International Conference «Mathematical and Information Technologies, MIT-2016»

28 August – 5 September 2016

Vrnjacka Banja, Serbia – Budva, Montenegro

Grigorieva I.   Захаров Ю.Н.   Dolgov D.  

Mathematical Modeling of Large Blood Vessel Aneurysm Development and Growth

Reporter: Захаров Ю.Н.

The paper is devoted to mathematical modeling of large blood vessel aneurysm development and growth. Aneurysm rupture can cause massive hemorrhage and most probably death. Aneurysm (an aorta area enlargement or a bulging area in its wall) size and possibly its geometrical pattern are considered to be its rupture risk factors.
Age, vascular walls erosion, as well as high blood pressure are supposed to be aneurysm risk factors. Some researchers consider vascular wall material fatigue to be somehow associated with the risk factors, though the reasons and mechanisms of aneurysm development are insufficiently studied.
We consider the blood to be incompressible, heterogeneous, two-component fluid with variable viscosity. Vascular wall material is considered to be homogeneous fluid-tight material with variable rigidity.
The paper shows the process of aneurysm development in blood vessels with different vessel geometry in the context of the elasticity reduction of particular vessel wall areas. Inclination of vascular wall muscle fibers and type of weakness zone impact on aneurysm development is under consideration.  The range of biomaterial fatigue models is shown. Fatigue impact on vascular wall tensile stress resistance due to fluid motion is estimated. Immersed boundary method is used for numerical calculation of differential problem. Numerical experiment results are shows.

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