This is the way I read this. The synth part of his brain died when he was stabbed. Nothing was necessarily removed (though, I suppose they could have done that to try and heal him, but I don't think it's important to the plot line, just that it "died" somehow). Then, his human brain was able to heal and "fill in" what went missing when his synth brain died.
The part I have trouble with is physically, after being in a coma for a year, you are not going to be able to walk around as if everything is fine. Your muscles would have completely atrophied. (Toby did kind of hint at this, as if the writers acknowledged the absurdity of it with an inside joke...) But, TV is always known for medical miracles... (I love when people suffer a gut shot, one of the most devastating ways to get shot when you survive and they are out of the hospital and just fine in a week.)