Computational Fluid Dynamics of the Flow of the Deformable Toroidal Embolic Agents Within Straight and Stenotic Pipes by Full Eulerian FSI Method

The effect of shape and size of embolic agents on embolization phenomena has been discussed clinically for transcatheter arterial chemoembolization (TACE). We numerically discussed the unique embolization behavior of new deformable toroidal microparticles in blood vessels by computational fluid dynamics simulations. We employed an Eulerian–Eulerian (full Eulerian) fluid–structure interaction (FSI) method to analyze the flow and deformation behaviors of a deformable torus in a cylindrical pipe. This method, based on the volume of fluid (VOF) method, is implemented in OpenFOAM and is verified by deformation tests with a visco-hyperelastic material in cavity flow. The torus exhibits multiple steady states depending on initial orientation, position, shear modulus, and the aspect ratio between major and minor radii, and the rotation angles of inclined tori reach approximately 80°. Deformation analysis of cross-sections reveals multiple deformation modes such as bending, rotation, and elongation over time. The equilibrium position of the torus is determined by the balance of various lift forces and becomes complex due to increased rotational diameter from elongation. Additionally, vortex structures and pressure gradients elucidate the mechanism that inclined tori are faster than horizontally oriented tori due to their deformation. Finally, flow tests of different microparticle shapes with the same surface area in a stenotic pipe show that the torus has the lowest pressure drop and flow rate reduction. These quantitative predictions are suggestive and encourage experimental study of toroidal microparticles as novel embolic agents in the future.