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Published online before print March 4, 2005, 10.1148/radiol.2351031799
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(Radiology 2005;235:184-189.)
© RSNA, 2005

Neuroradiology

Distribution of Cerebral Blood Flow in the Circle of Willis1

Jeroen Hendrikse, MD, A. Fleur van Raamt, MD, Yolanda van der Graaf, MD, Willem P. T. M. Mali, MD and Jeroen van der Grond, PhD

1 From the Department of Radiology (J.H., W.P.T.M.M., J.v.d.G.) and the Julius Center for Health Sciences and Primary Care (A.F.v.R., Y.v.d.G.), University Medical Center Utrecht, PO Box 85500, Hp E 01.132, 3508 GA Utrecht, the Netherlands. Received November 7, 2003; revision requested January 28, 2004; final revision received April 24; accepted June 17. Address correspondence to J.H. (e-mail: j.hendrikse@azu.nl).


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
PURPOSE: To prospectively determine the effect of anatomic variations in the circle of Willis on volume flow in the internal carotid arteries (ICAs) and basilar artery (BA).

MATERIALS AND METHODS: Institutional review board approval and informed consent were obtained. Phase-contrast magnetic resonance (MR) angiography was used to measure the volume flow in the BA and ICAs in 208 patients (182 men, 26 women; mean age, 60 years) with symptomatic atherosclerosis or risk factors for atherosclerosis. Patients with steno-occlusive disease were excluded, and flow values were normalized for age. Three-dimensional time-of-flight MR angiograms were used to assess the anatomy of the circle of Willis. Differences in volume flow between a complete circle of Willis, a circle with a missing A1 segment, and a circle with a fetal-type posterior cerebral artery were analyzed (analysis of variance and Scheffé post hoc tests).

RESULTS: The ICA volume flow in subjects with a complete configuration of the circle of Willis was 245 mL/min ± 65 (standard deviation). Flow in the contralateral ICA was significantly increased (P < .01) in subjects with a missing A1 segment (303 mL/min ± 56) compared with control subjects and compared with flow on the ipsilateral side (214 mL/min ± 94; P < .01). In subjects with a unilateral or bilateral fetal-type posterior cerebral artery, the ICA volume flow was increased (P < .01) and the BA volume flow was decreased (P < .01) in comparison with the flow in subjects with no fetal-type circle of Willis.

CONCLUSION: Large asymmetries in volume flow between the right and left ICAs or decreased volume flow in the BA is not necessarily caused by vascular disease but may be caused by variations in the anatomy of the circle of Willis.

© RSNA, 2005


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Adequate volume flow in the major feeding arteries of the brain is crucial to maintaining cerebral blood flow and cerebral function (1–3). In this respect, determination of volume flow (in milliliters per minute) in the internal carotid arteries (ICAs) and the basilar artery (BA) has been used for the evaluation of cerebral hemodynamic impairment in patients with obstructive disease of the ICAs or posterior circulation (4–6), arteriovenous malformations (7,8), acute neurotrauma (9), or cerebral ischemia (10–12), as well as in the evaluation of vascular interventions such as bypass surgery (13,14) or carotid endarterectomy (15–17). For the interpretation of the volume flow values found in these studies, reliable reference values for the ICA and BA flow are necessary. In a report of a population study by Buijs et al (18), reference values of ICA and BA flow in 250 subjects were described. However, there was no evaluation of the intra- and interindividual differences in flow values of the ICAs and BA in that study (18). It can be expected that variations in the anatomy of the circle of Willis affect the determination of volume flow in the major feeding arteries of the brain in a normal population.

In an anatomically complete circle of Willis, the ICAs distribute flow into the ipsilateral anterior cerebral artery and middle cerebral artery, and the BA distributes flow into both posterior cerebral arteries (PCAs). However, results of several studies have shown that up to half of healthy control subjects have an anatomic variant type of the circle of Willis, such as a missing A1 segment of the anterior cerebral artery or a fetal-type PCA (19–22). It is expected that these variations have a direct effect on volume flow in the ICAs and BA. To our knowledge, thus far no study has been performed to examine the importance of the anatomic variations in the circle of Willis in relation to the volume flow in the ICAs and the BA. Thus, the purpose of the present study was to prospectively determine the effect of anatomic variations in the circle of Willis on volume flow in the ICAs and BA.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Subjects
Two hundred eight consecutive patients (mean age, 59.9 years; range, 29–79 years) from the Second Manifestations of Arterial Disease (SMART) study who did not have hemodynamically significant (>70%) ICA and BA stenosis or occlusion at duplex ultrasonography (US) were included in the study. The study comprised 182 men (mean age, 59.8 years; range, 29–79 years) and 26 women (mean age, 60.4 years; range, 39–74 years). The numbers of patients in each age decile were as follows: 3rd decade, eight patients; 4th decade, 36 patients; 5th decade, 67 patients; 6th decade, 72 patients; and 7th decade, 25 patients. The 70% stenosis grading at duplex US was based on velocities obtained from an earlier duplex US study, in which measurements of carotid stenosis were evaluated according to North American Symptomatic Carotid Endarterectomy Trial criteria (23). The SMART study is a single-institution prospective cohort study that was started in September 1996. All eligible patients aged 18–79 years with symptomatic atherosclerosis or risk factors for atherosclerosis are screened for additional risk factors or severity of atherosclerosis. Definitions of the diseases for which patients qualify for enrollment are reported elsewhere (24). Starting in June 2001, patients without contraindications to magnetic resonance (MR) imaging (eg, pacemakers, claustrophobia) were included in the SMART-MR study. Patients with a major disabling stroke were excluded from the present analysis. The SMART and SMART-MR studies were approved by our institutional review board, and informed consent has been obtained for each patient.

MR Angiography
The MR investigations were performed by using a 1.5-T whole-body system (Gyroscan ACS-NT; Philips Medical Systems, Best, the Netherlands). On the basis of data from a localizer MR angiography slab in the sagittal plane, a two-dimensional phase-contrast section was positioned at the level of the skull base to measure the volume flow in the ICAs and the BA. Figure 1 illustrates the positioning of the two-dimensional phase-contrast section through the ICAs and the BA (repetition time msec/echo time msec, 16/9; flip angle, 7.5°; section thickness, 5 mm; field of view, 250 x 250 mm; matrix size, 256 x 256; eight signals acquired; velocity sensitivity, 100 cm/sec) (25,26). On an independent workstation (Easy Vision; Philips Medical Systems), quantitative flow values were calculated in each vessel by integrating velocities across manually drawn regions of interest that enclosed the vessel lumen closely. On the basis of two-dimensional phase-contrast MR angiograms, regions of interest were drawn by specialized brain MR imaging technologists with more than 5 years of experience performing volume flow measurements in the ICAs and BA. The volume flow measurements were corrected to the mean age of our population (60 years).



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  		Figure 1. Sagittal localizer MR angiogram (13.7/7, 20° flip angle) illustrates positioning of a two-dimensional phase-contrast MR angiographic section to measure the volume flow through the ICAs and BA. Quantitative flow values are obtained by integrating across manually drawn regions of interest that enclose the vessels. 1 = right-sided ICA, 2 = left-sided ICA, 3 = BA.

 
To visualize the circle of Willis, 50 sections were obtained with a three-dimensional time-of-flight technique (30/6.9; flip angle, 20°; field of view, 100 x 100 mm; matrix size, 256 x 256; two signals acquired; section thickness, 1.2 mm with 0.6 mm overlap) with subsequent reconstruction of maximum intensity projections. Morphologic assessment of the circle of Willis was performed with the individual source sections of the three-dimensional time-of-flight MR angiography data set by using the workstation (Easy Vision; Philips Medical Systems).

The anatomy of the anterior and posterior parts of each circle of Willis were assessed, on a separate workstation, on the basis of source images of the three-dimensional time-of-flight data set (21). Anatomic assessment for a missing A1 segment of the anterior cerebral artery or a fetal-type PCA was performed independently by two observers (J.v.d.G., with more than 10 years of experience, and A.F.v.R., with 2 years of experience, in brain MR imaging), with a consensus reading needed in 5% of cases. Examples of the three-dimensional time-of-flight MR angiograms of the circle of Willis for complete and variant-type circles are shown in Figures 2 and 3. With respect to the anterior variant type, the ipsilateral side of the circle was considered to be the side with an absent A1 segment (Fig 2). The contralateral side was considered to be the side of the A1 segment, which gives rise to both A2 segments. A fetal-type PCA indicated those circles in which the PCA arises from the ipsilateral ICA instead of from the BA (Fig 3).



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  		Figure 2. Three-dimensional time-of-flight MR angiograms (30/6.9, 20° flip angle) show an anatomically complete circle of Willis (left) and a variant-type circle of Willis (right) with a missing A1 segment of the anterior cerebral artery on the right. In the variant-type image, the ICA on the left (solid arrow) is feeding both anterior cerebral arteries (arrowheads) and the ipsilateral middle cerebral artery (open arrow).

 


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  		Figure 3. Three-dimensional time-of-flight MR angiograms (30/6.9, 20° flip angle) of a variant-type circle of Willis with a unilateral fetal-type PCA (left) and a bilateral fetal-type PCA (right). The ICAs (arrows) on the side of the fetal-type PCA (arrowheads) are feeding the ipsilateral PCA, in addition to the ipsilateral anterior cerebral artery and middle cerebral artery.

 
Statistical Analyses
Quantitative volume flow measurements were expressed as means ± standard deviations. Differences in volume flow between a nonvariant-type circle of Willis and a circle of Willis with a missing A1 segment, a unilateral fetal-type PCA, or a bilateral fetal-type PCA were analyzed by using analysis of variance and Scheffé post hoc tests (SPSS 10.1.0; SPSS, Chicago, Ill). Differences in age between men and women were tested by using a Student independent t test, and differences between men and women for variant types of the circle of Willis were tested by using the {chi}2 test with Yates correction. The effect of age on total volume flow was evaluated by using linear regression evaluation for the entire group. In all tests, P < .05 was considered to indicate a statistically significant difference.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
DISCUSSION
 REFERENCES
 
A 3.1 mL/min decrease in total volume flow was found per annum of age increase for the entire group (Fig 4, P < .001). No significant difference in age was found between men and women. No significant differences were found between men and women for the prevalence of variant types of the circle of Willis.



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  		Figure 4a. Graphs show total volume flow according to age as measured with two-dimensional phase-contrast MR angiography in (a) 147 subjects with a complete circle of Willis, (b) 50 subjects with a fetal-type circle of Willis, and (c) 11 subjects with a missing A1 segment. {square} = men, {bullet} = women.

 


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  		Figure 4b. Graphs show total volume flow according to age as measured with two-dimensional phase-contrast MR angiography in (a) 147 subjects with a complete circle of Willis, (b) 50 subjects with a fetal-type circle of Willis, and (c) 11 subjects with a missing A1 segment. {square} = men, {bullet} = women.

 


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  		Figure 4c. Graphs show total volume flow according to age as measured with two-dimensional phase-contrast MR angiography in (a) 147 subjects with a complete circle of Willis, (b) 50 subjects with a fetal-type circle of Willis, and (c) 11 subjects with a missing A1 segment. {square} = men, {bullet} = women.

 
In Table 1, the mean age-corrected volume flow in the ICAs and BA in subjects with a missing A1 segment of the anterior cerebral artery is compared with the volume flow in subjects with present A1 segments of the anterior circle of Willis. The left and right ICA volume flow data were pooled for the 197 subjects in whom both A1 segments of the anterior circle of Willis were present. The volume flow in the contralateral ICA was significantly increased in subjects with a missing A1 segment (n = 11) compared with subjects with both A1 segments present (P < .01) and compared with the volume flow in the ipsilateral ICA (P < .01). No significant differences in BA volume flow and total volume flow were found between the two groups.


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  		TABLE 1. Volume Flow in Relation to Anatomic Variation in the Anterior Circle of Willis

 
In Table 2, the mean age-corrected volume flow (normalized to an age of 60 years and based on the 3.1-mL/min decrease per annum of age increase) in the ICAs and BA of subjects with a unilateral or bilateral fetal-type PCA was compared with that in subjects with no fetal-type PCA. Data for the left and right ICA volume flow was pooled for the 158 subjects with no fetal-type posterior configuration of the circle of Willis. We also pooled data for the left and right ICA flow in the 13 subjects with a bilateral fetal-type PCA. In subjects with a unilateral fetal-type PCA, the volume flow in the ICA on the ipsilateral side (P < .01) and the volume flow in the BA (P < .01) were significantly different compared with the corresponding volume flow in the ICA and BA in a circle of Willis with feeding of the PCAs from the BA. The volume flow in the ICAs (P < .01) and BA (P < .01) was significantly different in subjects with a bilateral fetal-type PCA compared with that in subjects with feeding of the PCAs from the BA. No significant differences were found in total volume flow between subjects with a unilateral or bilateral fetal-type PCA and subjects with no fetal-type circle of Willis.


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  		TABLE 2. Volume Flow in Relation to Anatomic Variation in the Posterior Circle of Willis

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
REFERENCES
 
The most important findings of the present study are as follows: First, in subjects with a missing A1 segment, the volume flow in the contralateral ICA, which is feeding both anterior cerebral arteries, is significantly increased compared with volume flow in the ipsilateral ICA and compared with volume flow in the ICAs in subjects with present A1 segments of the anterior circle of Willis. Second, in subjects with a unilateral or bilateral fetal-type PCA, the volume flow in the ICA on the side of the fetal-type PCA is increased and the BA volume flow is decreased compared with corresponding flow values for a circle of Willis with feeding of the PCAs from the BA.

For the anterior part of the circle of Willis, the variant type with a missing A1 segment is present on up to 10% of angiograms (21). For this variant type, we found significantly (P < .01) increased flow in the ICA contralateral to a missing A1 segment, whereas decreased ICA flow was found on the ipsilateral side. The contralateral ICA is feeding the contralateral middle cerebral artery and both anterior cerebral arteries, whereas the ipsilateral ICA supplies only the ipsilateral middle cerebral artery. In clinical studies, asymmetries in ICA volume flow have been reported in patients with ICA stenoocclusive disease (6,17), giant vascular aneurysms (27), or arteriovenous malformations (7,8). The findings of the present study indicate that asymmetries in volume flow between the right and left ICAs are not necessarily caused by vascular disease but may be due to variations in the anatomy of the anterior circle of Willis.

In the posterior part of the circle of Willis, the variant type with a unilateral fetal-type PCA is present on up to 25% of angiograms, and a bilateral fetal-type PCA is present on up to 10% of angiograms (21,22). In subjects with a unilateral fetal-type PCA, volume flow on the side of the fetal-type PCA was increased compared with the volume flow through the ICA in a circle of Willis with feeding of the PCA from the BA. With a fetal-type PCA, the ipsilateral ICA is feeding the ipsilateral anterior cerebral artery, the ipsilateral middle cerebral artery, and, in addition, the ipsilateral PCA; this results in an increased volume flow. As a result, a stepwise decrease in BA volume flow was found when subjects with no fetal-type PCA circles were compared with subjects with a unilateral or a bilateral fetal-type PCA. The finding of a more than 50% decrease in BA volume flow in subjects with a bilateral fetal-type PCA indicates that absolute measurements of the volume flow in the BA should always be accompanied by an evaluation of the anatomy of the circle of Willis. In subjects with a bilateral fetal-type PCA, the remaining volume flow of 62 mL/min in the BA is used to feed branches of the BA that precede the circle of Willis, such as the superior cerebellar artery. Furthermore, we observed a nonsignificant increase in the total flow in subjects with a bilateral fetal-type PCA in comparison with subjects with no fetal-type PCA. A power analysis showed that, in future studies, 74 subjects are required in each group in order to investigate this difference. The absence of a significant difference between men and women for the prevalence of the variant types of the circle of Willis confirmed the results of a previous study (21).

Results of previous phantom studies showed that the systematic and statistical error of nontriggered two-dimensional phase-contrast MR angiography is less than 5% for flow measurements in vessels with a low pulsatility index and diameters such as those of the ICAs and BA (25,26). Furthermore, two-dimensional phase-contrast MR angiography may cause underestimation of flow in vessels with very small diameters (28). However, for the vessel diameters of the ICAs and BA, no underestimation in flow measurements is expected with two-dimensional phase-contrast MR angiography.

In the present study, the MR angiographic volume flow measurements of the brain-feeding arteries in the neck and the anatomic investigations of the circle of Willis were performed in subjects with symptomatic atherosclerosis or risk factors for atherosclerosis. By comparing the results of the present study with the results in a previous population-based MR angiography study, in which healthy subjects were also examined, no substantial differences in the volume flow and in the prevalence of variant-type circles were found (18). In the population in our study, small nondisabling infarcts may have led to a small decrease in parechymal volume and change in ICA and/or BA flow. However, small flow effects are unlikely to influence our main findings of flow changes associated with rather dramatic variations in the circle of Willis.

A limitation of the present study was that only the major variant types of the circle of Willis—that with a missing A1 segment and that with fetal-type PCA—were investigated. In addition to these variants, additional less dramatic anomalies might produce variations in volume flow. Furthermore, it is important that our absolute reference values for ICA and BA volume flow are verified at other institutions, because flow rates may vary with use of different MR techniques.

In conclusion, discrepancies between previously suggested reference volume flow values of the ICAs and BA and actual flow values in individual patients are not necessarily caused by vascular disease but may be explained by the presence of a variant type of the circle of Willis. In the present study, normal volume flow values of individual blood vessels to the brain were obtained for the most common variant types of the circle of Willis. These reference values may prove useful in the interpretation of volume flow values of the ICAs and BA in future clinical studies.


   ACKNOWLEDGMENTS
 
Investigators in the SMART study group are A. Algra, MD, PhD, Y. v. d. Graaf, MD, PhD, and D. E. Grobbee, MD, PhD, Julius Center for Health Sciences and Primary Care; J. D. Banga, MD, PhD, Department of Internal Medicine; B. C. Eikelboom, MD, PhD, Department of Vascular Surgery; L. J. Kappelle, MD, PhD, Department of Neurology; A. J. Rabelink, MD, PhD, Department of Nephrology; W. P. T. M. Mali, MD, PhD, Department of Radiology; and P. P. T. de Jaegere, Department of Cardiology, University Medical Center, Utrecht, the Netherlands.


   FOOTNOTES
 
Abbreviations: BA = basilar artery, ICA = internal carotid artery, PCA = posterior cerebral artery, SMART = Second Manifestations of Arterial Disease

Authors stated no financial relationship to disclose.

Author contributions: Guarantors of integrity of the study, J.H., W.P.T.M.M., J.v.d.G.; study concepts and design, J.H., J.v.d.G., Y.v.d.G.; literature research, J.H.; clinical studies, A.F.v.R., Y.v.d.G.; data acquisition, J.H., J.v.d.G.; data analysis/interpretation, J.H., A.F.v.R., J.v.d.G.; statistical analysis, J.H., J.v.d.G.; manuscript definition of intellectual content, J.H., J.v.d.G.; manuscript preparation and editing, J.H., J.v.d.G., Y.v.d.G., W.P.T.M.M.; manuscript review, J.v.d.G., Y.v.d.G., W.P.T.M.M.; manuscript final version approval, J.v.d.G., Y.v.d.G., A.F.v.R., W.P.T.M.M.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 

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