Application of Hybrid Dynamical Theory to the Cardiovascular System

In hybrid dynamical systems, the state evolves in continuous time as well as in discrete modes activated by internal conditions or by external events. In the recent years, hybrid systems modeling has been used to represent the dynamics of biological systems. In such systems, discrete behaviors might originate from unexpected changes in normal performance, e.g., a transition from a healthy to an abnormal condition. Simplifications, model assumptions, and/or modeled (and ignored) nonlinearities can be represented by sudden changes in the state. Modeling cardiovascular system (CVS), one of the most fascinating but most complex human physiological systems, with a hybrid approach, is the focus of this chapter. The hybrid property appears naturally in the CVS thanks to the presence of valves which, depending on their state (closed or open), divide the cardiac cycle into four phases. This chapter shows how hybrid models can be used for modeling the CVS. In addition, it describes a preliminary study on the detection of some cardiac anomalies based on the hybrid model and using the standard observer-based approach.