On modelling of glucose transport in hollow fibre membrane bioreactor for growing three-dimensional tissue

Hollow fibre membrane bioreactors (HFMBs) have been shown to overcome the diffusion limitation of nutrients (e.g., glucose) from the hollow fibres (lumens) to the porous regions of a scaffold (extra capillary space). However, direct monitoring of glucose diffusion inside the HFMBs is almost impossible due to their small size; thus, various computational modelling frameworks have been developed in the past. These models have defined that the glucose diffusivity in the cell culture medium used in the HFMBs as similar to the diffusivity in water. Similarly, other assumptions have been made which do not represent the nutrient transport processes in the HFMB accurately. In addressing these issues, a mathematical model is presented in this paper, where we employ experimentally deduced effective glucose diffusivities of tissue engineering membranes and scaffolds with and without cells along with glucose diffusivity in cell culture medium. The governing equations are non-dimensionalised, simplified and solved numerically. The results demonstrate the roles of various dimensionless numbers (e.g., Péclet and Damköhler numbers) and non-dimensional groups of variables on determining the glucose concentration especially in the scaffold region. The result of this study is expected to help optimize designs of HFMB as well as carry out more accurate scaling analyses.