Participation in this study will last between 36 and 67 days. Participation will involve nine points of contact with researchers, at least two of which will be in-person visits at the research clinic. The others will be conducted by phone. All points of contact will include assessments on possible bleeding and any new symptoms. The first two of these points of contact, will take place at the signing of the informed consent, which will involve a screening of medical records and random assignment of participants to receive either the LMWH dalteparin or placebo. Participants will self-administer a subcutaneous injection of their assigned treatment twice a day for 3 days before the surgery or procedure and for 6 days after. During the course of the study, when participants visit their primary physicians for regularly scheduled appointments, it will be recommended that they undergo two international normalized ratio (INR) tests of blood clotting ability between day 2 and 10 after the surgery or procedure. The remaining seven points of contact will occur sometime between the day before surgery and 37 days after surgery. One of the in-person visits will occur within the first week after surgery and will include assessments on possible bleeding, any new symptoms, and INR results.