Apparatus and method of preserving life organs, the apparatus having an organ container in which the organ may be subjected to elevated pressure, a pump pulsatilely delivering perfusate into the organ and an oxygenator to oxygenate the perfusate effluent from the organ. A constant pressure bias maintains a minimum pressure on the perfusate between pulses. A fluid flow control system delivers driving fluid in a pulsed manner to the pump at a selected rate and at selected pulse duration. The method includes delivering pulsed oxygenated perfusate to the organ and uniformly conducting perfusate away from the organ and providing a constant pressure bias on the perfusate. Loss or gain of liquid volume caused by waste secretion by the organ is compensated for.