Revisiting human cerebral blood flow responses to augmented blood pressure oscillations

Abstract

Key points

• Cerebral autoregulation is most effective in buffering against pressure fluctuations slower than 0.03 Hz (∼30 s). This suggests that frequency bands for characterizing cerebral autoregulation should be redefined

• Low cross‐spectral coherence below 0.03 Hz highlights the limitations of transfer function approaches

• Haemodynamic changes induced by lower body pressure could not fully explain the differences in autoregulation estimated from spontaneous vs. augmented fluctuations, and thus, observations of spontaneous fluctuations should not be relied on whenever possible.

Abstract

There is currently little empirical basis for time scales that are considered to be most significant in cerebrovascular counter‐regulation of changes in arterial pressure. Although it is well established that cerebral autoregulation behaves as a ‘high‐pass’ filter, recommended frequency bands have been largely arbitrarily determined. To test effectiveness of cerebral autoregulation, we refined oscillatory lower body pressure (LBP) to augment resting pressure fluctuations below 0.1 Hz by a factor of two in 13 young male volunteers, and thoroughly characterized the time and frequency responses of cerebral autoregulation. We observed that despite a threefold increase in arterial pressure power <0.03 Hz with oscillatory LBP, there was no change in cerebral blood flow power, indicating near perfect counter‐regulation. By contrast, in the range 0.03–0.10 Hz, both cerebral blood flow and arterial pressure power more than doubled. Our data demonstrate that cerebral autoregulation is most effective in buffering against pressure fluctuations slower than 0.03 Hz (∼30 s). This suggests that frequency bands of interest should be redefined and recording length should be increased considerably to account for this. Furthermore, low cross‐spectral coherence below 0.03 Hz, even when pressure fluctuations were augmented, highlights the uncertainty in transfer function approaches and the need to either report precision or use non‐linear approaches. Finally, haemodynamic changes induced by LBP could not fully explain the differences in autoregulation estimated from spontaneous vs. augmented fluctuations, and thus, observations of spontaneous fluctuations should not be relied on whenever possible.

Key points

• Cerebral autoregulation is most effective in buffering against pressure fluctuations slower than 0.03 Hz (∼30 s). This suggests that frequency bands for characterizing cerebral autoregulation should be redefined

• Low cross‐spectral coherence below 0.03 Hz highlights the limitations of transfer function approaches

• Haemodynamic changes induced by lower body pressure could not fully explain the differences in autoregulation estimated from spontaneous vs. augmented fluctuations, and thus, observations of spontaneous fluctuations should not be relied on whenever possible.

Introduction

Cerebral vasculature is unique in its ability to preserve consistent cerebral perfusion (termed ‘cerebral autoregulation’) by responding to changes in arterial pressure. Early analysis of spontaneous variations in arterial pressure and cerebral blood flow at rest suggested that autoregulation possessed the characteristics of a ‘high‐pass’ filter, where it becomes more effective as changes in arterial pressure become slower (Panerai et al. 1998; Zhang et al. 1998). However, because spontaneous pressure fluctuations are inconsistent and small in amplitude (Taylor et al. 1998), it was not possible to determine whether the low correlation between pressure and flow seen at low frequencies (<0.07 Hz) was indicative of autoregulation or simply noise (Giller & Mueller, 2003). To avoid this shortcoming, several methods of enhancing blood pressure (BP) oscillations have been used, from slow fixed‐frequency breathing (Diehl et al. 1995) to repeated squat‐stand manoeuvres (Birch et al. 1995) or thigh cuff deflation (Aaslid et al. 2007). Oscillatory lower body pressure (LBP) is one such method that has proven to reliably and effectively elicit arterial pressure fluctuations to characterize cerebrovascular responses (Hamner et al. 2004; Brothers et al. 2009; Hamner & Tan, 2014; Rickards et al. 2015; Merchant et al. 2017).

Oscillatory LBP produces graded periodic oscillations in venous pooling that are transduced into oscillations in arterial pressure. Thus, it can augment arterial pressure fluctuations in a controlled fashion at a desired frequency. Using oscillatory LBP in this manner confirmed the high‐pass nature of cerebral autoregulation (Panerai, 1998; Hamner et al. 2004). However, traditional application of oscillatory LBP relies on periodic negative pressure fluctuations at a fixed frequency, resulting in two inherent limitations. First, resting arterial pressure fluctuations (as well as those resulting from daily activities) vary across a relatively broad range of frequencies, and fluctuations at a fixed frequency may not be ecologically meaningful. Second, it is generally not possible to elicit arterial pressure fluctuations slower than ∼30  (i.e. <0.03 Hz) because the time course of baroreflex counter‐regulation compensates for the reduction in cardiac filling before the LBP cycle is completed. Our recent implementation of oscillatory LBP (Ishibashi et al. 2012b; Ishibashi et al. 2017; Yoshida et al. 2018) permits the precise control of both positive and negative pressures in a manner that allows for accurate replication and augmentation of the spontaneous fluctuations in arterial pressure observed at rest. Wide‐band augmentation of low frequency arterial pressure variability (as opposed to fluctuations at a fixed frequency) with both positive and negative pressures prevents effective baroreflex counter‐regulation and thus avoids the low frequency limitations inherent in traditional oscillatory LBP.

In the present study, we aimed to assess cerebral blood flow responses to ecologically‐relevant arterial pressure fluctuations, created by accurately amplifying fluctuations observed at rest across the entire frequency range of active autoregulation (0.008–0.1 Hz). We then characterized the cerebrovascular responses to both spontaneous and augmented fluctuations in the time and frequency domains to further understand the nature of cerebrovascular response to pressure fluctuations and to provide methodological insight into its assessment.

Methods

Thirteen healthy young (mean ± SE age 23.8 ± 0.5 years) male volunteers participated in the present study. All volunteers were non‐smokers, with normal weight (body mass index 21.7 ± 0.7 kg m^–2) and were free of cardiovascular and neurological disorders. All volunteers refrained from alcohol, caffeinated beverages, and heavy exercise for at least 24 h prior to study participation. The study was approved by the Research Ethics Committee of the Chiba University Faculty of Engineering (protocol number 27‐17). Written informed consent was obtained from all volunteers, and all protocols conformed with the Declaration of Helsinki.

Measurements

Prior to the study, volunteers emptied their bladder and offered water ad libitum to ensure they were properly hydrated. Subsequently, they were instrumented for impedance cardiography (ICG), arterial BP, end‐tidal CO₂ and cerebral blood flow measurements in a thermoneutral room. Beat‐by‐beat photoplethysmographic arterial pressure was recorded continuously using a Finometer (Finometer PRO; FMS, Amsterdam, The Netherlands), which was calibrated using clinical BP obtained from a built‐in non‐invasive oscillometric BP monitor. ECG and ICG were recorded using a polygraph system (AB‐621 G for ECG, AI‐601 G and ED‐601 G for ICG; Nihon Kohden Corp., Tokyo, Japan). End‐tidal CO₂ was recorded via an infrared carbon dioxide analyser (OLG‐2800; Nihon Kohden Corp.) connected to a nasal cannula. A transcranial Doppler ultrasonograph (2 MHz probe; MultiDop T2; DWL, Singen, Germany) was used to measure cerebral blood flow velocity at the M1 segment of the right or left middle cerebral artery at a depth of 50–65 mm. A probe fixation device (DiaMon; DWL) held the probe in place. After instrumentation, the volunteers were sealed inside a custom‐built LBP chamber in the seated position.

Experimental protocols

Once sealed in the LBP chamber, volunteers were asked to sit quietly for 20 min, during which time their breathing was paced at 0.25 Hz. During paced breathing, volunteers were coached to avoid hypo‐ or hyperventilation. Spontaneous data were acquired continuously throughout the 20 min. Subsequently, the protocols were repeated when the arterial BP fluctuations were augmented.

To create a broadband increase in the magnitude of arterial pressure, we used an electronically controlled custom LBP system with a pressure range of −60.00 to +60.00 mmHg controlled via a 10‐bit DA controller (Ishibashi et al., 2012a; Ishibashi et al. 2012b; Yoshida et al. 2018). The arterial pressure fluctuations observed below 0.1 Hz during the 20 min of seated rest were amplified in the time domain by a factor of two. This was accomplished by taking the Fourier transform of the BP recording at rest and magnifying the amplitude of the power spectral density (i.e. its real part) below 0.1 Hz by 4, at the same time as keeping the phase information (i.e. spectrum's complex part). The spectrum was then inverse Fourier transformed, and the resulting time series was used as input to the LBP chamber's proportional–integral–derivative controller with a maximum pressure change cut‐off of ± 20 mmHg for safety (Fig. 1). The LBP was applied for 20 min. By design, the relationship between the spectra of resting BP fluctuations and input to the LBP chamber and that between the input to and the actual pressure in the LBP chamber were highly coherent below 0.1 Hz (squared coherence 0.79 ± 0.02, mean ± SE; resting BP vs. LBP input, 0.77 ± 0.01 LBP input vs. actual LBP). Haemodynamic data were recorded continuously throughout the 20 min of LBP.

Figure 1.

Data from a representative subject

Data from a representative subject demonstrating how the spectral power of spontaneous fluctuations are used as the input to the proportional–integral–derivative controller of the LBP chamber to augment the arterial pressure fluctuations in the region below 0.1 Hz by a factor of two.

Data analysis

All signals were digitized and stored at 1000 Hz for offline analysis. Data were analysed using custom software written in Matlab (R2017b; MathWorks Inc., Natick, MA, USA) and R, version 3.4.3 (R Foundation for Statistical Computing, Vienna, Austria). The basal thoracic impedance (Z ₀), the delta impedance waveform (ΔZ) and its first derivative (dZ/dt) were calculated from the ICG signal. Changes in Z ₀ is inversely related to those in central blood volume (R ² = 0.99) (Ebert et al. 1986). Blood resistivity was assumed constant at 135 cm Ω. Stroke volume (SV) was estimated by Kubicek's method using the dZ/dt signal (Kubicek et al. 1966) after eliminating the noise of the dZ/dt signals by an adaptive filter that can select the components that are synchronous with the R–R interval of the ECG (Barros et al. 1995). The beat‐by‐beat heart rate was calculated from the R–R interval sequences of the ECG, and cardiac output was calculated as the product of stroke volume and heart rate. Beat‐by‐beat mean BP, cerebral blood flow velocity and breath‐by‐breath end‐tidal CO₂ were calculated from continuous waveforms and interpolated to 5 Hz. To assess cerebral autoregulation, the 1000 Hz waveforms of arterial pressure and cerebral blood flow were decimated to 5 Hz and low pass filtered with a cut‐off of 0.4 Hz. The mean waveforms, as well as breath‐by‐breath CO₂, heart rate and stoke volume via impedance cardiography, were subsequently averaged to provide overall means for each condition.

We used two approaches to assess cerebral autoregulation: linear transfer function analysis (Zhang et al. 1998; Hamner et al. 2004) and projection pursuit regression (Tan, 2012), which was shown to be able to capture the non‐linear pressure–flow relationship accurately and reliably.

Transfer function

Power spectral density estimates were calculated via Welch's average modified periodogram method (Welch, 1967). The filtered time series was divided into five segments of equal length (240 s) that overlapped by 50%. This windowing was chosen to optimize the trade‐off between frequency resolution and variance of the estimates in a statistical sense. The signal in each segment was linearly detrended, smoothed via a Hamming window and then fast‐Fourier transformed, and the power spectral density estimates were averaged across all windows. The product of the pressure signal with the complex conjugate of the cerebral blood flow velocity signals provides the cross‐spectrum from which coherence and transfer functions were derived.

Projection pursuit regression

Projection pursuit regression was used to identify a single non‐linear non‐parametric ridge function between arterial pressure and cerebral blood flow and has been described in detail previously (Tan, 2012). Briefly, the 5 Hz mean waveforms, described above, were bandpass filtered (0.01–0.06 Hz, centered at 0.03 Hz) before the pressure–cerebral blood flow relationship was estimated for each subject and condition. The pressure–flow relationship estimated via projection pursuit regression provided a ‘ridge’ function for each subject and condition, which was then parameterized by a piecewise linear function to provide four parameters: cerebral blood flow responses to decreases in arterial pressure (falling slope), those to increases in arterial pressure (rising slope), the pressure range within which autoregulation is most active (autoregulatory range) and the effectiveness of cerebral vasculature to buffer against pressure changes within the autoregulatory range (autoregulatory slope). For each range, a lower slope indicates more effective buffering of arterial pressure fluctuations.

Statistical analysis

Group‐level differences in haemodynamic variables between conditions (spontaneous vs. augmented) were compared via repeated measures ANOVA. We used a linear mixed‐effect model with a stepwise forward–backward selection approach to examine haemodynamic factors other than the BP that might contribute to any observed differences in autoregulatory measures obtained from spontaneous and augmented fluctuations. Accordingly, data were pooled across individuals and conditions (spontaneous vs. augmented). Each measure of cerebral autoregulation was used separately as the dependent variable, and haemodynamic variables were used as independent variables, with subject ID as the random effect term. We report the marginal R ², which is associated with the fixed effects of the model and expresses the variance explained only by the independent predictors as opposed to the variance explained by the repeated measures term.

For all statistical analyses, all variables were inspected for normality using Q–Q plots and, whenever required, they were transformed. We used inverse hyperbolic tangent transformation for coherence, logarithmic transformation for spectral powers and Box‐Cox transformation for all other variables, as required. However, for ease of interpretation, values are reported as the mean ± SE.

Results

Although mean BP did not change (P = 0.98) during LBP, both end‐tidal CO₂ and mean cerebral blood flow decreased (P < 0.01) (Table 1). When comparing end‐tidal CO₂ in the first and last minute of each session, there was a significant effect of both time (P < 0.01) and augmentation (P < 0.05) but no interaction (P = 0.35); this reflected the expected time‐effect of paced breathing, and reduction consequent to LBP (spontaneous: –2.00 ± 0.77 mmHg vs. augmented: –2.96 ± 0.86 mmHg). R–R interval increased (P < 0.01) and stroke volume tended to increase (P = 0.07). As a result, there was no change in cardiac output during LBP (P = 0.60). Power spectral densities and transfer function measures were averaged across frequency bands, selected post hoc based upon the range where pressure fluctuations were augmented (<0.1 Hz), as well as the nature of the observed cerebral blood flow response. In the low frequency (LF) (0.03 Hz–0.1 Hz) band, the magnitude of cerebral blood flow fluctuations roughly tracked the augmentation in pressure fluctuations, whereas, in the very low frequency (VLF) (0.008–0.03 Hz) band, there was no overall increase in the magnitude of cerebral blood flow fluctuations (Fig. 2 and Table 2). Note that these frequency band definitions differ from those commonly used in the literature (Claassen et al. 2016) and were chosen to delineate between the observed clear and active autoregulation below 0.03 Hz and a more pressure‐passive response above. The magnitude of fluctuations in arterial BP (i.e., its spectral density) increased significantly in the VLF (P < 0.01) and LF (P < 0.01) frequency bands (Fig. 2 and Table 2). As expected from how the frequency bands were defined, LF cerebral blood flow fluctuations increased significantly (P < 0.01), whereas VLF oscillations were not different (P = 0.30). Indeed, VLF cerebral blood flow fluctuations did not increase despite an almost three‐fold increase in the magnitude of arterial pressure fluctuations (Table 2), demonstrating active and efficient counter‐regulation. Consequently, VLF transfer function gain was almost twice as effective (spontaneous: 0.39 ± 0.05 vs. augmented: 0.23 ± 0.02, P < 0.01) as that derived from spontaneous fluctuations, despite the lack of difference in coherence or phase (Fig. 3 and Table 2). By contrast, there was little evidence of active autoregulation in LF band, wherein gain and phase did not change in response to augmented pressure fluctuations, indicating that the magnitude of cerebral blood flow fluctuations was augmented as that of arterial pressure increased. Indeed, increased coherence (spontaneous: 0.70 ± 0.02 vs. augmented: 0.75 ± 0.02, P < 0.01) indicates less effective autoregulation. In the time domain, augmented pressure fluctuations led to an increase in the PPR range of autoregulation, as well as decrease in the falling slope, without any significant change in estimated effectiveness of cerebral autoregulation (i.e. autoregulatory slope) (Fig. 4 and Table 2). This indicates that, although the relationship between arterial pressure and cerebral blood flow fluctuations estimated from spontaneous fluctuations reflects that estimated from augmented fluctuations, the former severely underestimates the region within which cerebral autoregulation is active.

Table 1.

Haemodynamic variables during rest and with BP oscillations augmented via lower body pressure

	Spontaneous	Augmented	P value
Mean blood pressure (mmHg)	88.8 ± 1.56	88.7 ± 2.07	0.98
Cerebral blood flow (cm s−1)	52.9 ± 3.25	49.3 ± 3.05	<0.01
Stroke volume (mL)	73.3 ± 3.14	75.3 ± 3.23	0.07
RR interval (ms)	815 ± 26	845 ± 25	<0.01
Cardiac output (L min−1)	5.42 ± 0.22	5.37 ± 0.23	0.60
End‐tidal CO2 (mmHg)	36.8 ± 1.30	34.3 ± 1.40	<0.01

Values are the mean ± SE.

Figure 2.

Average power spectral densities

Shaded bands show the group SEs.

Table 2.

Measures of cerebral autoregulation assessed from spontaneous (rest) and augmented (LBP) BP oscillations

		Spontaneous	Augmented	P value
Very low frequency (0.008–0.03 Hz)	MBP PSD (mmHg2 Hz−1)	356.8 ± 74.24	1044.1 ± 155.1	<0.01
	CBF PSD (cm2 s−2 Hz−1)	108.1 ± 16.5	129.0 ± 24.7	0.30
	Coherence	0.42 ± 0.04	0.42 ± 0.04	0.81
	Gain	0.39 ± 0.05	0.23 ± 0.03	<0.01
	Phase (°)	56.2 ± 7.7	66.7 ± 7.1	0.48
Low frequency (0.03–0.10 Hz)	MBP PSD (mmHg2 Hz−1)	167.9 ± 22.3	404.8 ± 49.7	<0.01
	CBF PSD (cm2 s−2 Hz−1)	65.8 ± 9.2	139.5 ± 24.7	<0.01
	Coherence	0.70 ± 0.02	0.75 ± 0.02	<0.01
	Gain	0.54 ± 0.04	0.54 ± 0.04	0.88
	Phase (°)	60.7 ± 3.7	61.2 ± 3.4	0.86
Projection pursuit regression	Falling slope	0.69 ± 0.08	0.33 ± 0.06	<0.01
	Autoregulatory slope	0.20 ± 0.04	0.16 ± 0.03	0.33
	Rising slope	0.66 ± 0.04	0.73 ± 0.07	0.41
	Range	7.07 ± 0.60	13.15 ± 1.14	<0.01

Values are the mean ± SE. MBP PSD, Mean Blood Pressure Power Spectral Density; CBF PSD, Cerebral Blood Flow Power Spectral Density.

Figure 3.

Transfer function estimates

Transfer function estimates based on both spontaneous and augmented fluctuations. Shaded bands show the group SEs.

Figure 4.

Pressure–flow relationship

Pressure–flow relationship estimated via projection pursuit. Breaks in the relationships, from left to right respectively, delineate the regions for falling slope, the autoregulatory range and slope, and the rising slope. Shaded bands show the group SEs.

To determine whether the observed differences in VLF gain, LF coherence, autoregulatory range and falling slope could be explained by the haemodynamic changes induced by LBP (Table 1), a stepwise linear mixed effects model was fit to the data. End‐tidal CO₂ and VLF arterial pressure power were significant contributors to VLF gain but explained less than 26% of the variance (marginal, or fixed effects, R ² = 0.26) (Table 3). Over half of the variation in differences in LF coherence were explained by changes in end‐tidal CO₂, LF arterial pressure power, as well as mean RR interval and arterial pressure (marginal R ² = 0.55) with LBP. The increase in autoregulatory range with augmented pressure fluctuations was largely explained by VLF arterial pressure power alone (marginal R ² = 0.67). By contrast, cardiac output, arterial pressure and end‐tidal CO₂ all significantly contributed to the change in falling slope at the same time as explaining 53% of the variation.

Table 3.

Linear mixed effect model of observed differences between spontaneous and augmented cerebral autoregulatory indices

	Dependent variable
Independent variable	VLF gain	LF coherence	Falling slope	Autoregulatory range
End‐tidal CO2	0.012†	0.007†	0.019‡	–
	(0.006)	(0.002)	(0.010)
ABP power	–0.0001‡	0.0002*	–0.0004*	0.007*
	(0.0001)	(0.00003)	(0.0001)	(0.001)
RR interval	–	0.0004*	–	–
		(0.0001)
Cardiac output	–	–	0.183*	–
			(0.067)
ABP	–	–0.001	–0.016†	–
		(0.002)	(0.008)
Observations	26	26	26	26
Log likelihood	–0.825	17.524	–15.733	–66.331
Marginal R 2	0.26	0.55	0.53	0.67

Numbers in parentheses are the SE of the regression coefficients.

ABP power denotes arterial blood pressure spectral power within the LF range for LF coherence, and within the VLF range for other dependent variables. Significant coefficients are denoted as: ^* P < 0.01; ^† P < 0.05; ^‡ P < 0.1

There were no significant correlations between any spontaneous measure and autoregulatory range or falling slope. However, augmented VLF gain was significantly correlated (r = 0.75, P < 0.01) with spontaneous VLF coherence; lower spontaneous VLF coherence predicted a lower VLF gain when arterial pressure oscillations were augmented by LBP.

Discussion

Our data show that cerebral autoregulation is primarily effective in buffering arterial pressure fluctuations slower than ∼0.03 Hz. Despite a three‐fold increase in arterial pressure power in the VLF band (0.008–0.03 Hz), we saw no change in cerebral blood flow power, indicating near perfect counter‐regulation (Fig. 2 and Table 2). By contrast, although there is evidence of some autoregulation (gain ∼0.5) and high‐pass filter characteristics in the LF band (0.03–0.10 Hz), cerebral blood flow oscillations more than doubled, demonstrating that the counter‐regulation was not nearly as effective. This finding suggests that the current recommendation for transfer function frequency bands (VLF: 0.02 Hz–0.07 Hz; LF: 0.07–0.2 Hz) to characterize cerebral autoregulation needs to be reassessed (Claassen et al. 2016).

One of the fundamental dilemmas of using transfer function analysis to identify and characterize cerebral autoregulation is that there may not be any apparent relationship between arterial pressure and cerebral flow if counter‐regulation is effective. However, the lower the cross‐spectral coherence, the less reliable transfer function estimates of gain and phase become. To avoid this problem, it is common to define frequency bands where coherence remains statistically different from zero, and thus provides reasonable confidence in gain and phase estimates. Unfortunately, our data suggest that doing so may move the focus away from the frequency range where autoregulation is most active. However, as the CARNet white paper notes (Claassen et al. 2016), the selection of frequency bands was not empirical as there is not ‘enough [evidence] available to justify choice of particular frequency bands for averaging values of coherence, gain, and phase’ and that their ‘recommendation aims to improve standardization’. Although it is important to be able to compare results across laboratories, the lack of evidence for these bands means that important findings could have been missed in the pursuit of consistency. For example, Claassen et al. (2009) used repeated squat–stand manoeuvres that demonstrated a finding similar to our own, although they ultimately reported no differences because they averaged across ‘standardized’ frequency bands. Indeed, there have been several calls in the recent literature for validation of these frequency bands so that artefactual truncation of spectral information can be avoided (Tzeng et al. 2012; Saleem et al., 2016; Tzeng & Panerai, 2018). The present study provides empirical evidence that the frequency band within which cerebral autoregulation is most active lies below ∼0.03 Hz.

This difference in the effectiveness of autoregulation below 0.03 Hz and within the 0.03–0.10 Hz band may reflect the classic conceit of ‘static’ and ‘dynamic’ autoregulation, where autoregulation is suggested to operate on two distinct timescales, possibly mediated by different mechanisms. The postulation of two different types of autoregulation appeared to be a convenient way to reconcile data obtained by ‘static’ vs. ‘dynamic’ methods (i.e. thermodilution vs. transcranial doppler), although our data show a clear distinction in the frequency domain centered around 0.03 Hz. This is consistent with recent work showing that static and dynamic indices are not correlated in healthy older adults (de Jong et al. 2017), suggesting that they could indeed be different reflexes. Our prior work showed an effect of calcium channel blockade at 0.03 Hz oscillatory LBNP, although not at higher frequencies (Tan et al. 2013), whereas sympathetic and cholinergic blockade had profound effects within the 0.06–0.10 Hz band (Hamner et al. 2010; Hamner et al. 2012). Therefore, as frequently theorized, myogenic factors could be largely responsible for autoregulation below 0.03 Hz, whereas neurogenic factors are responsible above this frequency.

Nonetheless, our findings have important methodological implications for transfer function analysis of cerebral autoregulation. Although 5 min resting recordings are de rigueur for spectral analysis, this is insufficient to analyse fluctuations below 0.03 Hz. In addition, coherence in the 0.008–0.03 Hz band remained low (spontaneous: 0.42 ± 0.04 vs. augmented: 0.42 ± 0.04) (Table 2), even in the presence of a substantial increase in the amplitude of arterial pressure fluctuations. This low coherence highlights the inherent uncertainty of transfer function gain and phase estimates to characterize autoregulation. This may be the factor underlying the apparent variability in reported transfer function parameters (Tzeng et al. 2012; Meel‐van den Abeelen et al. 2014; Claassen et al. 2016) and further highlights the importance of reporting the precision of the linear transfer function estimates (Gommer et al. 2010; Hamner et al. 2010; Tan & Taylor, 2014). Therefore, although cross‐spectral coherence <0.03 Hz may provide a good indication of whether cerebral autoregulation is intact or not, spectral gain and phase estimates in this band are always unreliable. An obvious alternative is to utilize non‐linear methods. Indeed, we have observed that projection pursuit regression was able to capture the effectiveness of cerebral autoregulation reliably, regardless of the magnitude of arterial pressure fluctuations. However, although there were no differences in effectiveness of autoregulation and the rising slope (i.e. cerebrovascular responses to increases in arterial pressure), we observed that the falling slope (i.e. cerebrovascular responses to decreases in arterial pressure) was significantly lower when the magnitude of pressure fluctuations were augmented. That falling and rising slope responded differently to augmentation of pressure fluctuations supports the idea of directionality, or hysteresis, in cerebral autoregulation (Panerai et al. 2018). It is also consistent with our prior observation that cerebrovascular responses to arterial pressure fluctuations become more apparent when reductions in central volume are more pronounced, partly as a result of changes in CO₂ (Yoshida et al. 2018). Moreover, prior data from both our laboratory (Yoshida et al. 2018) and other studies (Jeong et al. 2016) suggest that hypercapnia diminishes the ability of cerebral vasculature to respond to changes in arterial pressure and, conversely, hypocapnia may enhance cerebrovascular responses. Indeed, over half of the variation in the difference in the increase in falling slope was explained by LBP‐related changes in systemic haemodynamic variables (R ² = 0.53) (Table 3). The available literature supports an effect of CO₂ on autoregulation (Panerai et al. 1999; Maggio et al. 2013; Liu et al. 2014; Minhas et al. 2016). This is consistent with the apparent effect of CO₂ on falling slope. However, whether this effect is the result of a direct mechanistic link between autoregulation and CO₂ or indirectly a result of the effect of the latter on vascular tone remains to be established. In addition to decreased falling slope, autoregulatory range (i.e. the range of BPs within which autoregulation is active) was increased when arterial pressure fluctuations were augmented. However, two‐thirds of this difference was explained by the magnitude of pressure fluctuations alone (R ² = 0.67) (Table 3). This is consistent with the prior observations (Taylor et al. 1998; Hamner et al. 2004) indicating that the magnitude of spontaneous fluctuations may not always be sufficient to reliably engage physiological mechanisms counter‐regulating these fluctuations.

Whether or not spontaneous fluctuations are sufficient in amplitude to engage autoregulation has important implications in the debate on how best to assess autoregulation. Recently, Tzeng & Panerai (2018) contended that the relationship between spontaneous fluctuations in arterial pressure and cerebral blood flow ‘should’ be relied on whenever possible. By contrast, Simpson & Claassen (2018) argued that one needs to perturb the system via external stimuli to quantify the counter‐regulatory response. Those favouring spontaneous relationships often state that the mere act of perturbing the system can change it, rendering any estimated relations suspect. However, most stimuli faced by the human cerebral circulation are much greater in magnitude than those seen during quiet rest. We found that VLF gain, LF coherence, autoregulatory range and falling slope were all significantly altered when arterial pressure fluctuations were augmented. Although haemodynamic changes induced by LBP in end‐tidal CO₂, RR interval, cardiac output and mean arterial pressure explain some amount of the differences in LF coherence and falling slope; only the amplitude of arterial pressure fluctuations had any explanatory power for VLF gain and autoregulatory range (Table 3). This strongly suggests that it is not the system that has been changed by LBP but, instead, that spontaneous fluctuations are insufficient in amplitude to fully engage autoregulation. Unfortunately, inducing changes in arterial pressure via LBP is not always practical and clinical populations may not be able to safely tolerate large swings in arterial pressure. Alternative approaches may be used when LBP is not feasible (Ozturk & Tan, 2018) and any measure with predictive power, even based on spontaneous observations, can have clinical utility (Tzeng & Panerai, 2018). For example, both our laboratory (Otite et al. 2014; Santos et al. 2016; Brooks et al. 2018) and others (Immink et al. 2005; Sorrentino et al. 2011; Ma et al. 2016) have shown that spontaneous measures of cerebral autoregulation can discriminate pathophysiological impairments in cerebral autoregulation both at the population and individual level. However, the distinction between the clinical utility of a measure vs. determination of the physiology is a crucial one. Our results show that it is important to perturb the system to fully engage autoregulation, and the relationship between spontaneous fluctuations in arterial pressure and cerebral blood flow should not be relied on when the aim is to characterize the underlying physiology.

Limitations

All measurements were made in the seated position. The increased sympathetic activity and decreased venous return in the seated position may engage active cerebral autoregulation more than supine rest. Indeed, recent work has shown increased transfer function coherence and reduced gain (0.02–0.07 Hz) when comparing seated to supine positions as a result of increased arterial pressure variability in the upright posture (Garrett et al. 2017). This suggests that spontaneous relations from the supine position may be more dissimilar from augmented relationships than reported in the present study. Although sympathetic activity plays a significant role in cerebral autoregulation (Hamner et al. 2010; Hamner & Tan, 2014), we cannot speak definitely to whether or not sustained elevation in sympathetic outflow in seated position has any impact on our results.

Conclusions

Our findings indicate that cerebral autoregulation is most effective in buffering against pressure fluctuations slower than 0.03 Hz (∼30 s). Frequency bands of interest and minimum recording length should take this into account. Moreover, the low cross‐spectral coherence below 0.03 Hz highlights the uncertainty in transfer function approaches and underlines the necessity to either report the precision of estimates or to use non‐linear approaches. Lastly, the differences between measures of autoregulation estimated from spontaneous vs. augmented pressure fluctuations cannot be fully explained by haemodynamic changes induced by external perturbation, and thus, observations of spontaneous fluctuations should not be relied on whenever possible.

Additional information

Competing interests

The authors declare that they have no competing interests.

Author contributions

COT and KI conceived and designed the work, and acquired the data. COT and JWH analysed the data. All authors interpreted the data for the work. COT and JWH drafted the manuscript, and all authors revised it critically for important intellectual content. All authors approved the final version of the manuscript submitted for publication, and agree to be accountable for all asects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. All persons designated as authors qualify for authorship, and all those who qualify for authorship are listed.

Funding

No funding was received for the present study.

Biography

Jason W. Hamner is a biomedical engineer working in the Cardiovascular and Cerebrovascular Research Laboratories in the Department of Physical Medicine and Rehabilitation at Spaulding Hospital Cambridge. He has expertise in signal processing and data analysis, with a particular focus on cardiovascular and cerebrovascular haemodynamic control and autonomic neuroscience.