Fluctuations in resting depth of breathing (tidal volume) at constant breathing rate in the anesthetized adult rat exhibit fractal properties when analyzed by a rescaled range method characterized by a mean (±SD) exponent H=0.83±0.02 and 0.92±0.03 with and without sighs, respectively, for up to 400 breaths. Values of H determined from shuffled tidal volumes and simulated tidal volumes taken randomly from a Gaussian distribution of mean and variance approximating that of the actual data are consistent with the expected value of H=0.5 for an independent random process with finite variances. An empirical description is proposed to predict the change in H with length of time record.

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Let the slope s in Fig. 2 as a function of log T be s(logT) = H0+ ∫ 0logT(Hm−H0)P(Ι)dΙ, where the weighting function P(Ι), e.g., the Gamma variate P(Ι) = αΓ(n)(−1(αΓ)(n−1e−α, determines how rapidly with log T the maximum or long-term Hurst exponent Hm is achieved, Γ(n) is the Gamma function, α is a shape parameter, and n is the number of log T intervals over which the slope s evolves to Hm. It must be emphasized that justification for the smooth curve shown in Fig. 2 and the indicated values of Hm, α, and n, is heuristic, that is, the chosen rule and weighting function reproduce the observed changes in slope vs. log T during resting respiration.
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© 1993 American Institute of Physics.
1993
American Institute of Physics
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