This Article Abstract Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Request Permissions Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Blaber, A. P. Articles by Freeman, R. Search for Related Content PubMed PubMed Citation Articles by Blaber, A. P. Articles by Freeman, R.

(Stroke. 1997;28:1686-1692.)
© 1997 American Heart Association, Inc.

Articles

Transfer Function Analysis of Cerebral Autoregulation Dynamics in Autonomic Failure Patients

Andrew P. Blaber, PhD; Roberta L. Bondar, MD, PhD; Flo Stein, PhD, RVT; Paul T. Dunphy, PEng; Peyman Moradshahi, PEng; Mahmood S. Kassam, MASc, DrUniv; R. Freeman, MD

From the School of Kinesiology, Faculty of Health Sciences, The University of Western Ontario (A.P.B., R.L.B.), London, Ontario, Canada; the Centre for Advanced Technology Education, Ryerson Polytechnic University (A.P.B., R.L.B., F.S., P.T.D., P.M., M.S.K.), Toronto, Ontario, Canada; and The Autonomic and Peripheral Nerve Laboratory, Department of Neurology, Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, Mass (R.F.).

	Abstract

Top Abstract Introduction Methods Results Discussion Appendix 1 References

 
Background and Purpose Autonomic nervous system diseases affect systemic blood pressure regulation. Patients with autonomic nervous system diseases have consistently larger drops in blood pressure associated with standing than the normal population. Autonomic dysfunction and/or these changes in blood pressure may affect dynamic cerebral autoregulation.

Methods Heart rate, mean blood flow velocity (MBFV) of the middle cerebral artery via transcranial Doppler ultrasound, mean arterial blood pressure adjusted to brain level (MABP_brain) via Finapres, and end tidal CO₂ were measured continuously during graded tilt (after 5 minutes in supine position as baseline, -10°, +10°, +30°, +60°, -10°, and supine recovery) in autonomic failure patients and their age- and sex-matched control subjects. The dynamic response of MBFV to spontaneous variations in MABP_brain was investigated by cross-spectral analysis. The transfer gain and phase relationships between MBFV and MABP_brain were determined from the final 256 beats of each 5-minute–tilt segment. The transfer gain was normalized to mean MABP_brain and MBFV and then converted to decibels (dB).

Results MBFV variation (0.03 to 0.14 Hz) preceded MABP_brain by similar phase angles in patients and control subjects and in all tilt conditions (patients: 31±5°; control subjects: 30±5°; mean±SEM). Patients had a higher supine gain than control subjects (P<.05). Both patients and control subjects showed a significant decrease in gain with tilt and by 60° the patients were not different from the control subjects (supine to 60°: patients=5.23±0.77 to -1.65±0.89 dB; control subjects=1.74±0.82 to -1.80±0.62 dB).

Conclusions These data indicate an altered, yet present, autoregulatory response with autonomic failure.

Key Words: autoregulation • cerebral arteries • ultrasonics • tilt table • autonomic dysfunction

	Introduction

Top Abstract Introduction Methods Results Discussion Appendix 1 References

 
Autonomic failure patients have consistently larger drops in blood pressure when standing and may tolerate lower blood pressures before syncope than the normal population. Previous studies are divided as to whether autoregulation is present^{1 2 3} or not,^{4 5} with impaired blood pressure regulation and subsequent reduction in the lower limit of perfusion pressure that can be tolerated during tilt in patients with autonomic failure; there may be other changes in cerebral autoregulation that may protect against, or possibly exacerbate, orthostatic hypotension.

Cerebral autoregulation refers to the ability of the brain to maintain constant blood flow despite changes in CPP.^{6 7 8} Orthostatic stress, such as that induced by tilt, provides a challenge to the autoregulatory response. Two methods exist for evaluating cerebral autoregulation: the original static method, with measurements of cerebral blood flow made at various steady state levels of blood pressure,^{6 7 8} is used to establish the range of blood pressures in which this mechanism is effective; and the more recent dynamic method with rapid drops in MABP,^{9 10} is used to measure the rate and effectiveness of cerebral autoregulatory blood flow velocity responses to MABP changes. Although the dynamic analysis does not yield information relating to the shape of the autoregulatory curve, both methods have recently been shown to yield similar estimates of autoregulation in normal human subjects.¹¹

The static and dynamic methods both require the manipulation of blood pressure in the subject to measure the autoregulatory response, either by using vasoactive drugs or by inflating and deflating thigh cuffs. The dynamic autoregulation is calculated over the time domain using a second-order high-pass filter model.¹¹ Recent observations of the frequency response of cerebral blood flow velocity to blood pressure also point to cerebral autoregulation being a high-pass filter. The effects of slow variations in ABP (0.1 Hz)¹² on cerebral blood flow variation are damped by reflex changes in cerebral arteriole vessel diameters, whereas higher frequency changes are not affected and therefore pass directly to changes in cerebral blood flow. Diehl et al¹² showed that when patients breathed at six breaths per minute (0.1 Hz) the resulting 0.1 Hz variations in ABP produced a similar 0.1-Hz variation in MCA MBFV as measured by TCD ultrasonography. Furthermore, they showed that in the MCA, MBFV variation preceded ABP variation (a characteristic high-pass filter phase response) by 70° in the control subjects and 0° in subjects with severe stenosis.

We have shown¹³ that cerebral blood flow velocity varies naturally (without fixed interval breathing) in a fashion similar to that in MABP. We propose that these variations in blood flow velocity are related to the spontaneous variation in blood pressure. In the past, cross-spectral transfer function analysis was used to characterize the dynamic response of heart rate to changes in blood pressure to measure the arterial baroreflex gain¹⁴ and, more recently, to investigate renal autoregulation.¹⁵ If cerebral autoregulation dynamics could be measured in a similar fashion, then the need to elicit rapid changes in blood pressure with thigh cuffs would be removed, providing a more versatile measurement for clinical practice.

In this article we report results from autonomic failure patients and their age- and sex-matched healthy controls. We have previously shown that these autonomic failure patients have a larger decrease in blood pressure and cerebral blood flow velocity with tilt than their controls.¹⁶ By comparing the relationship between changes in the steady state (static) levels of MABP and MBFV with tilt, we concluded that the autoregulatory response was not different between patients and control subjects. In fact, there was a significant decrease in the estimated cerebrovascular resistance with tilt, characteristic of a functioning autoregulatory system.

In this study we investigated the dynamic relationship between MABP and MBFV using tilt in these autonomic failure patients and cross-spectral transfer function phase and gain. This method measures the dynamic response in the frequency rather than time domain: Although not equivalent, the cross-spectral transfer function phase and gain are related to the time constant and damping factor in the time domain.¹⁷ Analysis of the dynamic (phase and gain) response of cerebral blood flow velocity to MABP with tilt may provide useful information on the ability of cerebral blood vessels to dilate and constrict with changes in perfusion pressure and new insight into the behavior of the cerebral autoregulation mechanism in these patients.

	Methods

Top Abstract Introduction Methods Results Discussion Appendix 1 References

 
The protocol and data collection for this experiment are presented in our article on the steady state autoregulatory response during graded HUT.¹⁶ In the present article we focus on the dynamic beat-to-beat autoregulatory responses during graded tilt and report information pertaining to these analyses.

Eleven patients with autonomic failure¹⁸ and their age- and sex-matched controls were observed during the graded-tilt protocol (supine baseline, –10°, 10°, 30°, 60°, -10°, and supine recovery).¹⁶ Continuous analog signals were collected for heart rate (via electrocardiograph), blood pressure (via Finapres 2300, Ohmeda), percent end-tidal CO₂ (Petco₂), and respiratory rate (Datex Normocap 200), and MCA MBFV (TCD ultrasound; Transpect, Medasonics). The analog signals from these devices were recorded simultaneously at 12 kHz per channel using an 8-channel digital tape recorder (TEAC RD-111T, Teac Inc). Beat-by-beat analysis of these data was performed off-line. The MABP was adjusted to the level of the brain (MABP_brain). The Doppler image and blood pressure tracing were manually reviewed for anomalies and movement artifact. Any unusable blood flow velocity or blood pressure data were removed, and the time series was adjusted by interpolating new values from the two valid points surrounding the excluded segment. If more than 20% of any time series was interpolated, the results were deemed invalid.

Dynamic Autoregulation Analysis
The oscillatory components at individual frequencies of one signal can be related to a second signal through a cross-spectral transfer function (see "Appendix"). This transfer function describes associated relative power (gain) and timing (phase) over a range of frequencies and provides an estimate of reliability of the relationship between the two signals, called coherence¹⁹ (coh). This technique has been used to study respiratory sinus arrhythmia,^{20 21 22} the arterial baroreflex,^{14 23 24 25} and renal autoregulation.¹⁵

We performed cross-spectral analysis between MABP_brain and MCA-MBFV from the last 256 beats at each tilt condition. Briefly, with this analysis the MABP_brain and MBFV time series are transformed into a series of sine functions between 0.0 and 0.50 Hz by Fourier analysis. The amplitude and phase of MABP_brain and MBFV at each frequency were compared using a complex transfer function (see "Appendix"). A comparison of the amplitudes and phases of MABP_brain and MBFV provides the transfer gains and phases at each frequency.

The gain can be thought of as an indicator of what magnitude of change in MBFV is caused by a change in MABP_brain. With autoregulation, changes in arteriole vessel wall diameter attempt to minimize the effects of MABP_brain on MBFV. In this context, a smaller gain indicates more effective autoregulation. We applied cross-spectral analysis to the data in a fashion similar to that used by Holstein-Rathlou et al.¹⁵ In this case the gain at each frequency is representative of dynamic changes. This gain, in units of mm · s^-1 · mm Hg^-1, may then be normalized by the mean values¹⁵ of MABP_brain and MBFV over the 256 beats. In this case the normalization factor is MABP_brain/MBFV (pressure over flow velocity). This term has been previously used to estimate cerebrovascular resistance.¹⁶ The normalized gain therefore reflects the dynamic response of MBFV to MABP in a given condition and the cerebrovascular (static) resistance about which the variation occurs.

The phase describes the shift in degrees required to align the input signal (MABP_brain) at a specific frequency with the output signal (MBFV). Since all signals are assumed to be sine functions, the maximum possible phase shifts are ±180°. We report the results as a positive phase when the output signal lagged the input signal, and we report a negative phase if the output preceded the input signal.

A recent article¹² showed that at 0.10 Hz the phase and gain response in healthy control subjects was consistent with a high-pass filter. In the case of a high-pass filter, input will lead output. Because cerebral autoregulation functions as a high-pass filter, a negative phase angle should exist between MABP_brain and MBFV. High-pass filters dampen the output in the low-frequency region and allow high-frequency oscillations to pass through unaltered. On the basis of the model of Diehl et al,¹² we used a cutoff frequency of 0.15 Hz: low frequency below 0.15 Hz, representing autoregulation, and high frequency above 0.15 Hz. In this study, we decided to use the averaged gain and phase over the low-frequency range (0.03 to 0.14 Hz) to include 0.1 Hz and over a high-frequency range (0.15 to 0.30 Hz): gain_LF and phase_LF and gain_HF and phase_HF. This averaging technique has previously been used to calculate baroreflex gain.¹⁴ Coherence, a measure of the statistical reliability of the transfer function (see "Appendix"), was used to accept or reject individual values in the frequency band. Only those frequencies in which the squared coherence (Coh²) function of the cross spectrum between MABP_brain and MBFV was greater than 0.5¹⁴ (Fig 1, top right) were used to calculate the average gain (Fig 1, top right) and phase relationship (Fig 1, bottom right).

View larger version (29K): [in this window] [in a new window]   Figure 1. The velocity envelope of the transcranial Doppler signal from the MCA (top left) was used to calculate the MBFV for each beat and the ABP waveform (bottom left) was used to calculate MABP for each beat. From these, a time series of 256 beats for each test condition was constructed (left). A fast Fourier transform of 256 beat-by-beat MABPbrain and MBFV values was performed after elimination of linear trends and the application of a cosine tapered window. The autospectra were obtained as ensemble averages of five 128 beat subsets selected at equal intervals from the original 256 data points. At each frequency, the phase (not shown) and normalized power (see text) of MABPbrain and MBFV were determined. These were compared to identify the phase (top right) and normalized gain (bottom right) relationship between MABPbrain and MBFV. A negative phase indicates that changes in MBFV lead changes in MABPbrain. Note that the average phaseLF and gainLF was calculated between 0.03 and 0.14 Hz where coh2>0.5. In regions of low power (ie, >0.25 Hz) where signals are related, signal noise can generate high coherence.

Statistical analysis of variables across the tilt levels (baseline, -10°, 10°, 30°, 60°, -10°, and supine recovery), comparing patients with age- and sex-matched healthy control subjects, was performed using a nested (subjects within tilt) two-way repeated measures ANOVA. If main effects or interactions (P<.05) were detected, subsequent post hoc analysis with a Student-Newman-Keuls test was performed (P<.05). All data are reported as mean±SEM.

	Results

Top Abstract Introduction Methods Results Discussion Appendix 1 References

 
Because of technical difficulties and noise, only eight of the patients had sufficient TCD ultrasound data for analysis (patients¹⁸ 1 through 8). For statistical purposes, only these patients and their eight matched control subjects were used in the final analysis. None of these patients presented with presyncopal symptoms during the tilt test.

The mean normalized gain, phase, and coh² for patients and control subjects in the baseline and 60° HUT conditions are shown in Figs 1 and 2, respectively. In the baseline condition the gain is relatively flat over all frequencies in both groups. The phase of the transfer function shows the characteristic high-pass filter response, with a decrease in phase with frequency. During 60° HUT, both gain and phase decrease with decreasing frequency. The phase above 0.15 Hz was not different from 0° (patients: -0.12±0.12°; control subjects: -0.16±0.12°) and therefore measurements of gain in this region are not related to autoregulation. On the other hand, below 0.15 Hz, MBFV preceded MABP_brain by a phase angle of 31±5° in the patients and 30±5° in the control subjects. Phase_LF was not different between patients and control subjects and did not change with tilt (see Table). Before normalizing with the mean values of MABP_brain and MBFV at each tilt condition and converting them to dB, patients had a higher (P<.001) transfer gain_LF (11.3±0.6 mm · s^-1 · mm Hg^-1) than control subjects (6.8±0.6 mm · s^-1 · mm Hg^-1) with no significant changes with tilt. Significant changes with tilt were observed only after normalizing to MABP_brain and MBFV. In the baseline condition, normalized gain_LF was significantly higher in the patients than the control subjects (Table, P<.05). Also, in the baseline condition normalized gain_LF was positive (Table). As the angle of HUT was increased, the normalized gain_LF decreased to a negative value in both control subjects and patients at 60° HUT (Table). The normalized gain_LF at 60° HUT was not significantly different between patients and control subjects, but by supine recovery the patients had a significantly higher normalized gain_LF (Table).

View larger version (35K): [in this window] [in a new window]   Figure 2. Baseline normalized gain (top), phase (middle), and squared coherence (bottom) functions (mean=solid line±SEM=dashed lines) for control subjects (left) and patients (right).

View this table: [in this window] [in a new window]   Table 1. Transfer Function Normalized GainLF and PhaseLF in Autonomic Failure Patients and Control Subjects

End-tidal CO₂ responses were similar in both patients and control subjects, with patients dropping from 6.13±0.5% supine to 5.77±0.4% at 60° HUT, and control subjects dropping from 6.06±0.4% supine to 5.80±0.6% at 60° HUT. Resting hematocrit levels also were not significantly different between the patients (39.7±4%) and the control subjects (40.7±3%).

	Discussion

Top Abstract Introduction Methods Results Discussion Appendix 1 References

 
Cerebral autoregulation has previously been modeled as a high-pass filter.^{9 12} The phase response with frequency in this study is consistent with this model (Fig 1), with phase decreasing with frequency below 0.2 Hz; the average phase above 0.15 Hz was 0°, and below 0.15 Hz it was -30°. Transfer function analysis appears to be a valid method of investigating cerebral autoregulation dynamics. We have shown a difference in the dynamic autoregulatory gain between patients and control subjects. Patients had a significantly higher normalized gain_LF in the supine position than the control subjects, but at 60° HUT both patients and control subjects had similar normalized gains_LF. In the supine, but not 60° HUT, position, which is associated with low-frequency BPV, there was a proportionately higher variation in cerebral blood flow in the patients compared with the control subjects. This suggests a difference in autoregulation between the two groups.

Methodological Considerations
Before we discuss the theoretical and clinical implications of our findings, several methodological aspects of the study require discussion. The use of continuous noninvasive blood pressure monitoring has extended our ability to observe beat-to-beat BPV. The finger monitor can reliably track beat-to-beat changes in ABP,²⁶ and can be used for spectral analysis of BPV. Caution is needed when interpreting the low-frequency region. Omboni et al²⁶ found increased low-frequency power with the finger monitor when compared with intra-arterial measurements. We used the same blood pressure monitor for all subjects, with comparisons made between the patient and control groups. Interpretations were made on the basis of these inter-group comparisons only and not absolute values and therefore there should be no reason to doubt the validity of these comparisons.

The present study required continuous, beat-to-beat measurements of MCA blood flow dynamics. Transcranial Doppler ultrasonography, while noninvasive, does not measure flow directly but instead measures flow velocity. The relationship between the measured velocity changes and changes in actual cerebral blood flow depends on the diameter of the insonated vessel; a decrease in diameter will result in an increase in the velocity measured, whereas an increase in diameter will have the opposite effect (assuming that the actual flow level remains unchanged). Changes in velocity can only be equated to changes in flow, then, if changes in the diameter of the insonated vessel, in this case the MCA, are minimal.

Measurements of MCA caliber were not performed in the present study, since no reliable noninvasive technique currently exists for doing this. However, previous invasive studies have shown minimal changes in MCA diameter under a variety of conditions known to affect cerebral perfusion.^{10 27 28 29} This study presents a situation similar to one experienced in a previous TCD study in our laboratory that was based on lower body negative pressure³⁰ ; since a decrease in MBFV was observed with HUT, this could only be explained in two ways: Either blood flow in the territory of the MCA decreased or the diameter of the MCA increased. Previous studies have found an increase in sympathetic activity with HUT, which if anything may cause some vasoconstriction, not dilatation, of the MCA.³¹ Although this increase in sympathetic activity may have been reduced or even absent in patients, they would most likely have also experienced a drop in MCA blood flow, given the severe drop in arterial perfusion pressure observed during HUT. We therefore believe that our interpretation of the fall in MFV as indicating a fall in MCA blood flow during HUT is a reasonable one.

The other methodological consideration deals with the use of changes in MABP_brain to represent changes in CPP. Since CPP equals MABP_brain minus ICP, this assumption is valid only if changes in ICP are minimal. As was the case with MCA caliber, no reliable noninvasive technique currently exists for measuring ICP, and therefore it was not measured in the present study. However, the validity of assuming minimal ICP changes during HUT has been demonstrated by Rosner and Coley,³² who showed a drop in ICP of only 1 mm Hg for every 10° of HUT. This drop is much less than the MABP_brain changes we observed in the present study, and its effect on CPP changes would be minimal. Furthermore, ICP is expected to remain nearly constant within a given tilt segment, so it would not be a factor in our analysis of the dynamics within each segment. Most importantly, since ICP changes during HUT are thought not to be mediated by the autonomic nervous system,³² any changes in ICP should have had the same effect on the patient and control groups, and hence our comparison of the two groups would be valid.

Transfer Function Analysis
The method of transfer function analysis has been used extensively in the investigation of cardiovascular control,^{14 25 33} respiratory sinus arrhythmia,^{20 34 35} and renal autoregulation.¹⁵ As with any comparison of two signals, there is no precondition that the two signals are related. A finding of high coherence indicates that the variation in the two signals is similar to a high degree. This may indicate that the input signal variation produces the output signal variation or that both signals are affected by the same unmeasured input. Furthermore, no interpretation of cause and effect can be made from the results of the cross-spectrum alone, since cross-spectral analysis assumes an open loop between input and output, where in many cases there are both feed-forward and feedback mechanisms involved. Interpretation of the results from cross-spectral analysis must therefore be made with caution and only with the availability of other physiological measures and an understanding of the physiological process being investigated.

With cross-spectral analysis of arterial baroreflex, there is a strong physiological reason for expecting that feedback and feed-forward mechanisms are involved with the generation of the observed input (systolic blood pressure) and output signals (heart rate); with blood pressure changes there are concomitant changes in heart rate to change blood pressure in the opposite direction, this in turn will affect blood pressure. This feed-forward, feedback relationship has been confirmed by the observation of increased BPV when arterial baroreflex is reduced in autonomic failure patients¹⁸ or removed in heart transplant patients.³⁶ In the case of cerebral autoregulation, there should be little effect of changing cerebral vascular resistance on the measured ABP at the finger. The autoregulatory mechanism serves to minimize the effect of BPV on cerebral perfusion by altering cerebrovascular resistance through changes in arteriole vessel diameters in the brain. Although the effects of these changes on overall systemic arterial blood variation have not been measured, we have assumed them to be minimal.

We have reported the gain_LF before and after normalizing for MABP_brain and MBFV at each condition. Before normalizing we observed a significantly higher gain_LF in the patients that was almost double that found in the control subjects. This gain_LF was constant over all levels of tilt. These data indicate that the relationship of the variation in MBFV to MABP_brain was constant in all tilt conditions. In terms of autoregulation, this would indicate that in the patient group greater variations in MABP_brain were permitted to pass through as variation in MBFV, and the same degree of variation was permitted regardless of the mean values for MABP_brain or MBFV. This suggests a fundamental difference in cerebral autoregulation in patients with autonomic failure compared with healthy control subjects. Since autonomic failure patients experience larger postural changes in MABP_brain than healthy subjects, this increased gain_LF may be a compensatory response to the increased range of blood pressures experienced by autonomic failure patients.

We have previously reported the changes in MABP_brain and MCA MBFV in these patients and their controls.¹⁶ These data indicated that the cerebrovascular autoregulatory system was severely challenged in the patients but not the control subjects. MABP_brain in the patient group was significantly higher in the supine position and lower in the 60° HUT position than the control group (patients: 105±4.7 to 43±4.5 mm Hg; control subjects: 88±4.5 to 65±4.7 mm Hg). The patients had a significant decrease in MBFV from supine to 60° HUT (610±36 to 440±26 mm · s^-1) but the control subjects did not (560±24 to 440±24 mm · s^-1). In both groups the change in MBFV was less than the change in MABP_brain, suggesting a decrease in cerebrovascular resistance with tilt.¹⁶ This is consistent with autoregulation; as blood pressure decreases vessel diameter is increased to maintain perfusion.

We normalized our cross-spectral gain by multiplying by the ratio of the average MABP_brain to MBFV. This procedure was previously described in the calculation of renal autoregulatory gain.¹⁵ Since vascular resistance is calculated as pressure divided by flow, then the normalization of the cross-spectral gain produces a value that takes into account changes in cerebrovascular resistance associated with the variation. With normalization we found a significant decrease in the gain_LF in both patients and control subjects. The patients still had a significantly higher normalized gain_LF in the supine position, but by 60° HUT both patients and control subjects had a similar normalized gain_LF.

The decrease in the normalized gain_LF in both groups indicates that there was active autoregulation from supine to 60° heat-up tilt. The negative values at 60° HUT indicate that the effect of BPV on MBFV variation was damped. It is significant that both patients and control subjects were not different at 60° HUT, even though the patients' blood pressures were significantly lower. This indicates that the response of the patients at 60° HUT was similar to that of the control subjects. In other words, in a similar condition (60° HUT), the patients and control subjects behaved similarly in autoregulatory gain, despite the obvious differences in MABP_brain. This may be an adaptation in the autonomic failure patients to their condition of reduced systemic blood pressure regulation, allowing them to tolerate lower perfusion pressures than normal healthy subjects. It also may indicate that the autoregulatory curve in these patients is shifted to the left, as suggested by others.¹ This shift may be due to a shift in the autoregulatory set point; to the effect of reduced sympathetic outflow³⁷ with autonomic failure; or to increased tolerance developed by increased oxygen extraction.

The frequency phase and gain responses described by cross-spectral transfer function analysis are related to response time and damping factor in the time domain.¹⁷ We can make some statements in relation to previous articles that have looked at the dynamic response in the time domain. Yoshida et al³⁸ reported two responses in monkeys: a fast metabolic response of the order of seconds and a slow myogenic response of the order of minutes. Based on our frequency of 0.1 Hz and a phase lead of 30°, we can say that the phase response represents a response time of the order of seconds rather than minutes. Aaslid et al,³⁹ using thigh cuffs and carotid compression, reported a fast response time of approximately 7 seconds with a latency of 1 to 2 seconds in humans. In the autoregulation model presented by Tiecks et al¹¹ the damping factor has the same interpretation as the gain reported in this article: A higher gain or damping factor represents reduced autoregulation.

We have recently reported that the complexity of the MBFV signal increases with tilt.¹³ Complexity is thought to be related to the number of mechanisms interacting to produce the measured physiological signal, in this case MBFV.^{40 41 42} Although there was a trend toward increased complexity in the control subjects, only the patients had a significant increase in complexity, indicating that a greater number of mechanisms related to the regulation of MBFV (autoregulation) were involved at 60° HUT. Taken with these results this may indicate that a greater number of autoregulatory mechanisms were involved in the patients to produce the same gain. This is not surprising given the reduced systemic blood pressure regulation in these patients.

In conclusion, we have shown that cross-spectral transfer function analysis of blood pressure and cerebral blood flow velocity provides new insights into the investigation of cerebral autoregulation. These data confirm the high-pass filter model of cerebral autoregulation. Gain_LF in the autonomic failure patients was higher than the control subjects, suggesting a difference in autoregulation that may be of clinical significance. The patient and control groups had a decrease in the normalized cross-spectral gain_LF with tilt, which indicated a compensatory effect of dynamic autoregulation to the change in blood pressure through changes in vascular resistance. Both groups had similar normalized gain_LF at 60° HUT, suggesting similar autoregulation at that position despite the significantly lower MABP_brain in the patients. These changes may be adaptive to reduced systemic blood pressure due to autonomic failure. With autonomic failure, the autoregulatory curve may be shifted to the left and/or cerebral autoregulation may allow for more variation in MBFV in autonomic failure.

	Selected Abbreviations and Acronyms

 

ABP = arterial blood pressure BPV = blood pressure variation CPP = cerebral perfusion pressure gainHF = high-frequency gain gainLF = low-frequency gain ICP = intracranial pressure MABPbrain = mean arterial blood pressure adjusted to the level of the brain MBFV = mean blood flow velocity MCA = middle cerebral artery phaseHF = high-frequency phase phaseLF = low-frequency phase TCD = transcranial Doppler

View larger version (32K): [in this window] [in a new window]   Figure 3. 60° HUT normalized gain (top), phase (middle), and squared coherence (bottom) functions (mean=solid line±SEM=dashed lines) for control subjects (left) and patients (right).

	Acknowledgments

 
This research was supported by a joint NSERC, Medical Research Council, CSA grant under NSERC file #669-008-93 (Dr Bondar), and by grant FD-R-000393 from the Public Health Service (Dr Freeman).

	Footnotes

 
Reprint requests to Dr Roberta L. Bondar, Faculty of Health Sciences, School of Kinesiology, Thames Hall, Room 3110, The University of Western Ontario, London, Ontario, Canada N6A 3K7.

	Appendix 1

Top Abstract Introduction Methods Results Discussion Appendix 1 References

 
A fast Fourier transform (FFT) of interval time series of 256 equally spaced (using mean heart beat interval) MCA-MBFV (Fig 1, top left) and MABP_brain (Fig 1, bottom left) was performed after elimination of linear trends and the application of a cosine tapered window. The autospectra for input, S_xx(f), and output, S_yy(f), signals and the final cross-spectral power density, S_xy(f), of the paired time series were obtained as ensemble averages for five time-shifted 128 beat subsets of the original 256 data points.

Briefly the normalized transfer function, H(f), was calculated by dividing the value of the cross-spectrum, S_xy(f), by the input autospectrum, S_xx(f), at each frequency and then normalized to the mean values of the input (x) and output (y) variables.

(1)

The magnitude of H(f) and the phase, (f), were derived from the real, H(f)_r, and imaginary, H(f)_i, components of the complex transfer function as

(2)

(3)

The gain was then calculated as 20 log ||H(f)|| to give values in decibels (dB). A value of 0 indicates that the output varies by the same fraction of the mean value as the input. A negative value indicates that the output varies less than the input, and a positive value indicates that the output varies greater than the input. In general this gain can be thought of as an indicator of what magnitude of change in MBFV is caused by a unit change in MABP_brain. If autoregulation serves to regulate the effect of changing MABP_brain on MBFV, an increase in the gain would indicate reduced effectiveness (ie, more MABP_brain variation is transmitted to MBFV).

For each transfer function a squared coherence function was calculated.

(4)

The squared coherence (Coh²) function does not have direct physiological significance but can be used as a statistical measure of the reliability of the transfer function and of the linearity of the input/output relation.¹⁹

Received February 11, 1997; revision received May 13, 1997; accepted May 29, 1997.

	References

Top Abstract Introduction Methods Results Discussion Appendix 1 References

 
1. Thomas DJ, Bannister R. Preservation of autoregulation of cerebral blood flow in autonomic failure. J Neurol Sci. 1980;44:205-212.[Medline] [Order article via Infotrieve]

2. Brooks DJ, Redmond S, Mathias CJ, Bannister R, Symon L. The effect of orthostatic hypotension on cerebral blood flow and middle cerebral artery velocity in autonomic failure, with observations on the action of ephedrine. J Neurol Neurosurg Psychiatry. 1989;52:962-966.[Abstract/Free Full Text]

3. Caronna JJ, Plum F. Cerebrovascular regulation in preganglionic and postganglionic autonomic insufficiency. Stroke. 1973;4:12-19.[Abstract/Free Full Text]

4. Meyer JS, Shimazu K, Fukuuchi Y, Ohuchi T, Okamoto S, Koto A, Ericsson AD. Cerebral dysautoregulation in central neurogenic orthostatic hypotension (Shy-Drager syndrome). Neurol. 1973;23:262-273.[Free Full Text]

5. Lagi A, Bacalli S, Cencetti S, Pagetti C, Colzi L. Cerebral autoregulation in orthostatic hypotension: a transcranial Doppler study. Stroke. 1994;25:1771-1775.[Abstract]

6. Lassen NA. Cerebral blood flow and oxygen consumption in man. Physiol Rev. 1959;39:183-238.[Free Full Text]

7. Strandgaard S, Paulson OB. Cerebral autoregulation. Stroke. 1984;15:413-416.[Free Full Text]

8. Paulson OB, Strandgaard S, Edvinsson L. Cerebral autoregulation. Cerebrovasc Brain Metab Rev. 1990;2:161-192.[Medline] [Order article via Infotrieve]

9. Aaslid R, Lindegaard KF, Sorteberg W, Nornes H. Cerebral autoregulation dynamics in humans. Stroke. 1989;20:45-52.[Abstract/Free Full Text]

10. Newell DW, Aaslid R, Lam A, Mayberg TS, Winn HR. Comparison of flow and velocity during dynamic autoregulation testing in humans. Stroke. 1994;25:793-797.[Abstract]

11. Tiecks FP, Lam AM, Aaslid R, Newell DW. Comparison of static and dynamic cerebral autoregulation measurements. Stroke. 1995;26:1014-1019.[Abstract/Free Full Text]

12. Diehl RR, Linden D, Lücke D, Berlit P. Phase relationship between cerebral blood flow velocity and blood pressure: a clinical test of autoregulation. Stroke. 1995;26:1801-1804.[Abstract/Free Full Text]

13. Blaber A, Bondar RL, Stein F, Dunphy PT, Moradshahi P, Kassam MS, Freeman R. Complexity of middle cerebral artery blood flow velocity: effects of tilt and autonomic failure. Am J Physiol. In press.

14. Pagani M, Somers V, Furlan R, Dell'Orto S, Conway J, Baselli G, Cerutti S, Sleight P, Malliani A. Changes in autonomic regulation induced by physical training in mild hypertension. Hypertension. 1988;12:600-610.[Abstract/Free Full Text]

15. Holstein-Rathlou N-H, Wagner AJ, Marsh DJ. Tubuloglomerular feedback dynamics and renal blood flow autoregulation in rats. Am J Physiol. 1991;260:F53-F68.[Abstract/Free Full Text]

16. Bondar RL, Dunphy PT, Moradshahi P, Kassam MS, Blaber AP, Stein F, Freeman R. Cerebrovascular and cardiovascular responses to graded tilt in patients with autonomic failure. Stroke. 1997;28:1677-1685.[Abstract/Free Full Text]

17. Ogata K. Frequency response analysis. In: Modern Control Engineering. Englewood Cliffs, NJ: Prentice-Hall Inc; 1990:426-535.

18. Blaber AP, Bondar RL, Freeman R. Coarse grained spectral analysis of HR and BP variability in patients with autonomic failure. Am J Physiol. 1996;271:H1555-H1564.[Abstract/Free Full Text]

19. Triedman JK, Saul JP. Blood pressure modulation by central venous pressure and respiration: buffering effects of heart rate reflexes. Circulation. 1994;89:169-179.[Abstract/Free Full Text]

20. Saul JP, Berger RD, Chen MH, Cohen RJ. Transfer function analysis of autonomic regulation, II: respiratory sinus arrhythmia. Am J Physiol. 1989;256:H153-H161.[Abstract/Free Full Text]

21. Hirsch JA, Bishop B. Respiratory sinus arrhythmia in humans: how breathing pattern modulates heart rate. Am J Physiol. 1981;241:H620-H629.[Abstract/Free Full Text]

22. Berger RD, Saul JP, Cohen RJ. Assessment of autonomic response by broad-band respiration. IEEE Trans Biomed Eng. 1989;36:1061-1065.[Medline] [Order article via Infotrieve]

23. Hughson RL, Quintin L, Annat G, Yamamoto Y, Gharib C. Spontaneous baroreflex by sequence and power spectral methods in humans. Clin Physiol. 1993;13:663-676.[Medline] [Order article via Infotrieve]

24. De Boer RW, Karemaker JM, Strackee J. Relationships between short-term blood-pressure fluctuations and heart-rate variability in resting subjects, II: a simple model. Med Biol Eng Comput. 1985;23:359-364.[Medline] [Order article via Infotrieve]

25. De Boer RW, Karemaker JM, Strackee J. Relationships between short-term blood-pressure fluctuations and heart-rate variability in resting subjects, I: a spectral analysis approach. Med Biol Eng Comput. 1985;23:352-358.[Medline] [Order article via Infotrieve]

26. Omboni S, Parati G, Frattola A, Mutti E, DiRienzo M, Castiglioni P, Mancia G. Spectral and sequence analysis of finger blood pressure variability: comparison with analysis of intra-arterial recordings. Hypertension. 1993;22:26-33.[Abstract/Free Full Text]

27. Giller CA, Bowman G, Dyer H, Mootz L, Krittner W. Cerebral arterial diameters during changes in blood pressure and carbon dioxide during craniotomy. Neurosurg. 1993;32:737-741.[Medline] [Order article via Infotrieve]

28. Lindegaard K-F, Lundar T, Wiberg J, Sjøberg D, Aaslid R, Nornes H. Variations in middle cerebral artery blood flow investigated with noninvasive transcranial blood velocity measurements. Stroke. 1987;18:1025-1030.[Abstract/Free Full Text]

29. Huber P, Handa J. Effect of contrast material, hypercapnia, hyperventilation, hypertonic glucose and papaverine on the diameter of the cerebral arteries: angiographic determination in man. Invest Radiol. 1967;2:17-32.[Medline] [Order article via Infotrieve]

30. Bondar RL, Kassam MS, Stein F, Dunphy PT, Fortney SM, Riedesel ML. Simultaneous cerebrovascular and cardiovascular responses during presyncope. Stroke. 1995;26:1794-1800.[Abstract/Free Full Text]

31. Mano T, Iwase S, Watanabe T, Saito M. Age-dependency of sympathetic nerve response to gravity in humans. Physiologist. 1991;34:s121-s124.

32. Rosner MJ, Coley IB. Cerebral perfusion pressure, intracranial pressure, and head elevation. J Neurosurg. 1986;65:636-641.[Medline] [Order article via Infotrieve]

33. Malliani A, Pagani M, Lombardi F, Furlan R, Guzzetti S, Cerutti S. Spectral analysis to assess increased sympathetic tone in arterial hypertension. Hypertension. 1991;17(suppl III):III-36-III-42.

34. Blaber AP, Hughson RL. Cardiorespiratory interactions during fixed pace resistive breathing. J Appl Physiol. 1996;80:1618-1626.[Abstract/Free Full Text]

35. Freeman R, Saul JP, Cohen RJ. Transfer function and spectral analysis of heart rate in diabetic autonomic neuropathy. Muscle Nerve. 1995;18:74-84.[Medline] [Order article via Infotrieve]

36. Hughson RL, Maillet A, Dureau G, Yamamoto Y, Gharib C. Spectral analysis of blood pressure variability in heart transplant patients. Hypertension. 1995;25:643-650.[Abstract/Free Full Text]

37. Levine BD, Giller CA, Lane LD, Buckey JC, Blomqvist CG. Cerebral versus systemic hemodynamics during graded orthostatic stress in humans. Circulation. 1994;90:298-306.[Abstract/Free Full Text]

38. Yoshida K, Meyer JS, Sakamoto K, Handa J. Autoregulation of cerebral blood flow: electromagnetic flow measurements during acute hypertension in the monkey. Circ Res. 1966;19:726-738.[Abstract/Free Full Text]

39. Aaslid R, Newell DW, Stooss R, Sorteberg W, Lindegaard K-F. Assessment of cerebral autoregulation dynamics from simultaneous arterial and venous transcranial Doppler recordings in humans. Stroke. 1991;22:1148-1154.[Abstract/Free Full Text]

40. Peng CK, Mietus J, Hausdorff JM, Havlin S, Stanley HE, Goldberger AL. Long-range anticorrelations and non-Gaussian behavior of the heartbeat. Phys Rev Let. 1993;70:1343-1346.[Medline] [Order article via Infotrieve]

41. Yamamoto Y, Hughson RL. Extracting fractal components from time series. Physica D. 1993;68:250-264.

42. Butler GC, Yamamoto Y, Hughson RL. Fractal nature of short-term systolic blood pressure and heart rate variability during lower body negative pressure. Am J Physiol. 1994;267:R26-R33.[Abstract/Free Full Text]

This article has been cited by other articles:

				D. A. Low, J. E. Wingo, D. M. Keller, S. L. Davis, J. Cui, R. Zhang, and C. G. Crandall Dynamic cerebral autoregulation during passive heat stress in humans Am J Physiol Regulatory Integrative Comp Physiol, May 1, 2009; 296(5): R1598 - R1605. [Abstract] [Full Text] [PDF]

				M. Ichinose, S. Koga, N. Fujii, N. Kondo, and T. Nishiyasu Modulation of the spontaneous beat-to-beat fluctuations in peripheral vascular resistance during activation of muscle metaboreflex Am J Physiol Heart Circ Physiol, July 1, 2007; 293(1): H416 - H424. [Abstract] [Full Text] [PDF]

				K.-i. Iwasaki, B. D. Levine, R. Zhang, J. H. Zuckerman, J. A. Pawelczyk, A. Diedrich, A. C. Ertl, J. F. Cox, W. H. Cooke, C. A. Giller, et al. Human cerebral autoregulation before, during and after spaceflight J. Physiol., March 15, 2007; 579(3): 799 - 810. [Abstract] [Full Text] [PDF]

				C. H. Gibbons and R. Freeman Delayed orthostatic hypotension: A frequent cause of orthostatic intolerance. Neurology, July 11, 2006; 67(1): 28 - 32. [Abstract] [Full Text] [PDF]

				G. D. Mitsis, R. Zhang, B. D. Levine, and V. Z. Marmarelis Cerebral hemodynamics during orthostatic stress assessed by nonlinear modeling J Appl Physiol, July 1, 2006; 101(1): 354 - 366. [Abstract] [Full Text] [PDF]

				R. B. Panerai, P. J. Eames, and J. F. Potter Multiple coherence of cerebral blood flow velocity in humans Am J Physiol Heart Circ Physiol, July 1, 2006; 291(1): H251 - H259. [Abstract] [Full Text] [PDF]

				Y. Ogawa, K.-i. Iwasaki, S. Shibata, J. Kato, S. Ogawa, and Y. Oi The Effect of Sevoflurane on Dynamic Cerebral Blood Flow Autoregulation Assessed by Spectral and Transfer Function Analysis Anesth. Analg., February 1, 2006; 102(2): 552 - 559. [Abstract] [Full Text] [PDF]

				M. Latka, M. Turalska, M. Glaubic-Latka, W. Kolodziej, D. Latka, and B. J. West Phase dynamics in cerebral autoregulation Am J Physiol Heart Circ Physiol, November 1, 2005; 289(5): H2272 - H2279. [Abstract] [Full Text] [PDF]

				R. B. Panerai, M. Moody, P. J. Eames, and J. F. Potter Dynamic cerebral autoregulation during brain activation paradigms Am J Physiol Heart Circ Physiol, September 1, 2005; 289(3): H1202 - H1208. [Abstract] [Full Text] [PDF]

				J. W. Hamner, M. A. Cohen, S. Mukai, L. A. Lipsitz, and J. A. Taylor Spectral indices of human cerebral blood flow control: responses to augmented blood pressure oscillations J. Physiol., September 15, 2004; 559(3): 965 - 973. [Abstract] [Full Text] [PDF]

				M. R. Edwards, D. L. Devitt, and R. L. Hughson Two-breath CO2 test detects altered dynamic cerebrovascular autoregulation and CO2 responsiveness with changes in arterial PCO2 Am J Physiol Regulatory Integrative Comp Physiol, September 1, 2004; 287(3): R627 - R632. [Abstract] [Full Text] [PDF]

				M. Brys, C. M. Brown, H. Marthol, R. Franta, and M. J. Hilz Dynamic cerebral autoregulation remains stable during physical challenge in healthy persons Am J Physiol Heart Circ Physiol, August 7, 2003; 285(3): H1048 - H1054. [Abstract] [Full Text] [PDF]

				M. R. Edwards, Z. L. Topor, and R. L. Hughson A new two-breath technique for extracting the cerebrovascular response to arterial carbon dioxide Am J Physiol Regulatory Integrative Comp Physiol, March 1, 2003; 284(3): R853 - R859. [Abstract] [Full Text] [PDF]

				M. R. Edwards, J. K. Shoemaker, and R. L. Hughson Dynamic modulation of cerebrovascular resistance as an index of autoregulation under tilt and controlled PETCO2 Am J Physiol Regulatory Integrative Comp Physiol, September 1, 2002; 283(3): R653 - R662. [Abstract] [Full Text] [PDF]

				M J Hilz, F B Axelrod, U Haertl, C M Brown, and B Stemper Transcranial Doppler sonography during head up tilt suggests preserved central sympathetic activation in familial dysautonomia J. Neurol. Neurosurg. Psychiatry, May 1, 2002; 72(5): 657 - 660. [Abstract] [Full Text] [PDF]

				R. Schondorf, R. Stein, R. Roberts, J. Benoit, and W. Cupples Dynamic cerebral autoregulation is preserved in neurally mediated syncope J Appl Physiol, December 1, 2001; 91(6): 2493 - 2502. [Abstract] [Full Text] [PDF]

				J. M. Serrador, S. J. Wood, P. A. Picot, F. Stein, M. S. Kassam, R. L. Bondar, A. H. Rupert, and T. T. Schlegel Effect of acute exposure to hypergravity (GX vs. GZ) on dynamic cerebral autoregulation J Appl Physiol, November 1, 2001; 91(5): 1986 - 1994. [Abstract] [Full Text] [PDF]

				R. L. Hughson, M. R. Edwards, D. D. O'Leary, and J. K. Shoemaker Critical Analysis of Cerebrovascular Autoregulation During Repeated Head-Up Tilt Stroke, October 1, 2001; 32(10): 2403 - 2408. [Abstract] [Full Text] [PDF]

				J. Sato, M. Tachibana, T. Numata, T. Nishino, and A. Konno Differences in the dynamic cerebrovascular response between stepwise up tilt and down tilt in humans Am J Physiol Heart Circ Physiol, August 1, 2001; 281(2): H774 - H783. [Abstract] [Full Text] [PDF]

				R. B. Panerai, S. L. Dawson, P. J. Eames, and J. F. Potter Cerebral blood flow velocity response to induced and spontaneous sudden changes in arterial blood pressure Am J Physiol Heart Circ Physiol, May 1, 2001; 280(5): H2162 - H2174. [Abstract] [Full Text] [PDF]

				L. A. Lipsitz, S. Mukai, J. Hamner, M. Gagnon, and V. Babikian Dynamic Regulation of Middle Cerebral Artery Blood Flow Velocity in Aging and Hypertension Stroke, August 1, 2000; 31(8): 1897 - 1903. [Abstract] [Full Text] [PDF]

				M.P.M. Harms, W.N.J.M. Colier, W. Wieling, J.W.M. Lenders, N.H. Secher, and J.J. van Lieshout Orthostatic Tolerance, Cerebral Oxygenation, and Blood Velocity in Humans With Sympathetic Failure Stroke, July 1, 2000; 31(7): 1608 - 1614. [Abstract] [Full Text] [PDF]

				R. Zhang, J. H. Zuckerman, and B. D. Levine Spontaneous fluctuations in cerebral blood flow: insights from extended-duration recordings in humans Am J Physiol Heart Circ Physiol, June 1, 2000; 278(6): H1848 - H1855. [Abstract] [Full Text] [PDF]

				R. B. Panerai, S. L. Dawson, and J. F. Potter Linear and nonlinear analysis of human dynamic cerebral autoregulation Am J Physiol Heart Circ Physiol, September 1, 1999; 277(3): H1089 - H1099. [Abstract] [Full Text] [PDF]

				A.E. Baird, S. Warach, K. W. Muir, and D. G. Grosset Using Pathophysiology in Acute Stroke Trials Response Stroke, June 1, 1999; 30(6): 1293 - 1293. [Full Text] [PDF]

				R. B. Panerai, D. H. Evans, A. R. Naylor, A. Hetzel, K. Kempf, and S. Braune Influence of Arterial Blood Pressure on Cerebrovascular Reactivity Response Stroke, June 1, 1999; 30 (6): 1293 - 1295. [Full Text]

				R. B. Panerai, R. P. White, H. S. Markus, and D. H. Evans Grading of Cerebral Dynamic Autoregulation From Spontaneous Fluctuations in Arterial Blood Pressure Stroke, November 1, 1998; 29(11): 2341 - 2346. [Abstract] [Full Text] [PDF]

				R. Zhang, J. H. Zuckerman, and B. D. Levine Deterioration of cerebral autoregulation during orthostatic stress: insights from the frequency domain J Appl Physiol, September 1, 1998; 85(3): 1113 - 1122. [Abstract] [Full Text] [PDF]

				A. P. Blaber, R. L. Bondar, F. Stein, P. T. Dunphy, P. Moradshahi, M. S. Kassam, and R. Freeman Complexity of middle cerebral artery blood flow velocity: effects of tilt and autonomic failure Am J Physiol Heart Circ Physiol, November 1, 1997; 273(5): H2209 - H2216. [Abstract] [Full Text] [PDF]

				R. L. Bondar, P. T. Dunphy, P. Moradshahi, M. S. Kassam, A. P. Blaber, F. Stein, and R. Freeman Cerebrovascular and Cardiovascular Responses to Graded Tilt in Patients With Autonomic Failure Stroke, September 1, 1997; 28(9): 1677 - 1685. [Abstract] [Full Text]

This Article Abstract Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Request Permissions Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Blaber, A. P. Articles by Freeman, R. Search for Related Content PubMed PubMed Citation Articles by Blaber, A. P. Articles by Freeman, R.