Circle of Willis (COW) is defined as a vascular network formed at the base of the skull in the inter-peduncular fossa. Anatomically, its anterior part is constructed by the anterior cerebral artery (ACA), from either side. Additionally, the AcomA unites the right and left ACA. In the dorsal part of the COW, the unpaired basilar artery divides into the right and left posterior cerebral arteries (PCAs) and each connects to the bilateral internal carotid artery (ICA) through PcomAs [1,2,3]. The ACAs with middle cerebral arteries supply more than eighty percent of the cerebrum, while the rest part of it is provided by the PCAs . Usually, the anatomical variations in the COW are observed [3, 5]. The COW, its function is to protect the brain from ischemia and infarction, is the main structure that provides constant and regular arterial blood flow into the brain . Indeed, it is more sensitive to the lack of arterial blood and oxygen supply . Even though the brain accounts for two percent of the body weight, it needs one-sixth of the cardiac output and one-fourth of oxygen in every breath. The continuous and constant supply of blood and oxygen is crucial for brain function [4, 5]. The pairs of two arteries (two vertebral and two ICAs with cerebral branches) provide the blood/oxygen flow into the areas of the brain. In the anterior surface of the brain, these arteries, with cerebral branches, form a cerebral arterial channel called the COW [3, 5]. Thomas Willis (from 1621–1675), the British anatomist and physician, was the first to observe the clinical importance of the COW and showed its physiologic function .
Globally, of the 56.9 million deaths in 2016, fifty-four percent were due to the top ten causes of mortality. Of them, the first and the second killers are ischemic heart attack and stroke, respectively. They accounted for a combined 15.2 million deaths. These diseases have stayed the leading cause of mortality in the previous fifteen years, globally .
Stroke is, in the United States of America, the fifth cause of mortality. Besides, it is the main cause of adult disability . In this country, more than 795,000 persons face a stroke annually. Of these, 610,000 are found to be new stroke cases. Accordingly, every forty seconds a new case of stroke is detected and dies of a stroke per four minutes [8, 9]. Ischemic stroke responsible for more than eighty-seven percent of stroke cases and it can be subdivided into cardiogenic, atherosclerotic, lacunar, or cryptogenic sources [8, 10, 11]. The personal, social, and economic costs of ischemic stroke concerning the COW are substantial. Previously, several studies have revealed variations in the structure of the COW [5, 12, 13], and the sprouting of new vessels because of genetic and hemodynamic factors, the persistence of the arteries that normally disappear, and/or the disappearance that normally persist can be the variations [5, 12]. Importantly, the activity of the brain might not be influenced most of the time because of the presence of the collateral circulations, providing alternate routes for blood [5, 14, 15]. Besides, in cerebrovascular disease patients, COW can maintain adequate blood flow and reduce the damage of the affected areas through its potential redistribution role  and, notably, this compensation lies on the anatomical morphology of COW . On the other way, the variations in the COW may alert cerebral hemodynamics and result in various cerebrovascular diseases. In particular, the formation of the cerebral aneurysm correlates with the morphology of COW [16, 17]. Ischemic stroke can also develop when there is a diminished cerebral blood flow due to severe stenosis of the vessels, the occlusion of the cerebral artery by embolism, or both occur simultaneously [18,19,20,21].
Interestingly, due to the emerging of medical imaging like Magnetic Resonance Angiography (MRA), clinical researches widely used to study the morphology and variation of COW . The study done in China on a healthy population using these imaging techniques confirms the distribution of the variant types of COW, which provided the anatomical basis for future prognosis and treatment of cerebrovascular disease .
The variations of COW are clinically important because the COW has an essential role in cerebral hemodynamic as a collateral anastomotic network and persons with effective collateral circulations have a less risk of developing ischemic stroke as compared to those with ineffective collateral circulations [23,24,25,26,27,28,29,30].
The anatomical variations of COW have been proven to correlate with the formation of certain cerebrovascular diseases [1, 31, 32]. Although there are studies that study the variations of the anatomy of COW, it is not clear whether the presence of variation in the anatomy of COW is associated with ischemic stroke in a similar way among studies of different regions of the globe. Nowadays, interlinked problems related to cerebrovascular disease like ischemic stroke are become increasing. Strong evidence is needed about the pooled measure of association between COW and ischemic stroke. The finding of the review gives important evidence to the Health Care Professionals (Anatomists, Neurosurgeons, Medical students, for instance), Policy makers, Researchers, etc., and motivate them to give concern for it, to perform additional research, and to work with the risk factors. Thus, this systematic review and meta-analysis aimed to determine the pooled measure association between the anatomical variations of the COW and ischemic stroke using the available studies.