The method described where there are troughs with media and a thin film of water flowing through the bottom of the media is what many in Hydroponics call Modified NFT. I will warn that modified NFT can become a clogging nightmare depending on the size of the trough and the length of time you leave the plants in and how much you clean out the troughs when you harvest/re-plant. It seems a bit more appropriate to hydroponics than to Aquaponics in my experience.
There are Aquaponic operations that do use NFT but as noted, they filter the water well before sending it to the troughs. Biggest challenges with NFT seem to be with temperature and dissolved oxygen in the troughs.
In large media filled grow beds, provided you have enough of them to handle filtering for the amount of fish tank/fish you have and you add some composting worms, they don't fill up so to speak.
It is only when you expect small or shallow grow beds to filter for a large amount of fish tank and fish load that you wind up with clogging issues. Now I will amend that statement to warn people about certain very aggressive rooted plants like oh, BANANAS!!!!! MINT!!!!!!! and probably a few others but most of them perennial.
I have set up situations where a small grow bed is filtering a far larger amount of gunk than it should be expected to and they will clog up (like a 10 or even 50 gallon bed filtering like 300-700 gallons of tank.) They will clog up quickly even, like less than a season. But if you have more grow bed volume than tank volume, then clogging is going to be far less likely unless you let a beast banana break the bed or a mint monster take over.
I have seen this done at Ceres Community Environment Park, I attended the aquaponics course they have there and they have a NFT system. Led by Green Technology Project Manager Stephen Mushin and Biologist Dr Wilson Lennard, construction of the first prototype aquaponics system began in June 2010 and is now in the final stages of testing. http://www.ceres.org.au/greentech/aquaponics
What you can’t see in the image is the bio-filter that sits between the fish tank and the grow beds, it is a bio-filter and aerator made from 4 levels of crates, the top level has a aquarium white sponge filter media, the second layer has large stones to create aeration, the third layer has ceramic fish tank media, and the last layer has small stones that sits just above the water level of the grow beds.
Hope this helps
I'm going to follw this up. Looks like things are moving forward in the aquaponic world. Thanks for link.