V.N. Biktashev, A.V. Holden
Submitted to Chaos: December 14, 2000. Accepted: March 21, 2001. Published: Chaos, 11: 653-664, 2001
Surface imaging of electrical activity in isolated heart tissue and computational models of ventricular fibrillation show patterned irregularity. Such irregularity in spatially extended, nonlinear systems can result from stochastic and deterministic processes. We require methods and measures for characterising these patterns, that provide insight into the mechanisms of the evolving spatio-temporal irregularity, and that can be related to simple time series measures of local or global (e.g.the electrocardiogram) activity and stochastic models.
``Leading paragraph'':
The re-entrant ventricular arrhythmias of monomorphic ventricular tachycardia and fibrillation are produced by abnormal spatio-temporal patterns of propagation in the ventricular myocardium. These behaviours can be described by solutions of reaction-diffusion equation excitable medium models. The direct comparison of such solutions with existing experimental observations is virtually impossible as there are too many factors to be taken into account, including not only the complicated dynamics of the re-entrant waves of excitation in the tissue, but also the way the appearance of these waves on the surface is modified by the inhomogeneity, anisotropy and three-dimensional nature of heart tissue. One way of indirect comparison is to compare characteristics of the complexity of the model and the real data, that are invariant under these modifications of the signal. Karhunen-Loéve decomposition is a standard tool for evaluating the complexity of multidimensional signals. Comparison of the separate and conjoint complexities of the signals on the opposite sides of the preparation can be considered as an indicator how much three-dimensional effects are essential in the preparation behaviour.
postscript (7.3M)