Nonlinear modeling of the dynamic effects of arterial pressure and CO2 variations on cerebral blood flow in healthy humans

Dynamic cerebral autoregulation during brain activation paradigms

Dynamic cerebral autoregulation (CA) describes the transient response of cerebral blood flow (CBF) to rapid changes in arterial blood pressure (ABP). We tested the hypothesis that the efficiency of dynamic CA is increased by brain activation paradigms designed to induce hemispheric lateralization. CBF velocity [CBFV; bilateral, middle cerebral artery (MCA)], ABP, ECG, and end-tidal Pco2 were continuously recorded in 14 right-handed healthy subjects (21–43 yr of age), in the seated position, at rest and during 10 repeated presentations (30 s on-off) of a word generation test and a constructional puzzle. Nonstationarities were not found during rest or activation. Transfer function analysis of the ABP-CBFV (i.e., input-output) relation was performed for the 10 separate 51.2-s segments of data during activation and compared with baseline data. During activation, the coherence function below 0.05 Hz was significantly increased for the right MCA recordings for the puzzle tasks compared with baseline values (0.36 ± 0.16 vs. 0.26 ± 0.13, P < 0.05) and for the left MCA recordings for the word paradigm (0.48 ± 0.23 vs. 0.29 ± 0.16, P < 0.05). In the same frequency range, significant increases in gain were observed during the puzzle paradigm for the right (0.69 ± 0.37 vs. 0.46 ± 0.32 cm·s−1·mmHg−1, P < 0.05) and left (0.61 ± 0.29 vs. 0.45 ± 0.24 cm·s−1·mmHg−1, P < 0.05) hemispheres and during the word tasks for the left hemisphere (0.66 ± 0.31 vs. 0.39 ± 0.15 cm·s−1·mmHg−1, P < 0.01). Significant reductions in phase were observed during activation with the puzzle task for the right (−0.04 ± 1.01 vs. 0.80 ± 0.86 rad, P < 0.01) and left (0.11 ± 0.81 vs. 0.57 ± 0.51 rad, P < 0.05) hemispheres and with the word paradigm for the right hemisphere (0.05 ± 0.87 vs. 0.64 ± 0.59 rad, P < 0.05). Brain activation also led to changes in the temporal pattern of the CBFV step response. We conclude that transfer function analysis suggests important changes in dynamic CA during mental activation tasks.

Phase dynamics in cerebral autoregulation

Complex continuous wavelet transforms are used to study the dynamics of instantaneous phase difference delta phi 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 gamma = (sin delta phi)2 + (cos delta phi)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 group-averaged index gamma has two distinct peaks, one at 0.11 Hz [gamma = 0.59 +/- 0.09] and another at 0.33 Hz (gamma = 0.55 +/- 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 +/- 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.