APPLICATION OF THE LAW OF LAPLACE IN [STIMATION OF LEFT VENTRICULAR HYPERTROPHY IN RATS WITH EXPERIMENTAL HIGH BLOOD PRESSURE Thesis for tho Deana 69 M. S. MICHIGAN STA‘I‘E UNIVERSITY Esmaifi Koushanpour I961 LIBRARY Michigan State University APPLICATION OF THE LAW OF LAPLACE IN ESTIMATION OF LEFT VENTRICULAR HYPERTROPHY IN RATS WITH EXPERIMENTAL HIGH BLOOD PRESSURE BY Esmail Koushanpour A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physiology and Pharmacology 1961 ABSTRACT APPLICATION OF THE LAW OF LAPLACE IN ESTIMATION OF LEFT VENTRICULAR HYPERTROPHY IN RATS WITH EXPERIMENTAL HIGH BLOOD PRESSURE by Esmail Koushanpour It is postulated that a sustained change in pressure within the cardiovascular system results in an alteration of the physical dimensions of the heart. The heart is considered anatomically to be a specialized vessel with modified geometry. It is further assumed that, geometrically, the heart is com- posed of a cylindrical body and conical apex. This assumption allows us to assign elliptical geometry to the ventricular compartments. The ventricles are, thus, composed of two general curvatures: the major curvature (long axis) as part of an ellipse, and the minor curvature (short axis) as part of a circle. Data were obtained from normal and hypertensive rats. Tail systolic blood pressures were determined by a pulse pressure sensitive transducer. Arcs and chords of major and minor curvatures were measured and thickness of the ventricular wall at the point of intersection of the arcs was determined. Measurements were made on excised hearts (slightly inflated to approximate ventricular volume in isometric contraction). Radii of major and minor curvatures were determined from the ratio arc/chord of each curvature. The values for the radius 2 Esmail Koushanpour of the major curvatures were multiplied by a constant (1.31) to obtain the radius of the major curvature by elliptical approximation. The constant (1.31) was obtained by con- structing an ellipse having a major semi-axis twice as great as the minor semi-axis. Using Laplace's equation, P = T (l/Rl + l/R2), tension developed at the point of measurement of wall thickness was calculated. Assuming that tension developed is proportional to wall thickness, the prOportionality constant (k) is a measure of the contractile behavior of the ventricular wall. Data obtained for values of tension, (k), mean radii, and radial force (F) showed a definite left ventri- cular hypertrophy. Wet weight and dry weight determinations on the ventricles confirmed the estimated hypertrophy. ii ACKNOWLEDGEMENTS The author is indebted to Dr. W. D. Collings, professor of Physiology, Michigan State University, for his interest, encouragement, and advice during the course of this study and preparation of the manuscript. He also wishes to thank Dr. A. C. Burton, professor of Biophysics, University of Western Ontario, for his invaluable suggestions. I. II. III. IV. VI. VII. VIII. TABLE OF CONTENTS INTRODUCTION . . . SURVEY OF LITERATURE A. B. C. MATERIALS AND METHODS CALCULATIONS AND DATA RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS Heart and the Hemodynamics of Circulation Cardiac Compensation Myocardial Force in Relation to Blood Pressure LITERATURE CITED APPENDIX iii 12 17 28 54 69 71 74 Table 10. ll. 12. 13. 14. iv LIST OF TABLES Page Numerical Values of Parameters S, Sin 8, S/Sin S, and 1/2/Sin S . . . . . . . . . . . . . 31 Comparison of Body Weight and Food Consumption . . . . . . . . . . . . . . . . 40 Comparison of Blood Pressures and Hematocrits . 41 Comparison of Wet and Dry Weights of Ventricles 42 Comparison of Water Content and Dry Matter of Ventricles . . . . . . . . . . . . . . . . 43 Comparison of Left Ventricular Measurements . . 44 Comparison of Ratios of Major Arc to Major Chord and Minor Arc to Minor Chord . . . . 45 Comparison of Values for Product of Wall Thickness, t, and Sum of the Reciprocal of Principle Radii of Curvature . . . . . . 46 Comparison of Left Ventricular Radii and Calculated Tension and (k), Assuming Spherical Geometry . . . . . . . . . . . . 47 Comparison of Left Ventricular Radii and Calculated Tension and (k), Assuming Elliptical Geometry . . . . , . . . . . . 48 Comparison of Values for Mean Radius, Surface Area, and Volume, Assuming Spherical Geometry . . . . . . . . . . . . . . . . . 49 Comparison of Values for Mean Radius, Surface Area, and Volume, Assuming Elliptical Geometry . . . . . . . . . . . . . . . . . 50 Comparison of Spherical Principle Comparison of Radial Force Calculated from Both and Elliptical Approximations of the . . 9 Radll . O O O O O O O O O O O O O O 51 Results . . . . . . . . . . . . . . 52 LIST OF FIGURES Figure Page 1. Photograph of Apparatus Used To Measure Indirect Blood Pressure . . . . . . . . . . . . 21 2. Typical Calibration Graph of the Kind Used To Read Systolic Blood Pressure. . . . . . . . . . 23 3. Typical Blood Pressure Recording, Normal Pulse Wave Record, and Typical Calibration Record . . 24 4. Diagram Showing Sites of Major and Minor Arcs and Chords, and Wall Thickness Measurements . . 26 5. Standard Curve of Determination of Radius of the Curvature . . . . . . . . . . . . . . . . . . . 32 6. Diagram of Elliptical Model Used in Estimating the Radius of the Major Curvature of Left ventriCle O O O O O O O O O O I C O O O O O O O 35 7. Comparison of Blood Pressures of Normal and Hypertensive Rats . . . . . . . . . . . . . . . 55 8. Relationship between Blood Pressure and Ratio of Ventricular Wet Weight to Surface Area of Both Normal and Hypertensive Rats . . . . . . . 58 9. Relationship between Blood Pressure and Ratio of Ventricular Dry Weight to Surface Area of Both Normal and Hypertensive Rats . . . . . . . 59 10. Relationship between Blood Pressure and Tension of Normal and Hypertensive Rats, Showing Both Spherical and Elliptical Approximations . 66 11. Relationship between Tension and Radial Force of Normal and Hypertensive Rats, Showing Both Spherical and Elliptical Approximations . . . . 67 I. INTRODUCTION In recent years, much interest has been directed toward a better understanding of cardiac function and its active role in the hemodynamics of circulation. The mechanism of myocardial adaptation to variations of blood pressure has not been explored fully. . However, there are indications that a change in pressure within the cardiovascular system would have a definite effect on the physical dimensions of the heart. The function of smooth muscle within the vessel wall has been referred to as maintenance of "active tension" (Burton, 1951). A change in the pressure of circulating blood from a high value in the aorta to a low value in the capillaries is accompanied by an alteration in anatomical constituents and physical dimensions of blood vessels. Therefore, study of the physics of various constituents of the cardiovascular system is necessary in order to gain a fuller understanding of their physiological significance. The heart may be considered anatomically as a specialized vessel with a modified geometry. Similarity between the heart and the blood vessels has been the basis for applying to the heart physical laws governing the blood vessels. The purpose of this study is to apply the Law of Laplace to the heart to determine changes produced in cardiac muscle by experimental high blood pressure. II. SURVEY OF LITERATURE A. Heart and the Hemodynamics of Circulation The function of the heart in the cardiovascular system has been compared to a pump in a hydraulic system. However, there are three unique features possessed by the cardiac pump which distinguish it from reciprocating pumps employed in engineering. They are: (l) the force that must be supported by ventricles during cardiac action does not increase but decreases as systole progresses, (2) the muscle fibers need to exert a force of contraction only one-fourth of that of the distending force of blood pressure, and (3) ventricular filling in diastole indicates a "suction" action by the cardiac pump. The first feature of the cardiac pump was suggested by Gladstone (1929). He explained that cardiac systole involves two types of contractions: an early isometric period, and a later isotonic phase. The length of isometric period, other things being constant, depends upon the size of the force to be supported by the heart. Gladstone pointed out that the ia3tonic contraction phase begins only when the intraventicular pressure is sufficiently high to open the semi-lunar valves and eject blood. This indicates that the force supported by the heart actually declines as ventricular systole advances. The last two features (2 and 3 above) of the cardiac pump were proposed by Burch, Ray, and Cronvich (1952). These investigators,assuming the heart to be spherical, and using calculations from theoretical conditions, found that the total radial force, (FR), upon the internal walls of ventricles is equal to the product of the intraventricular pressure, (P), and the internal surface area, 4W R2. However, longitudinal force developed within the cardiac muscle is equal to the product of the internal pressure and the cross- sectional area, or FL = W R2 x P. This is the total force tending to separate the spherical ventricles into two hemispheres. Thus, the tensile force (longitudinal force) developed by cardiac muscle fibers necessary to maintain the radial force is one-fourth of any opposing blood pressure. Burch and co-workers contended that such a relationship between the tensile force and the distending force of blood pressure holds even if the heart is not assumed to be spherical in geometry. Catton (1957) attributes the peculiarity of the heart as a pump to the elastic nature of cardiac tissue and its contractile ability. Contraction of the heart is dependent on and adjustable to variations in flow and pressure of cir- culating blood. The energy required to maintain flow of blood in the circulation is provided by contraction of cardiac muscle. This mechanical energy, as expressed in Bernoulli's Theorem (Stacy, gt al., 1955), has three components: 2 E=Z+—E—-+V Pg 29 In this equation, the first term, (Z), represents gravitational potential energy or the energy required to raise blood to a height above the initial cardiac level. The second term (P/pg), where (P) is pressure in mass units per unit area, (p) is the mass unit volume, and (g) is the force of gravity, 2 represents the flow work. The last term (v /2g), where (v) is the velocity of blood, represents kinetic energy. Blood in the left ventricle possesses a form of potential energy during isometric contraction, whereas, blood in any of the arterial branches possesses all three energy components. When the body is at rest, all energy required for maintenance of circulation is provided by myocardial contraction. Only in the active state is the heart aided by the "thoracic pump" or "muscle pump,‘ and gravity. The contributions of these three mechanisms are small compared to cardiac contraction (Catton, 1957). Ability of cardiac muscle fibers to adjust to changing conditions in the circulatory system was considered in a series of experiments by Starling and Visscher (1927). They concluded that energy of cardiac muscle fiber contraction increases to an optimum value as the diastolic volume increases. This process of compensation by the heart was called, by Starling, the law of the heart. Validity of this law with regard to the heart in the unopened chest has been questioned recently (Rushmer, 1959). However, its applicability to the isolated heart is based on a fundamental property of the muscle discovered by Hill (1913). He showed that tension produced by the muscle is greater under isometric contraction than under isotonic contraction, and that a greater amount of energy is liberated when the muscle is stretched to a certain limit prior to contraction. The question whether a rise in arterial blood pressure will result in a corresponding increase in cardiac output has been investigated by two separate experiments on dogs. Evans and Matsuoka (1915) studied the effects of various mechanical conditions on cardiac efficiency in an isolated heart-lung preparation. They observed that a sustained alteration of blood pressure ranging from 40 to 170 mm. Hg, for a period of 15 minutes, did not significantly change the total cardiac output from a value of about 31 liters per hour. It was shown that a rise in blood pressure with constant cardiac output, or vice versa, results in a proportional increase of both oxygen uptake and mechanical efficiency of the heart followed by a subsequent decline. Maximal mechanical efficiency of about 20% was obtained by moderate increase of both blood pressure and cardiac output. Gollwitzer-Meier and co-workers (1938) studied oxygen consumption and cardiac output in an intact heart-lung preparation. They found that the intact heart is capable of performing the same amount of work as compared to the isolated heart, but with less oxygen uptake. The interplay of heart rate and arterial blood pressure was found to influence the total cardiac output. It was noted that a rise in arterial blood pressure from 103 to 165 mm. Hg was accompanied by a decrease in heart rate from 95 to 56 per minute. Cardiac output was increased by less than 3%, cardiac work was increased from 1.24 to 1.35 m. kg., and oxygen consumption was decreased from 3.0 to 2.2 ’ml. per minute. A fall in arterial blood pressure to about 62 mm. Hg resulted in an elevation of heart rate to 114 per minute, and an increase in oxygen uptake to a value of 4.3 ml. per minute. The general conclusion from these two experiments was that only one feature was common to both isolated and intact hearts, namely, that a sustained rise in arterial blood pressure will not result in an elevation of cardiac output. Efficiency of the heart as a pump has been studied from two aspects: as a mechanical pump, and as a converter of chemical energy into mechanical work (Evans and Matsuoka, 1915). In the first instance, efficiency depends upon physical structure of the heart and possible defects due to disease. In contrast, efficiency of the heart while converting chemical energy into mechanical work depends upon its ability to consume oxygen and metabolites. Experiments performed by Starling and Visscher (1927) have shown that over-all cardiac efficiency varies in accordance with conditions confronting the heart, and that cardiac muscle fibers have an unexplained ability to increase their oxygen consumption and energy output when a certain degree of stretching is imposed preliminary to contraction. B. Cardiac Compensation A fundamental property of cardiac muscle is the ability to adapt to changing demands of both central and peripheral circulations. In general, cardiac compensation occurs by means of three mechanisms: (1) an increase in the diastolic volume by an increase in the diastolic fiber length, (2) an increase in the force of contraction of the myocardial fibers, and (3) cardiac hypertrophy (Freis, 1960). The first two mechaniSms were briefly considered in the previous section. Cardiac hypertrophy has long been considered as the most important phase of cardiac compensation. However, there is no agreement on the nature of this hypertrophy. Enlarge- ment of the heart in animals with glomerulonephritis was observed by Richard Bright as early as 1845 (Braun-Menendez, 1946). This observation was pursued by Passler and Heinecke (1905) who found that when removal of one kidney and one-half of the other in dogs is followed, at certain intervals, by excising portions of the remaining hypertrophkad kidney tissue, the animals invariably develop high blood pressure. They noted that only 7 of the 18 operated dogs showed a definite cardiac hypertrophy. The degree of hypertrophy was determined by comparing the weights of right and left ventricles. The ratio of the weight of the right ventricle to that of the left was 1:2.26 in seven experimental dogs and 1:1.76 in the normal dog. The average increase in the blood pressure, determined by femoral cannulation, was about 21.5 mm. Hg. There was no mention of whether hypertrophy was due to hyperplasia of the cardiac muscle fibers or simply a result of enlargement of muscle fibers. Karsner, Saphir, and Todd (1925) made histological sections of three human hearts. One heart was hypertrophied as a result of chronic glomerulonephritis. The other two hearts, one normal and one atrophied, were from patients with pulmonary tuberculosis. Fibers and nuclei of various sections were counted and their findings confirmed the contention of Edens (1913) that in hypertrophied and normal cardiac muscle ratio of area of nucleus to that of cytoplasm is nearly the same. However, the hypertrophied heart has larger fibers as compared with that of the normal heart. Cardiac hypertrophy was found to be due to an increase in the dimensions of the muscle fibers as compared with that of the normal heart. Their observations revealed that the degree of variability in size of the muscle fibers is very much less in the hypertrophied and atrophied hearts as compared to that of the normal heart. On this basis, they believed that the phenomenon of variability is characteristic of normal tissues, and that such a condition in the normal tissue allows for greater degree of adaptability in the case of emergency. When cardiac hypertrophy occurs due to excess work by the heart, muscle fibers increase in size, and consequently a greater fiber uniformity prevails. These investigators concluded that the cardiac enlargement is due primarily to hypertrophy of the muscle fibers. Hyperplasia was not considered as the cause of cardiac hypertrophy. They further indicated that the limit of the reserve capacity of the hypertrophied heart is due to the fact that cardiac muscle fibers have reached, then, their maximum growth and functional strength. Harrison, Ashman, and Larson (1932) found a definite and interesting relationship between heart rate and thickness of cardiac muscle fibers. They noted that the slower the 10 heart rate, the thicker the cardiac muscle fiber, and vice versa. However, they observed that the hypertrophied heart has a much faster rate than normal. The authors contend that the physiological significance of this relationship is: a slower heart rate allows more time for diffusion of oxygen and metabolites to thicker fibers. Chanutin and co-workers (1932 and 1933) made an extensive study of the development of cardiac hypertrophy in rats with high blood pressure induced by partial nephrectomy. Results suggested that both cardiac hypertrophy and high blood pressure are the direct result of renal insufficiency, and that elevation of blood pressure in animals with renal insufficiency is necessary to excrete a high volume of less concentrated metabolites. The degree of compensation, in cardiac tissue and in blood pressure, depends upon the amount of renal tissue present. Too much removal of renal tissue was found to cause failure of these compensatory mechanisms. The index for the degree of cardiac hypertrophy was the ratio of heart weight to the body surface area. They found a high positive correlation between the ratio, heart weight/body surface area, and blood pressure. Hermann, Dechard, and Erhard (1941) attempted to produce cardiac hypertrophy in several ways. They found that wrapping the left kidney with gauze soaked in collodion and removing 11 the contralateral kidney about 4—7 days after the first operation was the most successful method for producing hypertrophy of the heart. The greatest amount of hypertrophy was found to occur about 50 days after nephrectomy. The average hypertrophy after 50 days was about 92%, whereas the average hypertrophy after 20 days was about 46%. In general, 30 days post-nephrectomy the maximum amount of cardiac hypertrophy occurred. Other experiments have shown that cardiac hypertrophy will result from any disturbance in the body function that leads to the elevation of blood pressure. Cardiac hypertrophy was found to be directly related to changes in pressure and flow of blood. Benzak (1958) studied cardiac output, reserve force of the heart, total peripheral resistance, and weights of the heart and other organs in normal rats and in rats with aortic coarctation below the diaphragm. She found that cardiac output dropped from a normal value of about 48 I 4 ml./min. to a value of about 31 I 5 ml./min. after the production of coarctation. Simultaneously, an increase in total peripheral resistance from a normal value of about 210,000 to 320,000 dynes second per cm._5 was observed. Cardiac hypertrophy was confined mostly to the left ventricle which showed an increase of about 45%.above the control weight three weeks following coarctation. 12 C. Myocardial Force in Relation to Blood Pressure Physical laws governing flow of fluid by a reciprocating pump demand a definite relationship between the capability of the pump to develop a driving force, and the pressure with which the fluid is compelled to flow. In the cardiac pump, which forces blood with a given pressure through vessels, such a fundamental relationship must also exist. Starling's law of the heart, which states that a change in the length of the ventricular muscle fibers influences their force of contraction, contributes little to our understanding of relationship between the force developed by the ventricular muscle during systole and the generated pressure. However, this is the essence of a recent paper by Burton (1957) in which he suggests that the Law of Laplace, previously applied to blood vessels, can provide pertinent information with regard to this vital relationship. Burton (1951), applying the Law of Laplace, showed that the diameter of a blood vessel is determined by a balance between two forces: a distending force (blood pressure), and a closing force (wall tension). A smaller vessel radius means a lesser tension required to oppose the distending force of blood pressure. Burton (1954) explained that the shape of pressure-flow curves in living vessels is a l3 reflection of anatomical structure of arteriolar walls. Smooth muscle has a viscoelastic property that is responsible for development of a greater tension when it is subjected to a sudden stretch. Local adjustment to low pressure variations is done by elastic tissue and to high pressure variations through collagen tissue. Smooth muscle is responsible for "active tension" which adjusts the response of both elastic and collagen tissues. As early as 1892 the importance of the role of shape and size of the heart in its pumping function was recognized. In that year, Woods applied the Law of Laplace to post-mortem human hearts. However, the scope of usefulness of this law was not fully described. Recent investigations in connection with the dilated heart and hypertensive cardiac hypertrophy (see Sections A and B) have renewed interest in application of the Law of Laplace to the heart. Burton (1957) suggested that the dilation of the heart, as predicted by this law, results in an increase in the principle radii of the curvature of ventricles. The Law of Laplace applied to ventricles has the formula, P = T (1/Rl + 1/R2), where (P) is pressure in dynes per square cm., (T) is tension in dynes per cm., and (R1) and (R2) are principle radii of ventricular curvatures in cm. Since the amount of tension developed by ventricular walls is proportional to thickness, Burton (1957) pointed out that 14 the Law of Laplace explained the great variations of the ventricular wall thickness. In the sharply curved region of the ventricle, such as the apex, the wall can be thin and still produce sufficient tension to develop the required pressure. In contrast, the Law explains that, at the region where the wall is nearly "flat,' such as midway up the ventricle, the wall must be thicker and the tension developed must be greater in order to produce the necessary pressure. This variation in wall thickness in accordance with developed tension explains the thinner right ventricular wall. It is in the Law of Laplace, Burtan believes, that reasons for phenomena of 'mechanical advantage" in the normal heart, and ”mechanical disadvantage" in the dilated heart should be sought. There are numerous experiments which demonstrate the significance of tension developed by cardiac muscle and its deviation from normal in cardiac decompensation during myo- cardial disease. Burch (1955) showed that the dilated heart must work harder and produce greater tension, as compared to normal heart, in order to maintain the same volume of output as systole progresses. The extent of this increase in external work and developed tension is determined by the magnitude of the cardiac enlargement. The amount of cardiac hypertrophy is reflected by the sum of the reciprocal of the principle 15 radii of curvature (l/Rl + l/R2), the "shape" factor, in the Law of Laplace. Experiments by Hartree and Hill (1921) on isolated skeletal muscle showed that oxygen consumption and heat liberation in the muscle is proportional to the product of tension and the time it is maintained. Therefore, oxygen consumption of cardiac muscle depends upon the sum of two factors: the mechanical work, ( P x A V), and the product of tension and time, (T x t). The expression, (J[P x A V), for the mechanical or external work of the heart was developed by Katz (1931) who made simultaneous pressure-volume curves recording by optical means on isolated perfused turtle heart preparation. Starling and Visscher (1927) showed that the total oxygen consumption of both normal and failing hearts depends upon diastolic volume and is relatively independent of the external work (JfP x A V) that the heart has to do. Burton (1957) pointed out that the Law of Laplace explains why diastolic volume can change the energy turnover of the heart, namely, by increasing the value of the product of tension and time. Therefore, the factor (T x t) should be given serious consideration when ascertaining cardiac performance. In this respect, both Burton (1957) and Rushmer (1959) believe that cardiac rate can be used as a better index of the total cardiac load. There is also evidence that in the early stages 16 of hypertension, minute volume output is increased, and that elevation of blood pressure causes an increase in the cardiac work. This increase is due primarily to rise of systolic blood pressure (Freis, 1960). Thus, when high blood pressure is present, the product of tension and time, as well as mechanical work, will be increased. If high blood pressure persists for a long period, ventricular hypertrophy is expected- 17 III. MATERIALS AND METHODS Albino rats of Hoppert (M.S.U.) strain, ranging in age from two to three months, and weighing from 138 to 245 grams with a standard deviation of i 5.65 grams (Table 2) were used in this experiment. All rats, and food jars were weighed weekly so that an assessment of gain or loss in weight and food consumption could be obtained during the course of experiment. All weighings were done on a 500 gram capacity Toledo Balance. Rats were divided into three groups. Group I was subjected to a surgical procedure introduced by Soskin and Saphir (1932). A flank incision was made on the left side and the kidney was brought to the surface. The adrenal gland was separated from its attachment to the kidney, and all fatty tissues surrounding the kidney were severed. No attempt was made to remove them from the surface of the kidney capsule. Then, all manipulations were stopped for 10 minutes, so that the kidney could resume its normal functional distension. Cotton gauze was cut into small rectangular pieces and placed in a petri dish. Collodion Merck (U.S.P. alcohol 24%) was poured over the gauze, and rectangular pieces were pasted around the kidney so as to form a snug capsule. Care was taken to keep the renal pedicle completely free from the wrapping material. After a lapse of two minutes, to allow 18 for the wrapping material to dry, the kidney was returned to its original position. The incision was closed by two layers of sutures. Lock stitches were used for peritoneum and muscle, and interrupted sutures for skin to prevent injury from chewing by the rat. After seven days, the rats were nephrectomized. The same process of manipulation of the kidney and a waiting period of 10 minutes was observed during the course of nephrectomy. Group II was subjected to a surgical procedure described by Grollman (1944). A flank incision was made on the left side and the kidney exposed as described above. Then, a small piece of No. 8 cotton thread was wrapped around the poles of the kidney in the form of a figure—eight and knotted tightly. The kidney was returned to its position and after closure of the left incision, the contralateral kidney removed with the same procedure described previously for Group I. The third group was sham—operated at random, with respect to right and left side, and used as controls. Anesthesia in the above operations was by intra- peritoneal injection of 3% sodium pentobarbital solution. The dose required was 30 mg. per kilogram body weight for females and 40 mg. per kilogram body weight for males. After recovery from anesthesia, the animals were returned to their . . . . . . . . o indiVidual steel ere cages in an air—conditioned room at 70 l9 Fahrenheit. Feed consisted of a special ration prepared by the Department of Animal Husbandry, Michigan State University, containing 22% protein, 7.5% crude fat, 4% crude fiber, 0.78% calcium, 0.45% chloride, 0.76% potassium, 0.35% sodium, and 0.67% phosphorous, with a T.D.N. of about 86.1%. Tap water was given ad libitum. Systemic hematocrit on tail blood was determined before operation and prior to sacrificing each animal. Blood samples were drawn, in duplicate, into microhematocrit tubes, sealed, and spun in an International Hemacrit Centrifuge for five minutes. Blood pressure of unanesthetized rats was determined before the experiment, and on the 7th. 10th, and 14th (final) days by a simple method devised especially for this study. The rat was led into a cone-shaped restraining cage made of mesh steel wire. The restrained rat was then placed on a large foam-rubber pad inside a 50 x 25 x 25 cm. wood box with sliding doors and glass top. Temperature of the box was maintained between 37-390 Centigrade with two 25 watt electric bulbs. The rat's tail was passed through a 16 mm. diameter pressure cuff made of surgical rubber, lining a rigid outside metal sleeve. The cuff was connected to a hand bulb from one side, and attached to a pressure transducer from the other side. The transducer was connected from one 20 end to a mercury manometer, and from the other to a Sanborn carrier amplifier and recorder. The pick-up of a pulse pressure detecting device, called "Infraton" (Beckman, Spinco Division, Palo Alto, California), was attached firmly by means of adhesive tape to the ventral side of the tail immediately distal to the cuff, and the leads of the pick-up were connected to one of the D.C. amplifiers of Sanborn polygraph. The apparatus can be visualized from the accompanying photograph (Figure l). Rats were placed in the warmed box for 10 minutes before each blood pressure measurement. The pressure cuff was inflated by means of a hand bulb until pulsations disappeared from the record. As the pressure was released, pulsations reappeared at the point where cuff pressure, read from the recording paper, was slightly less than that of the caudal artery. This pressure was designated as systolic blood pressure. Diastolic blood pressure cannot be determined with this apparatus. Systolic blood pressure was measured in triplicate for each animal at various times during experimental observation. Before and after each series of blood pressure readings the transducer was calibrated with a mercury manometer to ascertain the degree of fluctuation of the recording stylus during each day's run. No significant change in calibration occurred. A calibration record of the kind used 21 FIGURE 1 Photograph of apparatus used to measure indirect blood pressure. *_.——., 22 to read systolic blood pressure, and a typical blood pressure recording are shown (Figures 2 and 3). The indirect blood pressure recording method was comparedvfijfl1direct, simultaneous arterial pressure measure- ment from a cannula in the carotid artery. The direct reading apparatus consisted of a cannula attached to a pressure transducer which was connected to a calibrated Brush recorder. No significant difference could be observed between the two methods. This agrees with observations of Dodson and Mackaness (1957). The method used in this experiment for determining blood pressure of rat can be adapted, with some modification of the cuff, to measure blood pressure of other animals, both large and small. On the fourteenth day of observation, rats were anesthetized and the abdominal cavity was exposed. Sodium heparin (2 mg. per kilogram body weight) was injected into the inferior vena cava. The chest cavity was opened and the heart, with all its connecting vessels, was removed immediately. The heart was dissected free of adventitious tissues and emptied of blood by flushing with distilled water instead of saline to compensate for dehydration in the next step. Left ventricle, through aorta, was placed under a 20 cm. pressure I head of 95% ethyl alcohol for hypertensive rats, and a 10 cm. 23 FIGURE 2 Typical calibration graph of the kind used to read systolic blood pressure. SE \<\ 29C 0w OLQQ o» o» wm um S o o .0M .00\ .th .QQN 35/753350’ 29H WW N/ 24 FIGURE 3 Top- Typical blood pressure recording. Middle— Normal pulse wave record. Bottom- Typical calibration record. SPEED ' 5 M“. PER SEC. PULSE Mi . Av...“ SYSTOLIC 8.! SPEED- 50 MM PER sec. PULSE - WAVE Pumps mung _ ". ;.;;_;;' ........... .......... 25 pressure head for normal rats for 20 minutes. This was done to harden the cardiac muscle for subsequent measurements with the heart approximating ventricular volume during iso- metric (isovolumic) contraction of the systole. Major (long axis) and minor (short axis) arcs and chords, and heart wall thickness at the intersection of the two arcs, were measured, on the left ventricle in the following manner (Figure 4). A cotton thread was placed on the major left ventricular surface parallel to the interventricular septum and from a point just below atrioventricular valve ring to the apex. The linear distance of the thread was the arc length, and the distance between the two points was the chord length. The same procedure was followed for measuring the minor arc and chord at a site approximately midway between the base and the apex of the left ventricle. The method is roughly similar to that of E. W. Hawthorne (1961) who used a variable resistance strain gauge. Wall thickness was determined atthe intersection of the two arcs. Principle radii of the left ventricular curvatures were estimated by methods described in Part IV. After being measured, ventricles were separated from auricles and other non-ventricular tissues. Isolated ventricles were weighed and dried for 48 hours in an oven at a constant temperature of 970Centigrade, cooled in a dessicator, 26 FIGURE 4 Diagram showing sites of major and minor arcs and chords, and wall thickness measurements. to D E K‘B- major(long axis) are 58- major chord a) - minor (short axis) are CT) - minor chord E- point where wall thickness was measured 27 and dry weight determined. Previous experiments showed that heart tissues dried to constant weight in 48 hours at the above temperature. All heart weights were determined by a Voland and Sons chain-o-matic balance capable of measuring to the nearest 0.1 mg. 28 IV. CALCULATIONS AND DATA In this experiment, two types of calculations were employed for evaluation of raw data. The first type involved the use of the relationship found experimentally by Lee (1929) for determination of rat surface area, which is as follows: Surface Area (cm.2) = 12.54 x WO°6O where (W) is the rat body weight in grams. In order to obtain more uniform heart-weight data from animals with different body weights, the ratios of both wet and dry weights of the ventricles to the surface area were used in determining the degree of ventricular hypertrophy. The second type of calculation was used to determine the principle radii of the left ventricular curvatures so that the degree of hypertrophy could be estimated by application of the Law of Laplace. In this operation, two assumptions were made: (1) left ventricle has elliptical geometry; and (2) ventricular wall thickness is negligible as compared to the mean radius. The first assumption is a modification of Rushmer's observation (1951) that the ventricles are composed geometrically of a cylindrical body and conical apex. The second assumption is justified if it is accepted that the tension developed in the ventricular wall is proportional to the thickness. This latter relation is considered reasonable by Burton (1957). 29 Mathematically, four families of curves could fit the curvatures of the left ventricle. They are: (l) catenary, a curve in which a perfectly flexible chain hangs when suspended between two points, with a general equation of y = a cosh x/a, (2) circle with an equation of (x-a)2 + (y-b)2 = r2, (3) ellipse with a general equation of (x-h)2/a2 + (y-k)2/b 2 l, and (4) parabola with an equation of (x—a)2 =.i 2 p (y-b). In accordance with Rushmer's observation, any curve that can describe the left ventricular curvature must have a first derivative equal to zero at points of the ventricle with cylindrical geometry. An ellipse is the only one of the above four curves that can fulfill this requirement, and adequately describe the major (long axis) curvature of the left ventricle. Therefore, principle radii of the ventricular curvatures were estimated by assuming that the major (long axis) curvature is part of an ellipse and that the minor (short axis) curvature is part of a circle. The equation for estimating the radius of the minor curvature was derived from the following considerations. The radius of the circle as a function of the arc and the chord of a particular segment of the circle follows the equations: 8 = ——-, L = 2 R Sin (9/2) Then, L = 2 R Sin (S/2R) (l) where (S) is the arc length, (L) is the chord length, (6) is 30 the central angle describing the arc, and (R) is the radius of the circle. In order to determine the radius of a circular curvature for any arc and chord, a general graph was constructed from the following manipulation of equation (1). If the radius is allowed to have a numerical value of (1/2), the equation (1) takes the form, L = 2 (1/2) Sin (s/2 (1/2) ) = Sin 5. (2) A similar equation can be obtained by substituting other numerical values for radius. Numerical value (1/2) was chosen for simplicity. Dividing both sides of the equation (2) into (S) and (R) respectively, the following two equations will be obtained: S/L = 5/ Sin 3 (3)' and R/L 1/2/ Sin S. (4) From the table of Natural Functions for Angles in Radians, the values of (Sin S) for any value of (S) from S = .00 to S = 2.00 radians were compiled (Table 1). Then, the ratios S/Sin S and l/2/Sin S were calculated and the values of the ratio (l/2/Sin S = R/L) were plotted against the values of the ratio (S/Sin S = S/L) on an ordinary graph paper. A glance at this graph (Figure 5) indicates that, from the ratio (S/L), the ratio (R/L) can be determined. When the latter ratio is multiplied by the value for chord length, (L), the Table 1 Numerical Values of Parameters S, Sin S, S/Sin S, and l/2/Sin S s (radian) Sin s S/Sin s = S/L l/2/Sin s = R/L 0.10 0.09983 1.002 5.009 0.20 0.19867 1.007 2.517 0.30 0.29552 1.015 1.692 0.40 0.38942 1.027 1.284 0.50 0.47943 1.043 1.043 0.60 0.56464 1.063 0.866 0.70 0.64422 1.087 0.776 0.80 0.71736 1.115* 0.697* 0.90 0.78333 1.116* 0.638* 1.00 0.84147 1.188* 0.594* 1.10 0.89121 1.234* 0.561* 1.20 0.93204 1.287* 0.537* 1.30 0.96356 1.349* 0.519* 1.40 0.98545 1.420* 0.507* 1.50 0.99745 1.503* 0.501* 1.60 0.99957 1.600* 0.500* 1.70 0.99166 1.714* 0.504* 1.80 0.97385 1.848* 0.513* 1.90 0.94630 2.008* 0.528* 2.00 0.90930 2.200* 0.550* F'1' cure R. “The sign (*) indicates the points plotted in 32 FIGURE 5 Standard curve for determination of radius of the curvature. ' 0.70 E Q) E, 0.55 » \I Q Q: 3 b 0.50 » \ 0) E Q 5: 0.55 . Q: 0.50 L A20 /.40 A60 /.80 2.00 2.20 2.40 ARC LENGTH / CHORD LENGTH 33 result is the value of the radius for the particular arc and chord values. - Major curvature of the left ventricle is considered to approximate elliptical geometry. By definition, the absolute value of the reciprocal of the curVature (K) is called the radius of curvature, R. In mathematical expression, 1 In rectangular coordinates, the radius of curvature is given by the equation, 2 3/2 R = ( l + (dy/dx) ) . (6) . 2 2 (d y/dx ) In order to find the radius of an ellipse with an . 2 2 2 2 . equation of ( x /a + y /b = l ), one must determine the first and second derivatives of the equation describing the ellipse. The equation of an ellipse can be rearranged and written as follows: Y2 = b2 ( l - X2/a2) or y2 = b2/a2 (a2 - x2) 2 2 or y = b/a (a - x 1/2. (7) The first derivative of the equation (7) is, dy/dx .= b/a (1/2) (a2 — x2)'1/2(-2x) = —bx/a (a2 -x2)-l/2. (8) 34 The second derivative of the equation (7) is, d2y/dx2 = - ab (a2 - x2)-3/2. (9) Substituting :h1 equation (6) for the first and second derivatives, equations (8) and (9), rearranging and simplifying, we obtain an equation for the radius of an elliptical curvature: 2 2 2 3/2 R = _ (a — (a4 - b ) x ) . (10) a b Since we are dealing with the absolute value of equation (10), the negative sign before the expression can be ignored in calculating the numerical value of the radius. In order to evaluate the radius of the major curvature of the left ventricle by elliptical approximation and compare it with the value for radius by circular approximation, the following procedure was adopted. An ellipse was constructed with the major semi-axis (a) twice as great as the minor semi-axis (b). Specifically, When (b = l), by substituting numerical values for (a) and (b) in equation (10), a more simplified expression for the radius of the elliptical curvature was obtained: ( l6 — 3 X2 ) 16 3/2 R = (11) The radii of the elliptical curvature at points A, D. E, F, G, H, and B (Figure 6), by substituting for (x) in the equation (11) values zero, : 1/2, : 1,.1 3/2, and i 2, were found to 35 FIGURE 6 Diagram of elliptical model used in estimating the radius of the major curvature of left ventricle. 36 be 2.929, 3.394, 4.000, 3.394, 2.929, 1.758, and 0.500 respectively. The mean radius of the curvature having the above radii at the corresponding points can be calculated from the relationship, Mean Radius = (a/2 + b(; E :)°°° + n/2) . (12) Using the above values for the various radii, the value of the mean radius from the equation (12) will be: Mean Radius (0.500/2 + 1.758 + 2.929 + 3.394 + 4.000 + 3.394 + 2.929/2) / 6. Mean Radius 2.865. The value for the mean radius by circular approximatidn can be found if the values for arc AB and chord AB were known. The value for arc length can be calculated from the perimeter of the ellipse. The equation for perimeter of an ellipse is: P = 2 ( 4 + 1.1m + 1.2m2) (13) where ( m = b/a). Substituting for (m) in the equation (13), the perimeter will be equal to, P = 2 ( 4 + 1.1 (1/2) + 1.2 (1/2)2 ) = 9.70 The value of P/4 will be, P/4 = 2.425. This value is equal to the distance BE of the arc. The distance AE of the arc was found by direct measurement to be 1.012. Thus, from these two values, the total length of the arc AB will be, Length of Arc AB = 2.425 + 1.012 = 3,437, 37 The length of the chord AB can be determined by using the Pythagoras Theorem on the triangle ABC. Length of Chord AB = ( 32 + 0.8662 ) 1/2 = 3.122. The ratio S/L (arch length to chord length) is about 1.101. From the graph (Figure 5), the mean radius by circular approximation was found to be about 2.22. Thus, the ratio of mean radius of curvature by elliptical evaluation to the mean radius by circular approximation is about 1.31. This indicates that the mean radius of the major curvature of the left ventricle is 1.31 times that of the mean radius calculated by circular approximation. Consequently, to obtain the true value for the mean radius of the major curvature of the left ventricle, the calculated mean radius for the major curvature by circular approximation was multiplied by the constant 1.31. This procedure is considered justified, since the average ratio S/L, in the hypertensive animals was about 1.345, and in the normal animals about 1.300. These values do not seem to be very different from the value 1.101 obtained in the ideal condition. Secondly, the procedure used results in a greater numerical difference between the mean radius and the wall thickness, as indicated by their ratio. The ratio (mean radius/ wall thickness) was increased by about 19.2% in the hypertensive animals, and by about 19.9% in normal animals, when elliptical approximation was used instead of 38 spherical approximation. The significance of this difference will be discussed in Part V. In calculating the volume and surface area of the left ventricle, a spherical geometry was assumed. The radius for this sphere was the mean radius of the major and minor curvature's radii. The formulae employed were, (4/3n R3), for the volume, and (41rR2), for the surface area. No attempt was made to calculate the volume and the surface area of the left ventricle by assuming an elliptical geometry. This would have involved the process of integration of a series of measurements. The experimental procedure for making such an evaluation is under consideration. The values for radial force(Ffi) were calculated from the formula (FR.= P.A ), where (P) is pressure and (A) is area. The calculated values for volume and surface area refer to the total volume and outer surface area of the left ventricle. Since the thickness of the left ventricular wall varies from one point to another, calculated values do not indicate the internal change. It would be interesting to find a mathematical relationship between the inner and outer volumes and surface areas. This might indicate the manner in which the various ventricular parts respond to the changes in the blood pressure. It would further show the over-all dimensional changes of the heart, and relative changes in the ventricular dimensions and their relation to each other in response to alteration of blood pressure. 39 40 Table 2 Comparison of Body Weight and Food Consumption Initial 7th-day Final Weight Food Rat No. Sex Weight Weight Weight Change Consump. gm. gm. gm. gm. gm. Group I - Hypertensive 1 F 138 138 105 -33 92 2 F 163 166 142 -21 94 3 F 140 145 132 -8 126 4 M 157 174 131 -26 129 5 M 166 162 106 -60 102 6 M 180 178 150 -30 87 Group II - Hypertensive 1 M 213 195 195 -18 137 2 F 160 170 175 15 167 3 M 200 220 245 45 221 4 M 195 205 233 38 208 5 M 245 260 292 47 246 6 M 220 224 170 —50 134 7 M 205 195 225 20 178 8 M 225 215 230 5 165 9 M 225 230 252 27 214 10 M 220 250 280 60 242 Mean: 190.8 195.4 191.4 0.69 158.9 Standard Deviation: ‘: 8.35 'i 9.01 .115.23 '1 9.18 .i 13.6] Group III - Normotensive 1 F 190 195 208 18 258 2 F 195 195 200 5 217 3 F 185 185 185 O 148 4 F 215 208 215 0 165 5 F 220 218 220 0 146 6 F 192 190 192 0 144 7 F 195 195 196 l 176 8 F 212 212 215 3 150 9 F 242 243 245 3 214 10 F 203 208 212 9 166 Mean: 204.9 204.9 208.8 6.5 178.4 Standard Deviation: i_12.01 “i 3.60 .i 3.61 .i 1.25 .i 8.40 41 Table 3 Comparison of Blood Pressures and Hematocrits Initial 7th—day 10th-day Final Initial Final Rat No. B.P. B.P. B.P. B.P. Hct. Hct. mm. Hg mm. Hg mm. Hg mm. Hg % % Group I - Hypertensive l 108 153 192 195 44 41 2 148 140 195 176 43 22 3 135 149 170 198 37 33 4 135 140 170 214 36 32 5 130 165 190 135 35 26 6 104 178 210 210 40 44 Group II- Hypertensive 1 110 158 195 175 43 37 2 90 150 165 205 45 44 3 110 145 160 165 41 41 4 130 145 140 170 43 43 5 112 120 135 160 42 41 6 122 128 158 170 39 40 7 124 154 172 208 43 43 8 120 120 120 140 42 40 9 120 130 155 190 43 41 10 114 134 145 208 43 39 Mean: 119.5 144.3 167.0 182.4 41.2 37.9 Standard Deviation: i3'57 :_3.97 i_6.24 .i 6.23 :_0.74 .i 1.62 Group III - Normotensive 1 125 115 130 130 42 41 2 135 145 130 120 40 41 3 130 110 130 125 44" 43 4 110 110 120 125 40 41 5 110 115 120 120 40 41 6 115 125 130 135 40 40 7 125 125 120 125 41 42 8 130 125 128 125 42 43 9 120 120 122 120 42 44 10 135 130 128 130 42 41 Mean: 123.5 122.0 125.8 125.5 41.3 41.7 Standard Deviation:: 2.05 i.2-3l ‘: 1.01 .i 1.09 .i 0.29 .i 0.27 42 Table 4 Comparison of Wet and Dry Weights of Ventricles Wet Dry Wet Wt. x 100 Dry Wt. x 100 Rat No. Weight Weight Surface Area Surface Agea mg. mg. gm./cm.2 gm./cm. Group I - Hypertensive f 1 460.0 116.2 0.2248 0.0568 2 603.2 132.2 0.2457 0.0538 3 548.6 111.6 0.2336 0.0475 4 591.7 167.1 0.2532 0.0715 5 383.5 99.5 0.1864 0.0484 6 667.6 141.3 0.2634 0.0557 Group II - Hypertensive 1 646.4 144.5 0.2179 0.0487 2 508.9 135.0 0.1830 0.0486 3 597.5 160.6 0.1756 0.0472 4 554.7 133.2 0.1680 0.0404 5 861.0 204.2 0.2278 0.0540 6 698.7 138.7 0.2557 0.0508 7 609.0 143.3 0.1884 0.0443 8 610.4 143.1 0.1864 0.0437 9 756.5 168.6 0.2186 0.0458 10 823.0 182.3 0.2233 0.0495 Mean: 620.0 145.09 0.2157 0.0504 Standard Deviation: :31.13 .i 6.68 _ 0.0077 ‘: 0.0057 Group III - Normotensive 1 450.1 133.4 0.1460 0.0433 2 458.0 139.1 0.1520 0.0462 3 399.0 125.1 0.1388 0.0435 4 429.5 133.5 0.1365 0.0424 5 452.6 136.0 0.1419 0.0426 6 416.3 124.2 0.1418 0.0423 7 445.9 125.6 0.1498 0.0422 8 356.6 113.4 0.1134 0.0361 9 483.0 142.8 0.1420 0.0420 10 515.6 143.6 0.1653 0.0460 Mean: 440.7 131.67 0.1428 0.0427 Standard Deviation: : 9.59 .1 1.94 .1 0.0029 .: 0.0019 Table 5 Comparison of Water Content and Dry Matter of Ventricles Water Dry Rat No. Content Matter % %, Group I — Hypertensive ONLDDUJNH G) H O C [—1 Standard Deviation: ommqmmwaI—i Mean: 74.73 78.10 79.67 71.76 74.03 78.85 p II - Hypertensive 77.65 73.44 73.12 75.95 76.29 80.13 76.49 76.56 79.04 77.83 76.48 i 0.63 Group III - Normotensive .—l Standard Deviation: oomqmmwai—a Mean: 70.37 69.62 68.65 68.92 69.96 70.08 71.83 68.21 70.45 72.15 70.02 i 0.28 25.27 21.90 20.33 28.24 25.97 21.15 22.35 26.56 26.88 24.05 23.71 19.87 23.51 23.44 20.96 22.17 23.52 i 0.63 29.63 30.38 31.35 31.08 30.04 29.92 28.17 31.79 29.55 27.85 29.98 i 0.28 Table 6 Comparison of Left Ventricular Measurements 44 Major Major Minor Minor Wall Rat No. Arc Chord Arc Chord Thickness mm. mm. mm. mm. mm. Group I - Hypertensive 1 16.0 11.7 10.5 7.5 2.4 2 16.4 12.7 11.5 7.4 2.4 3 16.1 11.7 10.4 7.2 2.5 4 16.3 12.1 10.2 6.9 2.4 5 14.5 11.0 10.2 7.2 2.6 6 15.4 10.7 11.2 8.0 1.8 Group II - Hypertensive 1 17.2 11.6 10.7 7.1 2.5 2 13.9 10.9 10.4 6.9 2.7 3 15.4 12.4 10.2 7.2 2.4 4 14.0 11.2 10.4 6.7 2.6 5 18.5 14.3 12.8 8.8 2.7 6 14.4 11.2 11.3 7.7 2.8 7 13.2 10.0 9.3 6.7 2.6 8 15.7 10.6 10.5 7.1 2.5 9 15.1 11.6 10.5 7.4 2.6 10 18.2 13.0 12.5 8.2 2.8 Mean: 15.64 11.67 10.79 7.4 2.52 Standard Deviation: i 0.36 i_0.27 :_0.22 fl: 0.14 + 0.06 Group III — Normotensive 1 15.5 10.4 11.5 6.7 2.1 2 15.2 12.1 11.2 7.3 1.8 3 15.9 13.2 11.7 7.4 2.0 4 19.1 15.2 13.3 9.2 1.8 5 16.0 12.0 12.3 7.8 1.9 6 15.5 11.8 10.9 7.4 2.1 7 14.3 11.3 10.7 7.4 2.0 8 14.6 12.7 11.1 7.8 1.8 9 19.5 14.8 10.2 7.9 2.0 10 15.6 10.9 11.7 8.1 2.2 Mean: 16.12 12.44 11.46 7.7 1.97 Standard Deviation: i 0.38 .i 0.33 .1 0.19 .i 0.14 .i 0.03 Table 7 Comparison of Ratios of Major Arc to Major Chord and Minor Arc to Minor Chord Minor Arc Minor Chord Major Arc Major Chord Rat No. Group I - Hypertensive 1 1.37 1.40 2 1.29 1.55 3 1.38 1.44 4 1.35 1.48 5 1.32 1.42 6 1.44 1.40 Group II - Hypertensive 1 1.48 1.51 2 1.28 1.51 3 1.24 1.42 4 1.25 1.55 5 1.29 1.46 6 1.29 1.47 7 1.32 1.39 8 1.48 1.48 9 1.30 1.42 10 1.40 1.52 Mean: 1.34 1.46 Standard Deviation: .i 0.019 .1 0.013 Group III - Normotensive l 1.49 1.72 2 1.26 1.53 3 1.21 1.58 4 1.26 1.45 5 1.33 1.58 6 1.31 1.47 7 1.27 1.45 8 1.15 1.42 9 1.32 1.30 10 1.43 1.44 Mean: 1.30 1.50 Standard Deviation : 0.022 .i 0.025 46 Table 8 Comparison of Values for Product of Wall Thickness, t, and Sum of the Reciprocal of Principle Radii of Curvature Elliptical Spherical Rat No. Approximation Approximation + t (1/Rl 1/R2) Group I - Hypertensive 1 0.9314 1.0255 2 0.9192 1.0030 3 1.0055 1.1043 4 0.9838 1.0742 5 1.0561 1.1625 6 0.6955 0.7742 Group II - Hypertensive 1 1.0300 1.1315 2 1.1310 1.2396 3 0.9223 1.0046 4 1.0967 1.1960 5 0.8778 0.9612 6 1.0744 1.1894 7 1.1365 1.2537 8 1.0583 1.1690 9 1.0145 1.1144 10 1.0041 1.1038 Mean: 0.9961 1.0944 Standard Deviation: i_0.0276 i 0.0303 Group III — Normotensive 1 0.9288 1.0242 2 0.7839 0.7636 3 0.7406 0.8028 4 0.5526 0.6035 5 0.7182 0.7898 6 0.8209 0.9097 7 0.7440 0.8612 8 0.6260 0.6790 9 0.6720 0.7328 10 0.8406 0.9350 Mean: 0.7428 0.8102 Standard Deviation: + 0.0238 .i 0.0274 47 Table 9 Comparison of Left Ventricular Radii and Calculated Tension and (k), Assuming Spherical Geometry Major Minor 4 4 Rat No. Radius Radius Tension x 10 (k) x 10 cm. cm. dynes/cm. dynes/cm. Group I - Hypertensive 1 0.6025 0.3825 6.084 25.352 2 0.6776 0.3700 5.615 23.395 3 0.6002 0.3636 5.977 23.905 4 0.6268 0.3471 6.374 26.560 5 0.5775 0.3650 4.026 15.483 6 0.5404 0.4080 6.510 36.164 Group II - Hypertensive 1 0.5834 0.3557 5.155 20.620 2 0.5886 0.3457 5.953 22.048 3 0.6919 0.3650 5.255 21.897 4 0.6194 0.3350 4.927 18.951 5 0.7665 0.4435 5.992 22.193 6 0.6003 0.3873 5.336 19.056 7 0.5260 0.3424 5.751 22.119 8 0.5332 0.3571 3.992 15.967 9 0.6171 0.3752 5.910 22.731 10 0.6630 0.4108 7.035 25.123 Mean: 0.6127 0.3723 5.618 22.598 Standard DeviatiOn:i 0.0157 .i 0.0072 .i 0.205 ‘1 1.191 Group III — Normotensive 1 0.5221 0.3377 3.554 16.923 2 0.6631 0.3657 3.772 20.952 3 0.7630 0.3700 4.152 20.759 4 0.8330 0.4646 4.970 27.614 5 0.6276 0.3900 3.849 20.257 6 0.6242 0.3722 4.155 19.785 7 0.6136 0.3737 3.870 19.351 8 0.8040 0.3955 4.418 24.544 9 0.7785 0.4203 4.367 21.833 10 0.5526 0.4099 4.078 18.537 Mean: 0.6782 0.3900 4.119 21.056 Standard Deviation:: 0.0237 .i 0.0077 .i 0.087 .: 0.667 48 Table 10 Comparison of Left Ventricular Radii and Calculated Tension and (k), Assuming Elliptical Geometry Major Minor 4 4 Rat No. Radius Radius Tension X 10 (k) X 10 cm. cm. dynes/cm. dynes/cm.2 Group I - Hypertensive 1 0.7894 0.3825 6.699 27.913 2 0.8876 0.3700 6.127 25.528 3 0.7863 0.3636 6.563 26.254 4 0.8211 0.3471 6.961 29.001 5 0.7565 0.3650 4.431 17.043 6 0.7079 0.4080 7.246 40.256 Group II - Hypertensive 1 0.7644 0.3557 5.663 22.652 2 0.7711 0.3457 6.525 24.165 3 0.9064 0.3650 5.724 23.851 4 0.8114 0.3350 5.373 20.667 5 1.0041 0.4435 6.562 24.302 6 0.7964 0.3873 5.907 21.096 7 0.6891 0.3424 6.344 24.400 8 0.6985 0.3571 4.410 17.637 9 0.8084 0.3752 6.492 24.969 10 0.8685 0.4108 7.733 27.618 Mean: 0.8011 0.3723 6.173 24.835 Standard Deviation::_0.0205 i 0.0072 :_0.227 .: 1.330 Group III - Normotensive 1 0.6840 0.3377 3.919 18.661 2 0.8687 0.3657 3.674 20.410 3 0.9995 0.3700 4.500 22.502 4 1.0912 0.4646 5.428 30.157 5 0.8222 0.3900 4.233 22.277 6 0.8177 0.3722 4.604 21.925 7 0.8038 0.373/ 4.480 22.399 8 1.0532 0.3955 4.792 26.621 9 1.0198 0.4203 4.762 23.808 10 0.7239 0.4099 4.536 20.619 Mean: 0.8884 0.3900 4.493 22.938 Standard Deviation:: 0.0311 .i 0.0077 .i 0.105 .i 0.600 Comparison of Values for Mean Radius, Assuming Spherical Geometry Area, and Volume. Table 11 Surface 49 Mean Rat No. Radius Surface Area Volum cm. cm.2 cm. Group I - Hypertensive 1 0.4925 3.0485 0.5005 2 0.5238 3.4481 0.6019 3 0.4819 2.9178 0.4687 4 0.4869 2.9794 0.4834 5 0.4712 2.7897 0.4381 6 0.4742 2.8261 0.4465 Group II - Hypertensive 1 0.4695 2.7695 0.4335 2 0.4671 2.7420 0.4268 3 0.5284 3.5084 0.6178 4 0.4772 2.8613 0.4553 5 0.6050 2.5992 0.8515 6 0.4938 3.0636 0.5043 7 0.4342 2.3687 0.3426 8 0.4451 2.4893 0.3694 9 0.4961 3.0925 0.5114 10 0.5369 3.6228 0.6484 Mean: 0.4927 3.0567 0.5030 Standard Deviation: .i 0.0102 : 0.1325 ‘1 0.0310 Group III - Normotensive 1 0.4299 2.3222 0.3330 2 0.5144 3.3250 0.5701 3 0.5665 4.0324 0.7615 4 0.6488 5.2890 1.1439 5 0.5088 3.2533 0.5516 6 0.4982 3.1189 0.5181 7 0.4937 3.0623 0.5039 8 0.5998 4.5212 0.9039 9 0.5994 4.5150 0.9022 10 0.4813 2.9115 0.4670 Mean: 0.5341 3.6351 0.6655 Standard Deviation: i 0.0146 .1 0.1990 'i 0.0548 Comparison of Values for Mean Radius, Area, and Volume, Assuming Elliptical Geometry Table 12 Surface 50 Mean Rat No. Radius Surface grea Volume cm. cm. cm. Group I - Hypertensive 1 0.5859 4.3140 0.8423 2 0.6288 4.9686 1.0413 3 0.5749 7.4581 0.7958 4 0.5841 4.2875 0.8348 5 0.5608 3.9520 0.7389 6 0.5579 3.9118 0.7276 ‘EESEE_EI - Hypertensive 1 0.5600 3.9407 0.7355 2 0.5584 3.9181 0.7292 3 0.6357 5.0779 1.0761 4 0.5732 4.1292 0.7891 5 0.7238 6.5833 1.5883 6 0.5918 4.4006 0.8681 7 0.5158 3.3438 0.5751 8 0.5278 3.5009 0.6161 9 0.5918 4.4006 0.8681 10 0.6396 5.1408 1.0962 Mean: 0.5881 4.5830 0.8702 Standard Deviation: : 0.0125 :_0.2723 i 0.0605 Group III - Normotensive 1 0.5109 3.2797 0.5588 2 0.6172 4.7864 0.9847 3 0.6848 5.8935 1.3454 4 0.7779 7.6037 1.9716 5 0.6061 4.6168 0.9328 6 0.5950 4.4484 0.8821 7 0.5888 4.3566 0.8549 8 0.7244 6.5946 1.5925 9 0.7201 6.5155 1.5640 10 0.5669 4.0387 0.7632 Mean: 0.6392 5.2134 1.1450 Standard Deviation : 0.0182 i_0.2969 .: 0.0977 Table 13 Comparison of Radial Force Calculated from both Spherical and Elliptical Approximations of the Principle Radii Spherical Elliptical Rat No. Approximation Approximatign dynes x 10 dynes x 10 Group I - Hypertensive 1 79.2549 112.1554 2 80.9097 116.5882 3 77.0241 196.8789 4 85.0053 122.3267 5 50.2118 71.1321 6 79.1252 109.5226 Group II - Hypertensive 1 64.6152 91.9405 2 74.9416 107.0856 3 77.1778 111.7036 4 64.8514 93.5883 5 98.1101 140.4350 6 69.4365 99.7396 7 65.6843 92.7269_ 8 46.4628 65.3443 9 78.3361 111.4716 10 100.4639 142.5595 Mean: m 111.5750 Standard Deviation: i. 0.7234 7.6950 Group III - Normotensive 1 40.2484 56.8438 2 53.1967 76.5776 3 67.2000 98.2152 4 88.1412 126.7157 5 52.0496 73.8642 6 56.1340 80.0623 7 51.0332 72.6027 8 75.3458 109.8990 9 72.2355 104.2415 10 50.4621 69.9988 Mean: 61.5046 86.9021 Standard Deviation: .: 2.7800 1i 3.3700 52 n-.o H. moa.o H. .xoumma .QHHHm .mom.m ¢.nm+ mnH.o mm¢.¢ 40H x A.Eo\mmc>oc :oncme mom.o H. emo.o H. .xoumma .umnam .hqm.m v.om+ mao.m mHH.¢ 40H x A.EU\mmc>nv concme osmo.o.fl mmmo.o H. .moumma mQHHHm .mqo.m H.vm+ Homm.o mm¢H.O A m\H + m\Hvu momo.o H. enmo.o H. .moumma Hymnam .mme.m H.mm+ vvmo.a Noam.o A m\a + m\HVu oo.o_H mo.o.H .Hmo.o m.nm+ mm.m hm.H 2.251 mmmcon:u Hams nmoo.o.H mHoo.o H. Am.ao\.Emv.mmH¢ momwusm .omv.m o.mH+ vomo.o nmwo.o OOH x uan 3 Hum whoo.o H. mmoo.o H. AN.EU\.EmQ.mmH< momwusm .omo.» H.Hm+ an~.o mm¢a.o 00H x uanmz um: 86.6 H. «m.H_H mmv.o m.oa+ mo.m¢H no.HmH x.mec ugmHmz Hun mH.Hm.H mm.m.H .oom.¢ >.o¢+ 0.0mm p.044 A.mev uanmz um: ~6.H H. mm.o H. ..mmm.a m.mu m.nm ¢.H¢ Aucmogmmv “HuooumEmm mm.o H. mo.H_H .qmo.n m.mq+ ¢.mma m.mNH xmm .esv musmmmum ooon m. X w>HmcmHHmm>m HMEHOZ .Q.m H.cmmz .MMHQ mwSHm> Hmch mHHSmmm mo COmHnmmEoo ¢H magma 53 .Hm>mH 0.0 v 66 ucmoH6H00H6 .0 .Hw>mH 00.0 v 66 ucmonHc0Hm 0 0606.0 H. 0000.0 H. .x06006 .mHHHm 0000.0 0.60+ 0606.000 0000.66 600 x Ammc>6v mouom HmHomm 6000.0 H. 0060.0_H .xoummm .umsmm 0000.0 H.H0+ 0606.60 6006.06 000 x Ammcm6v 60006 060666 6000.0 H. 0600.0 H. .xoummm .QHHHm 00060.0 0.6 u 0666.0 0006.0 A.EUV 6006mm 0662 0000.0 H. 6600.0 H. .xoummm .ngmm 00060.0 6.0 u 0006.0 0606.0 A.Eov 600666 0662 000.0 H. 006.0 H. .xoummm .mHHHm 000.0 0.6 + 606.00 600.00 00H x x0.au\mmcm60.m 60666006 000.0 H. 066.0.H .xoummm .66606 600.0 0.0 + 606.00 660.00 60H x x0.EU\mmcm60 x ucmumcoo M. X m>HmcmHHmQ>m HmEHoz .D.m H.cmmz .MMHQ mmsam> Hmch A6mscHucoov 60 00669 54 V. RESULTS AND DISCUSSION Data are presented in two parts. The first part is composed of determinations of body weight, food intake, blood pressure, hematocrit, and wet weight and dry weight of ventricles. The secondpart of the data, measurements of left ventricular arcs and chords, and calculation of mean radius, tension, proportionality constant (k), and radial force, was obtained after making several assumptions as mentioned above.in discussion of calculations. In order to facilitate discussion, data in Tables 2—13 are summarized in Table 14 where mean values are tabulated. Comparison of mean final blood pressures of control and experimental animals indicates an increase of about 45.3% in the blood pressure of rats in Groups I and II (Table 3) at the termination of the experiment. Graphic comparison of blood pressure measurements at the four designated intervals is presented in Figure 7. Results are in full agreement with those obtained by Chanutin and co-workers (1932 and 1933) and Hermann and associates (1941). However, it should be noted that these investigators measured blood pressures only at the termination of experiment by means of direct carotid cannulation. There can be little doubt that the hypertension- inducing methods employed here, especially the one proposed by Grollman (1944), successfully produced high blood pressure. .mumu m>HmcmHHmm>£ 55 paw HmEHoc mo mmufiwmmum pooHQ mo cOmHHmmEOU b MMDUHm va 5 mama I wEHB H OH _I A! 11 1') 4 mHOHHCOU O mw>HmcmHHmn§m O OOH ONH owa 00H oma oom exnssald pong ’UIUI- 5H 56 A further indication that animals in Groups I and II developed high blood pressure was the decrease of about 8.5% in the mean value of final hematocrit of experimental animals as compared to controls. This accords with observations made on rats by Beckwith and Chanutin (1941). They found an increase in plasma volume and a subsequent decrease in red cell volume in hypertensive rats which were attributed to development of anemia. Since no blood or urine analyses were made in this study, the presence or absence of anemia in rats of Groups I and II cannot be confirmed. Wet weight of ventricles showed a 40.7% increase in hypertensive rats as compared to normotensive animals, suggesting a definite ventricular hypertrophy. Reliability of the wet weight determinations and their significance can be debated on the basis that ventricles were weighed after removal from alcohol following the ventricular measurements step. Data listed in Table 4 indicate that such an argument is not well- founded and can be discarded on the basis of the uniformity of wet weight determinations for both hypertensive and control animals, and the fact that the standard deviation in both groups was low. Furthermore, since the same procedure was employed in wet weight determinations of all three groups, any objection will be applicable to both normotensive and hypertensive rats. It should be noted also that the results 57 show, in a comparative sense, relative hypertrophy of ventricles of animals in Groups I and II as compared to those in Group III. There is no doubt that the degree of ventricular hypertro- phy as demonstratediby wet weight determinations is highly significant (Table 14). It is equally important to note that dry weight determinations indicate about 10.2% increase in mass of ventricles of hypertensive rats as compared to controls (Table 14). This difference suggests possible cardiac hyperplasia. In order to ascertain the degree of correlation of both wet and dry weights of ventricles with blood pressures, Figures 8 and 9 were prepared. Figure 8 shows that there exists a definite relationship between blood pressure and the ratio of wet weight to surface area. This correlation is in agreement with that suggested by Chanutin and co-workers (1932 and 1933). However, no conclusion as to the significance of the degree of correlation between ratio of dry weight to surface area and blood pressure (Figure 9) can be made from this graphic presentation. Left ventricular wall thickness measurements indicated that there was an increase of about 27.9% in hypertensive rats as compared to normotensives (Table 14). This is highly significant (p < .01) and agrees with the ventricular wet weight data. 58 .mumu m>HmcwHHmmmn cam HmEHo: £HOQ mo mmum mommuzm 0H HQmeB H63 HMHSUHHHcm> mo OHHMH paw whammmhm UOOHQ cmmBHwQ mHanOHHmHmm m mmDGHm mmum moMMHSm 00H x HanGB H03 mmHoHHHcm> ooww.o oomN.o oomH.o ooma.o OOHH.O maouucou O mm>HmcmHHmQ>m O om .Ill!: .1 OOH o 00008 o w o omH O. O .0 .0 .0 .0 O. A. 0 00m 0 o oo 0mm 811188815 pOOIH '111111- 6H 59 .mHmu m>HmcmHHmmhn paw HmEHoc £H0Q mo mmnm mommndw 0H uanm3 amp HmHSUHHucm> mo OHHmH paw mudmmmnm pooan GmmBHmQ QHsmCOHHMHmm m MMDOHh mmufl mumwndm .so\.E0 000 x N HLmHmB mun meUHHHGm> 0000.0 0vm0.0 0000.0 0m¢0.0 F1. 0 (d rm mw>HmcmHHwQ>m O mHOHHCOU O 0m 0,2 oma oom 0mm exnssexd pooIa ’UIUJ— 6H 60 The second portion of the data was obtained from application of the Law of Laplace, P = T (l/Rl + l/R2), to the left ventricle. Tail systolic pressure of rats was determined in mm. Hg and converted to dynes per square cm., using the equality 1 mm. Hg = 1.3333 x 103 dynes per square cm. Values for radii were obtained on excised and slightly inflated hearts whose volumes approximated the isometric (isovolumic) contraction phase of systole. This procedure was used for convenience in obtaining a fixed heart size. However, it should be admitted that tail systolic blood pressure is greater than the pressure generated by the left ventricle during the isometric (isovolumic) contraction phase to which the volume of excised hearts was presumably adjusted. This discrepancy could be avoided in future experiments by direct and simultaneous recording of cardiac pressure and dimensions. Refined techniques for this procedure have recently been described (Hawthorne, 1961). In the course of inflation, normotensive hearts were subjected to a pressure head approximately one-half of that of hypertensive hearts. The reason for this difference in pressure head was that intact, normotensive hearts were under a lower presSure load than the hypertensive hearts. The quantity, one-half, was selected by comparing the lowest blood pressure with the highest. It was found that the latter was 61 twice as great as the former. Calculated results of the Laplace data were obtained from initial measurements of four parameters, namely, blood pressure, wall thickness, arcs, and chords of both major and minor curvatures. Coupled with these four parameters were four major assumptions: (1) that the left ventricle has an elliptical geometry; (2) that major curvature is part of an ellipse, and minor curvature is part of a circle, (3) that the ellipse, in general, has a major semi-axis twice as great as the minor, and (4) that the tension developed is proportional to the ventricular wall thickness. Accuracy of initial measurements can be questioned only in the case of determinations of wall thickness, arcs, and chords of both major and minor curvatures. Blood pressure measurements have been carried out with an apparatus which is considered relatively free from error. However, values of the other three parameters cannot be so considered. On the other hand, it is more pertinent here to look for the relative difference between normotensive and hypertensive animals. With respect to the application of the Law of Laplace to the heart, Freis (1960) suggests that, "if there is cardiac dilatation.the principle radii of curvature of the ventricle will increase. Because of the Laplace equation, P = T (l/Rl + 1/R2), greater myocardial tension will be required 62 to produce a given intraventricular pressure." He points out further that, "this interpretation of Laplace's law must be accepted with some reservations, however, as the law applies primarily to situations in which the thickness of the wall is negligible in comparison to the radius of curvature." In the present study, calculation of the principle radii of curvatures show that there is a definite decrease in the mean radius of ventricular curvature at the point of intersection of major and minor arcs. This decrease is about 8.0% in the case of elliptical approximation and 7.8% by Spherical approximation (Table 14). It should be noted that a decrease in mean radius of curvature indicates that there should have been a definite increase in the surface area at this point. However, as calculated here, both surface area and volume decreased (Table 14). These results are not in contradiction with expected findings because values for the mean radius of curvature refer only to one point and not the entire surface area or volume of the ventricle. Furthermore, values for surface area and volume, as mentioned above in discussion of calculations, were obtained by assigning a spherical geometry to the left ventricle with the value of the calculated mean radius as its radius. Therefore, obviously, the reduction in the ventricular surface area and volume is due to the calculated decrease in mean radius. However, it should be 63 pointed out that this decrease in mean radius indicates that there has been a change in the ventricular curvature and suggests a possible geometrical interpretation of the nature of cardiac hypertrophy in response to pressure load. The interpretation suggested here is, if we assume the normal left ventricle has elliptical geometry, it will tend to assume spherical geometry in the hypertrophied state. The advantage of the spherical shape is obvious, as seen from the Law of Laplace. The pressure load is uniformly distributed through- out the ventricle and the required developed tension is produced equally by all parts. Since the tension developed is proportional to the wall thickness, this geometrical inter- pretation also accounts for the increase in ventricular wall thickness in hypertension and, hence, cardiac hypertrophy. Tables 9 and 10 list the principle radii of left ventricular curvatures by spherical and elliptical approximations, respectively. Both methods show a reduction of less than 10% in the major, and less than 5% in the minor, radii of the left ventricular curvatures. These results are not in accord with the predicted increase from the Laplace equation. The dis- crepancy lies in the fact that in accordance with the Law of Laplace, the principle radii of ventricular curvature should increase if there is cardiac dilatation. No application of Laplace's equation has been made to cardiac hypertrophy. It 64 is further suggested here that a distinction should be made between Cardiac dilatation and hypertrophy. This distinction, as Rushmer (1961) suggests, is based on the reSponse of the heart to two entirely different changes within the cardio- vascular system. Myocardial hypertrophy occurs in response to a chronic pressure load, as in arterial hypertension; whereas, cardiac dilatation results in response to an increased volume load. However, both conditions can be present at the same time. Rushmer (1961) remarks that, "the usual response to a chronic pressure load is myocardial hypertrophy with various degrees of ventricular dilatation unless heart failure should supervene. The thickened ventricular walls probably have diminished distensibility, requiring a greater effective filling pressure to attain a particular diastolic volume. In other words, the myocardial hypertrophy tends to permit utilization of the systolic reserve capacity with some sacrifice of distensibility. On the other hand, ventricular dilatation involves an encroachment on the diastolic reserve capacity, apparently with some sacrifice of the contractility, since these distended ventricles fail to empty as completely during systole as the normal." Therefore, it is suggested that ventricles in the present study have merely hypertrophied without any accompanying dilatation. Comparison of tension developed (Table 14) shows an 65 increase of 37.4% by elliptical and 36.4% by spherical approximations in hypertension. Also, elliptical approximation of radial force shows about 28.4% increase in hypertension as compared to controls; whereas, spherical approximation shows an increase of 21.1% (Table 14). These results substantiate theoretical considerations of Burch and co-workers (1952), Burch (1955), and Burton (1957). Values of proportionality constant (k) which are indicative of contractile behavior of ventricular wall at the point of measurements show an increase of about 10.7% in hypertensive as compared to normotensive animals as calculated by assuming elliptical geometry and about 9.7% increase when the spherical method was used (Table 14). Figure 10 shows the relationship between blood pressure and calculated values for tension in hypertensive and control rats. Figure 11 shows the relationship between calculated tension and radial force in hypertensive and normal animals. These graphs indicate that elliptical approximation provides a better picture of changes undergone by the ventricle in hypertension than spherical approximation. Another parameter which showed a slight difference between spherical and elliptical assumptions was the quantity t(l/Rl + 1/R2) or the "shape" factor (Table 14). This parameter refers to the over-all shape and size of the ventricle subjected to a given intraventricular pressure. It should be .mCOHumEonumam 0moHHQHHHm 0cm 060006306 QHOQ maHBOQm .mumu w>Hmcmuumm>£ 0cm HmEHOC mo :oncwu 0cm 60566000 00003 :mm3umn QHSmGOHumamM 66 0H MMDme .Eo\ mmc>p I 00OH x concmB b 0 m d s d m fl #11 6:000 69006050060030 0 o 0 o 0.0 ImEHxOMQmE O o 09 o 0 0600000006 600000600 0 O , o O O . 0 0 £000.66 mm>Hmcmuumm>m o 0 o Ionumm¢ m HmUHuwn m mHOHucou o 0 o 0 o O .0. o o. . 0 o . O . 0 0. o o o .0 o .0 .0 o 5H 0H Hm mm mm 8.1113 331d pOOTH x POT °mo/ seufip - Z 6'7 .mcoHHmEonnmmm HmoHumHHHw 0cm HmoHHmnmm £009 mcHBOSm .mumu m>Hmcwuumm>£ 0:6 HMEMOG mo mouom 060060 026 GOHmcmu cmwBqu mHnmCOHHmamm 0H mmeHm. mmcmp I ¢00 x mouom HMHUmm 000 ONH om 00 0 1 ,q . mm>HmCmuHmn§m 0 0 o o .xoummm A“. 00006 . o 0 60000080 0 O 0% 0 O nvnv mw>Hmamunmn§m o o 0 38.00900 0 0 o o o .0066 O 0 6000000000 0 0 0 o - 0. o “I. O o 0 o 0 0 u 0 o 0. 0T x uorsuel V °mo/ sauAp - 68 recalled that the justification for the application of the Law of Laplace, as mentioned above in discussion of calculations, was based upon an assumption that the ventricular wall thickness is negligible as compared to the radius of curvature. It was then mentioned that the ratio of the mean radius to wall thickness was increased by 19.2% for hypertensive and 19.9% for normotensive rats when elliptical approximation was used. These considerations, and data obtained, suggest that probably assigning elliptical geometry to the left ventricle is a better and closer approximation of its normal shape than the spherical geometry. This writer realizes that results presented are incomplete. Further methods should be devised to improve the quality and accuracy of initial ventricular measurements. It is believed that progress in such direction will result in much improvement of final data capable of shedding some light upon the nature of cardiac compensation in response to sustained high blood pressure. 69 VI. SUMMARY AND CONCLUSIONS This study was designed to compare estimation of cardiac hypertrophy in hypertension by means of two methods: application of the Law of Laplace, and wet weight dry weight determinations. In using the first method, data were obtained by assuming both spherical and elliptical geometry for the left ventricle. Results are encouraging and indicative of the applicability with some limitations, of the Law of Laplace in determining changes in physical dimensions of the left ventricle in response to variation in blood pressure. For an average increase of 45.3% in blood pressure, there were a 40.7% increase in wet weight and a 37.4% increase in tension. The usefulness of the Law of Laplace in estimating cardiac hypertrophy is affirmed. Precision and accuracy of the application of the Law of Laplace will naturally increase as new methods are devised to obtain more refined initial ventricu- lar measurements. Estimation of cardiac hypertrophy by application of the Law of Laplace provides more clues to the nature of hyper- trophy and effects of high blood pressure than the simple method of wet weight dry weight determinations. There was a definite change in curvatures of ventricular surface. Both wall tension and radial force increased in proportion to the 70 rise in blood pressure. Ventricular wet weight determination also showed a fairly good correlation with rise in blood pressure. Application of the Law of Laplace showed further that there was a definite change in contractile behavior of cardiac muscle wall, as indicated by the value of constant (k), in the equation, T = k.t, where (T) is wall tension, and (t) is wall thickness, and (k) is proportionality constant. Quantity (k) is the force that must be exerted per square cm. of cross-section of ventricular wall in order to generate required systolic pressure. Increase in value of constant (k) was paralleled by an increase of 10.2% in ventricular mass as shown by dry weight determinations. Data indicated that a better understanding of changes undergone by the heart during a sustained high blood pressure may result if the heart is assumed to be elliptical in geometry. It is concluded that when the heart is subjected to a sustained elevation of blood pressure, as in the case of renal hypertension, there will be a definite change in both physical dimensions and contractile behavior of the heart. The change in physical dimension is reflected by an alteration of curvatures of cardiac surface. Contractile ability of the heart is impaired due to hypertrophy accompanied by hyperplasia of cardiac muscle fibers. However, it is hypertrophy of muscle fibers that is primarily responsible for alteration in the contractile ability of cardiac muscle fibers. 71 VII. LITERATURE CITED Beckwith, J. R., and A. Chanutin. 1941. Blood Volumes in Hypertensive Partially Nephrectomized Rats. Proc. Soc. Exp. Biol. and Med., 46:66-69. Benzak, M. 1958. Cardiac Output in Rats during the Develop- ment of Cardiac Hypertrophy. Circulation Research 6:207-12. Braun-Menendez, E., J. C. Fasciolo, L. F. Leloir, J. M. Munoz, and A. C. Taquini. 1946. Renal Hypertension. 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Chanutin, A., and E. E. Barksdale. 1933. Experimental Renal Insufficiency Produced by Partial Nephrectomy. II. Relationship of Left Ventricular Hypertrophy, the Width of the Cardiac Muscle Fiber, and Hypertension in the Rat. Arch. Int. Med., 52:739—51. 72 Dodson, L F., and G. B. Mackaness. 1957. The Estimation of Basal Blood Pressure in the Rat by Tail Oscilloscope. Brit. J. Exp. Path., 38(6):618-27. Edens, E. 1913. Uber Herzhypertrophie. Deutsches Arch. f. Klin. Med., 111:288-309. Evans, C. L., and Y. Matsuoka. 1915. The Effect of Various Mechanical Conditions on the Gaseous Metabolism and Efficiency of the Mammalian Heart. J. Physiol., 49:378-401. Freis, E. D. 1960. Hemodynamics of Hypertension. Physiol. Rev., 40(1):27-54. Gladstone, S. A. 1929. A Few Observations on the Hemodynamics of the Normal Circulations; and the Changes which Occur in Aortic Insufficiency. Bull. Johns Hopkins Hospital, 44:83-121. Gollwitzer-Meier, K., C. Kroetz, and E. Krfiger. 1938. 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APPENDIX Statistical analyses were carried out as follows: - 2 Z.(X. --X) 1 1 Standard Deviation =)/ n - 1 Where Xi = Individual of sample population i = Mean of sample population n = Size of sample population The Unpaired Rank Analysis of "t" test of significance between two samples population means was performed using the following formula: X1 - X2 t = - 2 - 2 .. + .— 21 (X1 X1) 2 (X21 X2) (1 + 1 ) + - n1 n2 2 n1 n2 Where Xi = Individual of sample population 1 X2i = Individual of sample population 2 i1 = Mean of sample population 1 i2 = Mean of sample population 2 nl = Size of sample population 1 n2 = Size of sample population 2 With (nl + n2 - 2) degrees of freedom. ”"11 (11111111111111 (11111111111111) ill)“