Not everything that Quantic Dream thought up for Heavy Rain made it into the game, which is probably for the best.
As part of a behind-the-scenes look at the making of Heavy Rain, Quantic Dream has rounded up the the scenes and concept art that ended up on the cutting room floor, to show people the direction the story might have taken. Quantic Dream tweaked and revised the plot all the way through development, so some of the cut content is pretty much complete.
In a video released on PSN last week - which, much like this article from this point onwards, contains some pretty significant Heavy Rain spoilers - Quantic Dream explained, among other things, that Madison's insomnia stemmed from her past as a war correspondent in Iraq. It also revealed that the original script called for a psychic link between Ethan and the Origami Killer, and for Ethan to enter a terrifying sub-aquatic nightmare world whenever he blacked out. Quantic Dream cut the paranormal elements after realizing that they weren't a good fit with the rest of the game, but that decision was made fairly late on, so the levels, and the cutscenes that introduced them, were fully built and animated.
Knowing what to take out is just as important to writing a good story as knowing what to put in, and having played Heavy Rain, I have to say that I think the game is better for having lost all this content. Adding psychic powers to an otherwise realistic game would have been a mistake, and while the rest of the content was kind of interesting, it didn't really add very much to the story.