Physiological time series: distinguishing fractal noises from motions

Abstract.

Many physiological signals appear fractal, in having self-similarity over a large range of their power spectral densities. They are analogous to one of two classes of discretely sampled pure fractal time signals, fractional Gaussian noise (fGn) or fractional Brownian motion (fBm). The fGn series are the successive differences between elements of a fBm series; they are stationary and are completely characterized by two parameters, σ², the variance, and H, the Hurst coefficient. Such efficient characterization of physiological signals is valuable since H defines the autocorrelation and the fractal dimension of the time series. Estimation of H from Fourier analysis is inaccurate, so more robust methods are needed. Dispersional analysis (Disp) is good for noise signals while bridge detrended scaled windowed variance analysis (bdSWV) is good for motion signals. Signals whose slopes of their power spectral densities lie near the border between fGn and fBm are difficult to classify. A new method using signal summation conversion (SSC), wherein an fGn is converted to an fBm or an fBm to a summed fBm and bdSWV then applied, greatly improves the classification and the reliability of Ĥ, the estimates of H, for the times series. Applying these methods to laser-Doppler blood cell perfusion signals obtained from the brain cortex of anesthetized rats gave Ĥ of 0.24±0.02 (SD, n=8) and defined the signal as a fractional Brownian motion. The implication is that the flow signal is the summation (motion) of a set of local velocities from neighboring vessels that are negatively correlated, as if induced by local resistance fluctuations.