The primary purpose of this study is to demonstrate that a continuous infusion of intravenous (IV) heparin (UFH) for Venous thromboembolism (VTE) prophylaxis will restore prophylactic levels of heparin in high-risk critically ill medical patients as compared with guideline recommended subcutaneous heparin. Antifactor Xa assay, a laboratory test to measure the anticoagulant activity of heparin, or the ability of heparin to thin the blood, will be used to demonstrate that Intravenous administration is more effective.