An apparatus for perfusing an organ or tissue includes a perfusion circuit for perfusing the organ or tissue; an oxygenator for oxygenating perfusate that circulates through the perfusion circuit; and an oxygen supply device such as an oxygen concentrator or an oxygen generator configured to supply oxygen to the oxygenator. A method of perfusing an organ or tissue includes producing oxygen from a device such as an oxygen concentrator and an oxygen generator; supplying the produced oxygen, preferably as the oxygen is produced, to a perfusate to oxygenate the perfusate; and perfusing the organ or tissue with the oxygenated perfusate. The produced oxygen preferably has a concentration greater than the oxygen concentration in air.