Correlation in heart beat time series during exercise

Correlation in heart beat time series during exercise Correlations in time series have been widely studied in several fields like biology, physiology, finance, signal processing, geology, astronomy, etc. In this internship report we will study the rate variability in heart beat time series recorded during exercise. These time series are generated by physiologic processes that present an intense intrinsic complexity because they are highly non linear and non stationary. We believed that the heart rate variability can be quantified as the behaviour of the fluctuations around a macroscopic trend and with this in mind we will study the time correlations between them. A real time relation between the heart rate variability and the rate could serve to hasten the recovery of patients under rehabilitative treatments and to provide useful information to improve the performances of professional athletes. After a brief introduction, in Chapter 2 I will shed light on the state of the art in the field. For resting time series it has been shown using first fitting an autoregressive process and then detrended fluctuation analysis that for short time scales the fluctuations are correlated if the time series is recorded from an healthy individual and uncorrelated if they are recorded from a patient who is affected by congenital heart failure. In Chapter 3 I will show why strong trends in RR time series recorded during activity prevent the straightforward application of the previous techniques. I will then interpret anyway the results taking into accounts all the limitations of the used methods. A new analysis approach using the partial autocorrelation function will also be developed in this chapter. An analytical link between all the techniques will be outlined, and indeed the results will be consistent between all the methods and will point out that the fluctuations in the studied heart rate regimes are strictly anti-correlated. Anticorrelations are probably born from the coupling of the heart rate with the physiologic vascular regulation and respiration cycles. In the last chapter I will describe a recently invented, data driven algorithm called Empirical Mode Decomposition and its noise-aided versions that perform better than Fourier Decomposition on short, non linear and non stationary time series. Its output is consistent with the previously obtained results.