title: Clinical applicability of a mathematical model in assessing the functional ability of the communicating arteries of the circle of Willis.
abstract: BACKGROUND
  The brain collateral blood supply, which is essential in patients suffering from significant stenoses or occlusions of the extracranial arteries, remains difficult to assess accurately in practice. We compared data obtained from transcranial color-coded duplex sonography (TCCD) combined with carotid compression tests to morphometric autopsy data and to results given by a mathematical model of the cerebral macrocirculation.
  
  
  RESULTS
  In 16 moribund patients, anterior and posterior communicating arteries of the circle of Willis were divided into functional and non-functional based on the results of the TCCD combined with carotid compression tests. After death of the patients diameters and lengths of the main intracranial arteries were measured at autopsy and these values were treated with a mathematical model for calculating blood flow and blood pressure in all the segments of the arterial network. The diameters and the blood flows through the communicating arteries were found to be significantly higher in the group of functional arteries than in that of non-functional ones. However, blood flow was also shown to be dependent on other parameters such as the pressure difference between the two ends of the vessel.
  
  
  CONCLUSIONS
  Our data indicate that functional ability of the Willisian collaterals depends on morphological and functional parameters, and is therefore better assessed by a functional method, such as TCCD, than by a solely morphological one, such as cerebral angiography. Mathematically based circulation modeling, when it will be possible, could be a more comprehensive tool for delineating patients at a higher risk for hemodynamic cerebrovascular insufficiency.
authors.affiliation: Department of Surgery, Health and Medical Science Center, University of Debrecen, Debrecen, Hungary.
authors.forename: László
authors.initials: L
authors.lastname: Orosz
authors.forename: Arjan W
authors.initials: AW
authors.lastname: Hoksbergen
authors.forename: Csilla
authors.initials: C
authors.lastname: Molnár
authors.forename: Péter
authors.initials: P
authors.lastname: Siró
authors.forename: Francis
authors.initials: F
authors.lastname: Cassot
authors.forename: Jean-Pierre
authors.initials: JP
authors.lastname: Marc-Vergnes
authors.forename: Béla
authors.initials: B
authors.lastname: Fülesdi
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D001344:Autopsy; D001794:Blood Pressure / Q000502:physiology; D001921:Brain / Q000098:blood supply* / Q000473:pathology / Q000503:physiopathology; D015984:Causality; D002539:Cerebral Arterial Diseases / Q000000981:diagnostic imaging / Q000473:pathology / Q000503:physiopathology*; D002536:Cerebral Arteries / Q000000981:diagnostic imaging / Q000473:pathology / Q000503:physiopathology; D002560:Cerebrovascular Circulation / Q000502:physiology*; D002941:Circle of Willis / Q000000981:diagnostic imaging / Q000473:pathology / Q000503:physiopathology*; D005260:Female; D006439:Hemodynamics / Q000502:physiology; D006801:Humans; D008297:Male; D008875:Middle Aged; D008962:Models, Theoretical; D011237:Predictive Value of Tests; D020521:Stroke / Q000000981:diagnostic imaging / Q000473:pathology / Q000503:physiopathology*; D017585:Ultrasonography, Doppler, Transcranial