A valve frame is shaped to define a plurality of atrial arms, and a tubular portion that defines a lumen along a longitudinal axis of the valve frame. Prosthetic leaflets within the lumen are coupled to the frame. An outer frame defines a ring and a plurality of ventricular legs coupled to the ring. The ring circumscribes the tubular portion, and is defined by a pattern of alternating peaks and troughs. The tubular portion defines a row of upstream cells, and a row of downstream cells that is tessellated with the row of upstream cells. Each of the atrial arms is attached to, and extends from, a respective connection site at which adjacent upstream cells are connected to each other. Other embodiments are also described.
