The culture chamber of the present invention has a fluid-filled culture compartment in which cells, tissues and other biologicals are cultured. The culture compartment is transversed by one or more molecular weight cut-off membranes attached to a membrane carrier assembly. Incoming nutrients are transported through the membrane into the culture compartment and metabolic waste products are transported away from the fluid-filled culture compartment through the membrane and out the chamber outlet. Both reusable and disposable culture chambers are described for culturing cells, cell aggregates, particles, tissues and organoids.