Energy approach to the solution of the hydroelastic problem of the growth of a diverticulum of a fusiform aneurysm

This paper considers an energy approach to assessing the state of a cerebral aneurysm as a hydroelastic system consisting of an elastic vessel wall and oncoming blood flow. Assuming that the elastic energy of a vessel with an aneurysm in combination with the bending energy and kinetic energy is spent only on viscous flow dissipation in the structure, we performed a series of numerical calculations for model configurations of a fusiform aneurysm in the absence and in the presence of a diverticulum of different sizes relative to the size of the aneurysm body. It is shown that pressure-velocity diagrams are in good agreement with clinical data. Using numerical simulation, it is shown that a diverticulum of small size has a significant effect on hemodynamics inside the body of the aneurysm, and at a large diverticulum size, the vortex induced inside the diverticulum is almost completely localized in it.