I'll add
Ghost Hound and
Shion no Ou to the "traumatic background" list.
Ghost Hound does have some themes around psychiatry and neuroscience, so it might be somewhat closer to
NHK. That story is pretty unique, though. One other possibility might be
House of Five Leaves, though it's not set in contemporary Japan.
I also recommend this tag search:
http://forums.animesuki.com/tags.php?tag=psychological