I've been following this story since Friday: Ambassador Richard Holbrooke has died following a Type-A aortic dissection. This is the more lethal version to have, but either one can cause blood supply issues downstream in the kidneys, legs, or what have you.
He underwent more than 20 hours of surgery, most likely a partial aortic replacement in which a length of Dacron tubing is sewn in place of the damaged section. In this case, it looks like the replacement involved the arch and its connection to the heart and associated valve. The scariest complication in this case (before or after surgery) has blood being pumped into the pericardium, the sac in which the heart rests. If there's enough going in, it'll stop the heart.
I'd forgotten that John Ritter died of one of these things.