Applying continuous chaotic modeling to cardiac signal analysis

In the last decade, chaos theory has become a popular method for approaching the analysis of nonlinear data for which most mathematical models produce intractable solutions. The concept of chaos was first introduced with applications in meteorology. Since then, considerable work has been done in the theoretical aspects of chaos. Applications have abounded, especially in medicine and biology. A particularly active area for the application of chaos theory has been cardiology. Many aspects of heart disease have been addressed, including whether chaos represents the healthy or diseased state. Most approaches to chaotic modeling rely on discrete models of continuous problems, which are represented by computer algorithms. Due to the nature of chaotic models, both the discretization and the computer simulation can lead to propagation of errors that may overtake the actual solution. This article describes an approach to chaotic modeling in which a continuous model is developed based on a conjectured solution to the logistic equation. As a result of this approach, two practical methods for quantifying variability in data sets have been derived. The first is a graphical representation obtained by using second-order difference plots of time series data. The second is a central tendency measure (CTM) that quantifies this degree of variability. The CTM can then be used as a parameter in decision models, such as neural networks. It appears that measuring the degree of variability is a more useful measure of chaos, as demonstrated by the application of this work to the analysis of congestive heart failure patients as compared to normal controls.