The invention relates to a novel pulsating medical device comprising: a catheter (1) designed to be inserted into a blood vessel, having a diameter and comprising a rod at its insertion end, termed part A; and an inflatable component (6) housed around part of the catheter (1), termed part B, said inflatable component (6) being designed to be connected to an inflation means (9) connected to the other end of said catheter (1) and termed part C, so that said inflatable component can be inflated/deflated in a pulsed manner, the diameter of part B of said catheter (1) being less than the diameters of parts A and C of said catheter (1), and the diameters of parts A and C of said catheter (1) being approximately equal.