A treatment strategy for treatment of elevated pressure in a body conduit, such as a pulmonary vein, with a prosthetic partitioning device for placement in and/or about pulmonary veins is described, as well as delivery systems, and strategies for use thereof. A control device is configured to transmit signals to the prosthetic device to effectuate the repetitive transition between a first, less restricted flow configuration and a second, restricted flow configuration are described. A sensor device may be provided for monitoring physiological parameters of the patient, and can provide signals to the control device for effectuating the transition between the first and second configuration.