A catheter for delivering a therapeutic or diagnostic agent to a branch blond vessel of a major blood vessel comprises an elongated shaft having at least one lumen in fluid communication with an agent delivery port in a distal section of the shaft, an expandable tubular member on the distal section of the shaft, and a radially expandable member on the tubular member. The tubular member is configured to extend within the blood vessel up-stream and down-stream of a branch vessel, and has an interior passageway which is radially expandable within the blood vessel to separate blood flow through the blood vessel into an outer blood flow stream exterior to the tubular member and an inner blood flow stream within the interior passageway of the tubular member.