Chaotic Dynamics of ECG Waveforms at Global and Microscopic Scales: Theory and Applications

ABSTRACT

A theory is developed for describing the electrocardiogram (ECG) in terms of underlying cellular processes of ion transport. ECG evolvement over time is regarded as a sequence of partly overlapping self-similar transient potentials, with the generic mass potential (GMP) being the basic element. Using equations of the nonhomogeneous birth-and-death process (BDP), a particle model of GMP in the form of chaotic BDP is deduced. The formalism of deterministic chaos not only brings together the deterministic and stochastic factors underlying ECG genesis, but also does this with the minimum number of free parameters. No matter how complex the system of underlying ion transport, just a single parameter (the chaos factor), yet directly derived from microscopic scale equations, aggregates essential aspects of the ECG dynamics. This paradigm is investigated in numerical experiments, and qualified as the chaotic transformations effect. At the global level the mass effect of chaotic transformations is described by a system of nonlinear differential equations. Applications of this theory are supported by the method of high-resolution fragmentary decomposition which resolves component temporal overlap and reconciles the ECG waveforms with the dynamics of chaotic processes. This technique goes beyond conventional measures such as ECG peak amplitudes and latencies, and provides a more comprehensive analysis of the dynamics of ECG waveforms. In particular, the resolution of the component overlap provides means for recognising the complex composition of Q, R and S waves, and co-operative action of the systems producing R and S waves.