Finite element analysis in three-dimensional flow through a lateral saccular aneurysm.

: The three-dimensional flow pattern in a lateral saccular aneurysm was investigated by a finite element method. The aneurysm model had a dome-shaped diverticulum arising from one side of the straight circular tube. The steady Navier-Stokes equations and the equation of continuity were applied. The finite element equations were derived from the Galerkin process with each hexahedral element, in which velocities were approximated by quadratic polynomials and pressures by linear polynomials. The non-linear finite element equations were solved by a Newton-Raphson method. Calculations were performed of the steady flow at various Reynolds numbers. The conclusions for flow patterns with a Reynolds number of 1000 is as follows: (i) a separation vortex occurred in the whole circumferential region of the aneurysm, (ii) the separation vortex was distorted by the geometrical shape of the aneurysm, and (iii) two other vortexes induced by the separation vortex existed at the proximal and the distal wall of the aneurysm. These disturbances of flow through an aneurysm are thought to play a significant role in the formation of thrombi and the rupture of an aneurysm.