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Am J Physiol Regul Integr Comp Physiol 283: R653-R662, 2002. First published April 4, 2002; doi:10.1152/ajpregu.00452.2001
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Vol. 283, Issue 3, R653-R662, September 2002

Dynamic modulation of cerebrovascular resistance as an index of autoregulation under tilt and controlled PETCO2

Michael R. Edwards1, J. Kevin Shoemaker2, and Richard L. Hughson1

1 Cardiorespiratory and Vascular Dynamics Laboratory, Faculty of Applied Health Sciences, University of Waterloo, Waterloo N2L 3G1; and 2 Neurovascular Research Laboratory, School of Kinesiology, University of Western Ontario, London, Ontario, Canada N6A 3K7


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Transfer function analysis of the arterial blood pressure (BP)-mean flow velocity (MFV) relationship describes an aspect of cerebrovascular autoregulation. We hypothesized that the transfer function relating BP to cerebrovascular resistance (CVRi) would be sensitive to low-frequency changes in autoregulation induced by head-up tilt (HUT) and altered arterial PCO2. Nine subjects were studied in supine and HUT positions with end-tidal PCO2 (PETCO2) kept constant at normal levels: +5 and -5 mmHg. The BP-MFV relationship had low coherence at low frequencies, and there were significant effects of HUT on gain only at high frequencies and of PCO2 on phase only at low frequencies. BP right-arrow CVRi had coherence >0.5 from very low to low frequencies. There was a significant reduction of gain with increased PCO2 in the very low and low frequencies and with HUT at the low frequency. Phase was affected by PCO2 in the very low frequencies. Transfer function analysis of BP right-arrow CVRi provides direct evidence of altered cerebrovascular autoregulation under HUT and higher levels of PCO2.

transfer function analysis; Doppler ultrasound; brain blood flow; orthostasis


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

CEREBROVASCULAR AUTOREGULATION describes the process that maintains cerebral blood flow close to a desired set point, even though the arterial blood pressure is fluctuating from the mean or normal value. Cerebral blood flow can remain relatively constant across a range of arterial blood pressure from 60 to 150 mmHg (25). Recent technological developments have permitted exploration of the dynamic nature of cerebrovascular autoregulation. Cerebral blood flow is estimated from transcranial Doppler ultrasound measurement of the mean flow velocity (MFV) in the middle cerebral artery (MCA), while noninvasive blood pressure devices provide an estimate of the arterial blood pressure at the level of the MCA (BPMCA). Thus cerebrovascular autoregulation has been characterized by frequency domain analysis of the interrelationships between MFV and BPMCA (2, 4, 8, 11-13, 15, 34, 38). The beat-by-beat values of MFV and BPMCA are processed by cross-spectral analysis to yield amplitude and phase relationships of the transfer function with BPMCA as the input and MFV as the output. With the cross-spectral approach, there is often little or no coherence between BPMCA and MFV in the very-low (<0.07 Hz)-frequency (VLF) regions (4, 38), yet it is especially in this region where changes in BPMCA have little effect on the MFV. At higher frequencies, greater amplitude of change in MFV for a given change in BPMCA indicates the high-pass filter characteristic of the cerebrovascular system. Interestingly, changes in MFV are observed to precede changes in BPMCA (2, 4, 12, 13, 15, 38). Many researchers have explicitly stated that a greater phase lead of MFV before BPMCA is an indication of better autoregulation (2, 4, 12). Recently, this phase lead was suggested as evidence that the autonomic nervous system actively regulates cerebral blood flow in advance of changes in arterial blood pressure (7, 8), but this is inconsistent with the notion of autoregulation (15, 23). Thus there is a need to define an index of dynamic cerebral autoregulation that can accurately reflect the changes in the cerebrovasculature that allow cerebral blood flow to be maintained within the limits defined by the concept of cerebrovascular autoregulation.

Aaslid and colleagues (1, 36) evaluated cerebrovascular autoregulation by determining the rapidity of the response to a reduction in BPMCA by the sudden release of cuffs placed around the upper thighs. They calculated a dynamic index of cerebrovascular resistance (CVRi) from BPMCA/MFV and observed the changes in this variable as a function of the decrease in BPMCA as the cuffs were deflated after 3 min of circulatory occlusion of the legs. The CVRi has been frequently evaluated from steady-state data in supine and head-up tilt (HUT) postures (17, 29) to reflect cerebrovascular autoregulation. In this study, we explored the utility of CVRi as a beat-by-beat variable that can be related to changes in BPMCA so that a dynamic indicator of cerebrovascular autoregulation (15) can be studied under conditions of altered arterial PCO2.

In everyday life, the cerebrovascular system must adapt rapidly to the reduction in BPMCA that occurs on going from a supine to an upright posture. Coincident with the transition to an upright posture in many individuals is a reduction in arterial PCO2 (3, 21). Because a decrease in arterial PCO2 would increase CVRi (20) and modify autoregulation (1, 21, 33), we have controlled the end-tidal PCO2 (PETCO2) to maintain constant arterial PCO2 at hypo-, normo-, and hypercapnic levels in the supine to the tilt posture. We hypothesized that, consistent with the dynamic nature of cerebrovascular autoregulation, changes in CVRi would effectively follow the spontaneous modulation of BPMCA, especially in the lower-frequency ranges, to minimize the change in MFV. We further hypothesized that the dynamic indicator of cerebrovascular autoregulation derived from cross-spectral analysis of BPMCA to CVRi would detect reduced gain of autoregulation during hypercapnia compared with hypocapnia and during HUT compared with supine posture.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Subjects. Nine healthy subjects (6 men and 3 women, mean age 24.8 yr, range 22-34 yr) volunteered to participate in the study after being fully informed of the experimental details. The women were tested between days 3 and 10 of their menstrual cycle (follicular phase). All procedures were approved by the Office of Research Ethics at the University of Waterloo.

Experimental protocol. Subjects reported to the laboratory 3 h after a meal and after caffeine ingestion. Subjects were instrumented and placed in the supine position. Once subjects were determined to be in a steady-state resting condition (by monitoring blood pressure, respiration, and gas exchange), resting baseline respiratory rate, tidal volume, PETCO2, mean arterial blood pressure (MAP), and MFV were measured over a 10-min period.

Subjects performed three separate HUT tests to 45° each with a different level of PETCO2 presented in random order. A regulated breathing protocol was used across all conditions to control the effects of respiration on blood pressure and autonomic neural output (10, 31) and to allow us to achieve hypocapnic conditions. Respiratory frequency was fixed at 15 breaths/min by an auditory signal for the initiation of inspiration and expiration, while tidal volume was increased to 50% above baseline values by having the subjects reach specified end-inspiration and end-expiration points on an oscilloscope displaying the respiration signal. This breathing protocol resulted in a decrease in PETCO2 of 8-10 mmHg compared with normal resting levels. PETCO2 was then altered to one of three levels using a computer-controlled, dynamic end-tidal forcing system similar to that of Robbins et al. (27). Normocapnia (N-CO2) was maintained at resting PETCO2 levels determined during the baseline collection. Hypocapnia (LoCO2) and hypercapnia (HiCO2) levels were 5 mmHg below and above N-CO2, respectively. Each of the three PETCO2 conditions was maintained during 7 min of supine and 7 min of HUT, with a 5- to 10-min rest period between trials. Maximum deviation of PETCO2 was less than ±0.5 mmHg within a test.

Experimental measures. Heart rate was determined by standard electrocardiogram methods. Arterial blood pressure was determined from the finger using noninvasive arterial photoplethysmography (Finapres, Ohmeda, Englewood, CO). BPMCA was estimated from the noninvasive arterial blood pressure corrected for the vertical displacement from the transducer to the Doppler probe. MFV of the MCA was determined by transcranial Doppler ultrasonography (Transpect TCD MedaSonics, Freemont, CA) as described by Aaslid et al. (1). Briefly, after the application of ultrasound gel, a 2-MHz probe was placed over the temporal window to insonate the right MCA. The probe was securely positioned with a headband for the duration of the tests. Breath-by-breath ventilatory data were collected continuously using an ultrasonic flowmeter (Kou Consulting, Redmond, WA) and mass spectrometry (model MGA-1100, Perkin-Elmer Medical Gas Analyzer, Pomona, CA).

Data analysis. Data were recorded on digital format tape (TEAC, Montebello, CA) and transferred for analysis by a computer-based system to yield a data set sampled at 100 Hz. MFV was determined from the outer envelope of the fast Fourier-transformed Doppler signal. Beat-by-beat values were obtained for PETCO2, MAP, BPMCA, and MFV by averaging the calibrated waveforms over each cardiac cycle. CVRi was calculated for each heartbeat as BPMCA/MFV. The beat-by-beat data were aligned sequentially and resampled at the mean frequency of the R-R interval for each data set. Spectral and cross-spectral analyses were performed using Welch's averaged periodogram method (Matlab, Math Works, Natick, MA) between the input variable BPMCA and the output variable MFV or CVRi after removing the linear trends and filtering with an eighth-order low-pass Butterworth filter at 0.75 Hz. Gain values for the cross-spectral transfer functions are presented in absolute values (see Tables 3 and 4 and Figs. 3 and 4) as well as normalized values (see Figs. 3 and 4). Normalized gain was determined for each individual test for BPMCA right-arrow MFV by dividing absolute gain by the mean value of conductance (MFV/BPMCA) over that test. Likewise, for BPMCA right-arrow CVRi, normalized gain was obtained by dividing absolute gain at each frequency by the mean value of CVRi/BPMCA. By convention, a negative phase value indicates that the input preceded the output. Common practice is to accept a linear relationship between the input and output variables when squared coherence exceeded 0.5, permitting evaluation of transfer function gain and phase relationships (4, 37). This value was slightly greater than the exact value (0.45) in our study at which coherence was significantly different from zero (35). Frequency data were divided into three regions [VLF (0.03-0.07 Hz), low frequency (LF, 0.07-0.2 Hz), and high frequency (HF, 0.2-0.3 Hz)] to permit comparison with other studies (37) and on the basis of distinct regions of physiological response.

Statistics. Baseline data collected in the supine posture during normal breathing were compared with the N-CO2 supine values by paired t-tests. The steady-state data of the three levels of PETCO2 across two levels of tilt were analyzed with a three (HiCO2, LoCO2, and N-CO2)-by-two (supine and upright) ANOVA with repeated measures on both factors for each of the primary dependent variables. The same statistical model was applied at each frequency (VLF, LF, and HF) for autospectral power and for averaged transfer function gain and phase using data only when the squared coherence exceeded 0.5 for the spectral relationship between BPMCA right-arrow CVRi and BPMCA right-arrow MFV. Because of many missing data points in the VLF region (i.e., squared coherence <0.5) between BPMCA and MFV, this frequency was deleted from the analysis. The significance level was set at P < 0.05. If differences were detected, a Student-Newman-Keuls post hoc test was used. Values are means ± SD.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Steady-state and baseline averaged data. Mean data for spontaneous baseline data and for supine and HUT positions for all three levels of PETCO2 are presented in Table 1. There were no differences between baseline and supine N-CO2 for any variable except heart rate, where the difference was <3 beats/min. The measured PETCO2 from the three different gas trials was significantly different (P < 0.05), indicating that we were successful in lowering and elevating PETCO2 compared with N-CO2 levels.

                              
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  		Table 1.   Steady-state responses during supine and HUT positions across all gas conditions

There were small reductions in MFV on going from supine to HUT, but this was not significant (P > 0.05). There was a main effect of PETCO2 on MFV (P < 0.01), with higher values in HiCO2 and lower values in LoCO2 than in N-CO2 (Table 1). MAP was not different between supine and HUT, nor was it affected by the different levels of PETCO2 (P > 0.05). BPMCA was significantly reduced during HUT (P < 0.001).

CVRi was significantly different across the PETCO2 gas conditions (P < 0.001). Post hoc analysis indicated that CVRi was greater under LoCO2 and less under HiCO2 than with N-CO2. CVRi was also significantly decreased during HUT (P < 0.001). Heart rate was significantly increased during HUT (P < 0.001) but was not affected by the different levels of PETCO2 (P > 0.05).

Autospectral data. Representative time series data from the supine N-CO2 tests for a single subject are presented in Fig. 1. Group mean autospectral powers for LoCO2 and HiCO2 in HUT conditions are shown in Fig. 2. In the baseline and supine N-CO2 trials, there were no differences in autospectral power for MFV, BPMCA, or CVRi within the VLF and LF regions (Table 2). In the HF region, power tended to be greater in the N-CO2 trials than baseline because of the concentration of spectral power at the fixed breathing frequency, but this was significant only for CVRi. Across the controlled breathing trials, an effect of tilt was observed only in the LF region and only for MFV and BPMCA, but not for CVRi. An effect of PETCO2 was found only for CVRi spectral power with greater amplitude in LoCO2 than in N-CO2 and HiCO2, but this was significant only in the LF region (P < 0.05), and not in the VLF region (Table 2).


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  		Fig. 1.   Time series data for a single subject during the supine test in normocapnia (N-CO2). BPMCA, blood pressure at the level of the middle cerebral artery; MFV, mean blood flow velocity through the MCA; CVRi, cerebrovascular resistance index calculated from BPMCA/MFV.



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  		Fig. 2.   Autospectral plots of amplitude as a function of frequency for the variables shown in Fig. 1. Lines represent group mean and SE for hypocapnia (LoCO2, black and solid lines) and hypercapnia (HiCO2, gray and dashed lines) during head-up tilt.


                              
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  		Table 2.   Average autospectral power during supine and HUT across all gas conditions

Cross-spectral data: BPMCA right-arrow MFV. The BPMCA right-arrow MFV cross-spectral data for all frequencies and gas conditions are shown in Table 3. Transfer function gain, phase, and coherence for the group mean responses for LoCO2 and HiCO2 during HUT are shown in Fig. 3. Comparisons between baseline and N-CO2 could be made only at LF and HF because of the dropout of subjects in the N-CO2 trial at VLF due to low coherence for the BPMCA-MFV relationship. Between-subject variations were quite large, and there were no significant differences between baseline and N-CO2 for gain or phase (Table 3). A significantly greater gain for the BPMCA-MFV relationship was found in the HF region in the supine than in the HUT position. The positive values for phase indicate a phase lead with changes in MFV occurring before changes in BPMCA. The only significant effect of PETCO2 was found for phase in the LF region, with phase lead being greatest in LoCO2, followed by N-CO2 and HiCO2 (Table 3). Normalized gain was different between LoCO2 and HiCO2 in the LF range (Fig. 3). This difference occurred when the LoCO2 gain was divided by the lower conductance during the normalization process.

                              
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  		Table 3.   Transfer function gain and phase for BPMCA-MFV relationship



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  		Fig. 3.   Transfer function analysis for the BPMCA-MFV relationship showing group mean and SE for LoCO2 (black and solid lines) and HiCO2 (gray and dashed lines) during head-up tilt. Gain values are presented in absolute and normalized units as described in METHODS (see also Methodological considerations). Note low coherence in the very-low-frequency range.

Cross-spectral data: BPMCA right-arrow CVRi. The BPMCA right-arrow CVRi cross-spectral data for all frequencies and gas conditions are shown in Table 4, and the group mean responses for LoCO2 and HiCO2 during HUT are shown in Fig. 4. Coherence was >0.5 in eight or nine subjects in the VLF and LF regions and in at least seven subjects in the HF region. There were no differences between baseline and N-CO2 for gain or phase relationships. A significant effect of PETCO2 was found on transfer function gain for BPMCA right-arrow CVRi in the VLF and LF regions, with the greatest values in the LoCO2 trial, followed by N-CO2 and HiCO2 (Table 4). The differences in gain between LoCO2 and HiCO2 up to a frequency of ~0.2 Hz are shown clearly in Fig. 4. Figure 4 also shows that the normalization process tended to reduce the difference in gain between trials, but it was still evident. In the LF region, there was a significantly greater gain in the supine than in the HUT position. The negative sign on the phase values signifies that changes in CVRi followed those of BPMCA for all except VLF for LoCO2. For the phase relationship within the VLF region, there was a smaller phase lag for LoCO2 than for N-CO2, which was in turn less than for HiCO2.

                              
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  		Table 4.   Transfer function gain and phase for BPMCA-CVRi relationship



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  		Fig. 4.   Transfer function analysis for the BPMCA-CVRi relationship showing group mean and SE for LoCO2 (black and solid lines) and HiCO2 (gray and dashed lines) during head-up tilt. Gain values are presented in absolute and normalized units as described in METHODS (see also Methodological considerations). Note high coherence in the very-low- to low-frequency range.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The primary finding of this study was that transfer function analysis for the input variable BPMCA to the output variable CVRi provided a sensitive indicator of dynamic cerebrovascular autoregulation within the VLF and LF regions in the face of changes in arterial PCO2 and BPMCA. The gain for BPMCA right-arrow CVRi was reduced with HiCO2 and increased with LoCO2 compared with N-CO2. This method also detected a reduced gain in the HUT position that was significant within the LF range for BPMCA right-arrow CVRi. An overall main effect of PCO2 on the phase relationship for BPMCA right-arrow CVRi was observed in the VLF range. The observations of improved dynamic cerebrovascular autoregulation in LoCO2 or impaired autoregulation in HiCO2 were anticipated, inasmuch as they were consistent with the rates of recovery of MFV on release of the leg cuff under conditions of altered arterial PCO2 (1).

In contrast to the positive findings from the BPMCA-CVRi relationship, the transfer function analysis based on the BPMCA-MFV relationship had low coherence in the VLF range as expected (4, 38). It was thus unable to identify critical changes in cerebrovascular control within this frequency range. The BPMCA-MFV relationship failed to detect an effect of arterial PCO2 on gain, and it was able to detect an effect of supine vs. tilt on gain only in the HF range. The normalization process did identify an unexpectedly greater gain in LoCO2 than in HiCO2 in the LF range (Fig. 3; see Dynamic cerebrovascular autoregulation). A significant effect of arterial PCO2 on the phase relationship for BPMCA right-arrow MFV was found in the LF range as a reduction in phase for HiCO2 and an increase for LoCO2. Overall, these results from BPMCA right-arrow MFV spectral analysis revealed changes only at higher frequencies. Yet the autoregulatory process is referred to as a high-pass filter (4, 12, 38). Even though BPMCA and MFV are the measured variables, they do not provide insight into cerebrovascular autoregulation, inasmuch as changes in BPMCA are met by changes in cerebrovascular resistance to achieve relatively constant cerebral blood flow.

Methodological considerations. We calculated CVRi from the measured variables BPMCA and MFV. This index has been widely used in studies of cerebrovascular autoregulation (1, 21, 29). True vascular resistance is defined as the ratio of pressure gradient across a vascular bed to the flow through this bed. The three components, pressure gradient, flow, and vascular resistance, are not and cannot be independent variables (5). The pressure drop across the cerebral circulation is unknown, because we are unable to measure venous or intracranial pressure. However, for any body position, CVRi accurately reflects changes in cerebrovascular resistance. CVRi has limitations during transitions between body positions, inasmuch as the arterial pressure is modified by the hydrostatic component (BPMCA), while the intracranial and/or venous pressures are affected differently by posture (28). In the present study, the focus was on cross-spectral analysis of the BPMCA-CVRi relationship. In spectral analysis, the mean values are removed, and only the variations from the mean are considered. Thus any error in estimating CVRi in supine vs. HUT occurred in the steady state and might have influenced system static gain, whereas the calculated gain and phase relationships in the cross-spectral analysis are calculated strictly from changes about the mean value.

Transcranial Doppler ultrasound provides a continuous estimate of changes in cerebral blood flow. The major assumption of this method is that changes in cerebral blood flow are reflected primarily in MFV (measured in cm/s), while the vessel cross-sectional area (measured in cm2) remains essentially constant. Under conditions of altered BPMCA and arterial PCO2, Serrador et al. (32) were unable to detect changes in cross-sectional area of the MCA, so the assumption of constant cross-sectional area appears to be valid, although some authors present a different opinion (26). Continuous noninvasive estimates of arterial pressure by the finger cuff device have compared favorably with direct arterial measurements in several different laboratories (16, 38). For these reasons, Doppler ultrasound and continuous noninvasive blood pressure measurements have become widely accepted as a means of evaluating dynamic cerebral blood flow control.

Selection of the VLF, LF, and HF bands, consistent with Zhang et al. (37), was somewhat arbitrary, but the underlying physiology separates clearly for the VLF and HF regions, with the LF region as a transition zone. In the VLF region, there was very low coherence for BPMCA right-arrow MFV but much higher coherence for BPMCA right-arrow CVRi. In the HF region, the situation was reversed, inasmuch as low coherence was found for the BPMCA-CVRi relationship. The low coherence for BPMCA right-arrow MFV in the VLF region probably reflects the property of cerebrovascular autoregulation but could also indicate a nonlinear relationship that is not detected by coherence (24).

Normalization of gain is often employed as a means of reducing the between-subject variation and is useful in comparisons between different populations (30). The normalized gain can give an indication of the relative attenuation of the input to output (14, 19, 30). In the present experiments, we provide data for normalization only in the LoCO2 and HiCO2 conditions for HUT testing in Figs. 3 and 4. To obtain the normalized values, the absolute gains were divided by mean values of conductance (MFV/BPMCA) or the inverse of MFV (CVRi/BPMCA) for the BPMCA-MFV and BPMCA-CVRi relationships, respectively. In both cases, these normalization factors were greatly affected by the experimental conditions because of the alteration in steady-state vascular resistance with altered PCO2. This effect certainly influenced normalized gain for BPMCA right-arrow MFV in the LF region (Fig. 3). Our primary focus on the ability of the cerebrovascular system to maintain relatively constant blood flow was observed from the absolute gain. Normalized gain might provide additional insight under certain conditions (14, 19, 29) but resulted in an unexpected outcome in this study (see Dynamic cerebrovascular autoregulation: BPMCA right-arrow MFV).

Baseline vs. N-CO2 supine response. The baseline measurements collected during spontaneous breathing in the supine posture were very similar to those collected in the N-CO2 condition in the supine posture. There was a tendency for greater amplitude of the autospectral power at HF, but this was significant only for CVRi. The mechanism for this difference in distribution of power was related to the fixed breathing rhythm and tidal volume that concentrated spectral power at precisely 0.25 Hz (15 breaths/min). It can be concluded that the regulated breathing conditions imposed by the present experiment focused spectral power within the HF band, but they did not cause a significant change from the baseline condition.

Steady-state averaged data. The advantage of clamping PETCO2 at three different levels in the supine and HUT positions was that changes in cerebrovascular control could be identified independently as functions of posture or arterial PCO2. Consistent with the differences in arterial PCO2 were differences in steady-state MFV and CVRi that were similar to observations in previous research (1, 21, 22, 26).

With the transition from supine to 45° HUT posture, MAP remained approximately constant while BPMCA decreased. Subsequently, cerebrovascular resistance decreased to achieve approximately constant MFV in the face of reduced perfusion pressure. The finding of no significant reduction in MFV on going to HUT contrasts with several other studies (21, 29). Although part of the reason for the discrepancy with other studies might be the relatively low level of tilt in the present study, another reason for this difference could be the clamping of arterial PCO2 between the supine and HUT posture. HUT causes a reduction in arterial PCO2 in most individuals (3) so that a natural consequence of the reduced PCO2 with HUT is a relative increase in CVRi and decrease in MFV (6, 21). In the absence of change in arterial PCO2, the cerebrovascular system can adapt to maintain constant cerebral blood flow, at least in the face of small reductions in perfusion pressure.

Dynamic cerebrovascular autoregulation: BPMCA right-arrow CVRi. In this study, we evaluated cerebrovascular autoregulation from transfer function analysis of BPMCA right-arrow CVRi. In normal daily life, rapid adaptations of cerebrovascular resistance are essential for maintenance of cerebral blood flow, because BPMCA varies constantly as a result of changes in posture and spontaneous fluctuations in MAP. The spontaneous fluctuations are apparent in the autospectral power for BPMCA (Fig. 2), where VLF (~0.03 Hz), LF (~0.1 Hz), and HF (~0.25 Hz) peaks can be seen. Transfer function analysis (Fig. 3) shows that the large VLF amplitude in MFV (Fig. 2) was essentially independent of changes in BPMCA, as indicated by the very low coherence in this frequency range. In contrast, there was higher coherence for BPMCA right-arrow CVRi in the VLF-to-LF range (Fig. 4), indicating that changes in BPMCA evoked changes in CVRi that were effective to various degrees as affected by PCO2 in regulating cerebral blood flow. Furthermore, the negative phase detected for BPMCA right-arrow CVRi is consistent with the expected physiological response of changes in BPMCA causing changes in CVRi.

A change in the gain of BPMCA right-arrow CVRi suggests altered autoregulation. Our results that showed reduced gain for BPMCAright-arrow CVRi during HiCO2 and increased gain during LoCO2 are consistent with alterations in the range of the plateau region for cerebrovascular autoregulation under different levels of CO2 (see also Effects of CO2 on dynamic autoregulation). The normalization process reduced but did not eliminate the difference in gain between LoCO2 and HiCO2 in the HUT tests (Fig. 4). We also found with HUT that there was a significant reduction in LF gain for BPMCA right-arrow CVRi compared with the supine position and a similar trend in the HF region. Reduced autoregulatory response in the HUT position is consistent with the results from severe levels of lower body negative pressure (38). However, this finding contrasts with the suggestion of improved autoregulation during HUT that we would obtain from our data relating to BPMCA right-arrow MFV in the HF region as well as with data from other studies of HUT (4). A physiological interpretation of reduced BPMCA right-arrow CVRi gain with HUT might be that the decline in BPMCA toward the lower limit of the autoregulatory curve restricted the ability to respond dynamically to changes in cerebral perfusion pressure.

Phase relationships. Interpreting the relative phase lead of MFV preceding BPMCA has created confusion in terms of anticipated cardiovascular physiology (7, 8). Cencetti et al. (7) concluded that the phase lead of MFV before BPMCA indicated sympathetic neural control of the cerebrovascular system, rather than autoregulation, although this conclusion has been criticized (15, 23). Here we show that the phase lead of MFV before BPMCA is simply a mathematical consequence of natural phase lag of CVRi responding to changes in BPMCA by the mechanisms of autoregulation. The data for MFV, BPMCA, and CVRi have been reconstructed in Fig. 5 to illustrate the gain and phase relationships at one specific frequency in the LF region (selected to be 0.1 Hz). It can be appreciated that as BPMCA starts to rise (vertical reference line in Fig. 5), CVRi continued to decrease, and there was a lag of ~2.1 to 2.3 s (76.4° to 82.5°) before CVRi increased. During this time, because MFV = BPMCA/CVRi, it will be relatively high and, indeed, will appear to increase before the increase in BPMCA. The phase relationships displayed in Fig. 4 are consistent with a pure time delay of ~2 s for frequencies up to ~0.15 Hz. Above this frequency, the high-pass nature of cerebrovascular autoregulation is reflected by a phase approaching 0° for BPMCA right-arrow MFV and BPMCA right-arrow CVRi. The greater the phase lag for CVRi behind BPMCA, the smaller will be the phase lead of MFV before BPMCA, but this is not a linear relationship (Fig. 5). As discussed previously (see Methodological considerations), the three variables of flow, pressure gradient, and resistance are not independent, and MFV must precede BPMCA when it is CVRi that is responding via negative-feedback control mechanisms to the change in pressure.


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  		Fig. 5.   Schematic presentation of interrelationships between BPMCA, MFV, and CVRi at 0.1-Hz frequency. Each curve is centered on the appropriate mean value (see Table 1). Amplitude and phase relationships are depicted for each curve on the basis of low-frequency values of Tables 3 and 4. Vertical dashed line is a reference point taken at the minimum value of BPMCA to assist with understanding phase relationships. Solid lines (LoCO2) and dashed lines (HiCO2) show effects of altered arterial PCO2. HiCO2 caused a reduction in amplitude of CVRi and an increase in MFV. HiCO2 also caused a greater phase lag of CVRi behind BPMCA, which in turn caused reduced phase lead of MFV before BPMCA.

Effects of CO2 on dynamic autoregulation. Figures 3-5 have been used to highlight the differences in gain and phase under LoCO2 and HiCO2. There was a small elevation in BPMCA in the HiCO2 test compared with LoCO2, and the amplitude of the oscillation in BPMCA was slightly less in LoCO2, but these differences would not be sufficient to affect the cerebrovascular response by themselves. The primary effect of CO2 was on cerebrovascular resistance (1, 20, 21, 33). Even with the relatively small range of only 10-mmHg difference in PETCO2 between the LoCO2 and HiCO2 trials, there were clear differences in cerebrovascular responses. The overall vasodilation in response to increased PCO2 was responsible for the reduction in CVRi and, consequently, the elevated mean level of MFV. The increased PCO2 was also directly responsible for the smaller oscillations in CVRi in response to changes in BPMCA.

In the VLF range, there was a main effect of PCO2 on the phase relationship for CVRi after BPMCA. Because MFV is dependent on the changes in CVRi relative to those of BPMCA, the phase relationship between BPMCA and MFV must also change. With elevated PCO2, there was a significant reduction of the phase lead of MFV before BPMCA, consistent with previous research (2, 12, 22). Examination of the phase relationships between the three variables in Fig. 5 provides an explanation for this result. Impaired autoregulation really means that the oscillations in BPMCA are less effectively damped, so that MFV more closely tracks changes in pressure.

Dynamic cerebrovascular autoregulation: BPMCA right-arrow MFV. Giller (13) first described the frequency-dependent nature of autoregulation. Since that time, many authors have explored dynamic cerebrovascular autoregulation from the BPMCA-MFV relationship (4, 7, 8, 38). It has become common to characterize impaired autoregulation by observing greater variations in MFV, greater transfer gain between BPMCA and MFV, greater coherence, and a decreased phase relationship between BPMCA and MFV (2, 12, 37). In general, however, these relationships exist in the higher frequencies, while there is no coherence in the lower frequencies (4, 37). That is, autoregulation operates to reduce or eliminate the BPMCA-MFV relationship (13).

In the present study, transfer function analysis of the absolute gain between BPMCA and MFV failed to detect any effect of PCO2 (Table 3). Previous research has established that dynamic cerebrovascular autoregulation is a function of arterial PCO2 (1, 2, 12, 22, 37). However, in some studies the sample size was limited and the differences in gain induced by elevated CO2 were small (37) or detected only at the lowest frequency (22).

Contrary to expectations where HiCO2 was hypothesized to impair autoregulation, the normalized gain for the LoCO2 condition was greater than that for the HiCO2 condition in the LF region (Fig. 3). This finding was quite unexpected, inasmuch as it indicates reduced autoregulatory efficiency in LoCO2 compared with HiCO2. The normalized gain is greatly influenced by the normalizing factor, which in this case was the mean value of conductance. Thus the normalized gain was reduced more for HiCO2, because conductance was markedly increased. Alternatively, the relatively stiffer vessels in LoCO2 were less able to dampen the effects of variations in BPMCA at these frequencies. This latter observation has a parallel in studies of renal vascular autoregulation, where inhibition of nitric oxide synthesis caused a relative increase in resistance and increased transfer function gain (18). In this case, the dynamic autoregulation might be considered to be impaired, even though the static gain is improved by LoCO2 (1, 20, 33).

According to the finding of smaller gain values for BPMCA right-arrow MFV in the HF region, HUT appeared to enhance autoregulation. Although this was consistent with another study that used tilt as the orthostatic stress (4), it contrasted with findings from a study that employed high levels of lower body negative pressure (-50 mmHg) (38) as well as with our data from BPMCA right-arrow CVRi. The reason for the discrepancy where HUT appears to enhance autoregulation while lower body negative pressure impairs it needs to be resolved. Given the ability of the BPMCA-CVRi relationships to accurately describe the effects of PCO2 on autoregulation, the present study provides reason to believe that HUT causes impaired, not enhanced, autoregulation.

Comparison of cerebral with renal vascular responses. Frequency domain analysis has been used extensively to study autoregulation in the renal circulation (14, 19). Several parallels and some differences can be observed compared with the cerebral circulation. The renal studies have been performed on anesthetized or conscious animals in which renal blood pressure spontaneously varied or was manipulated (14, 18, 19). On the basis of different response times, two distinct mechanisms have been revealed: a myogenic response and a feedback mechanism based on tubuloglomerular filtration (14, 19). In the cerebral circulation, there appears to be one primary autoregulatory mechanism, although it might be found to have different mechanistic components, as in the mesenteric circulation (9). The rapidity of the cerebrovascular response observed in the present study is consistent with a myogenic mechanism. In the animal studies, inhibition of the myogenic component of renal autoregulation by the calcium channel blocker nifedipine caused increased normalized gain and reduced phase shift for the pressure-flow relationship (19). Directionally similar changes in normalized gain and phase were observed after inhibition of nitric oxide synthesis (18), even though nifedipine caused a slight (~18%) increase in renal vascular conductance while nitric oxide synthesis inhibition reduced conductance (~53%). Previous research suggested that cerebrovascular autoregulation is impaired in HiCO2 compared with LoCO2 (1, 20, 33). Consistent with this study and with the studies of renal circulation, the phase relationship for BPMCA right-arrow MFV was reduced in HiCO2. However, increased normalized gain was found in the LoCO2, rather than in the HiCO2, tests. The mechanism responsible for the disparity between renal and cerebral circulation based on the pressure-flow relationship is not obvious, although the effect of absolute vascular conductance on normalized gain appears to be an important factor.

The transfer function between blood pressure and renal vascular resistance has been investigated (14, 19), and the outcome has been consistent with transfer function analysis to the pressure-flow relationship. In our study, the hypothesized effect of HiCO2 on the cerebrovascular response was evident in the BPMCA right-arrow CVRi response and not BPMCA right-arrow MFV, so that the former appears superior in detecting changes in autoregulation.

Perspectives

Autoregulation is an important property in the cerebral (1, 25) and other vascular beds (14, 19). In most cases, autoregulation has been investigated by the blood flow response to changes in perfusion pressure. This study determined the effect of the input variable (blood pressure) on the manipulated variable (vascular resistance), which in turn acts to minimize changes in the regulated variable (blood flow) (15). In our study, transfer function analysis of the input-output relationship for BPMCA right-arrow CVRi was capable of detecting changes in gain and phase relationships as a result of altered arterial PCO2 and HUT within the VLF-to-LF (0.03-0.2 Hz) range. This is critical, inasmuch as it is in this region that autoregulation is operative. In contrast, the previous methods that computed transfer function relationships between BPMCA and MFV relied on a lack of signal within this frequency range as an index of efficient autoregulation. Furthermore, normalized gain for BPMCA right-arrow MFV yielded an unexpected finding that was contrary to concepts of autoregulation during altered arterial PCO2 on the basis of previous studies of static system gain (1, 20, 33). The BPMCA right-arrow CVRi transfer function relies on the inherent physical link between the two measured variables BPMCA and MFV to calculate CVRi. We believe that transfer function analysis of BPMCA right-arrow CVRi provides an intuitively attractive means of assessing cerebrovascular autoregulation, inasmuch as improved autoregulation is denoted by increased gain and reduced phase lag, as opposed to reduced gain and phase lead, if one uses the BPMCA-MFV relationship. The BPMCA right-arrow CVRi transfer function can be widely applied in research and clinical settings to investigate physiological and pathological factors that alter cerebrovascular autoregulation.


    ACKNOWLEDGEMENTS

The authors thank Dr. R. Bondar for the loan of transcranial Doppler ultrasound equipment.


    FOOTNOTES

M. R. Edwards was supported by a Natural Sciences and Engineering Council of Canada postgraduate scholarship and by a Canadian Space Agency graduate supplement. This research was supported by Heart and Stroke Foundation of Ontario Grant NA 4387, the Natural Sciences and Engineering Research Council, and the Canadian Space Agency (R. L. Hughson and J. K. Shoemaker).

The flexible Matlab coding for spectral analysis is available from the authors on request.

Address for reprint requests and other correspondence: R. L. Hughson, Cardiorespiratory and Vascular Dynamics Laboratory, Faculty of Applied Health Sciences, University of Waterloo, Waterloo, ON, Canada N2L 3G1 (E-mail: hughson{at}uwaterloo.ca).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

April 4, 2002;10.1152/ajpregu.00452.2001

Received 29 July 2001; accepted in final form 2 April 2002.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
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Am J Physiol Regul Integr Comp Physiol 283(3):R653-R662
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