Keywords: biomechanics, Willis circle arteries, aneurysm, hyperelastic material, Mooney-Rivling, finite element modeling, three-dimensional model.

The purpose of the study, presented in this paper, is to identify the hemodynamic and mechanical factors affecting growth, development and rupture of aneurysms. The solution of this problem will allow the evaluation of the blood flow in healthy arteries, and in arteries with aneurisms and make some recommendations for optimising the treatment of this disease.

To achieve this goal the following objectives have been formulated:

• investigate the mechanical properties of the circle of Willis arteries in the longitudinal and transverse directions and to achieve hyperelastic material constants of the artery wall;
• formulate and solve the boundary problem modelling the behaviour of human arteries of the circle of Willis;
• analyse the results of the simulations to determine the influence of mechanical factors on the pathogenesis of aneurysms.

To solve these problems are methods of the full-scale numerical experiment were used. The object of study were human Willis circle arteries. Numerical simulations of the closed circle of Willis taking into account the compliance of the walls were performed. The study of age and sex variability of the deformation and strength characteristics of the cerebral arteries, the stress-strain state and hemodynamics of the healthy and pathological Willis circle arteries (with aneurisms) was conducted.

Deformation-strength characteristics of the Willis circle arteries were determined. The strain energy Mooney-Rivlin function constants for the arteries of this type were found. Three basic factors: the shear stress at the wall, the effective stress in the arterial wall and blood pressure, leading to the formation of aneurysms were obtained. The application of the methodology of the finite element method to solve the related problems of elasto-hydrodynamic blood flow through the arteries was justified. The difficulties encountered in implementing the finite element method are described. The validity of using an integrated approach in the study of human arteries in normal and in the presence of pathology was proved.

The study presented in this paper enables the understanding of several key issues associated with intracranial aneurysms, including the reasons and factors affecting the occurrence of aneurysms, as well as their ability to predict the natural course.

The conclusions derived from this study clearly show the influence of mechanical factors on the appearance and development of the intracranial aneurisms and reveal the conditions under which they are most likely to break.

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