Cross-Correlation of Instantaneous Phase Increments in Pressure-Flow   Fluctuations: Applications to Cerebral Autoregulation
  We investigate the relationship between the blood flow velocities (BFV) in the middle cerebral arteries and beat-to-beat blood pressure (BP) recorded from a finger in healthy and post-stroke subjects during the quasi-steady state after perturbation for four different physiologic conditions: supine rest, head-up tilt, hyperventilation and CO_2 rebreathing in upright position. To evaluate whether instantaneous BP changes in the steady state are coupled with instantaneous changes in the BFV, we compare dynamical patterns in the instantaneous phases of these signals, obtained from the Hilbert transform, as a function of time. We find that in post-stroke subjects the instantaneous phase increments of BP and BFV exhibit well pronounced patterns that remain stable in time for all four conditions, while in healthy subjects these patterns are different, less pronounced and more variable. We propose a new approach based on the instantaneous phase increments cross-correlation to quantify the coupling between BP and BFV. We find that the maximum correlation strength is different for the two groups and for the different conditions. For healthy subjects the amplitude of the cross-correlation between the instantaneous phase increments of BP and BFV is small and attenuates within 3-5 heartbeats. In contrast, for post-stroke subjects, this amplitude is significantly larger and cross-correlations persist up to 20 heartbeats. We compare the results of our approach with three complementary methods: direct BP-BFV cross-correlation, transfer function analysis and phase synchronization analysis. 
Zhi Chen, Kun Hu, H. Eugene Stanley, Vera Novak, Plamen Ch. Ivanov