title: Modeling of human circle of Willis with and without aneurisms.
abstract: OBJECTIVE
  This paper includes results of the first stage of research aimed at the development of recommendations for physicians in order to help them to choose a particular type of cerebral arteries aneurysms treatment.
  
  
  METHODS
  Recent studies show that the majority of aneurysms develop as a result of hemodynamic and degenerative lesions of the vascular wall. Obviously, such wall damage can be studied using the methods of continuum mechanics and numerical simulations. Biomechanical modelling allows us to study hemodynamic parameters and stress-strain state of these arteries in health and disease, and to formulate practical recommendations for the necessity and reasonable selection of a particular type of cerebral arteries aneurysm treatment.
  
  
  RESULTS
  At this stage the realistic geometric models of arterial circle of Willis were built for its normal state and in the presence of aneurysms. The ultrasound analysis of circle of Willis was conducted in order to obtain blood flow parameters and the boundary conditions for carotid and vertebral arteries. Also, the mechanical properties of these arteries were investigated and constants of the Mooney-Rivlin strain energy function were obtained.
  
  
  CONCLUSIONS
  Thus, the boundary problem describing the behaviour of human Willis circle arteries was stated. Further, this problem will be solved numerically using the finite element method. The numerical results will be analyzed from the point of view of the influence of the mechanical factors on the emergence, growth and rupture of circle of Willis aneurysms.
authors.affiliation: Mathematical Modeling Subdepartment, Educational-Research Institute of Nanostructures and Biosystems, Saratov State University, Saratov, Russian Federation.
authors.forename: Dmitry
authors.initials: D
authors.lastname: Ivanov
authors.affiliation: Mathematical Modeling Subdepartment, Educational-Research Institute of Nanostructures and Biosystems, Saratov State University, Saratov, Russian Federation.
authors.forename: Alexander
authors.initials: A
authors.lastname: Dol
authors.affiliation: Biomechanics Subdepartment, Educational-Research Institute of Nanostructures and Biosystems, Saratov State University, Saratov, Russian Federation.
authors.forename: Olga
authors.initials: O
authors.lastname: Pavlova
authors.affiliation: Biomechanics Subdepartment, Educational-Research Institute of Nanostructures and Biosystems, Saratov State University, Saratov, Russian Federation.
authors.forename: Asel
authors.initials: A
authors.lastname: Aristambekova
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D002941:Circle of Willis / Q000473:pathology*; D005260:Female; D006801:Humans; D021621:Imaging, Three-Dimensional; D002532:Intracranial Aneurysm / Q000473:pathology*; D008297:Male; D008875:Middle Aged; D008953:Models, Anatomic; D008954:Models, Biological; D012984:Software; D018608:Ultrasonography, Doppler; D014711:Vertebral Artery / Q000000981:diagnostic imaging; D055815:Young Adult