Cross-correlation of instantaneous phase increments in pressure-flow fluctuations: Applications to cerebral autoregulation

Abstract

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 quasisteady 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 physiologic conditions, while in healthy subjects these patterns are different, less pronounced, and more variable. We propose an approach based on the cross-correlation of the instantaneous phase increments to quantify the coupling between BP and BFV signals. 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. Further, we show that the instantaneous phase increments of BP and BFV are cross-correlated even within a single heartbeat cycle. We compare the results of our approach with three complementary methods: direct BP-BFV cross-correlation, transfer function analysis, and phase synchronization analysis. Our findings provide insight into the mechanism of cerebral vascular control in healthy subjects, suggesting that this control mechanism may involve rapid adjustments (within a heartbeat) of the cerebral vessels, so that BFV remains steady in response to changes in peripheral BP.

Respiration drives phase synchronization between blood pressure and RR interval following loss of cardiovagal baroreflex during vasovagal syncope

“…The cross-dependency of phase dynamics of the two system is calculated by means of coefficients c1,2 as below (34): c 2 1,2 ϭ ͐ ͐ (‫ץ‬F1,2/‫ץ‬⌽2,1) 2 d⌽1d⌽2. The coefficient c describes the strength of one oscillator to drive the other.…”

“…Although contributions of baroreflex deficiency to circulatory collapse during vasovagal syncope have been proposed (11,16,17,19,20,29,37,41,43,46), they remain controversial because prior investigations have predominantly used linear, time-invariant methods to relate AP, HR, and respiratory signals to one another (11,17,19,43) via cross-correlation analyses (2) or transfer function analyses (9,47). However, the time courses of AP, HR, and respiration during orthostasis in fainters are highly nonlinear and time dependent and therefore poorly amenable to such analyses (12).…”

Investigation of Atrial Vulnerability by Analysis of the Sinus Node EG From Atrial Fibrillation Models Using a Phase Synchronization Method

“…Our basic approach is derived from the phase synchronization method [15], [16], which we then apply to evaluate synchronized atrial excitation. In addition, we use Shannon entropy (SE) [21] to assess the randomness of atrial synchronization.…”

“…We hypothesize that the atrium operates with the sinus node almost synchronously under a sinus rhythm and almost asynchronously before AF. In order to estimate synchronization in sinus EGs, we adopted entropic analysis and synchronization methods [15], [16] that are applied to a multielectrode ECG mapping system in order to obtain a full view of the disordered patterns resulting from the heterogeneous tissue.…”

Synchronization of groups of coupled oscillators with sparse connections

“…Synchronization, as a universal cooperative behavior and a fundamental mechanism of self-organizations in nature, has been extensively studied in recent years [1][2][3][4][5][6]. The synchronization of spatiotemporal systems have attracted much attention, and numerous interesting bifurcations and on-off intermittent behaviors are found [7].…”