A device for regulating blood pressure between a patient's left atrium and right atrium comprises an hourglass-shaped stent comprising a neck region and first and second flared end regions, the neck region disposed between the first and second end regions and configured to engage the fossa ovalis of the patient's atrial septum; and a one-way tissue valve coupled to the first flared end region and configured to shunt blood from the left atrium to the right atrium when blood pressure in the left atrium exceeds blood pressure in the right atrium. The inventive device may include a biodegradable material that biodegrades to offset flow changes caused by tissue ingrowth. The inventive device may reduce left atrial pressure and left ventricular end diastolic pressure, and may increase cardiac output, increase ejection fraction, relieve pulmonary congestion, and lower pulmonary artery pressure, among other benefits.