T.C.

BAHÇEŞEHİR UNIVERSITY

MATHEMATICAL MODELING OF

THE SIMPLIFIED HUMAN CARDIOVASCULAR SYSTEM

Capstone Project

Alper Aksu

İSTANBUL, 2010

T.C.

BAHÇEŞEHİR UNIVERSITY

FACULTY OF ENGINEERING

DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING

MATHEMATICAL MODELING OF

THE SIMPLIFIED HUMAN CARDIOVASCULAR SYSTEM

Capstone Project

Alper Aksu

Dr. Kamuran A. Kadıpaşaoğlu

İSTANBUL, 2010

T.C.

BAHÇEŞEHİR UNIVERSITY

FACULTY OF ENGINEERING

DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING

Name of the project: MATHEMATICAL MODELING OF THE SIMPLIFIED HUMAN

CARDIOVASCULAR SYSTEM

Name/Last Name of the Student: Alper Aksu

Date of Thesis Defense: 07/01/2011

I hereby state that the graduation project prepared by Alper Aksu has been completed

under my supervision. I accept this work as a “Graduation Project”.

07/01/2011

Dr. Kamuran A. Kadıpaşaoğlu

I hereby state that I have examined this graduation project by Alper Aksu which is

accepted by his supervisor. This work is acceptable as a graduation project and the student

is eligible to take the graduation project examination.

07/01/2011

Asst. Prof. Alkan Soysal

Head of the the Department of

Electrical & Electronics Engineering

We hereby state that we have held the graduation examination of Alper Aksu and agree

that the student has satisfied all requirements.

THE EXAMINATION COMMITTEE

Committee Member Signature

1. Dr. Kamuran A. Kadıpaşaoğlu ………………………..

2. ………………………….. ………………………..

3. ………………………….. ………………………..

ACADEMIC HONESTY PLEDGE

In keeping with Bahçeşehir University Student Code of Conduct, I pledge that this work is my

own and that I have not received inappropriate assistance in its preparation.

I further declare that all resources in print or on the web are explicitly cited.

NAME DATE SIGNATURE

1

2

ABSTRACT

MATHEMATICAL MODELING OF THE SIMPLIFIED HUMAN

CARDIOVASCULAR SYSTEM

Alper Aksu

Faculty of Engineering

Department of Electrical & Electronics Engineering

Advisor: Dr. Kamuran A. Kadıpaşaoğlu

JANUARY, 2011, 25 pages

The left ventricle is indispensable to sustain life, in end-stage congestive heart failure

patients who need a heart transplant but for whom a donor organ in not readily available.

These patients can be kept alive until transplant with the use of left ventricle assist devices

(LVAD). There is a need in Turkey to develop a new LVAD. The design, production and use

of domestic LVADs by engineers necessitate a good understanding of the cardiovascular

system physiology. Also, a testing platform is needed to verify the performance of new

LVAD designs before clinical application in initiated. Therefore, in this study, only the

LVAD will be modeled. To understand the cardiovascular mechanics, heart should be

modeled electrically, mechanically and hydraulically. After the modeling, mathematical

equations are established. In addition to previous projects, the cardiovascular system with a

LVAD will be modeled. While modeling the human cardiovascular system (HCS), the main

criteria are to establish the pressure changes in left ventricle (LV), left atrium (LA), aorta and

the volume changes in LV. In addition, the flow rate of the blood in several parts of the

cardiovascular system, the roles and effects of the elements in this system are considered.

After this project, the cardiovascular system with a LVAD can be analyzed easily and

effectively. Therefore, more efficient, economical, user friendly LVAD can be produced.

Key Words: Heart, Cardiovascular System, Modeling, Electrical, Mathematical, Matlab Applications in Cardiovascular Mechanics

3

ÖZET

İnsanın Basitleştirilmiş Kalp ve Damar Yapısının Matematik Modeli

Alper Aksu

Mühendislik Fakültesi

Elektrik-Elektronik Mühendisliği Bölümü

Tez Danışmanı: Dr. Kamuran A. Kadıpaşaoğlu

OCAK, 2011, 25 Sayfa

Bu projenin amacı kalbin sol karıncığını ve atardamar sistemini modellemektir. Kalp

mekaniğinin anlaşılabilmesi için kalbin elektrik, mekanik ve hidrolik olarak modellenmesi

gerekir. Bu modellemelerin sonucunda bir matematik model oluşturulur. Geçmiş modellerden

farklı olarak bu projede kalp ve damar mekaniğinin yanı sıra; yardımcı elemanın bağlı olduğu

bir kalbin kalp ve damar mekaniğinin modellenmesi amaçlanmaktadır. Bu modelleme

yapılırken sol karıncık hacim değişikliği ve kalbin bölümlerindeki basınç değişimleri temel

alınmaktadır. Bu değişkenlerin yanı sıra kalp ve damar mekaniğindeki kanın bulunduğu

bölgeye göre akış değerleri, kalp ve damar yapısındaki elemanların görevleri ve dolaşım

sistemine etkileri de göz önünde bulundurulmuştur. Bu modelleme sonucunda yardımcı

elemanlı kalbin kalp ve damar mekaniğinin daha etkin bir biçimde incelenmesi

amaçlanmaktadır. Böylece daha verimli çalışan kalbin sol karıncığına yardımcı elemanlar

üretilebilecektir.

Anahtar Kelimeler: kalp ve damar sistemi, modelleme, elektrik, matematik, MATLAB

4

Table of Contents

ABSTRACT ................................................................................................................................................ 2

ÖZET ........................................................................................................................................................ 3

INTRODUCTION ................................................................................................................................... 5

Background ......................................................................................................................................... 5

Anatomy .......................................................................................................................................... 5

Physiology ........................................................................................................................................ 5

Modeling.......................................................................................................................................... 9

METHODS .............................................................................................................................................. 11

Hydraulic model of the HCS and turn it to electrical model ............................................................. 11

Electrical Model Design ..................................................................................................................... 14

RESULTS ................................................................................................................................................. 17

CONCLUSION ......................................................................................................................................... 19

DISCUSSION ........................................................................................................................................... 19

TIMETABLE............................................................................................................................................. 21

REFERENCES .......................................................................................................................................... 21

5

INTRODUCTION

Heart is the most important part of the human body and, as a result, heart diseases can

be quite morbid or fatal for human beings. Researchers do experiments in order to develop a

better understanding of the design (anatomy), functioning (physiology), and modes of

breakdown of this organ (pathology).

Figure 1 Parts of the heart1

Background

Anatomy: The heart is separated into two parts: Right heart, which pumps blood

through the lungs, and left heart, which pumps blood through the peripheral arteries (Figure

1). Both the left and right heart have two parts. These are the ventricles and atria. Atria work

like a weak pump to provide the optimum blood pressure in the ventricles. Ventricles pump

blood to lungs (right) and to peripheral system (left). These ventricles and atria work like a

pulsatile pump. The time between two consecutive heart beats is called the cardiac cycle. The

length of this cycle (i.e. its frequency) is controlled by the sinus node, which is located near

the right atrium. According to energy requirement of the body, sinus node controls the rate of

ventricle’s contraction. The cardiac cycle can be separated into two periods simply. These are

systole and diastole. Diastole is the relaxation period of the heart and systole is the contraction

period of the heart. During ventricular systole, large amounts of blood accumulate in the atria

because of closed valves. The valve between left atrium (LA) and left ventricle (LV) is called

mitral valve (MV), the valve between left ventricle and aorta is called aortic valve (AV).

These valves prevent backflows.

Physiology: After opening mitral valve, LV starts filling with blood. This period is

called diastole. During diastole, left ventricle volume (LVV) increases about 120 milliliters

(mL). This volume is called end-diastolic volume (EDV). After this period, heart starts

6

contracting and left ventricular pressure (LVP) rises rapidly. Nevertheless, until the LVP

equals the pressure in aorta (AoP) AV does not open. Both valves are closed and this period is

called as isovolumetric contraction (IVC). In this period, LVP increases without blood

flowing. After this period, AV opens and blood starts flowing along aorta, capillaries, and

veins. This period is called systole. This period can be also called ejection period. During

systole, LVV decreases by about 70 ml. This volume is called the stroke volume (SV). The

remaining volume is about 40 ml and this volume is called end-systolic volume (ESV). After

reaching the max systole pressure, LVP starts dropping. Blood continues flowing from LV to

aorta until AoP is equal to LVP. When AoP is equal to LVP, AV closes. During closing AV, a

few mL of blood returns to LV and oscillation is observed on the AV. This oscillation reflects

on aortic pressure and creates the aortic notch. After closing AV, MV does not open

immediately. In this period, LVP decreases drastically without blood flowing. This period is

called isovolumetric relaxation (IVR). When LVP equals the left atrial pressure (LAP) the

mitral valve opens and the ventricle starts filling. Therefore, the cardiac cycle is completed.

In Guyton’s medical book, pressures and volume changes in heart are clarified, clearly

(Figure 2). Moreover, the stages of a cardiac cycle are indicated in this figure. Therefore, this

figure shows one of the design criteria of this project.

Figure 2 Pressures and Volume (PV) vs. Time in the Left Side of the Heart During

One Cardiac Cycle (Ref# 1).

7

Figure 3 PV Loop of the LV (Ref# 1).

Other design criteria of this project are PV loop of the LV (Figure 3) and the first

derivative of the LVP (Figure 4). In Figure 3, EW means ejection work or stroke work. Stroke

work is equal to the area of the PV loop2.

Figure 4

of the LV

3.

Elastance line in the PV loop is one of the major subjects in this project (Figure 5). In

Figure 5, normal elastance line is mentioned as Ees. According to this figure, the efficiency of

heart can be calculated. The efficiency of the heart is equal to SW over the area between Ees

and PV loop and SW4. Moreover, the area between Ees and PV loop is equal to the oxygen

demand of the heart in a beat.

8

Figure 5 Elastance Line in PV Loop5.

When elastance line is drawn in proportion to time, a variable is derived and it is

called as time varying elastance curve. This curve gives information about LV stiffness

throughout cardiac cycle6.

Figure 6 Time Varying Elastance

Time varying elastance is calculated by using this equation:

( ) ( )

( ) ( )

9

Modeling: In the past, several scientists have worked on the modeling of the heart and

arterial system. In 1969, Westerhof developed windkesseli model (WM) to describe the blood

flow from the heart into the Aorta7. In this paper, Westerhof established three and four

element WM (Figure 7). Using these models, he achieved aortic pressure like a normal

human. Moreover, he compared his models’ results to experimental result. He derived the

equation of the system. After that, he delivered the values of the elements in these models.

Figure 7 Westerhof’s 3WM and 4WM.

3WM: (

) ( )

( )

( )

( )

4WM: (

) ( ) (

) ( )

( )

( )

( )

In 1974, Croston designed 28-compartment lumped-parameter model8. In 2002,

Rupnic and Runvovc established an electric circuit to observe the steady state and transient

response of the system9. Kerner used MATLAB to establish the mathematical equations of

2WM, 3WM and 4WM 10

. Hlavac analyzed 2WM, 3WM and 4WM by using MATLAB11

.

Addition of Kerner’s solution, Hlavac showed us the RSSii and RMSE

iii of his system.

Abdolrazaghi developed 43-compartment lumped parameter model12

. In this paper, he

established an electrical circuit as a model of cardiovascular system. In this circuit, all part of

body is modeled and equations are shown. However, when output of the system and

experimental results are compared, it is clearly seen that this model is not accurate. Schroeder

and Koenig developed a cardiovascular analysis package using MATLAB13

. In this package,

there are 17 M-Files. This package has mathematical equations about cardiovascular system.

When the input is entered to this package, system gives output results of the cardiovascular

i Windkessel is the German word for “Air Chamber” ii RSS means the residual sum of squares

iii RMSE means root mean square error

10

system. Shim14

also worked on the neural effect on the heart. He investigated the effect of

neuron on the heart rate and arterial resistance (Figure 8).

Figure 8 Shim’s Control Mechanism

Burkhoff and Sagawa derived equations to predict the elastance line15

. Olufsen

established a control mechanism to clarify the blood flow in human body (Figure 9).

Figure 9 Olufsen Blood Flow Control Model16

.

Despite scientists’ work on this issue intensively, there are still gaps about the

knowledge of the heart and its accurate modeling. Hence, in this project, the main topic is the

modeling of the left part of the heart. While modeling the heart, firstly the physiology of the

human cardiovascular system (HCS) will be analyzed. Then, an electrical model of HCS will

be designed and tested by using MATLAB. After that, the mathematical model (MM) of this

11

system will be established and tested by using Matlab. Moreover, all the results including the

pressure-time and volume-time graphs of the system elements will be compared with the

clinical data. Furthermore, these results will be verified by physiological and experimental

data.

After constructing electrical equivalent circuit, the electrical model of new LVAD is

connected to this system. By changing the values of elements in the electrical circuit,

dysfunctions will be simulated and after that, LVAD will be “turned on”. Thanks to this

method, the effects of LVAD in the cardiac patient are observed. While modeling the HCS,

the main criteria of HCS are as follows: Aortic Pressure (AoP) is adjusted between 120-80

mmhg. Cardiac output (CO) is about 5-6 L/miniv

. The efficiency of the heart is about 44 %17

.

Heart rate (HR) is 60 beats/min, stroke volume (SV) is about 90-100 mL and maximum

elastance (Emax) is about 218

. The resistance is the length of the aorta, as called input

resistance (Rin), is about 1.1 ohms19

. The time constant (τ) is commonly used for representing

the isovolumic fall in LVP is about 1 second20

, the resistance between LV and aorta is called

as coupling resistance (Rc) is about 0.2 ohm21

, aortic capacitance is about 0.5-1.5 farad.

Moreover, pulmonary arterial pressure (PAP) is about 30-35 volt, left atrium pressure (LAP)

is about 0-10 volt, pulmonary vascular resistance is about 1.15 ohms22

and ejection fraction is

about 50-65 %23

. The period of the isovolumetric relaxation (IVR) is about 80 ms. The period

of the isovolumetric contraction (IVC) is about 40 ms. The ratio of the periods of systole and

diastole is

. When EDV is plotted against the SW

24, this is called as preload recruitable

stroke work (PRSW) is about 0.9525

. The graph of PRSW should be linear and the slope

should be around.

METHODS

Hydraulic model of the HCS and turn it to electrical model To create a MM of HCS, an electrical equivalent model of HCS is required. According to

our studies, the most efficient type of model is to understand the physiology of the HCS is

hydraulic model. Therefore, electric model is based on a hydraulic model which is clarified

the HCS. In terms of variables, a table below can be written (Ref# 7).

Table 1 Hydraulic vs. Electric Variables.

HYDRAULIC ELECTRIC

Pressure, P Voltage, V

Flow, Q Current, I

Volume, V Charge, Q

Resistance, R Resistance, R

Compliance, C Capacitance, C

iv CO=HR*SV

12

Figure 10 can be an example to understand a hydraulic model.

Figure 10 Hydraulic System26

.

Figure 11 can be also example to using a hydraulic model in simplified HCS.

Figure 11 Pa is afterload pressure and Pf is preload pressure of LV (Ref# 7).

Figure 12 is an example of the hydraulic model of simplified HCS.

Figure 12 Hydraulic Model of Simplified Human Cardiovascular System with Right

Part of the Heart27

.

13

Similar to this circuit, a hydraulic model of HCS is established as shown Figure 13.

Figure 13 Hydraulic Model of Simplified Human Cardiovascular System in This

Project.

Table 2 Symbols of the Hydraulic Model of the Simplified HCS.

Symbol Description

Servo Pump&LV Left Ventricle

LA Res.(LA Reservoir) Left Atrium

PVR Pulmonary Vascular Resistance

Pulm. Res.(Pulmonary Reservoir) Pulmonary Compliance

SVR Systemic Vascular Resistance

Ao. Compl. Aortic Compliance

Afterload Res.(Afterload Reservoir) Afterload Compliance

Air Tank Aortic Pressure

An electrical equivalent of the circuit HCS is established by using this hydraulic model.

While creating this electrical model, hydraulic and electrical elements are matched like table

below.

Table 3 Hydraulic vs. Electric Elements.

Hydraulic Electrical

Reservoir (m3) Capacitor (F)

Pump (mmHg) Ideal Voltage Source (V)

Resistance (dyn·s/cm5) Resistor (Ω)

Check Valve Diode

Mass (kg) Inductor (H)

14

Electrical Model Design

Figure 14 Electrical Model of the Simplified HCS in This Project.

In this project, the electrical equivalent circuit of HCS includes four parts. These parts

are outside the LV, LV, LA and peripheral system.

Outside of the LV, there are three elements. V-p is the energy source, which gives

energy to LV, to pump energy to the system and to simulate e( ). Mass outside piston and

spring outside piston also are used to create a pulsatile effect to the system with time varying

elastance. LV is modeled by using six elements. Air under piston and water above piston are

used same idea in hydraulic system. Both are the capacitance of LV. Piston and resistor are

used to model the oscillation and piston friction in the hydraulic system.

Peripheral system also includes three parts. These parts are aorta, pulmonary and

venous systems. For modeling the aorta in this circuit, five elements are used. Inertance of the

blood located in ascending aorta is modeled as an inductor in this electrical modelv. Input

impedance is the impedance, which is the total resistance of the arterial system. Therefore,

both these impedances are modeled as a resistor in this circuit. Aortic capacitance is the

arterial compliance of the aorta. Raort is used to adjust the time constant and the max and min

voltage value of the aortic capacitor.

For modeling the pulmonary system in this circuit, six elements are used. Inertance

arterial blood1 is the blood locates from arch to venous system. Therefore, this blood mass is

modeled as an inductor. Venous valve is the valve in the veins and this is modeled as diode.

Variable resistor is used to model the aortic pressure difference between exercising and

resting conditions. To control this resistor, exercise pump is used. When exercising condition,

blood flow in the pulmonary arteries is very fast. The faster blood flowing in pulmonary

arteries lead to less pulmonary arterial resistance. Resting human and manual switch are used

to affect the results in the runtime of the MATLAB. Thanks to this effect, the voltage

difference between resting and exercising human are observed.

v In addition, this element helps to observe the aortic notch.

15

For modeling the venous system, five elements are used. Rl and ri are used to adjust

the pulmonary arterial voltage. Venous/Pulmonary capacitance is used to model the

compliance of the lung and veins. PVR1 is used to adjust the voltage of this capacitor. PVR2

is the pulmonary vascular resistance. Therefore, this is modeled as a resistor.

For modeling the LA, five elements are used. V-p1 is a weak energy source, which

gives energy to LA, to pump blood to LV and simulates the “atrial kick” at the end of

diastole. Cla is the compliance of the LA, therefore, this modeled as a capacitor. RCla is used to

adjust the time constant and the max and min voltage value of the Cla. LLA are used to model

the blood in the LA. Therefore, this blood mass is modeled as an inductor. RLLA is used to

adjust the time constant of the LLA.

Additionally, MV and AV is the mitral and aortic valve in the heart. Therefore, these

valves are modeled as a diode.

Table 4 Symbols and Descriptions of the Electrical Model of the HCS.

Symbol Description

V-p Left Ventricle Pump

Mass Left Ventricle Inertance1

Piston Friction Left Ventricle Resistance

AV Aortic Valve

Piston Left Ventricle Inertance2

Water Above Piston Left Ventricle Compliance

Aortic Capacitance Aortic Capacitance

Input Impedance Input Resistance

Inertance Arterial Blood Arterial Blood Inertance

Venous Valve Venous Valve

Venous/Pulmonary Capacitance Venous/Pulmonary Capacitance

Variable Resistance Venous Resistance

Inertance Venous Blood Venous Blood Inertance

Exercised Pump Faster Blood Flow

PVR2 Pulmonary Vascular Resistance

CLA Left Atrium Compliance

RLLA&RCLA Left Atrium Resistance

V-p1 Left Atrium

MV Mitral Valve

In addition, the elements in this electrical circuit can be described as the analogy in

the HCS the table below.

16

Table 5 Matching between electrical circuit and analogical system of the HCS.

Electrical Element Electrical Role Analogy Analogical Role

V-p

(Voltage Source)

Provide current flow by

doing a potential

difference between two

points.

Left Ventricle Provide the blood flow in

the body.

Piston Friction

(Resistor)

Consume voltage

proportional to its

resistance

Left Ventricle Resistance Consume energy

proportional to its length.

Piston

(Inductor)

Make the current flow

easy.

Blood Inertance To overcome the

resistance to move static

blood in LV.

Water Above Piston

(Capacitor)

Storage the voltage in the

circuit proportional to its

capacitance

Left Ventricle

Compliance

Storage the blood to

delivery to the body.

AV

(Diode)

It allows flowing current

along one direction.

Aortic Valve It allows to flow blood

along one direction(from

LV to Aorta)

MV

(Diode)

It allows flowing current

along one direction.

Mitral Valve It allows to flow blood

along one direction(from

LA to LV)

Rc

(Resistor)

Consume voltage

proportional to its

resistance

Rc

(Coupling Resistance)

The resistance between

LV and Aorta.

Aortic Capacitance

(Capacitor)

Storage the voltage in the

circuit proportional to its

capacitance

Aortic

Compliance

The arterial compliance

in Aorta

Input Impedance

(Resistor)

Consume voltage

proportional to its

resistance

Input Impedance

(Input Resistance)

The arterial resistance in

Aorta

Inertance Arterial Blood

(Inductor)

Make the current flow

easy.

Blood Inertance in Aorta To overcome the

resistance to move static

blood in Aorta.

Venous Valve

(Diode)

It allows flowing current

along one direction.

Venous Valve It allows to flow blood

along one direction(from

Aorta to Venous)

Venous/Pulmonary

Capacitance

(Capacitor)

Storage the voltage in the

circuit proportional to its

capacitance

Venous/Pulmonary

Compliance

The venous and

pulmonary compliance in

the body.

Variable Resistance

(Resistor)

Consume voltage

proportional to its

resistance

Venous Resistance The venous resistance in

the body.

Inertance Venous Blood

(Inductor)

Make the current flow

easy.

Blood Inertance in

Venous

The venous inertance in

the body.

PULM

(Capacitor)

Storage the voltage in the

circuit proportional to its

capacitance

Pulmonary Compliance The pulmonary

compliance in the body.

PVR

(Resistor)

Consume voltage

proportional to its

resistance

Pulmonary Vascular

Resistance

The pulmonary

resistance in the body.

Water LA

(Capacitor)

Storage the voltage in the

circuit proportional to its

capacitance

Left Atrial Compliance The LA compliance in

the body.

LA Friction

(Resistor)

Consume voltage

proportional to its

resistance

Left Atrial Resistance The LA resistance in the

body.

V-p1

(Voltage Source)

Provide current flow by

producing voltage.

Left Atrium Help LV to provide the

blood flow.

17

RESULTS

Figure 15 PV vs. Time of the HCS.

PV Loops are drawn by using the main criteria such as elastance, preload recruitable

stroke work (PRSW),

and efficiency of the heart.

Figure 16 PV Loop of the LV with Elastance Line.

18

Figure 17 .

using Simulink

Figure 18

using mathematical solution.

Figure 19 PRSW of the LV.

19

CONCLUSION

In this project, AoP is between 120-80 mmHg and aortic notch can be observed. Also

in this project, LAP is about 10 mmHg and atrial kick is observed, clearly. SV is about 80 ml

in the expected results and in the Figure 15. Cardiac Output (CO) vi

is expected about 5 L.

According to Figure 15, CO is about 4.8 L. Cardiac Efficiency (µ) is expected 65% but in this

project, µ= 90 %.

Figures are almost same both expected and observed results. The period

of IVR is about 20 milliseconds (ms). The period of IVC is about 40 ms. These values are

halves of the expected IVR and IVC values. The ratio of the periods systole and diastole is

.

According to these results, we may say that this model is accurate to understand

simplified human cardiovascular system. Dysfunctions can be applied into this system and

after that; LVAD can be “turned on”. LVAD, describe LVADs in introduction, is an

extremely important device for cardiac patients. Therefore, this device should be developed

day by day. In this model, LA and PV loop should be better in the next progress. After these

enhancements, more efficient MM can be derived and it can be used to produce LVAD.

Thanks to this model, new LVADs can be more economical, user friendly. Furthermore, after

this project, maybe more technical LVAD can be produced.

DISCUSSION

According to results, it is said that the electrical model of this project is accurate and

precise in terms of LVP, LAP, LVV and AoP. Still, there is an incomplete part in this study.

LVAD is not connected to the cardiovascular system. In addition, LVP, aortic blood flow and

atrial kick can be more accurate. After LVAD is connected to the circuit, the accuracy of the

system can be discovered, obviously. In Hlavac’s study, AoP is very high and pressure line is

not smooth. Moreover, aortic notch cannot be shown. In this study, the conditions all of above

are achieved. In Kerner’s researches, AoP is almost 120-70 mmHg and pressure line is not

accurate. In this project, AoP is about 120-80 mmHg. In Abdolrazaghi’s study, LVP line is

very sharp. Atrial kick cannot be observed. In Giridharan’s paper, LVAD is connected the

circuit and investigated. In this project, LVAD cannot be connected the circuit.

This electrical model is one of the most applications of the model in for testing the

performance of an electrical LVAD model. In terms of LVAD, researchers study to model

accurate LVAD. Giridharan and Skliar studied on the control strategy of the LVAD28

. They

established a control mechanism to produce an accurate assist device by using mathematical

equations.

vi In this project, HR is assumed about 60 beat/min.

20

Figure 20 The Control Mechanism of the LVAD (Ref# 10).

Lampe established another type of control mechanism to control LVAD. He also

integrated PI controller to his control system.

Figure 21 Lampe’s Electrical Equivalent Circuit.

Figure 22 Lampe’s Control Loop.

21

TIMETABLE

Time&

Plans

2-6 Oct 9-13

Oct

16-20

Oct

23-27

Oct

30-4

Oct

7-11

Oct

14-18

Oct

21-25

Oct

28-8

Nov

Liter. Search

Hydr. Model

Design

Hydr. To

Electrical Model

Electical Model

Design

Time&

Plans

11-15

Nov

18-22

Nov

25-29

Nov

2-6

Dec

8-12

Dec

14-18

Dec

20-24

Dec

27-31

Dec

3-7

Jan

Calculations&

Graphs

Mathematical

Model

FinalReport&

Presentation

REFERENCES

1 Textbook of Medical Physiology-Eleventh Edition, Arthur C. Guyton and John E. Hall, Unit 3, Chapter 9, 2006

2 Effect of Loading Dose of Procaine Amide on Left Ventricular Performance in Man, Ghuzi lawad-Kanber,

M.B., F.C.C.P.,' * and Theodore R. Sherrod, M.D, 1974 3 Norepinephrine-induced acute heart failure in transgenic mice over expressing erythropoietin, Alexander

Deten, Junpei Shibata, Dimitri Scholz, Wilfred Briest, Klaus Wagner, Roland Wenger, Heinz Zimmer, 2004 4 Molecular basis of cardiac efficiency, Heiko Bugger and E. Dale Abel, University of Utah School of Medicine,

2008 5 http://ccnmtl.columbia.edu/projects/heart/circ4.html, January, 2011

6 In vivo murine left ventricular pressure-volume relations by miniaturized conductance micromanometry,

Dimitrios Georgakopoulos, Wayne A. Mitzner, Chen-Huan Chen, Barry J. Byrne, Huntly D. Millar, Joshua M.

Hare, and David A. Kass, 1997 7 Westerhof N, Bosman F, DeVries CJ, Noordergraaf A. Analogue studies of human systemic arterial tree. J

Biomech, 1969 8 Croston RC, Fitzjerrell DG. Cardiovascular model for the Simulation of exercise, lower body negative

pressure and tilt table experiments. In: Proceeding 5th

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Giolma and SA Altobelli, 1980 20

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Louis-Gilles Durand, 2004 22

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23

APPENDIX

In this circuit, LVAD is not connected. In the next study about this topic, LVAD can

be connected the circuit and outputs of the system can be adjusted. The informations of

LVADs are the table below.

Table 1. Information about LVADs28

.

Device Manufacturer Type Approval Status as of July 2009

Novacor World Heart Pulsatile.

Was approved for use in North America,

European Union and Japan. Now defunct

and no longer supported by the

manufacturer.

HeartMate XVE Thoratec Pulsatile.

FDA approval for BTT in 2001 and DT in

2003. CE Mark Authorized. Rarely used

anymore due to reliability concerns.

HeartMate II Thoratec

Rotor driven

continuous axial flow,

ball and cup bearings.

Approved for use in North America and

EU. CE Mark Authorized. FDA approval

for BTT in April 2008. Recently approved

by FDA in the US for Destination Therapy

(as at January 2010).

HeartMate III Thoratec

Continuous flow

driven by a

magnetically

suspended axial flow

rotor.

Clinical trials yet to start, uncertain future.

Incor Berlin Heart

Continuous flow

driven by a

magnetically

suspended axial flow

rotor.

Approved for use in European Union.

Used on humanitarian approvals on case

by case basis in the US. Entered clinical

trials in the US in 2009.

24

Jarvik 2000 Jarvik Heart

Continuous flow,

axial rotor supported

by ceramic bearings.

Currently used in the United States as a

bridge to heart transplant under an FDA-

approved clinical investigation. In Europe,

the Jarvik 2000 has earned CE Mark

certification for both bridge-to-transplant

and lifetime use. Child version currently

being developed.

MicroMed

DeBakey VAD

MicroMed

Continuous flow

driven by axial rotor

supported by ceramic

bearings.

Approved for use in the European Union.

The child version is approved by the FDA

for use in children in USA. Undergoing

clinical trials in USA for FDA approval.

VentrAssist Ventracor

Continuous flow

driven by a hydro-

dynamically

suspended centrifugal

rotor.

Approved for use in European Union and

Australia. Company declared bankrupt

while clinical trials for FDA approval

were underway in 2009. Company now

dissolved and intellectual property sold to

Thoratec.

MTIHeartLVAD MiTiHeart

Corporation

Continuous flow

driven by a

magnetically

suspended centrifugal

rotor.

Yet to start clinical trials.

C-Pulse Sunshine Heart

Pulsatile, driven by an

inflatable cuff around

the aorta.

Currently in clinical trials in the US and

Australia.

HVAD HeartWare

Miniature "third

generation" device

with centrifugal blood

path and hydro-

magnetically

suspended rotor that

may be placed in the

pericardial space.

Obtained CE Mark for distribution in

Europe, January 2009. Initiated US BTT

trial in October 2008 (completed February

2010) and US DT trial in August 2010.

DuraHeart Terumo

Magnetically levitated

centrifugal pump.

CE approved, US FDA trials underway as

at January 2010.

25

Thoratec PVAD

(Paracorporeal

Ventricular Assist

Device)

Thoratec

Pulsatile system

includes three major

components: Blood

pump, cannulae and

pneumatic driver (dual

drive console or

portable VAD driver).

CE Mark Authorized. Received FDA

approval for BTT in 1995 and for post-

cardiotomy recovery (open heart surgery)

in 1998.

IVAD -

Implantable

Ventricular Assist

Device

Thoratec

Pulsatile system

includes three major

components: Blood

pump, cannulae and

pneumatic driver (dual

drive console or

portable VAD driver).

CE Mark Authorized. Received FDA

approval for BTT in 2004. Authorized

only for internal implant, not for

paracorporeal implant due to reliability

issues.