Simple abrasion may be the best approach to removing the biofilm without causing harm to the PBR tubing. Cut a number of firm sponges that are slightly larger than the diameter of the tube. For example for a 2 cm tube, make a sponge cylinder that is 2.5 X 2.5 cm. Soak a sponge and add it to the PBR. If possible, connect the tube to a pressured water line or powerful pump. The water pressure should force the sponge through the PBR. If the first sponge makes it through the system successfully, repeat the process with several sponges that are spaced apart with water in between the sponges. Most biofilms show a strong resistance to harsh chemicals, but simple, repeated abrasion by something harder than the biofilm but softer than the tube should give you your desired results.
You can use compressed air and some kind of cleaning soft sponge. Air will push sponge through tubes and clean their walls from algae. You can later use magnets for cleaning fish tanks to remove any remaining algae.