Mechanism. Jaisre.K 1, Sudha Priyadarshini.N 2, Shenbaga Devi.S 3

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1 International Journal of Electrical Electronics and Communication Engineering Simulation of Models for Controlling Blood Volume Abstract: A physiological model of feedback mechanism for controlling blood volume is developed using the parameters from an existing model. These include values of Blood Volume, Cardiac Output, Arterial Pressure, Daily Fluid Intake, Urinary output and Extracellular Fluid Volume. Mathematical model is developed initially using the existing equations. From the biofeedback mechanism, it can be inferred by the increase in the blood volume; it is later controlled and normalised by the changes occurring in values of cardiac output, arterial pressure and urinary output. The previously existing misconceptions can be analyzed using this developed model. Along with the existing parameters total peripheral resistance is been added as a new parameters for this model and electrical analog for the same has been constructed. Keywords: Blood Volume, Cardiac Output, Arterial Pressure, Urinary Output, Daily Fluid Intake and Extracellular Fluid Volume. Mechanism Jaisre.K 1, Sudha Priyadarshini.N 2, Shenbaga Devi.S 3 1 PG Student, 2 Teaching Fellow, 3 Professor Department of ECE, College of Engineering, Anna University, Chennai, INDIA between 700 and 2000ml for 2 liters fluid intake. Extracellular fluid volume (ECFV) usually denotes all body fluid outside of the cells. Volume of ECF is typically 15 L. 2. BACKGROUND: Manjiri R. Purohit, V. D. Hajare Performance Evaluation of Heart from its Mathematical Model using Matlab Simulink. International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: , Volume-1, Issue-6, November 2012.[5] This paper presents the Mathematical modeling of the biological systems that plays a vital role in understanding of their activities and abnormalities associated with them. Various approaches are there in existence for the mathematical representation of the systems. This paper discusses mathematical modeling of the heart based on the activity of the heart by carotid baroreflex control mechanism as a stimulant. 1. INTRODUCTION: The term biofeedback can be defined as the biological response within a system that influences the continued activity of the system. In essence, it is the control of a biological reaction. Here the bio feedback mechanism is termed as the biological response which regulates mechanism to maintain system normal. The increase in blood volume from 5 liters should be returned back to 5 the same by changes in the other parameters like cardiac output, arterial pressure, urinary output and extracellular fluid volume within the cycle. While considering the existing model [1], some misconceptions are present which can be proven to be false. These false interpretations can be analyzed by our model. Blood is the fluid that circulates through the heart, arteries, and veins and is the chief means of transport within the body. The total quantity of blood in an individual depends upon body weight; a person weighing 70 kg has about 4.5 liters of blood in the body. Cardiac output is the volume of blood being pumped by the heart, in particular by a left or right ventricle in the time interval of one minute. Normal range 4 to 8 l/min. Arterial pressure is the pressure of the circulating blood on the arteries; arterial pressure is the product of cardiac output and vascular resistance. Its normal range 120/80mmhg. Urinary output is the total volume of urine excreted daily, normally 8 Prof. Jiří Holčík Windkessel model analysis in matlab Am. J. Physiol. 273 (2000) H19-H27[6] This paper briefly describes three Windkessel models and demonstrates application of Matlab for mathematical modelling and simulation experiments with the models. Windkessel models are usually used to describe basic properties vascular bed and to study relationships among hemodynamic variables in great vessels. Analysis of a systemic or pulmonary arterial load described by parameters such as arterial compliance and peripheral resistance is important for example in quantifying the effects of vasodilator or vasoconstrictor drugs. Jean-Pierre Montani1 and Bruce N. Van Vliet2 (2009). Understanding the contribution of Guyton s large circulatory model to long-term control of arterial pressure.[1]. This paper describes the Guyton s circulatory model is the instrumental exploration in the linkage between blood pressure and sodium balance in demonstrating the importance of renal salt and water balance in setting the blood pressure. In both the model and experimental data, any imbalance between salt intake and salt excretion leads to a progressive alteration of the degree of filling of the vascular system and simultaneous changes in blood pressure.

2 František Lopot,1 Bohdan Nejedlý,2 Sylvie Sulková3(2000) Continuous Blood Volume Monitoring and Ultrafiltration Control Hemodial Int, Vol. 4, 8 14, 2000[9]. This paper describes about the Continuous blood volume monitoring (CBVM) is believed to be a promising method for making the determination of patients dry weight more objective, and ultrafiltration (UF) control more appropriate. Although blood volume response to UF and the interrelation between blood volume changes and changes in hemodynamic parameters are highly individual, certain principles of this response and interrelation can be identified and exploited for effective use of CBVM. vessels that flow though the system increases and the extracellular fluid volume will be decided by the summation of the daily fluid intake, fluid loss and urinary output. So finally when the extracellular fluid volume changes that simultaneously changes the blood volume. 4.a BIOFEEDBACK MODEL FOR BLOOD VOLUME CONTROL The model shows that the system is a biofeedback mechanism as the inputs are inter dependent. Ones output depends in the input of the preceeding function. 3. METHODOLOGY: From the existing model the parameters are been selected and mathematical model is been deduced and simulated as the graphical model. EXISTING MODEL PARAMETER ESTIMATION MATHEMATICAL MODEL SIMULATION (GRAPHICAL MODEL) 4. BLOCK DIAGRAM: Figure 2: Biofeedback Mechanism For Blood Volume Control[2] After checking the normal conditions for the model the abnormal conditions also been analysed. The diabetic Figure 3: Output of the Biofeedback Mechanism [2] Figure1: Block Diagram of Biofeedback Mechanism for Blood Volume Control. The changes in blood volume implies the equal changes in the cardiac output by increasing the heart beat and that influences the arterial pressure to increase by the changes in the resistance of the blood flow and the viscosity of the blood flow and the urinary output increases by the melitus condition and the renial failure conditions are been analysed comparing to the normal conditions. 4.b MISCONCEPTIONS: The misconceptions are the misunderstanding factors that is been considerd in the model are as follows The Primary Renal dysfunction is the origin to hypertension.[1] 9

3 This is false interpretation for hypertension the primary renal dysfunction is not the origin of the hypertension, hypertension is the origin for the renal dysfunction. Some other conditions that would cause hypertension are Mineralocorticoid producing tumor, Coartation of aorta and Sympathetic over activity. So finally whatever the cause of hypertension, it ends in modifying kidney to excrete salt and H2O for given BP level otherwise it increases excretion and at end returns to regular BP level. The role of Central Nervous System in Blood Pressure regulation is limited.[1] The role of Central Nervous System functions for only rudimentary representation. The Effects of sympathetic stimulation is limited to renal effects. The Central Nervous System releases some substances to influence renal function are Vasopressin-peptide hormone, Adreno Cortico tropic hormone, Gamma-Melanocyte and Digitalis glycosides. Our existing model, central nervous system is not controlling Blood Pressure level; Central Nervous System controls only kidney renal functions. Total peripheral resistance can be defined by the resiatance that is offered by the vessel is been measured by the pressure that the blood leaves when the blood is been entering the blood vessel. This parameter is been included between the cardiac output and the arterial pressure as the resistance also describes the pressure changes. 4.d ELECTRICAL ANALOG MODEL: The electrical analog is been created for the cardiac output and arterial pressure, windkessel model is the model that been used for the equivalent electrial analog for the cardiac output and the arterial pressure. The winkessel model is a simplified model that the arterial system of the heart is been modelled as an electrical storage model as the arteries is the interconnected of storage system and these models are in three forms as two element winkessel model, three element and four element. Changes in Mean arterial pressure is linked with the changes total blood volume.[1] The Blood Pressure is not the function for total blood volume. Directly acting on kidney: Noradrenalin or angiotensin to promote sodium retention. Vasoconstriction increases Blood Pressure rapidly, that leads to natriuresis thus decrease blood volume. Vasoconstrictor agents decrease the vascular capacitance that permitting the maintenance of high BP value with a low blood volume. Simulation of these states in our model reveals a state of overfilling of circulation with increased Mean Circulatory Fluid Pressure & Arterial volume in excess despite the decreased total blood volume Whole body Blood flow auto regulation is the cause of volume-loading hypertension [1] Auto regulation is the organ or tissue that adjusts its blood flow by local mechanisms. And it is outside of the main feedback of renal body fluid feedback mechanism. Due to opposing Pressure induced distension of arterioles, auto regulation reduces the change in Extracellular Fluid Volume, Blood Volume & Cardiac Output that may otherwise be required to Increase Blood Pressure to achieve sodium balance. Auto regulation converts the renal fluid feedback mechanism for regulating the Blood Pressure in highly effective manner without changing the fluid volumes. 4.c IDENTIFICATION OF NEW PARAMETER: Apart from the used parameters blood volume, cardiac output, arterial pressure, urinary output, daily fluid intake and extracellular fluid volume the total peripherial resistance is also been added in the biofeedback mechanism. 10 Figure 4: Windkessel Model of the System[4] a)2wm- 2 Element Winkessel Model b)3wm- 3 Element Winkessel Model c)4wm- 4 Element Winkessel Model These models represents the hearts equivalent electrical model and the used elements in the winkessel model the R is the resistance of the blood vessel it s the total peripheral resistance, C is the compliance of the artery,r is the aortic or pulmonary valve pressure and L is the inertia of the blood flow. From these models the differential equations are got and finding the transfer function for the equations and been modeling in the MATLAB simulink. From the output of the winkessel models the arterial pressure is been analysed. 5. RESULTS AND DISCUSSIONS: When considering the model the changes in blood volume affects the cardiac output by increasing the heart

4 beat so if there is any increase in the blood volume that changes the cardiac output also. Table 1: Tablulation for blood volume and cardiac output Blood volume(liters) Cardiac output(l/min) Table 2: Normal Values of the Model No Parameters Normal range 1) Blood volume 3.5 to 5( liters) 2) Cardiac output 4 to 8 (liters/min) 3) Arterial Pressure 120/80(mmHg) 4) Urinary Output 0.8 to 2 (liters) 5) Daily fluid intake Upto 2 liters 6) 7) Extracellular fluid volume Total peripheral resistance 15 liters 9 to 20 (mmhg.min/l) After the cardiac output in the model the arterial pressure comes that changes due to the increase in cardiac output or due to the total peripheral resistance or the viscous nature of the blood. Table 3: Tabulation for Cardiac Output and Arterial Pressure Cardiac output(l/min) Arterial pressure(mmhg) Next the urinary output comes that is changed due to the renal vessels that flow through the system causes the urinary output to change. Table 4: Tabluation for Arterial Pressure and Urinary Output Arterial pressure(mmhg) Urinary output(l/day) pressure divided by the cardiac output Table 5: Total Peripheral Resistance Values Pressure ( mmhg) Cardiac Output (l/min) Total Peripheral Resistance (Mmhg.min/l) CONCLUSION Finally the model is been analysed by addition of the parameter in the model between the cardiac output and the arterial pressure and the equivalent electrical analog also been constructed and analysed. References (1) Jean-Pierre Montani1 and Bruce N. Van Vliet2 (2009)Understanding the contribution of Guyton s large circulatory model to long-term control of arterial pressure 2009 The Authors. Journal compilation. (2) Wylie Churchill-Davidson's A Practice of Anesthesia 7th Edition (3) Dr. Arthur C. Guyton textbook of medical physiology isbn international Edition ISBN X Copyright 2006, 2000, 1996, 1991, 1986, 1981, 1976, 1971, 1966, 1961, 1956 by Elsevier Inc. (4) Hauser, J. Parák, J. Ložek, M. Havlík, J.: system analyze of the windkessel models.in BioDat 2012 Conference on Advanced Methods of Biological Data and Signal Processing [CD-ROM]. Praha: České vysoké učení technické v Praze, 2012, vol. 1, p ISBN (5) Manjiri R. Purohit, V. D. Hajare(2012) Performance Evaluation of Heart from its Mathematical Model using Matlab Simulink International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: , Volume-1, Issue-6, November (6) Lambermont, B., et. al.: Comparison between Three- and Four-Element Windkessel Models to Characterize Vascular Properties of Pulmonary Circulation, Arch. Physiol. And Biochem. 105 (1997) Total peripheral resistance is been calculated by 11

5 (7) Evans RG,Malpas SC, Osborn JW& Fink GD (2005). Neural, hormonal and renal interactions in long-term blood pressure control. Clin Exp Pharmacol Physiol 32, (8) Guyton AC (1990). Long-term arterial pressure control: an analysis from animal experiments and computer and graphic models. Am J Physiol Regul Integral Comp Physiol 28, R865 R877. (9) František Lopot,1 Bohdan Nejedlý,2 Sylvie Sulková3(2000) Continuous Blood Volume Monitoring and Ultrafiltration Control Hemodial Int, Vol. 4, 8 14,