This brings back bad memories. My wife was in the hospital for the same exact thing 3 days after we got home from being married in April 2008. She was on Heparin as well and had to give herself shots in the belly.
I'm guessing Zakk will be on blood thinners for 6 months and then evaluated. He'll have to keep an eye on things every time he flies. It's serious business and it sucks. You have to watch what you eat and limit intake of alcohol.
Hopefully he won't be stuck taking meds the rest of his life.