experimental analysis into the main artery of 2 … · 3.9 crank slider mechanism 34 4.1 septum at...

EXPERIMENTAL ANALYSIS INTO THE MAIN ARTERY OF 2 CHAMBER

HEART MODEL DURING CARDIAC CYCLE

LOH QUO LIANG

Thesis submitted in fulfilment of the requirements

for the award of the degree of

Bachelor of Mechanical Engineering

Faculty of Mechanical Engineering

UNIVERSITI MALAYSIA PAHANG

JUNE 2013

vii

ABSTRACT

Regarding to the report from World Health Organization (WHO), the most killer disease

throughout the world is cardiovascular disease. There are millions of people deaths

because of this disease every year. So, it is important to study the blood pumping

mechanism in human body and what is the reason causing this device damage or fail to

operate normally in detail. The objective of this study is to develop a heart model for

investigating the patterns of fluid flow, and blood velocity diastolic. This heart model is

able to observe the fluid flow pattern in left and right ventricle in a pressurized pulsate

flow. A detail on fabrication, limitation, future improvement, and problem faced of heart

model are discussed in this study. The whole system will be conduct in a close system

which operated by using the combination of motor, and syringe. The results showed a

relationship between heart beat, velocity, and blood vessel diameter especially for

inferior, and superior vena cava can be establish. The result also proved that the

relationship between heart beat and the velocity, and the difference of pressure between

atrium and ventricle are directly proportional. Additionally, the relationship between

vortex formation and septum in the heart chamber can be established at the end of this

study. In conclusion, this study had succeeded to produce an equation relates to the

velocity, diameter and heart beat in inferior, and superior vena cava. This result can

contribute to future heart study as well as application in medical field.

viii

ABSTRAK

Menurut laporan World Health Organization (WHO), penyakit jantung merupakan

pembunuh utama di dunia. Berjuta-juta manusia maut akibat penyakit ini setiap tahun.

Jadi, kajian secara teliti pada jantung manusia untuk mengenal pasti kerosakan, dan tidak

berfungsi secara nomal adalah amat penting. Objektif kajian ini adalah untuk membina

model jantung dan menyiasat corak aliran bendalir, dan halaju darah semasa diastolik.

Model jantung ini dapat menyiasat corak aliran cecair dalam ventrikel kiri, dan kanan di

bawah tekanan dan aliran berirama. Prebincangan secara terperinci mengenai fabrikasi,

had, penambahbaikan dan masalah yang dihadapi model jantung juga akan dibincangkan

dalam kajian ini. Seluruh sistem bagi kajian ini akan berada dalam keadaan tertutup dan

konsep untuk model jantung ini adalah berasas kan kombinasi antara picagari dan motor.

Hubungan antara degupan jantung, halaju dan diameter saluran darah terutamanya bagi

inferior dan superior vena cava telah dijumpai. Selain itu, keputusan juga membuktikan

bahawa hubungan antara halaju dan perbezaan tekanan antara atrium dan ventrikel adalah

berkadar terus dengan kadar denyutan jantung. Hubungan antara pembentukan vorteks

dan septum dalam jantung juga dapat dikaji pada akhir kajian ini. Kesimpulannya, kajian

ini telah berjaya untuk mendapatkan persamaan yang berkaitan dengan halaju, diameter

dan denyutan jantung di inferior dan superior vena cava. Keputusan ini berkemungkinan

besar akan menyumbang kepada kajian jantung pada masa hadapan dan juga dapat

aplikasi dalam bidang perubatan.

ix

TABLE OF CONTENTS

Page

EXAMINER’S DECLARATION ii

SUPERVISOR’S DECLARATION iii

STUDENT’S DECLARATION iv

DEDICATION v

ACKNOWLEDGEMENTS vi

ABSTRACT vii

ABSTRAK viii

TABLE OF CONTENTS ix

LIST OF TABLES xii

LIST OF FIGURES xiii

LIST OF EQUATIONS v

LIST OF SYMBOLS xvii

CHAPTER 1 INTRODUCTION

1.1 Project Background 1

1.2 Problem Statement 2

1.3 Objectives 3

1.4 Scope of Study 3

1.5 Organization of the Thesis 3

CHAPTER 2 LITERATURE REVIEW

2.1 Introduction 4

2.2 Relationship between Leaflet Behaviour and Fluid Flow Pattern 4

2.3 Blood Flow in Left Ventricle 5

x

2.4 Continuous Blood Flow through Mitral Valve 6

2.5 Left Ventricle Deformation 7

2.6 Cardiac Movement Detection 8

2.7 Simulation of cardiac Motion by FEM 9

2.8 Coupling Simulation 10

2.9 Heart Cavity Profile Movement 11

2.10 Fluid Flow Formation in Left Ventricle 12

2.11 Mitral Valve Flow Prediction 13

2.12 Simulation of Blood Flow and Myocardium Muscle Motion of

Left Ventricle

14

2.13 Direct Simulation of Blood Flow in Left Ventricle 15

2.14 Fluid Viscosity in Human Body 16

2.15 Blood Velocity 17

2.16 Analysis 18

2.15.1 Limitation 20

2.15.1 Similarities 20

CHAPTER 3 METHODOLOGY

3.1 Introduction 22

3.2 Overview of the Methodology 22

3.3 Fluid Properties 24

3.4 Heart Valve Selection 26

3.5 System Design 26

3.5.1 Motor Selection and Piping Design 28

3.6 Heart Model Design 29

3.6.1 Calculation of Screw Distance on Perspex 30

3.6.2 Heart Model Curve Equation 31

xi

3.7 Data Acquisition Equipment 33

3.8 Calculation for Velocity 33

3.8.1 Calculation for Actual Velocity 34

3.8.2 Calculation of Velocity using Bernoulli

Equation

35

3.8.3 Calculation of Velocity Difference 36

CHAPTER 4 RESULT AND DISCUSSION

4.1 Introduction 37

4.2 Design Calculation 38

4.3 Data Obtain from Pressure Gauge 41

4.4 Velocity Derivation 55

4.5 Flow Vortex Formation 62

CHAPTER 5 CONCLUSION AND RECOMONDATION

5.1 Introduction 67

5.2 Conclusions 67

5.3 Recommendation 69

REFERENCES 70

APPENDICES

A Summary of Literature Review 74

B Raw Data Of Velocity 75

C Graph for Pressure Gradient 86

D Drawing and Dimension of Heart Model 93

E Achievement 95

xii

LIST OF TABLES

Page

2.1 Value of blood viscosity regarding to gender and shear rates 17

2.2 Summary of peak velocity at inferior and superior vena cava 18

3.1 Parameter involved in the calculation 25

4.1 Parameter involve in the calculation for screw distance on

Perspex

38

4.1 Sample result from left ventricle with 46.1538bpm 54

4.2 Comparisons of calculated and actual velocity in inferior vena

cava

60

LIST OF FIGURES

Page

2.1 Comparison of fluid flow vector after the valve from experiment

(a) and numerical (b) for leaflet thickness 0.16mm

5

2.2 3D vortex ring formation shown in simulation 6

2.3 Comparison of the result from MRI scans and modelling

experiment on the vortex formation in left ventricle

7

2.4 The sample of nodes, vector and deformation of the left ventricle 8

2.5 The picture of a normal person echocardiogram and the velocity

movement profile of left ventricle

9

2.6 Left ventricle deformation of simple cell orientation 10

2.7 Simple system configuration 11

xiii

2.8 Red marks in the echocardiogram images represent the segment

being analyze regarding to the displacement and direction

12

2.9 Vortex formation in left ventricle for normal person 13

2.10 Agreement between simulated and measured pressure result for

circular orifice

14

2.11 Meshes on ventricle wall and fluid geometries 15

2.12 Vortex ring formation sequence in left ventricle 16

2.13 Distribution of research focused issue among 12 studied journals 19

3.1 Overview of methodology 23

3.2 Drawing of heart modeling system 27

3.3 Fluid flow direction in the heart model 27

3.4 Actual heart modeling system 28

3.5 Design of left and right ventricle according to the curve equation 29

3.6 Shaded area in this figure shows the position of high pressure

concentration

30

3.7 Right ventricle main body mesh 32

3.8 Left ventricle main body mesh 32

3.9 Crank slider mechanism 34

4.1 Septum at right ventricle curve in Cartesian coordinate 40

4.2 Septum at right ventricle curve in Cartesian coordinate 40

4.3 Pressure reading in right ventricle at 9.5283bpm 41



xiv


.






4.12 Pressure reading in right ventricle at 43.9238bpm

45

4.13 Pressure reading in left ventricle at 14.2891bpm 46









4.22 Pressure different gradient at each heart beat in left ventricle 51

4.23 Maximum velocity different in right ventricle with different heart

beat

56

4.24 Maximum velocity different in left ventricle with different heart

beat

56

4.25 Comparison of calculated velocity and actual peak velocity

61

xv

4.26 Initial fluid entering for right ventricle 62

4.27 Rapid filling for right ventricle 63

4.28 Fluid discharging for right ventricle 63

4.29 Initial fluid entering for left ventricle 64

4.30 Rapid filling for left ventricle

64

4.31 Fluid discharging for left ventricle 65

LIST OF EQUATIONS

Page

1.1 Reynolds Number 2

2.1 Coupling simulation equation 1 10

2.2 Coupling simulation equation 2 10

3.1 Mixture density equation 25

3.2 Mixture volume ratio 25

3.3 Total mixture volume 25

3.4 Mixture volume ratio 25

3.5 Maximum pressure 31

3.6 Total force 31

3.7 Force exerted at the inlet area 31

3.8 Distributed load on the inlet area 31

3.9 Perspex deformation equation 31

3.10 Rotational speed 34

xvi

3.11 Shaft end velocity 34

3.12 Shaft end velocity with angle of rotation 34

3.13 Flow rate 34

3.14 Flow rate with angle of rotation and rotational speed 34

3.15 Velocity before entering heart model 35

3.16 Computed velocity before entering heart model 35

3.17 Computed velocity after entering heart model 35

3.18 Heart beat rate 35

3.19 Bernoulli’s equation 35

3.20 Velocity after entering heart model 35

3.21 Velocity after entering heart model with angle of rotation 36

3.22 Velocity difference 36

3.23 Flow continuity equation 36

3.24 Flow continuity equation for actual velocity 36

3.25 Computed velocity difference 36

4.1 Right ventricle septum equation 39

4.2 Left ventricle septum equation 39

4.3 Velocity difference from right ventricle graph 57

4.4 Right ventricle simultaneous equation 57

4.5 Right ventricle computed simultaneous equation 57

4.6 Velocity difference from left ventricle graph 58

4.7 Left ventricle simultaneous equation 58

xvii

4.8 Left ventricle computed simultaneous equation 58

4.9 Draft equation of velocity in the veins 58

4.10 Final equation for velocity in the veins 58

LIST OF SYMBOLS

Density of fluid

v Velocity of fluid

L Characteristic linear dimension

Dynamic viscosity of fluid

lvV Left ventricle volume

lvP Left ventricle inner pressure

aP Arterial blood pressure

_lv aR Resistance between left ventricle and aorta

0aP Left ventricle inner pressure before time dt

0lvV Left ventricle volume before time dt

R Resistance vessel

C Compliance

g Density of glycerin

xviii

w Density of water

b Density of blood

gV Volume of glycerin

wV Volume of water

g Gravitational acceleration

maxP Maximum pressure

I Second moment of inertia

N Rotational speed

rs Length of the rotational shaft

Vp Velocity of syringe piston

V1 Velocity of fluid at position 1

V2 Velocity of fluid at position 2

r1 Pipe radius at position 1

r2 Pipe radius at position 2

Ɵ Angle of rotational shaft from horizontal plane

B Heart beat rate

1

CHAPTER 1

INTRODUCTION

1.1 PROJECT BACKGROUND

Heart is a myogenic muscular organ to provide a rhythmic blood flow to the

blood vessels throughout whole body. The average of normal human heart beat rate is

about 72 beats per minute under the rest condition. Other than the cardiac muscle, a

human heart also consists of heart valve which is to prevent back flow of the blood in the

heart. Most of the mammal’s hearts consist of 4 heart valves. These valves ensure

unidirectional blood flow during cardiac cycle. Atrium and ventricle are the upper and

lower chambers where atria act as receiving chamber and ventricles act as discharging

chamber. Left and right hearts are separate by a thick wall of muscle call septum. Heart

valves are passive tissues which its opening and closing are depending on the difference

in blood pressure across the valves. Any failures of heart valve to perform will cause heart

disease. Heart valve disease can be group into two categories which are Stenosis and

Mitral Incompetence. Stenosis happen when the heart valve failed to open fully due to

stiffened valve tissue. Mitral Incompetence happens when the heart valve failed to

perform well and cause backflow of blood in the heart (Gonazalez, 2003).

Fluid flow structure in a cavity will be influence by the fluid velocity, flow rate,

pressure, continuity and also the physical properties of the cavity. The fluid flow pattern is

2

directly influenced by the properties of the blood and the structure of heart. This

phenomenon can be describe by studying the Reynolds number (Re) as in Eq.(1.1). In this

equation, it shows the flow pattern is inversely proportional to the dynamic viscosity of

fluid and directly proportional to the fluid density, velocity, and the dimension of the flow.

Fluid flow pattern can be generally categorized into 3 types which are Laminar,

Transitional and Turbulent flow on the bonds of Reynard Number. Blood flow in human

heart and arteries will have a high pressure and velocity during contraction. Hence the

Reynolds Number will be relatively high, and can be classify into Turbulent flow.

RevL

(1.1)

1.2 PROBLEM STATEMENT

Analysis on the heart is a wide field of study. Generally, study on heart can be

dividing to three categories which are analysis on structure, fluid flow, and valves. Most

of the previous studies had given more attention to the deformation of ventricle wall and

fluid flow pattern in left ventricleby numerical method. However, it is important to have a

modeling experiment to validate the results from the numerical study (Kanyanta, 2009).

Details of the actual geometry will influence the flow dynamics (Domenichini, 2006, Hart,

2000). Besides, pressure variation throughout the left ventricle cavity shows the

importance to the fluid flow effect in the heart chamber (Doyle, 2011). Unfortunately,

how does the heart structure, and blood pressure influence the flow at the heart and vortex

formation in the heart chamber during cardiac cycle is still under investigation.

3

1.3 OBJECTIVE

The aim of this research are to develop a heart model and to predict the

correlation between fluid flow patterns, diastolic blood velocity heart beat and vein

diameter in a pressurized rhythmic flow by applying different pressure and heart beat.

1.4 SCOPE OF STUDY

The scope of study will be organizes from:

1) This modeling experiment will only conduct in a close system.

2) The pipe diameter and flow rate ratio will be taken similar to actual human

body condition where the heart model is 2 times smaller than the actual

human heart.

3) Heart valve rigidity will be fixed at 2GPa to obtain more accurate result.

4) The flow-structure interaction will be analyzed in two dimensional

conditions.

5) Obtain a relationship between blood velocities, heart beat and vein diameter

during diastolic condition.

1.5 ORGANIZATION OF THE THESIS

This thesis is organized from:

1) Chapter 1- Introduce to the problem statements and scope for this study.

2) Chapter 2- Review of papers and discuss the limitation and similarities

among the journals.

3) Chapter 3- Heart model design and materials used.

4) Chapter 4- Result and discussion of the calculation and images.

5) Chapter 5- Conclusion and recommendations for future work.

4

CHAPTER 2

LITERATURE REVIEW

2.1 INTRODUCTION

Studies of the heart valve are divided into few categories which are the modeling

experiment, mathematical modeling, computational analysis, and simulation. The

modeling experiment of heart structure will give a better understanding on the function of

heart, and pattern of fluid flow thus, enhance the development in the heart structure study.

Additionally, the numerical study on the heart structure and fluid flow also play a

significant role on the development of artificial heart study.

2.2 RELATIONSHIP BETWEEN LEAFLET BEHAVIOUR AND FLUID

FLOW PATTERN

Hart (2000) is focusing on influence of aortic heart valve structure to the pattern

of fluid flow. The author studied the vortex formation after aortic valve during diastole

using numerical and modeling experiment. This modeling experiment applied different

aortic valve leaflet thickness and the flow is supplied periodically so the movement of the

leaflet can be established. Additionally, the finite element method was applied in this

experiment for fluid and structural computation. The aim of the author to employing

computational analysis is to validate the result on the structure of fluid flow from

5

simulation with the experimental model as shown in Figure 2.1. In the numerical study,

the author had involved two dimensionless parameters which are Reynolds and Strouhal

number are around 800 and 0.19 respectively.

Figure 2.1: Comparison of fluid flow vector after the valve from experiment (a) and

numerical (b) for leaflet thickness 0.16mm

Source: Hart 2000

2.3 BLOOD FLOW IN LEFT VENTRICLE

Left ventricle is the heart chamber which receives and delivers oxygenated blood

to the entire body. Domenichini et.al (2007) analyzed the structure of fluid dynamics in left

ventricle using the combination of numerical and experimental models. In the experiment

model, movement of blood throughout the heart chamber is caused by the dynamic

ventricle wall controlled by a computerized piston device. In this experiment, heart valves

does not included into the study. Two check valves are installed at mitral and aortic tubes to

avoid back flow. After the experiment, the result showed a strong agreement on the vortex

formation between numerical and experimental modeling. Vortex ring formation in the

numerical study (see Figure 2.2) had shown a clearer result compare to the modeling

6

experiment. Additionally, these results also agree that the fluid flow in the heart chamber is

more complex during diastolic phase (Domenichini, 2007).

Figure 2.2: 3D vortex ring formation shown in simulation

Source: Domenichini 2007

2.4 CONTINUOUS BLOOD FLOW THROUGH MITRAL VALVE

Mitral valve is also known as bicuspid valve which separate left ventricle and

atrium. Mushtak et. al (2010) used a continuous fluid flow in an open system through the

mitral valve and recored the flow by using digital camera. However, it is different with

the actual fluid flow in human heart valve because the blood flow in the heart is conduct

in a close system with pulsate flow. On the other hand, the numerical study by using Fluid

Structure Interaction (FSI) on the same heart design also had been carried out. The result

proved that the flows from both experiments are similar (see Figure 2.3). However, in the

FSI simulation, the authors used two parameters; the blood density and viscosity.

However the parameters used in the flow model are unknown (Al-Atabi 2010).

7

Figure 2.3: Comparison of the result from MRI scans and modeling experiment on the

vortex formation in left ventricle

Source: Al-Atabi 2010

2.5 LEFT VENTRICULAR DEFORMATION

Movement of the ventricle wall also is one of the factors which affect the pattern

of fluid flow in the heart chamber. Hence, a study of movement of the human heart

contraction by the help of the Magnetic Resonance Imaging (MRI) and been developed

by Bistoquet(2007). At the beginning of the study, the author used two assumptions:

1) Incompressibility of the myocardium muscle, and

2) Any point on the left ventricular wall will only move at the normal direction

to the original point.

These assumptions are made because the MRI cine does not contain enough

information to estimate both criteria during cardiac cycle. To observe the 3-D contraction

of the heart muscle, the author divided the heart into a few segments and use pseudo thin

plate to interpolate the nodes on that segment. These nodes are used to be a reference

8

point for the motion of the ventricle wall (see Figure 2.4 (b)). All the movements of the

nodes are represented in a vector form (see Figure 2.4 (c)). To validate this result, the

study on the patient that have heart disease and repetition of the MRI scanning had been

carried out on the same subject after four months and the result of the ventricle wall

deformation before and after four months are agreed well (Bistoquet, 2007).

Figure 2.4: The sample of nodes, vector and deformation of the left ventricle

Source: Bistoquet 2007

2.6 CARDIAC MOVEMENT DETECTION

Heart disease can be classified into structure and motion abnormalities. Both

types of disease can be detected by the echocardiogram. So, it is possible to carry out

automatic disease detection by using echocardiogram. One of the common methods used

is scale invariant features on edge-filtered motion magnitude mapping on the

echocardiogram (Kumar, 2010). The sources of this method are coming from the

Echocardiogram videos. The interest point on the feature will be selected from the

edge-filtered features and the motion will be detected in two dimensional (see Figure 2.5).

9

Figure 2.5: The picture of a normal person echocardiogram and the velocity movement

profile of left ventricle

Source: Kumar 2010

2.7 SIMULATION OF CARDIAC MOTION BY USING FEM

In order to obtain a similar shape as human left ventricular shape, using a set of

MR images to extract a 2-D feature of heart is required. However, to obtain a more

accurate data 3-D feature is needed for the simulation. So as to generate 3-D image data,

3-D smoothing filter is one of the method used (Amano 2007). Beside the 3-D images,

cell orientation and material properties of left ventricular tissue are also important

criterions which affect the heart muscle movement. Figure 2.6 illustrated the shape of the

left ventricle deformation model during end of diastole and systole by using FEM. The

result showed that the contracting force is varying depends on the cell orientation.

(Amano 2007).

10

Figure 2.6: Left ventricle deformation of simple cell orientation

Source: Amano 2007

2.8 COUPLING SIMULATION

Nobuaki (2005) combined the simulation result from the mechanical and

circulation model to obtain a high accuracy result regarding to the volume, pressure, and

contraction force respect to time. The convergence calculation will be the coupling

method use in this experiment. The basic concept of this coupling method is shown in

Figure 2.7. There are two main equations used in this experiment:

_

lv lv a

lv a

dV P P

dt R

(2.1)

0 0( ) ( ) . 0aa a lv lv

Pc P P V V dt

R (2.2)

The FEM solver and circulation simulator (windkessel model) are used to obtain

the coefficients in the calculation model. In order to solve the Equation 2.1 and 2.2, the

11

author had also fixed the boundary condition during isovolumic contraction, ejection,

isovolumic relaxation, and filling phase.

Figure 2.7: Simple system configuration

Source: Nobuaki 2005

2.9 HEART CAVITY PROFILE MOVEMENT

Similar to Kumar (2010), Riyadi (2009) also used the images from

echocardiogram to detect the cardiac movement of healthy left ventricle. The

methodology involved several tasks such as the collection of echocardiogram images, the

computation of optical flow field and the extraction of the movement profile. The optical

flow field is computed regarding to the intensity of the image which is similar to the

method for analyzing the echocardiogram images. The author separates the left

ventricular images into few segments. The result showed the displacement and direction

(angle) profile regarding to different segments (see Figure 2.8). This result can contribute

to the medical field to detect the abnormality of the human heart.

experimental analysis into the main artery of 2 … · 3.9 crank slider mechanism 34 4.1 septum at...

Documents