I buy frozen heart last the upgrade doesn't help as much as the other gear and you rarely get that much gold anyways. By the time you get thornmail you shouldn't be dying all the time. I get thornmail to stay up longer and fight 3-4 enemies at once. The damage it does helps you kill hit and runners, burst melee, and tanks. Without buying thornmail you are a lot less likely to kill two out of three or all three players when you get jumped or suicide attack a group. If someone like Xin jumps on you he won't be able to kill you because you are being healed by three separate spells hitting him for damage and your armor removes a lot of his damage.

This has more than enough AP and the Runes are just what I prefer as I mentioned. Saying I don't need the cooldown ones pretty much completely misses the entire point of this build which is using requiem more often. This build is for playing a specific way not what you think is optimal for Karthus.

Mine is a down vote. Sorry, but here are my reasons and im going to explain them so you can fix your guide and you dont thing im a troll.
First: You have Celerity / Focus runes.... and you already have 35% CDR (Cooldown reduction) you should just get Blue buff.

Second: You have Thornmail and Glacial Shroud ._. armor items on Karthus ._. wtf! karthus is made to die and he will die no matter what item you get. and Frozen Heart ( Item you should do when you finish Glacial shroud, this guide is SO incomplete ) anyways Frozen heart passive reduces the enemy atack speed and gives a lot of armor, that kind of counters the thornmail, Big LOL.

Third: You dont have That much AP, and you should have a lot of AP, you are karthus, a big AP mass of trolling great escapes .

Fourth: Tons of things that they have nothing to do here, for example that cat thing ._. you should expend the 5000 letters in useful things, for example how to smart cast your Q