Systems and methods of the invention generally relate to prolonging viability of bodily tissue in static cold storage and hypothermic machine perfusion techniques by reducing the rate of edema through the application of compressive force to the bodily tissue via a compression device. Compression devices of the invention may comprise biocompatible materials and may apply compressive force through incorporation of elastic materials, through expandable bladders, or other means. Certain embodiments include perfusion devices comprising a pneumatic system, a pumping chamber, and an organ chamber. 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 organ chamber is configured to receive the perfusate along with a bodily tissue fitted with a compression device. Both the organ chamber and the pumping chamber are configured to substantially automatically purge excess fluid.
