Quantitative MRI-based measurement of blood flow in the rat-circle of Willis by Bruker PharmaScan 70/16

We introduce a new mathematical model of aneurysm of the circle of Willis. It is an ordinary differential equation of second order that regulates the velocity of blood flow inside the aneurysm. By using some recent methods of nonlinear analysis, we prove the existence of solutions with some qualitative properties that give information on the causes of rupture of the aneurysm.

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Blood Flow in the Circle of Willis: Modeling and Calibration

Multiscale Modeling and Simulation ◽

10.1137/07070231x ◽

2008 ◽

Vol 7 (2) ◽

pp. 888-909 ◽

Cited By ~ 68

Author(s):

Kristen DeVault ◽

Pierre A. Gremaud ◽

Vera Novak ◽

Mette S. Olufsen ◽

Guillaume Vernières ◽

...

Keyword(s):

Blood Flow ◽

Circle Of Willis

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Computational Fluid Dynamics Simulation of the Blood Flow in the Circle of Willis

Advances in Bioengineering ◽

10.1115/imece2002-32516 ◽

2002 ◽

Cited By ~ 1

Author(s):

M. Harazawa ◽

T. Yamaguchi

Keyword(s):

Blood Flow ◽

Blood Supply ◽

Internal Carotid ◽

Complex Geometry ◽

Cerebral Aneurysms ◽

Cerebrovascular Diseases ◽

Circle Of Willis ◽

Dynamics Simulation ◽

The Brain ◽

Internal Carotid Arteries

The blood supply for the brain is born by four arteries, that is, two internal carotid arteries and two vertebral arteries. They are mutually connected at the cerebral base, and form a closed arterial circle, called the circle of Willis, so that the safety of the brain blood supply is increased. However their anastomoses show a very wide variety of atypism. If some of anastomses are very thin, or even do not exist, the safety of the blood supply is not secured. This is particularly important when some diseases such as cerebral thrombosis occurs and the blood flow supply stops unilaterally. Redistribution of the blood supply in such cases is thought to be strongly affected by geometrical configuration of the anastomoses. It is also known that cerebral aneurysms, which may induce serious cerebrovascular diseases, preferentially occur at the circle of Willis. Complex blood flow pattern has been suspected of having an influence on this preference. This is again dependent on complex geometry of the circle.

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Are the Variants of the Circle of Willis Determined by Genetic or Environmental Factors? Results of a Twin Study and Review of the Literature

Twin Research and Human Genetics ◽

10.1017/thg.2018.50 ◽

2018 ◽

Vol 21 (5) ◽

pp. 384-393 ◽

Cited By ~ 4

Author(s):

Bianka Forgo ◽

Adam Domonkos Tarnoki ◽

David Laszlo Tarnoki ◽

Daniel Tamas Kovacs ◽

Laszlo Szalontai ◽

...

Keyword(s):

Risk Factors ◽

Blood Flow ◽

Cardiovascular Risk ◽

Environmental Factors ◽

Cardiovascular Risk Factors ◽

Transcranial Doppler Sonography ◽

Circle Of Willis ◽

Significant Difference ◽

Altered Blood ◽

Mz Twins

Background: Anatomic variants of the circle of Willis (CW) are commonly observed in healthy subjects. Genetic and environmental factors influencing these variants remain unclear. Our aim was to assess the genetic and environmental background affecting variant CW phenotypes. Methods: A total of 122 adult healthy twins from the Hungarian Twin Registry (39 monozygotic (MZ) and 22 dizygotic (DZ) pairs, average age 49.7 ± 13.4 years) underwent Time-of-Flight magnetic resonance angiography and transcranial Doppler sonography. We investigated the anterior and posterior CW according to morphological categories. Prevalence and concordance rates of CW variants were calculated. MZ twins discordant for CW variants were analyzed for cardiovascular risk factors and altered blood flow. Results: Complete CW (45.0%) and bilaterally absent posterior communicating artery (PCoA) (22.5%) were the most prevalent variants in the anterior and posterior CW, respectively. There was no significant difference regarding the prevalence of variants across zygosity except for bilaterally hypoplastic PCoA (p = .02). DZ concordance was higher compared to MZ twins regarding morphological categories of the CW. Cardiovascular risk factors were not significantly associated with variant CW in MZ twins discordant to CW morphology. Flow parameters did not differ significantly among MZ twins discordant to CW variants. Conclusion: CW variants may not be determined by substantial genetic effects and are not influenced by altered blood flow in healthy individuals. Further investigations are needed to identify potential environmental factors affecting these variants.

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Distribution of internal carotid artery blood flow in the pony

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.1983.244.1.h142 ◽

1983 ◽

Vol 244 (1) ◽

pp. H142-H149 ◽

Cited By ~ 2

Author(s):

J. A. Orr ◽

L. C. Wagerle ◽

A. L. Kiorpes ◽

H. W. Shirer ◽

B. S. Friesen

Keyword(s):

Blood Flow ◽

Carotid Artery ◽

Internal Carotid Artery ◽

Internal Carotid ◽

Electromagnetic Flowmeter ◽

Circle Of Willis ◽

Relative Distribution ◽

Brain Blood Flow ◽

Radioactive Microspheres ◽

Total Brain

This study determined whether blood flow through the internal carotid artery (ICA) could be used to sample total cerebral blood flow in the pony. To answer this question we considered both the anatomic arrangement of the ICA in cadavers and the relative distribution of ICA blood flow to cerebral and extracerebral tissue using radioactive microspheres. Acrylic corrosion casts of the ICA indicated that this vessel traveled directly to the base of the brain, contributing to the formation of the circle of Willis, and did not send any significant branches to other tissues. Two vessels (internal ethmoidal artery and internal ophthalamic artery) did arise anteriorly from the circle of Willis and were, therefore, indirectly supplied by the ICA. Injection of radioactive microspheres of 15 microns diameter indicated that blood flow to extracerebral structures supplied by the internal ethmoidal and internal ophthalamic arteries was less than 5% of total ICA blood flow. Increases in ICA blood flow as measured with an electromagnetic flowmeter during isocapnic hypoxia (arterial PO2 near 40 Torr) in the awake pony (n = 6) were compared with increases in total brain flow as measured with radioactive microspheres (n = 6). ICA blood flow increased 40% compared with a 38% increase in total brain blood flow as measured with microspheres. We conclude that the ICA supplies predominantly brain tissue (approximately 95%) and that changes in ICA blood flow are representative of changes in total brain blood flow in the awake pony.

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