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A model for fluid and mass transport in a single module of a tissue engineering hollow fibre bioreactor (HFB) is developed. Cells are seeded in alginate throughout the extra-capillary space (ECS), and fluid is pumped through a central lumen to feed the cells and remove waste products. Fluid transport is described using Navier-Stokes or Darcy equations as appropriate; this is overlaid with models of mass transport in the form of advection-diffusion-reaction equations that describe the distribution and uptake/production of nutrients/waste products. The small aspect ratio of a module is exploited and the option of opening an ECS port is explored. By proceeding analytically, operating equations are determined that enable a tissue engineer to prescribe the geometry and operation of the HFB by ensuring the nutrient and waste product concentrations are consistent with a functional cell population. Finally, results for chondrocyte and cardiomyocyte cell populations are presented, typifying two extremes of oxygen uptake rates.

Original publication




Journal article


Math Med Biol

Publication Date





329 - 359


Alginates, Bioreactors, Cells, Cultured, Equipment Design, Glucose, Glucuronic Acid, Hexuronic Acids, Humans, Hydrodynamics, Kinetics, Lactic Acid, Mathematical Concepts, Models, Biological, Oxygen Consumption, Rheology, Tissue Engineering