Severe brain disease - probably - but they are also decaying dead bodies with no functioning circulation.
And some of them don't even have complete bodies (like bicycle girl).
As they rapidly consume flesh, nothing is digested either. I guess a well-fed zombie just gets bigger and bigger? (except bicycle girl - and man would watching her feed ever be gross!)
On Talking Dead, the guests discussed whether we'll ever see a snapping, severed head. They said it's possible.