Fractal fluctuations in human respiration

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Abstract
The present study was designed to characterize respiratory fluctuations in awake, healthy adult humans under resting conditions. For this purpose, we recorded respiratory movements with a strain-gauge pneumograph in 20 subjects. We then used Allan factor, Fano factor, and dispersional analysis to test whether the fluctuations in the number of breaths, respiratory period, and breath amplitude were fractal (i.e., time-scale-invariant) or random in occurrence. Specifically, we measured the slopes of the power laws in the Allan factor, Fano factor, and dispersional analysis curves for original time series and compared these with the slopes of the curves for surrogates (randomized data sets). In addition, the Hurst exponent was calculated from the slope of the power law in the Allan factor curve to determine whether the long-range correlations among the fluctuations in breath number were positively or negatively correlated. The results can be summarized as follows. Fluctuations in all three parameters were fractal in nine subjects. There were four subjects in whom only the fluctuations in number of breaths and breath amplitude were fractal, three subjects in whom only the fluctuations in number of breaths were fractal, and two subjects in whom only fluctuations in breath number and respiratory period were fractal. Time-scale-invariant behavior was absent in the two remaining subjects. The results indicate that, in most cases, apparently random fluctuations in respiratory pattern are, in fact, correlated over more than one time scale. Moreover, the data suggest that fractal fluctuations in breath number, respiratory period, and breath amplitude are controlled by separate processes.

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