Alper_Aksu-Undergrad Design Project

T.C.
BAHÇEŞEHİR UNIVERSITY
MATHEMATICAL MODELING OF
THE SIMPLIFIED HUMAN CARDIOVASCULAR SYSTEM
Capstone Project
Alper Aksu
İSTANBUL, 2010

T.C.
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.
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

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 LV3
.
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 model 8
. 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 RMSEiii
of his system.
Abdolrazaghi developed 43-compartment lumped parameter model 12
. 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 line 15
. 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 SW24
, 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)
Mitral Valve It allows to flow blood
LA to LV)
Rc
(Resistor)
Consume voltage
proportional to its
resistance
Rc
(Coupling Resistance)
The resistance between
LV and Aorta.
Aortic Capacitance
(Capacitor)
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)
easy.
Blood Inertance in Aorta To overcome the
resistance to move static
blood in Aorta.
Venous Valve
(Diode)
Venous Valve It allows to flow blood
Aorta to Venous)
Venous/Pulmonary
Capacitance
(Capacitor)
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)
easy.
Blood Inertance in
Venous
The venous inertance in
the body.
PULM
(Capacitor)
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)
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
Annual Pittsburgh conference modeling simulation, 1974
9
Rupnic M, Runvovc F. Simulation of steady state and transient phenomena by using the equivalent electronic
circuit. J Computer Methods Programs Biomed, 2002

22
10
Daniel Kerner Ph.D. :Solving Windkessel Model Using Matlab
11
Martin Hlavac: Windkessel Model Analysis in Matlab
12
Abdolrazaghi M, Navidbakhsh M, Hassani K, Mathematical Modeling and Electrical Analog Equivalent of the
Human Cardiovascular System, Springer Science Business Media, 2010
13
HEART: an automated beat-to-beat cardiovascular Analysis package using MATLAB, Mark J. Schroeder, Bill
Perrault, Daniel L. Ewert, Steven C. Koenig, 2004
14
Mathematical Modeling of Cardiovascular System Dynamics Using a Lumped Parameter Method, Eun Bo
Shim, Jong Youb Sah, Chan Hyun Youn, Japanese Journal of Physiology, 2004
15
Ventricular Efficiency Predicted by An Analytical Model, Daniel Burkhoff and Kiichi Sagawa, 1986
16
Modeling Cerebral Blood Flow Control During Posture Change From Sitting to Standing, Mette Olufsen, Hien
Tran, Johnny Ottesen, 2004
17
Cardiac efficiency, C.L. Gibbs and C.J. Barclay, 1995
18
Arterial elastance and heart-arterial coupling in aortic regurgitation are determined by aortic leak severity,
Segers P, Morimont P, Kolh P, Stergiopulos N, Westerhof N, Verdonck P, 2002
19
Aortic input impedance in normal man: relationship to pressure wave forms, JP Murgo, N Westerhof, JP
Giolma and SA Altobelli, 1980
20
Measurement of ventricular relaxation : An alternative index of isovolumic relaxation to the time constant,
King C. Lee, 1988
21
A ventricular-vascular coupling model in presence of aortic stenosis, Damien Garcia, Paul J. C. Barenbrug,
Philippe Pibarot, Andre´ L. A. J. Dekker, Frederik H. van der Veen, Jos G. Maessen, Jean G. Dumesnil, and
Louis-Gilles Durand, 2004
22
http://en.wikipedia.org/wiki/Vascular_resistance
23
Cotran, Ramzi S.; Kumar, Vinay; Fausto, Nelson; Nelso Fausto; Robbins, Stanley L.; Abbas, Abul K. Robbins
and Cotran pathologic basis of disease. St. Louis, Mo: Elsevier Saunders, 2005
24
Single-beat determination of preload recruitable stroke work relationship: derivation and evaluation in
conscious dogs, Mohanraj K. Karunanithi, BE, MBiomedEa
andMichael P. Feneley, MD, 2000
25
Comparison of preload recruitable stroke work, end-systolic pressure-volume and dP/dtmax-end-diastolic
volume relations as indexes of left ventricular contractile performance in patients undergoing routine cardiac
catheterization, Feneley MP, Skelton TN, Kisslo KB, Davis JW, Bashore TM, Rankin JS, 1992
26
Cardiovascular Mechanics, Roger G. Mark, Massachusetts Institute of Technology, 2007
27
Continuous flow total artificial heart: modeling and feedback control in a mock circulatory system, Khalil
HA, Kerr DT, Franchek MA, Metcalfe RW, Benkowski RJ, Cohn WE, Tuzun E, Radovancevic B, Frazier
OH, Kadipasaoglu KA, 2008
28
Control Strategy for Maintaining Physiological Perfusion with Rotary Blood Pump, Guruprasad A.
Giridharan, Mikhail Skliar, University of Utah, 2003

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.

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