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Phase Relationship Between Cerebral Blood Flow Velocity and Blood Pressure

A Clinical Test of Autoregulation
Originally published 1995;26:1801–1804


    Background and Purpose This study investigates the usefulness, as a test of dynamic autoregulation, of phase shift angle analysis between oscillations in cerebral blood flow velocity (CBFV) and in arterial blood pressure (ABP) during deep breathing.

    Methods Fifty healthy volunteers, 20 patients with occlusive cerebrovascular diseases (OCD), and 10 patients with arteriovenous malformations (AVM) took part in the study. All subjects received transcranial Doppler monitoring of both middle cerebral arteries (MCAs). In addition, continuous blood pressure monitoring was performed with the use of noninvasive servo-controlled infrared finger plethysmography during deep breathing at a rate of 6/min. With the use of a high-pass filter model of autoregulation, autoregulation was quantified as phase shift angle between oscillations in CBFV and ABP at a frequency of 6/min. A phase shift angle of 0° indicates total absence of autoregulation, while 90° can be gauged as optimal autoregulation. In addition, vasomotor reactivity of both MCAs to CO2 stimulation was assessed among patients and calculated as percent increase in CBFV per millimeter of mercury of increase in CO2.

    Results All normal subjects showed positive phase shift angles between CBFV and ABP (mean±SD, 70.5±29.8°). OCD patients presented with significantly decreased phase shift angles for the MCA only on the pathological side (51.7±35.1°; P<.05). Patients with AVM showed significantly reduced phase shift angles on both the affected side (26.8±13.5°; P<.001) and the unaffected side (40.6±26.6°; P<.01). In patients’ groups, phase shift angle and vasomotor reactivity correlated significantly (r=.66; P<.001) after results from all MCAs were pooled.

    Conclusions Results confirm the high-pass filter model of cerebral autoregulation: Normal subjects showed predicted positive phase shift angles between CBFV and ABP oscillations. Patients with expected autoregulatory disturbances showed significant decreases in phase shift angles. Close correlations existed between autoregulation and CO2-induced vasomotor reactivity.

    Autoregulation is the property of small cerebral arteries to maintain CBF constant during changes in ABP. Autoregulation testing involves introductions of variations in ABP and simultaneous measurements of CBF responses. Aaslid et al1 recently developed an autoregulation test for clinical application using TCD to record CBFV during stepwise reductions in ABP by deflation of leg cuffs. They showed that intact autoregulatory responses are characterized by initial pressure-passive decreases in CBFV followed by returns to baseline CBFV within a few seconds. Using the same paradigm, Newell et al2 demonstrated that time courses in CBFV expressed as deviations from baseline in percentage were nearly identical to responses in CBF measured directly within the ICA. Relative changes in CBFV seem to reflect relative changes in CBF during autoregulation testing, and thus TCD offers an appropriate method to measure dynamic cerebral autoregulation.

    In biological and artificial feedback control systems, high-pass filtering is a typical response of the system to the introduction of a disturbance. In the context of autoregulatory feedback control systems, variations in ABP can be considered a disturbance of the system. The goal of autoregulation is to keep influences of disturbances on CBF as low as possible. The CBFV response to a step change in ABP in the studies cited above was similar to the response of a high-pass filter to a step change in the input signal: an initial step in the output signal followed by slow recovery. This suggests that the dynamics of autoregulatory systems may be described in terms of high-pass filtering.

    If the high-pass filter model of cerebral autoregulation is correct, it should be possible to predict the CBFV response to each type of ABP variation. The present study was undertaken to test the CBFV response to sinusoidal oscillations in ABP and to evaluate the usefulness of this simple test in assessing human cerebral autoregulation.

    Subjects and Methods

    Fifty healthy subjects (25 female), aged 44.7±15.0 years (mean±SD), were tested by the autoregulation test as normative controls. Twenty patients (11 female) with OCD, aged 48.7±17.9 years, and 10 patients (5 female) with intracranial AVMs, aged 34.3±15.8 years, served as samples with expected disturbances of cerebral autoregulation. In the OCD group, 12 patients had been treated with unilateral balloon occlusion of the ICA because of ICA aneurysms. Two patients had atherosclerotic occlusions of the ICA (1 unilateral, 1 bilateral), 3 patients had high-degree ICA stenoses (>70%; 2 unilateral, 1 bilateral), and 3 patients had stenoses of the MCA (2 unilateral, 1 bilateral). The 10 AVMs were mainly fed by the MCA; 5 patients had large AVMs (diameter >6 cm), and 5 patients had medium-sized AVMs (diameter 3 to 6 cm). All cerebral arterial stenoses/occlusions and AVMs were diagnosed and graded angiographically. All participants gave their informed consent.

    Sinusoidal oscillations in ABP were elicited by slow breathing at a rate of 6/min for 60 seconds. Every 5 seconds subjects received instructions to breathe in or to breathe out. This test is used in clinical neurophysiology as a standardized paradigm for assessing vagally mediated heart beat variations.3 Continuous monitoring of ABP and heart rate demonstrates that slow breathing evokes sinusoidal oscillations at the respiratory frequency for both parameters. The following parameters were recorded continuously during slow breathing: (1) CBFV of both MCAs by TCD, with the use of a bilateral TCD monitor (Multidop-X, DWL); (2) continuous ABP; and (3) heart rate with noninvasive servo-controlled infrared finger plethysmography (Finapres, model 2300, Ohmeda).

    In both patient groups, in addition to autoregulatory testing, CO2 reactivity was assessed in both MCAs. Details of CO2 testing are described elsewhere.4 Relative increases in CBFV during hypercapnia per increases in end-expiratory CO2 pressure (expressed as %/mm Hg) were determined in the calculation of VMR. VMR reference values were taken from control subjects of Diehl et al4 (78 intracranial arteries from 15 normal subjects, aged 18 to 63 years).

    Under the high-pass filter model of cerebral autoregulation, variations in ABP should be transmitted to CBFV according to the following equation:

    where CBFV(f) and ABP(f) are frequency domain expressions of time courses for CBF and ABP, respectively, at a given frequency, f. HP(f) represents the gain and phase shift angle of the high-pass filter at this frequency. A high-pass filter produces a frequency-dependent phase shift angle [φ(f)] between the input signal [ABP(f)] and the output signal [CBFV(f)], which is given by the formula

    where T is the time constant of the high-pass filter. φ(f) approaches 0° at very high frequencies and 90° at relatively slow frequencies, depending on the value of the time constant T. Fast Fourier transformation was used to calculate the amplitudes and phases of the recorded parameters at a frequency of 6/min during the slow breathing paradigm. Assuming a high-pass filter mechanism of autoregulation, we expected to find a positive phase shift angle (somewhere between 0° and 90°) between CBFV and ABP under normal conditions. In the case of disturbed autoregulation, the phase shift angle between both parameters should be smaller, ie, CBFV should follow ABP more passively.

    Parametric data are expressed as mean±SD. Differences between groups were assessed with the use of one-sided Mann-Whitney tests for independent samples. One-sided significance levels were calculated because lower phase shift angles and lower VMR values, respectively, were expected in patients. Pearson′s correlation coefficient, r, was used to describe the correlation between quantitative variables. Significance levels were set at P=.05.


    In all normal subjects and patients, slow breathing elicited a near sinusoidal oscillation in ABP at a frequency of 6/min. CBFV showed similar oscillations to ABP, with expected positive phase shift angles (Fig 1). A phase shift angle was considered reliable when it remained constant over several breathing cycles. Otherwise, subjects/patients were trained to perform the breathing test more regularly. Six control subjects and 4 patients needed training to achieve required breathing rhythms and reliable phase shift angles. In normal control subjects, CBFV of both MCAs oscillated nearly synchronously (mean absolute difference in phase shift angle, 3.2±2.9°). Further analysis was thus restricted to the right MCA. Positive phase shift angles were observed against ABP oscillations between 29.8° and 133.2° (mean±SD, 70.5±29.8°) (Table 1). Phase shift angle and age did not correlate significantly (r=.20).

    In 20 OCD patients, a total of 23 MCAs were in the affected hemispheres, while 17 MCAs were unaffected. The phase shift angle in CBFV of pathological vessels was significantly reduced compared with normal values (Table 1; P<.05). For this comparison, we excluded data from the left-sided MCAs in the 3 patients with bilateral vascular pathology to achieve a sample of independent measures. Phase shift angles on unaffected sides were not significantly different from those in control subjects (P>.05). A typical example of a patient with left MCA stenosis is shown in Fig 2. Similar differences between patient data and control values were also found for VMR (Table 2).

    In AVM patients, phase shift angles were strongly reduced in CBFVs ipsilateral to the AVM when compared with control values (Table 1; P<.001). CBFV of the contralateral MCA also showed significantly decreased phase shift angles compared with control values (P<.01). Comparable results were also found for VMR (Table 2).

    In the two patient groups, we pooled VMR and phase shift angle data, respectively, from occluded and normal sides to calculate correlation coefficients between both parameters. A close correlation existed between the two parameters (r=.66; P<.001).


    TCD has been previously demonstrated to be a valuable tool for quantifying dynamic cerebral autoregulation.125 While the test paradigm of the Aaslid/Newell group needs a special device for stepwise decreases in ABP, the slow breathing test presented here requires only the patient’s capability to breathe at a constant slow rate. After some training, all subjects/patients succeeded in producing sinusoidal oscillations in blood pressure at a breathing frequency of 6 cycles per minute. These fluctuations were transmitted to CBFV. As expected from the high-pass filter model of autoregulation, CBFV oscillations showed a positive phase shift angle against ABP of approximately 70°, with a lower normal limit of approximately 30°.

    The methodical validity of our autoregulation test may be questioned by the fact that we did not prove the constancy of the MCA diameter during the breathing test. This is a critical point, because in principle CBFV changes can be elicited by fluctuations in MCA diameter at the insonation site. However, since even the strong blood pressure step used by the Aaslid/Newell group obviously did not significantly change the MCA diameter2 (see introductory paragraph), it is unlikely that oscillations in MCA diameter will be induced by the slight ABP waves in our paradigm.

    We tested the clinical validity of the phase shift angle in CBFV as a measurement of cerebral autoregulation in two groups of patients known to be prone to autoregulatory disturbances. Patients with OCD have increased cerebrovascular resistance at proximal vessel sites (ICA or MCA). Peripheral cerebral resistance vessels dilate under such conditions to compensate for the cerebral perfusion pressure drop caused by the proximal increase in resistance. Since maximal dilatory capacity of arterioles is limited, counter regulation against blood pressure variations becomes more and more difficult with increasing proximal resistance. In consequence, VMR to vasodilating stimuli such as hypercapnia diminishes, as demonstrated by 133Xe CBF measurements6 and by TCD.789 This could also be shown in our OCD patients who exhibited a significant VMR decrease in the affected MCA. As predicted by the high-pass model, the phase shift angle was also significantly reduced in the affected vessels. In extreme cases phase shift angles were equal to 0° (Fig 2), and CBFV showed a blood pressure–passive behavior. In common with the VMR results, phase shift angles of nonaffected MCAs did not differ from normal values.

    Two different mechanisms are responsible for disturbed autoregulation in AVM patients. In AVM feeders, a large part of nonnutritional flow supplies the AVM nidus, which does not contain the arteriolar bed necessary for autoregulation.410111213 Nonfeeders (eg, the contralateral MCA) may demonstrate autoregulatory failure when the AVM produces a strong drop in cerebral perfusion pressure at the level of the circle of Willis that exceeds the lower limits of autoregulation (steal phenomenon).414 Pathological autoregulation in AVM feeders—and also, to a lesser degree, in nonfeeders—has been proven by several TCD studies with the use of the CO2 test.41516 In our sample of AVM patients, feeders showed a strong and nonfeeders a moderate reduction in VMR. Again, phase shift angles of feeding and nonfeeding MCAs showed decreases comparable to VMR.

    Phase shift angles and VMR values were more affected in AVM patients than in OCD patients. Since 12 of the 20 OCD patients had balloon occlusions of one ICA, these data cannot be generalized to a population with exclusively atherosclerotic OCD.

    In addition to subgroup analysis, we compared VMR and phase shift angle by calculating correlation coefficients between both variables in pooled patient groups. A substantial correlation of r=.66 was found. This indicates that these different tests of hemodynamic responsiveness (VMR, static response to an increase in arterial CO2; phase shift angle, dynamic autoregulation) measure essentially the same cerebrovascular property.

    This does not, however, prove the equivalence of metabolic regulations of CBF (a part of which is the CO2-dependent H+ activity) and autoregulation. Several authors consider cerebral autoregulation an intrinsic myogenic mechanism that is unrelated to metabolic or neuronal control of CBF.1718 On the other hand, Aaslid et al15 have suggested that the same feedback loop is involved in metabolic regulation and dynamic autoregulation of CBF, because the time responses of blood flow changes to functional stimuli and to blood pressure steps are practically identical. Diehl et al19 recently presented a cybernetic model of metabolic regulation that predicts a low-pass filter response in CBF to functional stimuli and a high-pass filter response to blood pressure variations, using the same metabolic feedback loop. However, this model does not exclude the existence of an additional myogenic component in cerebral autoregulation.

    Irrespective of the exact mechanism of autoregulation, the hemodynamic state in OCD and AVM patients is caused primarily by a disturbance of autoregulation due to a drop in cerebral perfusion pressure and not to an uncoupling of metabolism and CBF. Thus, the measurement of dynamic autoregulation seems to be more appropriate than the assessment of CO2 responsiveness in these patients. Furthermore, in contrast to CO2 stimulation, the deep breathing test is totally without stress for patients. However, the TCD CO2 test is a well-established tool in the management and monitoring of patients with OCD.789 Further studies will be needed to demonstrate the clinical usefulness of dynamic autoregulation testing, for example, in deciding whether an OCD patient may profit from extracranial-intracranial bypass surgery.

    In conclusion, deep breathing at a constant rate elicits sinusoidal oscillations in blood pressure at the respiratory frequency that are transmitted to CBFV. In accordance with our high-pass filter model of autoregulation, a positive phase shift angle occurs between CBFV and ABP oscillations. This phase shift angle is significantly reduced in patients with a presumed disturbance of autoregulation. Phase shift angle and VMR as assessed by CO2 stimulation are significantly intercorrelated. Further studies will show whether dynamic autoregulation testing is an equivalent or even a better alternative to TCD CO2 testing.

    Selected Abbreviations and Acronyms

    ABP=arterial blood pressure
    AVM=arteriovenous malformation
    CBF=cerebral blood flow
    CBFV=cerebral blood flow velocity
    ICA=internal carotid artery
    MCA=middle cerebral artery
    OCD=occlusive cerebrovascular disease
    TCD=transcranial Doppler ultrasonography
    VMR=vasomotor reactivity<\/.>

          Figure 1.

    Figure 1. Recordings of heart rate (HR) in beats per minute (bpm), ABP, and CBFV of both MCAs in a healthy subject during forced breathing at 6/min. Bars indicate the positive phase shift angle between oscillations in CBFV and ABP.

          Figure 2.

    Figure 2. Recordings of heart rate (HR) in beats per minute (bpm), ABP, and CBFV of both MCAs in a 61-year-old male subject with severe stenosis of the left MCA during forced breathing at 6/min (poststenotic insonation of left MCA). Bars indicate the missing phase shift angle between oscillations in CBFV of left MCA and in ABP (CBFV follows passively ABP) and the positive phase shift on the normal side.

    Table 1. Phase Shift Angles Between CBFV and ABP of Different Groups

    SamplePhase Shift Angle, °P1
    Control subjects
    Right MCA (n=50)70.5±29.8
    OCD patients
    Affected MCA (n=23)51.7±35.1<.052
    Unaffected MCA (n=17)81.3±31.2>.05 (NS)
    AVM patients
    Affected MCA (n=10)26.8±13.5<.001
    Unaffected MCA (n=10)40.6±26.6<.01

    Values are mean±SD.

    1Significance of differences in patients vs control subjects is indicated (one-sided Mann-Whitney test).

    2Data from three left-sided MCAs in patients with bilateral vascular pathology were excluded in calculation of the significance level.

    Table 2. VMR Values of Different Groups

    SampleVMR, %/mm HgP1
    Control subjects
    Intracranial arteries (n=78)5.26±1.61
    OCD patients
    Affected MCA (n=23)3.12±1.62<.0012
    Unaffected MCA (n=17)5.05±1.26>.05 (NS)
    AVM patients
    Affected MCA (n=10)1.08±.39<.001
    Unaffected MCA (n=10)3.57±2.14<.01

    Values are mean±SD.

    1Significance of differences in patients vs control subjects is indicated (one-sided Mann-Whitney test).

    2Data from three left-sided MCAs in patients with bilateral vascular pathology were excluded in calculation of the significance level.


    Correspondence to Dr Rolf R. Diehl, Department of Neurology, Alfried Krupp Krankenhaus, Alfried-Krupp-Str 21, 45117 Essen, Germany.


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