Pathological blood-flow-induced shear stresses are associated with atherosclerosis, a cardiovascular disease that is a leading cause of deaths in the US. Our previous study found differences in a vortical structure within an artery bifurcation that led to an atherosclerosis-prone shear stress distribution. The vortex structures showed differences in moment of formation, downstream transport, and lifespan between a healthy and disease-prone artery geometries. Additionally, a difference in axial pressure gradient was detected. Thus, a fundamental study concerning pressure gradient effects on vortical structures is performed. CFD simulations are used to study the impact of an axial pressure gradient on the formation of a vortex ring in a radially confined space. The characteristic 'formation number' and the maximum circulation dependencies on the applied pressure gradient will be discussed.