A nonlinear analysis of cardiovascular diseases using multi-scale analysis and generalized hurst exponent

Congestive heart failure (CHF) and arrhythmia (ARR) are common heart diseases that affect a growing population of patients worldwide. In this work, we employ multi-scale analysis (MSA) to estimate generalized Hurst exponent (GHE) from electrocardiogram (ECG) records under CHF, ARR, and normal sinus rhythm (NSR). As a result, fractal correlations in short and long fluctuations of CHF, ARR, and NSR are measured. Then, a set of six statistical tests are applied to GHE estimates to check how they are different at each time scale between two different ECG conditions. Particularly, the goal is verify if two different ECG conditions can be statistically differentiated by short or by long fluctuations. The battery of statistical tests includes Kolmogorov–Smirnov, Kruskal–Wallis, Wilcoxon rank sum, Student t-test, Ansari–Bradley, and F-test. The results from MSA show evidence that CHF, ARR, and NSR all exhibit multi-fractal properties. Besides, the results from statistical tests revealed that long fluctuations statistically differentiate CHF and ARR, ARR and NSR, and CHF and NSR. Therefore, long fluctuations account most for the characterization of CHF, ARR, and NSR. Our findings are helpful to better understand the mechanics of heart disease and normal heart beats, and also promising to eventually designing computer-aided diagnosis systems for CHF and ARR classification.