Correlation Integral and Frequency Analysis of Cardiovascular Functions

To study the dynamics of the cardiovascular system several cardiovascular functions are measured at different sites of the human body. Measured time series of peripheral blood flow, respiration, electrical activity of the heart (ECG), and instantaneous heart rate (IHR) derived from the ECG are analysed in time and frequency domains and in phase space. Correlation integrals are calculated for the original signals and their surrogates. The auto and crosscorrelation functions and the Fourier spectra are also presented. All measured data of the physiological origin are corrupted by noise. To some extent they also contain non-stationarities. Therefore, the correlation integral is first analysed on numerically generated quasi-periodic time series and the effect of added noise is studied. The scale that is corrupted by noise is also analytically examined. An upper dimension which may reliably be estimated is evaluated. The results presented suggest that the calculated correlation integral cannot be used as a quantitative characterization of an attractor reconstructed from measured time series. Hence, only the relative qualitative differences between slopes of the correlation integral of measured time series and their surrogates are analysed. For all measured time series the slopes of their correlation integrals differ from those of their surrogates suggesting deterministic nature of the system that governs cardiovascular dynamics. It is also shown that all time series contain the same five characteristic peaks in their frequency spectra.

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