Apparatuses and methods for treating a wound by applying reduced or negative pressure to the wound can include a wound cover, a fluid collection container, a vacuum pump, an inflation pump, and one or more conduits. The wound cover can be configured to move between at least a relatively rigid, generally raised position and a relatively flexible, generally collapsed position according to a predetermined program or in response to input from a user or one of more sensors. In some embodiments, the wound cover can be configured to move between at least the relatively rigid, generally raised position and the relatively flexible, generally collapsed position by adjusting the air pressure in one or more channels in the wound cover or by adjusting or by adjusting the length of piezoelectric or other length changing material supported by the wound cover.