Numerical simulation of the blood flow in the human cardiovascular system.
This paper describes a numerical model of the human cardiovascular system. The model is composed of 15 elements connected in series representing the main parts of the system. Each element is composed of a rigid connecting tube and an elastic reservoir. The blood flow is described by a one-dimensional time-dependent Bernoulli equation. The action of the ventricles is simulated with a Hill's three-element model, adapted for the left and right heart. The closing of the four heart valves is simulated with the aid of time-dependent drag coefficients. Closing is achieved by letting the drag coefficient approach infinity. The resulting system of 32 non-linear ordinary differential equations is solved numerically with the Runge-Kutta method. The results of the simulation (pressure-time and volume-time dependence for the atria and ventricles and pressure forms in the aorta at a heart rate of 70 beats per minute) agree with the physiological data given in the literature. The model's input aortic impedance is 31.5 dyn s cm-5 which agrees with literature data given for aortic input impedance in man 26-80 dyn s cm-5). Long-term stability of the system was achieved. The cardiovascular system presented here can also be simulated at higher and varying heart rates--up to 200 beats per minute. The results of calculations for some pathological changes (e.g. valvular abnormalities) are discussed.
Zácek
M
M
Institute of Hydrodynamics CAS, Prague, Czech Republic.
Krause
E
E
D000465:Algorithms; D001011:Aorta / Q000502:physiology; D016275:Atrial Function; D001775:Blood Circulation; D001794:Blood Pressure; D001808:Blood Vessels / Q000502:physiology; D001810:Blood Volume; D006321:Heart / Q000502:physiology; D006339:Heart Rate; D006351:Heart Valves / Q000502:physiology; D018056:Hemorheology; D006801:Humans; D008955:Models, Cardiovascular; D018924:Vascular Capacitance; D016276:Ventricular Function