A Mathematical Model of the Canine Circulation

Abstract

A lumped-parameter model of the canine closed-loop circulation has been developed. The model consists of the following components: the right heart (atrium and ventricle), pulmonary circulation (pulmonary arteries, capillaries, and veins), left heart (atrium and ventricle), systemic circulation (aorta, systemic arteries, systemic veins, and the vena cavae). The passive elements, the arteries and veins, are represented by their resistive, compliant, and inertial properties.In addition to the mathematical description of the arteries and veins of both the systemic and pulmonary circulations, this model makes use of the time-varying elastance (instantaneous pressure-volume relationship) to describe the nature of the source pumps in the intact circulation. Using elastance functions adopted for both the left and right atria and ventricles, the model produces realistic left and right atrial and ventricular pressure and volume waveforms. Model parameters associated with the systemic and pulmonary circulations have been estimated so that the pressure waveforms at various points in the circulation are in agreement with data from animal experiments. The model can generate realistic pressure waveforms on a beat-to-beat basis and yields good estimates of mean blood pressures, cardiac output and ejection fraction for a normal dog. Furthermore, the model allows the description and specification of blood volume distribution within the entire closed circulation, and the changes in blood volumes can be monitored dynamically. We conclude that our model provides a useful theoretical framework for analyzing experimental studies of the circulatory system.