A wound therapy apparatus is disclosed that includes a wound interface securable to a skin surface around a wound bed to form an enclosed space over the wound bed that is fluid-tight. The wound therapy apparatus-may include a dressing engaged with the wound interface to contact the wound bed. A spacer may be disposed within the enclosed space proximal of the dressing to define a plenum between portions of the wound interface and a proximal side of the dressing. Gas within the enclosed space may have an O2 concentration greater than the O2 concentration in atmospheric air. The dressing may include a hydrophobic material, hydrophobic material, or a distal layer comprised of silicone having fenestrations therein, in various aspects. The pressure p0 within the enclosed space may vary over a pressure range pmin≤;p0≤;pmax. Related methods of use are also disclosed.