Human Heart Modelling using Hydro Electro Mechanical Systems

FINAL PROJECT REPORT

Human Heart Modelling using Hydro Electro

Mechanical Systems

COURSE

SYSTEMS AND CONTROL THEORY

Spring 2014

Under the guidance of

Dr. Wilfrido Moreno, Ph.D. Electrical Engineering Professor

Presented by

Mr. Magendran Mathivanan

(UID : U29552115)

Abstract:-

This paper introduces a new mathematical modelling of human heart as a hydro electro

mechanical system (HEMS). This paper simulates the human heart based on three main functions:

hydraulic, electrical and mechanical parameters. Hydro-mechanical model developed then has been

transformed into electrical domain and simulation has been carried out according to the mathematical

model or formulations obtained using Laplace transform. This electrical model / circuit is then tested by

MATLAB based simulations and results found are comparable with the normal ECG waveforms so that

these simulated results may be useful in clinical experiments. In this model basic electrical components

have been used to simulate the physiological functions of the human heart. The result is a simple

electrical circuit consisting of main electrical parameters that are transformed from hydraulic models and

medical physiological values. Developed MATLAB based mathematical model will primarily help to

understand the proper functioning of an artificial heart and its simulated ECG signals. A comprehensive

model for generating a wide variety of such signals has been targeted for future in this paper. This

research especially focuses on modelling human heart as a hydroelectro-mechanical system with three

case studies.

List of Figures Page .No

1. Fig 1. Morphology of a mean PQRST-complex

of an ECG recorded from a normal human. ..3

2. Fig 2. The compartmental electrical model of

hydro electro mechanical system (HEMS) ...4

3. Fig 3. Compartmental Hydro Electro Mechanical System ...4

4. Fig 4. The ECG output of the Simulink model I ...8

5. Fig 5. The response of State Space Model. ...9

6. Fig 6. The step response of State Space model .10

7. Fig 7. The ECG output of the Simulink model II .10

8. Fig 8. The response of State Space Model. 11

9. Fig 9. The step response of State Space model 12

List of Tables Page .No

1. Table 1. The system parameters and their units ..5

2. Table 2. Parameters associated with different pressures and valves ..7

3. Table 3. Table comparing Simulation Values ..12

CONTENT Page .No

Abstract

List of figures

List of tables

Introduction .1

System Model .4

Equations governing the model .6

Results .8

Case I .8

Case II .11

Conclusion .13

Bibliography

Appendix A: SIMULINK Files

Appendix B: Copy of the Paper

Human Heart Modelling using Hydro Electro Mechanical Systems

SYSTEM & CONTROL THEORY I Page 1

CHAPTER 1

INTRODUCTION

Heart disease is the main cause of death worldwide, especially in the developed and developing

countries. Treatments of such diseases have various forms, from the simplest such as following

appropriate diets to very complex and dangerous forms such as heart transplantation. Due to

improvements in technology, it is possible to find out new opportunities, for example new medical assist

devices or predictive medical instruments which help to be aware of the dangerous situations to occur in

due time to our health. To realize such goals since the 1960s, various mathematical modeling of human

heart have been studied using physical models of the real systems as the reference domain. Mathematical

models have been widely used in the simulation of cardiovascular systems. The human cardiovascular

system is highly complex and involves many control mechanisms. The model of Windkessel is a famous

example of such a discrete model. Although computer analysis of numerical models have taken the place

of the physical models in many cases, physical electrical models are still indispensable in testing the

reliability, functionality and the control of human cardiovascular system. Short term heart rate control is

mainly mediated by the central nervous system. Danielsons research group integrated the mathematical

models of nervous systems with the Windkessel model, to investigate the control mechanism of the heart

in a different way. To replace the functions of real human heart for a limited time, artificial heart pumps

have been used. This pump mainly replaces left ventricular failure. Three generations of pumps are

present: pulsatile pumps, rotary pumps with contact bearing and rotary pumps with noncontact bearing.

The last developed pump as an artificial heart assist device is a magnetically levitated axial flow heart

pump.

An electromechanical biventricular model, which couples the electrical property and mechanical

property of the heart, has been constructed and the right ventricular wall motion and deformation have

been simulated. The excitation propagation has been simulated by electrical heart model, and the resultant

active forces have been used to study the ventricular wall motion during systole. The simulation results

are found to be compatible with the models theoretical results. It suggests that such electromechanical

biventricular model can be used to assess the mechanical function of two ventricles as well. A third-order

model of the cardiovascular system designed to illustrate biological system simulation has been described.

The model is considered to be extremely simple which allows concentrating on the simulation and

computation dimensions but not on the physiological complexity. Heart pumping action is derived from a

variable capacitor, and the systemic circulation is modeled as an RC filter. With the rapid development of

computer and medical image technology, finite element method (FEM) has become one of the main tools



to study cardiovascular mechanics as well. A third-order model of the cardiovascular system uses real

geometric shape and fiber structure with a 3-D finite element biventricular model.

Electrocardiography is the recording of the electrical activity of the heart. Traditionally this is in

the form of a trans thoracic (across the thorax or chest) interpretation of the electrical activity of

the heart over a period of time, as detected by electrodes attached to the surface of the skin and recorded

or displayed by a device external to the body. The recording produced by this noninvasive procedure is

termed an electrocardiogram (also ECG or EKG). It is possible to record ECGs invasively using

an implantable loop recorder.

An ECG is used to measure the hearts electrical conduction system. It picks up electrical

impulses generated by the polarization and depolarization of cardiac tissue and translates into a

waveform. The waveform is then used to measure the rate and regularity of heartbeats, as well as the size

and position of the chambers, the presence of any damage to the heart, and the effects of drugs or devices

used to regulate the heart, such as a pacemaker.

A single sinus (normal) cycle of the ECG, corresponding to one heartbeat, is traditionally labeled with the

letters P, Q, R, S, and T on each of its turning points (Fig. 1). The ECG may be divided into the following

sections.

P-wave: A small low-voltage deflection away from the baseline caused by the depolarization of the atria

prior to atrial contraction as the activation (depolarization) wave front propagates from the SA node

through the atria.

PQ-interval: The time between the beginning of atrial depolarization and the beginning of ventricular

depolarization.

QRS-complex: The largest-amplitude portion of the ECG, caused by currents generated when the

ventricles depolarize prior to their contraction. Although atrial repolarization occurs before ventricular

depolarization, the latter waveform (i.e. the QRS-complex) is of much greater amplitude and atrial

repolarization is therefore not seen on the ECG.

QT-interval: The time between the onset of ventricular depolarization and the end of ventricular

repolarization. Clinical studies have demonstrated that the QT-interval increases linearly as the RR-

interval increases . Prolonged QT-interval may be associated with delayed ventricular repolarization

which may cause ventricular tacky arrhythmias leading to sudden cardiac death .

ST-interval: The time between the end of S-wave and the beginning of T-wave. Significantly elevated or

depressed amplitudes away from the baseline are often associated with cardiac illness.



T-wave: Ventricular repolarization, whereby the cardiac muscle is prepared for the next cycle of the

ECG.

Fig 1. Morphology of a mean PQRST-complex of an ECG recorded from a normal human.

Baroreceptors, although well established, have been investigated extensively. The goal of such

research is to understand the mechanisms of the total artificial heart and obtain a better mathematical

model as well as a simple physical analog model of the total artificial heart.



CHAPTER 2

SYSTEM MODEL

The Hydro Electro Mechanical System(HEMS) model developed is given in Fig. 2 below. The

model is based on symmetry property of human cardiovascular and circulatory system and is made of two

parallel equivalent circuits.

Fig 2. The compartmental electrical model of hydro electro mechanical system (HEMS)

The compartmental electrical model of Yalcinkaya, Kizilkaplan and Erbas with the defined

system parameters (hydraulic and electrical parameters and their units) are given:-

Fig 3. Compartmental Hydro Electro Mechanical System



The parameters related to the diagram and their respective units are described in the tables

below:-

Table 1. The system parameters and their units



EQUATION GOVERNING THE MODEL:-

The HEMS model is represented by the following equations with the boundary conditions taken

into account:-

QA (t) =QA1 (t) + QM (t), QM (t) = QB (t) + QC (t),

QB (t) = QB1(t) +QBO (t) + QM1 (t), QM1 (t) = QD1 (t) + QDO (t) +QX (t),

QC (t)= QC1 (t) + QCO (t) + QM2 (t), QM2 (t) = QE1 (t) + QEO (t) + QY (t),

QF (t) = QX (t) + QY (t), and QF (t) = QF0 (t) + QF1 (t)

Writing the first leg of equations from the fig 2,

P1 (t) + P2 (t) + P4 (t) + P6 (t) = PIN (t)

Substituting the values of internal parameters, we derive:

Differentiating on both sides:

Applying Laplace transforms on both sides:



Similarly considering the second leg from fig 2,

P1 (t) + P3 (t) + P5 (t) + P6 (t) = PIN (t)

Substituting the values of internal parameters, we derive:

Differentiating on both sides:

Applying Laplace transformation,

The following table gives the parameters associated with different pressures and valves:

Table 2. Parameters associated with different pressures and valves



CHAPTER 3

RESULTS

The model was simulated using MATLAB Simulink to assess its ability to reproduce the ECG

signal of the heart. The model is simulated with the mentioned parameters and the ECG signal derived is

as shown:

3.1 SIMULINK

Based on the mathematical formulation obtained, by using the MATLAB simulation facility, case study

have been done. The system is made of four main elements with their mathematical models defined

separately; the main elements are the pacemaker, heart, sensor and circulatory system.

While the circulatory system and the pace maker have the same transfer function, the transfer

function of heart changes according to the state of heart and hence the sensing signal changes its value.

Case I:-

The Laplace transform of the heart defined by QA(s) / PIN(s) is

Result:-

Fig 4. The ECG output of the Simulink model I



This signal is similar to the original ECG signal.

The State space representation is of the12th order due to the degree of the main elements:-

; C = [ 0 0.0028 0.0947 0.3208 0.9799 1.8681 2.3521 2.4264 1.7653 0.8806 0.3362 0.0297];

The State space model is constructed in Simulink and the model is run. The output is compared to the

output of above Simulink model.

The output is similar to the above graph:

Fig 5 The response of State Space Model.



The step response of the A, B, C, D Parameters derived :

Fig 6. The step response of State Space model

Case II:-

The Laplace transform of the heart defined by QA(s) / PIN(s) is

Result:-

The output we get:-

Fig 7. The ECG output of Simulink model II



The State space representation is:

; C = [0 0.0143 0.1754 0.5870 1.6744 3.0596 3.8056 3.8457 2.7617 1.3747 0.5148 0.0493];

The State space model is constructed in Simulink and the model is run. The output is compared to the

output of above Simulink model.

Fig 8. The response of State Space Model.



The step response of the state space equations is as follows:-

Fig 9. The step response of State Space model

The parameters of the ECG signals are calculated and tabulated as follows:

Parameters Simulation-1 Simulation-2

P-wave 0.069 sec No P-wave

QT-interval 0.3749 sec 0.38 sec

PR- interval 0.20 sec No PR- interval

QRS-complex 0.139 sec 0.15 sec

T-wave 0.175 sec 0.20 sec

Table 3. Table comparing Simulation Values



CHAPTER 4

CONCLUSION

In the past many mathematical models of the heart have been developed using different

softwares. The motion of the heart wall, cardiac electrical deformations are some of them used to describe

the simulation results of the system. Simple cardio models are designed to demonstrate the simulations of

the biological system. The computer results are close enough to the physiological data so that verification

of the model is possible.

This project is based on the mathematical modelling of human heart as a Hydro Electro

Mechanical System (HEMS). The MATLAB simulation results agree well with the data obtained from

clinical studies. The models, case studies have been developed and tested with good feedbacks. The

system is made of a reference signal, a pacemaker, an artificial heart, a group of sensors and a circulatory

system. The results are given in the tables and figures above. The P wave was very negligible in the first

simulation and almost zero in the second simulation; this needs more attention for future case studies. The

simulation results produce sharp RS complex which needs investigation in term of simulation parameters

as real RS complex do not possess sharp curve characteristics. The four building blocks used in

simulations have to be improved as the ECG is not only a result of proper functioning of heart but also

needs proper and parallel functions of circulatory and cardiovascular subsystems of human whole

biological system.

Bibliography

1. L. Xia, M. Huo, F. Lio, B. He, and S. Crozier, Motion Analysis of Right Ventricular Wall Based on an Electromechanical Biventricular Model, Proceedings of the 26th Annual International Conference of the IEEE EMBS San Francisco, CA, USA, September 1-5, 2004.

2. A.M. Cook, J.G. Simes, A Simple Heart Model Designed to Demonstrate Biological System Simulation, IEEE Transactions on Biomedical Engineering, Vol. Rme-19,No. 2, March 1972.

3. Y. Wu, P.E. Allaire, G. Tao, D. Olsen, Modeling, Estimation, and Control of Human Circulatory System With a Left Ventricular Assist Device, IEEE Transactions on Control Systems Technology, Vol. 15, No. 4, July 2007.

4. W. Shi, M.-S. Chew, Mathematical and Physical Models of a Total Artificial Heart, IEEE International Conference on Control and Automation, Christchurch, New Zealand, December 9-

11, 2009.

5. E.H. Maslen, G.B. Bearnson, P.E. Allaire, R.D. Flack, M. Baloh, E. Hilton, M.D. Noh, D.B. Olsen, P.S. Khanwilkar, J.D. Long, Feedback Control Applications in Artificial Hearts, IEEE Control Systems Magazine, Vol.18, No.6, pp.26-34, December 1998.

APPENDICES:

SIMULINK Models:

1) Simulink model of heart

2) State Space model

Human Heart Modelling using Hydro Electro Mechanical Systems

Documents

Transcript of Human Heart Modelling using Hydro Electro Mechanical Systems