Analysis of cardiac rhythms using a dynamics perspective: nonlinearities, randomnesses and chaos

Abstract

Biological rhythms are fundamental for the comprehension of the physiological functioning of organisms, being useful in disease prevention and treatments. Cardiac rhythm is a remarkable example of bio-rhythms and is treated in this work by evaluating the electrical activity of the heart based on ECG observations. A mathematical model composed by three nonlinear oscillators coupled by time-delayed connections is employed for cardiac system description. Numerical simulations provide synthetic ECGs and a great variety of cardiac responses, including normal and pathological behaviors, is reproduced. In this regard, mathematical modeling can be useful to highlight distinct kinds of behavior, being interesting for clinical purposes. Also, numerical simulations are compared with experimental ECGs. Besides, deterministic and non-deterministic situations are treated showing the possibility of the combination of nonlinear and random aspects to define the rhythmic complexity. Nondeterministic aspects are incorporated by considering random connections between oscillators. Two stochastic approaches are investigated: parametric, considering couplings described by random variables; and nonparametric, by means of random matrix theory. Different tools including Poincaré maps, bifurcation diagrams, RR histograms and Lyapunov exponents are employed in order to show interesting possibilities that can help in identification, monitoring and controlling cardiac rhythms.