The invention concerns a circuit comprising a bag (111) comprising two flexible films (145, 146) and routing network connectors, and a press (110) comprising a first shell (114) and a second shell (113) clamping the bag to form pipes (104) between the films, the first shell comprising a pinch valve (120) which comprises an actuator (121) comprising a movable member (124) and in register with the moveable member an elastically compressible pad (131) which, when the valve is in an open position, has a resting configuration in which a second face (33) of the pad is concave and locally delimits a shaping channel (118), and, when the valve is in a closed position, has a pinching configuration in which the second face (133) is convex, with the pipe and the pad sandwiched between a shaping channel (116) and the moveable member.