Tissue engineering methods and biochamber apparatus are provided for making tissue grafts for implantation into a patient. The methods include applying a sustained low magnitude pressure gradient transmurally across a permeable scaffold material using a media containing cells, preferably microvascular epithelial cells, to be deposited on the scaffold for the production of tissue grafts, preferably vascular grafts, to promote accelerated adhesion and maturation of cells on the scaffold material. Biochambers for preparing tubular tissue grafts are provided which contain connectors for holding a graft substrate, proximal and distal tubing for connection to an optional perfusion system, and structure for switching between transmural flow of a cell suspension across the graft substrate and translumenal flow through the lumen of the graft.