Síntese e análise de sinais de variabilidade da freqüência cardíaca pela modelagem NARMAX com entrada sintética

Abstract

This work deals with the study of heart rate variability (HRV). These signals corresponds to the instantaneous variation of the cardiac frequency, has been studied increasing in last three decades, either as the focus of the study, either as auxiliary subject in the study of the cardiovascular system. Until the late eighties the tools used in the study of the HRV series were predominantly some statistical indices, as the standard deviation, and the power spectrum; these tools still being wide employed. From the late eighties, some tools of nonlinear dynamics had started to gain important prominence in literature. In this period, the HRV signal was yet investigated as being purely random, as well as having deterministic dynamics. From this, this work has as general objective to investigate the signal of HRV by means of mathematical modeling, considering it as a signal that presents an deterministic dynamics embedded in an important random component. In specific, the objectives are to present a modeling procedure that makes possible to get models that consider the dynamic and random aspects of the HRV signals, that, when iterated, present supported fluctuations and that to be similar to the original signals in some aspect and that they are capable to assimilate something of the underlying dynamics. The chosen mathematical representation for the models was the polynomial NARMAX. Due to the characteristics of the HRV signals was necessary to construct an artificial signal to be used as exogenous variable in NARMAX models. Before applying the modeling procedure on the HRV series and in order to validate it, it was applied on three known dynamical systems in literature, they are the logistic map, the Rssler's system and the Hénon's map. It is presented, in this work, the results of the studies of two HRV series of 24h duration, of the same volunteer with good health. To validate the results from the HRV series, classical indices in the study of these signals had been used, like SDNN and also nonlinear indices like approximated entropy, DFA (detrended fluctuation analysis) and symbolic dynamics. The results shows to be promising, because either in the validation stage of the modeling procedure, i.e., when the modeling procedure was applied to the dynamical systems, either in the study of the HRV series, the obtained models had been capable of to assimilate in some way the original system either in dynamical aspect either in the stochastic aspect. This facts shows the contribution of this thesis.