An apparatus to oxygenate and perfuse a bodily tissue for extracorporeal preservation of the bodily tissue. The apparatus may be used to transport donor organs for transplant. The apparatus includes a pneumatic system, a pumping chamber, and an organ chamber. The pneumatic system is configured for the controlled delivery of fluid to and from the pumping chamber based on a predetermined control scheme. The pumping chamber is configured to diffuse a gas into a perfusate and to generate a pulse wave for moving the perfusate through a bodily tissue. The pumping chamber is configured to substantially automatically purge excess fluid from the pumping chamber to an area external to the apparatus.