Physiological time series: distinguishing fractal noises from motions

Many physiological signals appear fractal, in having self-similarity over a large range of their power spectral densities. They are analogous to one o f two classes of discretely sampled pure fractal time signals, fractional G aussian noise (fGn) or fractional Brownian motion (fBm). The fGn series are the successive differences between elements of a fBm series; they are stat ionary and are completely characterized by two parameters, sigma(2), the va riance, and H, the Hurst coefficient. Such efficient characterization of ph ysiological signals Is valuable since Il defines the autocorrelation and th e fractal dimension of the time series. Estimation of H from Fourier analys is is inaccurate, so more robust methods are needed. Dispersional analysis (Disp) is good for noise signals while bridge detrended scaled windowed var iance 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 ( H) over cap, the estimates of H, for the times series. Applying these metho ds to laser-Doppler blood cell perfusion signals obtained from the brain co rtex of anesthetized rats gave A of; 0.24+/-0.02 (SD, n=8) and defined the signal as a fractional Brownian motion. The implication is that the flow si gnal is the summation (motion) of a set of local velocities from neighborin g vessels that are negatively correlated, as if induced by local resistance fluctuations.