Integrative Cardiovascular Physiology: A Mathematical Synthesis of Cardiac and Blood Vessel Hemodynamics

The cardiovascular system is analyzed as a feedback regulator. The controlling system is identified as being the medullary cardiovascular centers as well as those endocrine glands which operate upon the heart and blood vessels; the controlled system comprises the mechanical and gas exchanger elements of the cardiovascular system. The present analysis is restriced to the mechanical section of the controlled system. Equations are first formulated to define the steady-state operation of an isolated ventricle and of an isolated "circuit." Two ventricles are then combined with a single "open" circuit, the pulmonary, to obtain equations describing the operation of the Starling heart-lung preparation. Finally, the system is "closed" by introducing a second circuit, the systemic, and equations are obtained for the behavior of this complete mechanical system. These equations define steady-state valvues for each of the system's dependent variables (cardiac output; ventricular volumes and work; systemic arterial and venous pressures; pulmonary arterial and venous pressures; systemic and pulmonary blood volumes and their distribution between artery and vein) for any given set of values for the 14 independent variables (cardiac frequency; "strength," viscance, and compliance of each ventricle; systemic and pulmonary arteriolar resistances; systemic arterial and venous compliances; pulmonary arterial and venous compliances; and total blood volume). Comparison of predicted behavior with experimetal data indicates that the mathematical model so obtained is a useful one.

[1]  E. Starling,et al.  Experiments on the pulmonary circulation , 1913, The Journal of physiology.

[2]  E. Starling,et al.  On the mechanical factors which determine the output of the ventricles , 1914, The Journal of physiology.

[3]  E. Starling,et al.  On the constancy of the systolic output under varying conditions , 1914, The Journal of physiology.

[4]  E. Starling,et al.  The regulation of the heart beat , 1914, The Journal of physiology.

[5]  Y. Kuno.  Contributions to the physiology of the pulmonary circulation , 1915, The Journal of physiology.

[6]  I. D. Daly.  A Closed-Circuit Heart-Lung Preparation.--Effect of Alterations in the Peripheral Resistance and in the Capacity of the Circulation , 1926 .

[7]  M B Visscher,et al.  The regulation of the energy output of the heart , 1927, The Journal of physiology.

[8]  G. Liljestrand,et al.  The Immediate Effects of Muscular Work on the Stroke and Heart Volume in Man1 , 1938 .

[9]  Isaac Staur,et al.  RÔLE OF THE “STATIC BLOOD PRESSURE” IN ABNORMAL INCREMENTS OF VENOUS PRESSURE, ESPECIALLY IN HEART FAILURE. I. THEORETICAL STUDIES ON AN IMPROVED CIRCULATION SCHEMA WHOSE PUMPS OBEY STARLING'S LAW OF THE HEART , 1940 .

[10]  L. Katz,et al.  THE DYNAMIC ALTERATIONS IN HEART FAILURE IN THE ISOLATED HEART AND HEART-LUNG PREPARATION , 1945 .

[11]  E. Landis,et al.  CENTRAL VENOUS PRESSURE IN RELATION TO CARDIAC "COMPETENCE," BLOOD VOLUME AND EXERCISE. , 1946, The Journal of clinical investigation.

[12]  Bernstein.  Cardiac output in man , 1948 .

[13]  R. Riley,et al.  Studies of the pulmonary circulation at rest and during exercise in normal individuals and in patients with chronic pulmonary disease. , 1948, The American journal of physiology.

[14]  E BERGLUND,et al.  Ventricular Function: I. Starling's Law of the Heart Studied by Means of Simultaneous Right and Left Ventricular Function Curves in the Dog , 1954, Circulation.

[15]  G. A. Brecher,et al.  Cardiac variations in venous return studied with a new bristle flowmeter. , 1954, The American journal of physiology.

[16]  R. W. Jones,et al.  Respiratory responses to CO2 inhalation; a theoretical study of a nonlinear biological regulator. , 1954, Journal of applied physiology.

[17]  E. Berglund.  Ventricular function. VI. Balance of left and right ventricular output: relation between left and right atrial pressures. , 1954, The American journal of physiology.

[18]  R. F. Rushmer.  Applicability of Starling's law of the heart to intact, unanesthetized animals. , 1955, Physiological reviews.

[19]  D. Sabiston,et al.  Performance of the heart: changes in left ventricular end-diastolic pressure and stroke work during infusion and following exercise. , 1955, Physiological reviews.

[20]  D. W. Richards.  Discussion of Starling's law of the heart. , 1955, Physiological reviews.

[21]  S. Sarnoff.  Myocardial contractility as described by ventricular function curves; observations on Starling's law of the heart. , 1955, Physiological reviews.

[22]  L. Katz,et al.  Registration of Left Ventricular Volume Curves in the Dog with the Systemic Circulation Intact , 1955, Circulation research.

[23]  W. Hamilton.  Role of the Starling concept in regulation of the normal circulation. , 1955, Physiological reviews.

[24]  L. Katz.  Analysis of the several factors regulating the performance of the heart. , 1955, Physiological reviews.

[25]  A. Guyton,et al.  Determination of cardiac output by equating venous return curves with cardiac response curves. , 1955, Physiological reviews.

[26]  O. Gauer.  Volume changes of the left ventricle during blood pooling and exercise in the intact animal; their effects on left ventricular performance. , 1955, Physiological reviews.

[27]  E. Ogden,et al.  Factors Altering the Filling of the Isolated Left Ventricle of the Dog Heart: Effects of Epinephrine and Norepinephrine , 1956, Circulation research.

[28]  Gerhard A. Brecher,et al.  Relation of Negative Intraventricular Pressure to Ventricular Volume , 1957, Circulation research.

[29]  G. Anrep,et al.  Observations on the pulmonary circulation: Pulmonary Circulation in the Heart-Lung Preparation. , 2022, The Journal of physiology.