Exit this door and kill the unsuspecting guard protecting the organic liquefier machine button. Turn it off, the bridge will lower, and you must kill the Gladiator to get across safely.
Walk back up the ramp from which you came down to drop down into the red human goo in the corner. Quickly jump up to the dry area containing a secret - a Quad Damage power-up. Hit the green button to open a small compartment to crawl through back to the top.