Abstract: A perfusion system for non-surgically isolating and perfusing an organ, particularly the liver (101), in a patient, and including; by-pass cathether apparatus having inlet and outlet lumens (111, 112) introducible into the blood vessels of the organ percutaneously and devised so as to by-pass the blood flow past the organ in a by-pass circuit; perfusion catheter apparatus having inlet and outlet lumens (114, 116) introducible into the blood vessels percutaneously and being devised so as to lead the flow of perfusion fluid in a perfusion circuit through the organ; occlusive seals (106, 108) for isolating the organ from the systemic blood flow; pump apparatus including a by-pass pump (261), a perfusion fluid pump (124) and a suction pump (134) for establishing a negative relative pressure at the perfusion outlet from the organ; and control apparatus (128) coupled to the pumps (124, 126, 134) so as to control the operation thereof such that the outflow of fluid from the organ exceeds the inflow of fluid into the