This clinical study will document the value of intravenous heparin administration in patients presenting with venous thrombosis complicating an indwelling central catheter. The further benefit achieved from thrombolytic therapy in patients not achieving clot lysis on heparin will be defined by repeat venography and over an escalating dose range of the thrombolytic agent. The preferred prophylactic approach to maintaining vascular patency will be assessed over 3 months of follow up by comparison of low dose coumadin with self administered heparin in those patients who achieve initial successful lysis.