Disclosed herein are designs for improved inflatable structures for use during minimally invasive cardiovascular procedures. These inflatable structures facilitate the perfusion of blood through an anatomical structure, such as a heart valve, during the cardiovascular procedure. The inflatable structures are formed of a plurality of balloons arranged radially around a central location. The plurality of balloons form a lumen through which blood flows. Each balloon of the plurality is shaped or configured to stabilize the adjacent balloons, limiting their movement relative to each other. For example, some embodiments can feature balloons with a keystone shape that limits movement of the balloons inward toward the lumen. Some implementations can also include a support coil running through the lumen. The support coil holds enables the lumen to be open to perfusion even in the early stages of balloon inflation.