A method and a kit for the prevention of venous stenosis associated with the use of hemodialysis AV shunts. The kit may use a bifurcated needle for providing access to the shunt or blood vessel. One of the arms is used for returning the blood to the subject after dialysis treatment, while the other arm is used for inserting a device for cleaning the vein, the device being either an autonomous crawling device, or a passive tethered device moved down the vein by the blood flow. The autonomous crawling device may be a series of sequentially inflatable chambers, the stenosis being cleared by pressure from the outer walls of the chambers when inflated and moved. The passive device may be an element having a flexible disc-like structure, whose flexible peripheral edge slides along the inner walls of the blood vessel, compressing or clearing the material attached thereto.