An experimental investigation of the hemodynamic variations due to aplastic vessels within three-dimensional phantom models of the circle of Willis

Influence of circle of Willis modeling on hemodynamic parameters in anterior communicating artery aneurysms and recommendations for model selection

Computational fluid dynamics (CFD) has been utilized to calculate hemodynamic parameters in anterior communicating artery aneurysm (AComA), which is located at a junction between left and right A1 and A2 segments. However, complete or half circle of Willis (CoW) models are used indiscriminately. This study aims to suggest recommendations for determining suitable CoW model. Five patient-specific CoW models with AComA were used, and each model was divided into complete, left-half, and right-half models. After validating the CFD using a flow experiment, the hemodynamic parameters and flow patterns in five AComAs were compared. In four out of five cases, inflow from one A1 side had a dominant influence on the AComA, while both left and right A1 sides affected the AComA in the remaining case. Also, the average difference in time-averaged wall shear stress between the complete and half models for four cases was 4.6%, but it was 62% in the other case. The differences in the vascular resistances of left and right A1 and A2 segments greatly influenced the flow patterns in the AComA. These results may help to enhance clinicians' understanding of blood flow in the brain, leading to improvements in diagnosis and treatment of cerebral aneurysms.

Exploring the anatomical configurations of the cerebral arteries in a cohort of South African patients

The cerebral arteries, specifically the anterior cerebral artery (ACA) and posterior cerebral artery (PCA), work together with the smaller calibre arteries to provide effective communication between the anterior and posterior circuits of the brain via the circle of Willis (CoW). Morphologic variations of the cerebral arteries and the CoW may alter blood flow to the brain, resulting in intracranial vascular disorders associated with stroke, and aneurysms. This study aimed to document the morphology of the cerebral arteries and the CoW in the South African population. Two hundred and thirty-nine computed tomography angiography scans were assessed. Cerebral arteries and CoW normal morphology and variations were classified as complete, absent, or hypoplastic. The ACA A1 was absent in 4.91%, hypoplastic in 30.40%, fenestrated in 1.06%, and typical in 63.6%. The ACA A2 was absent in 0.42%, hypoplastic in 26.28%, and typical in 69.44%. We found triple ACA A2 in 2.98%, azygos in 1.28% and fenestrated in 1.28%. The middle cerebral artery (MCA) was hypoplastic in 7.35% and typical in 92.64%. The PCA was hypoplastic in 28.74% and typical in 71.25%. Knowledge of the configuration of the CoW plays a significant role in guiding therapeutic decision-making in treating various neurovascular pathologies.

Anatomical variations in the circle of Willis on magnetic resonance angiography in a south Trinidad population

Objectives

This article seeks to determine the prevalence of a complete circle of Willis (CoW) and its common morphological variations in a south Trinidad population, while also investigating the influence of gender, age, and ethnicity on CoW morphology.

Methods

A prospective, descriptive, cross-sectional study was done on the magnetic resonance images for consecutive patients who had a brain MRI/magnetic resonance angiography at a tertiary health institution in south Trinidad between October 2019 and September 2020. Patients with significant cerebrovascular disease and/or a history of prior neurosurgical intervention were excluded.

Results

A complete CoW was seen in 24.3%, with more complete circles observed in younger participants (≤45 years) and Afro-Trinidadians. No gender predilection for a complete CoW was demonstrated. The most common variations in the anterior and posterior parts of the circle were a hypoplastic anterior communicating artery (8.6%, n = 13) and bilateral aplastic posterior communicating arteries (18.4%, n = 28), respectively.

Conclusions

Significant variations exist in the CoW of a south Trinidad population with a frequency of complete in 24.3%, and more complete circles in younger patients and Afro-Trinidadians. Gender did not influence CoW morphology.

Advances in knowledge

Structural abnormalities in the CoW may be linked to future incidence of cerebrovascular diseases and should therefore be communicated to the referring physician in the written radiology report. Knowledge of variant anatomy and its frequency for a particular populations is also required by neurosurgeons and neuro-interventional radiologists to help with preprocedural planning and to minimize complications.

Investigation of Cerebral Hemodynamics During Endovascular Aspiration: Development of an Experimental and Numerical Setup

PURPOSE

Acute ischemic stroke is a life-threatening emergency caused by an occlusion of a cerebral artery through a blood clot. Aspiration thrombectomy is an endovascular therapy for the removal of vessel occlusions. However, open questions regarding the hemodynamics during the intervention remain, motivating investigations of blood flow within cerebral arteries. In this study, we present a combined experimental and numerical approach to analyze hemodynamics during endovascular aspiration.

METHODS

We have developed an in vitro setup for investigations of hemodynamic changes during endovascular aspiration within a compliant model of patient-specific cerebral arteries. Pressures, flows, and locally resolved velocities were obtained. In addition, we established a computational fluid dynamics (CFD) model and compared the simulations during physiological conditions and in two aspiration scenarios with different occlusions.

RESULTS

Flow redistribution within cerebral arteries after ischemic stroke is strongly dependent on the severity of the occlusion and on the volume flow extracted by endovascular aspiration. Numerical simulations exhibit an excellent correlation of R = 0.92 for flow rates and a good correlation of R = 0.73 for pressures. Further on, the local velocity field inside the basilar artery had a good agreement between CFD model and particle image velocimetry (PIV) data.

CONCLUSION

The presented setup allows for in vitro investigations of artery occlusions and endovascular aspiration techniques on arbitrary patient-specific cerebrovascular anatomies. The in silico model provides consistent predictions of flows and pressures in several aspiration scenarios.

The Role of Hemodynamics through the Circle of Willis in the Development of Intracranial Aneurysm: A Systematic Review of Numerical Models

Background: The role of regional hemodynamics in the intracranial aneurysmal formation, growth, and rupture has been widely discussed based on numerical models over the past decades. Variation of the circle of Willis (CoW), which results in hemodynamic changes, is associated with the aneurysmal formation and rupture. However, such correlation has not been further clarified yet. The aim of this systematic review is to investigate whether simulated hemodynamic indices of the CoW are relevant to the formation, growth, or rupture of intracranial aneurysm. Methods: We conducted a review of MEDLINE, Web of Science, and EMBASE for studies on the correlation between hemodynamics indices of the CoW derived from numerical models and intracranial aneurysm up to December 2020 in compliance with PRISMA guidelines. Results: Three case reports out of 1046 publications met our inclusion and exclusion criteria, reporting 13 aneurysms in six patients. Eleven aneurysms were unruptured, and the state of the other two aneurysms was unknown. Wall shear stress, oscillatory shear index, von-Mises tension, flow velocity, and flow rate were reported as hemodynamic indices. Due to limited cases and significant heterogeneity between study settings, meta-analysis could not be performed. Conclusion: Numerical models can provide comprehensive information on the cerebral blood flow as well as local flow characteristics in the intracranial aneurysm. Based on only three case reports, no firm conclusion can be drawn regarding the correlation between hemodynamic parameters in the CoW derived from numerical models and aneurysmal formation or rupture. Due to the inherent nature of numerical models, more sensitive analysis and rigorous validations are required to determine its measurement error and thus extend their application into clinical practice for personalized management. Prospero registration number: CRD42021125169.

An in vitro Assessment of the Haemodynamic Features Occurring Within the True and False Lumens Separated by a Dissection Flap for a Patient-Specific Type B Aortic Dissection

One of the highest mortality rates of cardiovascular diseases is aortic dissections with challenging treatment options. Currently, less study has been conducted in developing in vitro patient-specific Type B aortic dissection models, which mimic physiological flow conditions along the true and false lumens separated by a dissection flap with multiple entry and exit tears. A patient-specific Stanford Type B aortic dissection scan was replicated by an in-house manufactured automatic injection moulding system and a novel modelling technique for creating the ascending aorta, aortic arch, and descending aorta incorporating arterial branching, the true/false lumens, and dissection flap with entry and exit intimal tears. The physiological flowrates and pressure values were monitored, which identified jet stream fluid flows entering and exiting the dissection tears. Pressure in the aorta’s true lumen region was controlled at 125/85 mmHg for systolic and diastolic values. Pressure values were obtained in eight sections along the false lumen using a pressure transducer. The true lumen systolic pressure varied from 122 to 128 mmHg along the length. Flow patterns were monitored by ultrasound along 12 sections. Detailed images obtained from the ultrasound transducer probe showed varied flow patterns with one or multiple jet steam vortices along the aorta model. The dissection flap movement was assessed at four sections of the patient-specific aorta model. The displacement values of the flap varied from 0.5 to 3 mm along the model. This model provides a unique insight into aortic dissection flow patterns and pressure distributions. This dissection phantom model can be used to assess various treatment options based on the surgical, endovascular, or hybrid techniques.

Investigation of Flow Changes in Intracranial Vascular Disease Models Constructed with MRA Images

This study aimed to develop a magnetic resonance imaging (MRI)-compatible flow delivery system and individualized models of circle of Willis (CoW), which include 50% and 100% blockage in internal carotid artery (ICA50 and ICA100), and 100% blockage in vertebral artery (VA100). Images were obtained using 3D time-of-flight and phase-contrast magnetic resonance angiography (MRA) sequences, and changes in velocity and flow direction at CoW models were analyzed. For the ICA50 and VA100 models, the flow was similar to that of the normal model. For the ICA 50 model, it was found that 50% blockage did not affect cerebral blood flow. For the VA100 model, decreased flow in the posterior cerebral artery and a change to the flow direction in the posterior communicating artery were found. For the ICA100 model, particularly, decreased flow in the ipsilateral middle and anterior cerebral arteries and a change to the flow direction in the ipsilateral anterior cerebral artery of the CoW were found. These results demonstrated that the flow system with various CoW disease models tailored to individual characteristics could be used to predict stroke onset more quickly. For the ICA50 and VA100 models, the possibility of cerebral infarction was significantly lower. On the other hand, for the ICA100 model, there was a high possibility of decreased flow, which could lead to cerebral infarction.

Distribution of variations in anatomy of the circle of Willis: results of a cadaveric study of the Malawian population and review of literature

Introduction

the circle of Willis is an anatomical structure of clinical importance particularly in the evaluation of neurovascular diseases. Individuals show considerable variations in the anatomical configuration of the circle of Willis. A cross-sectional study was conducted to determine the distribution of morphological variations of the circle of Willis in Malawians and compare with other ethnic groups.

Methods

brains were collected from twenty-four recently deceased black Malawians during autopsy at Queen Elizabeth Central Hospital, a referral teaching hospital in Blantyre, Malawi and fixed in 10% buffered formalin. Digital images of the interpeduncular region (exposing the circle of Willis) were taken with an 18.4 megapixels camera from the base of the brain. Whole-circle and segmental parameters of the circle of Willis were assessed using the Osiris computer programme and classified based on a 22-type classification scheme.

Results

the following morphological variations were observed: hypoplasia, aplasia, asymmetry and accessory vessels. Typical circle of Willis was seen in 26% of the cases. Only six of the original twenty-two types were observed. Consistent with most previous studies, types 1, 3, 4, 6, 8 and 9 were common while types 10-22 were rare. Three variants not previously described in the original scheme (unilateral PcoA aplasia, AcoA duplication, and PcoA aplasia with contralateral PcoA hypoplasia) were observed in this study.

Conclusion

anatomical variations of the circle of Willis in Malawians seem to be distributed in similar frequencies and patterns as in other more-diverse populations. Circle of Willis variants with potential predilection for atherogenesis and aneurysm formation exist in the Malawian population. These should be considered in clinical practice.

Hemodynamic modeling of the circle of Willis reveals unanticipated functions during cardiovascular stress

The circle of Willis (CW) allows blood to be redistributed throughout the brain during local ischemia; however, it is unlikely that the anatomic persistence of the CW across mammalian species is driven by natural selection of individuals with resistance to cerebrovascular disease typically occurring in elderly humans. To determine the effects of communicating arteries (CoAs) in the CW on cerebral pulse wave propagation and blood flow velocity, we simulated young, active adult humans undergoing different states of cardiovascular stress (i.e., fear and aerobic exercise) using discrete transmission line segments with stress-adjusted cardiac output, peripheral resistance, and arterial compliance. Phase delays between vertebrobasilar and carotid pulses allowed bidirectional shunting through CoAs: both posteroanterior shunting before the peak of the pulse waveform and anteroposterior shunting after internal carotid pressure exceeded posterior cerebral pressure. Relative to an absent CW without intact CoAs, the complete CW blunted anterior pulse waveforms, although limited to 3% and 6% reductions in peak pressure and pulse pressure, respectively. Systolic rate of change in pressure (i.e., ∂P/∂t) was reduced 15%-24% in the anterior vasculature and increased 23%-41% in the posterior vasculature. Bidirectional shunting through posterior CoAs was amplified during cardiovascular stress and increased peak velocity by 25%, diastolic-to-systolic velocity range by 44%, and blood velocity acceleration by 134% in the vertebrobasilar arteries. This effect may facilitate stress-related increases in blood flow to the cerebellum (improving motor coordination) and reticular-activating system (enhancing attention and focus) via a nitric oxide-dependent mechanism, thereby improving survival in fight-or-flight situations.NEW & NOTEWORTHY Hemodynamic modeling reveals potential evolutionary benefits of the intact circle of Willis (CW) during fear and aerobic exercise. The CW equalizes pulse waveforms due to bidirectional shunting of blood flow through communicating arteries, which boosts vertebrobasilar blood flow velocity and acceleration. These phenomena may enhance perfusion of the brainstem and cerebellum via nitric oxide-mediated vasodilation, improving performance of the reticular-activating system and motor coordination in survival situations.

An in vitro assessment of atrial fibrillation flow types on cardiogenic emboli trajectory paths

Atrial fibrillation is the most significant contributor to thrombus formation within the heart and is responsible for 45% of all cardio embolic strokes, which account for approximately 15% of acute ischemic strokes cases worldwide. Atrial fibrillation can result in a reduction of normal cardiac output and cycle length of up to 30% and 40%, respectively. A total of 240 embolus analogues were released into a thin-walled, patient-specific aortic arch under normal (60 embolus analogues) and varying atrial fibrillation (180 embolus analogues) pulsatile flow conditions. Under healthy flow conditions (n = 60), the embolus analogues tended to follow the flow rate split through each outlet vessel. There was an increase in clot trajectories along the common carotid arteries under atrial fibrillation flow conditions. A shorter pulse period (0.3 s) displayed the highest percentage of clots travelling to the brain (24%), with a greater percentage of clots travelling through the left common carotid artery (17%). This study provides an experimental insight into the effect varying cardiac output and cycle length can have on the trajectory of a cardiac source blood clots travelling to the cerebral vasculature and possibly causing a stroke.

The impact of compliance on Stage 2 uni-ventricular heart circulation: An experimental assessment of the Bidirectional Glenn

The Bidirectional Glenn (BDG) or cavopulmonary connection is typically undertaken to volume unload the single ventricle in an effort to preserve ventricular and atrioventricular valve function. The geometry of this surgical palliation has been shown to influence the fluid energy loss as well as the distribution of flow that enters through the superior vena cava. In-vitro and in-silico studies to date have been performed on rigid wall models, while this investigation looks at the impact of flexible thin walled models versus rigid walls. Rigid and compliant models of two patient-specific Glenn geometries were fabricated and tested under various flow conditions, within a biosimulator capable of replicating patient specific flow conditions. It was found that the compliant models exhibit greater levels of energy loss compared to the rigid models. Along with these findings greater levels of turbulence was found in both compliant models compared to their rigid counterparts under ultrasound examinations. This shows that vessel compliance has a significant impact on the hemodynamics within hypoplastic left heart syndrome.

Experimental validation of computational fluid dynamics for solving isothermal and incompressible viscous fluid flow

In order to validate a computational method for solving viscous fluid flows, experiments are carried out in an eccentric cylindrical cavity showing various flow formations over a range of Reynolds numbers. Especially, in numerical solution approaches for isothermal and incompressible flows, we search for simple experimental data for evaluating accuracy as well as performance of the computational method. Verification of different computational methods is arduous, and analytic solutions are only obtained for simple geometries like a channel flow. Clearly, a method is expected to predict different flow patterns within a cavity. Thus, we propose a configuration generating different flow formations depending on the Reynolds number and make the experimental results freely available in order to be used as an assessment criterion to demonstrate the reliability of a new computational approach.

Demographic age-related variation in Circle of Willis completeness assessed by digital subtraction angiography

OBJECTIVE:

Incomplete circle of Willis (CoW) configuration is an important risk factor for cerebrovascular pathology, namely aneurysm formation and ischemic stroke. This study was performed to characterize CoW variation using digital subtraction angiography and to identify demographic and physiologic features that may influence the risk of having an incomplete CoW configuration.

MATERIALS AND METHODS:

A retrospective review of 274 patients who underwent cerebral angiography by a single surgeon for any indication was conducted. Each CoW branch was graded as normal, hypoplastic, or aplastic. Univariate and multivariate regression analyses were conducted to assess the impact of age, gender, race, and certain comorbidities on CoW configuration.

RESULTS:

A complete CoW was identified in 37.23% of patients. In univariate analysis, patients <40 years old were more likely to have a complete CoW (odds ratio [OR]: 4.973, 95% confidence interval [CI]: 2.610–9.476, P < 0.001) as were patients <70 years old (OR: 2.849, 95% CI: 1.131–7.194, P < 0.05). Univariate analysis on demographic factors and comorbidities revealed CoW completeness to decrease with hypertension (OR: 0.575, 95% CI: 0.347–0.951, P = 0.031) and diabetes mellitus (OR: 0.368, 95% CI: 0.180–0.754, P = 0.006). Multivariable logistic regression analysis used to assess the impact of age on CoW completeness showed age to be an independent predictor of complete CoW, with an inverse correlation between increasing age and CoW completeness (OR: 0.955, 95% CI: 0.937–0.973, P < 0.001) after controlling for potential confounders including hypertension and diabetes mellitus.

CONCLUSIONS:

CoW configuration shows considerable variation with age; however, further investigation is required to elucidate the full impact of other demographic and vascular risk factors on CoW anatomy.

PIV investigation of the flow fields in subject-specific vertebro-basilar (VA-BA) junction

Background

As the only arterial structure of which two main arteries merged into one, the vertebro-basilar (VA-BA) system is one of the favorite sites of cerebral atherosclerotic plaques. The aim of this study was to investigate the detailed hemodynamics characteristics in the VA-BA system.

Methods

A scale-up subject-specific flow phantom of VA-BA system was fabricated based on the computed tomography angiography (CTA) scanning images of a healthy adult. Flow fields in eight axial planes and six radial planes were measured and analyzed by using particle image velocimetry (PIV) under steady flow conditions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Re}=300$$\end{document}Re=300, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Re}=500$$\end{document}Re=500. A water–glycerin mixture was used as the working fluid.

Results

The flow in the current model exhibited highly three-dimensional characteristics. The confluence of VAs flow formed bimodal velocity distribution near the confluence apex. Due to the asymmetrical structural configuration, the bimodal velocity profile skewed towards left, and sharper peaks were observed under higher Reynolds condition. Secondary flow characterized by two vortices formed in the radial planes where 10 mm downstream the confluence apex and persists along the BA under both Reynolds numbers. The strength of secondary flow under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Re}=500$$\end{document}Re=500 is around 8% higher than that under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Re}=300$$\end{document}Re=300, and decayed nonlinearly along the flow direction. In addition, a low momentum recirculation region induced by boundary layer separation was observed near the confluence apex. The wall shear stress (WSS) in the recirculation area was found to be lower than 0.4 Pa. This region coincides well with the preferential site of vascular lesions in the VA-BA system.

Conclusions

This preliminary study verified that the subject-specific in-vitro experiment is capable of reflecting the detailed flow features in the VA-BA system. The findings from this study may help to expand the understanding of the hemodynamics in the VA-BA system, and further clarifying the mechanism that underlying the localization of vascular lesions.

An In-Vitro Flow Study Using an Artificial Circle of Willis Model for Validation of an Existing One-Dimensional Numerical Model

A one-dimensional (1D) numerical model has been previously developed to investigate the hemodynamics of blood flow in the entire human vascular network. In the current work, an experimental study of water-glycerin mixture flow in a 3D-printed silicone model of an anatomically accurate, complete circle of Willis (CoW) was conducted to investigate the flow characteristics in comparison with the simulated results by the 1D numerical model. In the experiment, the transient flow and pressure waveforms were measured at 13 selected segments within the flow network for comparisons. In the 1D simulation, the initial parameters of the vessel network were obtained by a direct measurement of the tubes in the experimental setup. The results verified that the 1D numerical model is able to capture the main features of the experimental pressure and flow waveforms with good reliability. The mean flow rates measurement results agree with the predictions of the 1D model with an overall difference of less than 1%. Further experiment might be needed to validate the 1D model in capturing pressure waveforms.

A Patient-Specific Three-Dimensional Hemodynamic Model of the Circle of Willis

Circle of Willis (CoW) is one of the most important cerebral arteries in the human body and various attempts have been made to study the hemodynamic of blood flow in this vital part of the brain. In the present study, blood flow in a patient specific CoW is numerically modeled to predict disease-prone regions of the CoW. Medical images and computer aided design software are used to construct a realistic three-dimensional model of the CoW for this particular case. The arteries are considered as elastic conduits and the interactions between arterial walls and the blood flow are taken into account. Mooney-Rivlin hyperelastic model is used to describe the behavior of arterial walls and blood is considered as a non-Newtonian fluid obeying the Carreau model. An available experimental-based pulsatile velocity profile is used at the entrance of the CoW. The finite element-based commercial software, ADINA, is used to solve the governing equations. Blood pressure and velocity and arterial wall shear stress are calculated in different regions of the CoW. A simplified form of the model is also compared with the available published data. Results affirmed that the proposed computational model has the potential to capture the hemodynamic characteristics of the CoW. The computational results can be used to determine disease-prone locations for a given CoW.

Completion of the Circle of Willis Varies by Gender, Age, and Indication for Computed Tomography Angiography

OBJECTIVE

The circle of Willis (CoW) is the foremost anastomosis and blood distribution center of the brain. Its effectiveness depends on its completion and the size and patency of its vessels. Gender-related and age-related anatomic variations in the CoW may play an important role in the pathogenesis of cerebrovascular diseases. In this study, we analyzed computed tomography angiograms (CTAs) to assess for differences in CoW completion related to gender, age, and indication for CTA.

METHODS

A total of 834 CTAs were retrospectively analyzed for all CoW vessels to compare the incidence of complete CoW and variation frequency based on gender, age, and indication.

RESULTS

The incidence of complete CoW was 37.1% overall. CoW completion showed a statistically significant decrease with increasing age for all age groups in both men (47.0%, 29.4%, 18.8%) and women (59.1%, 44.2%, 30.9%). Completion was greater in women (43.8%) than in men (31.2%) overall and for all age groups. These gender differences were all statistically significant except for the 18-39 years age group. The most frequent of the 28 CoW variations were absent posterior communicating artery (PCOM) bilaterally (17.1%), right PCOM (15.3%), and left PCOM (10.9%). Ischemic stroke and the 18-39 years age group of hemorrhagic stroke showed a statistically significant reduction in completion relative to trauma.

CONCLUSIONS

The incidence of complete CoW is likely greater in women for all age groups and likely decreases with age in both genders. The most frequently absent vessel is likely the PCOM, either unilaterally or bilaterally. Completion may play a role in ischemic stroke and a subset of patients with hemorrhagic stroke.

The role of the circle of Willis in internal carotid artery stenosis and anatomical variations: a computational study based on a patient-specific three-dimensional model

BACKGROUND

The aim of this study is to provide better insights into the cerebral perfusion patterns and collateral mechanism of the circle of Willis (CoW) under anatomical and pathological variations.

METHODS

In the current study, a patient-specific three-dimensional computational model of the CoW was reconstructed based on the computed tomography (CT) images. The Carreau model was applied to simulate the non-Newtonian property of blood. Flow distributions in five common anatomical variations coexisting with different degrees of stenosis in the right internal carotid artery (RICA) were investigated to obtain detailed flow information.

RESULTS

With the development of stenosis in unilateral internal carotid artery (ICA), the cerebral blood supply decreased when the degree of stenosis increased. The blood supply of the ipsilateral middle cerebral artery (MCA) was most affected by the stenosis of ICA. The anterior communicating artery (ACoA) and ipsilateral posterior communicating artery (PCoA) functioned as the important collateral circulation channels when unilateral stenosis occurred. The blood flow of the anterior circulation and the total cerebral blood flow (CBF) reached to the minimum in the configuration of the contralateral proximal anterior cerebral artery (A1) absence coexisting with unilateral ICA stenosis.

CONCLUSIONS

Communicating arteries provided important collateral channels in the complete CoW when stenosis in unilateral ICA occurred. The cross-flow in the ACoA is a sensitive indicator of the morphological change of the ICA. The collateral function of the PCoA on the affected side will not be fully activated until a severe stenosis occurred in unilateral ICA. The absence of unilateral A1 coexisting with the stenosis in the contralateral ICA could be the most dangerous configuration in terms of the total cerebral blood supply. The findings of this study would enhance the understanding of the collateral mechanism of the CoW under different anatomical variations.

Experimental study of hemodynamics in the Circle of Willis

BACKGROUND

The Circle of Willis (CoW) is an important collateral pathway of the cerebral blood flow. An experimental study of the cerebral blood flow (CBF) distribution in different anatomical variations may help to a better understanding of the collateral mechanism of the CoW.

METHODS

An in-vitro test rig was developed to simulate the physiological cerebral blood flow in the CoW. Ten anatomical variations were considered in this study, include a set of different degrees of stenosis in L-ICA and L-ICA occlusion coexist with common anatomical variations. Volume flow rates of efferent arteries and pressure signals at the end of communicating arteries of each case were recorded. Physiological pressure waveforms were applied as inlet boundary condition.

RESULTS

In the development of L-ICA stenosis, the total CBF decreases with the increase of stenosis degree. The blood supply of ipsilateral middle cerebral artery (MCA) was affected most by the stenosis of L-ICA. Anterior communicating artery (ACoA) and ipsilateral posterior communicating artery (PCoA) function as important collateral pathways of cerebral collateral circulation when unilateral stenosis occurred. The blood supply of anterior cerebral circulation was compensated by the posterior cerebral circulation through ipsilateral PCoA when L-ICA stenosis degree is greater than 40% and the affected side was compensated immediately by the unaffected side through ACoA. Blood flow of the anterior circulation and the total CBF reached the minimum among all cases studied when L-ICA occlusion coexist with the absence of PCoA.

CONCLUSION

The results demonstrated the flow distribution patterns of the CoW under anatomical variations and clarified the collateral mechanism of the CoW. The flow ACoA is the most sensitive indexes to the morphology change of ipsilateral ICA. The relative independence of the circulation in anterior and posterior sections of the CoW is not broken and the function of ipsilateral PCoA is not activated until a severe stenosis of unilateral ICA occurs. PCoA is the most important collateral pathway of the collateral circulation and the missing of PCoA has the highest risk of stroke when the ipsilateral ICA has severe stenosis. These findings may provide the basis for future therapeutic and diagnosis applications.