A 60-year-old man with a history of Type 2 DM, HD and CKD Stage 3 is admitted to the medical ICU secondary to septic shock. He remains hypotensive with SBP below 90 despite IV fluid resuscitation. He is then started on norepinephrine (Levophed) via a central line placement in the left internal jugular vein (LIJ). Soon after the placement of the central line, the patient’s left upper extremity is swollen and tender with 2+ pitting edema. An ultrasound of the left upper extremity shows that patient has a deep vein thrombosis (DVT). He has no history of previous DVT’s.
What is the next best step in the management of this patient?