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1 Evaluation of cardiac output using nonuniform hybrid electrical impedance model based on forward lumped parameter and both-hands impedance measurement system Kwangseok Seo The Graduate School Yonsei University Department of Biomedical Engineering

2 Evaluation of cardiac output using nonuniform hybrid electrical impedance model based on forward lumped parameter and both-hands impedance measurement system A Dissertation Submitted to the Department of Biomedical Engineering and the Graduate School of Yonsei University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Kwangseok Seo Feb 2012

3 This certifies that the dissertation of Kwangseok Seo is approved. Thesis Supervisor: Prof. Hyungro Yoon Thesis Committee Member: Prof. Kyoungjoung Lee Thesis Committee Member: Prof. Taemin Shin Thesis Committee Member: Prof. Sei-jin Chang Thesis Committee Member: Prof. Byung-su Yoo The Graduate School Yonsei University Feb 2012

4 Acknowledgements 저와함께계시고순간순간명철한지혜와능력을주신하나님께감사와영광을드립니다. 삶과학문에있어실천으로그깊이와넓음을몸소보여주시고, 늘자상한가르침으로오늘까지이끌어주신윤형로교수님께진심으로감사드립니다. 바쁘신가운데도부족한논문을심사기간내내따뜻하고세심하게지도해주신이경중교수님, 신태민교수님, 장세진교수님, 유병수교수님께머리숙여감사드립니다. 학부와대학원생활동안학업을통해많은가르침으로배움의기회를주신이윤선교수님, 김동윤교수님, 윤영로교수님, 김영호교수님, 김한성교수님, 정병조교수님께도깊이감사드립니다. 특별히학업의끈을놓지않고엔지니어로서의삶을그릴수있도록본이되어주신오건민회장님께진심으로감사드립니다. 학업과인생의대선배로서본이되어주신길문종회장님과김기원사장님께감사드립니다. 연구실에서함께하며성실함을보여주신염호준박사님, 임택균박사님, 홍수용선배님께감사드립니다. 그리고늘친동생처럼아끼고도와주신전대근박사님, 치열함과긍정으로삶에진지할수있도록이끌어주신김응석박사님, 성실함과겸손함을행동으로알려주신박성빈박사님께진심으로감사드립니다. 길지는않았지만연구실생활을통해작은부분까지보살펴주신김동석선배님, 이정우선배님, 강동원선배님, 이찬오선배님께감사드립니다. 특히논문을준비하는동안불평없이한결같이도와준명헌이와연식이, 민용이, 찬솔이, 주홍이에게도고마움을전합니다. 그리고돌아보면너무즐거웠던시간을함께한문재국선배님, 김해관선배님과진술이와홍일점유나에게도감사의맘을전합니다. 늘당당하고자랑스러운친구상돈이와나에게만은항상따뜻한현웅이, 부족한저를항상믿어주는재영이, 언제봐도멋진광재, 끈임없이노력하는정인철박사, 한결같은계형이에게진심으로고마움을전합니다. 그리고 MI FORUM의모든형제들 - i -

5 에게감사의말씀을드립니다. 지칠때마다따뜻한관심과사랑을주신류기홍박사님과형수님께특별히감사드립니다. 항상도움만받게되는성홍모박사님, 이전박사님그리고이승형선배님께도감사의맘을전합니다. 후배지만배울것이많은조성필박사, 김태균박사, 기수, 덕현, 균정에게도고마움을전합니다. 그리고모든대학원선 후배님들께진심으로감사드립니다. 함께살면서슬픔은나눠서반이되고즐거움은함께해서배가될수있었던영대, 수일, 재원, 희경, 정진, 대연, 호정이와모든 95동기들에게형제애로감사합니다. 가장가까운곳에서큰힘이되어주는한상훈선배님과김성환선배님, 이미동료로서훌쩍커버린기태, 지용, 준섭, 현륭, 동영및동고동락한메디게이트동료여러분께진심으로감사드립니다. 치열한사회에서만났지만형재같이따뜻하게오랜시간함께해주신현계환사장님, 기윤성사장님, 임도진사장님, 성용훈사장님과이상대사장님께도늘감사드립니다. 희망과꿈으로어린시절부터함께해온신혜, 민규, 혜정, 혜숙이와윤영, 문선, 치영, 호정과은진교회여러분께멀리서감사의마음을전합니다. 그리고늘기도와말씀으로도와주시는예원교회김진형목사님과예원교회식구들께도진심으로감사드립니다. 부족한사위를믿고지켜봐주시는장인어른과항상밝은미소와기도로힘이되어주시는장모님, 미국에서공부하시는처형가족특히이쁜주희, 큰처남부부와작은처남까지모두사랑하고감사드리며가까이서돌봐주시는이모부님과이모님에게도감사의마음을전합니다. 그리고항상물심양면으로아낌없이도와주시고격려의말씀을아끼지않으셨던고모님, 고모부님과힘들때마다힘이되어주신외가댁식구들에게도진심으로감사드립니다. - ii -

6 지금의제가있기까지묵묵히희생으로버팀목이되어준우리재호형, 언제나막내를자랑스러워하고챙겨주는우리수연이누나, 가장으로서남자가가야할길을알려주시고무한한사랑으로모든것을내어주신존경하는아버지, 기도와겸손으로일생을헌신하시는생각만하면눈시울이뜨거워지는우리어머니사랑합니다. 용의해에태어날아직은엄마뱃속에있는소중한튼똘이와작은것에도감사하고기뻐할줄아는내삶에소중함과열정, 그리고목표자체가되어준사랑하는아내하보라에게희망찬미래와함께감사와사랑한다는말을전합니다. 마지막으로넘치는사랑을주신모든분들께빚지는마음으로이작은결실을바칩니다 년 1 월 서광석드림 - iii -

7 Table of Contents List of Figures... vi List of Tables... ix Abstract... x Chapter 1 Introduction Purpose Research hypotheses Definition of terms... 4 Chapter 2 Literature Review Methods for determining stroke volume and cardiac output Physiological background Measurement of cardiac output limitation of existing method Impedance cardiograpy Measurement principle of impedance cardiography The method of stroke volume calculation Lumped parameter model Heart model Artery model Chapter 3 Methods Subjects Experimental procedure Development system for SV and CO determination System configuration Measurement of ICG using both hands iv -

8 3.4 Mathematical analysis of non-uniform hybrid model based on forward lumped parameter Determination of SV and CO Algorithm by non-uniform hybrid model based on forward lumped parameter Developed system reproducibility Statistical analysis Chapter 4 Results SV and CO estimation by development System SV and CO predication by non-uniform hybrid electrical impedance model based on forward lumped parameter Evaluation of CO by non-uniform hybrid electrical impedance model based on forward lumped parameter and both hands impedance measurement system Chapter 5 Discussion Chapter 6 Conclusions References Abstract(in Korean) Appendix 1- IRB Approved Appendix 2- Clinical Trial Report Appendix 3- Case Record Form Appendix 4- Explanation Appendix 5- Consent v -

9 List of Figures Figure 2.1. The anatomy of heart Figure 2.2. The cardiac cycle with four different phases... 7 Figure 2.3. Relationship between ventricular diastolic-end volume of ventricle... 9 Figure 2.4. Effect of sympathetic nerve stimulation of heart on stroke quotient Figure 2.5. Effect of sympathetic nerves on contraction and relaxation of ventricle Figure 2.6. Main factors for deciding cardiac output Figure 2.7. Schematic view of the factors that play an important role in the regulation of the cardiac output Figure 2.8. The Fick method to determine the cardiac output Figure 2.9. Examples of two indicator dilution curves with recirculation at the end and the area filled with dot is the area under the extrapolated curve Figure Electrode attachment method Figure Effect of distance between electrodes and electrode size on current pass Figure Representing the beating ventricle as a Windkessel with inflow and outflow valves and a time-varying compliance Figure 3.1. Flow of participants throughout the trial Figure 3.2. Experimental procedure Figure 3.3. Experimental environment Figure 3.4. System configuration Figure 3.5. Hardware block diagram Figure 3.6. The result of body impedance calibration Figure 3.7. Produced system and hand-grip electrode Figure 3.8. Results of vector plot through modeling Figure 3.9. Pressure-Volume diagram for either ventricle Figure A typical blood vessel Figure Flow of blood from heart to upper and lower parts through aorta Figure Diagram of lossless and lossy transmission equation vi -

10 Figure Non-uniform hybrid systemic circulation model based on forward lumped parameter Figure Non-uniform hybrid upper and lower model based on forward lumped parameter Figure Impedance equivalence model for model presented in this study Figure Flowchart of the proposed algorithm for SV and CO determination Figure 3.17 Pulse raw data of thoracic and both-hands pulses (a) and Spectra arrived at by FFT analysis of thoracic and both-hands pulses (b) Figure Time domain reconstruction of (a)thoracic and (b)both-hand spectra over firstfour peak frequency Figure Reconstructed flow waveform by non-uniform hybrid Model based on forward lumped parameter Figure Reproducibility experiment protocol Figure 4.1. Measured and estimated SV(ml) in (a) male and (b) female Figure 4.2. Measured and estimated CO(l) in (a) male and (b) female Figure 4.3. Scatter plot graphs of relationship between measured and estimated SV (ml) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female Figure 4.4. Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between measured and estimated SV(ml), plotted against the mean in (a) male and (b) female Figure 4.5. Scatter plot graphs of relationship between measured and estimated CO (l) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female Figure 4.6. Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between measured and estimated CO(l), plotted against the mean in (a) male and (b) female Figure 4.7. Measured and modeled SV(ml) in (a) male and (b) female Figure 4.8. Measured and modeled CO(l) in (a) male and (b) female vii -

11 Figure 4.9. Scatter plot graphs of relationship between measured and estimated SV (ml) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female Figure Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between measured and estimated SV(ml), plotted against the mean in (a) male and (b) female Figure Scatter plot graphs of relationship between measured and estimated CO (l) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female Figure Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between measured and estimated CO(l), plotted against the mean in (a) male and (b) female Figure Modeled and estimated SV(ml) in (a) male and (b) female Figure Modeled and estimated CO(l) in (a) male and (b) female Figure Scatter plot graphs of relationship between modeled and estimated SV (ml) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female Figure Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between modeled and estimated SV(ml), plotted against the mean in (a) male and (b) female Figure Scatter plot graphs of relationship between modeled and estimated CO (l) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female Figure Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between modeled and estimated CO(l), plotted against the mean in (a) male and (b) female viii -

12 List of Tables Table 3.1. Baseline Characteristics of Included Participants Table 3.2. Properties of each organ (at 100kHz) Table 3.3. Reproducibility test Table 4.1. Description of physioflow SV, CO and developed system SV (ml), CO(l) Table 4.2. Paired Samples Test and Wilcoxon Signed Ranks Test results between physioflow and developed system SV, CO in males (N=54) Table 4.3. Paired Samples Test and Wilcoxon Signed Ranks results between measured and estimated SV, CO in females (N=18) Table 4.4. Description of physioflow SV, CO and modeled SV (ml), CO(l) Table 4.5. Paired Samples Test and Wilcoxon Signed Ranks Test results between physioflow and modeled SV, CO in males (N=54) Table 4.6. Paired Samples Test and Wilcoxon Signed Ranks Test results between physioflow and modeled SV, CO in females (N=18) Table 4.7. Description of modeled SV, CO and developed system SV (ml), CO(l) Table 4.8. Paired Samples Test and Wilcoxon Signed Ranks Test results between modeled and developed system SV, CO in males (N=54) Table 4.9. Paired Samples Test and Wilcoxon Signed Ranks Test results between modeled and developed system SV, CO in females (N=18) ix -

13 Abstract Evaluation of Cardiac output by non-uniform hybrid electrical impedance model based on forward lumped parameter and both hands impedance measurement system Kwangseok Seo Dept. of Biomedical Engineering The Graduate School Yonsei University In this dissertation, cardiac output using non-uniform hybrid electrical impedance model, which is based on the forward lumped parameter and the both-hands impedance measurement system, is proposed. This noninvasive method for cardiac output monitoring has been clinically accepted as a replacement for thermo dilution, the gold standard in cardiac output measurement. Alternatively, measurement using impedance cardiogram, which has several distinct advantages, has been identified as a promising method for cardiac output measurements. The thoracic impedance cardiogram (ICG) has been proposed as a noninvasive, continuous, operator-independent, and cost-effective method for cardiac output monitoring. However, this method is generally regarded to be restrictive because measurements are performed using a band or spot-type electrode adhered to the body. Traditionally, lead has been used for such measurements, thus rendering the entire system highly inconvenient because the assistance of - x -

14 a specialist is required. Further, the development and attachment of the lead electrode, used with the traditional system, is both expensive and complicated. In this dissertation, we evaluate the effectiveness of the proposed non-uniform hybrid model, which is based on the forward lumped parameter. This system seeks to combine the existing lumped parameter method and the non-uniform hybrid model to create a coherent system capable of leveraging the advantages of both approaches. For developing an effectiveness rating for cardiac output measurements using both hands, the presented model was mathematically interpreted and the relevant results were compared and analyzed against the stroke volume and the cardiac output of the thoracic impedance measurements (Physio FlowR-PF104D, Manatec Biomedical, France). To develop the non-uniform hybrid electrical impedance model, based on the forward lumped parameter and the both-hands impedance measurement system, 80 subjects (58 male, 22 female) from Yonsei University and the surrounding areas, aged years, participated in this study. All participating subjects completed stroke volume and cardiac output tests through PhysioFlow and the developed system. In the developed system, electrodes are used to gripping on both-hands instead of attaching to the chest. Similar to previously adopted noninvasive cardiac output tests, the developed system measures stroke volume through impedance changes over each cardiac cycle. Additionally, this study compares cardiac output measurements in the thorax and in both hands. These measurements and comparisons were verified using the presented non-uniform hybrid model. To verify the proposed approach, statistical methods such as correlation analyses, paired T-test, and the Bland-Altman plot were used. For verification of the non-uniform hybrid electrical impedance model, the presented value of r, scatter plot, and the Bland-Altman plot of measured and estimated SV and CO were used. - xi -

15 The results were as follows: 1) The SV/CO obtained from the PhysioFlow and the proposed approach (developed system) showed significant correlation in both male and female SV (r = 0.715, P < 0.001; r = 0.704, P < 0.001, respectively) and CO (r = 0.826, P < 0.001; r = 0.804, P < 0.001, respectively). 2) The SV/CO obtained from the PhysioFlow and the proposed approach (non-uniform hybrid electrical impedance model based on the forward lumped parameter) demonstrated significant correlation in both male and female SV (r = 0.735, P < 0.001; r = 0.827, P < 0.001, respectively) and CO (r = 0.767, P < 0.001; r = 0.853, P < 0.001, respectively). 3) The SV/CO obtained from the non-uniform hybrid electrical impedance model and the development system showed significant correlation in both male and female SV (r = 0.788, P < 0.001; r = 0.812, P < 0.001, respectively) and CO (r = 0.802, P < 0.001; r = 0.823, P < 0.001, respectively). From these results, it can be concluded that SV and CO can be measured using the bothhands cardiac output measurement method at low cost and convenient without the help of a specialist. Furthermore, this system was verified by using the developed model as a substitute for the existing method. Key words: Cardiac output (CO), Stroke volume (SV), Impedance cardiogram (ICG), Hand grip electrode, PhysioFlow(PF104D) - xii -

16 Chapter 1 Introduction For many patients in the intensive care unit, emergency medicine unit, or those being investigated for some cardiovascular complaint, simply measuring heart rate (HR) and blood pressure does not provide adequate data on their hemodynamic state. Together with an electro cardiogram (ECG) and blood pressure (BP) monitoring, the measurement of cardiac output (CO) and stroke volume (SV) can play a major role in the diagnosis and therapy of chronic cardiac conditions such as heart failure, hypertension, coronary artery disease, pericardial disease, obstructive lung, pleural disease, and renal disease/dialysis [1 3]. CO determination is an important procedure in interventional cardiology and has also been used in cardiothoracic surgery [4]. CO and SV are the functional expressions of cardiovascular performance and can be used to confirm the need for, or efficacy of, various treatment options. CO and SV are reliable indicators of cardiac performance, the measurement of which is essential for the monitoring and assessment of cardiac disorders or other conditions of hemodynamic compromise. These two parameters essentially define the average blood flow in the entire cardiovascular system. In light of the intended use of cardiac output as a medical diagnostic tool, the associated measurement technique must be clinically acceptable and reliable. In clinical practice, several, invasive CO- and SV-estimation methods are available, such as Fick s method, dye-dilution, and thermo-dilution. Currently, thermo-dilution is the most commonly used method for measuring cardiac output. It is still the gold standard in CO and SV estimation. These require catheterization of the patient, which itself adds to the morbidity and sometimes mortality of the patient. When catheterization is performed, the thermodilution method may be utilized to monitor cardiac output and make appropriate decisions regarding flow modulation through drug therapy. Outside intensive care units, however, - 1 -

17 catheters are usually removed, and the thermo-dilution method is abandoned. It gives only intermittent measurement of cardiac output of the patient. Consequently, little information is available regarding cardiac output after the critical stages of recovery. To date, noninvasive methods have been clinically accepted as replacements for the thermo-dilution method, which was traditionally the gold standard for cardiac output measurement [5, 6]. Alternatively, the impedance cardiogram method, with its numerous advantages, is a promising method for measuring cardiac output [7-9]. A thoracic impedance cardiogram (ICG) approach has been proposed as a noninvasive, continuous, operatorindependent, and cost-effective method for cardiac output monitoring. Currently existing impedance based cardiac output monitors operate by emitting a low voltage (2.5 to 4 ma), high-frequency (50 to 100 khz), and alternating electric current through the thorax via spot or band electrodes. The electrical impedance changes, caused by changes in the volume and velocity of blood flow in the thoracic aorta (within the thorax), are detected via the electrodes as pulsatile decreases in impedance (dz). The impedance can also be further expressed as its derivative (dz/dt). This derivative has been shown to be proportional to the stroke volume. Along with heart rate, stroke volume can indicate the CO of the patient. Charloux et al. researched the effects of thoracic hyperinflation through ICG and Koobi et al. used full-body ICG to compare thermo dilution and the direct Fick s method in order to show that ICG reliably and reproducibly estimates CO in sedated preoperative patients without marked valvular disease [10]. However, this method is considered restrictive, because it requires the application of band or spot-type electrodes on the body. As previously mentioned, the inclusion of lead in the attachment process materializes into compounded expense and inconvenience because specialists must be involved

18 1.1 Purpose This study presents a system for detecting clinical indicators of Stroke Volume (SV) and Cardiac Output (CO), which reflect hemodynamic function of cardiovascular activity through electric impedance measurement method using both hands, rather than measurement of Cardiac Output using previously accepted invasive methods, ultrasound, and thorax-related measurements. The purposes of this study were to (1) develop a system for detecting SV and CO through the noninvasive and convenient both-hand ICG measurement method, (2) develop the nonuniform hybrid model based on the forward lumped parameter and present the advantages of the previous lumped parameter method and non-uniform hybrid model to evaluate the effectiveness of a combined system, (3) conduct mathematical interpretation of the presented model and compare the SV/CO results for the thoracic impedance to verify the effectiveness of the both-hand CO measurement presented in this study. 1.2 Research hypotheses It was hypothesized that: 1) During cardiac systole, blood is released through the main artery and the electrical impedance method can detect the discharge of blood. 2) The increasing number and decreasing size of blood vessels trends from the central to the peripheral blood vessel system. It shows the biggest change in discharge near the center of the body. If the injected current, passing through both hands, contains discharge from the left ventricle, it can draw the same result as the original cardiac output measurement

19 3) According to the blood dynamic methods, through the use of the direct parameter model of Systemic Simulation, we can effectively estimate the indirect cardiac output and thus compile a proposed system model. 1.3 Definition of terms 1) Stroke Volume (SV) : Amount of blood pumped by the left ventricle each heart beat[ml] 2) Cardiac Output (CO): Amount of blood pumped by the left ventricle each minute[l/min] CardiacOutput Heart Rate X Stroke Volume 3) Impedance Cardiogram (ICG): Harmless current is exerted to measure impedance change in artery according to the amount of blood during cardiac impulse in voltage form. This method achieves noninvasive acquisition of data according to cardiac impulse and monitors dynamic function of heart, such as cardiac output, Stroke Volume, and contractile power of heart muscle. 4) Z 0 (Body impedance): Basic impedance of the body segment limited by receiving electrodes [Ω] [Ω] 5) Z(ICG): Changes of the impedance of the segment limited by receiving electrodes 6) dz/dt(1'st derivation of ICG): The maximum of the first derivative of the impedance signal (Ω/sec) 7) Bland-Altman plot: A statistical method of data plotting used in analyzing the agreement between two different assays

20 Chapter 2 Literature Review This chapter consists of three parts: 2.1. Methods for determining stroke volume and cardiac output describes the physiological background of the cardiovascular system and explains the existing method for measuring SV and CO and relevant limitations. 2.2 Methods for determining impedance cardiogram, uses an impedance cardiogram to explain principles for determining CO and SV, and introduces various calculation methods. 2.3 Lumped Parameter Model explains the approach method and trend of previous model-based studies. 2.1 Methods for determining stroke volume and cardiac output Physiological background 1) The heart The heart is enclosed in a double-walled sac, which is called the pericardium. The pericardium protects the heart, anchors it to the surrounding structure and prevents over filling of the heart with blood. The heart wall consists of three layers. The outer wall is called the epicedium, the middle layer the myocardium and the inner layer, the endocardium. The pericardium is often infiltrated with fat, especially in older people. The myocardium is the thickest of the three layers and is the layer that actually contracts. The endocardium consists of a white sheet of endothelium resting on a connective tissue layer and covers the connective tissue skeleton of the valves. The heart functions as a pump and can be divided in four chambers, the left atrium, the left ventricle, right atrium and right ventricle, see Figure

21 The left atrium and the left ventricle are separated by the mitral valve. From the left ventricle the blood flows into the circulatory system through the aortic valve into the aorta. The blood enters the right atrium through three veins. The superior vena cava returns blood from above the diaphragm, second the inferior vena cava returns blood from below the diaphragm and the last returning blood flow is from the coronary veins of the heart. The right atrium and right ventricle are separated by the tricuspid valve. The blood enters the pulmonary artery through the pulmonary valve. Then the blood flows to the right lung and left lung through the right pulmonary artery and left pulmonary artery. Figure 2.1. The anatomy of heart. 2) The cardiac cycle The cardiac cycle can be divided in four phases: the diastolic phase, the isovolumic contraction phase, the ejection phase and the isovolumic relaxation phase, see Figure 2.2. In the first part of the diastolic phase when the mitral valve is opened the ventricle is filled with - 6 -

22 blood. In the last part of the diastolic phase an action potential is generated by the sinus node, located in the right atrium and causes an additional filling of the left atrium. The action potential will travel rapidly through both atria and through the A-V bundle and the conducting system and causes the initiation of the contraction of the ventricles. The ventricular pressure will increase and causes the mitral valve closure and marks the beginning of the isovolumic contraction phase. In this phase the ventricular volume remains constant, but the ventricular pressure increases. When the ventricular pressure rises above the pressure in the aorta, the aortic valve will open and the ejection phase begins. During the ejection phase, the aortic and ventricular pressure increase to its maximum and then decreases, at the point where the ventricular pressure is less than the aortic pressure, a slightly aortic back flow occurs which results in the closure of the aortic valve. This marks the beginning of the isovolumic relaxation phase. In this phase the ventricular volume remains constant and the pressure of the ventricle will decrease. As soon as the ventricular pressure drops below the atrial pressure, the mitral valve will open and the cardiac cycle begins again. Figure 2.2. The cardiac cycle with four different phases, diastolic, isovolumic contraction, ejection, and isovolumic relaxation and the time course of left ventricular pressure (plv), aortic pressure (pao), left atrial pressure (pla) and left ventricular volume (Vlv). Typical volumes of left ventricle at two time points are the end-diastolic volume EDV and end-systolic volume ESV

23 3) The cardiovascular system The function of the circulation, which consist of the heart and the blood vessels, is to supply the tissues in the body with oxygen and nutrients and to transport waste products away. The regulation of the circulation to satisfy the oxygen demands through the body is controlled by the autonomic nervous system. The autonomic nerves system can be divided in the sympathetic nervous system and the parasympathetic nervous system. The sympathetic nervous system is activated in stressful, emotional situations or by physical activity and the parasympathetic nervous system is more active in rest, and for example stimulates the organs for digesting food. When sympathetic stimulation excites the blood flow to a particular organ, often parasympathetic stimulation inhibits it. That is, the two systems occasionally act reciprocally to each other. However, the blood flow to most organs is mainly controlled by one of the two systems. For the control of blood flow, the effect of the two systems on arterial pressure, on the blood vessels, and on the heart are most significant. Blood pressure is regulated by means of the baroreceptor reflex. The baroreceptor reflex is the most powerful tool in the control of systemic arterial pressure. Baroreceptors are lying in the walls of the carotid sinus and the aortic arch. As soon as the blood pressure falls and the baroreceptors are less stimulated, the sympathetic nervous system is activated and the parasympathetic activity is decreased. As a consequence, heart rate and cardiac contractility increase and the small arteries and large arterioles are constricted. This way the arterial blood pressure is regulated towards steady state again. Most blood vessels are constricted by sympathetic stimulation. Sympathetic constriction of the small arteries and the large arterioles increases the resistance and therefore reduces the blood flow through the vessels. Sympathetic stimulation of the veins decreases the volume of these vessels and therefore translocates the blood into the heart. Parasympathetic stimulation has little or no effect on blood vessels. It merely dilates vessels in certain restricted areas, such as in the blush area of the face. The heart is controlled by both systems. Sympathetic stimulation increases the heart rate and enhances cardiac contractility. Parasympathetic stimulation causes mainly the opposite effects, it decreases the heart rate and also slightly decreases contractility. In short, sympathetic activity increases the effectiveness - 8 -

24 of the heart as a pump whereas parasympathetic stimulation decreases the pumping capability of the heart. 4) End diastolic volume (Frank-Starling s law) End-diastolic volume (EDV) is the intraventricular blood volume directly before contraction. This is also called pre-load as it is the work quantity imposed on the ventricles of heart before contraction. The stroke volume per session is in direct proportion with the preload. Heart ventricles perform stronger contraction during the contraction period if more blood is filled during diastole. Thus, the stroke quotient increases with the end-diastolic capacity under identical conditions. This relation is presented on the ventricular function curve (see Figure 2.3). The relation between stroke quotient and end-diastolic capacity is called the Frank-Starling mechanism. Under stable conditions, the length of the heart muscle is not optimal for contraction like skeletal muscle but is positioned in the up-phase of the curve. Thus, the length of the myocardial fiber is increased with the increase in blood within ventricles along with an increased contractile force. Figure 2.3. Relationship between ventricular diastolic-end volume of ventricle (Frank- Starling s mechanism) - 9 -

25 In Frank-Starling s mechanism, end-diastolic capacity increases with higher venous return, thus the quantity of blood returning to the heart through veins, during an identical pulse rate. Furthermore, cardiac output is automatically increased with increased pulse rate. 5) Contractility of the myocardium The sympathetic nerve is diffused throughout the entire heart muscle, and the norepinephrine secreted from sympathetic nerves combines with the beta-adrenaline operational acceptor to increase ventricle contractility. Ventricle contractibility refers to the contraction in stable end-diastolic capacity. Plasma epinephrine also combines with the same acceptor to increase ventricle contractility. Figure 2.4. Effect of sympathetic nerve stimulation of heart on stroke quotient As shown in Figure 2.4, ventricle contractility is increased in the Frank-Starling mechanism under identical end-diastolic capacity, and thus identical length of heart muscle,

26 due to the stimulation of the sympathetic nerves. In other words, an increase in contractibility leads to greater emission of blood within the end-diastolic ventricle. Increased stimulation of sympathetic nerves for a ventricle not only increases contractibility but also expedites contraction and relaxation of the ventricle to increase pulse rate (see Figure 2.5). Increased pulse rate reduces the ventricular filling time at diastole. However, this problem is partially compensated as a large part of the cardiac cycle can be used to fill up the ventricle with accelerated contraction and relaxation speed by sympathetic nerves. Figure 2.5. Effect of sympathetic nerves on contraction and relaxation of ventricle 6) Afterload Afterload is the resistance force generated in the ventricular wall during blood eruption in the left ventricle. Increased afterload reduces stroke volume. This is because arterial blood pressure acts as load for contracted ventricular muscles like skeletal muscle. Increased load in ventricular muscles reduce contraction of heart muscle. Thus, increase in arterial blood pressure reduces stroke quotient. Figure 2.6 presents a diagram of the effect on CO by main factors that decide stroke quotient and heart rate

27 Figure 2.6. Main factors for deciding cardiac output 7) Cardiac output Cardiac output is the amount of blood that is pumped by the heart into the aorta each minute. It equals the product of heart rate and stroke volume. With a heart rate at rest of 70 beats/min and a stroke volume of 70ml the heart pumps about 4:9L=min and this amount can increase to about four to seven times during heavy exercise. Stroke volume (SV) represents the difference between volume of blood in the ventricle at the end of the diastolic phase, the end-diastolic volume (EDV) and the volume of blood that remains in the ventricle after its contraction, the end-systolic volume (ESV): SV[ ml] EDV[ ml] ESV[ ml] (2.1)

28 The pumping ability of the heart depends on contractility, preload, afterload and heart rate. The most important factors that affect the SV by causing changes in EDV or ESV are the contractility, the force of contraction of the cardiac muscle cells, preload, which is the degree of stretch of the cardiac muscle cells before contraction and the afterload, the pressure that must be overcome for the ventricles to eject blood from the heart. Afterload influences stroke volume by affecting the velocity of contraction. The intact heart can increase its contractility with the help of the Frank-Starling mechanism. The Frank-Starling mechanism means the intrinsic ability of the heart to adapt to changing loads of inflowing blood. The heart pumps all the blood that comes to it into the aorta without allowing excessive damming of blood in the veins. If the amount of blood returning to the heart is increased (larger EDV), causing the preload to increase, the cardiac muscle is stretched more and, in turn, contracts with increased force. The increased force of contraction is probably caused by the fact that the contractile proteins become more sensitive for calcium when they are stretched. Also the contractility can be increased by extrinsic control by the sympathetic nervous system activity. The contractility increase caused by the activation of the sympathetic nervous system is independent of the stretch of the cardiac muscle fiber and the EDV. The sympathetic stimulation is responsible for the increases in heart rate. In contrast the parasympathetic nervous system reduces the heart rate. The factors that are involved in the regulation of the cardiac output are shown in Figure

29 Figure 2.7. Schematic view of the factors that play an important role in the regulation of the cardiac output

30 2.1.2 Measurement of cardiac output 1) Fick method The cardiac output can be calculated by using the Fick principle. The Fick principle is based on the uptake of oxygen by blood as it flows through the lungs. It is assumed that all oxygen molecules in the pulmonary vein has its origin from the blood in the pulmonary artery or from the oxygen transported from the lung to the blood. The oxygen that enters the blood is reflected by the difference in oxygen content between the pulmonary vein and the pulmonary artery, assuming that no oxygen is consumed by the tissues between the pulmonary artery and vein. Because the entire output of the right heart passes through the lungs, assuming that there are no shunts across the pulmonary system, the blood flow through the lungs is equivalent to cardiac output. This can be written as [11]: F O2 CO CO C C ao2 ao2 F O2 C CO C vo2 vo2 (2.2) with F O2 the oxygen flow from lung to blood in mlo 2 / min, CO the cardiac output in L / min and C vo2 and C ao2 the oxygen contents of vein and artery in mlo 2 / L. In Figure 2.8 an example of the Fick method is shown. Because it is impossible to measure the rate at which oxygen is taken up by the capillaries, the rate of oxygen uptake must be measured at the mouth. Then F O2 is often expressed as V O 2. The error introduced by measuring oxygen at the mouth is unimportant if the period of measurement is much longer than the time of a single breath. [12] The VO 2 can be measured by making use of spirometry. The values of C vo2 and C ao2 can be determined indirectly by taking blood samples at the appropriate location. Because the concentrations fluctuate due to the pulsations caused by respiration and circulation the values has to be averaged for a sufficient time. The arterial oxygen content of

31 blood can be sampled at any convenient location in the large arteries, since oxygen transfer to the tissues only take place in the capillaries. Figure 2.8. The Fick method to determine the cardiac output In contrast, the venous oxygen content in blood can very significant between measuring sites, because it depends on how much oxygen the organs have extracted. Only where the different oxygen contents from the veins merge, like the right atrium, right ventricle or pulmonary artery, the so called mixed venous oxygen content, can be measured. The oxygen in the blood is primarily bounded to hemoglobin as oxyhemoglobin. The O 2 carrying capacity of hemoglobin Hb is 1.34 (ml O 2 / gram Hb). The oxygen content of the blood can then be calculated by: C C ao2 vo2 Hb1.34 S Hb1.34 S ao2 vo P 0.031P ao2 vo2 (2.3)

32 with Hb the concentration of hemoglobin in blood in gram / L. S ao2 and S vo2 are the oxygen saturation of blood in %. The oxygen saturation at the arterial site, S ao2 can also be measured continuously with a pulse oximeter. The mixed venous oxygen saturation, S vo2, can be measured continuously with a pulmonary artery catheter. P ao2 and P vo2 represents the partial pressure of oxygen at the arterial and venous site in mmhg and is the solubility coefficient of oxygen in blood in ml O 2 / L mmhg. For the continuously measurement of the cardiac output the partial oxygen pressures are often ignored, because it has only a small contribution. 2) Indicator dilution methods The indicator dilution method is very similar to the Fick method, but instead of the measurement of oxygen, the concentration of an indicator is measured. In indicator dilution methods a bolus of an indicator is brought into the blood stream and the concentration of the indicator is measured downstream. There are many indicators like chemicals, inert gases, radioactive isotopes, dyes and heat. [11] The indicator dilution method is based on the following theory. If the concentration of a small known bolus that is uniformly dispersed in an unknown volume V is determined, and the volume of the injected indicator is known, then the unknown volume can be determined too [13]: dv( t) ( t) dt (2.4) where (t) and (t) V are the instantaneous flow and volume of the carrier. Then the next expression counts too: c( t) dm dv (2.5)

33 with m and c (t) the mass of the tracer and its concentration at time t. Then the following equation can be derived: dv ( t) ( t) dt 1 c( t) dm dt (2.6) Because only the averaged flow determines how much indicator is transported and not the fluctuations of the flow the previous equation can be rewritten into [19, 22]: m 0 CO ( t) c( t) dt CO 0 m c( t) dt 0 c( t) dt (2.7) The instantaneous flow (t) can be expressed as the cardiac output CO and put out of the integral. Before the concentration decreases to zero, some of the indicator has already circulated and passes the measurement site for the second time, this is also called recirculation, see Figure 2.9. Because of this phenomenon an extrapolation is necessary for the calculation of the area of the curve without circulation. The basic assumption of indicator dilution techniques for the injection of a bolus are that the blood flow is constant during the measurement, there is no loss of the indicator, and the mixing of the indicator is uniform and the rapid injection can be modeled as an impulse

34 Figure 2.9. Examples of two indicator dilution curves with recirculation at the end and the area filled with dot is the area under the extrapolated curve. 3) Doppler ultrasound Measurement of stroke volume using trans-esophageal echocardiography can be achieved by measuring blood quantity flowing through the left ventricular outflow tract, aorta, or pulmonary artery. In this case, blood flow is laminar flow rather than turbulent flow, the conduit in which blood flow passes through continuously maintains a circle form and the area is assumed to be π (radius) 2. A continuous wave Doppler or pulsed wave Doppler is used to acquire the following expression: CO VTI CSA cos HR VTI : Velocity Time Interval CSA : Cross Sectional Area (2.8)

35 4) Impedance cardiogram Capacity change in the thorax triggers changes in the thoracic electrical bio-impedance. If changes in thoracic resistance are measured according to the ventricular depolarization, stroke volume can be continuously measured. The alternating current resistance cardiac impulse method is a noninvasive method in which four sets of ECG electrodes are attached to the thorax to emit sample micro-currents and detect bio-current resistance on both sides of the thorax. To measure bio-current resistance of the thorax, low-voltage, high-frequency pulses of alternating currents are applied and detection is simultaneously performed in two sets of electrodes located near the neck and xiphoid process. Owing to recent technical and program advances, high correlation was presented between the two methods in several studies conducted with regard to the use of the thermo-dilution method on healthy adults, critical patients, and surgical patients (excluding heart surgery patients) [14, 15] Limitation of existing method 1) Thermal indicator dilution method By using the Swan-Ganz catheter to measure cardiac output, the thermo-dilution method can simultaneously measure systematic circulation resistance, pulmonary arterial pressure, and pulmonary artery wedge pressure to be useful for diagnosing hemodynamically unstable patients. However, measurement is inaccurate for cases with low cardiac output. 2) Dye dilution method Using indocyanine green as the indicator of cardiac output, dye-dilution was the most commonly used method before the thermo-dilution method. This method is disadvantageous in that it presents difficulties in calculating the area under the primary recurring curve and in that, arterial blood must be collected

36 3) Lithium dilution method This method calculates cardiac output by measuring the concentration of lithium through the detection device connected to the peripheral artery catheter after injecting lithium chloride through the central venous catheter or peripheral vein catheter. This method can achieve quick, easy measurement of cardiac output by using the previously inserted central venous catheter and arterial catheter without inserting the pulmonary artery catheter. Lithium is excreted through urine without metabolism within the body and is not combined with plasma or protein. Although clinical utility has been verified among young critical patients and in the intensive care unit after coronary artery surgery, data on the clinical utility in a surgical environment remains insufficient as sudden hemodynamic changes are presented with the frequent collection of arterial blood. 4) Doppler ultrasound method The accuracy of the cardiac output calculated using this method depends on the accuracy of the blood vessel diameter measurement and the parallelism of the ultrasound beam and the direction of blood flow. Although this method presents high accuracy and clinical credibility, it is disadvantageous in that it is dependent on the operator and has a long measurement time. 5) Impedance cardiogram method This method is disadvantageous in that it is easily affected by electric interference, the attachment status of the ECG electrode, and can exhibit low resistance to alternating current in relatively heavy patients. In addition, the accuracy of this method is low for patients that have received heart surgery, and in patients with pulmonary edema or aortic valve disease [16]

37 2.2 Impedance Cardiogram Measurement principle of impedance cardiography 1) The impedance signal The thoracic impedance consists of three components. The largest component, the baseline impedance Z 0, is the electrical impedance of the total thoracic mass, which include the different tissues, fluid and air. The second component corresponds with the changes due to respiration, Z r (t). The third component is related to the changes caused by the cardiac cycle, Z c (t). This gives the next equation [17]: Z(t) = Z 0 + Z r (t)z c (t) (2.9) The values of Z 0 is about 25Ω for healthy men. The changes of the impedance signal induced by respiration is about 1Ω. The third and smallest variation due to the cardiac cycle in the impedance signal is approximately 0.1Ω to 0.2Ω. The contribution to the changes in the thoracic impedance signal, especially the cardiac related changes Z c, has its origin for about 61% from the lungs, 23% from the large arteries and about 13% from the skeletal muscles. [18] The amplitude caused by the respiratory component is much larger than the amplitude of the cardiac component, but the frequency of the cardiac component is higher than at the respiratory component. Therefore, in the first derivative of Z, the thoracic impedance change from the respiratory and cardiac component together, strongly reffects the signal of the cardiac component.[19] 2) Frequency and current value Impedance (Z; ohm) is composed of a complex amount because it generates phase-shift in biomaterial Impedance (Z: ohm) is a complex quantity because it generates phase shift in the biomaterial and in the time domain. The skin is composed of small inosculations of cells and

38 small cell membranes. As the skin includes a capacitor component, lower impedance is presented with higher frequency. The result is that the skin can be regarded as an insulator due to such a capacitor substance. Because skin impedance is extremely high at low frequencies (<1 khz), the electrical impedance can be ignored and the results obtained in the deep skin layer can be determined using high frequencies (>100 khz) [20]. There is general agreement in the medical community that frequencies between khz should be used and that the amplitude of the sinusoidal current curve, ought to rest somewhere between 1 and 5 ma [21]. However, some designers use a lower-than-suggested value of current. The lower boundary application is the suggestion leading to obtain the sufficient signal-to-noise ratio. A 1-mA current can create muscle excitation below 20 khz frequency and the skin-electrode impedance at 100 khz is approximately 100 times lower than that at low frequencies. This helps to diminish the unwanted impact of the changes in the skinelectrode impedance, occurring during motion, into measurable cardiac signals. However, applied currents of frequency greater than the 100 khz threshold result in stray capacitance. 3) Electrode types and Topography There are two main methods for measuring bioimpedance: bipolar and tetrapolar. In the bipolar method there are two electrodes that play a critical role in application and receiving. The current density in the regions near the electrodes is higher than in other parts of the tissue, thus influencing the overall impedance measurement in a non-uniform manner. The total impedance signal is a superposition of two components: the skin-electrode impedance (modified by blood flow-induced movement) and the original signal (caused by blood flow). In practice, it is difficult to separate the two variables. The scheme of the bipolar impedance measurement is presented in Figure 2.10(a). In a four-electrode (tetrapolar) configuration, the application electrodes and receiving are separated. Figure 2.10(b) presents the scheme of the tetrapolar impedance measurement and the typical means of obtaining the impedance cardiography signal. The constant amplitude current oscillates between the application electrodes; from this the voltage changes are detected on the receiving electrodes. Because the

39 amplitude of the current constant, this voltage is proportional to the impedance of the tissue segment limited by the band electrodes. The voltage changes are proportional to the impedance changes between the receiving electrodes. The main advantage of this method over the bipolar method is that the current density distribution is more uniform. Another advantage is that the disturbances caused by electrode impedances are minimized. (a) Bipolar (b) Tetra polar Figure Electrode attachment method 2-electrode methods are affected by the contact impedance of the electrodes and by the impedance frequency dependence observed during the impedance measurement. However, the 4-electrode method is a method for indirectly measuring impedance to remove electrode impedance and contact resistance. As presented in Figure 2.11, current enters deeply into the skin with greater distance between current-injected electrodes. Thus, the arrangement or distance of the electrodes affects the measurement of stroke volume and cardiac output

40 Furthermore, the electrode form can also affect cardiac output. In the study conducted by Jennifer J. Mcgrath, band-type and spot-type electrodes were used to measure ICG to present approximately 2x differences between the results of the targeted cardiac output. When compared with the use of band type electrodes, the use of spot electrodes can increase the signal quality, because it minimizes the motion artifact. Spot electrodes have approximately 45% higher signal-to-noise ratio than band electrodes, and present a low Z 0 value according to the degree of skin contact. These factors generate difference in results during the use of different types of electrodes [22]. Figure Effect of distance between electrodes and electrode size on current pass

41 2.2.2 The method of stroke volume calculation There are different methods of calculation a stroke volume (and in the consequence other hemodynamic parameters) using impedance signal, the characteristic points on the impedance waveform and parameters describing the physical dimension of the analysed segment of the human body. The usage of the different formulas may lead to the marked scattering of the results. Historically, the first was Kubicek formula [23, 24] derived from the Nyboer works [25, 26] signal. Let me describe shortly some of the formulas and methods using the historical order. 1) Nyboer Formula Atzler and Lehman [27], for the first time suggested that changes in electrical impedance of the chest are related to the blood volume translocation in the thorax observed during the cardiac cycle. Their investigations were developed by Nyboer et al. [25] and Nyboer [26], who presented a formula describing the relationship between changes in blood volume in any segment of the body and the changes in its impedance: 2 L0 V 2 Z0 Z (2.10) where V, changes of the blood volume of the body segment [cm 3 ]; ρ, blood resistivity [Ω cm]; L 0, distance between receiving electrodes [cm]; Z 0, basic impedance of the body segment limited by receiving electrodes [Ω]; Z, changes of the impedance of the segment limited by receiving electrodes [Ω]. It is generally accepted that changes in the thoracic impedance Z are caused mainly by the ejection of blood from the left chamber to the aorta and are proportionate to the stroke volume (SV). Kubicek et al. [23] suggested this interpretation in

42 2) Kubicek Formula Kubicek suggested modification of Nyboer s formula (2.1) replacing Z = (dz/dt) max ET, and substituting V = SV, in a cardiac version of the impedance method [23, 24]. This resulted in establishing the basic impedance cardiography formula named after Kubicek: SV L 0 ( dz / dt 2 Z ) 0 2 max ET (2.11) where SV stroke volume [cm 3 ], (dz/dt) max, the maximum of the first derivative of the impedance signal [Ω / s], ET, ejection time [s], time of blood ejection from the left chamber, determined by selection of characteristic points on (dz/dt) trace, (other symbols are explained with Nyboer formula above). 3) Sramek Formula Sramek proposed another method of calculating stroke volume using 3 components: volume of electrically participating tissues (VEPT which is a function of patient s gender, height and weight), ventricular ejection time (VET), which has the similar meaning as LVET or ET in Kubicek formula and the ejection phase contractility index (EPCI), which is a product of maximal amplitude of the dz/dt signal (dz/dt) max and TFC (which is an Z -1 0 ). His idea was to show in the formula that SV is directly proportional to the physical size of a patient (i.e., to VEPT body habitus scaling constant), directly proportional to duration of delivery of blood into the aorta (i.e., to VET), and (SV is directly proportional to the peak aortic blood flow (i.e., to EPCI). This lead to the formula: SV VEPTVET EPCI (2.12)

43 where VEPT, volume of electrically participating tissues (a function of patient s gender, height and weight); VET, ventricular ejection; EPCI, ejection phase contractility index. When substituting the above symbols by the expression used in the Kubicek formula it gives: SV (0.17H) 4.25 Z 0 3 ( dz / dt) max ET (2.13) where H, the height of the subject in [cm], (dz/dt) max, is the maximal amplitude of the dz/dt signal [X / s], ET, left ventricular ejection time [s], Z 0, the base impedance of the segment limited by the receiving electrodes [X]. Sometimes this formula is presented as: SV 3 L Z 0 ( dz / dt) max ET (2.14) where L 0, the distance between receiving electrodes [cm]; L 0, is assumed to be.17 of the height of the subject. This resulted in occurrence of the factor 0.17H in the earlier formula. 4) Sramek-Bernstein Formula Some researchers use another formula for SV calculation called the Sramek-Bernstein equation: SV (0.17H ) 4.25 Z 0 3 ( dz / dt) max ET (2.15) It is based on the assumption that the thorax is a truncated cone with length L and circumference C measured at the xiphoid level [28-31]. It was checked that C / L ratio is equal to 3.0 regardless of age or sex (with the exception of newborns). Also L is assumed to be 0.17 of the height (H) and a correction factor (d) relating actual and ideal weight was introduced. Bernstein and Lemmens [32], suggested another formula called N (Bernstein)

44 The formula is given below: VITBV ( dz / dt) max SV ET 2 Z 0 (2.16) where V ITBV, 16 W 1.02 [ml], empirical formula for intra-thoracic blood volume estimation when W is expressed in [kg]. Dimensionless index of transthoracic aberrant conduction; the way of its determination is given in the mentioned paper [32]. They verified the results using N (Bernstein) with those obtained by thermo-dilution method in 106 cardiac postoperative patients and achieved the better accordance between the measurements in comparison to the usage of the other formulas. The Kubicek, Sramek and Sramek-Bernstein equations are based on different methodological assumptions but both are able to provide a reliable SV estimation. 5) TaskForce Monitor Method The Kubicek formula is the consequence of the cylindrical model of the thorax applied in the theoretical considerations. Sramek noted that this model is too simple to give the precise determination of the SV. He abandoned the cylindrical model of thorax and assumed that the thorax is the frustum of a parameters dependant on some anthropometric parameters. The volume of electrically participating tissues (VEPT) which is a function of patient s gender, height and weight. The task force monitor, producers of stationary equipment, followed the way of the usage of anthropometric measures to estimate the electrically participating volume of the thorax named by them as (V th ) [33]. They noted that shape of the body is neither an exact cylinder nor a frustum but more or less determined by the fact of whether the patient is underweight, normal or obese: underweight people will tend to have a more cylindrical thorax shape while obese people will have a more frustum-shaped thorax. They suggested that the grade of leanness/obeseness can be estimated by the body mass index (BMI), whereby a BMI

45 of 25 is considered to be the border between normal and marginal overweight [33]. They used a tilt tests to determine the influence of the body composition as well as the base impedance Z 0 on Vth. Thus the V th is described according to the formula: V th C H 1 3 BMI Z 0 n (2.17) where C 1, powers m and n are subject to proprietary non-disclosure [33]. Since BMI is defined as W / H 2, the following equation was implemented: SV C H 1 3 W / H Z m 0 2 n ( dz / dt) Z max 0 ET (2.18) and after simplifications: SV n 32n W H C1 ( dz / dt) m1 Z 0 max ET (2.19) 6) PhysioFlow Method The PhysioFlow designers did not reveal the exact formula for SV calculations. The idea of that calculations were presented in the Appendix I of the paper by Charloux et al. [34]. In contrary to the previous formulas they did not use the baseline values of the impedance Z 0 or the physical parameter like a distance between the receiving electrodes L 0, although they use BSA (so weight and height of the subjects). They used, however, the Haycock formula, BSA W H (2.20)

46 for BSA instead of that provided by Dubois and Dubois [35]. There are several steps in calculation of SV (or SVI) using PhysioFlow (they called SVI by SVi). A first evaluation of SVi, called SVical, is computed during a calibration procedure based on 24 consecutive heart beats recorded in the resting condition. The largest impedance variation during systole (Z max Z min ), and the largest rate of variation of the impedance signal (dz/dt) max, called the contractility index (CTI) is stored. The SVi calculation depends on the ventricular ejection time (ET). The designers of the PhysioFlow have chosen to use a slightly different parameter, called the thoracic flow inversion time (TFIT), expressed in [ms]. The TFIT is the time interval between the first zero value following the beginning of the cardiac cycle (starting from QRS in ECG) and the first nadir after the peak of the ejection velocity (dz/dt max ). Afterwards, the TFIT is weighted [W(TFIT)] using a specific algorithm where the pulse pressure (PP) (the difference between systolic arterial pressure and diastolic arterial pressure) and the momentary HR is used. They introduced their method of SV calculations basing on the assumptions that the aortic compliance contributes to the signal waveform. For example, Chemia et al. [36] have demonstrated the existence of a linear relationship between aortic compliance and the SV/PP ratio. In the algorithm the PP, calculated from a sphygmomanometer measurement, is introduced at the end of the Physio Flow calibration phase. Similarly, certain in relationship with. Second foundation of their method is the of the influence of the oscillatory and resonance phenomena on the ICG signal morphology. They spotted that Murgo et al. [37] described a relationship between the pressure waveform and aortic impedance or momentary HR. Thus they used the HR as a second factor entering into the algorithm. As a result of the above concepts, SVical is computed according to the following formula: SVi cal k dz / dt) ( Z Z ) W( TFIT ) ( max max minx cal (2.21)

47 Where k is a constant, and the subscript cal indicates the parameters measured during the calibration phase. Thus SVical represents the baseline reference. During the data acquisition phase, the variations of the parameters described above are analyzed and compared to those obtained during the calibration procedure. For instance, the designers demonstrated that the SV variations result mainly from a combination of contractility fluctuations (CTI) or (dz/dt)max changes and of TFIT variations. So, the stroke volume index is calculated basing on the calibrated value of SVi and the factor based on TFIC, CTI and their calibrated values: SVi SVi cal (( CTI / CTI ) ( TFIT / TFIT cal cal 1 / 3 )) (2.22) They claim that this concept is supported by a study by Moon et al. [38], who showed that changes in SV, for example during exercise, are correlated with variations in dz/dt, but inversely correlated with variations in left ventricular ejection time. They noted that in all equations used by other impedance cardiography devices, these two parameters appear as a product. The main advantage of that formula over other is that positioning of the electrodes is not critical, since Z 0 evaluation is unnecessary

48 2.3 Lumped Parameter Model Studies on cardiovascular system models have been conducted in many different contexts within physiology and biomedical engineering. However, most research has been completed through experimental and clinical studies. Due to the recent development of numerical analysis methods and the accumulation of a wide variety of experimental data on cardiovascular activity, computer simulation models are appearing that may have profound impact on the future of cardiovascular research. The currently presented numerical analysis models related to cardiovascular activity are mainly composed of models based on the centralized parameter method because of the simplicity of the method and the clarity of the concept. In 1959, many centralized parameter simulation models were presented for cardiovascular activities as a result of the presentation of the optimal dynamic model by Grodins [39]. In general, these simulation models vary according to their research purpose and the predominant methods employed by the researchers [40-48]. These studies also include the centralized parameter method for important circulation systems such as the coronary circulation system, cerebral circulation system, and pulmonary circulation system [44, 45, 49-55]. System models for comprehensive hemodynamic modeling and the development of cardiovascular auto-control mechanisms have likewise been introduced since 1959 [46] Heart model The heart can be described on a beat-by-beat basis or in terms of average performance. The latter generally involves defining cardiac output as a function of average filling (atrial or end-diastolic) pressure. Cardiac output increases with increasing filling pressure until a flow maximum is reached. This description is the Frank-Starling curve often illustrated graphically in textbooks. A mathematical representation can be used in modeling if a minimal (and timeaveraged) description of cardiac performance is acceptable. Analyzing the performance of the

49 heart on a beat-by-beat basis is more representative since the dynamics of both cardiac filling and cardiac emptying are involved. Models of the left and right hearts are generally qualitatively similar with the left heart being quantitatively stronger than the right. In simplest terms, the ventricle is described as a chamber with time-varying compliance. The compliance is a scale factor which translates any given ventricular volume into a ventricular pressure. Ventricula r P ressure 1 Ventricula r Compliance ( t) Volume (2.23) Pressure, compliance, and volume are all variables and functions of time. Compliance is large during diastole and small during systole. The pressure-volume relationship is combined with a mathematical description of inflow and outflow dynamics (see Figure 2.12). Flow occurs when the pressure gradient is favorable and valves prevent backflow. For instance, P Atrial Pressure Ventricular Pressure (2.24) Inflow P Resistance of Inflow Tract when when P 0; P 0. Inflow 0 (2.25) In short, the ventricle is thought of as a Windkessel with time-varying compliance and valves. Time is the independent variable but compliance is a direct function of time. In 1982, Cambell et al. [56] presented a variable capacitor model for ventricles comprised of 5 different factors. The temporal change of ventricular compliance was based on the values presented from the animal experiment conducted by Sunagawa and Sagawa [57]. As this ventricular model is relatively simple and correlates well with experiment results, it is now employed in

50 most theses related with the cardiovascular system [46, 57-59]. According to previous studies, the maximum compliance value of the diastole-end point of the left ventricle is between approximately 1.7 and 6.7ml/mmHg, while the minimum compliance value of the contraction-end point is approximately 0.5ml/mmHg [60]. Figure Schematic representation of a beating ventricle; Windkessel model is shown with inflow and outflow valves and a time-varying compliance Artery model In cardiovascular activity modeling, the artery is expressed as a combination of a resistor, capacitor, and inductor. The resistor represents the viscous dissipation of blood flow, the capacitor represents the compliance of the blood vessel, and the inductor represents the speed inertia effect of blood flow. Thus, a cardiovascular activity model is composed by appropriately arranging these arteries according to their respective purposes. However, most studies were conducted on the centralized parameter model [61-66] or dispersed artery model,

51 as in previous arterial modeling [67-70]. One-factor centralized parameter models allow for simple calculations and are very useful in selecting related constants. However, differences or changes in values cannot be narrowed to specific arterial parts. On the other hand, accurate values as they relate to arterial parts can be acquired through the excessive use of factors but this method is weak in selecting related constants. The dispersed arterial model assumes that the artery is a one-dimensional blood vessel. This treatment allows the observer to solve a number of hydro-mechanical equations and achieve a detailed estimation of the pressure waves of an artery. Traditionally, these modeling methods treat the artery as a composition of individual working parts. However, the calculation process is complex and significant difficulties are presented in selecting deterministic coefficients. Thus, this study used the centralized parameter model for cardio-circulation and used the dispersed artery model for the blood flow of the upper and lower parts in the artery. The combined model is called the nonuniform hybrid model based on the forward lumped parameter and measures cardiac output in both hands

52 Chapter 3 Methods In this chapter, the subjects, experimental procedure, development system for SV and CO determination, mathematical analysis of the non-uniform hybrid model, algorithm for the nonuniform hybrid model, and the statistical methods used for analysis are described. 3.1 Subjects 80 subjects volunteered to participate in this study from Yonsei University and the surrounding area. 50 Subjects who had a no known medical history and/or a history not including cardiovascular disease were selected from a pool of applicants. Also in the study were 30 subjects who had a negative medical history and/or cardiovascular disease. Before data collection, all subjects were given a brief explanation of all test protocols, signed a written informed consent document, and completed the explanation (Appendix 4) and consent forms (Appendix 4). All methods and procedures of the study were approved by the Yonsei University Medical Ethics Committee for the use of Human Subjects. To make the both-hand cardiac output measuring system more efficient than the previous one, we set the difference between two averages of the cardiac output at 0.2L/min and assumed a standard deviation of To set the power of the test at 80%, we set the level of significance (α) at 0.05 and the level of significance (β) at 0.2. We collected data from a statistically appropriate number of the subjects, as determined by the following equation: N min 2 (1 ) ( Z 2 d Z ) 2 (3.1)

53 c t N : minimumnumber of subject min : standarddeviation of primary variable = 2.0 d 90% : confidencelevelof :rate between the number of : : limitationof achievingparity between two treatment 1.0 rate between the number of used conferenceinterval experimental groupsubjectsand controlgroupsubjects experimental groupsubjectsand controlgroupsubjects 1 Eight subjects in the cardiovascular disease group were dropped due to non-compliance or acute illness; data from the drop-outs were excluded from the analysis. Therefore, a total of 72 subjects, 50 from the non-cardiovascular disease group and 22 from the cardiovascular disease group, were used for data analysis (see Figure 3.1). The subjects (50 male, 22 female; years) had the following baseline characteristics (Table 3.1). Table 3.1. Baseline Characteristics of Included Participants Variable Total N=72 Male n=50 female n=22 Age(years) 31.1± ± ±22.7 Height(cm) 170.2± ± ±5.2 Weight (kg) 67.7± ± ±11.5 BMI (kg/m2) 23.3± ± ±4.4 SBP at resting (mmhg) 122.5± ± ±20.6 DBP at resting (mmhg) 71.6± ± ±13.2 MBP at resting (mmhg) 87.1± ± ±17.6 All data = mean ± SD n = sample size; BMI = body mass index, SBP = systolic blood pressure, DBP = diastolic blood pressure, MBP = mean blood pressure

54 Figure 3.1. Flow of participants throughout the trial

55 3.2 Experimental procedure This study included reference data for stroke volume and cardiac output from Physio FlowR (PF104D, Manatec Biomedical, France) to verify our ICG system using the bothhand impedance model presented. Physio FlowR has been used in various studies to measure cardiac output using the ICG technique. Focusing on the thorax, this technique has the advantage of observing changes in cardiac output during exercise; these results were also verified as accurate in numerous other studies. According to Anne Charloux et al, a mean difference of 0.04L/min was observed in the resting stage and 0.04L/min in the motor stage in each method according to the accuracy evaluation by PhysioFlow and Fick s method. According to the research results for evaluating the accuracy and resuscitation of PhysioFlow, collected by Ruddy Richard et al, it was observed that a high correlation of R = 0.94 was shown in the p < 0.01 section when comparing Fick s method to PhysioFlow, using a sample size of 146 subjects. Furthermore, according to the research results of N. Tordi et al, a difference of R2 = 0.85 and a mean difference = 0.06 L/min was observed through the comparison of the two non-invasive measurement methods. This comparison revealed a high level of accuracy such that the difference between the two models was approximately 0.12%. In particular, as cardiac output can be monitored during exercise, it has been frequently used as an implement for monitoring cardiac output during high-strength exercise. This type of measurement often monitors an individual s maximum oxygen intake [71-73]. As PhysioFlow and the system presented in this study both inject current in the thorax or both hands, a handful of side effect of this intervention can be observed. Thus, it is impossible to simultaneously conduct the same experiment with an electrode attachment. Thus, PhysioFlow data was acquired through the electrode attached on the thorax, and then the electrode was removed to acquire data through the proposed system

56 Figure 3.2. Experimental procedure The experiment method for this study is presented in Figure 3.2. The content and process of the experiment were also explained to the experimental subject and a consent form was acquired from subject. After taking a 10-minute rest, the data acquired through PhysioFlow and the both-hand electrode was used to measure the ECG and ICG from the developed system. The data measured from PhysioFlow saves stroke volume and cardiac output at an interval of 10 seconds for 5 minutes. If there is no change in the stroke volume or cardiac output for 5 minutes, the effectiveness of the data was judged adequate to commence the experiment. Z 0 (Body impedance), Z (ICG), and dz/dt were used to calculate the ECG, stroke volume, and cardiac output for HR detection. Furthermore, the measured parameters were substituted into the Kubicek equation to calculate SV and CO

57 Figure 3.3. Experimental environment

58 3.3 Development system for SV and CO determination System configuration To correct the disadvantages of the existing thoracic impedancee measurement method, this study used a hand gripped electrode to measure the impedance of the cardiac cycle, thus necessitating the production of a new form of hardware (see Figure 3.4). Hand gripped electrodes often consist of a current high (CH), current low (CL), voltage high (VH), or voltage low (VL) operative mode. Furthermore, impedance and ECG were simultaneously measured by using a single integrated electrode system. For analog signals released from the system, Power Lab (ML880, AD Instrumentation, Australia) and LabVIEW were used to acquire data with 12bit resolution through a 1kHz sampling frequency. Figure 3.4. System configuration

59 1) Hardware The block diagram of produced hardware is as presented in Figure 3.5. Figure 3.5. Hardware block diagram

60 As direct current cannot be injected deep into the body, alternating current must be used instead. Thus, the Wien-Bridge Oscillator was used to form a 100kHz sine wave and the Howland Current Source was used to inject this into the body to generate a 1mA constantcurrent. Constant-current formed in the current is injected into the body through CH/CL electrodes. The current is changed to a voltage according to the changes in impedance and current injected via the ohm rule, according to the change in impedance in the aorta observed every cardiac cycle. These changes in voltage are detected through VH and VL. Furthermore, to simultaneously measure impedance change, signals and ECG, VH, VL, and CL were used to measure the ECG of Lead I. For voltage detected through VH and VL, the difference between the two electric potential differences was acquired through the difference amplifier. As this potential difference is an alternating current signal, it must be converted to direct current form. A True RMS converter (AD536, Analog Devices, Inc. USA) with 2MHz bandwidth and 0.2% Accuracy was used to convert to direct current voltage. This measurement value was presented as the resistance value of the human body, or in other words, the body impedance. The signal released through the True RMS converter is a voltage value. To detect changes in impedance for every cardiac output, this voltage value must be converted to an impedance value. Figure 3.6 presents the resistance value according to each voltage value after being calibration through the True RMS converter

61 Figure 3.6. The result of body impedance calibration Body impedance includes ICG information for measuring cardiac output. Furthermore, the impedance values derived from changes in lung volume are also included for each breath. As the body impedance and breathing impedance are much higher than the ICG impedance, the measurement of the body and breathing impedances produces a high level voltage while ICG presents minute voltage changes reflecting tiny impedance changes. Thus, to amplify the ICG signals, the existing body or breathing impedance levels must be eliminated. As ICG information is distorted when a High Pass Filter is used to remove this DC substance, this hardware passes the body s impedance signal through a 0.03Hz Low Pass Filter. The hardware also extracts this filtered signal from the body s impedance signal to remove the DC substance. The signal with removed DC substance passes the 0.03Hz High Pass Filter and 30Hz Low Pass Filter to be amplified to 0.1ohm/volt. The result is an impedance change of ohm, according to blood movement in the aorta that was converted to a voltage form to acquire ICG

62 2) Lead configuration In the tetra-polar impedance measurement, four electrodes are used: one pair (I+, I ) for injecting the excitation current and the other one (V+, V ) for measuring the voltage caused by the current. Changes in the measured voltage reflect the conductivity changes of the measured tissue region. Tetra-polar measurement configuration is usually favored over the bipolar one due to its capability of focusing the measurement sensitivity field into the area of interest and ignoring the electrode skin impedance. The sensitivity field strength in the tissue is formed as the dot product of the lead fields of current electrodes J LE and voltage electrodes J LI. (3.2) Thus, the measured impedance value Z is obtained as where ρ is the conductivity distribution within the volume conductor v, the tissue region under examination. V + and I+ wires are connected to a vertical pair of electrodes, V wire in the upper electrode

63 3.3.2 Measurement of ICG using both hands 1) Handgrip electrode This study used an electrode in both hands instead of attaching one electrode directly to the thorax. This non-invasive cardiacc output test, to measure stroke volume throughh impedance changes in each cardiac cycle, produced the hand-grip electrode in Figure 3.7 to minimize the number of binding parts generated during measurement in the thorax. Figure 3.7. Produced system and hand-grip electrode

64 2) Finite element model To verify that current flows accurately reflect impedance changes in the aorta during the both-hand tests, we used ANSYS (ver.11.0, ANSYS Multiphysics, USA) to carry out finite element modeling (FEM). Two models that can replace both arms (A6, A7) and several models that have entered the material property values for organs have been presented as one model to verify the form of current passage observed during the adoption of current in the end parts of both arms (A8, A9). Furthermore, to check for the existence of meaningful current flow through the aorta, a verification vector plot was created. Each model uses the material property value presented by S. Gabriel. The material property value of each organ in 100kHz, the current used in this system, is as presented in Table 3.2 [74-76]. Table 3.2. Properties of each organ (at 100kHz) Parameter Model Permittivity Conductivity(S/m) Blood A Bone A5, A6, A Fat A Heart A Lung A Muscle A6, A Skin A6, A Liver

65 ANSYS was used to carry out modeling by changing from 1Hz to 100kHz. The results verified that the current injected through the electrode flowed through the blood to the opposite side of the electrode. It was verified that most of the current flowed to the aorta, which included blood, while the remaining current flowed to other organs. The remaining current including blood allows for the measure of the body impedance (Z 0 ) of each organ. 1 VECTOR STEP=1 SUB =1 FREQ= JT ELEM=2 MIN= = MAX= = Y Z X Cardiac Model Analysis for Impedance Method Figure 3.8. Results of vector plot through modeling

66 3.4 Mathematical analysis of non-uniform hybrid model based on forward lumped parameter Resistance and compliance vessel The blood vessel can be classified into resistance vessel and compliance vessel based on previous studies conducted by Sunagawa and sagawa [77]. Pressure-Volume Diagram of ventricle based on maximum value of end-diastole and minimum value of end-systole is used. Figure 3.9. Pressure-Volume diagram for either ventricle

67 1) Resistance vessel Flow in resistance vessels is defined as the following. Blood vessels are assumed to be rigid.. Figure A typical blood vessel, V = volume of the vessel, P 1 = upstream pressure, P 2 = downstream pressure, P ext = external pressure, Q 1 = inflow, Q 2 = outflow. P1 P R Q 2 (3.3) R : Constant called the resistance of the vessel 2) Compliance vessel However, the blood vessels of the human body simultaneously possess characteristics of Resistance and Compliance rather than rigid. Thus, Aorta model must consider the Compliance characteristic in Cardiac output model. V V D CP (3.4) V D : Dead volume at P = 0 C : Constant called the compliance of the vessel P : Pressure

68 Thus, the Volume V(t) for ventricle release in relation to time is V( t) V C( t) P( t) D (3.5) C(t) : Compliance of Time(t) Systolic case Diastolic case C (t) C (t) : Increase : Decrease Thus, the formula can be summarized as V ED V C P, VES VD C systole PA and Stroke Volume becomes D diastole V V stroke VED VES C diastole PV C systole PA the difference between diastole volume and systole volume. P V : Pressure of veins P A : Pressure of aorta As Ventricle Compliance is C(t) = 0 during Systole and Ventricle Compliance is C(t) = Max during Diastole, the generally presented Stroke Volume and Cardiac Output can be defined as the following. V stroke C diastole P V (3.6) CO HR C P diastole V (3.7)

69 Cardiac Output can be classified into Left Cardiac Output and Right Cardiac Output. Left Cardiac Output manages systemic circulation while the Right cardiac output manages pulmonary circulation. Furthermore, small C diastole (Compliance) is presented by thick Left Ventricle, and larger P PV (blood pressure passing through the left atrium/left ventricle from the pulmonary vein to the aorta) than P SV (blood pressure passing through the right atrium/right ventricle from the pulmonary vein to the aorta) causes larger Left Cardiac Output( Q L K L P : blood going to aorta) than Right Cardiac Output ( PV Q R K R P : PV blood going to pulmonary vein). However, the atmospheric pressure of the surrounding area of the heart is assumed as 0. The general Cardiac Output used in the evaluation of cardiac function according to the structural principle of Stroke Volume or Cardiac Output is the Left Cardiac Output Q K P : blood going to aorta used in systemic circulation. ( L L PV Thus, in the Cardiac output Model used in the development of verification model of the both hand cardiac output detection system developed in this study, the blood released through the Aorta flows through the upper part of body (both hands) and lower part of body. The sum of blood delivered to the upper part of body (both hands) and lower part of body is assumed to be identical to the total amount of blood released through the Aorta. Furthermore, aorta, upper part vessel and lower part vessel for releasing and delivering blood are defined as the mixed model combining the characteristics of Resistance Vessel and Compliance Vessel. According to the structural characteristics of the circulation system, this study applied the lossless transmission equation of the Telegrapher s Equation used in previous Cardiac Output Model studies in the upper part (both hands) applied in this study and applied the lossy transmission equation on the lower part of the body. Based on this system, Forward Lumped Parameter-based non-uniform hybrid Model was presented

70 Figure Flow of blood from heart to upper and lower parts through aorta

71 3.4.2 Electrical circuits analogy As the Forward Lumped Parameter-based non-uniform hybrid Model handles the flow of blood, it is important to first match up the hydromechanics parameters with electrical parameters. Electricity was originally understood to be a kind of fluid. This hydraulic analogy is still conceptually useful for understanding circuits. This analogy is also used to study the frequency response of fluid mechanical networks using circuit tools, in which case the fluid network is termed a hydraulic circuit. Poiseuille's law corresponds to Ohm's law for electrical circuits ( V I R ), where the pressure drop ( P ) is analogous to the voltage and volumetric flow rate( Q ) is analogous to the current(i) Transmission line equation The development of the model of this paper is based on the application of the equation of continuity and Newton s conservation of momentum to a liquid-filled, thin-walled elastic tube. The differential equations determined are restricted by some physical approximations in order to emphasize geometric and elastic taper and to lump the inertial effects of the blood. Closed form solutions for pressure and flow (for oscillatory steady-state conditions) are obtained based on methods developed for non-uniform transmission line analysis. The major assumptions of the model are that the blood vessel wall can be represented as a thin elastic tube, the variation of parameters in the radial direction is negligible. 1) Lossless transmission equation The lossless transmission equation applied on the upper part depends only on the compliance(c), inertance(l) and gain first-order partial differential equation for blood vessel distance (x) and transmission time (t)

72 Figure Diagram of lossless and lossy transmission equation t t x V x C x t x I ), ( ) ( ), ( (3.8) t t x I x L x t x V ), ( ) ( ), ( (3.9) Lossless transmission equation is expressed in the following formula according to electrical circuits analogy. t t x P x C x t x Q ), ( ) ( ), ( (3.10) t t x Q x L x t x P ), ( ) ( ), ( (3.11) P(x,t) : Blood Pressure at Point Q(x,t) : Total Blood Flow along the Aorta at Point C(x) : Aorta hydraulic capacitance L(x) : Aorta hydraulic inertance

73 2) Lossy trransmission equation Lossy transmission equation was applied for the blood released from the Left Ventricle through the Aorta to consider the effect according to the flow through the upper and lower parts. Unlike Lossless Transmission Equation, Resistance(R) and Inertance(L) are considered in Lossy Transmission Equation to gain first-order partial Differential Equation for blood vessel distance (x) and transmission time (t). V ( x, t) L( x) I ( x, t) R( x) I( x, t) x t (3.12) Lossy Transmission Equation is expressed in the following formula according to Electrical Circuits Analogy. P( x, t) L( x) Q( x, t) R( x) Q( x, t) x t (3.13) P(x,t) : Blood Pressure at Point Q(x,t) : Total Blood Flow along the Aorta at Point C(x) : Aorta hydraulic capacitance L(x) : Blood Linertance R(x) : Blood hydraulic Resistance according to Poisseuille Equation Non-uniform hybrid model based on forward lumped parameter The Forward Lumped Parameter-based non-uniform hybrid Model presented according to the Lossless Transmission Equation and Lossy Transmission Equation is as follows. The model consists of six compartments, which represet the left and right ventricles (l and r),

74 systemic arteries and veins (a and v), and pulmonary arteries and veins (pa and pv). Each compartment consists of a conduit for viscous blood flow, which is characterized by either a linear or nonlinear resistance(r) and a volume storage element, which is characterized by either a linear or nonlinear compliance (C) with an associated unstressed volume (Q0). The reference (ref) pressure is atmospheric pressure (or ground) for the systemic compartments and intrathoracic (th) pressure for the ventricular and pulmonary compartments. The four ideal diodes represent the ventricular inflow and outflow valves and ensure unidirectional blood flow. The most distinguishing characteristic in the Forward Lumped Parameter-based non-uniform hybrid Model presented in this study is the classification of systemic circulation according to the upper part and lower part. The previous studies have assumed systemic circulation as a single resistance parameter. This is because model was developed focused on the blood released from the aorta. However, this study compared cardiac output measured in thorax and in both hands and assumed systematic circulation as inertance for cardiac output measured in both hands according to verification through the presented non-uniform hybrid model based on forward lumped parameter. Inertance assumed in systemic circulation can be classified into upper and lower parts as presented in the following

75 Figure Non-uniform hybrid systemic circulation model based on forward lumped parameter Centralized parameter-based systemic circulation model can be classified into upper and lower parts as presented in the following. lossless transmission equation and lossy transmission equation can be applied in the presented model

76 Figure Non-uniform hybrid upper and Lower model based on forward lumped parameter Forward Lumped Parameter-based non-uniform hybrid Model presented according to Lossless Transmission Equation and Lossy Transmission Equation is interpreted as the following. The pressure and flow of blood transmitted through aorta through the previously presented Lossless Transmission Equation and Lossy Transmission Equation is organized in the following Transmission Equation. t t x P x C x t x P ), ( ) ( ), ( (3.14) ), ( ) ( ), ( ) ( ), ( t x Q x R t t x Q x L x t x P (3.15) where P(x, t) is blood pressure at point x; Q(x, t) is total blood flow along the aorta at x;

77 A(x) is the cross-sectional area at x; E(x) is the modulus of elasticity of the vessel wall at x; h(x) is the vessel wall thickness at x; Vessel Resistance R(x) is induced through Hydraulic Analogy grafting Electrical Circuits Analogy of V=IR in hydrodynamics. Electrical Circuits Analogy in the central equation of hydrodynamic Hagen-Poiseuille Equation becomes Hydraulic resistance P( x, t) R( x). ( x) volumetric flow rate Q According to Standard Fluid Dynamics, R (x) of Transmission Equation is dv dt R 2 8L ( x) ( R 4 R 8 R 2 2 ) v P L (3.16) (3.17) 8L R( x) v 2 A( x) (3.18) Compliance C(x) is organized as the following according to this principle

78 C( x) A( x) E( x)( h( x) / 2R( x)) (3.19) Blood Inertance L (x) is organized as the following. L( x) A( x) (3.20) where v is effective blood viscosity and is blood density. However, Inertance L (x) presents various differential powers according to Aorta diameter to assume Lumped inertance L as analytical solution of Forward Lumped-based nonuniform hybrid Model presented in this study. Lumped inertance L presents Constant Power according to diameter. Based on assumption of Lumped inertance L, L (x) does not present changes in time to present L (x) = 0. Thus, Lossy Transmission Equation can be converted as the following. P( x, t) R( x) Q( x, t) x (3.21) The taper of the aorta is defined as the exponential geometry [78] for gaining large effect through small movements in comparison with line shape and is presented as the following

79 r x r e 2 kx ( ) o (3.22) Third, the modulus of elasticity of the vessel wall has been shown to increase with distance from the heart [79], and therefore may be given in terms of radius as E( x) Eo r( x) E r o o e kx / 2 (3.23) where E 0 is the distal elasticity of the aorta wall. The hydraulic capacitance, which varies with the radius as given by Patel et al. [80], can now be written as C( x) 4 o 2r e E h( x) 0 2kx (3.24) The hydraulic resistance is defined as R( x) 8v 2kx e 4 ro (3.25) Based on lossless transmission equation and lossy transmission equation, the lumped parameter-based non-uniform hybrid upper and lower model with taper and non-uniform elasticity characteristics can be expressed as the equivalent circuit of the following hybrid systemic circulations impedance model and can be interpreted as the frequency domain (sdomain) according to laplace Transform

80 Figure Impedance equivalence model Input impedance is the cardiac output released through the aorta, the existing method for measuring cardiac output. Z 1 of input impedance transmitted to the upper part through laplace transform can be calculated. Furthermore, this study uses laplace transform to calculate output impedance Z 0 for cardiac output data measured through both hands to extract S-domain equation of Transfer function of the presented model. Thus, the developed system was verified by comparing cardiac output modeled through the transfer function of the presented model and the cardiac output measured through both hands. According to equivalent circuits analysis techniques, the solution to these equations which characterize of the upper part may be combined with the lumped inertance LC characteristic in order to obtain pressure and flow transfer functions for any sectional length of the upper

81 part(both arms). The pressure transfer function is defined in terms of complex frequency s, the upper part vessel taper coefficient k, the effective resistance R1 and capacitance C1 per unit length at the upper part vessel, and the lumped inertance L [81]: P TP ( s) P out in ( s) 1 ( s) F1 ( ) F2 ( ) F3 ( ) F4 ( ) F5 ( ) F6 ( ) (3.26) Where 2 1( ) k k F e cosh sinh 2 s LC1 F3 ( ) e 2 ( k) F4 ( ) e 2 sr1c 1 2k F2 ( ) e sinh 2 4k 2k 2 k sinhcosh sinh k sinhcosh sinh ( k) 2k F5 ( ) e sinh cosh k 2 2 sinh (3.27) (3.28) (3.29) (3.30) (3.31) sl( k) F ( ) e R sinhe k cosh sinh cosh 4k 4k 6 k 1 sinh (3.32)

82 The term represents the propagation parameters 2 k sr1c 1 (3.33) while the length of the entire aorta, l a = 2λ, is a fixed parameter. The transfer function of cardiac model is composed of F (3.34) 1( ), F2 ( ), F3 ( ), F4 ( ), F5 ( ), F6 ( ) This was deducted by using the model characteristic of output being 1 during input of (t) in laplace transform. Thus, it presents that output is affected by 6 input factors. R1; the per unit length value of the resistance at the root of the aorta C1; the per unit length value of the capacitance taken at the same location as R1 K ; the aorta taper coefficient ; represents the propagation parameters a : length of aorta L ; The lumped inertance parameter L is taken as a constant, nominal value of 1.06x106kg/m4. The assumption that this value is always approximately the nominal value is supported in the literature [81]. Once the parameters are identified, they can be applied to an expression of input impedance which is also a function of the identified parameters [81] ( k ) l jl 2 LR1C a 1 2 R1e ( k) e Z ( ) l ( k ) l LC 2 a a ( k) e ( e 1) 2 l a (3.35)

83 Once the model impedance has been evaluated, it can be utilized along with an experimental measure of aortic pressure (reduced by FFT for frequency-domain analysis) to determine flow in the proximal aorta; pressure and flow are related linearly in the frequency domain through the complex impedance term: Q ( ) 1 n P1 ( n ) Z ( ) 1 n (3.36) Where ω n represents the n-th harmonic component of the waveforms; Q 1 (ω n ) represents the blood flow phasor at frequency ω n ; P 1 (ω n ) is aortic (input) pressure phasor; Z 1 (ω n ) is aortic input impedance. Accordingly, the time-domain waveform q(t) can be reconstructed from the complex flow terms, Q 1 (ωn), by an inverse digital fast fourier transform (IFFT) analysis. The stroke volume is calculated in the time domain by integration of q(t), with a zero baseline introduced to the oscillatory waveform by a separate algorithm. The cardiac output (CO) is then readily computed from integration of the flow waveform and multiplication of the resultant stroke volume by heart rate: CardiacOut put HR SV HR T 0 q( t) dt (3.37) where SV is the stroke volume; HR is the heart rate; q(t) is the time domain flow waveform; T is the period of the cardiac cycle

84 3.5 Determination of SV and CO Algorithm by non-uniform hybrid Model based on forward lumped parameter Thoracic and both hands pulse Data was analogue low-pass (20 Hz) and high-pass (0.1 Hz) filtered, sampled at 1 khz, and stored on compatible PC through PowerLab of ADinstruments. A block diagram of SV and CO Algorithm by non-uniform hybrid model based on forward lumped parameter is given in Fig Figure Flowchart of the proposed algorithm for SV and CO determination

85 Calibration of the externally measured pulses to pressure waveforms was performed prior to the measured transfer function calculation. Fourier analysis was performed by the fast fourier transform (FFT) algorithm [82] requiring exactly N = 2 n samples of data, where n is a positive integer. More specifically, the FFT algorithm utilized had a high processing speed, requiring N/2 log 2 N operations [83]. The objective was to calculate the FFT on strings of pulses exhibiting periodicity and a general consistency in wave shape. For this, the selection for N had to be large enough to distinguish spectral components of the two quasi-periodic signals present in the data collected: the arterial pressure pulse and respiration. While large quantities of data were collected (60,000 samples, for each signal, approximately 1min), the presence of noise imposed some restrictions on the selection of N. Pulses corrupted by this noise are inconsistent in terms of general wave shape, with an apparent loss of periodicity in salient features of the wave. A sample length of 8192 (2 13 ) acceptable pulses was analyzed. Even for signals which appeared to be only quasi-periodic, this data length encompassed cardiac cycles (depending on the heart rate or first frequency) and was large enough to provide good resolution of the harmonic peaks as well as approximately linear phases. Spectra arrived at by FFT analysis of thoracic and both-hands pulses in figure 3.17(a) are presented in figure 3.17(b). While the pulses shown in figure 3.17(a) are indeed very noisy, they are representative of real data. The efficacy of the selected FFT algorithm is evident in the display of sharp spectral peaks over the region of interest (approximately 1-6 Hz) despite the noise level paramount in the time-domain tracings. The horizontal axis of the spectral plot is given in Hz while the vertical is given in terms of power (mv 2 /Hz) normalized with respect to the mean. While the first heart frequency and harmonic peaks are certainly discernible, noise peaks are apparent in the spectra

86 (a) (b) Figure 3.17 Pulse raw data of thoracic and both-hands pulses (a) and Spectra arrived at by FFT analysis of thoracic and both-hands pulses (b) However, for all data analyzed, the first peak due to breathing artifact ( Hz) was salient yet distinct from the first harmonic peak (1-2 Hz). Filtering of relevant spectral information was based on peak selection. The average first frequency for the pulses analyzed was determined from the first peak of the invasively measured arterial waveform which was essentially noise-free. The apparent accuracy in the magnitude and phase of the transfer function of selected peaks or three harmonics is apparent in the waveforms reconstructed from the spectra at these harmonics. Typical reconstructions for thoracic and both hands pulses appear in figure

87 (a) (b) Figure Time domain reconstruction of (a)thoracic and (b)both-hand spectra over firstfour peak frequency The effects of breathing and motion artifact on the magnitude and particularly the phase content of the transfer function are essentially eliminated. Fixed values for typical human aortas as determined by experimental measurements and applied [79, 84]. Using the optimal values of R 1, C 1, k and L determined, along with a fixed value for, the input impedance magnitude and phase components at the harmonics were calculated [85]. The phasor components of the throacic flow Q 1 (w n ) were computed from the phasors of the filtered bothhands pressure C 1 (w n ) and the aortic input impedance Z 1 (w n ) at the first (n = 1) and 2 to 3 harmonics cardiac frequency. Figure 3.19 illustrates typical flow waveforms reconstructed (IFFT) from the flow phasors computed. Recall that the model-derived parameters (i.e., impedance) are oscillatory so that after the IFFT is performed, a zero level or baseline must be reintroduced to the time-domain waveform prior to calculation of the SV and CO by both-hands pulse first peak frequency

88 Figure Reconstructed flow waveform by non-uniform hybrid model based on forward lumped parameter

89 3.6 Developed system reproducibility The measurement of five different age-specific subjects (three males and two females) was repeated five times for reproducibility verification. The protocol for five repetitions of measurement (Rest 10 min, ECG/ICG Measurement 5 min, and Rest 3 min) is described in Figure Figure Reproducibility experiment protocol The result of this reproducibility verification for the five different age-specific subjects is shown in Table 3.3. Table 3.3. Reproducibility test 1 Developed system SV Mean±SD Physioflow Modeled SV SV Subject 1 (female, 18years) ± Subject 2 (male, 22years) ± Subject 3 (male, 30years) ± Subject 4 (female, 48years) ± Subject 5 (male, 59years) ±

90 3.7 Statistical analysis All of the analyses were performed using the SPSS 17.0 for Windows (SPSS, Inc., Chicago, Illinois,USA) and LabView 8.6 (National Instrument, USA). Descriptive statistics were calculated for all data and were expressed as a mean value ±SD. All measured physiological variables were tested for normality and associations between selected variables. The stroke volume and cardiac output data gained in the Physio flow were used on a total of 80 subjects to achieve statistical cross-verification of data gained through the cardiac output measurement system using both hand impedance measurement method, non-uniform hybrid model based on forward lumped parameter and reference method The paired T-tests Test and Wilcoxon Signed Ranks Test analyses were used to discern any significant difference between measured SV and CO by cardiac output equipment and estimated SV and CO based on developed model by proposed approach. The Pearson product moment correlation coefficient(r) used to assess relationships between measured SV and CO and estimated SV and CO. Bland-Altman plot and Scatter plot graphs were also used to assess the agreement between two methods [86]

91 Chapter 4 Results In this chapter, the following is presented: 1) SV and CO predictions via the development system. 2) SV and CO predications via the non-uniform hybrid electrical impedance model based on the forward lumped parameter. 3) Evaluation of cardiac output by the non-uniform hybrid electrical impedance model and the both-hands impedance measurement system. There was significant correlation between PhysioFlow and the developed system, across the two subject groups. The first group was comprised of 50 subjects who have no medical history and/or no history of cardiovascular disease (SV: r = 0.810, CO: r = 0.914, P < 0.001) and the second was 30 subjects who had a medical history and/or cardiovascular disease (SV: r = 0.832, CO: r = 0.918, P < 0.001). According to the resultant data from PhysioFlow and the developed system, each of two subject groups shows statistical significance. Therefore we distinguished between the male group (n = 54) and the female group (n = 18) and then conducted our analysis. For verification of the development system, statistical methods such as correlation analyses, coefficient of variation, paired T-test, and the Bland-Altman plot were used. For verification of the non-uniform hybrid electrical impedance model, the value of r, a scatter plot, and the Bland-Altman plot were presented to compare between PhysioFlow and the developed system for SV and CO

92 4.1 SV and CO estimation by development System Description of measured SV, CO from PhysioFlow method and SV, CO from proposed approach Development system are presented in Table 4.1. Correlation between physioflow and developed system were investigated. Table 4.1. Description of physioflow SV, CO and developed system SV (ml), CO(l) Developed PhysioFlow CV CV System r SV CO Male (n=54) Female (n=18) Male (n=54) Female (n=18) 89.39± ± *** 84.13± ± *** 6.18± ± *** 6.05± ± *** ***p<0.001; Data are presented as mean±sd; r = correlation coefficient between physioflow and developed system SV, CO Developed system SV was over estimated as compared with physioflow SV in male and was over estimated in female. There was significant correlation between physioflow and developed system SV in both male and female (r=0.715, P<0.001; r=0.704, P<0.001, respectively). Developed system CO was over estimated as compared with physioflow CO in male and was over estimated in female. There was significant correlation between physioflow and developed system CO in both male and female (r=0.826, P<0.001; r=0.804, P<0.001, respectively). Figure 4.1 shows comparison of values between physioflow and developed

93 system SV, CO. Developed system CV was over estimated as compared with physioflow CV in male and was over estimated in female. (a) male (N=54) (b) female (N=18) Figure 4.1. physioflow and developed system SV in (a) male and (b) female (a) male (N=54) (b) femalee (N=18) Figure 4.2. physioflow and developed system CO(l) in (a) male and (b) female

94 Results of the paired samples t-test and the Wilcoxon signed ranks in males were presented in Table 4.2, respectively. Results indicate no significant difference between physioflow and developed system SV, CO in males (p>0.05). Table 4.2. Paired Samples Test and Wilcoxon Signed Ranks Test results between physioflow and developed system SV, CO in males (N=54) Mean ± SD t p Physioflow SV Developed system SV 0.35± Physioflow CO Developed system CO -.004± Results of the paired samples t-test and the Wilcoxon signed ranks in females were presented in Table 4.3, respectively. Results indicate no significant difference between physioflow and developed system SV, CO in females (p>0.05). Table 4.3. Paired Samples Test and Wilcoxon Signed Ranks results between measured and estimated SV, CO in females (N=18) Mean ± SD t p Physioflow SV Developed system SV -0.79± Physioflow CO Developed system CO -.069±

95 Figure 4.3 shows a relationship between physioflow and developed system SV(ml). Pearson product moment correlation coefficients (r) demonstrate positively significant relationships between physioflow and developed system at SV in both (a) males (N=54, r = 0.715, p<0.001) and (b) females (N=18, r= 0.704, p<0.001). Outside line indicate 95% prediction interval for prediction model. (a) male (N=54) (b) female (N=18) Figure 4.3. Scatter plot graphs of relationship between physioflow and developed system SV with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female

96 Figure 4..4 shows Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between physioflow and developed system SV, as plotted against the mean value. ( a) male (N=54) (b) female (N=18) Figure 4.4. Bland-Altmann plot with estimated mean bias and 95% limits of agreement for difference between physioflow and developed system SV, plotted against the mean in (a) male and (b) female

97 Figure 4.5 shows a relationship between physioflow and developed system. Pearson product moment correlation coefficients (r) demonstrate positively significant relationships between physioflow and developed system at CO in both (a) males (N=54, r = 0.826, p<0.001) and (b) females (N=18, r= 0.804, p<0.001). Outside line indicate 95% prediction interval for prediction model. (a) male (N=54) (b) female (N=18) Figure 4.5. Scatter plot graphs of relationship between measured and estimated CO (l) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female

98 Figure 4..6 shows Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between physioflow and developed system CO, as plotted against the mean value. ( a) male (N=54) (b) female (N=18) Figure 4.6. Bland-Altmann plot with estimated mean bias and 95% limits of agreement for difference between physioflow and developed system CO, plotted against the mean in (a) male and (b) female

99 4.2 SV and CO predication by non-uniform hybrid electrical impedance model based on forward lumped parameter Description of measured SV and CO from PhysioFlow method and Modeled SV and CO from proposed approach (non-uniform hybrid electrical impedance model based on forward lumped parameter) are presented in Table 4.4. Correlation between physioflow and modeled SV and CO were investigated. Table 4.4. Description of physioflow SV, CO and modeled SV (ml), CO(l) PhysioFlow CV Modeled CV r SV CO Male (n=54) Female (n=18) Male (n=54) Female (n=18) 89.39± ± *** 84.13± ± *** 6.18± ± *** 6.05± ± *** ***p<0.001; Data are presented as mean±sd; r = correlation coefficient between physioflow and modeled SV, CO Modeled SV was under estimated as compared with physioflow SV in male and was over estimated in female. There was significant correlation between physioflow and modeled SV in both male and female (r=0.735, P<0.001; r=0..827, P<0.001, respectively). Figure 4.7 shows comparison of values between physioflow and modeled SV. Modeled CO was under estimated as compared with physioflow CO in male and was over estimated in female. There was significant correlation between physioflow and modeled CO in

100 both male and female (r=0.767, P<0.001; r=0.853, P<0.001, respectively). Figure 4.8 shows comparison of values between physioflow and modeled CO. Modeled CV was under estimated as compared with physioflow CV in male and was over estimated in female. (a) male (N=54) (b) female (N=18) Figure 4.7. Physioflow and modeled SV(ml) in (a) male and (b) female (a) male (N=54) (b) femalee (N=18) Figure 4.8. Physioflow and modeled CO(l) in (a) male and (b) female

101 Results of the paired samples t-test and the Wilcoxon signed ranks in males were presented in Table 4.5, respectively. Results indicate no significant difference between physioflow and modeled SV, CO in males (p>0.05). Table 4.5. Paired Samples Test and Wilcoxon Signed Ranks Test results between physioflow and modeled SV, CO in males (N=54) Mean ± SD t p Physioflow SV Modeled SV 0.41± Physioflow CO Modeled CO 0.02± Results of the paired samples t-test and the Wilcoxon signed ranks in females were presented in Table 4.6, respectively. Results indicate no significant difference between physioflow and modeled SV, CO in females (p>0.05). Table 4.6. Paired Samples Test and Wilcoxon Signed Ranks Test results between physioflow and modeled SV, CO in females (N=18) Mean ± SD t p Physioflow SV Modeled SV -2.29± Physioflow CO Modeled CO -0.19±

102 Figure 4.9 shows a relationship between physioflow and modeled SV(ml). Pearson product moment correlation coefficients (r) demonstrate positively significant relationships between physioflow and modeled at SV in both (a) males (N=54, r = 0.735, p<0.001) and (b) females (N=18, r= 0.827, p<0.001). Outside line indicate 95% prediction interval for prediction model. (a) male (N=54) (b) female (N=18) Figure 4.9. Scatter plot graphs of relationship between physioflow and modeled SV (ml) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female

103 Figure shows Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between physioflow and modeled SV, as plotted against the mean value. ( a) male (N=54) (b) female (N=18) Figure Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between physioflow and modeled SV(ml), plotted against the mean in (a) male and (b) female

104 Figure 4.11 shows a relationship between physioflow and modeled CO(l). Pearson product moment correlation coefficients (r) demonstrate positively significant relationships between physioflow and modeled at CO in both (a) males (N=54, r = 0.767, p<0.001) and (b) females (N=18, r= 0.853, p<0.001). Outside line indicate 95% prediction interval for prediction model. (a) male (N=54) (b) female (N=18) Figure Scatter plot graphs of relationship between physioflow and modeled CO (l) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female

105 Figure shows Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between physioflow and modeled CO, as plotted against the mean value. ( a) male (N=54) (b) female (N=18) Figure Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between physioflow and modeled CO(l), plotted against the mean in ( a) male and (b) female

106 4.3 Evaluation of CO by non-uniform hybrid electrical impedance model based on forward lumped parameter and both hands impedance measurement system Description of modeled SV and CO from non-uniform hybrid electrical impedance model based on forward lumped parameter method and SV and CO from development system are presented in Table 4.7. Correlation between modeled and developed system SV and CO were investigated. Table 4.7. Description of modeled SV, CO and developed system SV (ml), CO(l) Developed Modeled CV CV System r SV CO Male (n=54) Female (n=18) Male (n=54) Female (n=18) 89.35± ± *** 86.42± ± *** 6.17± ± *** 6.24± ± *** ***p<0.001; Data are presented as mean±sd; r = correlation coefficient between modeled and developed system SV, CO Developed system SV was over estimated as compared with modeled SV in male and was under estimated in female. There was significant Correlation between modeled and developed system SV in both male and female (r=0.788, P<0.001; r=0.812, P<0.001, respectively). Figure 4.13 shows comparison of values between modeled and developed system SV. Developed system CO was over estimated as compared with model CO in male and was

107 under estimated in female. There was significant Correlation between modeled and developedd system CO in both male and female (r=0.802, P< <0.001; r=0.823, P<0.001, respectively) ). Figure 4.14 shows comparison of values between modeled and developedd system CO. Developed system CV was under estimated as compared with modeled CV in male and was under estimated in female. (a) male (N=54) (b) female (N=18) Figure Modeled and estimated SV(ml) in (a) male and (b) female (a) male (N=54) (b) femalee (N=18) Figure Modeled and estimated CO(l) in (a) male and (b) female

108 Results of the paired samples t-test and the wilcoxon signed ranks in males were presented in Table 4.8, respectively. Results indicate no significant difference between modeled and estimated SV in males (p>0.05). Table 4.8. Paired Samples Test and Wilcoxon Signed Ranks Test results between modeled and developed system SV, CO in males (N=54) Mean ± SD t p Modeled SV Developed System SV -0.39± Modeled CO Developed System CO -0.02± Results of the paired samples t-test and the Wilcoxon signed ranks in females were presented in Table 4.9, respectively. Results indicate no significant difference between measured and estimated SV in females (p>0.05). Table 4.9. Paired Samples Test and Wilcoxon Signed Ranks Test results between modeled and developed system SV, CO in females (N=18) Mean ± SD t p Modeled SV Developed System SV 1.49± Modeled CO Developed System CO 0.12±

109 Figure 4.15 shows a relationship between modeled and developed system SV(ml). Pearson product moment correlation coefficients (r) demonstrate positively significant relationships between modeled and developed system at SV in both (a) males (N=54, r = 0.788, p<0.001) and (b) females (N=18, r= 0.812, p<0.001). Outside line indicate 95% prediction interval for prediction model. (a) male (N=54) (b) female (N=18) Figure Scatter plot graphs of relationship between modeled and developed system SV (ml) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female

110 Figure 4.16 shows Bland-Altman plot with estimated mean bias and 95% limits of agreement for differencee between modeled and developed system SV, as plotted against the mean value. ( a) male (N=54) (b) female (N=18) Figure Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between modeled and developed system SV(ml), plotted against the mean in (a) male and (b) female

111 Figure 4.17 shows a relationship between modeled and developed system CO(l). Pearson product moment correlation coefficients (r) demonstrate positively significant relationships between modeled and developed system at CO in both (a) males (N=54, r = 0.802, p<0.001) and (b) females (N=18, r= 0.823, p<0.001). Outside line indicate 95% prediction interval for prediction model. (a) male (N=54) (b) female (N=18) Figure Scatter plot graphs of relationship between modeled and developed system CO (l) with 95% prediction interval line(orange) and 95% confidence interval line (brown) in (a) male and (b) female

112 Figure shows Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between modeled and developed system CO, as plotted against the mean value. ( a) male (N=54) (b) female (N=18) Figure Bland-Altman plot with estimated mean bias and 95% limits of agreement for difference between modeled and estimated CO(l), plotted against the mean in (a) male and (b) female

113 Chapter 5 Discussion The purposes of this study were to (1) develop a system for detecting SV and CO through the noninvasive and convenient both-hand ICG measurement method, (2) develop the nonuniform hybrid model based on the forward lumped parameter and present the advantages of the previous lumped parameter method and non-uniform hybrid model to evaluate the effectiveness of a combined system, (3) conduct mathematical interpretation of the presented model and compare the SV/CO results for the thoracic impedance to verify the effectiveness of the both-hand CO measurement presented in this study. There were several assumptions made in this study. (1) There are no differences presented in the results of both-hand cardiac output measurement and thoracic cardiac output measurement. (2) To realize improved resolution in the measurement of cardiac output by using both hands, identical results can be acquired using the thoracic measurement technique. (3) Effectiveness evaluation can be conducted on the both-hand cardiac output measurement system presented in this study through the both-hand cardiac output estimation model. Based on this assumption, the both-hand cardiac function assessment system was developed in consideration of user convenience and the non-uniform hybrid model based on the forward lumped parameter was presented to verify the developed system. As the amount of blood released to the entire body can vary per cardiac impulse, the cardiac output refers to the indicator that not only reflects cardiac function but presents the status of the entire circulation system and is controlled through the autonomous adjustment of body tissue. Cardiac output is generally proportional to the amount of oxygen or nutrients required by tissue. Maintaining and adjusting cardiac output is one of the most complex

114 functions in the circulatory system and, in general, invasive methods must be used to accurately measure cardiac output. Invasive methods present a high risk and require highly skilled surgical specialists. To complement this weakness, non-invasive methods such as the Doppler ultrasound and thoracic impedance cardiogram methods have been researched. However, various limitations still exist (e.g., long measurement time, inconvenience, and high cost). The user-convenient both-hand ICG measurement system was developed to overcome these limitations. ANSYS was used to present a dimensional model of both hands and the upper body using material property values. Observations were made as to whether significant current flow was presented to the aorta during injection of current in both arms. Current injected through the electrode flowed down one arm to move most current to the thoracic blood. The current was released through the opposite arm. A majority of the currents reflected changes to the blood in the aorta when ICG was measured in both hands, instead of using the previous thoracic measurement method. A system with enhanced resolution was designed to achieve measurement in both arms and acquire the data required for comparison. The non-uniform hybrid model was developed to use ICG waveform measurements to calculate a model-based SV and CO. Comparative analysis was made with reference equipment. To verify the developed system, ICG waveforms measured in PhysioFlow and in the developed system were applied to the model to substitute measured ICG parameters. The Kubicek equation was also used to compare the SV and CO values between the two collection techniques. The developed system for measuring SV and CO appears to have overestimated their values when compared to the PhysioFlow SV and CO results. However, there was significant correlation between the developed system and PhysioFlow in both males and females (SV: r = 0.715, P < 0.001; r = 0.704, P < 0.001, CO: r = 0.826, P < 0.001; r = 0.804, P < 0.001, respectively). The values measured in thorax and in both hands were statistically similar, thus satisfying the previously established hypothesis. This result signifies that the developed model is the appropriate model for verifying the values of both-hand measurement. The high statistical correlation presented

115 between the results of the developed model and system is appropriately verified in the bothhand measurement. The system and measurement method proposed was verified by the previously utilized ICG method, through comparison with reference equipment, and by means of a model-based verification obtained against the results of previous studies. Thus, this method can be considered a viable, new measurement method based on the impedance technique, but without the traditional disadvantages of the technique

116 Chapter 6 Conclusions In summary, limitations are still present in the many methods for measuring SV and CO, the clinical indicators that reflect hemodynamic function and overall cardiovascular activity. To solve these limitations, an electric impedance measurement method using both hands was used as a more convenient, non-binding measurement method to develop a system for detecting clinical indicators of cardiovascular activity. To evaluate the effectiveness of the proposed system, a forward lumped parameter-based non-uniform hybrid Model was presented and mathematical interpretation was conducted. The results were compared with the previous thoracic impedance method. The developed system overestimated SV and CO when compared to PhysioFlow. Despite this overestimation, there was significant correlation between the developed system and PhysioFlow in both males and females (SV: r = 0.715, P < 0.001; r = 0.704, P < 0.001, CO: r = 0.826, P < 0.001; r = 0.804, P < 0.001, respectively). The high statistical correlation presented between the results of the developed model and system was verified via the both-hand measurement method. It can be judged through this study that SV and CO can be simply and inexpensively measured without the help of a specialist and without visiting the hospital through the both-hand cardiac output measurement method developed through this study. Furthermore, this system was verified through the developed model to be proposed as the method for substituting the previous method. The limitations of this study are as follows: 1) the analysis was only achieved according to gender although samples for non-diseased and diseased subjects still exist, and 2) the comparison between the measurement data did not exist through the thermo-dilution technique, the CO gold standard. Furthermore, comparison was not achieved through the previous model. Thus, future studies must be conducted that analyze samples divided across various categories

117 (i.e., gender, age, and heart disease) to categorize according to the disease status. Furthermore, the thermo-dilution technique must be used to acquire CO and comparison must be made with the results of the developed system to achieve accurate verification of measurement in the system

118 References [1] M. A. Silver, et al., "Evaluation of impedance cardiography as an alternative to pulmonary artery catheterization in critically ill patients," Congestive Heart Failure, vol. 10, pp , [2] R. L. Summers, et al., "Case Report," Congestive Heart Failure, vol. 10, pp , [3] R. F. Wright and J. Gilbert, "Clinical decision making in patients with congestive heart failure: the role of thoracic electrical bioimpedance," Congestive Heart Failure, vol. 6, pp , [4] P. Sullivan, et al., "Comparison of bioimpedance and thermodilution measurements of cardiac output during aortic surgery," Canadian journal of anaesthesia= Journal canadien d'anesthésie, vol. 37, p. S78, [5] J. Conway and P. Lund-Johansen, "Thermodilution method for measuring cardiac output," European Heart Journal, vol. 11, p. 17, [6] J. M. Levett and R. L. Replogle, "Thermodilution cardiac output: a critical analysis and review of the literature," Journal of Surgical Research, vol. 27, pp , [7] M. Muzi, et al., "Determination of cardiac output using ensemble-averaged impedance cardiograms," Journal of Applied Physiology, vol. 58, pp , [8] W. C. Shoemaker, et al., "Multicenter trial of a new thoracic electrical bioimpedance device for cardiac output estimation," Critical care medicine, vol. 22, p. 1907,

119 [9] X. Wang, et al., "An impedance cardiography system: a new design," Annals of Biomedical Engineering, vol. 17, pp , [10] T. Kööbi, et al., "Non-invasive measurement of cardiac output: whole-body impedance cardiography in simultaneous comparison with thermodilution and direct oxygen Fick methods," Intensive care medicine, vol. 23, pp , [11] J. Blom, "Introduction to Monitoring of respiration and Circulation," ed: Technische Universiteit Eindhoven, [12] H. Fritts Jr and A. Cournand, "The application of the Fick principle to the measurement of pulmonary blood flow," Proceedings of the National Academy of Sciences of the United States of America, vol. 44, p. 1079, [13] M. Mischi, "Contrast echocardiography for cardiac quantifications," [14] A. C. Perrino Jr, et al., "Intraoperative cardiac output monitoring: comparison of impedance cardiography and thermodilution," Journal of cardiothoracic and vascular anesthesia, vol. 8, pp , [15] W. C. Shoemaker, et al., "Multicenter trial of a new thoracic electrical bioimpedance device for cardiac output estimation," Critical care medicine, vol. 22, p. 1907, [16] 노규정, et al., " 원저 : 전신마취시 Thoracic Electric Bioimpedance, 경식도 Doppler, 온도희석법에의한심박출량측정의상호비교," 대한마취과학회지, vol. 26, pp , [17] R. L. Summers, et al., "Bench to bedside: electrophysiologic and clinical principles of noninvasive hemodynamic monitoring using impedance cardiography," Academic emergency medicine, vol. 10, pp ,

120 [18] B. Van der Meer, et al., "Impedance cardiography," Intensive care medicine, vol. 22, pp , [19] H. Bogaard, et al., "The haemodynamic response to exercise in chronic obstructive pulmonary disease: assessment by impedance cardiography," European Respiratory Journal, vol. 12, p. 374, [20] M. Akay, Wiley encyclopedia of biomedical engineering: Wiley-Interscience, [21] J. Webster, Medical instrumentation: application and design: Wiley-India, [22] J. J. McGrath, et al., "Comparability of Spot Versus Band Electrodes for Impedance Cardiography," Journal of Psychophysiology, vol. 19, p. 195, [23] W. Kubicek, et al., "Development and evaluation of an impedance cardiac output system," Aerospace medicine, vol. 37, p. 1208, [24] W. Kubicek, et al., "IMPEDANCE CARDIOGRAPHY AS A NONINVASIVE METHOD OF MONITORING CARDIAC FUNCTION AND OTHER PARAMETERS OF THE CARDIOVASCULAR SYSTEM*," Annals of the New York Academy of Sciences, vol. 170, pp , [25] J. Nyboer, et al., "Radiocardiograms-the electrical impedance changes of the heart in relation to electrocardiograms and heart sounds," J. Clin. Invest, vol. 19, p. 963, [26] J. Nyboer, Plethysmograph: impedance, [27] E. Atzler and G. Lehmann, "über ein neues Verfahren zur Darstellung der Herztätigkeit (Dielektrographie)," European Journal of Applied Physiology and Occupational Physiology, vol. 5, pp ,

121 [28] D. P. Bernstein, "A new stroke volume equation for thoracic electrical bioimpedance: theory and rationale," Critical care medicine, vol. 14, p. 904, [29] D. P. Bernstein, "Continuous noninvasive real-time monitoring of stroke volume and cardiac output by thoracic electrical bioimpedance," Critical care medicine, vol. 14, p. 898, [30] B. B. Sramek, "Cardiac output by electrical impedance," Medical electronics, vol. 13, p. 93, [31] B. Sramek, "Thoracic electric bioimpedance. Basic principles and physiologic relationships]," Ceskoslovenská fysiologie/ústrední ústav biologický, vol. 42, p. 111, [32] D. Bernstein and H. J. M. Lemmens, "Stroke volume equation for impedance cardiography," Medical and Biological Engineering and Computing, vol. 43, pp , [33] J. Fortin, et al., "Non-invasive beat-to-beat cardiac output monitoring by an improved method of transthoracic bioimpedance measurement," Computers in Biology and Medicine, vol. 36, pp , [34] A. Charloux, et al., "A new impedance cardiograph device for the non-invasive evaluation of cardiac output at rest and during exercise: comparison with the direct Fick method," European journal of applied physiology, vol. 82, pp , [35] D. Du Bois and E. F. Du Bois, "Clinical calorimetry: tenth paper a formula to estimate the approximate surface area if height and weight be known," Archives of internal medicine, vol. 17, p. 863, [36] D. Chemla, et al., "Total arterial compliance estimated by stroke volume-to-aortic

122 pulse pressure ratio in humans," American Journal of Physiology-Heart and Circulatory Physiology, vol. 274, p. H500, [37] J. P. Murgo, et al., "Aortic input impedance in normal man: relationship to pressure wave forms," Circulation, vol. 62, pp , [38] J. K. Moon, et al., "Stroke volume measurement during supine and upright cycle exercise by impedance cardiography," Annals of Biomedical Engineering, vol. 22, pp , [39] F. S. Grodins, "Integrative cardiovascular physiology: a mathematical synthesis of cardiac and blood vessel hemodynamics," Quarterly Review of Biology, pp , [40] E. O. Attinger and A. Anné, "SIMULATION OF THE CARDIOVASCULAR SYSTEM*," Annals of the New York Academy of Sciences, vol. 128, pp , [41] A. Avolio, "Multi-branched model of the human arterial system," Medical and Biological Engineering and Computing, vol. 18, pp , [42] J. Dagan, "Pulsatile mechanical and mathematical model of the cardiovascular system," Medical and Biological Engineering and Computing, vol. 20, pp , [43] H. Hardy, et al., "A digital computer model of the human circulatory system," Medical and Biological Engineering and Computing, vol. 20, pp , [44] J. LaCourse, et al., "Simulations of arterial pressure pulses using a transmission line model," Journal of biomechanics, vol. 19, pp ,

123 [45] V. Sud and G. Sekhon, "Analysis of blood flow through a model of the human arterial system under periodic body acceleration," Journal of biomechanics, vol. 19, pp , [46] M. Ursino, "Interaction between carotid baroregulation and the pulsating heart: a mathematical model," American Journal of Physiology-Heart and Circulatory Physiology, vol. 275, p. H1733, [47] R. Croston, et al., "Computer model of cardiovascular control system responses to exercise," Journal of Dynamic Systems, Measurement, and Control, vol. 95, p. 301, [48] D. G. Boyers, et al., "Simulation of the human cardiovascular system: a model with normal responses to change of posture, blood loss, transfusion, and autonomic blockade," Simulation, vol. 18, pp , [49] T. Ejaz, et al., "The high zero-flow pressure phenomenon in coronary circulation: a simulation study," Frontiers of Medical &# 38; Biological Engineering, vol. 11, pp , [50] G. N. Jager, et al., "Oscillatory Flow Impedance in Electrical Analog of Arterial System:: Representation of Sleeve Effect and Non-Newtonian Properties of Blood," Circulation research, vol. 16, pp , [51] J. Y. Kresh, et al., "Model-based analysis of transmural vessel impedance and myocardial circulation dynamics," American Journal of Physiology-Heart and Circulatory Physiology, vol. 258, pp. H262-H276, [52] E. Magosso and M. Ursino, "Modelling study of the acute cardiovascular response to hypocapnic hypoxia in healthy and anaemic subjects," Medical and Biological Engineering and Computing, vol. 42, pp ,

124 [53] G. Porenta, et al., "A finite-element model of blood flow in arteries including taper, branches, and obstructions," Journal of Biomechanical Engineering, vol. 108, p. 161, [54] W. Schreiner, et al., "Simulation of coronary circulation with special regard to the venous bed and coronary sinus occlusion," Journal of Biomedical Engineering, vol. 12, pp , [55] M. Ursino, et al., "An integrated model of the human ventilatory control system: the response to hypoxia," Clinical Physiology, vol. 21, pp , [56] K. Campbell, "A Pulsatile Cardiovascular Computer Model for Teaching Heart-Blood Vessel Interaction," Physiologist, vol. 25, pp , [57] K. Sunagawa and K. Sagawa, "Models of ventricular contraction based on timevarying elastance," Critical reviews in biomedical engineering, vol. 7, p. 193, [58] E. Bo Shim, et al., "Computational modeling of the cardiovascular system after Fontan procedure," Medical Data Analysis, pp , [59] T. Heldt, et al., "Computational modeling of cardiovascular response to orthostatic stress," Journal of Applied Physiology, vol. 92, pp , [60] L. J. DELL'ITALIA and R. A. WALSH, "Application of a time varying elastance model to right ventricular performance in man," Cardiovascular research, vol. 22, p. 864, [61] D. Burkhoff, et al., "Assessment of Windkessel as a model of aortic input impedance," American Journal of Physiology-Heart and Circulatory Physiology, vol. 255, pp. H742-H753,

125 [62] K. Campbell, "A Pulsatile Cardiovascular Computer Model for Teaching Heart-Blood Vessel Interaction," Physiologist, vol. 25, pp , [63] T. L. Davis and R. G. Mark, "Teaching physiology through simulation of hemodynamics," 1990, pp [64] A. C. Guyton, et al., "Some problems and solutions for modeling overall cardiovascular regulation," Mathematical Biosciences, vol. 72, pp , [65] T. Kenner, "Physical and mathematical modeling in cardiovascular systems," Quantitative cardiovascular studies, vol. 41, p. 109, [66] R. White, et al., "Fundamentals of lumped compartmental modelling of the cardiovascular system," Advances in cardiovascular physics, vol. 5, pp , [67] R. Braakman, et al., "A dynamic nonlinear lumped parameter model for skeletal muscle circulation," Annals of Biomedical Engineering, vol. 17, pp , [68] V. Rideout and J. Katra, "Computer simulation study of the pulmonary circulation," Simulation, vol. 12, p. 239, [69] J. Z. Wang, et al., "Incremental network analogue model of the coronary artery," Medical and Biological Engineering and Computing, vol. 27, pp , [70] M. Zagzoule and J. P. Marc-Vergnes, "A global mathematical model of the cerebral circulation in man," Journal of biomechanics, vol. 19, pp , [71] A. Charloux, et al., "A new impedance cardiograph device for the non-invasive evaluation of cardiac output at rest and during exercise: comparison with the direct Fick method," European journal of applied physiology, vol. 82, pp ,

126 [72] P. LEPRETRE, et al., "Effect of Exercise Intensity on Relationship between [latin capital V with dot above] O2max and Cardiac Output," Medicine & Science in Sports & Exercise, vol. 36, p. 1357, [73] N. Tordi, et al., "Measurements of cardiac output during constant exercises: comparison of two non-invasive techniques," International journal of sports medicine, vol. 25, pp , [74] C. Gabriel, et al., "The dielectric properties of biological tissues: I. Literature survey," Physics in medicine and biology, vol. 41, p. 2231, [75] S. Gabriel, et al., "The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz," Physics in medicine and biology, vol. 41, p. 2251, [76] S. Gabriel, et al., "The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues," Physics in medicine and biology, vol. 41, p. 2271, [77] K. Sunagawa and K. Sagawa, "Models of ventricular contraction based on timevarying elastance," Critical reviews in biomedical engineering, vol. 7, p. 193, [78] J. A. Nelder and R. Mead, "A simplex method for function minimization," The computer journal, vol. 7, p. 308, [79] D. J. Patel, et al., "Relationship of radius to pressure along the aorta in living dogs," Journal of Applied Physiology, vol. 18, pp , [80] D. Patel, et al., "In vivo pressure-length-radius relationship of certain blood vessels in man and dog," Pulsatile Blood Flow, McGraw-Hill, New York, p. 277,

127 [81] W. Welkowitz, "Engineering Hemodynamics: Application to Cardiac Assist Devices," Journal of Clinical Engineering, vol. 13, p. 79, [82] J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput, vol. 19, pp , [83] M. Akay, Biomedical signal processing: Academic Press San Diego, [84] D. Fry, et al., "In vivo studies of pulsatile blood flow: The relationship of the pressure gradient to the blood velocity," Pulsatile Blood Flow, McGraw-Hill, New York, pp , [85] W. W. Nichols, et al., "Input impedance of the systemic circulation in man," Circulation research, vol. 40, pp , [86] J. Martin Bland and D. G. Altman, "Statistical methods for assessing agreement between two methods of clinical measurement," The lancet, vol. 327, pp ,

128 Abstract (in Korean) Forward lumped parameter 기반의 non-uniform hybrid electrical impedance model 과양손임피던스시스템의 유효성검증을통한심기능평가 연세대학교대학원 의공학과 서광석 본학위논문에서는무구속적인심기능평가를위해 1)Forward lumped parameter 기반의 non-uniform hybrid electrical impedance model 을제안하고, 2) 양손임피던스를이용한심박출량검출시스템을제안및유효성을검증한다. 현재임상에서피검자의심박출량을측정함에있어주로이용되는 Fick 방법 (Fick method), 지시물질희석법 (Indicator dilution) 등은침습정인방법으로위험성, 부작용및고도의기술요구와비용, 측정횟수의제한, 환자의고통등여러문제점들을내포하고있다. 이러한문제를해결하고자흉곽임피던스를이용한심박출량이연구되었다. 그러나피검자의흉곽에고가의 band 와 spot 형태의전극을부착해야함에따라여전히구속적이다. 본학위논문에서는효율적인심기능평가를위해기존의집중식파라미터방법을보완한 forward lumped parameter 기반의 non-uniform hybrid electrical impedance model 을제안하였으며, 무구속적이며경제성을고려한크롬양손전극을이용한심박출량검출시스템을개발하였다. 제안된모델과개발된양손임피던스를이용한심박출량검출시스템그리고레퍼런스인 physioflow(pf104d, Manatec Biomedical, France) 의 1 회박출량 (stroke volume) 과심박출량 (cardiac output) 을상호비교함에따라제안된모델과개발된시스템의유효성을평가하였다

129 제안된모델및시스템의유효성평가를위해총 80 명의피검자중탈락자를제외한총 72 명 ( 남자 54 명, 여자 18 명 ) 을대상으로수행되었으며, 실험전모든피검자들에게실험프로토콜설명및동의서를획득하였다. 본논문의실험은연세대학교원주의과대학원주기독병원임상시험심사위원회 (IRB) 의승인을얻어진행되었다. 본논문에서제안한시스템의재현성검증을위해각연령대별 1 명씩, 남자 3 명, 여자 2 명, 총 5 명의피검자에대하여 5 회반복측정을하였다. 실험을통하여얻어진제안된모델과개발된시스템그리고 physioflow 의 1 회박출량과심박출량결과를상관계수 (r), 변동계수 (CV), 대응표본 t-test, Bland-Altman plot 분석을이용하여상호검증하였다. 그결과 1) physioflow 와제안된시스템의 1 회박출량 ( 남자 : r = 0.715, P < 0.001; 여자 : r = 0.704, P < 0.001) 및심박출량 ( 남자 : r = 0.826, P < 0.001; 여자 r = 0.804, P < 0.001), 2) physioflow 와제안된모델의 1 회박출량 ( 남자 : r = 0.735, P < 0.001; 여자 : r = 0.827, P < 0.001) 및심박출량 ( 남자 : r = 0.767, P < 0.001; 여자 r = 0.853, P < 0.001) 3) 제안된모델과제안된시스템의 1 회박출량 ( 남자 : r = 0.788, P < 0.001; 여자 r = 0.812, P < 0.001) 및심박출량 ( 남자 : r = 0.802, P < 0.001; 여자 r = 0.823, P < 0.001) 으로제안된시스템, 모델및 physioflow 에서유의한결과를확인하였다. 본학위논문에서는제안된 forward lumped parameter 기반의 non-uniform hybrid electrical impedance model 과양손임피던스를이용한심박출량검출시스템을통해유의한 1 회박출량과심박출량의검출이가능함을검증하였으며, 심박출량측정방법의제한점을개선한편리하고경제적인방법으로서기존임피던스측정방법의대안으로서사용될것으로기대된다. 주요어 : 심박출량 (Cardiac output), 1 회박출량 (Stroke volume), Impedance cardiogram (ICG), 양손크롬전극, PhysioFlow (PF104D)

130 Appendix 1- IRB Approved

131

132 Appendix 2- Clinical Trial Report