DETECTION OF ANOMALOUS DIFFUSION USING CONFIDENCE-INTERVALS OF THE SCALING EXPONENT WITH APPLICATION TO PRETERM NEONATAL HEART-RATE-VARIABILITY

The scaling exponent of the root mean square (rms) displacement quanti fies the roughness of fractal or multifractal time series; it is equiv alent to other second-order measures of scaling, such as the power-law exponents of the spectral density and autocorrelation function. For s elf-similar time series, the rms scaling exponent equals the Hurst par ameter, which is related to the fractal dimension, A scaling exponent of 0.5 implies that the process is normal diffusion, which is equivale nt to an uncorrelated random walk; otherwise, the process can be model ed as anomalous diffusion. Higher exponents indicate that the incremen ts of the signal have positive correlations, while exponents below 0.5 imply that they have negative correlations. Scaling exponent estimate s of successive segments of the increments of a signal are used to tes t the null hypothesis that the signal is normal diffusion, with the al ternate hypothesis that the diffusion is anomalous. Dispersional analy sis, a simple technique which does not require long signals, is used t o estimate the scaling exponent from the slope of the linear regressio n of the logarithm of the standard deviation of binned data points on the logarithm of the number of points per bin. Computing the standard error of the scaling exponent using successive segments of the signal is superior to previous methods of obtaining the standard error, such as that based on the sum of squared errors used in the regression; the regression error is more of a measure of the deviation from power-law scaling than of the uncertainty of the scaling exponent estimate. App lying this test to preterm neonate heart rate data, it is found that t ime intervals between heart beats can be modeled as anomalous diffusio n with negatively correlated increments. This corresponds to power spe ctra between 1/f(2) and 1/f, whereas healthy adults are usually report ed to have 1/f spectra, suggesting that the immaturity of the neonatal nervous system affects the scaling properties of the heart rate. [S10 63-651X(98)14911-5].