Study of mixed-mode oscillations in a nonlinear cardiovascular system

Abstract

Problems related to cardiovascular dynamics and its representation by responses of electric circuit models with a novel estimation method for continuously tracking cardiac output and total peripheral conductance focus the main attention of this paper. The incorporation of nonlinearity in the performed analysis is one of the main features of this study what requires special attention both in modeling and solution procedures. The presented method takes into account intra-beat dynamics of arterial blood pressure and includes an appropriate model of arterial compliance. Inspected intra-beat parameters were taken into account for models of pulsate cardiovascular dynamics. Continuous monitoring of cardiac output, total peripheral conductance, left ventricular ejection fraction, left ventricular end-diastolic volume, and arterial blood pressure create the solid basis for distinguishing between cardiogenic, hypovolemic, and septic shocks. The task of tracking patient cardiovascular dynamics, which is particularly useful in the intensive care unit setting, is realized by applying an effective model with elements mapping appropriate relations existing in real clinical conditions. A lumped-parameter continuous-time electrical circuit model of cardiovascular dynamics is established. The adopted circuit model improves methods for fast manhandle of large quantities of clinical data and extracting from them kinetic parameters that can more importantly influence on the improvement of the dynamics of studied cardiovascular illness processes. When two or three (out of five) parameters of the circuit change simultaneously, various relaxation, mixed-mode, chaotic, and unstable oscillations are detected. Results of performed computer simulations of cardiovascular processes with the focus on mixed-mode oscillations as the dynamical switches between small-amplitude oscillations and large-amplitude oscillations are presented.