ABSTRACT FOURIER ANALYSIS OF THE TIME CURVES OF THE BASIC CARDIAC PARAMETERS OF ACUTELY-PREPARED OPEN-CHEST CATS AND TURTLES UNDER VARIOUS EXPERIMENTAL CONDITIONS By Esmail Koushanpour Cardiovascular waveforms are periodic sinusoids. Therefore, to obtain information on the source of distortion of contours from pressure and flow records, the curves must be analyzed into their components. The goal of such analysis is to present as uniquely as possible the inter- vals which are of most interest so that significant information is not discarded in an averaging process. Fourier analysis of the cardiac time curves involves the representation of an empirical function as it is re- corded and not the statistical characteristics of the empirical function. Using a variable Whitney gauge (mercury-filled latex rubber tub- ing), intraventricular and aortic catheters, and a force-displacement strain gauge, simultaneous records of cardiac circumference, pressure within the heart, and aortic pressure were obtained in acutely prepared open-chest turtles and cats. To analyze the cardiac time curves by the Fourier method, from a series of control or experimental records, a cardiac cycle was selected at random. Each cycle was then divided into ten equal time intervals. The amplitude values at each of these time Esm ail Koushanpour intervals were punched on standard IBM punch-cards and fed into a 160-A Fortran Control Data digital computer programmed to print out the values for area under the curve, sine and cosine coefficients, and amplitude and phase angle values for the first five harmonics. Spectral and harmonic analyses of cardiac waveforms after adrenalin showed that this drug stimulates turtle heart muscle directly, whereas its action on the cat heart is initially on the conductive system and secondarily on the myocardium. Acetylcholine infusion decreased the force of cardiac contraction and prolonged the systolic phase of the cycle. However, acetylcholine infusion in the cat, in addition to car- diac depression, resulted in peripheral vasodilation. Moreover, it was shown that stimulation of vagus in the cat produces its effect primarily on the heart. These conclusions were based on the changes in the frequency distribution of impedance amplitude and impedance phase angle of the analyzed cardiac function curves. The action of adenylic acid in the cat was primarily on the aorta and not on the heart. The reduction in vascular impedance after adenylic acid was attributed to the vasodilating effect of this drug. Alteration of peripheral resistance by occlusion of the aorta resulted in an increase in vascular impedance and distensibility. Reduction in venous return, by occluding both vena cavae, produced a marked decrease in the inertial characteristics, whereas augmentation of venous inflow resulted in an increase in the distensibility or the elastic components of the vascular system. Esmail Koushanpour It is concluded that the application of Fourier transform is a more realistic approach to the analysis of periodic pressure and flow changes in the circulation. It is suggested that such analysis is capable of deciding the true phasic pattern of the arterial pulse in addition to elucidating the hemodynamic changes of the vascular system. FOURIER ANALYSIS OF THE TIME CURVES OF THE BASIC CARDIAC PARAMETERS OF ACUTELY-PREPARED OPEN-CHEST CATS AND TURTLES UNDER VARIOUS EXPERIMENTAL CONDITIONS By Esmail Koushanpour A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physiology and Pharmacology 1963 ACKNOWLEDGMENTS The author expresses his gratitude to Dr. W. D. Collings, Professor of Physiology, Michigan State University, for over four years of teaching and encouragement, and his critical scrutiny during the course of this investigation and preparation of the manuscript. The writer also wishes to thank members of guidance com- mittee, Drs. W. L. Frantz, E. P. Reineke, and L. F. Wolterink for their interest and critical suggestions during the course of the study. The author is also indebted to Dr. J. R. Hoffert who kindly helped in the preparation of the original photographs, and to Mr. R. K. Bhatnagar who assisted generously in preparation of some of the experimental animals. ii TABLE OF CONTENTS INTRODUCTION ......................................... SURVEY OF LITERATURE ............................... Determinants of Cardiac Performance 1. Three Fundamental Discoveries II. The Law of Uniformity of Behavior III. Starling Law of the Heart IV. Wiggers' Law of Initial Tension V. Modern Views of Cardiac Control Dynamics of Ventricular Function under Experimental Conditions I. Effect of Thoracotomy on Cardiac Function 11. Cardiodynamic Actions of Drugs III. Hemodynamics of Hypervolemia IV. Cardiac Performance and Peripheral Resistance Analysis of Cardiac Time Curves I. Qualitative Description of Cardiac Function Curves II. Mathematical Analysis of Cardiac Time Curves MATERIALS AND METHODS .............................. Expe rim ental Anim a1 3 Turtle Experiments ll 12 l3 18 20 22 23 33 37 37 37 Cat Experiments Cardiac Response to Nervous Stimulation Effect of Anoxia Acute Occlusion of Major Vessels Effect of Drugs on Cardiac Function Cardiac Function and Hypervolemia Physical Characteristics of the Monitoring Instruments Used 1. Detecting and Sensing Elements II. Recording and Read-out Devices Fourier Analysis of Cardiac Time Curves CALCULATIONS ....................................... Estimation of Residual and Stroke Volumes from Circumference Mathematical Derivation of Tension Time Curves RESULTS AND DISCUSSION ............................. Turtle Experiments Cat Experiments Changes in Cardiac Function with Drugs Changes in Peripheral Resistance and Venous Return I. Occlusion of Vessels II. Venous Infusion iv Page 40.. 44 44 44 45 45 46 53 59 61 68 68 72 75 76 96 112 144 145 159 Page SUMMARY AND CONCLUSIONS .......................... 168 REFERENCES CITED .................................... 173 APPENDICES ........................................... 182 A. AN INTRODUCTION TO THE USE OF COMPUTERS 183 I. General 184 II. Components of a Computer 185 III. Applications 186 IV. Communication with a Computer 187 V. Types of Programs 188 B. A PROGRAM AND DETAILED INSTRUCTIONS FOR COMPLETE FOURIER ANALYSIS ON 160-A FORTRAN .............................. . 190 Table 10. 11. 12. 13. LIST OF TABLES Comparison of Some Cardiac Parameters in Turtles Comparison of Basic Cardiac Parameters Under Various Conditions in Turtles ..................... Comparison of First Fourier Coefficients of Basic Cardiac Parameters Under Various Conditions in Turtle s ......................................... Fourier Components for Left Ventricular Pressure, Left Aortic Pressure, and Left Ventricular Circum- ference Under Various Conditions in Turtles ........ Comparison of Wet Weight of Ventricles as Percent- ages of Body Weight and Body Surface Area in Cats . . Comparison of Some Cardiac Parameters in Cats ...... Right Common Carotid and Pulse Pressure of Cats Before and After Thoracotomy and the Ratio of Carotid Pressure to Wet Ventricular Weight ......... Changes in Systolic Blood Pressure and Pulse Rate Under Various Conditions in Cats .................. Fourier Components for Right Common Carotid Pressure Under Various Conditions in Cats ........ Changes in Systolic Blood Pressure Under Various Conditions in Cats ............................... Comparison of First Fourier Coefficients of Right Carotid Pressure Under Various Conditions in Cats . . Comparison of Dose-Duration of Various Drugs ....... Effect of Various Drugs on Systolic Blood Pressure and Pulse Rate in Cats ........................... vi Page 77 81 83 85 97 98 101 105 107 109 110 113 117 Table Page 14. Comparison of First Fourier Coefficients of Basic Cardiac Parameters Under Various Conditions in Cats. . 119 15. Effect of Various Drugs on Systolic Blood Pressure and Pulse Rate in Cats ................................. 129 16. Comparison of First Fourier Coefficients of Basic Cardiac Parameters Under Various Conditions in Cats . 131 17. Changes in Systolic Blood Pressure and Pulse Rate Under Various Conditions in Cats .................... 139 18. Comparison of First Fourier Coefficients of Basic Cardiac Parameters Under Various Conditions in Cats . 140 19. Changes in Systolic Blood Pressure and Pulse Rate Under Various Conditions in Cats ................... 148 20. Comparison of First Fourier Coefficients of Basic Cardiac Parameters Under Various Conditions in Cats . 150 21. Fourier Components for Left Ventricular and Pulmonary Artery Pressures Under Various Conditions in Cats . . . . 165 22. Fourier Components of Aortic Pressure Under Various Conditions in Cats ................................. 166 23. Fourier Components of Ventricular Circumference Under Various Conditions in Cats .................... 167 Figure LIST OF FIGURES Top--Position of Circumference (Volume) Transducer Around the Turtle Ventricle ........................ Bottom--Position of Circumference (Volume) Transducer Around the Cat Ventricles .......................... Typical Records of Cardiac Function Curves in Turtle . . . . Top--Typica1 Records of Cardiac Function Curves in Cat . Bottom--Changes in Cardiac Time Curves After Adrenalin Injection in Cat ........................... Standard Calibration Curve for Statham Model (31-32-450 Force-Displacement Transducer ..................... Top--'Diagram of the Wheatstone Bridge in Which the Variable Resistance Gauge (Rg is included in R1) Forms Part of an Arm ............................. Bottom--The Plot Showing the Experimental Deter- mination of the Gauge Factor (F) for the Variable Re sistance Gauge .................................. Typical Illustration of the Procedure Used To Divide Various Function Curves into Equal Time Intervals . . . . Top--Changes in the Left Aortic Pressure Curve After Adrenalin Injection in Turtle ........................ Middle--Changes in Ventricular Function Curves After Adrenalin Injection in Turtle ........................ Bottom--Changes in Ventricular Function Curves After Acetylcholine Injection in Turtle ..................... Variations of Impedance with Pulsating Frequency of the Turtle Ventricle Under Control Conditions, After Adrenalin Injection, and After Acetylcholine Injection . . viii Page 39 41 43 43 57 60 60 67 79 79 79 89 Figure 10. 11. 12. 13. 14. 15. 16. Variations of Impedance Phase Angle with Pulsating Frequency of the Turtle Ventricle Under Control Conditions, After Adrenalin Injection, and After Ac etylcholine Infusion .............................. Comparison of the Time Course of Tension of the Turtle Ventricle Under Control Conditions and 30 Sec. After 10 pg. of Adrenalin Injection ....................... Comparison of the Time Course of Tension of the Turtle Ventricle Under Control Conditions and 10 Sec. After 50 pg. of Acetylcholine Injection .................... Top--Changes in the Right Common Carotid Pressure Pulse After Pneumothorax and Thoracotomy in the Cat . Bottom--Change in the Right Common Carotid Pressure Pulse as a Result of Pulsus Alternans in the Cat ...... Top--Cardiac Time Curves Under Control Conditions in the Cat ......................................... Bottom--Change in Contours of Ventricular Function Curves 60 Sec. After 9 pg./kg. of Adrenalin Injection in the Cat .......................................... Top-~Changes in Contours of Cardiac Time Curves 40 Sec. After 20 pg. /kg. of Acetylcholine Injection in the Cat ........................................... Bottom--Changes in Contours of Ventricular Function Curves 10 Sec. After 200 ug./kg. of Acetylcholine Infusion in the Cat ................................. Variations of Impedance with Pulsating Frequency of the Cat Ventricle Under Control Conditions, After Adrenalin Injection, and After Acetylcholine Infusion .......................................... Variations of Impedance Phase Angle with Pulsating Frequency of the Cat Ventricle Under Control Condi- tions, After Adrenalin Injection, and After Acetyl- choline Infusion ................................ '. . . ix Page 103 103 115 115 116 116 121 123 Figure Page 17. Top-«Changes in Contours of Cardiac Time Curves 40 Sec. After 9 pg. /kg. {of Adenylic Acid Injection in the Cat ............................................... 126 Bottom--Changes in Contours of Ventricular Function Curves 30 Sec. After 120 pg./kg. of Histamine Infusion in the Cat ................................. 126 18. Variations of Impedance of the Cat Aorta with Pulsating Frequency Under Control Conditions, After Nor- adrenalin Injection, and After Adenylic Acid Infusion . . . 132 19. Variations of Impedance Phase Angle with Pulsating Frequency of the Cat Aorta Under Control Conditions, After Nor-adrenalin Injection, and After Adenylic Acid Infusion .......................................... 133 20. Comparison of the Time Course of Tension of the Cat Aorta Under Control Conditions, After Adrenalin Injection, After Nor-adrenalin Injection, and After Adenylic Acid Infusion. ............................. 135 21. Top--Changes in Contours of Cardiac Time Curves During Stimulation of Right Intact Vago-sympathetic Trunk in the Cat .................................. 137 Bottom--Changes in Contours of Cardiac Function Curves During Stimulation of Left Intact Vago- sympathetic Trunk in the Cat ........................ 137 22. Variations of Impedance with Pulsating Frequency of the Cat Aorta Under Control Conditions, After Acetyl- choline Injection, and During Right Vagus Stimulation . . 142 23. Variations of Impedance Phase Angle with Pulsating Frequency of the Cat Aorta Under Control Conditions, After Injection of Acetylcholine, and During Right Vagus Stimulation ................................. 143 24. Top--Changes in Cardiac Time Curves During Occlusion of Thoracic Aorta in the Cat ........................ 147 Bottom-~Changes in Contours of Cardiac Function Curves During Occlusion of Thoracic Aorta in Cat ............ 147 Figure 25. 26. 27. 28. 29. 30. 31. Top--Ventricu1ar Time Curves During Occlusion of Both Vena Cavae in the Cat ......................... Bottom-—Changes in Contours of Ventricular Function Curves During Occlusion of Both Vena Cavae in the Cat. Variations of Impedance with Pulsating Frequency of the Cat Aorta Under Control Conditions, After Thoracic Aorta Occlusion, After Pulmonary Artery Occlusion, and After Both Vena Cavae Occlusion ................ Variations of Impedance Phase Angle with Pulsating Frequency of the Cat Aorta Under Control Conditions, After Thoracic Aorta Occlusion, After Pulmonary Artery Occlusion, and After Both Vena Cavae Occlusion ......................................... Comparison of the Time Course of Tension of the Cat Aorta Under Control Conditions, After Thoracic Aorta Occlusion, After Pulmonary Artery Occlusion, and After Both Vena Cavae Occlusion ................... Top--Changes in the Contours of Ventricular Function Curves 100 Sec. After 50 m1. of Saline Infusion in the Cat ............................................... Bottom--Changes in the Contours of Cardiac Time Curves 400 Sec. After 50 m1. of Saline Infusion in Cat ........ Variations of Impedance with Pulsating Frequency of the Cat Aorta Under Control Conditions, 40 Sec. After 50 m1. Saline Infusion, 100 Sec. After 50 m1. Saline Infusion, and 400 Sec. After Saline Infusion ........... Variations of Impedance Phase Angle with Pulsating Frequency of the Cat Aorta Under Control Conditions, 40 Sec. After 50 m1. Saline Infusion, 100 Sec. After 50 m1. Saline Infusion, and 400 Sec. After 50 ml. Saline Infusion ..................................... xi Page 152 152 153 154 158 160 160 162 163 INTRODUCTION Recent studies on the dynamic performance of the heart on open- chest and intact animals have increased markedly our knowledge of cardiac function (Rushmer, 1961). These investigations have become possible through development of highly mechanized and complex elec- tronic recording and data processing instruments. With the rapid advances in physiological technology there is a growing need for con- tinuous monitoring and analysis of physiological data. The impact of this technological progress has opened a new era in physiology in which mathematical and physical analysis of physiological phenomena are replacing the usual statistical methods. This is not to say that statis- tical treatment of physiological data is not useful. However, since sta- tistical inferences place great emphasis upon the pooled effect of a population and not the individual contributions to the over-all effect, little if any, gain can be obtained from statistical analysis alone. This is particularly true in the case of the cardiovascular system. The signal variations, such as pressure, volume, flow, and tension curves recorded from the various components of the cardiovascular system are multiple- harmonics time curves. In order to determine the over—all changes in these recorded signals under various physiological conditions, we must determine changes in the individual components which are coded in these signals during each cardiac cycle. Since the recorded signal variations of the cardiovascular system are periodic in occurrence, the tendency has been to consider them as multiple sine and cosine curves with finite frequency. One suitable method for analysis of such multiple-harmonics time curves is the application of a mathematical method known as Fourier analysis. This method has been applied to the analysis of human electro- cardiogram (Thompson, 1962), and pressure-flow curves in femoral artery of dogs (McDonald, 1955, and Randall and Stacy, 1956). In the present study, using a variable resistance gauge (a mercury- filled rubber tube), intraventricular and aortic catheters, and a force- displacement strain gauge, simultaneous records of the circumference, pressure, and weight changes in the heart were obtained in acutely- prepared open-chest cats and turtles. Then, by Fourier analysis of the data an attempt was made to describe quantitatively the changes in the cardiac function curves of these two animals under acute experimental conditions. This method of analysis is considered to be a powerful tool by means of which we can gain an insight into the mechanisms of changes in cardiac function, for example, after epinephrine, acetylcholine, or adenylic acid injection. Fourier analysis of the cardiac time curves was processed by writing a special program in FORTRAN for l60-A Fortran Control Data computer. SURVEY OF LITERATURE Determinants of Cardiac Performance The cardiovascular system is composed of two functionally and anatomically different components, namely, the heart and the blood vessels. The heart functions basically as a pump in imparting energy to the blood and propelling it through the vascular tree. The blood vessels function as conduits through which blood is transported from one region of the animal body to the other. The interplay of the ana- tomical constituents of these two components as manifest in their functions should be considered when the function of the cardiovascular system as a whole is evaluated. The circulatory system can be re- garded as a black box which generates certain sinusoidal functional curves through the interaction of its components. These generated curves, under a given condition, have coded within them the individual contribution of the components. Therefore, the generated functional curves can be considered as a sum of the fractionate functions of the various components. To gain an understanding of the nature of the action of the components of this black box, attempts have been made to analyze the output curves of the system. Since the nature and useful- ness of any analysis depends upon the method by which the functional curves have been obtained, our understanding of the system has been conditioned by the techniques used. Early studies on the functional activity of the cardiovascular system have been done on cardiac and skeletal muscles of cold-blooded animals. The basic assumptions in these studies have been that the two types of muscle systems are similar in functions. It should be realized that much has been learned about cardiovascular physiology from studies on skeletal muscle. I. Three Fundamental Discoveries In 1871 H. P. Bowditch performed the first classical studies in ellucidating the functional activity of the cardiac muscle. Using the apex of the frog's ventricles, Bowditch showed that the amplitude of cardiac contraction remains the same regardless of the strength of the applied stimulus. This phenomenon, some seven years later was phrased into the well-known "all or none'I law by the French investi- gator L. A. Ranvier. Bowditch also demonstrated that the heart muscle exhibits "treppe" or ”staircase" phenomenon which indicates that the individual stimulus exerts a beneficial after-effect on the responsiveness pattern of the cardiac muscle. The second fundamental discovery was the result of the investi- gations of Howell and Donaldson (1884). Using the Newell Martin heart- lung preparation in the dog, they showed that the heart has some intrinsic mechanisms which allow it to adjust its output to the venous input. When venous inflow to a 76 gm. heart was increased, the cardiac output increased from 480 to 1964 ml. per min. and the stroke volume increased from 5. 2 to 21. 6 ml. per beat. The increase in venous inflow resulted in the elevation of the right atrial pressure from 10 to 60 cm. of blood. However, when the right atrial pressure was restored to 10 cm. of blood the cardiac output was reduced to 400 ml. per min. and the stroke volume to 2. 38 ml. per beat. The non-linear relation between the venous inflow and the output of blood from the heart was interpreted as a sign of deterioration of cardiac performance as a result of a short period of strain. In 1895, Otto Frank published his famous treatise on the "dynamics of heart muscle” which contained the results of experiments leading to the third fundamental discovery. In this work, he attempted "to corre- late as far as possible the mechanical reactions of cardiac muscle with the well-known responses of skeletal muscle previously established by A. Frick, J. von Kries, and Blix. " The latter investigators established the so-called initial length and tension diagrams for the skeletal muscles under various conditions. Otto Frank made isometric and isotonic recordings of the contracting frog's atria and ventricles under various degrees of diastolic filling and pressure. He found that the stepwise increase in the presystolic volume and pressure determined the magnitude of the ”all or none" response of the heart. These three classical discoveries formed the foundation upon which the designs of the future experiments were based. II. The Law o_f Uniformity of Behavior In 1906, Y. Henderson using improved plethysmographic and cardiometric techniques obtained records of the ventricular activity under various filling and emptying conditions. He found that the contour of the volume curve is affected by the coronary blood flow. Henderson (1906) regarded the mammalian auricle as an elastic reservoir and not as a force pump. Based on various experiments, he stated that the ventricular volume curve resembles the form of an isotonic or an after- loaded muscle curve. Henderson (1906) concluded that the cardiac cycle consists of three phases: (1) ventricular systole which represents the contraction and discharge phase of the cycle, (2) ventricular diastole representing the relaxation and filling of the cycle, and (3) diastasis which is the period of the resting phase of the cardiac cycle. In subsequent studies, Henderson (1909, 1913, 1923) demonstrated that the diastolic volume is the primary determinant of the cardiac function. He concluded that: (1) under normal condition of venous in- flow, diastolic volume is determined by a fixed ventricular relaxation pattern, (2) additional increase in venous inflow does not affect the diastolic capacity and subsequent systolic ejection, and (3) greater in- crease in venous inflow is accommodated only by increasing the heart rate. III. Starling's Law _o_f_ Initial Length In 1914 Patterson, Piper, and Starling carried out a series of experiments on the isolated heart-lung preparation. This artificial circulatory scheme, although it had limitations, was a useful method of controlling the changes in heart rate, mean arterial pressure, and venous inflow. After a series of elaborate experiments, Starling (1918) pro- posed the well-known law of the heart based on the following conclusions: 1. When peripheral resistance and venous inflow is held con- stant, changes in heart rate from 60 to 160 per minute did not alter cardiac output per minute significantly. This con- clusion was diametrically opposed to that of Y. Henderson (1913). 2. When heart rate and mean arterial pressure were kept con- stant, changes in venous inflow resulted in a definite change in the diastolic size of the ventricle and cardiac output. A compensatory increase in stroke volume occurs in proportion to the degree of ventricular distension in diastole up to a critical point. 3. During the compensatory state pressure increased in both atria. However, during decompensation pressure increased in the left atrium and dropped in the right atrium. 4. The output of the fatigued and fresh hearts could be the same if the atrial pressure and presystolic volume of the fatigued heart were greater than that of the fresh heart. IV. Wiggers' Law o_f_ Initial Tension In 1922, C. J. Wiggers and L. N. Katz, using an improved heart-lung preparation as well as optical manometers and cardiometric techniques, made detailed analytical studies of the changes in heart rate, venous inflow, and mean arterial pressure and their relation to presystolic ventricular volume. They concluded that the systolic ejec- tion is determined not by presystolic size, but by the presystolic ten- sion, coronary blood supply, humoral agents, and the nerves which innervate the ventricular muscle. These findings were re-evaluated subsequently by Wiggers (1927, 1928, 1938, 1952) and Katz (1927, 1928, 1955, 1960). Wiggers (1928) noted that the changes in initial volume and pres- sure are always in the same direction except in premature beat and after epinephrine. In the latter two conditions, changes in cardiac activity vary in the direction of changes in initial volume and not the initial pressure. These findings were in accord with Starling's concept that the cardiac regulation is in terms of initial volume and the initial pressure. Katz (1928), using an isolated perfused turtle heart demon- strated that despite the constant initial pressure, the changes in ampli- tude, duration, and tention-time of the pressure curve varied in the same direction as the initial volume. He concluded that in the turtle cardiodynamic regulation depends on the initial volume and not the initial intraventricular pressure. No influence of the lateral pressure on cardiac activity was found. V. Modern Views o_f Cardiac Control The early experiments which culminated in the establishment of various laws governing the cardiac function were all performed on isolated heart or heart-lung preparations. It was only natural to raise the question as to whether the results of experiments on isolated heart can be applied to intact animals. Katz (1927), reviewing the researches of previous investigators stated that studies on the isolated heart have produced two schools of thought. One school believes that the increase in initial tension causes a prolongation of systole, whereas, increasing peripheral resistance shortens the period of ventricular systole (Wiggers and Katz, 1922). The second school maintains that both these efforts are the results of increase in the length of the myocardial fibers (increase in volume) and not the change in initial tension (Starling, 1918). Katz (1927), on the basis of his own studies, concluded that the heart-lung preparation can be considered as a useful tool in cardiodynamic studies in that it eliminates some of the variables. However, this method intro- duces other variables of its own and "does not allow the independent variations of two important factors, namely, the initial tension of the left ventricle and the arterial load. ” Attempts have been made to analyze the cardiodynamic function under various conditions from the dynamic changes in pressure pulse 10 contours. Katz and Wiggers (1927) used a method of analysis of pres- sure pulse contours to evaluate results of the various studies on the heart-lung preparation and their application to intact animals. They concluded that changes in the contour of pressure pulses reflect variation in the systolic pattern of the ventricle and that these changes, as observed in open-chest animals with nervous system intact, do not correspond to those obtained in the heart-lung preparation which lacks innervation. Therefore, results from the heart-lung preparation cannot be extra- polated to those of intact animals nor to open-che st animals. In 1955 Katz, reviewing literature of the past three decades, stated that the end-diastolic volume has proven to be only one of the determinants of the regulation of cardiac performance. Other factors which are equally, if not more, important are peripheral resistance, humoral and neurogenic factors, cardiac contractility and distensibility, heart rate and systolic residual volume. Recent studies on the cardiodynamic function of the intact heart by means of modern techniques have questioned the applicability of Starling's law of the heart, based on the heart—lung preparation, to the intact heart in closed chest animals. Recording intraventricular pressure, circum- ference, and diameter of both right and left ventricles in intact dogs, Rushmer and associates (1951, 1953, 1954, 1956, 1959, 1961) showed that the immediate effects of exercise were an increase in the heart rate with progressive reduction in the systolic and diastolic diameters. 11 Rushmer (1954) found no evidence of greater diastolic distension during exercise as demanded by Starling's law of the heart. As a result of a series of experiments, Rushmer (1954) concluded that the increase in stroke volume in response to exercise is primarily achieved by a greater systolic ejection which encroached upon the "systolic reserve volume. " Hawthorne (1961) reported his observations on the instantaneous dimensional changes in the left ventricle in unanesthetized intact dogs. He postulated that ”during ejections the ventricle tends to become ellip- tical, and during filling it becomes more circular. " Since the works of Rushmer and his group (1961) many other in- vestigators have recorded the various cardiac parameters in intact animals under various conditions. Remington (1962) reviewing the recent progress made in muscle physiology states that any understand- ing of the functions of skeletal, smooth, and cardiac muscles must await the analysis of the time course of the contraction process. Dynamics o_f Ventricular Function Under Experimental Conditions Wiggers (1952) classifies the determinants of myocardial response into two categories: (1) the primary coefficients which induce direct myocardial action, such as the effects of drugs, nervous system, and local metabolites, and (2) the secondary coefficients producing a change in the cardiac output by altering the venous inflow. The effect of primary coefficients is characterized by the change in initial tension and amplitude 12 of ventricular contractions in the same direction. The effects of secondary coefficients are characterized by the changes of initial ten- sion and amplitude of contractions in the opposite direction. In the body these two coefficients operate simultaneously. I. Effect 52 Thoracotomy on Cardiac Function The heart is situated within the pericardium in an environment which is slightly subatmospheric. The existence of negative pressure within the thoracic cavity has been considered necessary to the normal cardiac function. When the chest of the animal is opened the heart is reduced in size and the cardiac performance will be below par (Rushmer, 1961). The marked changes in cardiac function following thoracotomy have been studied by a number of investigators. Ferguson, Shadle, and Gregg (1953) observed that in open chest dogs blood pressure was lower, heart rate was faster, and the peripheral resistance was somewhat greater than the closed chest dogs. They found that the degree of direc- tional correlation between the end-diastolic pressure, stroke work, stroke volume, and cardiac output was a function of whether the chest was closed or open. Ferguson and co-workers (1953), however, found no correlation between the presence of pericardium and cardiac function in open or closed chest dogs. Rushmer, Finlayson, and Nash (1954) made cinefluorographic studies on closed and open chest dogs. After intravenous injection of 50 ml. of thorotrast, films were taken from cardiac silhouette after each of the following procedures: (1) surgical 13 anesthesia induced by intravenous Nembutal, (2) thoracotomy, and (3) the application of a cardiometer. They found a consistent diminishing of the area of cardiac silhouette and of the left ventricular chambers. The systolic ejection was more complete (greater emptying) in open chest as compared with closed chest dogs. It was concluded that the response of the heart in the open chest animal cannot be extrapolated to the intact heart, since in the open chest condition the heart tends to become larger in response to an increased load. It appears possible that many of these hearts could not have become smaller. II. Cardiodynamic Actions o_f Drugs The regulation and control of ventricular contraction in the intact unanesthetized animals are the results of the interplay of many different factors including the heart rate, coronary blood supply, hormones (such as 1-‘epinephrine and norepinephrine), autonomic nervous system, and perhaps many others. Physiologists have long been interested in the manner by which these factors, in particular hormones and nervous sys- tem, regulate and modify myocardial contractility and cardiac perform- ance. Since the discovery of the humoral agents presumably released at the effector endings of cardiac nerves, attempts have been made to stimulate the action of these substances by exogenous preparation and intravenous administration. Among the drugs most widely used are l- epinephrine and l-norepinephrine. The amount of these substances 14 released at the nerve endings is very small. Cannon and Rapport (1921) found that the amount of epinephrine released as a result of afferent stimulation is about 3. 5 to 3. 7 ug/kg. /min. Wiggers (1927) studying the mechanism of cardiac stimulation by drugs in dogs observed that epinephrine increases the maximum systolic pressure, systolic dis- charge, and increases pulse pressure. This effect of epinephrine was found to be independent of whether vagus nerves were intact or cut and whether the heart rate is slowed or accelerated. The greater systolic discharge, following epinephrine injection, was thought to be entirely due to the increased velocity of discharge. Wiggers (1927) further ob- served that the effect of epinephrine on the heart is augmented by the alteration of secondary factors such as peripheral resistance and initial tension. In animals with intact vagus, large doses of epinephrine were found to cause A-V block through the intact vagus stimulation. However, after vagotomy, an A-V block may be removed by epinephrine. Wiggers concluded that epinephrine exerts the following actions on the overall performance of the heart: (1) steeper isometric pressure gradient, (2) higher maximum pressure, (3) increased pulse pressure, and (4) abbreviation of the duration of systole. Goldberg and co-workers (1948) studied the hemodynamic response of man to norepinephrine and epinephrine. They found that infusion of 0. 15 to 0. 30 [lg/kg. /min. of epinephrine for 11 to 14 minutes resulted in an increased systolic pressure and cardiac output and a decrease in 15 peripheral resistance. They concluded that epinephrine is an overall vasodilator and a cardiac stimulant drug. Goldberg and associates (1948) observed that the bradycardia resulting from infusion of 0. 2 pg./kg./min. of nor-epinephrine is of vagus origin, because it is abolished by atropine. They showed that in man nor-epinephrine pro-3 duces an increase in both systolic and diastolic pressure, an increase in peripheral resistance, but no change in cardiac output. Infusion of both epinephrine and nor-epinephrine combined in equal amounts resulted in a slight fall in the mean blood pressure, increased cardiac output, and decreased peripheral resistance. Ahlquist (1950) reporting on the comparative effects of epinephrine and arterenol-isopropyl arterenol mixture confirmed the results of earlier investigations that epinephrine is a vasoconstrictor and exciting agent but is less active than arterenol. Ahlquist further confirmed the theory that the pressor response to epinephrine is diminished by its simultaneous vasodilating action. Brown and Boxill (1951) and Brown (1952) determined dose-response curves for l-epinephrine and l-norepinephrine by injecting progressively logarithmically spaced doses of drugs into dogs. They found that the dose-response curves for both drugs were rectangular hyperbolas having the equation, mXY + nY - X = 0, where X is pg. of base per kg. of body weight, Y is the rise in blood l6 pressure in mm. Hg, and m and n are constants so chosen that g; is the asymptote parallel to the X-axis and int—1 the asymptote parallel to the Y-axis. The values of m and n were determined by locating the center of each hyperbola by the method of least squares, using the Legrange method of undetermined multiplier. They found no evidence of any significant vasodilating action of any of these drugs until a dosage level of about 5 pg. /kg. is reached. At this dose level a marked after- depression of blood pressure was observed. The cardiovascular responses to l-epinephrine and l-norepinephrine in animals with intact and denervated pressoreceptors were studies by Boxill and Brown (1953) and Hilton and Brown (1954). They confirmed the earlier findings that in the presence of amounts of circulating l-epinephrine and l—norepinephrine sufficient to elevate systemic blood pressure, the pressoreceptor reflexes are incapable of limiting either the rise in blood pressure or the peak blood pressure attained. These investigators concluded that if these drugs have any effect upon duration of the blood pressure rises, the pressoreceptor reflexes prolong the rise. Therefore, it appears that pressoreceptor reflexes are important as protecting agents against hypotension, but not against hypertension. The action of l-norepinephrine upon pulmonary arteriolar resistance in man was investigated by Fowler and co-workers (1951). They found that infusion of l-norepinephrine resulted in increased pulmonary artery and brachial artery pressure, increased peripheral resistance, diminished 17 cardiac output and bradycardia. They postulated that increase in pulmonary artery pressure by the action of l-norepinephrine is a protective measure against edema formation and is due to the increased "capillary" or venous pressure in lungs. Increase in pulmonary venous pressure is thought to cause an increase in left atrial pressure which in turn induces pulmonary artery hypertension. Peripheral venous constriction was postulated by Fowler and associates (1951) to be the reason for systemic hypertension following l-norepinephrine injections. This implies that a definite increase in the systemic peripheral resis- tance is produced during the period of drug administration. If the systemic peripheral resistance (R) is related to mean blood pressure (P) and flow (Q) by the equation, R = g, then any change in R should alter the steady state values of P and Q. Jochim (1952) studied the effect of various doses (0. 5 to 25. 0 pg. /kg.) of l—epinephrine and l-norepine- phrine on the vascular resistance of intact carotid artery of dogs. He found that both drugs produced a steady decrease in flow and increased vascular resistance. The effect of drugs on flow lasted much longer than the effect on blood pressure. Akers and Peiss (1963) made a comparative study of the effect of epinephrine and nor-epinephrine on the cardiovascular system of turtle, alligator, chicken, and opossum. They found that both drugs produce an increase in the diastolic pressure in turtle. However, no change in heart rate was observed. They postulated that the increase in diastolic 18 pressure in turtle could be due to the peripheral vasoconstriction. Since no change in the distensibility of the blood vessels was assumed, increased pulse pressure was attributed to action of the drug on myo- cardial fibers. Akers and Peiss (1963) concluded that a) epinephrine is more potent than norepinephrine in turtle, b) epinephrine produces an increase in initial velocity of myocardial contraction and, c) epi- nephrine is destroyed by a process of non-enzymic oxidation. III. Hemodynamics 2f Hypervolemia Cardiovascular response to phasic volume changes of circulating fluid has often been considered as an index of cardiac performance. Henderson (1906), using cardiometric techniques, recognized that the change in the form of ventricular volume curves during cardiac cycle could provide information on the nature of cardiac contraction and relaxation. Wiggers and Katz (1922), using improved cardiometric methods, took cognizance of the fact that a good system of recording volume changes of the heart is one which translates the changes in volume into moderate tension changes. In a series of studies, on open chest dogs, Wiggers and Katz (1922) observed that an increase in the venous inflow produced by infusion of saline solution results in an increased right atrial pressure and greater output of the right ventricle. These two factors will improve the left ventricular emptying and elevate the initial tension. The characteristic effects of hypervolemia were a l9 steeper gradient of the isometric contraction curve, a quicker rise of pressure to a higher peak during ejection, and a prolongation of systole. Gregg and Wiggers (1933) studied the circulatory effects of acute experimental polycythemic hype rvolemia in dogs. Infusion of concen- trated blood produced an increased spleen volume and urine output. These two compartments accounted for more than one-half of the total volume of the injected fluid. Following infusion the pulse pressure was increased by elevation of systolic pressure. They observed further that polycythemic hypervolemia produced an increase in the diastolic pres- sure and venous pressure accompanied by a prolongation of the isometric contraction phase of systole. It was postulated that polycythemic hyper- volemia results in an increase of venous pressure, increased diastolic size of the heart, and augmentation of cardiac output and systemic sys- tolic pressure. Ventricular response to alteration of venous return, as determined by myographic studies, has offered considerable insight into the mech- anisms of myocardial adaptation to increased load. DiPalma and Reiss (1948) made extensive myographical studies in the cat of the effect of changes in venous return and peripheral resistance on ventricular con- traction. Increasing venous return with infusion of physiological saline (30 ml. at a rate of 10 ml. /min.) resulted in a decreased myographic excursion. Reducing venous return by means of occlusion of the inferior vena cava resulted in decreased arterial pressure and in an increased 20 myographic excursion of both ventricles. They concluded that a rise in venous return causes a fall in myocardial tension, whereas decreased venous return results in increased myocardial tension. DiPalma and Reiss (1948) maintain that these results are in accord with the assump- tion that the heart is a hollow elastic sphere. When undergoing change, the volume of the heart increases by 1/3 R3 while the surface area in- creases by RZ. Therefore, changes of volume cannot be ascertained from changes in surface area. During increased venous return, they postulate, the heart muscle becomes thinner, thus resulting in a de- creased force of contraction as determined myographically. It is further postulated that when a drug decreases cardiac contractility, it must do so by increasing the radius of the sphere. Recent studies of Cotton (1953) on circulatory changes affecting cardiac force provide more insight into mechanisms of cardiac adapta- tion. Using multiple strain gauge arches, Cotton found that any part of the myocardial syncytium is representative of the rest of myocardium. Furthermore, changes in heart rate had very little effect on the force of myocardial contraction. When Ringer-Locke solution was infused (20 ml. /kg.) rapidly no significant increment in the force of cardiac con- traction was observed. IV. Cardiac Performance and Peripheral Resistance The effect of increased peripheral resistance on patterns of ventricular contractions has been investigated by means of partial or 21 total occlusion of thoracic aorta. Wiggers (1952) points out that the most obvious effect of increased peripheral resistance produced by this method is prolongation of the isometric contraction phase of the cardiac cycle. In addition, due to a higher aortic pressure, duration of systole is markedly shortened. The peak systolic pressure is also increased. Therefore, immediate response to a sudden increase in peripheral resis- tance is an increase in initial tension and a shortened systolic contraction. If occlusion persists, there will be an increased diastolic size of the heart, and higher presystolic ventricular tension. Furthermore, Wiggers (1952) believes that contour changes in the pressure pulse reflect changes in the pattern of ventricular function during various segments of the cardiac cycle. Gupta and Wiggers (1951) studied basic hemodynamic changes pro- duced by aortic coarctation of various degrees. They showed an aortic stenosis must be about 55 to 60 percent of the initial diameter before a significant elevation of aortic and left ventricular pressure could be observed. They postulated that reduction in diastolic pressure and ele- vation of aortic and left ventricular pressure, observed in aortic coarc- tation, is due to reduction in distensibility of the aortic compression chamber. Gupta and Wiggers (1951) noted that contour of the central aortic pulse in coarctation depends on the degree of stenosis as well as stroke volume and left ventricular competence. The ascending plateau of the aortic pressure pulse and the displacement. of its peak toward the 22 end of systole was thought to result from increased peripheral resis- tance. Altered contour of the central aortic pulse during coarctation is postulated by Gupta and Wiggers (19 51) to be due to an abnormal pattern of ventricular ejection. They concluded that, in aortic coarctation, the compression chamber is greatly reduced in size and its walls are sub- jected to a greater stretch. Therefore, the changes in systolic pressure (in part) and those of diastolic pressure (entirely) are attributed to the increase in the volume elasticity coefficient (El-I"; ) of the aortic compres- sion chamber. With progressive reduction of the pulmonary artery diameter Fineberg and Wiggers (1936) found that both right ventricular and aortic pressures fall. This is opposite to the effect of aortic stenosis. They postulated that decreased right ventricular pressure is associated with an increase in initial ventricular tension. Wiggers and co-workers (1952) concluded that in evaluating clinical stenosis from the results of the experimental aortic stenosis cognizance should be taken of the location of the stenosis and the condition of coronary filling and cardiac anoxia. Analysis 2f Cardiac Time Curves The ventricular pump creates a pulsating pressure flow through non-rigid tubes. The constancy of flow of blood through the non-rigid blood vessels is due to elasticity of the vessels. Therefore, a detailed hemodynamic consideration of the cardiovascular system must include the physical effects of vascular branching, the variable calibre and dis- tensibility of muscular arteries, and the reverberating pressure waves 23 set up (Wiggers, 1952). Importance of vessel distensibility and its role in maintenance of steady flow and pressure of blood were recognized as early as 1880 by C. S. Roy who studied the elastic characteristic of excised aortae. Roy noted that the thermo-elastic property of animal tissue differs from that of rigid material (metal) in that the animal tissue shows an increase in temperature when stretched. The metal shows a loss of temperature upon stretching. Roy (1880) further noted a marked difference between the tension—length diagram of excised aortae of young and old species. In 1881, Grashey, using the sphygmographic method, made an extensive study of wave propagations in elastic tubes and arterial pulse transmission in man. He concluded that the factors which produce reflection of waves in elastic tubes are identical with those which change resistance and/or velocity of flow such as dilation or constriction of the tube. 1. Qualitative Description o_f Cardiac Function Curves The aortic compression chamber accommodates the stroke volume output in a finite period of time by means of two mechanisms: (1) forward movement of blood (kinetic energy of flow), and (2) distension of the elastic aorta due to pressure increment in the ventricle (potential energy of pressure). These phenomena are stated in Bernoulli's equation: 2 +V—+Z:E' 2g ‘6th where (P) is the pressure difference between two points in the 24 cardiovascular system, (p) is the density of the blood, (v) is the velocity of flow, (Z) is the reference datum (zero pressure with respect to the heart), and (E') is the total mechanical energy. Dynamic interplay of kinetic energy of flow and potential energy of pressure is indicated by the velocity of pulse wave transmission. Physiologists have long been interested in the physical factors responsible for the pulse wave trans- mission. In 1878, Moens stated that the relationships between the physi- cal factors which determine the velocity of propagation of a pressure pulse through elastic tubes filled with fluid are governed by elasticity, thickness of the wall, bore of the tube and density of the fluid. Assum- ing that the modulus of elasticity of the tube wall is constant, wall thickness is negligible as compared to tube diameter, and the generated pressure wave is small, Moens derived the following useful equation: where (vp) is the pulse wave velocity in m. /sec. , (E) is Young's modulus of elasticity in gm. /cm. 2 (E = Vg—S ), (a) is wall thickness in cm. , (w) is fluid density in gm. /cm.3, (d) is the internal diameter in cm. , (g) gravitational constant, and (K) is a constant. On the basis of various experiments Moens assigned K = 0. 9. In 1878, Korteweg, independent of Moens, derived an equation of propagation of a wave whose speed is controlled by the lateral displace- ment of the walls of the elastic tubes similar to the arterial system. 25 Korteweg's equation has the form, In 1922 Bramwell and Hill, assuming the blood densitytobe con- stant at l. 055 and wall thickness negligible, applied Korteweg's equation to the propagation of pulse wave in arterial system. They derived an equation relating the pulse wave velocity to the physical characteristics of the arterial system, _ Ed Vp 2Rp where (vp) is the velocity of the front of the pulse wave, (E) is the modulus of elasticity, (d) is the wall thickness of the artery, (R) is the radius of the artery at the end of diastole, and (p) is the density of the . . dP . . blood. Substituting p = l. 055 and E = Vd_V and neglecting (d), in the above equation, an expression is obtained which relates the pulse wave velocity to the elastic modulus or the volume and pressure changes within the arterial system, v =0.3571/V£ . p d Bramwell and Hill (19 22) attributed the discrepancy between calculated and observed values to the effect of viscous drag of the arterial wall when it was subjected to a rapid stretch. On the basis of several experi- ments, they concluded that the efficiency of circulation can be charac- terized by: (l) the greatest possible amount of blood flow for a given 26 pressure (small velocity) and (2) the existence of high, constant flow through capillaries. Bramwell and Hill (19 22) maintained that low velocity of the pulse wave is a sign of both an efficient and a continuous circulation. They concluded that pulse wave transmission is purely a mechanical phenomenon and that pulse wave velocity depends on diastolic pressure and elasticity of the arterial system. In 1937 Woodbury and Hamilton, using the Hamilton optical manometer connected to a 26 gauge hypodermic needle, made a compara- tive study of the systolic and diastolic pressures and pressure pulse contours in rat, pigeon, starling, robin, canary, sparrow, frog, turtle, and carp. In order to make inferences about the hemodynamics in these species, they calculated the rate of descent of the arterial pressure. This calculation was based on the assumption that a short portion of the pressure pulse curve is linear. Since blood pressure is the result of cardiac output and peripheral resistance, these investigators believed that such a calculation will provide an insight into the mechanisms of cardiac function. Plotting the logarithm of the rate of descent against pressure, they obtained a straight line with equation, P 10g%t- = KP+C, P where (Ed?) is the rate of descent of pressure, (P) is pressure in mm. Hg, (K) is the slope of the linear relationship, and (C) is a constant. Woodbury and Hamilton (19 37) suggested that this equation is similar to that proposed by Otto Frank in 1899, 27 dP_EP dt W ’ dP . . . where (- a?) is the decrement in the rate of descent, (P) is pressure in mm. Hg, (E) is volume elasticity coefficient, and (W) is the resis- tance of the system. Upon integration of Frank's equation, log-€51: logE +logP - log W. If W is assumed to be constant, the above equation becomes, log %§- = log E .+ log P Combining this last equation with log g = KP + C, gives an expression which relates volume elasticity coefficient to some function of pressure, logE =KP -10gP+C. Woodbury and Hamilton (1937) showed that K remains constant for any pressure and does not change after epinephrine injection. This implies that volume elasticity (E) varies directly with some function of pressure under various physiological conditions. They observed further that the rate of descent of arterial pressure in diastole is more rapid in smaller animals than in larger ones. Duration of diastole was shorter in smaller animals as compared with larger ones, and the short diastolic period is associated with thin muscle fibers. Woodbury and Hamilton (1937) concluded that any assessment of the ratio of percentage of cycle time devoted to systole and diastole must be coupled with the considera- tion of the stasis of coronary blood flow. Furthermore, blood pressure level is a characteristic of the species and is not related to the size of the animal. 28 Physi010gists have long been interested in the interpretation of the recorded pressure pulses as a means of understanding cardiac function. In 1922 Koch theoretically considered the force of contraction of frOg's cardiac muscle as a summation of fractionate contraction. Wiggers (1927) considered intraventricular pressure curves as a graphic record of the tension developed by the myocardial fibers. The contour, ampli- tude, and duration of various segments of the pressure pulse curve were regarded by Wiggers as an index of the dynamics of contraction processes of the myocardium. Since not all the parts of the heart are excited at the same time, then intraventricular pressure cannot be considered as an addition of contractions in phase but rather as a summation of many rapidly succeeding fractionate contractions. Wiggers (1952) believes that, ”The dynamics of ventricular contractions, which concerns itself with the mechanisms through which cardiac output is altered, can be evaluated to a considerable extent by a rigid analysis of pressure pulses recorded from the ventricular cavities. ” In order to make physiological inferences from the recorded pressure pulses a certain measure of assurance of the reliability and faithful registration of the recording and detecting instru- ments is a minimum requirement. As Wiggers (1952) states, ”Theoretic physical formulations and practical tests have demonstrated that reliable curves can be recorded by a manometer system which has an adequate frequency and proper damping characteristics expressed by the logarithmic decrement of its free vibration. ' In order to distinguish the true contour 29 of the ventricular pressure pulses from that of artifacts and distortions of the recording and sensing instruments a number of factors should be investigated carefully. The change in position of catheter within the heart cavity during systole and diastole will affect the contour of the recorded pulses. The sensitivity of the manometer and the speed at which the pressure pulses are recorded will affect the contour of the pulse. Therefore a judicious balance between ordinate and abscissal values is obviously important in the registration of pressure pulses. Review of recent literature on circulatory disorders reflects the growing interest in using the velocity of pulse wave transmission as a key to better understanding of the physiology of circulation, in general, and circulation pathology in senility and hypertension, in particular. Dow and Hamilton (1939) made an experimental study of the velocity of the pulse wave transmission through the aorta. They reported that when pulse wave velocity is plotted against the distance from the heart, the curve obtained has a general shape which is concave toward axes. The slope of the curve gives the velocity of the foot of the wave at any point in the circulatory system. Occlusion of the thoracic aorta resulted in an increase in pulse cycle due to depressor reflex of the vagus nerve. Pulse wave velocity increased with occlusion, but fell off when depres- sor activity set in. Dow and Hamilton (1939) concluded that the pulse wave velocity corresponds to different functions of the diastolic pressure in the thoracic and abdominal portion of the aorta. They postulated that 30 the slowing of pulse wave velocity, after vagus stimulation, could be due to the fact that, l'vagus stimulation either nervous or hormonal brings about a change in the elasticity of the arterial wall by varying the tone of the smooth muscle fibers. " Hamilton and Dow (1939) further studied the standing waves in the pulse propagated through the aorta. Using optical manometers, they recorded pressure pulses from carotid, aorta, iliac, and femoral arteries in dog and found a progressive increase in the systolic pressure toward periphery. Hamilton and Dow (1939) suggested that since wave reflection and resistance to flow go hand in hand, then, "any increase in pressure within an artery is bound up with an increase in its content of blood. ” Furthermore, standing waves “show that the proximal and distal ends of the aorta-femoral system accommo- date alternatively, each at the expense of the other, an excess of blood. ” Hamilton and Dow (19 39) concluded that, ”In a system without a continuous flow this would mean the oscillation of a certain amount of blood back and forth from one-half of the system to the other. Actually, in a flowing stream, it may represent an alternate acceleration and retardation of the flow from the proximal to the distal end. " Hamilton (1944) suggested that the fundamental difference in hemo- dynamics of turtle, dog, and man can be understood from the patterns of the recorded pressure pulses. The smooth pressure curve observed in turtle, Hamilton believes, is due to the filling and emptying of the arterial tree (the compression chamber). In higher animals, such as dog and man, 31 the complex pattern of the pressure curve is due to filling, emptying, and pulse waves of arterial origin. The observed contour of the carotid pulse is due to the superimposition of the carotid filling and emptying curve on the aortic and fundamental filling and emptying curves. If there is any vasoconstriction or occlusion in some point downstream, there will be an increase in the amplitude and frequency of the carotid standing wave. Using this method of analysis, Hamilton (1944) attributes the rise of pressure central to occlusion of an artery to three factors: (1) increased peripheral resistance, (2) increased velocity energy, and (3) creation of a new standing wave. The marked alteration of the con- tour of pressure pulse following the administration of large doses of acetylcholine is attributed to the instantaneous elimination of the standing wave. Hamilton believes that the presence or absence of the reflected wave can be used to determine the cause of disturbance. As blood pres- sure falls the velocity of pulse wave transmission increases and the frequency of the standing waves decreases. Therefore, study of the pressure pulse contour offers an insight into the changes in the reflected wave produced by vasoconstriction or vasodialation. The work of Hamilton (1945, 1947, and 1948) and Remington (1945 and 1945) on the measurement of cardiac output from a central aortic pressure pulse is of great interest in understanding the pressure-flow patterns in large arteries. In a series of experiments, these investi- gators and their colleagues have established an essentially empirical 32 formula that relates various subdivisions of the pulse contour with the volume ejected. Remington (1952) showed that the prediction of the empirical formula under normal conditions is fairly good but when con- ditions are altered the correlation becomes poor. Alexander and Webb (1947), taking cognizance of the effect of the distensibility of the arterial system on the contour of pressure pulse, suggested that analysis and synthesis of arterial pulses recorded from periphery, should be based on the summation of transmitted and reflected waves. This, they be- lieved, is a sound and logical method of quantitatively describing phasic changes of these pulses under normal and experimental conditions. Based on this type of analysis, Alexander and Webb (1947) studied the changes in the contour of the femoral arterial pulse of dog during hemor- rhagic shock. They concluded that the shock pulses differ significantly from the hemorrhage pulses in the prolonged slow fall of the descending limb. This difference in the form of the recorded shock and hemorrhagic pulses was attributed to a definite qualitative change in the contour of thereflected wave. While such a theoretical synthesis of pulse does not in itself prove the mechanism of changes in pulse contour observed in the animal, they believed that this method offers a rational approach to the interpretation of pulse form. On this basis, Alexander (1953) studied the genesis of the aortic standing wave and concluded that the analysis of the standing wave is difficult since arterial pulse waves are distorted in transmission by the hysteresis properties of the vessels. Alexander 33 (1953) pointed out further that vascular impedance is determined by two properties of the vascular bed, namely, the diameter and the modulus of elasticity of the blood vessels. These two factors determine the propagation and transmission of pressure wave in the vascular system. A distortion in the contour of the advancing pressure pulse can be inter- preted as a change of the vascular impedance. Hardung (1962), using mathematical and physical models, discussed the nature of propagation of pulse wave in viscoelastic tubings. He concluded that in the strict physical sense, the standing wave is possible only in the absence of damping. Since anatomical and physical characteristics of the blood vessels have been considered as sources of damping and vascular im- pedance (Alexander, 1953), then the existence of the standing wave in the vascular system can be regarded as an experimental artifact. The limitations and shortcomings of the qualitative methods of analyzing pressure pulses and relating the distortion of the contour to definite anatomical pathology led investigators to seek quantitative methods of pulse analysis. II. Mathematical Anaiysis _o_f Cardiac Time Curves In the past, cardiovascular physiologists used the method of transient analysis in explaining the functional significance of the pressure pulse contour. In applying transient analysis to individual pulse forms, some model of circulatory systems must be postulated in advance. For 34 example it may be applied as in the case of the "windkessel" model (Taylor, 1957). The disadvantage of this method is twofold. First, no rigorous circulation model accounting for all the observed facts is available. Second, this method is based on single pulse analysis and considers the pulse as an isolated event, so that the analysis has been, in effect, aimed at determining the transient response of the arterial system to a single excitation. The explanation of the genesis of pressure pulse contour, on the basis of "aortic standing wave, " by Hamilton (1947) and Alexander (1949) serves as an illustration of the application of the transient analysis. Since the cardiovascular system is a dynamic sys- tem, a more profitable approach to the pulse analysis is the "steady- state" method. In applying this method the only assumption made is that the system is linear to a first approximation. However, a more realistic approach is to express the periodic-flow and pressure changes in the circulations in terms of Fourier series. McDonald (1955), reviewing the recent literature on pulse wave analysis, stated that the hemodynamic investigations in the past have tended to treat the arterial system as a whole and from this arose theories, such as the ”windkessel” of Frank, and the system of standing waves of Hamilton. Although these concepts have been fruitful in their application, McDonald (1955) pointed out that these general theories involve too many assumptions in their approximations of the arterial 35 tree to a simple system of elastic tubes. Therefore, it is difficult to apply rigorous physical analysis to these theories. McDonald (1955) maintained that the function of physical analysis may be regarded at the outset as being a means of deciding the true phasic pattern of the arterial pulse in addition to elucidating the hemodynamic changes. In a series of experiments, he studied the pressure-flow patterns in the femoral artery of dogs. He suggested that the relation of pressure to flow resembles that of voltage to current. On the basis of this analogy, Poiseuille's equation of flow would be analogus to D.C. theory of flow and description of pulsatile flow would be similar to the A. C. theory of flow. By applying Fourier analysis to the recorded pressure and flow curves, he concluded that flow pattern is related to the pressure gradient and not to the pressure level. This conclusion was based on the dis- similar contour of pressure and flow curves. The calculations of flow from the pressure gradient agreed very well with the phase relations of the flow pattern. Such calculations predicted the systolic flow well. There were variations in the back flow and diastolic forward flow. McDonald's studies influenced his colleague Womersley to publish a series of papers (1955, 1957, 1958, and 1958) on the nature of oscillation of flow in arteries. Womersley derived a series of equations which describe the dynamics of pulsatile pressure and flow in the arterial system as it is in the living system. McDonald and Taylor (1957) studied the pulse velocities of harmonic 36 components of the pulse wave in the dog and concluded that distortions in the contour of the pulse wave with distance are due to changes in the phase relations of the wave components. Applying Fourier analysis to pulse waves recorded simultaneously at two points in the aorta, they calculated the phase-shift over a given distance and phase velocity for a given frequency. McDonald and Taylor (1957) found that oscillations of the lower frequency travelled faster than those of higher frequency. The increase in velocity of lower frequencies was attributed to the effect of reflections within the arterial system. This conclusion was based on the finding that when additional reflection is produced by occluding a major vessel, there was a further increase in the phase velocity. They suggested that ”the foot-to-foot velocity bears a reasonable relation to the elastic properties of the arteries in spite of the existence of reflec- tions. " Although theoretical considerations of Taylor (1957) and experi- ments of Taylor (1957), McDonald (1955) and McDonald and Taylor (1957) have demonstrated the usefulness of Womersley's mathematical model and equations, any generalizations of the theory and model must await additional refined and controlled experiments. MATERIALS AND METHODS Experimental Animals Mature false map female turtles (Graptemys pseudogeographica), ranging in size from 7 x 7 to 11 x 11 inches, and in weight from 785 to 1512 grams (Table l) and young female domestic cats (Felis catus), about one year old, ranging from 1.70 to 4. 00 kilograms (Table 5) were used in this inve stigation. Turtle Expe rim ents Turtles were anesthetized by pithing the brain. Then a 3-inch diameter hole was drilled in the middle of the upper half of the plastron. This window exposed the heart and its attached vessels. Minimum bleeding and dehydration occurred during the experiment. The peri- cardium was exposed and partially removed so as to make the heart and the vessels accessible to the monitoring instruments. Exposed tissues were kept moist at all times with cold-blooded Ringer's solution. After 15 minutes, allowing for the animal to recover from surgical shock, two No. 100 polyethylene tubings 20 cm. in length were connected each to a 22 gauge needle which was inserted into the left ventricle and the left aortic arch. Pressures were recorded by Statham model P23AC pressure transducer. The left ventricular circumference was moni- tored by placing a specially constructed variable resistance gauge (a 37 38 mercury-filled latex rubber tubing) around the ventricle (see figure 1 for the site). In some cases records of volume changes of the heart during the cardiac cycle were obtained by both gravimetric and myo- graphic methods. The sensing and recording instruments used and their physical characteristics will be discussed later. Each turtle, serving as its own control, was given an intracardiac injection of approximately 20 micrograms of adrenaline chloride and acetylcholine chloride. The immediate and subsequent cardiovascular changes were monitored continuously until the cardiac time curves returned to their control contours. In order to ascertain the accuracy of the recorded changes in cardiac signals, injections were repeated two or three times in some animals. In most cases, the same changes in the contours and amplitudes of the time curves were observed. One source of difficulty in these experiments was the frequent coagulation of the blood at the tip of pressure catheters, even though catheters contained a 2 per cent heparinized Ringer's solution. Another difficulty was the occasional slipping of the variable resistance gauge used to record the changes in the cardiac circumference. However, this slipping could easily be monitored on the recording polygraph and was easily adjusted prior to the start of an observation. Upon the termination of each ex- periment, the heart was removed and ventricle was separated from auricles and other non-ventricular tissues. The ventricular thickness was measured at approximately midway between the base and the apex. 39 FIGURE 1 Top--Position of circumference (volume) transducer around the turtle ventricle. Bottom--Position of circumference (volume) transducer around the cat ventricles. R.A.A. L.A.A. RIGHT ATRIUM VENTRIC LE / VOLUME TRANSDUCER LEADS INHOMI NATE ARTERY szeos vsm N PRECAVA AL ' RIGHT PULMONARY/ / ARTERY ARTERY PULMONARY AORTA SYSTEMIC AORTA LEFT AURICLE RIGHT AURIC LE RIGHT VENTRICLE VOLUME TRANSDUCER LEADS POSTCAVA DIAGRAM OF CAT HEART 40 The wet weight of the ventricle was determined by a Voland and Sons chain-o-matic balance capable of measuring to the nearest 0.1 mg. The circumference of the variable resistance gauge was measured for subsequent determination of the stroke volume using formulae derived in the calculations section of this thesis. In order to determine the time relation of electrical and mechan- ical activities of the heart, in some turtles, lead 11 of electrocardiogram was recorded simultaneously with ventricular and aortic pressures and ventricular circumference. A typical record of these recordings is shown in figure 2. Cat Expe riments Cats were anesthetized by intraperitoneal injection of sodium pentobarbital (30 mg. per kilogram body weight), placed on a constant temperature heating pad, and fastened in position on the animal board. A midline incision was made on the neck, both common carotid arteries and vago-sympathetic trunks were exposed, and a tracheal cannula was introduced into the sectioned trachea. Blood pressure from the right common carotid was recorded by means of a No. 100 polyethylene tubing 25cm. in length connected to a Statham model P23A pressure transducer. Blood pressure and the lead II of electrocardiogram were recorded while the animal was recovering from the initial surgery and prior to the exposure of the thorax. After 15 minutes, a midline incision was made 41 FIGURE 2 Typical records of cardiac function curves in turtle. Top--From above downwards, left ventricle and left aortic pressure pulses, left ventricular circumference, and lead II electrocardiOgram. Bottom--From above downwards, left aortic pressure pulse, left ventricular pressure pulse, left ventricular cir- cumference, and lead 11 electrocardiogram recorded at speed of 50 mm./sec. £IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIMH /\ ( ‘ IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIM f/K In loft ante pronoun Loft auricular noun. 2 . 0 cl. duotolo (AU one“. ‘\ I I Left auricular om ”Juan‘s-c. 3.0 u. C“..- O O M ” unawar- 42 over the body of the sternum and superficial vessels were tied off to prevent skin bleeding. Then, the thorax was exposed by cutting the sternum from the tip of the xyphoid-sternal junction to the suprasternal notch. Mammary arteries and veins of both sides were carefully separated and the rib-cage was spread open by means of a spreader so that the heart and the attached vessels were accessible to the sensing instruments. From this point on the cat was given artificial respiration using a standard laboratory pump with its rate adjusted to the respiratory rate of the closed-chest animal. The cat was left undisturbed for 30 minutes to recover from the surgical shock of thoracotomy. During this period changes in the contour and amplitude of the right common carotid artery pressure, lead II of electrocardiogram, and in some animals, femoral venous pressure and the arterial hematocrit were monitored. When the animal maintained a relatively stable hemodynamic status, as judged by the constancy of the carotid pressure curves, additional sensors for recording cardiac function curves were introduced. Ventricular circumference changes were monitored (see figure 1 for the site). The intraventricular, aortic, and pulmonary artery pressures were recorded by means of No. 190 polyethylene tubings, each 25 cm. in length, con- nected to an 18 gauge needle. A typical record of the cardiac function curves is shown in figure 3. In some cats simultaneous records of volume changes were obtained by means of both the variable resistance gauge and the gravimetric methods. 43 FIGURE 3 Top--Typica1 records of cardiac function curves in cat. From above downwards, left ventricular pressure pulse, ventricular circumference, and lead 11 electrocardiogram recorded at speed of 50 mm./ 88C. Bottom--Changes in cardiac time curves after adrenalin injection in cat. From above downwards, right carotid pressure pulse, ventricular pressure pulse, and ventricular circumference. Note distortion of both pressure pulse contours and disappearance of incisura in the carotid pressure pulse. minim 3.0 a. thank mun-um I..- m /\ ° 10 m 0 “cm “I..."hmhd Edwardian...“- bod 30 Id... 44 Each cat, serving as its own control, was subjected to several different experimental treatments in the following order. Cardiac Response_t_c_> Nervous Stimulation In order to simulate sudden cardiac inhibition and study the resultant changes in the contours of the recorded cardiac parameters, faradic stimulation of 30 volts strength and a frequency of 30 cps. was applied to either right or left vago-sympathetic trunk for periods rang- ing from 10 to 30 seconds. Effect o_f Anoxia The changes in ventricular function curves were studied under acute anoxia produced by stopping the artificial respiration pump for periods of 30 and 60 seconds. These two time periods were chosen so as to isolate the acute hemodynamic changes due to anoxia and those due to non-anoxic stimulants such as increased pulmonary resistance. Acute Occlusion o_f Major Vessels Cardiovascular responses to sudden changes of the diameter of the major vessels leading to and away from the heart have been of great interest. Acute reduction in venous return to the heart was produced by occluding the superior vena cava, or inferior vena cava, or both vena cavae simultaneously for a period of 30 seconds. 45 Changes in the inflow to and outflow from the left ventricle were induced by means of acute occlusion of pulmonary artery and thoracic aorta respectively for a period of 30 seconds. Since complete occlusion of the thoracic aorta may actually enhance coronary blood flow, then pulmonary artery occlusion can be used to analyze the effect of coro- nary insufficiency upon the mechanisms of ventricular functions. Effect_c_)_f Drugs o_n Cardiac Function Cardiotonic, cardiodepressor, and vasodilator drugs were used to simulate the responses of cardiac function to different emergency conditions such as exercise and shock. For this purpose 20 micrograms each of adrenaline chloride, nor—adrenaline, acetylcholine chloride, and adenylic acid were injected either through the femoral vein or the cen- tral aorta. In addition to above drugs, 20 pressor units of pitressin and 0. 275 mg. of histamine base were injected intravenously and their effects upon the dynamic changes of the ventricular time curves were monitored. Cardiac Function and Hypervolemia In order to study the effect on the heart of sudden changes in the total circulating fluid within the vascular system, 50 ml. saline, warmed to 370 Centigrade and equal to approximately 50 per cent of the total blood volume (calculated on the basis of 7 per cent body weight (Hamlin and Gregersen, 1939 and Conley, 1941), were infused into the superior vena cava at a rate of approximately 10 ml. per minute. Care was taken 46 not to occlude the superior vena cava during infusion. Cardiac re- sponse to hypervolemia during and after infusion was monitored continuously. Upon termination of the experiment, the heart was removed and right and left ventricular wall thickness was measured approximately midway between the base and apex. Then, the wet weight of the ven- tricle was determined by Voland and Sons chain-o-matic balance. The circumference of the variable resistance gauge was also measured for the subsequent calculation of ventricular residual and stroke volumes. Physical Characteristics of the Monitoring Instruments Used In physiological investigations two types of recording instruments are used. One type is a mechanical system which is composed of iner- tial elements (mass), elastic components, and frictional resistance. The other type is the electrical system which has analogous units, namely, inductance, capacitance, and resistance. It is the combination of these three elements which allows the system to behave similar to a damped- harmonic oscillator. An oscillator responds to changes of a function with respect to ti_m_e. An ideal oscillator is one which shows no time shift between the input and output signals. In a mechanical system the inertia and the elastic components are associated with this time shift, while in an elec- trical system it is the inductance and the capacitance which cause the 47 phase lag between the input and the output signals. It is the presence and magnitude of such a phase lag that are the cause of the distortion of the input signals. In order to study the time dependence of an in- strument two types of input signals have been introduced generally into the system. One type is the transient signal such as the square wave which has a signal occurrence in a finite time. The other is the steady state signal which is periodic in occurrence such as sinusoidal signals. When an input signal is introduced into a mechanical instrument, the output signal is affected by the three elements of the system, namely, inertia, elasticity, and friction. The physical quantities associated with these three elements are acceleration, velocity, and displacement, respectively. The relation between the input signal (F) and the output signal is best described by the following mathematical equation (Stacy, 1960) 2 F=M§—§-+Rg-XE+SX (1) dt where, x = displacement, t = time, M = inertial constant, R = frictional or viscous constant, and S = stiffness constant. For an electrical system the terms M, R, and S are replaced by L (inductance), R (resistance), and l/C (capacitance) respectively. 48 Thus, the fundamental equation (1) takes the form, 2 Fng—Z’E+Rd—X+ (2) dt t 9'“ Since in the electrical system the quantity (x) represents the electrical charge (q), then its variation with time is the current (I). When the dx dZX . . . corresponding values for x, d_t’ and -—2— are substituted in equation (2), dt an expression is obtained which describes the relation between the input and output signals in an electrical system. 2 d1 (H q : _+ _ _. FLdtz Rdt+C (3) Equations (1) and (3) are second-order differentials. They can describe the behavior of three types of instruments, namely, zero-order, first- order, and second—order. A zero-order instrument is one in which the inertia (M) and damp- ing friction (R) have negligible effects on the output signals. Thus, by setting M and R equal to zero, equation (1) becomes, F = Sx. (4) This equation states that the output signal is proportional to the input signal. The proportionality constant being (S) which is the elastic (calibration) constant. Furthermore, equation (4) indicates that the input signal is not in any way distorted by the recording instrument. A first-order instrument contains, in addition to the elastic ele- ment (S), some Viscous friction (R), or in addition to capaCitance (C) 49 some electrical resistance (R). The mathematical equations describing the behavior of a first-order mechanical and electrical instrument are, respectively, dx : —— + S 5 F R dt x ( I (:11 q : -—- + —, 6 and F R t C I I Equations (5) and (6) indicate the factors which distort the output signals of the recording instrument. The source of distortion is the time re- quired to move the elastic membrane by the motion of the fluid in the mechanical system or to charge the condenser by passing current through a resistor in an electrical system. Solving equation (5) for x under the condition of a stg function input signal, we obtain, t x=§(1-e T) (7) where T = ‘15:" The quantity T is called the time constant or the charac- teristic time of the instrument. The reciprocal of the time constant, S . that is % = _R' is called the damping coefficient (Stacy, 1960). Equation (7) states that the rate of change of displacement (x) decreases as the time (t) increases. If the input signal is sinusoidal, that is F = FO sinwt, such as the generated cardiac signals, then equation (5) becomes, dx ° _—_ __ + S FOSInwt Rdt x (8) 50 where (w) is the angular frequency in radians, and is related to fre- quency (f) by the following equation, to = ZTTf. (9) Solving equation (8) for (x) under the condition of large values of time (t), we obtain Fo sin (wt - a) .I 22 x=S 1+Tw (10) Equation (10) indicates that the shape of the waveform of the output sig- nal is the same as that of the input signal. Therefore, there is no dis- tortion of the output signals. However, the term (a) in equation (10) indicates that there is a time lag between the input and the output signals. The magnitude of this time lag is determined by the following equation, a = arctan (Tea). (11) Sinusoidal signals encountered in nature have different frequencies and vary in both phase and magnitude with respect to their lowest fre- quency (Stacy, 1960). To understand the functional behavior of these types of sinusoidal signals frequent use is made of Fourier transform. That is, a sinusoidal function f(t) can be written in terms of its harmonic components as follow 5 , oo f(t) : A0 + Z Ansin(nwt- I3). (12) n=o This simple analysis of a sinusoidal function offers an insight into the usefulness of Fourier transform in decoding time-variable biological 51 waveforms into their harmonic components. The phase lag of each harmonic is given by the equation, {in = arctan T (mo) (13) and the amplitude of each harmonic is expressed by the ratio 1 V 1+ T2(n00)2 (14) Equations (13) and (14) indicate the range of frequencies at which an in— strument will best reproduce a time-variable biological input function. Therefore, the frequency-response of an instrument must be determined prior to its use in physiological experiments. The frequency response curve of an instrument is the plot of response against all frequencies for a constant input signal. The relation between maximum frequency response (fm) and the time constant of the instrument (T) for a response which is 95 per cent of the low frequency value is (Stacy, 1960) 1 0.95 = I 1 + T2(21Ifm)2 (15) This equation can be written in the following useful form, _ 0.34 _ 0.054 fm ‘ 211T " T (16) A second-order instrument is one which has inertia in the case of a mechanical system or inductance in the case of an electrical system. Equations (1) and (3) are the differential equations for these two systems. The presence of inertia results in the response leading the input at low frequencies, whereas the presence of the elastic component or capacitance 52 causes the response to lag behind the input signals at high frequencies. These two factors allow an input signal with intermediate frequency to be reproduced faithfully and without any distortion or phase lag. The frequency at which such an output can be obtained is called the natural frequency (fn) of the instrument and is determined from the equation _1I_§ fn—ZTT M. (17) Another important facet of instrumentation for physiological research deals with the range and sensitivity of the monitoring devices. Therefore, the relationship between the range of an instrument and its sensitivity must be considered prior to its use for physiological investigations. Sensitivity of an instrument can be described in two ways. One is the deflection sensitivity, which is the amount of deflection per unit input signal (Trimmer, 1950). The second type is, as Trimmer (1950) calls it, the scale sensitivity of the instrument. This latter terminology refers to the amount of input signal required to produce a given output deflection. Range of an instrument is also described in terms of the scale range and frequency range. The significance of these two terms will become clear later. The instruments used in this investigation fall into two categories: (1) the detecting and sensing elements, and (2) the recording and read- out devices. 53 I. Detecting and Sensing Elements Three types of detecting devices were used in this study. The first type was the Statham model P23AC pressure transducer for re- cording changes in the arterial pressure. This transducer consists of an unbounded strain gauge mounted in such a way that the movement of the sensitive diaphragm results in the shortening of two elements and the lengthening of the remaining two elements. The four elements of the strain gauge form the four arms of a Wheatstone bridge. Since the transducer elements are housed as a unit they are not subject to changes in the ambient temperature. Statham model P23AC has inertia, elastic, and frictional elements. Therefore, this transducer is a second-order instrument and its fre- quency response, sensitivity, and range of operation must be considered with respect to equations (3) and (17). The manufacturer of Statham model P23AC pressure transducer lists the following specifications: Usable range: 0 to +750 mm. Hg Sensitivity--maximum: 0. 05 mm. Hg/cm. paper deflection minimum: 100 mm. Hg/cm. paper deflection (minimum = 2000 x maximum) Recommended minimum reliable measurement: 0.025 mm. Hg Gauge factor: 0.8 cu. mm./100 mm. Hg When transducer connected to No. 5 catheter (PE 190) 100 cm. in length, the transducer will have a natural frequency of 9 cps. and damping approximately 50 per cent of critical. 54 In 1913, Otto Frank derived an equation for determination of natural frequency (fn) of a manometer system. This equation has the same form as equation (17). Frank's equation states that the natural frequency (fn) varies directly with volume elasticity coefficient (E) and indirectly with effective mass (M). Volume elasticity is defined by the equation, dP E = 23—); (18) or the change in volume per unit change in pressure. Effective mass is defined by equation, sL M = 2 (l9) TI’R where, s = specific gravity of manometer fluid, L = length of connecting tubing and catheter, and R radius of connecting tubing and catheter. Substituting corresponding values for (E) and (M) from equations (18) and (19) into equation (17), we get, 1 .EIIIR2 n = 2: sL (20) Equation (20) can be rearranged in such a way that an expression relating natural frequency to characteristics of catheters is obtained, 1 IE fn 2 ?s- RW/r (21) Eauation (21) assumes that the catheter is sufficiently thick so that it has negligible resonant frequency. The term '15ng is constant for the 55 same manometer system and, using the manufacturer's specifications for the Statham model P23AC transducer, the constant has a value of 1500. Thus, equation (21) becomes, R f = 1500 —— (22) n _J—f— In turtle experiments, PE 100 tubing was used. This tubing was 20 cm. in length with an inner diameter of 0. 086 cm. and wall thickness of 0. 041 cm. Substituting these values in equation (22) we obtain a value of 31 cps for the manometer used to record pressure pulse in turtle. The frequency of occurrence of cardiac function curves as determined by the heart rate has an upper limit less than 2 cps. Therefore, the manometer system used had adequate frequency response to record dynamic changes of the various harmonics of the cardiac time curves. In cat experiments, PE 100 tubing, of above specifications, was used to record right common carotid artery pressure. However, the length of the catheter was 25 cm. Thus, using equation (22), the natural frequency of the manometer system in this case was approximately 26 cps. Ventricular, aortic, and pulmonary artery pressures were re- corded using PE 190 catheters. This tubing was 25 cm. in length with an inner diameter of 0.12 cm. and wall thickness of 0. 05 cm. Substi- tuting these values in equation (22), the natural frequency was found to be 18 cps. The frequency of occurrence of cardiac time curves, as determined from heart rate, had an upper limit of approximately 5 cps. 56 Therefore, the manometer system had adequate frequency response to record faithfully and without distortion various cardiac time curves. One of the serious problems which reduces the frequency response of a manometer system is the presence of air bubbles in the system (Hamilton, Brewer, and Brotman, 1934). To avoid this problem, heparinized Ringer's solution was boiled and allowed to cool to room temperature prior to its use in filling the transducer and connecting tubings. Myographic and gravimetric changes of ventricular functions in both turtle and cat were recorded using Statham model Gl-32-450 force displacement transducer. This strain gauge was calibrated at the sen- sitivity which was sufficiently adequate to record changes in ventricular time curves. Figure 4 shows the calibration curve used for thie purpose. Model Gl-32—450 force displacement transducer consists of a bounded strain gauge in a Wheatstone bridge connection and measures the strain produced on a cantilever beam by the force applied. Ventricular circumference changes were recorded by a variable resistance gauge (a mercury-filled rubber tube). The gauge operates on the principle that when it is stretched the resistance is changed (Eagan, 1960, 1961). The sensing element of the gauge used in this study consisted of a thin latex rubber tubing (obtained from Huntington Rubber Mills, Box 570, Portland, Oregon), having an inside diameter (1. D.) of 0. 35 mm. and an outside diameter (O. D.) of 1. 25 mm. The rubber tubing was 57 20 - 15 b Weight gm. 10 I- 5 I- O A L 1 L 0 2.5 5.0 7.5 10.0 Pen deflection at x5 attenuation FIGURE 4 Standard calibration curve for Statham model Gl-32-450 force-displacement transducer. 58 filled with clean mercury under slight pressure. Each end of the tubing was sealed off by inserting a small piece of silver wire. The electrical continuity between the two silver pieces was established by a suitable galvanometer. Then, lead wires (multi-strand copper wire) were soldered, at each end, to the short silver wires. A layer of insulation was placed over the lead-gauge connections by applying liberally latex rubber cement. The entire assembly was left undisturbed overnight until the insulating layers were dried and hardened (Eagan, 1960). To calibrate the gauge used, the strain gauge resistance which was part of one arm of Wheatstone bridge circuit was shunted by an open- circuited resistor of considerably higher value (Perry and Lissner, 1962). When this resistor circuit is closed a definite bridge unbalance will result. This bridge unbalance can be considered as a controlled strain and as such it will appear on the polygraph record. The size of the cali- bration resistor RC is selected so that the resistance change obtained by shunting the gauge is equal to that produced by a particular strain. The change in resistance of a strain gauge (with known initial re- AL sistance Rg and gauge factor F) for any assumed strain €(= T) is AR = FeRg. (23) Similarly, the change in resistance of the parallel combination of the strain gauge and the calibration resistor is R RC AR 2 R - FEW. (24) g g c 59 Equating equations (23) and (24) and solving for Rc' we obtain R (1- Fe) : _L—_ ARC F6 . (25) Figure 5 shows (top) the Wheatstone bridge diagram in which the strain gauge forms part of an arm, and (bottom) the plot of experimental determination of the gauge factor. In practice, resistances R2 = R3 = R4 = 150 ohms and R1 = 149 + gauge resistance = 150 ohms. The variable resistance gauge used in this study was reliable over a range from 1 mm. to more than 100% of the resting length. The response time of the gauge was approximately 0. 01 seconds. Therefore, no change in the frequency response of the recording instrument was produced. 11. Recordifl and Read-Out Devices Pulsating d-c signals from the sensing transducers were fed into a Grass model 5 polygraph (manufactured by Grass Instrument Company) which uses a chopper-type d-c amplifier. The sequence of operation of the amplifiers is (1) conversion of d-c signals into an a-c signal by means of a chopper, (2) amplification of the a-c signal to the desired level using an a-c amplifier, and (3) conversion of the a-c signal back to a d-c signal. The d-c amplifiers had a frequency range from d-c to 45 cps. Amplitude linearity of direct-writing oscillographs was 2 per cent for the central 40 mm. and 4 per cent for the central 50 mm. of paper. Writing points had curvilinear motion and the recording paper used had curvilinear lines. 60 FIGURE 5 Top--Diagram of the Wheatstone bridge in which the variable resistance gauge (Rg is included in R1) forms part of an arm. Bottom--The plot showing the experimental determination of the gauge factor (F) for the variable resistance gauge. L: 5 nova—95 3 no?) I... u u Aconcagua... 0.3-3 .- 10 a I 79- .loofl...a lion-- Iaoofluu I102."- fig I8:- Baa—E5 88 u: Baggaggggaga 10 2|- «.0 n6 :88 :3: 3233.589. 8. .5 8.8:. 8:3 8 85:38.8 61 This latter feature partially compensated for the disadvantages of curvi- linear recording. Fourier Analysis _o_f Cardiac Time Curves The goal of analysis is to represent as uniquely as possible the intervals of interest so that the significant information is not discarded in an averaging process. In the following paragraphs, a mathematical method of analysis is considered which is better suited for analyzing cardiac function curves than the ave raging process of the statistical method. This analysis is applicable to any time-variable signal which is periodic in occurrence, such as the recorded signal variations of the cardiovascular system. Furthermore, since these signals are usually recorded at fixed points, they are functions of time only. Because these signals are used as a basis for clinical interpretation, it is desirable to use more exact mathematical analysis (Fourier transform) to differen— tiate quantitatively between signals which are "normal" and those which are not. Most of the analyses performed on the various cardiac parameters in the past have been more or less of a statistical nature. It should be recognized that the statistical inference, by its nature, does not provide all the information on the chosen sample. The statistical analysis pro- vides information only on the pooled—effect and not on the individual variations. For instance, a given dose of epinephrine raises blood 62 pressure by a certain amount. Establishing its relative statistical sig- nificance does not necessarily explain why administration of epinephrine caused a given rise in blood pressure. It is this latter phenomenon that we are interested in, and statistics cannot provide the desired informa- tion. Unless there is prior knowledge of how information is coded into a given signal, a unique representation should be the goal of the analysis. One particular method of representation involves the use of Fourier transform. Using this method, the recorded signal variations in analog form are converted into a frequency spectrum as a function of time in digital form. Since Fourier analysis involves the use of harmonic func- tions, a brief introduction to harmonics appears to be in order before describing the method of Fourier analysis. A function f(x) is considered to be a periodic function if it can be written as f(x) =f(x+T) (26) where T is the period of occurrence of function f(x). The simplest periodic function which describes an harmonic function can be defined as (Webster, 1955), y(x) = A sin (01x + (ID) (27) where A amplitude of the function, 8 ll angular fr equenc y, and (I) phase angle. 63 The graph of the harmonic function given by equation (27) is ob- tained from the graph of familiar sine curve by uniform compression (or expansion) along the ordinate axes plus a shift along the x-axis. Using the trigonometric formula for sum of two angles, equation (27) can be decomposed into its components, y(x) = A(cos cox sincp + sin 0.x cos (b). (28) Setting A sin ¢ = a, and A cos CI) = b, in the above equation, then every harmonic function such as given by equation (27) can be written as, y(x) = a cos wx + b sin wx. (29) Since the period of occurrence (T) is twice the cycle length (T = 2L) and the angular frequency (w) varies inversely with the period (0) = 3%), then any harmonic function with period of 2L can be written as, 1%). T (30) y(x) = a cos (1T3) + b sin ( Equation (30), which is the basis of Fourier analysis, states that any periodic time-waveform function such as f(t) defined in the interval 0 S t S L, where L is the cycle length (L = -:- T) can be expanded by Fourier transform. However, it should be understood that this expan- sion is possible if the function f(t) has a finite number of points of ordinary discontinuity and a finite number of maxima and minima in the above interval (Hildebrand, 1962 and Webster, 1955). In practice, there is no discontinuity in empirical functions which have passed through amplifiers, because the amplifiers have finite bandwidth. Thus, the 64 problem of convergence of a series at points of discontinuity need not be considered. Using Fourier transform the function f(t') can be represented in a chosen interval as follows, n‘ITt nII't o :— __ ' — . 3 f(t) 2 +n2:l(Ancos( :: ) + Bn Sin( 1 ) ( 1) Using Fourier integrals, coefficients A0, An' and En are determined for that interval as follows, 1 L =— 32 AO LI f(t) dt ( ) O . 2 L n‘Irt An :II f(t)cos(-—L-)dt, for n=0.l,2,. . . (33) O B _3 f(t) ' (ll-‘T—Emt forn=12 3 (34) n L] Sln L I I 9 9° ° ' 0 If an empirical function has its highest frequency (N) equal to the highest harmonic representation (n) by Fourier series, then we can say that the function f(t) has 2N +1 terms or 2N +1 degrees of freedom. If the highest frequency representation in the function f(t) is W, then N = W T. (35) Therefore, there are 2WT + 1 possible degrees of freedom involved in a signal representation with a highest frequency (W) and duration (T). 65 When the signal is fed into an a-c amplifier, the average value of the output signal will approach zero. This implies that the first term in equation (31) will become zero and the empirical function f(t) will have ‘ZWT terms or 2WT possible degrees of freedom. The remaining terms of the series in equation (31) will converge to the function f(t) in the interval 0 to T if the coefficients An and Bn in equations (33) and (34) are known to a sufficient order of accuracy (Lowenberg, 1961). Using Fourier analysis an attempt is made to represent an empir- ical function as it is recorded and not the statistical characteristics of the empirical function. Fourier representation of an empirical function f(t) involves determination of the amplitude and phase spectra. The amplitude spectrum, Cn' of the chosen interval is obtained from evalu- ation of the following equation, c =-\/A2+B2. (36) n n n It should be noted that for a single frequency (n =1) all the points on a circle of the radius Cn are equivalent and therefore the value of the phase angle is ignored. The amplitude spectrum is constructed by plotting Cn against frequency (n). The phase spectrum, Dn’ of the function f(t) for the chosen inter- val is determined from evaluation of the following equation, A — _51 Dn - arctan (Bn). (37) The phase spectrum is constructed by plotting Dn against frequency. 66 In order to apply the above theoretical analysis to actual record- ings of cardiac time-waveforms the recorded empirical functions were treated as follows. From a series of records, either control or experi- mental, one cardiac cycle was selected at random. Each cycle was then divided into 10 equal time intervals and the values of various cardiac parameters were computed at each of these time intervals (see figure 6). These values were punched on standard IBM punch-cards and fed into a 160-A FORTRAN computer programmed to print out values for A0, An’ B , Cn’ and Dn for n =1 to n =10. The actual program used and the n detailed instruction for preparation of data are described in Appendix B. 67 FIGURE 6 Typical illustration of the procedure used to divide various cardiac function curves into equal time intervals. From above downwards, right carotid pressure, aortic pressure pulse, and ventricular circumference recorded at speed of 100 mm. / sec. 1.....111. ..'..1.. systole 7 I Ventricv‘ilir cued-£1 ram _7 1 . . Control Kauai-drug ' 1- ’ -_ spa -ioo-erv-n—‘m ~— I I CALCULATIONS Ventricular weight as percentages of body weight and body surface area (except in turtle) were calculated (Table l) and (Table 5). Surface area was calculated using Rubner's surface area law (Kleiber, 1961), Surface Area = 0.107 x WZ/3 where (W) is body weight in kilograms. Expressing ventricular weight (or any organ weight) as a function of body surface area gives a rela- tively linear and uniform relation when animals of different weight groups are compared. Estimation _cg Residual and Stroke Volumes from Circumference End systolic volume (residual) and stroke volume output were esti- mated from the measurement of the circumference of the variable resis- tance gauge (a mercury-filled rubber tubing). Tables 1 and 6 show these values for turtle and cat ventricles respectively. Calculations were carried out using the following sets of equations. The circumference (C) is expressed mathematically by the relation, c = 2nR (1) where (R) is the radius. Koushanpour and Collings (1961), Rushmer (1961) and others have suggested a physical model of the heart in which the ven- tricles were considered as ellipsoid in geometry. The volume of an ellipsoid is given by equation, 68 69 V=-4§17abc (2) where (a) is the major semi-axis along the x-axis, and (b=c) are the minor semi-axes along the y- and z-axes, respectively. The maximum lengths of the minor semi-axes (b=c) are equal to the diameter meas- ured at the center of the ellipse. From equation (1) we have, (3) Measurements on the surface of the ventricles of cats and turtles used have shown that the outer volume of the combined ventricles is approximately equal to one-half of the ellipsoid. This information allows one to estimate the value of (a), major semi-axis, which is taken to be (a =2b). Thus, we can write, a = 2b = —. (4) Assuming that both ventricles have equal outputs and equal volumes, then the end-systolic volume of the left ventricle (VEL) is given by, xgnI—I x (—I . (5) The first (13) indicates that the total volume of both ventricles is one- half the ellipsoid generated by the ventricular curvatures. The second (%) stands for the fact that volume of the left ventricle is one-half of the total volume of both ventricles. Equation (5), when rearranged, can be written as, 3 _2c VEL‘3 (6) 1T 70 Substituting for (11') the value of 3.14, and carrying out the arithmetical calculations, equation (6) becomes, V — 0 0675 C3 (7) EL ‘ ' ‘ Equation (7) gives the value for outer end-systolic volume of the left ventricle. To estimate the inner-end-systolic volume the equation (7) is corrected for ventricular mass by the following relation, 3 2 VEL 0. 0675 C - gm (8) 2 where (m) is the ventricular mass and the coefficient (3) stands for the fact that on the average (see ventricular thickness values in Table 6) the left ventricle has roughly 2/3 greater mass than the right ventricle. In the case of turtle, equation (8) was modified as follows, v —0 0675 c3 1 (9) EL — . - 2 m. The coefficient (15) in equation (9) stands for the fact that the left cham- ber of turtle heart has one-half as much mass as both chambers of turtle heart In order to estimate the stroke volume output of the left side of the heart, it was assumed that approximately 10 per cent of the blood volume is contained within the heart chambers (Kjellberg _e_t__a_1. , 1949). Using the value of 7 per cent for blood volume as a percentage of body weight (Hamlin and Gregersen, 1939 and Conley, 1941) the total amount of blood in diastole in the left ventricle is given by, V : 1 DL 2 x 0.1x 0.07 x w (10) where (W) is the body weight in kilograms. The above equation can 71 be written in a compact form, after calculation of coefficients, VDL = 0.0035 W. (11) The stroke volume output of the left ventricle can be estimated by sub- tracting equation (8) from (11), SVL = 0.0035 W - (0.0675 C3 - gm). (12) The stroke volume output of the left chamber of turtle heart was estimated from the assumption that the total blood volume is approxi- mately 9 per cent of body weight (Semple, 1960). Therefore, equation (10) was modified as follows, 1 VDL - 2 x 0.1 x 0.09 x W (13) where (W) is the body weight in gram. After calculation of coefficients, equation (13) can be written as, = 0.004 W. 4 VDL 5 (1 ) The stroke volume output of the left chamber of turtle heart can be estimated by subtracting equation (9) from (14), 3 1 SVL = 0.0045 W - (0. 0675 C - 2 m). (15) Equations (12) and (15) can equally be applied to hearts under con- trol and experimental conditions. In order to account for changes in the left ventricular stroke volume under experimental conditions the values of VEL in equations (8) and (9) should be corrected by a constant. This constant is calculated from the ratio of the first Fourier coefficient (A0) of control over the experimental conditions. This correction factor 72 for end-systolic volume is in accord with recent findings of Rushmer (1959) that under certain experimental conditions the immediate changes in minute volume output are brought about by alteration of end-systolic volume. Mathematical Derivation o_f Tension Time Curves One of the important determinants of cardiac function is the tension developed during the cardiac cycle (Burton, 1957). Many attempts have been made to determine the course of tension developed during cardiac cycle using gravimetric and myographic methods (Wiggers, 1952). Using Laplace's surface tension law (P = g?) (Landau and Lifshitz, 1959) and making use of simultaneous recordings of the intraventricular pressure, aortic pressure, and combined ventricular circumference, an expression is derived which relates tension time curves to those of pressure and circumference time curves. If it is assumed that ventricles are spherical in geometry, then Laplace's surface tension law can be applied in its simple form, P = %. The ventricular circumference (C) as recorded by the variable resistance gauge is related to radius by equation (1). The volume of a sphere is given by equation, V = %n R3. (16) Assuming that the volumes of the right and left ventricles are equal, then the volume of the left ventricle is given by, 73 l 4 3 = - - . l7 VL 2 x 317R ( ) Substituting for (R) in equation (17) its corresponding value from equa- tion (1), an equation relating the volume to circumference is obtained, V = —1T(— . (18) Equation (16) gives the volume of any spherical object. Therefore, when equations (16) and (18) are set equal, an expression is obtained in which the radius of the left ventricle is related to the circumference of both ventricles, R = — (-—I - (19) Taking the cube root of above equation gives the following relation, R = 1. 26 (2%). (20) Since (17) is a constant, equation (20) can be written as, R = 0.194 C. (21) It should be noted that equation (21) applies equally to hearts with geometry other than sphere. In the case of non—spherical heart the coefficient (0.194) should be modified so as to obtain an exact mathe- matical relationship between radius and circumference. Substituting the value of (R) from equation (21) into Laplace's surface tension law for sphere, an expression is obtained which relates tension to the products of pressure, circumference, and a constant, T = 0.194 P x C. (22) 2 Since tension (T) is given in units of dynes per cm. , by using a proper 74 conversion factor (1 mm. Hg = 1330 dynes per cm.2) equation (22) can be written in the following form, T =258PxC. (23) This is an extremely useful equation. It states a fundamental relation- ship between tension, pressure, and circumference changes of the ven- tricle which is independent of the shape and size of the heart. Although equation (23) was derived by assuming that ventricles are spherical in geometry, it should be noted such an assumption is not contained in equation (23). Therefore, equation (23) can be used to calculate the ten- sion developed by the myocardium at any time during the cardiac cycle from simultaneous records of the pressure and circumference time curves. RESULTS AND DISCUSSION The object of this study was to analyze mathematically the recorded cardiac waveforms. The manner by which information is coded in the recorded signal variations from the heart and attached vessels is not known. Fourier analysis was applied to the time curves so that a time spectrum of the individual coded signals could be determined. In apply- ing this mathematical method two assumptions were made. First, that the heart, during its cycle, generates a periodic signal which can be represented as a sum of sinusoids. Second, that we know nothing of the sequence of the physical forces which generate such a signal. Analysis was performed on a graphical record of the generated signal. The characteristics of the sensing and recording instruments were discussed in the previous section. However, before presenting the results, it is necessary to point out that the recording polygraph utilized a curvilinear moving stylus and a curvilinear chart paper. The question arises as to whether such a recording system lends itself to a mathematical analysis which bases its information on the rectilinearly determined values. The author justifies the procedure used on the basis of the following reasons. First, to eliminate partially the disadvantages of curvilinear recording, the chart paper used was also curvilinear (Stacy, 1961). Second, since Fourier analysis involves the determination of a series of points on the recorded pulse, it is immaterial whether these points are connected to 75 76 a given base-line by a curvilinear or rectilinear line. Moreover, the same recording system and procedure for obtaining the points were used throughout the study. The next point which requires consideration is whether certain instrumental undulations in the record will in any way reduce the use- fulness of the method and the results obtained. In this study more than 5, 000 records were analyzed. Special care was taken, both during the recording and in the course of analysis, to discard those records which in the judgment of the author contained obvious artifacts. Because of lack of instruments, no attempt was made to compare the signals re- corded by the system used with another system, such as optical manometry. However, casual comparison of the records obtained by the system used with those published in the literature, using optical manometry, showed satisfactory agreement. Therefore, results ob- tained in this study using the recording system described are believed to be reliable and relatively free of experimental artifacts. Turtle Experiment 5 The turtle heart has long been used as experimental material to determine cardiac function. The assumption has been that since the turtle heart is free from a specialized conductive system, it could be used to study the mechanical aspect of cardiac function. Table 1 presents data on comparison of some cardiac parameters in the turtle. The last .Q .m pad 532 m0 GoflmfidoamU Gm popdfiocm «o: 0.83 >25. v... 77 oahd NJ. m .0 ovod mdod mom .Q.m ._I. 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The modulus of the first harmonic (column 4) for adrenalin shows a 2. 5 fold increase (152 for adrenalin and 60 for control). However, no change in the argument of the sine function is observed (1. 55 for adrenalin and l. 5 for control). The modulus of the second harmonic (column 5) shows a change in sign for adrenalin as compared with the control. This shift of modulus (-33 for adrenalin and +29 for control) might be related to the manner of action of adrenalin upon turtle heart. The significance of this interpretation will be discussed shortly. The harmonic analysis of acetylcholine experiments shows the expected decrease in the modulus as compared with the control. This is because the value of the modulus of various harmonics, as calculated by Fourier integrals (see section on Fourier analysis in Materials and Methods part of the thesis) refers to the amplitude of the component frequencies of the pulse. Since the value of the amplitude (the numerical value of the modulus) indicates the pres- sure deve10ped by the heart, then any change in amplitude reflects the force of myocardial contraction. Examination of the acetylcholine data (Table 4, line 3) shows that the moduli of the first and second harmonics remain unchanged. This is interpreted to mean that acetylcholine pro- longs the systolic phase of the cardiac cycle and decreases the force of 87 contraction of the myocardial fibers. Further graphical support for these conclusions will be presented below. Harmonic analysis of the left aortic pressure is presented in Table 4. The moduli of first and second harmonics show a marked in- crease after adrenalin injection. The argument of the sine function also shows a definite increase. Note that the third harmonic of the aortic pressure curve appears when adrenalin is infused. This is in contrast to ventricular pressure. Moreover, there is no change in sign of modulus of the second harmonic as compared with that of the left ven- tricular pressure. One is tempted to attribute the change in sign of modulus for ventricular pressure, as compared with aortic pressure, to the difference in the action of adrenalin on the heart and aorta. How- ever, validity of such a conclusion requires further experimentation. Fourier components of ventricular circumference time curves (Table 4) reveal the dynamic difference in the action of adrenalin and acetylcholine upon turtle heart. Adrenalin infusion resulted in an in- crease in cardiac output as shown by increase in A0 values and the value of moduli of first and second harmonics. Whereas, acetylcholine in- fusion resulted in prolongation of systole as shown by the rise and fall of values of the moduli of first, second, and third harmonics (compare columns 4, 5, and 6 last line). In a pulsatile system impedance is defined as the ratio of pulsatile pressure to pulsatile flow (McDonald, 1960). An estimate of the arterial 88 input impedances, at the various component frequencies of the pulse, will give information about the presence or absence of reflected waves. Since flow is directly related to the pressure gradient, then any increase in impedance and pressure is accompanied by a decrease in pulsatile flow. This explains the observation that peripheral vasoconstriction produces an increase in pulse pressure and a reduction in blood flow. Moreover, since impedance can be regarded as a measure of the degree of ”obstruction" to flow where pulsatile flow occurs, then it is impera- tive toldetermine this impedance under various experimental conditions. To analyze further the action of drugs on the heart, ventricular impe- dance at each sinusoidal frequency was computed from the ratio of the pressure component to the circumference component. The phase angles (their significance is discussed below) associated with impedance were computed also. Then, amplitude impedance and impedance phase angle spectra were constructed. . Figure 8 shows the variation of impedance for the turtle ventricle. Each curve represents five different experi- ments. In essence, all curves had the same contour distribution over the frequency analyzed. In this figure, note that the adrenalin curve (broken line) shows an initial increase in impedance which is indicative of increased force of ventricular contraction and wave reflection. The impedance amplitude falls off rapidly as ventricular systole progresses (at higher frequencies). On the other hand, the acetylcholine curve (dotted line) indicates that the drug appears to act as a relaxing and 89 FIGURE 8 Variations of impedance with pulsating frequency of the turtle ventricle under control conditions (solid line), after adrenalin injection (broken line), and after acetylcholine injection (dotted line). 3 (Impedance units = mm. Hg/cm. /sec.) IMPEDANCE 80 7O 60 50 4O 30 20 10 Control Adrenalin _— Acetylcholine FREQUENCY (CPS) 90 vasodilating agent, resulting in decreased force of contraction and pro- longing the ejection phase of ventricular systole. These conclusions are based on a decrease in impedance (at low frequencies) and a shift of the minimum impedance by one frequency upward, from 5 to 6 cps. In addi- tion the observed alteration, by drugs, in the impedance distribution might be attributed to the vasomotor activity of the blood vessels in the turtle (figure 8). This is in agreement with deductions made by McDonald (1960) on similar observations in the dog. Other than this, the physio- logical significance of such curves (figure 8) is not known at present. Randall and Stacy (19 56) computed the magnitudes and phase rela- tionships of Fourier components of the pulsatile blood pressure and blood flow in the femoral artery. The relationship between these sinusoidal components was studied as a function of their frequency. Based on such analysis, they concluded that in a system in which flow is determined by friction only, the magnitude of the impedance is independent of the fre- quency of the sinusoidal pulsations. Moreover, the pressure and flow fluctuations are in phase. If the predominant factor determining the flow is compliance of the system, then the flow fluctuations precede pressure fluctuations. However, when the system is predominantly inertial, then pressure fluctuations precede flow fluctuations. The points at which phase angle fluctuation crosses the abscissa is called “resonant” frequency and indicates that the impedance is entirely a viscous resistance or pres- sure and flow fluctuations are in phase. Therefore, a system which 91 contains all three components, namely, friction, inertia, and com- pliance will exhibit a complex behavior characterized by combinations of the individual characteristics. Peterson (1954) observed that the relationship of flow and pressure in a pulsatile system is variable and that such variability can be attributed to three parameters, namely, mass, friction, and distensibility. He concluded that, a) these three parameters vary in a nonlinear fashion and affect each other, b) that the vascular pressure pulse is the sum of these three factors, and c) that despite constant stroke volume, the pulse pressure amplitude varies considerably. Variation in impedance phase angle of the turtle ventricle is shown in figure 9. The control curve (solid line) indicates that pressure pre- cedes flow fluctuations at frequencies below 2. 5 cps and above 4. 5 cps. These two segments of the curve (solid line) demonstrate the effects of the inertial components of cardiac function. On the other hand, the compliance (distensibility) of the system (that is, when flow precedes pressure) is indicated at frequencies above 2. 5 and below 4. 5 cps. The adrenalin curve (broken line) shows a definite reversal of the above pat- tern, whereas the acetylcholine curve (dotted line) shows a shift of the curve toward the lower frequencies. This is the first time that the actions of adrenalin and acetylcholine on the sequence of the physical forces which generate cardiac time curves in the turtle have been thus demonstrated. This insight into the mechanism of action of these drugs 92 FIGURE 9 Variations of impedance phase angle with pulsating frequency of the turtle ventricle under control conditions (solid line), after adrenalin injection (broken line), and after acetylcholine infusion (dotted line). LEQUENCY (CPS) ix 5 ‘~o K ‘0 e .m n .m. I n I... a 1 m m w n r e o d c C A A o P p b D b u u n O 5 0 5 O 5 0 5 O 5 2. 1.. 1. 0. O. L L 7m 7m . - . . . madam...” HMDmmHMnH maxim—Him 304nm Amzfloév 0002.0. 0080.0 moz> 300m .Ew .mM .02 00.04 003.15 00H x 03mg? 00>? 0.00903 0.0003 000303 >pom 000 mH .mO 83....»ng BM? .mO ZOmHm/wnBZOU m 030H. 98 2. .o 0.00 .0 0.0 .o .0 .o 000 .0 .o .m + ON .m 0H .m .00. .m .0 .N H .0 822 om .m cm .00 .0 .00 0. 00 H0 NH .N NN .m .0 .0. N .0 00 mo .m N00 .H 0. .00 m .m m .00 m0 3 .0. 3 .0 H .m m H 0.0 8 .N 3 .H N .00 m H m0 I I I I I N0 2. .N ow .m .0 .m N m .H 00 0000 .N o... .m m .m N .0 0: 3 .m 000. .m w .0. m 0 o I I I N .0 00 om .H. OH .00 o .0. m .0 H m... .m ow .N .0 .0. 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These changes in moduli of various harmonics, based on previous interpretation given to numerical value of modulus, reflect alterations in cardiac contraction. Since the numerical values of the moduli reflect the sum of the contributions of the contractile force of myocardial fibers, then any change in values of moduli can be interpreted as a change in force of contraction of the heart. In the case of the greater pulse, the modulus of the first har- monic shows a marked increase indicating a more vigorous cardiac contraction. However the somewhat reduced value of the modulus of the first harmonic of the smaller pulse indicates a much weaker myo- cardial contraction which is sustained longer. This latter point is shown by the substantial increase in the moduli of the second and third harmonics. Therefore, the Fourier analysis of pulsus alternans curves provides additional support to the currently accepted theory of the genesis of pulsus alternans. Table 10 presents the data on blood pressure during inspiration, expiration and pulsus alternans, and after thoracotomy in cat. The area under the pressure pulse curves, as calculated by the first. Fourier coef- ficient, for the above conditions are shown in Table 11. Note that the values of systolic pressure, as indicated in Table 10, do not reflect the dynamic and time distribution changes of the blood pressure under the above conditions. For instance, changes in blood pressure due to 109 000.0050 00.0.: 000nm .0. 0. I. 0.0.900 0.0m 003m 030. I I 03030.02 I oom 0.: I I 0N0 I oom mH m: com I I m: 0.0 I I mo I 0: MH I I on m: 000 NH omH o: o: I omH w I I we I mNH N. I I .0. 0.0 .0. "Wm H .0. 0.0.0 m I I .8 I 0.0 0 0. I I .0. 0.0. 0 .0. 0.00 N .0. 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U00050.... .000 0000.00 00Cw0m 000:0 00000m 0mc0p0oo0m mm .8200 .02 :00030... 0000 .0090 0000 00000000008 :00000m: 0000300m 000m 003m 00000000nm 000 000004 000008 0.8000 U0080.00 @840 E MH ImO .HOMhhmH m0 00908 130 drugs. The area under the pressure pulse curves for various cardiac parameters after drug infusion is shown in Table 16. The effect of various drugs on the carotid, aortic, and pulmonary artery pressure and stroke volume (change in ventricular circumference, AC) can easily be deduced from these two tables. Figure 18 shows the plot of varia- tions of impedance amplitude of cat aorta under control, after nor- adrenalin and after adenylic acid infusion. Each curve represents five different experiments. In essence, all curves had similar contour dis- tribution over the frequency analyzed. Note that nor-adrenalin curve (broken line) shows a definite increase in impedance at lower frequencies. This rise in impedance is due to an increase in the frequency of wave reflection from periphery which is the result of vasoconstriction. The Fourier treatment of the data makes this conclusion possible. At approximately 3 cps there is a further increase in impedance which falls off Slowly. The adenylic acid curve (dotted line) shows a pattern which is somewhat Similar to that of nor-adrenalin but it is displaced down- ward. The impedance spectra for these two drugs are in accord with their vasoconstricting and vaso-dilating action which were explained above. Variations of impedance phase angle of cat aorta are shown in figure 19. The nor-adrenalin curve (broken line) shows that initially flow precedes the pressure fluctuations. However, shortly after 1 cps there is a rapid increase in inertial forces which indicate acceleration 131 0000000000 003nm .0. 00 .0 00. .0 00. .00 o0. .00 o0 .00 3 .000 - - o0 .00\.01 000 Qfiwemumwm on .0 C0 .0 - - 1.00 .00 .00 .0.0. - - 0 .00\000§ 0.0 000000000nm 00. .o 00 .o - - E .000 00 .00 00 .000 o0 .00 00 .00\.01 00 00 .0 00 .0 Q0 .00 00. .0.0 00 .000 00 .000 - - o0 .00\.01 00 00H000000I0OZ 00 .0 00 .o - - 00 .00 00 .00 O0 .00 o0 .00 00 .00\ .01 00 E .o 00 .0 - - 000. .0000 so .000 00 .0.00 8 .000 00 .00\.01 0 0.0. .0 00. .0 00 .00 E .00 1.2. .00 1.00 .00 - - 00 .00\.01 0 o0 .0 00. .0 00 .0. 8 .0.0 00 .00 00 .000 - - o0 .00\.01 0. oo .0 00. .0 - - 00 .00 8 .000 00 .00 00 .000 0 .00\.01 000 00 .0 om .0 - - 1.00.00 .00 0.0. - - 0 .00\.01 0. .00 0.09.. 000.050.... Hvuwaoa QHOMQm HON—HAN OHOHOQ HON—H400 OHOHQM HQHHAV OHOHOm .0000 ID»... MT 000:0 Io< mm 00200 I044. mm .8000 I040». .02 00 0000000000008 70 Al 00.90000nm 00d0000nw 00d0000n~ O .0000 .0c0> >0000< .Hdnm 0000000. 0000000 0.3.0 7: 07500007000 00000003, 00075 000.002.3000 0400000 0000000 0o 0070000000000 00.000000 0.0000 00 7000000000030 0: 00308 132 FIGURE 18 Variations of impedance of the cat aorta with pulsating frequency under control conditions (solid line), after nor-adrenalin injection (broken line), and after adenylic acid infusion (dotted line). IMPEDANCE 140 120 100 80 6O 4O 20 Control Nor -adrena1in Adenylic acid FREQUENCY (CPS) 133 FIGURE 19 Variations of impedance phase angle with pulsating frequency of the cat aorta under control conditions (solid line), after nor-adrenalin injection (broken line), and after adenylic acid infusion (dotted line). FREQUENCY (CPS) " ‘l ' I Nor -adrenalin — — 1m .00.... n o C r 0 . 0 0 _ . . 0 5 O 5 O 5 O 5 0 7m 1. 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Constriction of the aorta changes the inertial characteristics of the system into a predominantly compliant character- istics. The same changes seem to occur after vena cavae occlusion. In both cases there is a definite delay in the frequency at which resistive forces are overcome, that is when curves cross the abscissa and pres- sure and flow fluctuations come into phase. The similarity in the impedance phase angle spectra after thoracic aorta and venal caval occlu- sion could be explained as a result of the similarity of physiological effect of occluding these vessels. Occlusion of thoracic aorta would bring about a reduction in the venous return. The same results are obtained following occlusion of both vena cavae. Therefore, it is not surprising that Fourier analysis of occlusion of these vessels depicts the similar response evoked by the heart. The effect of pulmonary occlusion upon the variation of impedance phase angle is somewhat different. Initially, there is a marked exaggeration of the inertial characteristics of the system. However, after approximately 3 cps the elastic elements replace the inertial components of the system. It is difficult to relate spectral changes to the physiological phenomena during the course of such experiments. However, the significance of the contour distortion (spectral changes) can be appreciated if two things are kept in mind. First, the components of the pulse proceed in time with different speeds, and changing the phasic relations between the 156 components. Second, the amplitudes of the components are damped in a different way; because the components with higher frequencies under- go a higher damping than the components with the lower frequencies (Hardung, 1962). Harmonic analysis of the aortic pressure and ventricular cir- cumference curves under control and during occlusion of various vessels are presented in Tables 22 and 23, respectively. The area under the pulmonary artery pressure, after occlusion of the same vessel, shows approximately a 4-fold increase over the control (Tables 22 and 21). There was a corresponding increase in the moduli of the three har- monics, but relatively little or no change occurred in the argument of the sinusoidal function. The area under the aortic pressure, after occlusion of the same vessel, showed a marked increase as compared to the control (Table 22). A significant increase in the moduli of the three harmonics was observed also. But little or no change occurred in the argument of the sine function. In the case of the occlusion of vena cavae, the area under the curve, the moduli of the three harmonics, and the argument of the sine function showed a marked decrease as com- pared to control. Table 23 shows the harmonic analysis of the ventricular circumference curves under control and during occlusion of various vessels. The area under the curve, after pulmonary occlusion, shows a marked increase over the control. The observed changes in the various parameters of cardiac harmonics demonstrate the importance of the 157 interplay of the amplitude and phase relations of the various components of the pulse. Comparison of the time course of tension of the cat aorta is pre- sented in figure 28. Note the rapid initial rise in tension after occlusion of thoracic aorta. The tension-time curve after pulmonary artery occlu- sion shows, qualitatively, a similar contour distribution as compared with the control. There was approximately a 30% increase in the ten- sion after thoracic aorta or pulmonary artery occlusion. There was, on the average, an 80% reduction in the aortic tension after occlusion of both vena cavae. From a comparative standpoint, it should be noted that tension developed by myocardium during the cardiac cycle, as computed from the area under the curve, shows a marked difference between the turtle and the cat. On the average, the turtle heart developed some 50% more tension than the cat heart (figures 10 and 20). However, it should be noted that, on the average, cats used in this study had a mean pressure of approximately 50% greater than the mean blood pressure of the turtle. Since oxygen consumption of the heart is directly related to the amount of tension developed by the myocardium (Burton, 1957), then one would find it difficult to account for the development of such a tension by turtle heart. It is commonly believed that the turtle, being a cold blooded animal, consumes less oxygen as compared with mammals. Therefore, the observed contradiction, in the relation of oxygen consumption to 158 FIGURE 28 Comparison of the time course of tension of the cat aorta under control conditions (solid line), after thoracic aorta occlusion (broken line), after pulmonary artery occlusion (centered line), and after both vena cavae occlusion (dotted line). TENSION (DYNES/ CM.) 240 200 160 120 80 40 V Control: Area = 22. 5 Thoracic aorta occlusion: Area = 29. O _— Pulmonary artery occlusion: Area = 29. 0 Both vena cavae occlusion: Area = 6. 4 ....... 8\ \ \ . \_ /,,\\ ,6 ‘\ \\ / ,' K - TIME - SECONDS 159 tension and the latter to pressure, could be explained as a consequence of the geometry and mechanics of the turtle heart as compared with cat heart. The relation of tension to pressure and geometry of the heart is elegantly described by Laplace's surface tension law (Burton, 1957). Since the geometrical configuration of the heart is the primary factor in determining the total tension developed, then the high value of tension of the turtle heart over the cat heart could be related to the shape and not to the difference in oxygen consumption. II. Venous Infusion The influence of changes in the venous inflow on cardiac function was studied by means of intravenous infusion of saline in three cats. There are two objections to the use of saline infusion as a means of increasing venous inflow to the heart. First, saline infusion causes a reduction in blood viscosity, thus augmenting the volume flow. Second, infusion of saline dilutes the blood, hence reducing the oxygen carrying capacity of the blood (Katz, 1927). Since the immediate effects of in- creased venous inflow were of interest here, the disadvantages of saline infusion were considered to be of no great consequence. The effect of a sudden increase in venous inflow on the contour of the various cardiac time curves is shown in figure 29. Note the marked alteration in the systolic uptake and diastolic drainage segments of the pressure curve as compared to the control (figure 13, top photograph). 160 FIGURE 29 1 Top--Changes in the contours of ventricular function curves 100 sec. | after 50 m1. of saline infusion in the cat. From above down- wards, right carotid pressure, aortic pressure, and ventricular circumference recorded at a speed of 100 mm. /sec. Bottom--Changes in the contours of cardiac time curves 400 sec. after 50 m1. of saline infusion in cat. From above downwards, right carotid pressure, aortic pressure, and ventricular circumference recorded at a speed of 100 mm. /sec. 0 ma hum 3.0 'III. 8.0 ,P- a . \\ o I o systole instructs and“ locommumu . ”shot-nun - -——- had ll-“ .__- ' -- .. 3.0 an. M '0‘:ch mm..mma 50.1. d on“. 161 The pattern of the ventricular contraction, as reflected by the time course of the circumference record, shows a definite alteration in both amplitude and contour. There was a marked increase in stroke volume output after saline infusion which was maintained for approximately 5 minutes. To ascertain the time course of cardiac response to sudden increase in venous inflow, a series of pressure and circumference records, obtained at intervals of 40, 100, and 400 sec. after saline infusion, were subjected to Fourier analysis. The variations in am- plitude impedance of the cat aorta are shown in figure 30. Note that immediately after infusion there is a rise in vascular impedance. However, as systole progresses there is a decline in the magnitude of impedance at 2 cps. Furthermore, it is interesting to note that approxi- mately 100 sec. after infusion the impedance spectrum returns to normal. In fact, the curve depicting the time course of ventricular function 100 sec. after saline infusion shows crests and troughs similar to the control curve. In contrast, the characteristics of the cardiac response, 400 sec. after infusion, show close resemblance to that of 40 sec. after infusion. The delayed increase in the vascular impedance, as shown 400 sec. after infusion, could be explained as a consequence of myocardial adaptability to the increased circulatory load, causing a more vigorous contraction against the high vascular impedance. The variations of impedance phase angle after infusion are shown in figure 31. Following saline infusion there is a definite alteration in the time course 162 FIGURE 30 Variations of impedance with pulsating frequency of the cat aorta under control conditions (solid line), 40 sec. after 50 ml. saline infusion (centered line), 100 sec. after 50 ml. saline infusion (broken line), and 400 sec. after saline infusion (dotte d line). IMPEDANCE 100 80 O‘ O vb» O 20 Control Saline infusion 40 sec. —-— 100 sec. —— _— 400 sec. ------ -. FREQUENCY (CPS) 163 FIGURE 31 Variations of impedance phase angle with pulsating frequency of the cat aorta under control conditions (solid line), 40 sec. after 50 m1. saline infusion (centered line), 100 sec. after 50 ml. saline infusion (dotted line), and 400 sec. after 50 m1. saline infusion (broken line). IMPEDANCE PHASE ANGLE (RADIANS) PRESSURE LEADS FLOW LEADS Control Saline infusion 40 sec. -—-— 100 sec. ------- / 400 sec. __ ’ FREQUENCY (CPS) 164 of interplay of the three basic circulatory forces, namely, mass, fric- tion, and distensibility. All three infusion curves show a definite phase reversal between frequencies 1 to 3 cps. It should be noted that at these frequencies the compliant characteristics (when flow precedes pressure) replace the inertial characteristics (when pressure precedes flow) of the system. This phase reversal is interpreted as an indication of an increase in vascular capacity necessary to accommodate the augmented blood volume following saline infusion. At approximately 3 cps, the inertial characteristics of the system predominate indicating an increase in venous return during the diastolic phase of the cardiac cycle. Fourier components of the ventricular function curves after saline infusion are shown in Tables 22 and 23. There is a marked increase in the area under the aortic pressure curves after infusion of saline (Table 22), as compared to the control. The moduli of the first and the third harmonics of all three curves show a definite increase over the control values. In addition, there is a change in the sign of the second modulus of the 100 and 400 sec. after infusion curves. 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N 3+ 8 .o H 3 .8 3 8833.88 03820880186088 .832 - 3.~8 388m 8.3+ 3 .3 :8... 8. .8.+ 3 .o H o .3 3 8833.88 883989833 .832 33.3 :83 ~.o+ 8: c8... 8. .8+ .3 .3 E. 3 3+ H .o H 3 .m 38 80.380 UZHOEHNTH UHCOEHNHIH UHGOEHMTH .Q .m H waded: . . . 8802 . uameummuh. 8:838. 8.8.833 3.88.8 o... 83 .oz mH .mO mHZMZOnEZOU MHHMDOR MN 3an SUMMARY AND CONSLUSIONS Graphic records of cardiac function curves of the turtle and the cat under a variety of experimental conditions were subjected to Fourier analysis. The conditions and assumptions upon which the application of Fourier transform to cardiac pulses is based and the difficulty in inter- pretation of the data are discussed. It is pointed out that a requirement for application of Fourier analysis to cardiac time curves is that the system should be in a "steady state" condition. This implies that any alteration in frequency must be allowed to settle down before Fourier method is applied. One of the fundamental difficulties in applying Fourier transform is the fact that circulatory system is non-linear. The conse- quence of this non-linearity is that one cannot relate, with absolute accuracy, the harmonics of pressure with those of flow. However, since the effect of such a non-linearity is small and negligible in a first approximation, one could justify the use of Fourier analysis in such a non-linear system. The results obtained from Fourier analysis of cardiac curves, as processed by a l60-A Fortran Control Data Digital Computer, are two- fold. First, plots of amplitude impedance and phase angle impedance spectra were constructed in order to provide graphical illustration of the time course of cardiac function curves under various experimental conditions. Secondly, the first three harmonics of various cardiac 168 169 time curves were computed. Within the limits of the experimental and analytical techniques of obtaining data from graphical records, the first three harmonics were sufficient to synthesize the original curve. This was verified by the computer. Spectral and harmonic analyses of the cardiac waveforms obtained in the present study indicate that: l. Adrenalin stimulated the turtle heart muscle directly, whereas its action on the cat heart was initially on the conductive system and secondarily on the myocardium. This conclusion was based on the dif- ference in the distribution of the cardiac impedance of these two species in response to adrenalin infusion. In addition, adrenalin resulted in an increase in the distensibility of both the turtle and cat hearts. This inference was bsed on the comparison of the cardiac impedance phase angle under control conditions and after adrenalin injection. 2. Acetylcholine infusion in the turtle resulted in decreased force of contraction and prolonged the ejection phase of the cardiac cycle. This was deduced from a sustained reduction of cardiac impedance after the drug. However, in the cat, injection of acetylcholine produced, in addition to cardiac depression, vasodilation of blood vessels. This conclusion was based on decreased impedance at lower frequencies indicating a reduction in wave reflection due to peripheral vasodilation. The marked difference in the quantitative values of vascular impedance at various frequencies, after vagus stimulation as compared to 170 acetylcholine infusion, were interpreted to indicate that stimulation of vagus nerve produces its effect primarily on the heart. This was based on a smaller reduction in the impedance of the aorta. Therefore, Fourier analysis of cardiac function curves provided a quantitative dif- ference in the action of acetylcholine and the stimulation of vagus with respect to generation and propagation of the pressure pulse. 3. Adenylic acid infusion resulted in a reduced vascular impedance and persistance of the compliance characteristics of the system. This implied that adenylic acid, acting as a vasodilator, decreases vascular impedance and results in a flow under a reduced pressure gradient. 4. Alteration of the total peripheral resistance, by acute occlu- sion of the cat aorta, produced a marked increase in vascular impedance and distensibility. 5. Reduction in the venous return to the left heart, by occluding pulmonary artery increased the inertial characteristics of the vascular system. This was in contrast to decreased effects of inertial components of the aorta when both vena cavae were occluded. Occlusion of thoracic aorta and vena cavae resulted in similar impedance phase angle spectra. This similarity was attributed to the similarity of the physiological effects of occluding these vessels. Occlusion of aorta would bring about a reduc- tion in the venous return. The same results are obtained following occlusion of both vena cavae. Therefore, it is not surprising that Fourier analysis of such occlusion curves depicts the similar response evoked 171 by the heart. 6. Sudden augmentation of the venous inflow, by saline infusion, produced a definite increase in the distensibility of the elastic com- ponents of the vascular system. This was interpreted as an indication of an increase in vascular capacity necessary to accommodate the augmented blood volume following saline infusion. A modification of Laplace's surface tension law was used to com- pute tension-time curves for hearts and aortae under various experi- mental circumstances. On the average, the turtle heart developed 50% more tension than the cat heart. Since oxygen consumption is directly related to the amount of tension developed by the myocardium, then the high value of tension of the turtle heart, as compared to the cat heart, was attributed to the shape and not to the difference in the oxygen consumption. In the course of this investigation it was assumed that the heart is a black box generating a periodic waveform whose contour reflects the interplay of the various physical forces. Therefore, by subjecting the signals from the vascular system to Fourier analysis it was hoped to establish spectral patterns which would help to identify the physical com- ponents of the system. In this respect the effort was successful. 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APPENDICES 182 APPENDIX A AN INTRODUCTION TO THE USE OF COMPUTERS 183 AN INTRODUCTION TO THE USE OF COMPUTERS I. General The computer is a device which, in general, performs on stored data four different operations, namely, addition, subtraction, multipli- cation, and division, and is capable of making a decision, that is, whether the sum of given numbers is zero, positive, or negative. There are two general types of computers. First, an analogue computer which involves no explicit use of special "language. " Analogue data are rep- resented by magnitudes of physical quantities, such as length, voltage, pointer deflection, etc. Such quantities, in general, have a continuous range of values which are obtained through readings or measurements. The recorded analogue physical variables are converted into voltages in the computer and related to each other by arbitrary scale factors. Second, the digital computer in which physical variables are represented by a finite number of characters or symbols, such as the decimal num- ber system, the binary number system, and the alphabet. Most instru- ments used in biomedical research display their output in analogue form. Very often a transducer of some sort is employed to convert the quantity being measured into electrical signals. Therefore, it is necessary to use an analogue-to-digital converter to make useful arithmetical opera- tions on the stored data. The fundamental difference between the two types of computers is one of speed. The advantage of the analogue 184 185 computer is that it allows the analysis and synthesis of a system with speed and efficiency. However, there are certain types of problems which can be solved with greater accuracy with a digital computer than with an analogue computer. Therefore, the type of computer used depends on the type of problem to be solved. 11. Components _o_fa Computer A modern computer consists of five constituent parts: input, output, control, arithmetic, and memory units. The input unit serves as a device for presenting the raw data to the computer in the form of punched-card or tape. The output unit presents the results to the investigator in the desired form, as card, tape, or paper print-out. The control unit is a device which orders the activities of the computer from a set of instructions in a previously written program. The arithmetical component is designed basically to perform the operations of addition, subtraction, multiplication, and division. However, in new computers, the arithmetical unit can perform logical as well as dis- criminatory operations. The final component of the computer, namely, memory or storage unit is the most important part of the machine. It is capable of retaining large amounts of coded information. The storage unit is constructed, at the present, almost exclusively from magnetic materials of different forms: (1) magnetic tape for relatively slow speed but large capacity records, (2) a magnetized surface on a rotating drum I‘ll I.-. 186 for less extensive storage but faster speed, and (3) high speed storage utilizing small cores of rectangular loop ferrite materials. 111. Applications The major advantage of the digital computer is its versatility accruing from the fact that it is basically a symbol manipulator. The analogue computer, in contrast, has a limited application. The most significant use of the analogue computer is the solution of differential equations, including simultaneous nonlinear differential equations. The input and output of the analogue computer can both be time function variables. However, this property of the ana10gue computer is shared by the digital computer. When using the digital computer to solve various types of differential equations we must resort to some methods of numerical analysis. This method generally involves converting the analogue signals to digital form, sampling the physical variables at an appropriate rate, and quantifying each sample to form a number. The digital computer is then capable of performing all the necessary calcu- lations in the interval between samples, and then delivering a result which can be reconverted to analogue form when desired. This appli- cation of the digital computer requires additional analogue-to-digital and digital-to-analogue converters which are quite expensive. In general, all digital computers have a high basic cost, whereas analogue computers may be built to solve special problems at a reasonable cost. 187 Computers can be programmed to perform a wide variety of operations. Since the solution of any physical problem can be reduced to simple Operations, such as addition, subtraction, multiplication, and division, then, theoretically, any problem no matter how difficult can be solved by the computers. The advantage of the computer over human brain is the reliability of its memory and its speed. Some of the general applications of computers are listed below: 1. Computers are able to read and write. 2. Computers are able to memorize information in coded form for long or for short periods of time. 3. Computers are able to follow instructions precisely. 4. Computers are able to operate rapidly, accurately, and usually, more economically than men assigned to perform identical tasks. IV. Communication with a Computer The set of ordered instructions given to computers before inputting the raw data is called the program. Complete programming requires three things: 1. The problem must be completely defined and every logical eventuality within the scope of the problem must be preconceived. 2. A method or methods of solving the problem must be known. However, the computer may be instructed to choose the best solution under a given set of boundary conditions. 188 3. The method of solution must be "known" to the computer. This involves the complete set of ordered instruction or program. It should be noted that a programmer is not always a problem solver . V. Types_o_f Programs The degree of sophistication of programming language is increas- ing continuously. In general, there are three types of languages used for programming. One language is the so-called machine-oriented language, by means of which each step of a machine operation is exe- cuted. Another language is the smbolic language which has a one-to- one correspondence with the machine language and replaces the numeri- cal instructions with alphabetical symbols. The third type of language is the Eoblem-oriented language which requires a special compiler to translate the terms into symbolic and machine language. The compiler itself is a computer program that gives the computer the instructions required to convert the initial instructions into the numeric language of the computer. The problem-oriented languages require different com- pilers for each type of machine with which the program is to be run. One such problem-oriented language that is in use is FORTRAN, which is a mathematical, or formula-translaring, language. Another problem- oriented language is COBOL, which is used in business calculations. From one program statement in COBOL or FORTRAN, a compiler will 189 generate several machine instructions by which that segment of the program can be carried out. When the entire program has been written on cards or tape, it can then be fed into the computer, for which a com- iler program has also been written. In compiling this introduction the author has made extensive use of the following three references: 1. Booth, A. D. 1962. Some Applications of Digital Computers in Medicine. Phys. Med. Biol., 6: 377-388. 2. Moyer, J. H. (Editor). 1962. Application of Computers in Cardiovascular Disease. New York: The American Heart Association, Inc. 3. Strong, J. D. and G. Hannauer. 1962. APractical Ap- proach to Analogue Computers. Instruments and Control Systems, 35: 60-71. APPENDIX B A PROGRAM AND DETAILED INSTRUCTIONS FOR COMPLETE FOURIER ANALYSIS ON 160-A FORTRAN 190 191 The following is the detailed FORTRAN program for complete Fourier analysis with a typical set of data used. * ESMAIL KOUSHANPOUR DOCTORAL THESIS c PROGRAM ESMAIL KOUSHANPOUR DIMENSION X(10), BETA(10), TIME(10), A(lO), 3(10), C(10), D(10) FORMAT (1H9, 4F15.5) FORMAT (F7.3) FORMAT (1H0,F10.5) FORMAT (I3) U'IbWNl-J FORMAT (1H1, 19H ESMAIL KOUSHANPOUR/1H0,44H FOURIER ANALYSIS OF 1 CARDIAC TIME CURVES) 6 FORMAT (3H2 A0) 7 FORMAT (8H2 A, B, c, D) PRINT 5 READ 4,No Do 16 JJ=1,No READ 2, T, (TIME(I), I=l,10) Do 16 II=1,3 READ 2, (X(I). I=1,10) A0 = 0.5*(X(I) + x(10)) FIELD = 0 DO 11 I = 1,9 11 FIELD = X(I) + FIELD FIELD = 2.0*FIELD A0 = (A0 + FIELD)*.1 PRINT 6 PRINT 3, AC DC 15 N=1,lO DO 12 J=l,1O lillllllll‘v'il‘llll‘nl 192 12 BETA(J) = (3.14*TIME(J))/T 0.5*(X(l)*COSF(N*BETA(1)) + X(10)*COSF(N*BETA(10))) SORT 0 Do 13 1:2,9 X(I)*COSF(N*BETA(I))+ SORT A(N) l3 SORT SORT = SORT*2. A(N) = (A(N) + SORT)*.2 B(N) = .5*(X(l) *SINF(N*BETA(1) + X(10)*SINF(N*BETA(10))) SORT = 0 DO 14 I=2.9 14 SORT = X(I)*SINF(N*BETA(I)) + SORT SORT = SORT*2. B(N) = (B(N) + SORT)*.2 C(N) = (A(N)*A(N) + B(N)*B(N))**.5 15 D(N) = ATANF(A(N)/B(N)) DO 16 I=l,lO PRINT 7 PRINT 1, A(I), B(I), C(I), D(I) 16 CONTINUE END Number of Data Set .400 Cycle Length .040 tl .080 t2 .120 t3 .160 t4 .200 t5 .240 t6 .280 t7 .320 t8 .360 .400 Aortic 15.000 12.500 7.500 25.000 37.500 42.500 32.500 30.000 25.000 20.000 193 t9 t10 Pressure Pulse (mm. Hg) Ventricular Circumference (cm.) 1.700 1.900 2.400 3.700 3.700 3.350 3.150 3.150 2.300 1.600 Change .100 .300 .800 2.100 in Ventricular Circumference (cm.) 194 2.100 1.750 1.550 1.550 .700 .000 The integration scheme employed in this program is the well- known trape zoidal method. Instruction for Use_o_f Program and Data Preparation The first data card indicates to the computer the number of times the entire calculation should be repeated. For example, in the case of the above data, the entire operation will be repeated 3 times. The sec- ond data card indicates the cycle length (T) in seconds for each individual pulse curve. The next 10 data cards are the time intervals starting from t1 = . 040 to t10 = T = . 400. The remainder of 30 cards are the actual values Obtained from the pulse curves after dividing each one into 10 equal time intervals in the manner shown in figure 6. This program is written for a special case in which there are only 10 points on the curve. If it is desired to divide the pulse curve or any periodic phenomenon into more or less than 10 points the program re- quires a minor modification. rm... Eta-1 a..- 8... fins“. PU .31...”