will be discussed
below. However, the different components act in different directions, counterbalancing each other.
Finally, in terms of the tendency of the curve it is possible to observe in Figure 4.3 that the
axial hydraulic force decreases in magnitude (increasing in the positive direction) with increasing
flow rates. Therefore, the relevance of the axial hydraulic force decreases for higher flow rates
(within the range of the relevant flows for the pump that were simulated). These results are
consistent with the results of Song et al. (2004), Untaroiu et al. (2005) and Godbole et al. (2012).
55
In order to understand the observed behaviour and get more information about the axial
hydraulic force, the contribution of the different components of the force was evaluated separately
and their results are present in Figure 4.4.
Figure 4.4 - Graph presenting the relationship between each component of the axial hydraulic force and the flow rate
(l/min): momentum force - red (N) and the resultant force acting in the shrouds - blue (N), based on the analytical
model.
It should be noted that since the resultant axial hydraulic force corresponds to the difference
between the momentum force and the force in the shrouds (as shown in Equation (3.3)), the
magnitude of the resultant axial hydraulic force corresponds to the distance between the resultant
axial hydraulic force acting on the shrouds and the momentum force, in Figure 4.4. Thus, the
decrease of this distance with the increase of the flow rate illustrates the decrease of the axial
hydraulic force with flow rate. This decrease is generated by the fact that the resultant force in the
shrouds decreases quicker (reducing its magnitude in the negative direction, increasing in the
positive direction) than the momentum force increases. These results are consistent with Zhou et
al. (2013) and Sato & Miyashiro (1980).
Analysing the components of the axial hydraulic force individually, and starting with the
momentum force, its increase with the flow rate was expected since the momentum force (for the
same fluid and at the same area) is only dependent on the flow rate – Equation (3.19) corroborates
this dependency. Thus, this component becomes more relevant to the resultant axial hydraulic
-0,60
-0,40
-0,20
0,00
0,20
1 3 5 7 9
Forc
e sh
roud
s/M
omen
tum
[N]
Flow rate [l/min]Force acting in ShroudsMomentum force
56
force at higher flow rates, becoming more intense (in terms of magnitude) than the axial hydraulic
force acting on the shrouds for flows close to 9/min.
Advancing to the axial resultant force on the shrouds, this force is decreasing in magnitude
with the increase of the flow rate (as shown in Figure 4.4). Since both forces in the shrouds are
decreasing, this behaviour implies that the impeller front shroud force reduces more in magnitude
than its rear shroud equivalent. In terms of magnitude, the resultant force on the shrouds reaches
a maximum of 0.56N for the lowest simulated flow rate (1l/min), reaching almost 500 times the
value of the momentum force for this flow rate.This discrepancy in the magnitudes of the two forces
was also reported by Sato & Miyashiro (1980). However, with increase in flow rate, the contribution
of the force on the shrouds becomes less relevant.
In order to better understand the resultant force in the shrouds, each of its components
(front and rear shroud force) was plotted against each other, in Figure 4.5.
Figure 4.5 - Graph presenting the relationship between each component of the resultant axial hydraulic force acting
on the shrouds and the flow rate (l/min): Force acting on the rear shroud - blue (N) and force acting on the front
shroud - red (N), based on the analytical model.
Firstly, it can be concluded that both forces display a similar tendency, decreasing in
magnitude with the increase of the flow rate. The main cause for this behaviour is the decrease of
-15,00
-10,00
-5,00
0,00
5,00
10,00
15,00
1 3 5 7 9
Forc
e in
fron
t/re
ar s
hrou
d [N
]
Flow rate [l/min]
Force in Rear ShroudForce in Front Shroud
57
the static pressure rise above the impeller inlet with flow rate, ΔPim – Figure 4.1. In both shrouds
the forces display a maximum magnitude at 1l/min and a minimum at 9l/min.
Despite partially compensating one another, the two components have different magnitudes.
This slight difference in them generates the resultant force in the shrouds, which has a magnitude
that is dozens of times smaller than each of the individual forces. The difference in the magnitude
of the forces can be explained as the combination of two factors: first, the different pressure profile
developed in each clearance of the front and rear shrouds (due to the different fluid rotations in
each of the clearances); second, the difference in the transversal area where this pressure acts in
each shroud (coming from the different diameters – dFS and dRS)(Godbole et al. 2012).
The pressure profile of each shroud is influenced by the leakage flow in the impeller
clearances. This leakage flow (coming from the impeller outlet) carries the angular momentum
ρ.Qlf .c2u.rI into the impeller sidewall gap, and thus enhances the fluid rotation radially from the
outer to the inner radius of each clearance (c2u is the local tangential velocity near the each shroud
at the impeller outlet). In turn, this increase in the fluid rotation leads to a pressure drop radially
along each shroud (Girdhar & Moniz Lobanoff & Ross 1992; Gülich 2010).
Figure 4.6 and Figure 4.7 plot the local rotation factors for each shroud (kFS, kRS) against the
radius ratio (xRS, xFS) radially along each shroud clearance. As defined in section 3.2, kFS and kRS
are the ratios of the angular fluid velocity to the impeller speed in each gap. These figures illustrate
the increase of the fluid rotation radially along the shrouds clearances, with higher values of kFS
and kRS for lower values of xFS and xRS. This tendency of the rotation factor along the radial radius,
for inward leakage fluid, was also reported by Gantar et al. (2000) and Gülich (2010). Moreover,
as the flow rate in the pump decreases, the rotation factors in each shroud increase, since the
leakage flow increases, Figure 4.1b section 4.1.3. This behaviour of the rotation factor with the
flow rate is consistent with Gülich (2010). Note, however that this increase in the leakage flow and
rotation factors with increasing flows is very moderate, since the rotation speed of the pump is kept
constant at 2400 rpm. In fact, as it can be observed in the Figure 4.7 , two of the curves overlap
entirely (1 l/min and 3 l/min).
58
Figure 4.6 - Graph representing the local rotation factors along each radius ratio for the front shroud, for each flow
rate – 1l/min (blue), 3l/min (red), 5l/min (black), 7l/min (blue dotted) and 9l/min (red dotted).
Figure 4.7 - Graph representing the local rotation factors along each radius ratio for the rear shroud, for each flow
rate – 1l/min (blue), 3l/min (red), 5l/min (black), 7l/min (blue dotted) and 9l/min (red dotted).
0,4
0,5
0,6
0,7
0,8
0,9
1
0,2 0,4 0,6 0,8 1
Fron
t rot
atio
n fa
ctor
, kFS
[-]
Radius ratio front shroud , xFS [-]
9 l/min 7 l/min 5 l/min3 l/min 1 l/min
0,4
0,5
0,6
0,7
0,8
0,9
1
0,2 0,4 0,6 0,8 1
Rear
Rot
atio
n fa
ctor
, kRS
[-]
Radius ratio rear shroud, xRS [-]
9 l/min 7 l/min 5 l/min3 l/min 1 l/min
59
Comparing the two shrouds, it can be observed that the rotation factors in the front shroud
are larger than in the rear shroud. This difference in the rotation is due to two factors. On the one
hand, there are differences in the radii of the shrouds: in this case, the smaller inner radius of the
front shroud (rRS > rFS) leads to a larger circumferential velocity at the end of the shroud, near the
impeller inlet. On the other hand, there are differences in the leakage flows – a larger leakage flow
leads to a larger angular momentum, and thus to larger rotation factors (Gülich 2010; Hergt &
Prager 1991). In this specific case, the leakage flows in the front and rear shrouds do not differ
significantly (Figure 4.1b), so this effect is not very noticeable. Therefore, the combination of these
factors leads to a larger rotation factor in the front shroud, resulting in a larger pressure drop.
Besides the pressure profile, a second factor must also be considered to understand the
differences in the magnitudes of the forces in the front and rear shrouds - the transversal area
where the pressures act. The front shroud presents a smaller inner diameter (dRS > dFS), and so
the developed pressures acts upon a larger area. This factor counterbalances the effect of the
larger pressure drop, contributing to higher magnitudes on the front shroud. Similar conclusions
can also be found in Godbole et al. (2012), Zhou et al. (2013) and Curtas et al. (2002) works.
The combination of the two factors, pressure and area, determines the relative magnitude
of the two forces. For the studied flows, the bigger area of the front shroud plays a more significant
role than the differences in the pressure profiles, and so the front shroud force is stronger than the
rear shroud force.
60
4.2.2 Simulation with Variable Rotation Speed
The relationship between the axial hydraulic force and the angular rotation speed of the
impeller is presented in Figure 4.8.
Figure 4.8 - Graph presenting the relationship between the axial hydraulic force (N) and the rotation speed (rpm),
based on the analytical model.
As in the previous section, three aspects were considered in order to analyse the relation
between axial hydraulic force and the rotation speed: the direction, the magnitude and the tendency
of the curve.
The resultant axial hydraulic force acts in the negative direction (from the front side to the
rear side of the impeller) for all rotation speeds. The conclusions from the analysis of the previous
section (axial hydraulic force versus flow rate, Figure 4.3) remain valid - the forces acting on the
front side of the impeller display a higher magnitude than the force acting on the rear side.
As for the magnitude of the resultant axial hydraulic force, it to display values in the order of
10-1N. The resultant axial hydraulic force reaches a maximum of 0.64N at the fastest rotation speed
(3000 rpm) and a minimum of 0.24N at the slowest rotation speed (1800 rpm). Once again, it is
important to notice that the individual components of the axial hydraulic force counterbalance each
other, leading to a lower magnitude of the resultant axial hydraulic force, with the closed impeller
being the main reason for this counterbalancing response (Bloch & Budris 2015).
Finally, in terms of the tendency, the axial hydraulic force increases in magnitude with
increasing rotation speeds. Thus, the relevance of the axial hydraulic force in the ReinVAD LVAD is
-0,80
-0,70
-0,60
-0,50
-0,40
-0,30
-0,20
-0,10
0,001800 2100 2400 2700 3000
Axia
l Hyd
rual
ic F
orce
[N]
Rotation Speed [rpm]
61
bigger for higher rotation speeds of the impeller. This behaviour was again expected, given the
dependency between the pressure distribution and the hydraulic force on the impeller. The faster
the rotation speed of the impeller, the higher will be the pressure rise that develops around the
impeller, as shown in Figure 4.2 in section 4.1.3. These results are consistent with Song & Wood
(2004), and Untaroiu, Wood, et al. (2005).
Figure 4.9 presents each component of the axial resultant force (momentum force and
resultant force on shrouds). The analysis of these individual forces clarifies the behaviour of the
resultant hydraulic force.
Figure 4.9 - Graph presenting the relationship between each component of the axial hydraulic force and the rotation
speed (rpm): momentum force - red (N) and the resultant force acting in the shrouds - blue (N), based on the
analytical model.
As previously explained, the magnitude of the axial hydraulic force corresponds to the
distance between the momentum force and the resultant axial hydraulic force acting on the
shrouds, in Figure 4.4.
Since the momentum force is constant in all of the rotation speeds simulated, the axial
hydraulic force on the shrouds is exclusively responsible for the variation of the resultant axial
hydraulic force. The force in the shrouds increases (in the negative direction) with faster rotation
speeds, resulting in an increase of the difference between this force and the momentum force.
Hence, the magnitude of the axial hydraulic force increases.
-0,70
-0,50
-0,30
-0,10
0,10
1800 2100 2400 2700 3000
Forc
e Sh
roud
s/M
omen
tum
[N]
Rotation Speed [rpm]
Force acting in the shroudsMomentum Force
62
The fact that the momentum force remains constant for all the simulated rotation speeds
was expected, since the momentum force (for the same fluid and at the same area) is only
dependent on the flow rate – Equation (3.19) corroborates this dependency. Since in this
simulation the flow rate was maintained constant at 5l/min (cardiac output of a health heart in
rest), the momentum force is constant too. The constant magnitude of 0.05N is almost negligible
since, as evaluated in the axial hydraulic force versus flow rate results, the momentum force only
becomes relevant at higher flow rates, Figure 4.9.
Evaluating now the axial resultant force on the shrouds, it can be noticed in Figure 4.9 that
this force is increasing in the negative direction with the increase of the rotation speed. Hence, the
impeller front shroud force is bigger than the corresponding one in the rear shroud. The resultant
force on the shrouds reaches a maximum magnitude of 0.59N at the fastest rotation speed of the
impeller (3000 rpm). For all rotation speeds, the force acting on the shrouds presents a larger
magnitude than the momentum force. The same conclusion was reported by Zhou et al. (2013)
and Sato & Miyashiro (1980).
In order to analyse each component of the resultant force acting on the shrouds and
understand their relationship, the front and rear shroud forces are plotted against each other, in
Figure 4.10.
Figure 4.10 - Graph presenting the relationship between each component of the resultant axial hydraulic force acting
on the shrouds and the rotation speed (rpm): Force acting on the rear shroud - blue (N) and force acting on the front
shroud - red (N), based on the analytical model.
-25,00
-15,00
-5,00
5,00
15,00
25,00
1800 2100 2400 2700 3000
Forc
e in
fron
t/re
ar s
hrou
d [N
]
Rotation Speed [rpm]
Force in Rear ShroudForce in Front Shroud
63
Both forces display a similar tendency, increasing in magnitude with faster rotation speeds.
The main cause for this behaviour is the increase of the static pressure rise above the impeller
inlet with increasing speeds, ΔPim – Figure 4.2.
As previously discussed, the difference in the magnitude of each one of these forces can be
explained by differences in the pressure profile in each clearance of the front and rear shrouds and
differences in the transversal areas (Godbole et al. 2012). Again, the bigger transversal area of the
front shroud (given its smaller inner radius) is the dominant effect, leading to a higher magnitude
of the front shroud force, relatively to the rear shroud force, for all the simulated rotation speeds.
Analysing in more depth the pressure drop, once again it was expected to be larger in the
front shroud. Figure 4.13 and Figure 4.14 plot the local rotation factors for each shroud (kFS, kRS)
against the radius ratio (x) radially along each shroud clearance, illustrating the increase of the fluid
rotation radially along the shrouds clearances. The same behaviour of the rotation factor along the
radial radius was reported by Gantar et al. (2000) and Gülich (2010). It should be noted that as
the rotation speed in the pump increases, the rotation factors in each shroud increase significantly,
via increases in the leakage flows (Figure 4.2b). Gülich (2010) and Hergt & Prager (1991) reported
the same tendency of the rotation factors with the increase of the rotation speed of the impeller,
and so did Teo et al. (2010) and Chan et al. (2000), while studying the leakage flow in magnetically
suspended centrifugal impellers.
Figure 4.11 - Graph representing the local rotation factors along each radius ratio for the front shroud, for each
rotation speed of the impeller– 1800 rpm (blue), 2100 rpm (black), 2400 rpm (red), 2700 rpm (blue dotted) and
3000 rpm (red dotted).
0,4
0,5
0,6
0,7
0,8
0,9
1
1,1
0,2 0,4 0,6 0,8 1
Fron
t rot
atio
n fa
ctor
, kFS
[-]
Radius ratio front shroud , xFS [-]
3000 rpm 2700 rpm 2400 rpm2100 rpm 1800 rpm
64
Figure 4.12 - Graph representing the local rotation factors along each radius ratio for the rear shroud, for each
rotation speed of the impeller– 1800 rpm (blue), 2100 rpm (black), 2400 rpm (red), 2700 rpm (blue dotted) and
3000 rpm (red dotted).
Figure 4.11 and Figure 4.12 illustrates that the rotation factors in the front shroud are larger
than in the rear shroud. This can again be explained by a combination of effects: on one hand, the
smaller inner radius of the front shroud leads to a larger circumferential velocity of the fluid at the
end of the shroud, near the impeller inlet. On the other hand, the larger leakage flow in the rear
shroud (Figure 4.2b) partially counterbalances this effect. As such, it can be noted that for one
same radius ratio (e.g., x = 0.365), the rear shroud presents a higher local rotation factor. However,
since the front shroud presents a smaller inner radius, it reaches smaller radius ratios, and
corresponding larger local rotation factors. Combining these effects, the front shroud presents a
larger average rotation factor, implying a larger pressure drop.
Moreover, it should be noted that some local rotation factors (for the front shroud and a
rotation speed of 3000 rpm) reach values above 1, which means the local tangential velocity of the
fluid in the sidewall gap exceeds the circumferential speed ω.r of the impeller. Gülich (2010)
referred that rotation factors above of 1 are expected to happen for high leakage flows and low
radius ratios, such as in this case. In this particular region, the impeller is accelerated by the fluid
rotation.
0,4
0,5
0,6
0,7
0,8
0,9
1
1,1
0,2 0,4 0,6 0,8 1
Rear
Rot
atio
n fa
ctor
, kRS
[-]
Radius ratio rear shroud, xRS [-]
3000 rpm 2700 rpm 2400 rpm
2100 rpm 1800 rpm
65
4.3 Comparison with Available Data
In this section, an additional validation of the developed model is presented, by comparing
the model results with available CFD data for the ReinVAD LVAD.
It is important to note that, due to the inherent different methodologies, the data was not
expected to match the results of the model perfectly. Instead, the purpose of the validation was to
evaluate if both analyses result in the same behaviours / tendencies of the forces, in order to
validate the accuracy and usefulness of the developed model.
In fact, recalling one of its major purposes, this model is meant to support the design of the
pump by giving insight into the reactions of the various axial hydraulic force components to changes
in key variables and allowing for quick simulations. These were the two major limitations of the
CFD model, which only outputted final numbers for the resulting force and did not allow for quick
estimates. As such, the main success criteria of this model will be the accurate prediction of
tendencies, even if the absolute values differ mildly from the CFD simulation.
Regarding the first simulation, Figure 4.13 illustrates that both the CFD data and the
developed model present the same tendency, with the axial hydraulic force showing a decrease in
magnitude (increase in the positive direction) with increasing flows in both of the simulations.
Hence, the model tendency predictions are validated in this respect, and the two curves show a
sample correlation coefficient of approximately 0.8.
Figure 4.13 - Graph presenting the relationship between the axial hydraulic force (N) and the flow rate (l/min) by the
mathematical model developed – blue and the CFD data available for the ReinVAD pump – red.
-1,20
-1,00
-0,80
-0,60
-0,40
-0,20
0,001 3 5 7 9
Axia
l Hyd
raul
ic Fo
rce
[N]
Flow Rate [l/min]
Mathematical model developedCFD Data
66
Regarding the second simulation, Figure 4.14 illustrates, as with the previous results, that
the CFD data and the developed model present the same tendency. Specifically, the axial hydraulic
force displays an increase in magnitude (increase in the negative direction) with increasing rotation
speed in both of the simulations. The model tendency predictions are thus validated in this respect,
and the two curves show a sample correlation coefficient of approximately 0.9.
Figure 4.14 - Graph presenting the relationship between the axial hydraulic force (N) and the rotation speed (rpm) by
the mathematical model developed – blue and the CFD data available for the ReinVAD pump – red.
4.4 Summary and Discussion
This chapter focused on the presentation and analysis of the results of the axial hydraulic
force model. First of all, the scenarios of the simulations were defined, and key inputs were
quantified: physiologic conditions, pump design and additional data. Based on these initial
conditions two distinct simulations were performed, testing the axial force response to two major
variables of its operating conditions: flow rate and rotation speed.
The results from each simulation were presented, analysed and discussed. It was
concluded that the magnitude of the axial hydraulic force reduces with increasing flow rates and
increases with increasing rotation speeds.
These results were found to be in line with the relevant literature. Furthermore, the results
of the resultant axial hydraulic force were compared with available CFD data, and both simulations
were found to present consistent tendencies and very similar behaviours, displaying a strong
correlation.
-1,20
-1,00
-0,80
-0,60
-0,40
-0,20
0,001800 2100 2400 2700 3000
Axia
l Hyd
raul
ic F
orce
[N]
Rotation Speed [rpm]
CFD DataMathematical model developed
67
Chapter 5
Conclusions and Future Developments
5.1 Conclusions
Blood pumps are a critically important clinical option to combat cardiovascular diseases
such as heart failure, presently the major cause of death in the world. Since conventional therapy,
using medication is not always successful, and the availability of heart transplants is limited,
mechanical cardiac assist devices have become an increasingly accepted treatment strategy.
Furthermore, over the course of the 20th and 21st centuries, these devices have shown fast
improvements. In fact, starting with the heart-lung machine and passing through three different
generations of blood pump technology, researchers have continuously made tremendous
progresses in this field. The ReinVAD LVAD is one such blood pump, currently under development,
and belongs to the third generation of blood pumps, which is characterized by the magnetic
levitation of the rotor, eliminating mechanical contact and wear.
The development of blood pumps implies an in-depth study of the hydraulic forces acting up
them. These forces are a particularly important issue for the third generation blood pumps such
as ReinVAD LVAD, given the need to stabilize the suspended rotor using a magnetic field. Authors
who have studied similar pumps have generally concluded that axial hydraulic forces decrease with
increasing flows and increase with faster rotation speeds, while radial hydraulic forces in single
volutes are generally much less relevant than the axial hydraulic forces.
The core of this thesis consisted in the development of an analytical model for the axial
hydraulic forces acting on the ReinVAD LVAD. This model considered both the force acting on the
shrouds (caused by the leakage flow in the sidewall gaps of the pump), and the momentum force
(associated with the change of the momentum of the fluid). A simplified approach to estimate the
radial force was also implemented, which validated the assumption that the magnitude of this force
was less relevant for ReinVAD LVAD, concluding that it was in a range of 0 to 10-5N (addressing
one the objectives of this work).
Applying the axial hydraulic force model in simulations of the response of the axial hydraulic
force to changes in two key variables, a set of important conclusions was drawn:
68
For the simulated range, the axial hydraulic force decreases in magnitude with increasing flows,
in the negative direction, going from a maximum of 0.57N to a minimum of 0.29N. This
behaviour is justified by the fact that the slight increase in the momentum force is smaller in
absolute value than the decrease in the force in the shrouds. The decrease in the force in the
shrouds is generated by the differences of the forces in the front and rear shrouds, which are
in turn influenced by the different pressure profiles and transversal areas of each shroud. The
results of the model indicate that the differences in the pressure profile, associated to
differences in the fluid rotation, are influenced by different leakage flows and different radii sizes.
For the simulated range, the axial hydraulic force increases in magnitude in the negative
direction, with faster rotation speeds, going from a maximum of 0.57N to a minimum of 0.29N.
This behaviour is generated by increases of the force in the shrouds, since the momentum force
is not affected by changes in the speed. This growth in the force in the shrouds is driven by the
fact that the force acting on the front shroud increases more in magnitude than the force acting
on the rear shroud. Again, the behaviour of the forces in the shrouds is determined by the
respective pressure profiles and transversal areas.
Combining these conclusions, it can be stated that, all other things being equal, lower flows
and higher rotation speeds result in higher axial hydraulic forces.
Through a comparison of the results of the various simulations with previously obtained CFD
data of the ReinVAD LVAD, the axial hydraulic force model was concluded to be accurate
(addressing another one of the objectives of this work).
In summary, it was concluded that this model, by being accurate, successfully addresses
the three remaining objectives of this dissertation. In fact, the model results can reliably be used
to support the design of the pump, by quickly simulating how the resultant axial hydraulic force
and each of its components respond to changes in different variables. Furthermore, the simulations
gave insights into the mechanisms that generate the behaviours of each component of the axial
hydraulic force. Finally, since the model was developed in MATLAB® and SIMULINK ®, this model
is suitable for integration in the PID controller.
69
5.2 Future Developments
The ReinVAD LVAD is currently under development, and so it still presents significant
potential for further study. In the particular case of this project, some areas of relevant future work
are listed below.
Validating the model with experimental data: In addition to the CFD comparison, an
experimental investigation into the hydraulic forces that act on the impeller could be
beneficial in the validation of the mathematical model.
Evaluating different variables that influence the hydraulic forces: Some design parameters
in the pump could be changed in order to reduce the experienced hydraulic forces. One
particularly promising area of investigation is the sizing of the clearances. The developed
mathematical model suggests a dependency between the clearances in the pump and the
axial hydraulic forces, so simulating different pump designs with different sizes of
clearances could have a significant impact on managing the axial hydraulic force.
Developing a more robust model for the hydraulic radial force: In this dissertation, the
hydraulic radial force was studied with a simplified model based on Stepanoff (1957), since
the literature review suggested its magnitude would not be very relevant (Untaroiu,
Throckmorton, et al. 2005). However, for a more in-depth study of this force, a more
complex analysis could be developed. A similar model to the one of Adkins & Brennen
(1988) could be implemented in order to evaluate if significant hydraulic radial forces occur
in certain extreme conditions of the pump.
Integrating the mathematical model in the PID Controller: The model developed in this
investigation was implemented in MATLAB®/SIMULINK® in order to facilitate the
integration process into the PID controller (under development by ReinVAD company).
However, for the final integration, some modification in the model will be required. In
particular, an accurate model of the pressure distribution over the entire pump should be
defined in order to avoid any dependence of CFD data. In order to address this
requirement, an initial linear model or a more complex non-linear model could be
implemented and validated with available data.
70
71
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Appendix I - Auxiliary Calculation of Radial
Hydraulic Force
As described in the section 3.4.1 of the approach of Stepanoff (1957), Equation (3.21) was
used to estimate the radial force in the ReinVAD pump.
The estimation of the radial hydraulic force was performed for five different flow rates
between 1l/min and 9l/min (the same flows evaluated for the axial hydraulic force – section 3.4.1).
Note that for the calculation the flow rate ratio is used, Equation (3.20); thus, all the flow rates are
divided by the flow at the best efficient point - 5l/min.
The geometric variables required for the calculation are presented in Table AI.1.
Table AI.1 - Dimension of the pump, according with Figure 3.6, in millimetres (mm).
Variable Value (mm)
b 3 6
oax 1 2
oax 2 2
b 4= b 3+ oax 1+ oax 2 6+2+2=10
For the calculation the pressure head, H, for each flow rate, is also needed. The pressure
head represents the height of a column of fluid of specific weight, γ, required to generate such a
pressure difference, ∆PP (Munson et al. 1988). The specific weight, γ, is the weight per
unit volume of a material, given by γ=g.ρ.
The pressure difference in the pump is retrieved from CFD data, Table AI.2, and the density
of the blood was described in section 4.1.1.
H =∆PP
γ =
∆PP
g.ρ (AI.1)
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Table AI.2 - CFD data static pressure rise in the pump (mmHg) for different flow rates in the pump (l/min).
Flow Rate (l/min) Pressure rise on the pump (mmHg)
1 113.504
3 111.224
5 107.363
7 83.743
9 59.921
A simple MATLAB® code was implement in order to calculate the radial force for the
different flows, with the conditions mention bellow.
%% Inputs
rho = 1060; % blood mass density [kg/m^3] g = 9.8; % gravitational acceleration [m/(s^2)] d_I= 0.038; % diameter at impeller [m] b_3=0.06; % O_ax1 = 0.002; % overlap volute-impeller at front side O_ax2 = 0.002; % overlap volute-impeller at rear side b_4 = b_3+O_ax1+O_ax2; Q_bep =5; % flow rate at best efficient point [l/min]
%% Variables
Q= [1,3,5,7,9]; % Flow rate [l/min] p =[16095, 15771, 15224, 11875, 8497]; % Pressure rise [Pa]
%% Auxiliary calculation
H=p/(rho*g); % static pressure head [m]
c=0.36*(1-(Q/Q_bep).^2);
%% Radial Force Fr = c.*H.*di.*b_4;
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Appendix II – SIMULINK® and MATLAB® Code
Appendix II.I – MATLAB ® Code
The code presented below was developed in MATLAB ® to initialise each variable (geometric
conditions, physiologic conditions and inputs of the model) in the SIMULINK ® model.
%% % Hydraulic_axial_force_model_initial % Script for initializing the Hydraulic_axial_force_model
tic()
%% Natural constants
g=9.807; % gravitational acceleration
[m/(s^2)]
%% Physiological variables
dens_b = 1060; % blood mass density [kg/m^3]
visco_b = 3.5*10^-3; % blood viscosity [Pa.s]
%% Pump design and dimensions
b_1 = 0.005; % blade inlet width [m] b_2 = 0.004; % blade outlet width [m] b_3 = 0.006; % volute inlet width [m]
d_I = 0.038; % diameter at impeller [m] d_V = 0.0385; % diameter at volute [m] d_FS = 0.010; % diameter at front shroud [m] d_RS = 0.014; % diameter at rear shroud [m]
r_I = d_I/2; % radius at impeller [m] r_V = d_V/2; % radius at volute r_FS = d_FS/2; % radius at front shroud [m] r_RS = d_RS/2; % radius at rear shroud [m]
x_FS = d_FS/d_I; % Ratio of front shroud and the impeller diameter [m] x_RS = d_RS/d_I; % Ratio of rear shroud and the impeller diameter [m]
O_ax1 = 0.002; % overlap between the volute-impeller at front side [m] O_ax2 = 0.002; % overlap between the volute-impeller at rear side [m]
s_ax_FS = 0.00015; % x-distance front shroud/casing [m] s_ax_RS = 0.00015 ; % x-distance front shroud-casing [m]
c_ax_FS = s_ax_FS + O_ax1; %x-distance casing inlet/front wall [m] c_ax_RS = s_ax_RS + O_ax1; %x-distance casing inlet/rear wall [m]
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%% Momentum Force Block
A_in = b_1*d_FS*pi(); %cross-sectional area of inlet [m^2]
%% Inputs for the Simulink model
Hydraulic_axial_force_model_inputs () % calling inputs
simulation_time=toc() % time counting
The code presented below presents a five for-loop to call the SIMULINK® model
(Hydraulic_axial_force_model) various times to calculate all possible combinations of the variable
inputs and fill in the results table “Final_Results” with all the inputs and the different components
of the axial hydraulic force.
%% Legend
% rotation_speed - rotation speed [rpm] % Q - flow [l/min] % delta_p_im - difference pressure [mmHg] % Q_lf_FS - Leakage flow in front shroud [l/min] % Q_lf_RS - Leakage flow in rear shroud [l/min]
%% Inputs for the simulink program
%script for calling a simulink model (Hydraulic_axial_force_model)
various times. %variable inputs are 'rotation_speed', 'Q', 'delta_p_im' and
'Q_lf_FS', and 'Q_lf_RS' %that will be defined in this script. %various combinations will be examined, using five for-loop
rotation_speed_vec= linspace (2400, 2400, 1); Q_vec=linspace (1, 9,5); delta_p_im_vec= [93.6, 78.6, 75.0, 64.9, 54.6];
Q_lf_FS_vec= [0.214, 0.198, 0.188, 0.166, 0.153];
Q_lf_RS_vec = [0.239, 0.238, 0.209, 0.1620.120];
Ni=length(rotation_speed_vec); Nj=length(Q_vec); Nk=length(delta_p_im_vec); Nl=length (Q_lf_FS_vec); Nm=length(Q_lf_RS_vec);
simulation_vec=zeros(12,Ni*Nj*Nk*Nl*Nm); z=0; %counting
for i=1:1:Ni
for j=1:1:Nj
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for k=1:1:Nk
for l=1:1:Nl
for m=1:1:Nm
z=z+1 %+1 going through every loop
rotation_speed=rotation_speed_vec(i); Q=Q_vec(j); delta_p_im=delta_p_im_vec(k); Q_lf_FS= Q_lf_FS_vec (l); Q_lf_RS= Q_lf_RS_vec (m);
sim('Hydraulic_axial_force_model'); f_axial=F_ax.data(2); Fm= Fm.data(2); F_FS=F_FS.data(2); F_RS=F_RS.data(2); F_HS=F_HS.data(2); k_fs =k_fs.data(2); k_rs= k_rs.data(2);
simulation_vec(1,z)=rotation_speed; simulation_vec(2,z)=Q; simulation_vec(3,z)=delta_p_im; simulation_vec(4,z)=Q_lf_FS; simulation_vec(5,z)=Q_lf_RS; simulation_vec(6,z)=impel_x_pos; simulation_vec(7,z)=f_axial; simulation_vec (8,z)=Fm; simulation_vec (9,z)=F_HS; simulation_vec (10,z)=F_FS; simulation_vec (11,z)=F_RS; simulation_vec (12,z)=k_fs; simulation_vec (13,z)=k_rs; end end end end end
%% Final Results Table
row_names = {'Rotation Speed','Flow rate',... 'Pressure rise in impeller',... 'Leakage Flow front shroud',... 'Leakage Flow rear shroud',... 'Impeller axial position',... 'Resultant Axial Force',... 'Momentum Force'... 'Resultant Force on shrouds'... 'Axial Force on front shroud'... 'Axial Force on rear shroud'... 'Rotation FS'... 'Rotation RS'};
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Final_Results =table(simulation_vec,... 'Rownames', row_names);
Lastly, a MATLAB® function for each shroud of the pump was created for the calculation of
the rotation factors in each shroud through a step-wise procedure, described in section 3.2.
%% Function to calculate the rotation speed factor in front shroud
function mean_k_fs = fcn(r_FS,r_V,c_ax_FS,coeff_Q_lf_FS,Re,r_I)
%% Step-wise calculation of rotation Front Shroud
N=10000; r = linspace ( r_I, r_FS, N);
k_0_FS = 1/(1 + (r_V/r_I)^2 * ((r_V/r_I) + (5*(c_ax_FS/r_I)))^(1/2) );
k=zeros(1,N); k(1)= 0.55; %Initial iterative point x = zeros (1,N);
for n =1:N x(n) = r(n)/r_I; end
for n = 1:(N-1)
k(n+1) = k(n)+(((((0.079* x(n)^1.6)/(coeff_Q_lf_FS* (Re)^0.2))*... (((((1-k_0_FS)/k_0_FS)*k(n)) ^1.75)-... ((abs(1-k(n)))^1.75)))-(2*k(n)/x(n)))*(x(n+1)- x(n)));
end
mean_k_fs = mean (k);
%% Function to calculate the rotation speed factor in rear shroud
function mean_k_rs = fcn(r_RS,r_V,c_ax_RS,coeff_Q_lf_RS,Re,r_I)
%% Step-wise calculation of rotation factor Rear Shroud
N=10000;
r = linspace ( r_I, r_RS, N);
k_0_RS = 1/(1 + (r_V/r_I)^2 * ((r_V/r_I) + (5*(c_ax_RS/r_I)))^(1/2) );
k=zeros(1,N); k(1)= 0.55; %Initial iterative point
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x = zeros (1,N);
for n =1:N x(n) = r(n)/r_I; end
for n = 1:(N-1)
k(n+1) = k(n)+(((((0.079* x(n)^1.6)/(coeff_Q_lf_RS* (Re)^0.2))*... (((((1-k_0_RS)/k_0_RS)*k(n)) ^1.75)-... ((abs(1-k(n)))^1.75))) - (2*k(n)/x(n)))*(x(n+1)- x(n))); end
%% Mean value of all rotations speed factors
mean_k_rs = mean (k);
Appendix II.II – SIMULINK ® Blocks
Figure AII.1 presents the different components of the resultant axial hydraulic force in
SIMULINK ®. The blocks “Resultant force in the shrouds” and “Momentum force” are subsystems
that comprise a set of blocks to calculate these components.
Figure AII.1 - Main blocks of the resultant hydraulic force: axial hydraulic force on impeller shrouds and momentum
force.
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The “Momentum Force” subsystem describe Equation (3.19) and it is composed by the
blocks of Figure AII.2.
Figure AII.2 - “Momentum Force” subsystem block.
The “Resultant force in the shrouds” subsystem is composed of two more subsystem that
represent each component of the resultant force in the shrouds, Figure AII.3.
Figure AII.3 - “Resultant force in the shrouds” subsystem block.
The subsystems “Axial hydraulic force on front shroud“ and “ Axial hydraulic force on rear
shroud“ are very similar, being described by Equation (3.15) and Equation (3.16), respectively.
They only differ regarding to the dimensions of each shroud (dFS and dRS). Therefore, only the
subsystem representing the “Axial hydraulic force on front shroud“ was detailed in this Appendix.
The “Axial hydraulic force on front shroud” subsystem (as well as the “Axial hydraulic force
on rear shroud“), displayed in Figure AII.4, is composed of two additional subsystems, “Pressure
component”, displayed in Figure AII.5 and “Rotation component”. Note that this “Rotation
component” subsystem, Figure AII.6, displays a mathematical function block for the calculation of
the rotation factor through a step-wise procedure, as defined in section 3.2.
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Figure AII.4 - “Axial hydraulic force on front shroud” subsystem block.
Figure AII.5 - “Pressure component” subsystem block.
Figure AII.6 - “Rotation component” subsystem block.
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89
Appendix III - Additionally CFD Data
Table AIII.1 and Table AIII.2 present the CFD data used as an input for each of the developed
simulations: variable flow and variable rotation speed.
Table AIII.1 - CFD data for leakage flow in rear and front shroud (l/min), and static pressure rise in the impeller
(mmHg) for different flow rates in the pump (l/min).
Table AIII.2 - CFD data for leakage flow in rear and front shroud (l/min), and static pressure rise in the impeller
(mmHg) for different rotation speeds of the impeller pump (l/min).
Flow Rate (l/min)
Leakage flow in rear shroud (l/min)
Leakage flow in front shroud (l/min)
Static pressure rise in impeller (mmHg)
1 0.239 0.214 93.6
3 0.238 0.198 78.6
5 0.209 0.188 75.0
7 0.162 0.166 64.9
9 0.120 0.153 54.6
Rotation Speed (rpm)
Leakage flow in rear shroud (l/min)
Leakage flow in front shroud (l/min)
Static pressure rise in impeller (mmHg)
1800 0.093 0.100 36.7
2100 0.147 0.140 54.1
2400 0.209 0.188 75.0
2700 0.283 0.239 97.1
3000 0.351 0.297 121.5
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Table AIII.3 present the CFD data of the axial hydraulic force, suggesting that variations in
the position of the rotor have a very small effect on the magnitude of the axial force. Impeller axial
position was defined as the distance between the centre of the impeller and the centre of the volute
(measured in the axial direction, according to the positive direction defined in Figure 3.5). As such,
an impeller axial position of 0 mm corresponds to the impeller being centered.
Table AIII.3 - CFD data of axial hydraulic force (N) for different axial positions (mm).
Impeller axial position (mm) Axial hydraulic force (N)
0.12 -0.57
0.09 -0.58
0.06 -0.64
0.03 -0.47
0 -0.50