Cardiac interbeat (RR) time series under healthy conditions have a complex temporal structure with multiscale correlations. In contrast, synthetic time series are most likely the output of simpler dynamical systems, and therefore, will be anticipated to have a less complex temporal structure.
Entropy has been proposed as a quantitative measurement of time series complexity. However, traditional measures, such as approximate entropy, only quantify the degree of regularity on a single time scale. We have proposed a new method to calculate multiscale entropy from complex signals. Given a time series, we first construct consecutive coarse-grained time series. Then, for each of these new time series, we calculate an entropy measure plotted as a function of the coarse-graining scale factor.
In order to distinguish between physiologic and synthetic time series, we first applied the method to a learning set of RR time series derived from healthy subjects. We empirically established selected criteria characterizing the entropy dependence on scale factor for these datasets. We then applied this algorithm to the CinC 2002 test datasets. We found 20 of 50 time series that did not match the criteria developed from the training set and these were classified as synthetic. One limitation of our method is that it cannot distinguish simulated 1/f noise from physiologic 1/f heart rate spectra. To improve our result, we visually inspected power spectra of all time series. Two additional time series were re-classified as synthetic based on the fact that their power spectra showed pure 1/f scaling without the expected peak at the respiratory frequency.
Using only the multiscale entropy method, we correctly classified 48 of 50 (96%) time series. In combination with Fourier spectral analysis, we correctly classified all time series. In contrast, a standard complexity measure (approximate entropy) did not provide good separation.
In summary, a new multiscale entropy method has the capacity to distinguish between time series generated by different mechanisms. This technique may be applied to a wide variety of other physiologic and physical time series.
Supported by the National Institute of Biomedical Imaging and Bioengineering (NIBIB) under NIH grant number R01EB030362.