Before everybody goes all crazy on this, Let me clear this for all of you,
The woman is Pshycologically Ill. We do not know if she was a born muslim or not, because the article says she became obsessed with islam after going to egypt.
Now, The procedure for "exorcism" in islam is nothing but only reading verses on your own , or someone who has strong believe to just read it out infront of the person whos suffering. That is all. NOthing more than that is actually in Islam.
However, many muslims, practise their own variations, which is nothing more than not following islam.
There is no such concept of sacrifisinng one for the love of God conncept.
Please watch this Video
http://www.youtube.com/watch?feature=player_embedded&v=qxke8niolp4
There asre some interesting videos from him Dr. Zakir Naik(many on youtube are dubbed over too, just to show tht he gives hate speech etc so be careful). One of the videos i recommend watching his is, Similarities between Christianity and Islam.
Hope that helps..