Scaling Properties of Cerebral Hemodynamics

Summary

Cerebral autoregulation (CA) is a vital protective mechanism that maintains relatively stable cerebral blood flow despite variations in systemic pressure as large as 100 Torr. It is commonly perceived to operate as a high-pass filter which transmits rapid changes in blood pressure but strongly attenuates and delays low-frequency perturbations. The ongoing search for clinically significant measures of CA integrity fuels the study of relations between the statistical properties of arterial blood pressure fluctuations (ABP) and those of blood flow velocity in major cerebral arteries, for example in middle cerebral artery (MCA). Using the method of averaged wavelet coefficients (AWC) we find that in the healthy subjects the scaling properties of both time series may be characterized by two exponents. The short time scaling exponent determines the statistical properties of fluctuations in short-time intervals while the Hurst exponent H describes the long-term fractal properties. Surprisingly, the group-averaged Hurst exponents coincide: H _ABP = H _MCA = 1 . To explain this effect, we employ complex continuous wavelet transforms to characterize autoregulation in terms of the wavelet gain and instantaneous phase difference between the arterial blood pressure and cerebral flow velocity. In the very low frequency (0.02–0.07 Hz) part of the spectrum, where autoregulation is most strongly pronounced, the damping of ABP slow oscillations weakly depends on frequency. In this frequency range phase difference evolves slowly over time and has an almost uniform distribution. Thus, CA not only dampens low frequency oscillations but also randomizes their phases. However, phase randomization of fractional Brownian motion does not affect its scaling properties. Consequently, fractal dynamics of arterial pressure is essentially carried over to cerebral blood flow.