Fractal Dimension as a Diagnostic Tool for Cardiac Diseases

Abstract

The discovery of fractal geometry has been one of the major developments in mathematics. Fractals, defined as self-similar structures, provide a new approach to the understanding of irregular structures. The dimensions of complete fractals can be easily calculated as real numbers with the fractal geometry approach. However, most of the structures in nature do not demonstrate self-similarity fully, and different approaches are needed for dimension calculations. These structures with semi-fractal properties are known as quasi fractals. Fractals derived from time series are called statistical fractals and they are an example for quasi fractals. Various methods have been developed to estimate the dimensions of statistical fractals. In this study, the methods which predict dimension in statistical fractals were investigated and the most suitable method for time series was identified. Fractal dimensions were calculated by using ECGs of 236 individuals, and the data set was divided into four disease groups and a control group of healthy individuals. Various statistical analyses were performed using the fractal dimensions of the graphs computed with MATLAB. Statistical hypothesis tests showed that the differences between the group mean of fractal dimensions are significant. Fractal dimensions of ECGs have the potential to be used as a diagnostic tool in the diagnosis of heart diseases.