Nonlinear forecasting and the dynamics of cardiac rhythm

Since the initial development of the electrocardiogram, cardiologists have made dramatic advances in the description and understanding of cardiac arrhythmias. Despite these successes, the analysis of cardiac rhythm has remained largely descriptive. Recently, the principles of nonlinear dynamics, or chaos theory, have been applied to the quantitative analysis of cardiac rhythm in a variety of diverse situations. In chaos theory, three types of signals can be defined: periodic signals, which repeat themselves over some finite time interval, chaotic signals, which, while deterministic, demonstrate complex behavior and do not repeat themselves, and random signals, which are unpredictable and nondeterministic. The technique of nonlinear forecasting defines trajectories in a suitably defined phase space and uses the future evolution of trajectories that are close to each other over short distances to make predictions for times further into the future. The ability to reliably predict the future evolution of the trajectories derived from any signal is an important characteristic of the underlying dynamics of the signal and can therefore used to determine those dynamics. The foundation of nonlinear forecasting is reviewed, and an algorithm is described that can be used to determine the underlying dynamics of a signal and has been applied to the analysis of R-R interval data.