Annals of Indian Academy of Neurology
ORIGINAL ARTICLE
Year
: 2015  |  Volume : 18  |  Issue : 4  |  Page : 391--397

Magnetic resonance angiographic evaluation of circle of Willis: A morphologic study in a tertiary hospital set up


Shankar Rao Naveen, Venkatraman Bhat, Gadabanahalli Ashok Karthik 
 Department of Radiology, Narayana Health, Multispeciality Hospital, Mazumdar Shaw Cancer Center, Bangalore, Karnataka, India

Correspondence Address:
Venkatraman Bhat
309, Greenwoods Apt, Royal Gardenia, Bommasandra, Bangalore - 560 099, Karnataka
India

Abstract

Background: Anatomy of circle of Willis (CW) shows wide variation in different individuals, population groups, and has vital clinical significance in causation and presentation of clinical disease. This study evaluates the anatomical variations, incidence of various common anomalies of CW in south Indian tertiary hospital set up, using three-dimensional time-of-flight (3D-TOF) magnetic resonance angiography (MRA). Materials and Methods: A total of 300 patients referred for neuroimaging study over a period of 2-year were included in the analysis. In this prospective and retrospective study, 198 men and 102 women; mean age, 55 years) underwent 3D-TOF MR angiograms of the CW using a 1.5-tesla MR scanner. Images were reviewed for anatomical configuration of the CW using maximum intensity projection (MIP) and 3D volume rendered images. Results: On analysis, a complete CW was seen in 50 (16.6%) of 300 subjects. An incomplete anterior and posterior CW was found in 66 (22%) The remaining 184 (61.3%) subjects had partially complete CW configuration. The most common type of CW in a single subject was anterior variant type A and posterior type variant E. Conclusion: We observed wide variation in CW configuration in our patients. The prevalence of complete configuration of the circle is 16.6%; slightly higher in females and younger subjects. Complete anterior circle was present in 77.3%. Most common anterior variant is type A (normal anterior configuration) with a prevalence of 66%. The most common posterior circle variant is type E (hypoplasia or absence of both PcomA) with 32.6%. Overall, CW variants are slightly more common among the women in comparison to men. Incidence of associated anomalies like aneurysm or arteriovenous malformation (AVM) was comparable to that described in literature.



How to cite this article:
Naveen SR, Bhat V, Karthik GA. Magnetic resonance angiographic evaluation of circle of Willis: A morphologic study in a tertiary hospital set up.Ann Indian Acad Neurol 2015;18:391-397


How to cite this URL:
Naveen SR, Bhat V, Karthik GA. Magnetic resonance angiographic evaluation of circle of Willis: A morphologic study in a tertiary hospital set up. Ann Indian Acad Neurol [serial online] 2015 [cited 2019 Nov 11 ];18:391-397
Available from: http://www.annalsofian.org/text.asp?2015/18/4/391/165453


Full Text

 Introduction



Vascular anatomy of CW had been subject of extensive autopsy studies as well as in vivo imaging studies.(1-8)CW is constituted by two internal carotid arteries (ICAs) and basilar artery anastomosing at the base of the brain. The carotid arteries and their branches supply the anterior portion of the brain referred to as the anterior circulation. Whereas, posterior circulation refers to vertebrobasilar system that supplies the posterior portion of the brain. The anterior communicating arteries (A com As) and posterior communicating arteries (PcomAs) are component vessels of the CW and designated as the primary collateral pathways. Other pathways, known as the secondary collateral pathways, may also be recruited. Examples include flow reversal through the ophthalmic arteries, reversed flow through the anterior choroidal artery, and anastomosis between the cortical branches of the intracerebral arteries (leptomeningeal collaterals). The collateral potential of the CW is believed to be dependent on the presence and size of its component vessels, [1],[2],[3] which vary among normal individuals. [3],[4],[5],[6],[7],[8],[9],[10]

Considerable anatomic variation exists in the CW. Recent cadaveric study has shown 21 types of CW variations. [9] Classification presented in the work of Chen et al., [11] is adopted in our presentation for the simplicity of the scheme. There are 10 types of variations (A-J) in anterior and posterior circle which are illustrated in the figures [Figure 1] and [Figure 2]. One common variation consists of relative narrowing of proximal part of the posterior cerebral artery (PCA) with large ipsilateral PcomA, so the ICA supplies the posterior cerebrum. In another variation, the AcomA is a large vessel, such that a single internal carotid supplies both the anterior cerebral arteries (ACAs). In third variation, ACA gives rise to both post-communicating segments and supplies retrograde flow to the ipsilateral pre-communicating segment, which, in turn, gives rise to the ipsilateral middle cerebral artery (MCA; both ACAs and both MCAs are supplied by a single ICA). Physiologically, arrangement of the cerebral arteries in the CW creates deficiencies, redundancies; also provide potential collateral pathways in cerebral circulation. If one part of the circle becomes blocked or narrowed, blood flow from the other arteries can preserve the cerebral perfusion by maintaining enough flow to avoid ischemia.{Figure 1}{Figure 2}

The CW is an important potential collateral pathway in maintaining adequate cerebral blood flow in patients with ICA obstruction. With the advances in microneurosurgery and the more effective ability to deal with occlusive neurovascular disease surgically and by interventional methods, the accurate knowledge of the intracranial vascular anatomy has become increasingly important.

Based on anatomical [12],[13],[14] and radiological studies, [7],[15],[16] it has been shown that more than half of healthy subjects have anatomical variations in the CW. Recent studies have investigated the role of the CW in the development of collateral flow in ICA obstruction; these studies were based on mathematical models [17],[18],[19] and used transcranial Doppler ultrasound, [20],[21],[22],[23],[24],[25] digital contrast-enhanced angiography, [3],[26] or magnetic resonance angiography (MRA). [2],[3],[27],[28],[29] MRA has previously been shown to be well-suited to investigate the CW, in view of the fact that it is able to provide morphological as well as hemodynamic information concerning blood flow direction in individual vessels accurately. [30],[31] Previous studies have demonstrated that three-dimensional time-of-flight (3D-TOF) MRA is a sensitive, noninvasive modality suitable for detecting the anatomy of the CW in healthy volunteers and patients with carotid artery disease. [11],[32]

Aims and objectives

The purpose of this study is to evaluate and to describe the prevalence and pattern of CW, arterial variants (aplasia, hypoplasia) and anomalies (arteriovenous malformations (AVMs) and aneurysms) in noncontrast 3D-TOF-MRA in the study group. In addition to providing a standard of reference for future research on the circle with 3D TOF MRA, the purpose of this study was to investigate whether any age- or sex-related differences could be found in circle morphology.

 Materials and Methods



In a prospective and retrospective observational study, 300 patients referred for neuroischemic study protocol from February 2010 to July 2011 were included in the study. Study was approved by the institutional review board. Informed consent from the patient or guardian was obtained before scanning. All patients (198 men and 102 women; mean age, 55 years) underwent 3D-TOF MR angiograms of the CW. Images were obtained with the sequence of spoiled gradient-recalled acquisition (SPGR) using a 1.5-tesla MR scanner (Achieva; Philips Medical Systems, The Netherlands). Patients with pacemaker, ferromagnetic intracerebral aneurysm clips, or other metallic implants and patients with claustrophobia were excluded. Severely ill, uncooperative patients who were not able to remain stable for study duration were also excluded. Images were reviewed for CW anatomy and configuration.

Scanning technique: Patients were imaged in supine position, wherever necessary, after sedation with midazolam 0.07-0.08 mg/kg intramuscular (IM; approximately 5 mg IM) administered up to 1 h before the study in uncooperative patients. Examination was done with a dedicated head coil. Monitoring of vital signs of patient was performed throughout the scanning. Dedicated, optimized high-resolution 3D-TOF MRA protocol with repetition time (TR)/echo time (TE)/flip angle of 19/5.7 ms/16°, respectively, with isotropic resolution of 0.6 0.6 0.6 mm 3 was used. T1-weighted volume scans and T2-weighted multisection fast-field echo anatomic scans were obtained for the detection of brain abnormalities. Scanning parameters included; slice thickness 1.2 mm, 0.6 mm slice overlap, field of view of 100 100 mm, and matrix 0.6 0.6 0.6 mm 3 andTR-19 ms, TE - 5.7ms, and flip angle-16°. Totally 50 slices covering a volume of 30 mm (50 0.6 mm effective slice thickness) was obtained. The total imaging time was approximately 15 min, of which the 3D TOF MRA sequence required 3 min 24 s. These axial source images were post-processed by the maximumintensity projection (MIP) algorithm [Figure 3]a to produce eight projections rotating about the section axis. All component vessels of the CW were assessed by measuring the diameter on the individual MIP images. Whenever there was doubt in determining the diameter of vessel due to overlap in the MIP images, the TOF source images were then reviewed on the advanced workstation (Philips ADW 4.0 workstation). Occasionally, it was necessary to cutoff the unwanted branching vessel on the images in order to betterdepict the target vessels and assess correct diameter. Vessels visualized as continuous segments of at least 0.8 mm in diameter, were considered present. Those smaller than 0.8 mm in diameter were considered as hypoplastic. [11],[33] The images were also reviewed with volume rendering technique and evaluated in all the angles [Figure 3]b. Arteries when seen as noncontinuous segments were considered as absent. The anterior and posterior parts of CW were evaluated separately and classified according to the scheme. The prevalence of each anatomic variant was documented.{Figure 3}

 Results



Study group consisted of 300participants (198 men and 102 women; mean age, 55 years) [Graph 1a and b [SUPPORTING:1]]. Incidence of various types of CW is documented in [Table 1]. Common morphological types of CW variations [Table 2] and common types of anterior and posterior circulation are illustrated in [Table 3]. The prevalence of the variants of the anterior and posterior circle of Willis (CW) for different age groups of both sexes and for total subjects are also shown in Graph 2 [SUPPORTING:2]. Variant type A [Figure 4]a was the most common type of anterior part of the CW in all age groups and sexes [Table 2] and [Graph 2]a and b.{Figure 4}{Table 1}{Table 2}{Table 3}

Anterior CW variants

The anterior CW was complete in 232 out of 300 participants (77.3%), with a normal configuration (Type A) seen in 198 subjects. In two patients, two AcomAs [Figure 4]b were observed. The anterior circle was incomplete in 67 participants who had compromised anterior collateral flow, AcomA was absent in 39 [Figure 4]c1 and 2]. The remaining 28 subjects had A1 hypoplasia or aplasia [Figure 5]g and h. The most common type of anterior collateral was type A [Figure 4a1 and 2], in which all component vessels were competent.{Figure 5}

Posterior circle variants

The prevalence of the variants of the posterior part of CW was shown for different age groups and both sexes in [Table 2]. The prevalence of unilateral fetal-type posterior communicating artery (FTP com A; posterior part variants B, F, G and H) was 16% and bilateral FTP com A (posterior part variants C, I, and J) was found in 7%. A higher percentage of incomplete collaterals were observed in the posterior part of the circle compared with the anterior collaterals. An adult configuration complete posterior circles [Figure 6]a was observed in 51 participants, and transitional variant [Figure 6]b and c was observed in 29 participants. A FTP CW was seen in 69 (23%) of the 300 subjects. Of the 69 subjects with FTP, 56 (18.6%) were classified as having partial FTP [Figure 6]b and c, [Figure 7]g, [Figure 8]j in which a hypoplastic P1 segment was present, and 13 (4.3%) were found to have a full FTP in which a P1 segment was absent [Figure 7]f and [Figure 8]h. The most common type of posterior variation was type E [Figure 7]e, in which bilateral P com A were absent. Of the 56 participants with a partial FTP, a unilateral FTP was found in 35 participants and bilateral FTP was seen in 21 participants.{Figure 6}{Figure 7}{Figure 8}

Entire circle

[Table 1] and [Figure 4] and [Figure 5] shows the prevalence of complete, partially complete, and incomplete configuration of the entire CW for different age groups, both sexes, and total subjects. There was statistically significant difference among different age and sex groups. Higher prevalence of complete CW was found in younger group (below 50 years; 33.9% of younger older subjects versus 6.8% of older subjects) and in females (28.4% of women versus 10.6% of men).

Combined analysis of entire circle

In the combined analysis, a complete CW was seen in 50 (16.6%) of 300 subjects. An incomplete anterior and posterior CW was found in 66 (22%) of 300 subjects. The remaining 184 (61.3%) subjects had partially complete CW configuration. The most common type of CW in a single subject was anterior variant type A and posterior type variant E. Incidentally three patients had aneurysms, one subject was having AVM and another subject was having persistent trigeminal artery on MR angiograms [Figure 9].{Figure 9}

 Discussion



The configuration of the CW has been investigated in many anatomical and clinical studies. [3],[4],[5],[6],[7],[8],[9],[10] There are only a few studies that have systematically investigated the configuration of the CW in a general population. [9],[10] There is a great clinical significance to CW variations, allowing prognostication of intracranial ischemia in incomplete circles.

MRA has demonstrated high sensitivity in evaluation of component vessels in the CW. [29] Though well-accepted clinically, sensitivity of 3D time-of-flight (TOF) MRA depends on the blood flow velocity of the vessel, and the technique may have difficulties in visualizing small vessels in the CW with slow or turbulent flow. [34] In most studies, MRA 3D acquisitions were made with either steady state precession (FSSP) or spoiled gradient technique (SPGR) using 1.5-tesla systems. Using FSSP technique, an axial slab with a thickness of 52 mm and 64 partitions was placed over the entire CW. A gradient-echo sequence (fast imaging with steady-state precession) with a matrix of 256 3 512 and a field of view of 200 mm was used, which yields a voxel size of 0.78 3 0.39 3 0.81 mm 3 acquisition time of 11 min 47 s. [30] Typical parameter used in SPGR technique were 45 ms TR, 4.9 ms TE, 20° flip angle, 256 × 192 matrix in a 14 cm field of view, and 42 mm slab with 60 serial axial slices of 0.7 mm thick with total imaging time of 10 min. [11]

Our study focuses on anatomical variants of the CW. In the evaluation process, like in earlier studies, we have considered the following vessels forming part of the CW: The A com A, the pre-communicating segment (A1) of the ACA, the pre-communicating segment (P1) of the PCA, the P com A, and ICA. CW configuration can be categorized in to three different types based on the structure of P1, P2 segment of PCA, and P Com A. Configurations are the adult type, transitional type, and fetal type. In adult configuration, P1 diameter is larger than the PComA diameter. In transitional configuration, diameters of both arteries are equal and equally contribute in formation of P2 of PCA. Fetal or embryonic configuration diameter of the P1 is smaller than diameter of P Com A and P2. [9] In previous studies, the prevalence of a complete anterior circle varied from 74 to 90% in different ethnic groups, [9],[35],[36],[37] almost similar to our observation. Autopsy studies, however, showed lower incidence of complete circles. [36] One recent cadaveric study has reported variation of CW in 40% with maximum variation in Pcom A (50%) followed by A com A (40%). [9] In the present study, the prevalence of entirely complete CW was 16.6%, higher in females than males (28.4 and 10.6%, respectively) and young than older subjects (33.9 and 6.8%, respectively). Previous studies have shown higher incidence of complete circles in female patients and younger patients. [11],[33],[37] Diameter of the proximal arteries measured on MRA in control studies tend to be larger in male show tendency to decrease with age. Our observation is similar to earlier studies. Additionally, average age of male subjects was 63 years and that of the female 47 years, which might partly explain higher visualization in female subjects. The most common variant in anterior circulation is type A, which is normal pattern in both the sexes. Type A variant in anterior circulation in common among women (n = 71, 69.6%) slightly more frequent compared to men (n = 127, 64.1%). Type E variant of posterior circulation is most common in both the sexes. It is also common in men (n = 69, 34.8%), slightly more compared to women (n = 29, 28.4%).

In a large study of Indian subcontinental patients, Kapoor et al., [14] observed that 45.2% conformed to the typical pattern. In the rest of the study group there were variations. In other studies, complete CW was observed in 4.6-72.2%. [10],[37] The major variation is observed in incidence of complete CW, in autopsy studies, ranging from 14.2 to 52.3%; [36] relatively lower than clinical observation. Several reasons could account for this variation; first, the subject selection difference, healthy volunteers were included in some studies with additional subjects without vascular disorders or even some with neurological disease. [28],[38] Second reason could be due to the difference in observation method, like studies wherein phase-contrasted MR angiography was utilized in addition to TOF study. [28] Third reason is related to the criteria set for what constitutes a complete-circled configuration. We applied the criterion of the vessel diameter less than 0.8 mm as absence in determining the prevalence of various anatomical variants. Some autopsy studies used 1 mm as their lower limit. [16],[36] Although TOF-MRA demonstrates high sensitivity in detecting intracranial arteries, this technique has its disadvantages. Slow or turbulent flow may not be demonstrated in the TOF-MRA images, even though the vessels are patent. Therefore, the prevalence of the complete configuration of circle may be underestimated. The incidence of incomplete configuration of the circle is 22%. Among these variations, a single major ICA supplying several cerebral arterial territories, with little collateral flow provided by other arteries, should be taken note carefully. Such variation, called isolated circulation, is an important observation for preoperative surgical planning; especially when temporary or permanent occlusion of the parent artery is anticipated. In such instance, temporary occlusion of the ICA during carotid endarterectomy would lead to the risk of ischemic insult in the watershed area between these separately perfused territories.

Reasons for variations in the segments of the CW have been hypothesized. Genetic factors [10] and postnatal development of the brain following occlusive diseases [39] are main theories. From the evolutionary standpoint, it is noteworthy that variations of the cerebral arteries seem to be equally common in humans as well as animals. [40]

We noted transitional-type posterior circles in our population, with an incidence of 4%. Interestingly, we also observed higher occurrence of posterior variant (variant J) in the study population. We believe that, these observed variants call for need of larger population-based studies to improve our understanding of regional variations.

In a large study involving north Indian subject groups, intracranial saccular aneurysm was present in 1% [14] and AVMs in 1.4% in the PCA. In our study, aneurysms were detected in 1%; noted in both the A com A and the left ACA. AVMs were found in a single case (0.33%) in the right parietooccipital region. Persistent left trigeminal artery was noted in another. Hence, our observations are in conformity with earlier studies.

 Conclusion



The morphological variations demonstrated by TOF-MRA in our study provide an important reference source for CW variations in the regional population. Our findings confirm the view that the configuration of the CW vary largely in our general population. The prevalence of complete configuration of the circle was16.6% and is slightly higher in females than males and younger (below 50 years) than older subjects. Complete anterior CW is more common with incidence of 77.3% of all the subjects. The most common anterior circle variant is type A (normal anterior configuration) with a prevalence of 66%. The most common posterior circle variant is type E (hypoplasia or absence of both Pcom As and isolation of the anterior and posterior parts of the circle at this level) with incidence of 32.6%. Overall, CW variants are slightly more common among the women in comparison to men. Incidence of associated anomalies, like aneurysm and AVM, is comparable to that described in literature.

 Acknowledgements



Authors would like to thank the valuable contribution of radiology collegues, Dr. Dayananda, Dr. Murugan, Dr. Shiv Kumar Swamy and neurology colleagues for their contributions towards this work.

References

1Mull M, Schwarz M, Thron A. Cerebral hemispheric low-flow infarcts in arterial occlusive disease: Lesion patterns and angio-morphological conditions. Stroke 1997;28:118-23.
2Miralles M, Dolz JL, Cotillas J, Aldoma J, Santiso MA, Gimenez A, et al. The role of the circle of Willis in carotid occlusion: Assessment with phase contrast MR angiography and transcranial duplex. Eur J Vasc Endovasc Surg 1995;10:424-30.
3Schomer DF, Marks MP, Steinberg GK, Johnstone IM, Boothroyd DB, Ross MR, et al. The anatomy of the posterior communicating artery as a risk factor for ischemic cerebral infarction. N Engl J Med 1994;330:1565-70.
4Hillen B. The variability of the circulusarteriosus (Willisii): Order or anarchy. Acta Anat (Basel) 1987;129:74-80.
5Hillen B. The variability of the circle of Willis: Univariate and bivariate analysis. Acta Morphol Neth Scand 1986;24:87-101.
6Krabbe-Hartkamp MJ, van der Grond J, de Leeuw FE, de Groot JC, Algra A, Hillen B, et al. Circle of Willis: Morphological variation on MR angiograms. Radiology 1998;207:103-11.
7Macchi C, Catini C, Federico C, Gulisano M, Pacini P, Cecchi F, et al. Magnetic resonance angiographic evaluation of circulusarteriosuscerebri (circle of Willis): A morphologic study in 100 human healthy subjects. Ital J Anat Embryol 1996;101:115-23.
8Barboriak DP, Provenzale JM. Pictorial review: Magnetic resonance angiography of arterial variants at the circle of Willis. Clin Radiol 1997;52:429-36.
9Gunnal SA, Farooqui MS, Wabale RN. Anatomical variations of the circulus arteriosus in cadaveric human brains. Neurol Res Int 2014;2014:687281.
10Iqbal S. A comprehensive study of the anatomical variations of the circle of Willis in adult human brains. J Clin Diagn Res 2013;7:2423-7.
11Chen HW, Yen PS, Lee CC. Magnetic resonance angiographic evaluation of circle of Willis in general population: A morphologic study in 507 cases. Chin J Radiol 2004;29:223-9.
12Alpers BJ, Berry RG, Paddison RM. Anatomical studies of the circle of Willis in normal brain. AMA Arch Neurol Psychiatry 1959;81:409-18.
13Ozaki T, Handa H, Tomimoto K, Hazama F. Anatomical variations of the arterial system of the base of the brain. Arch Jpn Chir 1977;46:3-17.
14Kapoor K, Singh B, Dewan LI. Variations in the configuration of the circle of Willis. Anat Sci Int 2008;83:96-106.
15Jongen JC, Franke CL, Soeterboek AA, Versteege CW, Ramos LM, van Gijn J. Blood supply of the posterior cerebral artery by the carotid system on angiograms. J Neurology 2002;249:455-60.
16Papantchev V, Hristov S, Todorova D, Naydenov E, Paloff A, Nikolov D, et al. Some variations of the circle of Willis, important for cerebral protection in aortic surgery - A study in Eastern Europeans. Eur J Cardiothoracic Surg 2007;31:982-9.
17Cassot F, Vergeur V, Bossuet P, Hillen B, Zagzoule M, Marc-Vergnes JP. Effects of anterior communicating artery diameter on cerebral hemodynamics in internal carotid artery disease: A model study. Circulation 1995;92:3122-31.
18Hillen B, Drinkenburg BA, Hoogstraten HW, Post L. Analysis of flow and vascular resistance in a model of the circle of Willis. J Biomech 1988;21:807-14.
19Dickey PS, Kailasnath P, Bloomgarden G, Goodrich I, Chaloupka J. Computer modeling of cerebral blood flow following internal carotid artery occlusion. Neurol Res 1996;18:259-66.
20Anzola GP, Gasparotti R, Magoni M, Prandini F. Transcranial Doppler sonography and magnetic resonance angiography in the assessment of collateral hemispheric flow in patients with carotid artery disease. Stroke 1995;26:214-7.
21Baumgartner RW, Baumgartner I, Mattle HP, Schroth G. Transcranial color-coded duplex sonography in unilateral flow-restrictive extracranial carotid artery disease. AJNR Am J Neuroradiol 1996;17:777-83.
22Baumgartner RW, Baumgartner I, Mattle HP, Schroth G. Transcranial color-coded duplex sonography in the evaluation of collateral flow through the circle of Willis. AJNR Am J Neuroradiol 1997;18:127-33.
23Doblar DD. Cerebrovascular assessment of the high-risk patient: The role of transcranial Doppler ultrasound. J Cardiothoracic Vasc Anesth 1996;10:3-14.
24Klotzsch C, Popescu O, Berlit P. Assessment of the posterior communicating artery by transcranial color-coded duplex sonography. Stroke 1996;27:486-9.
25Zbornikova V, Lassvik C. Relationship between the flow pattern and vasomotor reactivity in the ophthalmic artery, siphon and vessels within the circle of Willis in unilateral internal carotid artery occlusion. Neurol Res 1996;18:521-7.
26Bladin CF, Colchester AC, Hawkes DJ, Seifalian AM, Iqbal N, Hardingham CR. Morphological and hemodynamic assessments of carotid stenosis using quantitative digital subtraction angiography. Stroke 1996;27:1672-8.
27Patrick JT, Fritz JV, Adamo JM, Dandonna P. Phase-contrast magnetic resonance angiography for the determination of cerebrovascular reserve. J Neuroimaging 1996;6:137-43.
28Ross MR, Pelc NJ, Enzmann DR. Qualitative phase contrast MRA in the normal and abnormal circle of Willis. AJNR Am J Neuroradiol 1993;14:19-25.
29Davis WL, Turski PA, Gorbatenko KG, Weber D. Correlation of cine MR velocity measurements in the internal carotid artery with collateral flow in the circle of Willis: Preliminary study. J Magn Reson Imaging 1993;3:603-9.
30Stock KW, Wetzel S, Kirsch E, Bongartz G, Steinbrich W, Radue EW. Anatomic evaluation of the circle of Willis: MR angiography versus intra-arterial digital subtraction angiography. AJNR Am J Neuroradiol 1996;17:1495-9.
31Patrux B, Laissy JP, Jouini S, Kawiecki W, Coty P, Thiébot J. Magnetic resonance angiography (MRA) of the circle of Willis: A prospective comparison with conventional angiography in 54 subjects. Neuroradiology 1994;36:193-7.
32Kato T, Indo T, Yoshida E, Iwasaki Y, Sone M, Sobue G. Contrast-enhanced 2D cine phase MR angiography for measurement of basilar artery blood flow in posterior circulation ischemia. AJNR Am J Neuroradiol 2002;23:1346-51.
33Hartkamp MJ, van Der Grond J, van Everdingen KJ, Hillen B, Mali WP. Circle of Willis collateral flow investigated by magnetic resonance angiography. Stroke 1999;30:2671-8.
34Brunereau L, Lévy C, Arrivé L, Bousson V, Marsot-Dupuch K, Bousser MG, et al. Anatomy of the circle of Willis with 3D time of flight magnetic resonance angiography and analysis of partitions. J Radiol 1995;76:573-7.
35Mohamed AM, Ahmed AI. Three dimensional magnetic resonance angiography of the circle of Willis: Anatomical variations in general Egyptian population. Egypt J Radiol Nucl Med 2011;42:405-12.
36De Silva KR, Silva R, Gunasekera WS, Jayesekera RW. Prevalence of typical circle of Willis and the variation in the anterior communicating artery: A study of a Sri Lankan population. Ann Indian Acad Neurol 2009;12:157-61.
37Fawcett E, Blachford JV. The circle of Willis: An examination of 700 specimens. J Anat Physiol 1905;40:63-70.
38Riggs HE, Rupp C. Variation in form of the circle of Willis. The relation of variations to collateral circulation: Anatomic analysis. Arch Neurol 1963;8:8-24.
39Stehbens WE. Etiology of intracranial berry aneurysms. J Neurosurg 1989;70:823-31.
40Kapoor K, Kak VK, Singh B. Morphology and comparative anatomy of circulus arteriosus cerebri in mammals. Anat Histol Embryol 2003;32:347-55.