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Is the Healthy Human Heartbeat Fractal?

Figure: Scaling analyses for two 24-hour interbeat interval time series are shown in Fig. 3. The solid circles represent data from a healthy subject, while the open circles are for the artificial time series generated by randomizing the sequential order of data points in the original time series. (a) Plot of tex2html_wrap_inline1173 vs tex2html_wrap_inline1175 by the DFA analysis. (b) Fourier power spectrum analysis. The spectra have been smoothed (binned) to reduce scatter.

To test whether heartbeat time series exhibit fractal behavior, we can apply the DFA algorithm to the full, 24-hour data sets excerpted in Fig. 3. Figure 5 compares the DFA analysis of the interbeat interval time series for the healthy subject with the randomized control time series. For the healthy subject, DFA analysis shows scaling behavior with exponent tex2html_wrap_inline1203 over 3 decades, consistent with 1/f-type of dynamics as previously reported [20, 21]. As expected, the randomized control data set shows a trivial exponent tex2html_wrap_inline1161, indicating uncorrelated randomness. Power spectrum analysis confirms the DFA results. The tex2html_wrap_inline1231 exponent derived from the power spectrum, however, is less accurate because the stationarity requirement for Fourier analysis is not satisfied in this case.