Closure devices that selectively control blood flow between the right atrium and the left atrium of a heart of a patient. The control of blood flow can be based on detected values from a pressure sensor. The closure devices can include a body configured to engage native tissue when the device is deployed across the septal wall. In a first state at least a portion of (an inner surface of) a lumen is closed, preventing blood flow through the closure device. In a second state, the lumen is open to enable blood flow from the left atrium to the right atrium. A closure element can be selectively adjusted to control the flow of blood through the lumen. A volume of an expandable chamber can be increased or decreased to place the closure device into the first state or the second state.