A cannula (92) for moving fluids between a pump (50) and the circulatory system of a patient (14). The cannula (92) includes a liner (94) having an intermediate portion (96) between a proximal portion (98) and a distal portion (100), and a lumen (102) extending between the proximal and distal portions (98, 100). At least the intermediate portion (96) of the liner (94) is constructed from a tissue in-growth material for supporting the growth of endothelial cells. A jacket (1 10) surrounds at least part of the liner (94).