Determinants of the occurrence of vortex rings in the left ventricle during diastole

Abstract

This study employs classical inviscid fluid dynamics theory to investigate whether LV diastolic inflow volume and the size of the LV play a role in vortex ring formation. Fluid injection across an orifice into a large container results in the generation of a vortex ring having a constant size and speed. Relations between the vortex size and speed and the injection were obtained by applying conservation laws regarding kinetic energy, impulse and vorticity; the initial state was computed using a bolus injection model, and the final state by using the Kelvin vortex model. An important parameter in the equations is the relative injection length, i.e., the ratio of the length of the injected bolus and the radius of the orifice ( L R ). Its estimated highest value in man, L R = 15 , produces a rather thick vortex ring (relative thickness 0.77). Comparable results following from the Hill vortex model convinced us that the Kelvin vortex model can be applied in the whole range of injection lengths in the human left ventricle. In an in vitro model it is shown experimentally that vortex rings can be generated for L R in the range from 2 to 16. The measured traveling speed of the vortex ring is in fair agreement with the theory, as well as the ring radius for large injections. A vortex ring located in a narrow channel cannot reach its proper traveling speed. The method of images is used to estimate the speed reduction of vortex rings within a cylinder. It turns out that propagation of vortex rings is possible when the ratio of orifice to cylinder radius is less than about 0.5. Further narrowing of the cylinder impedes propagation of the vortex ring. We conclude that the size of the left ventricle is an important factor for the generation of vortex rings in human ventricles, whereas the injection volume is not. Probably, vortex rings will not develop in the average normal ventricle, whereas they can be generated in dilated ventricles having a diameter which is more than twice as large as the mitral valve orifice diameter.