Mathematical Modeling of Cardiovascular System Dynamics Using a Lumped Parameter Method

This work reviews the main aspects of cardiovascular system dynamics with an emphasis on modeling hemodynamic characteristics by the use of a lumped parameter approach. The methodological and physiological aspects of the circulation dynamics are summarized with the help of existing mathematical models. The main characteristics of the hemodynamic elements, such as the heart and arterial and venous systems, are first described. Distributed models of an arterial network are introduced, and their characteristics are compared with those of lumped parameter models. We also discuss the nonlinear characteristics of the pressure-volume relationship in veins. Then the control pathways that participate in feedback mechanisms (baroreceptors and cardiopulmonary receptors) are described to explain the interaction between hemodynamics and autonomic nerve control in the circulation. Based on a set-point model, the computational aspects of reflex control are explained.