in aquaculture, it's common to use accordion screen filters that look like this:
the simplest way to break down the organic debris caked on them is to throw the screen in a bucket with lots of (from pool supply) chlorine over night and rotate in a clean one that's already cleaned and ready to go. After soaking the screen in chlorine, hose it out and soak overnight in a bucket with lots of sodium thiosulfate to neutralize any remaining chlorine.
I would think you can do the same thing with any other mechanical filters.