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Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series
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9.Computer software of DFA algorithm is available upon request; contact C.-K. Peng (e-mail: peng[chaos.bih.harvard.edu).
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18.ECG recordings of Holter monitor tapes were processed both manually and in a fully automated manner using our computerized beat recognition algorithm (Aristotle). Abnormal beats were deleted from each data set. The deletion has practically no effect on the DFA analysis since less than \% of total beats were removed. Patients in the heart failure group were receiving conventional medical therapy prior to receiving an investigational cardiotonic drug; see D. S. Baimet al., J. Am. Coll. Cardiol. 7, 661–670 (1986).
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20.Typical regression fit shows excellent linearity of double log graph (indicated by correlation coefficient for both groups. However, usually data from healthy subjects show even better linearity on log-log plots than data from subjects with heart disease. Our estimate of a is consistent with the previous analysis in Ref. 3. Note, however, that in Ref. 3 the analysis was performed on the interbeat increment data to avoid the problem of non-stationarity. Therefore, the scaling exponent computed in Ref. 3 is smaller than the a exponent computed by DFA by a value of 1 (due to the integration process in DFA).
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24.A further refinement (not presented here) may be obtained by not arbitrarily setting the crossover scale to be 16 beats for all data sets. Instead, each individual data set could have its own ranges for fitting and that depend on the specific crossover point in the given data set.
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26.We also tested these calculations by varying the fitting range for . We find that the results are very similar when we measure from 16 beats to 128 beats. However, when we move the upper fitting range for from 128 beats to 256 beats or more, the pathologic data sets show larger variation of leading to less obvious separation from normal subjects. This is partly due to the fact that, for finite length data sets, the calculation error of F(n) increases with Therefore, scaling exponents obtained over larger values of n will have greater uncertainty.
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