plex continuous wavelet transforms are used to study the dynamics of instantaneous phase difference ⌬ between the fluctuations of arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) in a middle cerebral artery. For healthy individuals, this phase difference changes slowly over time and has an almost uniform distribution for the very low-frequency (0.02-0.07 Hz) part of the spectrum. We quantify phase dynamics with the help of the synchronization index ␥ ϭ ͗sin⌬͘ 2 ϩ ͗cos⌬͘ 2 that may vary between 0 (uniform distribution of phase differences, so the time series are statistically independent of one another) and 1 (phase locking of ABP and CBFV, so the former drives the latter). For healthy individuals, the groupaveraged index ␥ has two distinct peaks, one at 0.11 Hz [␥ ϭ 0.59 Ϯ 0.09] and another at 0.33 Hz (␥ ϭ 0.55 Ϯ 0.17). In the very low-frequency range (0.02-0.07 Hz), phase difference variability is an inherent property of an intact autoregulation system. Consequently, the average value of the synchronization parameter in this part of the spectrum is equal to 0.13 Ϯ 0.03. The phase difference variability sheds new light on the nature of cerebral hemodynamics, which so far has been predominantly characterized with the help of the high-pass filter model. In this intrinsically stationary approach, based on the transfer function formalism, the efficient autoregulation is associated with the positive phase shift between oscillations of CBFV and ABP. However, the method is applicable only in the part of the spectrum (0.1-0.3 Hz) where the coherence of these signals is high. We point out that synchrony analysis through the use of wavelet transforms is more general and allows us to study nonstationary aspects of cerebral hemodynamics in the very low-frequency range where the physiological significance of autoregulation is most strongly pronounced. cerebral blood flow; transcranial Doppler sonography; wavelets; synchronization THE STATISTICAL PROPERTIES of physiological fluctuations, such as those found in the time series for heartbeat dynamics (10, 28), respiration (1, 27, 40), human locomotion (11, 39), and posture control (4), have been the focus of interdisciplinary research for more than two decades. This research has underscored the significance of nonlinear and nonstationary aspects of intrinsic variability of many physiological phenomena. Such variability seems to indicate the adaptability of the underlying control systems. The change of paradigm, associated with how we view the dynamics of physiologic phenomena, has not, to date, significantly influenced the interpretation of fluctuations in cerebral hemodynamics. In particular, the mathematical analysis of the fluctuations in either intracranial pressure or cerebral blood flow (CBF) velocity (CBFV) in major arteries is largely confined to traditional spectral methods.A healthy human brain is perfused with blood flowing laminarly through cerebral vessels, providing brain tissue with substrates such as oxygen and glucose. It turns out that CBF...

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We introduce a wavelet transfer model to relate spontaneous arterial blood pressure (ABP) fluctuations to intracranial pressure (ICP) fluctuations. We employ a complex continuous wavelet transform to develop a consistent mathematical framework capable of parametrizing both cerebral compensatory reserve and cerebrovascular reactivity. The frequency-dependent gain and phase of the wavelet transfer function are introduced because of the non-stationary character of the ICP and ABP time series. The gain characterizes the dampening of spontaneous ABP fluctuations and is interpreted as a novel measure of cerebrospinal compensatory reserve. For a group of 12 patients who died as a result of cerebral lesions (Glasgow Outcome Scale (GOS) = 1) the average gain in the low-frequency (0.02- 0.07 Hz) range was 0.51 +/- 0.13 and significantly exceeded that of 17 patients with GOS = 2 having an average gain of 0.26 +/- 0.11 with p = 1x10(-4) (Kruskal-Wallis test). A time-averaged synchronization index (which may vary from 0 to 1) defined in terms of the wavelet transfer function phase yields information about the stability of the phase difference of the ABP and ICP signals and is used as a cerebrovascular reactivity index. A low value of synchronization index reflects a normally reactive vascular bed, while a high value indicates pathological entrainment of ABP and ICP fluctuations. Such entrainment is strongly pronounced in patients with fatal outcome (for this group the low-frequency synchronization index was 0.69 +/- 0.17). The gain and synchronization parameters define a cerebral hemodynamic state space (CHS) in which the patients with GOS = 1 are to large extent partitioned away from those with GOS = 2. The concept of CHS elucidates the interplay of vascular and compensatory mechanisms.

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