Nonlinear dynamics methods for tachogram series analysis based on detrended fluctuation analysis and Higuchi's fractal dimension

Nonlinear dynamics is useful for determining correlations in non-stationary of highly heterogeneous time series. In this work two computational methods derived from nonlinear dynamics were used to analyze tachograms of healthy subjects and patients with Congestive Heart Failure (CHF); such methods were the Detrended Fluctuation Analysis (DFA) and the Higuchi's Fractal Dimension (HFD). First, both methods were applied separately. In DFA, marked differences could be observed in the obtained graphs and results from healthy subjects and CHF patients, a main difference was between the number of crossovers that led to a cumulative change in slopes (Δα), it was higher in the second ones which is explained by the increased presence of crossovers; in HFD case such differences were not very evident. With the obtained results from HFD new series were generated of the differences between each point and its corresponding point of the linear fit, then by plotting these series low-frequency oscillations were present, to characterize these oscillations DFA and HFD methods were used together. The obtained results let us infer that the use of these methods can help us to get more information from physiological signals (ECG for this work) and have a wider overview of a patient's health state.