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The typical time frame where blood clots in your veins, DVT's, are at the highest risk are the first 3-5 days after surgery. This begins at the time you begin your surgery until you are more mobile afterwards. There are many measures that your doctors will take to avoid and minimize these risks.
It is appropriate to use Lovenox both before and after surgery. The risk of bleeding is slightly higher if administered before surgery but not excessively so. If Lovenox is administered 6-8 hours after surgery and compression boots are used after surgery then you can reduce the risk of bleeding without appreciably increasing the risk of a blood clot. Having said that, abdominoplasty does have a higher risk of a blood clot compared to other cosmetic procedures.