Journal of the
Korean Mathematical Society JKMS

A new mathematical model of pumping heart coupled to lumped compartments of blood circulation is presented. This lumped pulsatile cardiovascular model consists of eight compartments of the body that include pumping heart, the systemic circulation, and the pulmonary circulation. The governing equations for the pressure and volume in each vascular compartment are derived from the following equations: Ohm's law, conservation of volume, and the definition of compliances. The pumping heart is modeled by the time-dependent linear curves of compliances in the heart. We show that the numerical results in normal case are in agreement with corresponding data found in the literature. We extend the developed lumped model of circulation in normal case into a specific model for arrhythmia. These models provide valuable tools in examining and understanding cardiovascular diseases.

Keywords: mathematical model, lumped model, heart, circulation,cardiovascular system, arrhythmia, and irregular heart beats

MSC numbers: 92O35, 92C50, 76Z05