The present invention relates to a stent including a variable porosity, tubular structure having pores defined by structural surfaces. The tubular structure has a low porosity region in proximity to or at either end of the tubular structure, where the low porosity region is less porous than other regions located on the tubular structure and fully or partially obstructs passage of fluid. Any arcuate path that starts at one point within the low porosity region and goes around the perimeter of the tubular structure to stop at the same point within the low porosity region must have at least a portion that is outside of the low porosity region. Also disclosed is a method of modifying blood flow within and near an opening of an aneurysm in a blood vessel by deploying one or more stents of the present invention near an opening of the aneurysm in a blood vessel.