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

Abstract

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 exchange elements of the cardiovascular system. The present analysis is restricted 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 values for each of the system''s dependent variables (caridac 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 experimental data indicates that the mathematical model so obtained is a useful one.