Advances in Chemical Physics, Vol.133, Part B. Fractals, by Yuri P. Kalmykov, William T. Coffey, Stuart A. Rice

By Yuri P. Kalmykov, William T. Coffey, Stuart A. Rice

Fractals, Diffusion and leisure in Disordered advanced structures is a different guest-edited, two-part quantity of Advances in Chemical Physics that keeps to file fresh advances with major, updated chapters via the world over well-known researchers.

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Additional info for Advances in Chemical Physics, Vol.133, Part B. Fractals, Diffusion, and Relaxation (Wiley 2006)

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Instead we present a single explanatory technique that is relatively straightforward and that allows us to introduce the measure of interest. We use the allometric aggregation technique on real data to relate the variance and mean, as we discussed. Now we apply the allometric aggregation approach to the beat-to-beat intervals shown in Fig. 2, a typical HRV time series for a healthy young adult male. The data points in the figure are connected to aid in visualizing how the time intervals between heartbeats are changing.

When heart rate is atypical, say 120 bpm, in contrast to its usual 60 bpm, quantifying the variation in heart rate becomes very important. The degree of deviation from normality is determined by the interpretation of the size of the variation and how it is used to identify associated patterns. There are a number of ways to assess HRV, some 16 in all, each related to scaling in one way or another and most being FVSM, but we do not want to go into all of them here. Instead we identify the quantity that is the most revealing of the nature of HRV, but again we shall not go into a detailed discussion of the many ways of estimating this quantity.

Consequently, the fractal scaling was found to reside in the statistical properties of the fluctuations and not in the geometrical properties of the dynamic variable. As with the heart, the variability of breathing rate using breath-to-breath time intervals is denoted by breathing rate variability (BRV), to maintain a consistent notation. Examples of HRV and BRV time series data on which scaling calculations are based are shown in Fig. 4. A typical BRV time series for a senior citizen at rest is shown at the top of the figure; the simultaneous HRV time series for the same person is depicted at the bottom of the figure.

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