The basic hypothesis of this study is that the @entity438 may enlarge and @entity397 due to dynamic instabilities of the blood flow and pressure inside the @entity439 . The specific question we attempted to answer is: which parameter(s) of aneurysmal geometry can serve as a reliable predictor(s) for @entity1756 ? We consider an idealized cylindrical @entity439 of the @entity1 common carotid artery and develop a mathematical model of blood flow through a normal artery and @entity439 connected in series. The mathematical model is nonlinear. It comprises nonlinear rheological properties of the normal artery and aneurysmal materials, and the inertial and resistance properties of the blood flow. The model equations were solved numerically and analyzed by methods of nonlinear dynamics. The critical aneurysmal diameter (CAD) is defined as a boundary point between the stable and unstable states of the model equations. The results confirm that a limit point of flow stability can occur only for a certain difference between aneurysmal and artery radii which are pre-disposed from a difference in their material properties. It was shown that CAD is dependent on both @entity439 and age of @entity1 . Finally, the results suggest that the ratio between aneurysmal and normal artery diameters is a more reliable predictor of the @entity1756 than the diameter alone. We conclude that an @entity439 diameter twice that of the normal artery could be dangerous.

Biomathematical modeling and analysis of blood flow in an XXXX .

@entity1 :: ('9606', 'Species') :: ['human', 'patient'] @entity438 :: ('MESH:D002532', 'Disease') :: ['intracranial aneurysm'] @entity397 :: ('MESH:D012421', 'Disease') :: ['rupture'] @entity439 :: ('MESH:D000783', 'Disease') :: ['aneurysm', 'aneurysmal length'] @entity1756 :: ('MESH:D017542', 'Disease') :: ['aneurysmal rupture']
@entity438 :: (MESH:D002532,Disease) :: ['intracranial aneurysm']
