  We study the middle cerebral artery blood flow velocity (MCAfv) in humans
using transcranial Doppler ultrasonography (TCD). Scaling properties of time
series of the axial flow velocity averaged over a cardiac beat interval may be
characterized by two exponents. The short time scaling exponent (STSE)
determines the statistical properties of fluctuations of blood flow velocities
in short-time intervals while the Hurst exponent describes the long-term
fractal properties. In many migraineurs the value of the STSE is significantly
reduced and may approach that of the Hurst exponent. This change in dynamical
properties reflects the significant loss of short-term adaptability and the
overall hyperexcitability of the underlying cerebral blood flow control system.
We call this effect fractal rigidity.
