Cardiovascular Engineering: An International Journal, Vol. 4, No. 2, June 2004 ( C  2004) Numerical Model of the Human Cardiovascular System–Korotkoff Sound Simulation FRANTI ˇ SEK MAR ˇ S ´ IK, ∗, ¶ SV ˇ ETLANA P ˇ REVOROVSK ´ A, ∗ ZDEN ˇ EK BRO ˇ Z, † and V ´ IT ´ EZSLAV ˇ STEMBERA ‡ The numerical simulation of the Korotkoff sounds is realized by a 14 segment hemodynamic model of the cardiovascu- lar system developed in the Institute of Thermomechanics, Czech Academy of Sciences. The cardiovascular system is modeled by four segments of the pulsating heart and by 10 vascular segments of pulmonary and systemic circuits connected with the heart in series. To better understand the generation of Korotkoff sounds the systemic arterial flow is studied in detail by a distributed parameter model. The anal- ysis of self-excited oscillations in a collapsible tube (i.e., the systemic artery) is based on a one-dimensional model where the effect of expected flow separation is replaced by the change of viscous friction along the tube. Key words: cardiovascular system; Korotkoff sounds; numerical simulation. INTRODUCTION There are many models of the whole cardiovascular system (CVS) or of the various parts of this circulatory sys- tem. One of the first concepts of hemodynamic modeling was published by Leaning et al. (1983), but without any numerical realization. A model based on electric-circuit analogy (Schima et al., 1990) utilized a detailed lumped representation of the cardiovascular system including ven- ∗ Institute of Thermomechanics, Czech Academy of Sciences, Czech Republic. † Faculty of Nuclear and Technical Physics, Czech Technical University, Czech Republic. ‡ Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic. ¶ To whom correspondence should be addressed at Institute of Thermo- mechanics, Czech Academy of Sciences, Dolejˇ skova 5, 182 00 Prague 8, Czech Republic. E-mail: marsik@it.cas.cz tricular contractility to simulate the effects of a cardiac assist device which could be used for a cardiovascular control system. Other examples of cardiovascular and res- piratory system modeling include the models developed by Batzel et al. (2002) and ˇ Z´ aˇ cek and Kraus (1996) who developed a model composed of 15 compartments con- nected in series representing the main parts of the car- diovascular system. There is a model-based physiology- teaching tool (SimBioSys Physiology Labs Plus, Critical Concepts, Inc., Chicago, IL) to answer questions about the function of the heart, the lungs, and their autonomic control. The hemodynamics of the whole human cardiovas- cular system is modeled numerically by a lumped pa- rameter compartment model (Pˇrevorovsk´ a and Marˇ s´ ık, 2001) and is used to show the influence of viscoelas- tic blood vessels on hemodynamic characteristics, such as systemic vascular resistance, mean blood pressure, and cardiac performance. The whole circulatory system is modeled by four compartments representing the pul- sating heart and by 10 vascular segments of the pul- monary and systemic circuits connected with the heart in series. The scheme of this model is shown in Figure 1. The model simulates one-dimensional flow of incom- pressible blood through the network of elastic blood ves- sels. The heart compartments are considered to consist of anisotropic and viscoelastic incompressible material. The cardiovascular system is described by its hemodynamic variables, i.e., blood pressure, volume, and by cardiovas- cular parameters such as blood vessel compliance and resistance. Blood inertia and physico-chemical variables such as the cardiac action potential, calcium, potassium, and sodium concentrations are included in the model as well. 193 1567-8822/04/0600-0193/0 C  2004 Plenum Publishing Corporation