Time-domain methods for quantifying dynamic cerebral blood flow autoregulation: Review and recommendations. A white paper from the Cerebrovascular Research Network (CARNet)

Abstract

Cerebral Autoregulation (CA) is an important physiological mechanism stabilizing cerebral blood flow (CBF) in response to changes in cerebral perfusion pressure (CPP). By maintaining an adequate, relatively constant supply of blood flow, CA plays a critical role in brain function. Quantifying CA under different physiological and pathological states is crucial for understanding its implications. This knowledge may serve as a foundation for informed clinical decision-making, particularly in cases where CA may become impaired. The quantification of CA functionality typically involves constructing models that capture the relationship between CPP (or arterial blood pressure) and experimental measures of CBF. Besides describing normal CA function, these models provide a means to detect possible deviations from the latter. In this context, a recent white paper from the Cerebrovascular Research Network focused on Transfer Function Analysis (TFA), which obtains frequency domain estimates of dynamic CA. In the present paper, we consider the use of time-domain techniques as an alternative approach. Due to their increased flexibility, time-domain methods enable the mitigation of measurement/physiological noise and the incorporation of nonlinearities and time variations in CA dynamics. Here, we provide practical recommendations and guidelines to support researchers and clinicians in effectively utilizing these techniques to study CA.

Keywords: CARNet; cerebral autoregulation; cerebral blood flow; time-domain methods; white paper.

Figure 1.

Overview of time-domain approaches for evaluating dCA.

Figure 2.

Example of a three-hour monitoring period of autoregulation in patients suffering from traumatic brain injury. ABP and CPP are shown in the upper panel, whereas ICP in the second horizontal panel. CBv in the left MCA (fourth horizontal panel), measured with TCD, was overall stable (defined as FVl). dCA was monitored using Mx (bottom panel) and PRx (third horizontal panel), which are represented using a color code where green and red indicate normal and altered pressure reactivity, respectively. The graph shows that in spite of the low ICP, CA is continuously fluctuating.

Figure 3.

ARX vs ARMAX analysis for a representative set of 5 min experimental resting MAP-CBv recordings resampled at 1 Hz. (a) The estimated impulse responses in the time and (b) the frequency domain (blue ARX; red ARMAX). The top and bottom subplots of (b) depict the gain (cm/s/mmHg) and phase as a function of frequency. We applied a 2-fold cross-validation scheme, whereby the first 50% of the data is used for training and the rest 50% for testing and vice versa. The minimum NMSE was achieved using ARX model orders with ( $n_a$ , $n_b)=(2\text{,}4)$ and ARMAX models orders with ( $n_a$ , $n_b,n_c)=(2,3,2)$ .

Figure 4.

(a) Raw tracings of BP, cerebral blood velocity (CBv) (monitored in the middle cerebral artery), and PCO₂ at 0.05-Hz and 0.10-Hz repeated squat-stands. (b) schematic tracings of MAP and CBv during a repeated squat-stand performed at 0.05 Hz. Enlarged regions depict how the variables were used to calculate ΔCBv_T/ΔMAP_T. Blue color indicates variables used to calculate ΔCBv_T/ΔMAP_T during acute decreases in MAP. Red color indicates variables used to calculate ΔCBv_T/ΔMAP_T during acute increases in MAP. ΔMAP_T, absolute change in MAP; ΔCBv_T, absolute change in CBv; MAP_max, maximum MAP; MAP_min, minimum MAP; CBv_max, maximum CBv; CBv_min, minimum CBv; Time_MAPmax, time at maximum MAP; Time_MAPmin, time at minimum MAP; Time_CBvmax, time at maximum CBv; Time_CBvmin, time at minimum CBv; ΔMAP, absolute change in MAP from minimum to maximum or from maximum to minimum; ΔCBv, absolute change in CBv from minimum to maximum or from maximum to minimum; ΔTime_MAP , time interval between minimum to maximum or between maximum to minimum MAP; ΔTime_CBv, time interval between minimum to maximum or between maximum to minimum CBv. Modified with permission of P. Brassard from.

Figure 5.

Two-input, single-output system. $h_x\left(m\right)$ is the impulse response that describes dCA as the dynamic relationship between MAP and CBv, whereas $h_z\left(m\right)$ describes the dynamic relationship between PETCO₂ and CBv. dCA can be assessed based on the characteristics of $h_x\left(m\right)$ . The inclusion of PETCO₂ as a second input provides a less biased estimate of $h_x\left(m\right)$ , since the effects of PETCO₂ on CBv are accounted for by $h_z\left(m\right)$ .

Figure 6.

Average estimated impulse response function between (a) MAP (input) and CBv (output) and (b) PETCO₂ (input) and CBv (output) obtained via the LET for a group of healthy elderly adults. Modified with permission from under the Creative Commons CC-BY license.

Figure 7.

(a) Time-varying cross-correlation coefficient between PETCO₂ (breath-to-breath data) and CBv (both sampled at 1 Hz) obtained during 40 min of spontaneous fluctuations, estimated using overlapping sliding windows of 160s. The x-axis represents time in seconds and the y-axis the lags of the cross-correlation function. Peaks (yellow) at negative lags indicate delayed CBv response compared to the PETCO₂ signal. The pure time delay corresponding to the effects of PETCO₂ on CBv range between 3 to 15s and (b) Power spectral density (in dB) of the corresponding MAP (blue), PETCO₂ (red) and CBv (green) signals.

Figure 8.

(a) The mean PETCO₂, CBv and phase lead (PL) at 1/12 Hz from 11 subjects during an hypercapnic step. In the bottom subplot the solid line shows mean phase lead and the dashed-dotted line is the standard deviation. To track variations, the RLS algorithm was used. During hypercapnia, the phase lead decreases indicating decrease in autoregulatory function. On return to normocapnia, a more rapid change in autoregulation is observed. Used with permission of J. Liu from; permission conveyed through Copyright Clearance Center, Inc and (b) Time-varying MAP and PETCO₂ first-order kernels from a representative subject suffering from vasovagal syncope during a head-up tilt protocol. The blue dashed vertical lines define the onset of the tilting phase. The red vertical dashed lines denote the time of syncope occurrence, and the green dashed lines denote the time point when MAP reached its minimum value. Used with permission of Elsevier and K. Kostoglou from.

Figure 9.

Screen copy of our MMPF analysis software. The data shown in this plot are from a healthy subject. The top three panels on the left show CBv (left side and right side) and ABP signals, respectively. The colored curves in these panels show the results after removing faster fluctuations from the original signals. The bottom left panel shows the corresponding intrinsic modes for these three signals (red: ABP; blue: CBv on right side; green: CBv on left side). The vertical red dashed box (around 40–50 s) identifies the Valsalva maneuver. The spontaneous oscillations in these signals during resting conditions prior to the Valsalva maneuver can also be visualized. One of these oscillations (around 14–22 s) is identified by two vertical red lines. The result of the ABP–CBv phase shift analysis of this period is plotted in the right panel. A reference line (dotted black line), indicating synchronization between ABP and CBv, is shown in this panel for easy comparison. The result is representative of normal autoregulation where CBv leads ABP (by about 50 degrees in phase). Modified with permission from under the Creative Commons CC-BY license.