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 Hillʹs 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 modelʹs 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.