Relationships Between Cerebral Regional Blood Flow Velocities and Volumetric Blood Flows and Their Respective Reactivities to Acetazolamide
Background and Purpose The technique of transcranial Doppler ultrasonography (TCD) is widely used for assessment of cerebral blood flow velocity. Whether measurement of changes in TCD velocity can be used for studying volumetric cerebral blood flow variations remains a matter of debate. We therefore investigated the relationship between flow velocity and volumetric cerebral blood flow before and during acetazolamide-induced vasodilation.
Methods The middle cerebral artery mean blood flow velocity (MV) measured by TCD and the corresponding regional and hemispheric cerebral blood flows assessed with 133Xe single-photon emission CT were measured in 52 unselected patients. Absolute values of flow and velocity before and after stimulation and their reactivity to acetazolamide were compared. When the correlation was statistically significant, the linearity of the relationship was tested.
Results Absolute values of hemispheric cerebral blood flow were correlated with MV both before (r=.315, P=.02) and after acetazolamide (r=.436, P=.001), whereas regional cerebral blood flow was correlated with MV only after acetazolamide (before, r=.262, P=.06; after, r=.446, P=.001). All these relationships fitted a linear model. In contrast, there was no correlation between acetazolamide-induced relative increments of flow and velocity.
Conclusions Our results support a linear model describing the relationship between absolute values of flow and velocity when arterial section is the slope and anastomotic blood flow is the intercept. In contrast, relative increments in volumetric flow and velocity may be proportional only if anastomotic flow is negligible, ie, in subjects without cerebrovascular disease. We conclude that, for patients with cerebrovascular disease, TCD does not satisfactorily model cerebral vasoreactivity in terms of volumetric cerebral blood flow.
Transcranial Doppler ultrasonography offers a noninvasive approach to cerebral hemodynamics.1 By instantaneous determination of ultrasonic frequency shifts, this technique allows continuous measurement of blood velocity to be made within the large intracranial vessels, from the common carotid and vertebral arteries to secondary branches downstream from the circle of Willis. However, assimilation of frequency shifts to volumetric blood flow or to vascular resistance is still a matter of controversy,2 fueled by an abundant literature.3 4 5 6 7 8 9 10 11 12 13 14 15 16
Comparison of TCD with reference methods has been undertaken under various conditions in both animal models and healthy volunteers as well as in cerebrovascular patients. Discrepancy between volumetric blood flow and blood velocity measurements may be explained by the experimental conditions. We thus investigated the mathematical nature of the relationships between flow velocity and volumetric flow and between their respective variations in response to cerebral vasoreactivity tests. To this end, we measured rCBF and hCBF (133Xe tomoscintigraphy) and MV in the MCA (TCD) as well as their variations observed during an ACZ-induced vasodilation.
Subjects and Methods
The study protocol was approved by the hospital ethics committee. The 52 unselected subjects gave informed written consent for their participation. They had been referred to the hospital (by a physician who did not take part in the study) to undergo CBF measurement before and during an ACZ test.
The characteristics of the population and the indications for the ACZ test are presented in Table 1⇓. All subjects were free of vasoactive medication and had a temporal window suitable for TCD examination. Subjects with bilateral high-grade stenosis of the MCA or internal carotid artery were excluded because the results could have been perturbed by turbulent flows.
Blood pressure and heart rate were measured with a sphygmomanometer by the acoustic method with patients at rest in the supine position.
Petco2 was measured with an infrared analyzer (Sirecust, Siemens).17
We measured MCA MV using the pulsed TCD technique (Medasonics Transpect, 2 MHz, Mediag), as previously described.18 The Doppler probe was fixed over the temple with a special headset. Depth of focus was increased until bidirectional flow appeared (bifurcation of the internal carotid artery). It was then progressively decreased until an exclusively positive signal, typical of the MCA, was obtained and until this signal reached its maximum value. MV was recorded over an 8-second period, with the patient at rest in the supine position, without any acoustic or visual distraction. For these MV measurements, within-investigator variability was 3% and between-investigator variability 6%.18 In patients with unilateral or predominantly unilateral carotid or MCA lesions, the contralateral side was chosen for examination. In the other patients, the side of examination was randomized.
CBF was investigated with a dedicated SPECT (TOMOMATIC 64, Medimatic) with a spatial resolution of 1.7 cm. Measurements were made with the subject supine with closed eyes, without any acoustic or visual distraction. The patient's head was oriented so that three 2-cm-thick slices, located 1, 5, and 9 cm above the orbitomeatal line, were scanned. The principles of the technique and the methods of calculating CBF have been described elsewhere.19 20 133Xe (10 mL of a solution containing 60 mCi, 2200 mBq) was injected intravenously over a 1-minute period followed by 10 mL of physiological saline. CBF values are expressed in milliliters per minute per 100 g. For each region of interest, a computer program (head independent region of interest software, Medimatic) made automatic adjustments for the size of each brain and calculated flow values for each zone. The rCBF of the MCA territory and the ipsilateral hCBF were calculated on slice 2.
After the measurements of blood pressure and heart rate, a catheter was inserted into a forearm vein for xenon and ACZ injections. In a first sequence, before ACZ injection, patients underwent a SPECT determination of CBF (CBF1), which lasted 5 minutes. Petco2 was then measured, and a TCD determination (MV1) was immediately performed. ACZ (1 g dissolved in 20 mL of saline) was then injected over a period of 5 minutes.
After a 20-minute rest, a second sequence was performed in which blood pressure, heart rate, CBF2, Petco22, and MV2 were determined.
The relative increments of rCBF and hCBF (ΔCBF) were calculated in each patient as ΔCBF=100(CBF2−CBF1)/CBF1; the relative increments of MV (ΔMV) were calculated as ΔMV=100(MV2−MV1)/MV1.
Results are expressed as mean±SD. Data obtained before and after ACZ were compared with paired Student's t test.
Correlations between parameters were tested with the least-squares method. When two parameters are significantly correlated, a hypothesis of no association between these two parameters can reasonably be rejected. When the correlation was statistically significant (P<.05), we distributed MV values into classes of n±1 cm·s−1 (n being an odd number) and performed a test of variance ratio21 to determine whether a linear relationship could be refuted. This test was a one-way ANOVA. F is the variance of the deviation from the line (degree of freedom is the number of classes minus two) divided by the residual variance (degree of freedom is the number of points minus the number of classes). A significant F value indicates that a linear relationship can be refuted. With a nonsignificant F value, we considered the linear hypothesis to be acceptable and calculated the equation of the line (with the confidence intervals of slope and intercept).
ACZ administration did not significantly affect blood pressure or heart rate but induced the usual decrease in Petco2 (Table 3⇓). rCBF, hCBF, and MV significantly increased by a mean of 39%, 40%, and 41%, respectively (Table 3⇓).
For all significant correlations, the linearity tests led us to not refute a linear relationship and to calculate the equation of the line (Table 2⇑).
The TCD technique offers several advantages over other methods used for evaluation of cerebral hemodynamics: it is noninvasive and easy to perform, and it allows continuous measurement of blood flow velocity. It is thus tempting to propose TCD for the assessment of CBF. Numerous experimental and clinical studies have been undertaken over the last 10 years (Table 5⇓) to address the question of agreement between TCD and various “CBF” measurements (133Xe clearance measurements coupled9 10 11 16 or not3 6 8 13 14 15 with tomography, electromagnetic flowmetry,4 radioactive microspheres,5 thermodilution,7 arteriovenous oxygen difference,12 or positron emission tomography14 ), but their results are apparently difficult to reconcile. When quantitative agreement was tested, the usual approach was a correlation study, but a significant correlation between two parameters does not mean that the first one is equivalent to the second one. It only makes it unlikely that these two parameters vary independently. The question of quantitative agreement must be resolved with other statistical methods.22 Our aim was quite different as we performed correlation studies not to evidence an equivalence of the two methods (ie, TCD and SPECT) but to determine the nature of the mathematical relationship between two parameters (ie, blood velocity in a large cerebral vessel and the corresponding tissue blood flow).
Our results are apparently paradoxical: absolute values of velocities and flows were related before (except for rCBF and MV, P=.06) and after ACZ, but although their relative increments were similar in magnitude (mean of ≈40%), they were not correlated despite a large sample size (52 patients). This lack of correlation is in contrast with the high levels of significance obtained when absolute values of flows and velocities are compared. This suggests that inaccuracy of the techniques used or inadequate power of the statistical analysis cannot account for such a result.
In our study, in the three situations in which correlations between absolute values of flows and velocities were statistically significant, we tested the linearity of the relationship and found no reason to reject the linear hypothesis (Table 2⇑). The relationship between CBF and MV can thus be described according to a linear model \mathit|<|y|>||<|=|>|\mathit|<|a|>||<|+|>|\mathit|<|bx|>|where y is CBF and x is MV.
If we further analyze the model from a theoretical point of view, it is evident that rCBF is related to MV in the main arterial vessel of the region and to the vessel section (S), given the equation\mathit|<|ABF|>||<|=|>|\mathit|<|S|<|\cdot|>|MV|>|where ABF is arterial blood flow. It is also evident that rCBF is the sum of ABF in the main artery and of other flows directed to (or originating from) the vascular bed of the artery, ie, distal cortico-cortical anastomotic blood flows (anBF) (Fig 3⇓).
Transposed into the above equation and applied to rCBF and MV, these relations give\mathit|<|rCBF|>||<|=|>|\mathit|<|anBF|>||<|+|>|\mathit|<|(S|<|\cdot|>|MV)|>|In this equation, y is rCBF, the intercept is anBF, and slope is the main artery section S. This section is the mean section within the whole sample (and can be extrapolated to the whole population of patients). Applied to the MCA, such an approximation is acceptable because interindividual variability of its diameter in adults is relatively weak (mean diameter is 2.52 mm, and its variance is 0.79 mm223 ) compared with CBF or MV variabilities under pathological conditions.
If we accept these hypotheses, ACZ-induced MCA vasodilation may explain the increase in the slope after ACZ, keeping in mind that the difference between the slopes was not statistically significant.
More interestingly, if rCBF1 is related to MV1 (y1=a1+b1x1) and rCBF2 to MV2 (y2=a2+b2x2), it appears that\mathit|<|y|>|_|<|2|>|/\mathit|<|y|>|_|<|1|<|=|>||>|(\mathit|<|a|>|_|<|2|>||<|+|>|\mathit|<|b|>|_|<|2|>|\mathit|<|x|>|_|<|2|>|)/(\mathit|<|a|>|_|<|1|>||<|+|>|\mathit|<|b|>|_|<|1|>|\mathit|<|x|>|_|<|1|>|\mathit|<|)|>|The relationship between y2/y1 (ie, the relative increment of rCBF) and x2/x1 (ie, the relative increment of MV) cannot be linear, except if intercept a1=a2=0, ie, if anBF is zero or nonexistent. Under this condition only, Equation 2 becomes\mathit|<|y|>|_|<|2|>|/\mathit|<|y|>|_|<|1|>||<|=|>|\mathit|<|b|>|_|<|2|>|\mathit|<|x|>|_|<|2|>|/\mathit|<|b|>|_|<|1|>|\mathit|<|x|>|_|<|1|>|and indicates a linear relationship between the relative increments.
In contrast, if anBF does exist, the relative increments of rCBF and of CBF velocities should no longer be linearly related. This would occur when the theoretical and the actual vascular beds of a cerebral artery significantly differ. Since cerebral atherosclerosis and ischemia can induce changes in capillary perfusion heterogeneity,24 leading to functional cortico-cortical anastomoses, one major cerebral artery may then supply a territory adjoining its theoretical vascular bed.
A similar theoretical demonstration applied to hCBF leads to identical results. By analogy with Equation 1, hCBF is the sum of (1) the flow in the MCA (S·MV) and (2) additional flows in other arteries supplying the entire hemisphere (adBF):\mathit|<|hCBF|>||<|=|>|\mathit|<|adBF|<|+|>||>|(\mathit|<|S|<|\cdot|>|MV|>|)In this equation, y is hCBF, the intercept is adBF, and slope is the MCA section S. The relationship between the relative increments of hCBF and MV is likely to be linear only if flow and velocity vary in the same proportions in all arteries of the hemisphere during ACZ, ie, if cerebrovascular reactivity is homogeneous. Such a condition is not fulfilled in cerebrovascular patients. In other terms, the presence of a cerebrovascular disease precludes the observation of a linear relationship between relative increments of CBF and MV in the large arteries. These variations may be related, but the nonlinear mathematical relationship makes simple extrapolations from the one to the other very hazardous and a true concordance unlikely.
The theoretical demonstration used here for the relative increments of CBF and MV induced by ACZ can also be applied to other maneuvers such as hypercapnia or hypocapnia. Indeed, a thorough analysis of the literature (Table 5⇑) shows that the two studies that did not establish a significant correlation between quantitative variations of similar parameters were performed in patients with cerebrovascular disease,15 16 as was our investigation. Other studies performed in cerebrovascular patients either demonstrated a positive correlation but did not test linearity3 6 14 (quantitative agreement studies could have led to different results) or established a qualitative agreement9 11 or an agreement between TCD reactivity and a mean transit time.14 In all other studies (without cerebrovascular disease), a significant correlation was established without any linearity test.
In conclusion, CBF reactivity in patients with cerebrovascular disease must be assessed by a volumetric blood flow measurement approach. Measurement of blood velocity by the TCD technique investigates a different reactivity that is at least qualitatively9 11 or sometimes quantitatively3 6 related to CBF reactivity, but the relationship between the two estimations of cerebrovascular reactivity is unlikely to be linear. Hence, data on cerebrovascular reactivity obtained with the TCD technique in cerebrovascular patients should not be considered representative of quantitative volumetric flow reactivity. In healthy subjects or in patients with no significant cerebrovascular disease, further studies are needed to confirm whether (as seems likely) the two approaches do provide equivalent results.
Selected Abbreviations and Acronyms
|CBF||=||cerebral blood flow|
|hCBF||=||hemispheric cerebral blood flow|
|MCA||=||middle cerebral artery|
|MV||=||mean blood flow velocity|
|Petco2||=||end-tidal partial pressure of CO2|
|rCBF||=||regional cerebral blood flow|
|SPECT||=||single-photon emission CT|
This study was supported by Assistance Publique, Hôpitaux de Paris, Direction de la Recherche Clinique. We thank Agnès Barrier and Christine Dronneau for their excellent technical assistance and Dr Richard Sercombe for revising the English language.
- Received March 5, 1996.
- Revision received June 20, 1996.
- Accepted June 24, 1996.
- Copyright © 1996 by American Heart Association
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