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

Abstract

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 (extracapillary space). However, direct monitoring of glucose diffusion inside the HFMBs is almost impossible because of 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 was similar to the diffusivity in water. Similarly, other assumptions have been made that 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‐dimensionalized, 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.

Effects of Scaffold Pore Morphologies on Glucose Transport Limitations in Hollow Fibre Membrane Bioreactor for Bone Tissue Engineering: Experiments and Numerical Modelling

“…This effect is important due to its potential in limiting the glucose concentration, which is essential for cell growth in the scaffold region. In agreement with [ 29 ], the current work also showed that the lowest concentration will occur at the largest value of R . This is due to an increase in diffusion distance from the inlet ( c = 1) toward the outlet of the bioreactor.…”

“…This can be attributed to the increase in the diffusion distance of glucose due to the increase in the bioreactor length. The results in this paper demonstrated similar trends when compared to [ 29 ] for a similar combination of porous materials and therefore are not shown in this paper. However, it suffices to note that the bioreactor length should be considered carefully, keeping in mind the glucose transfer limitation while developing a larger bioreactor scale, especially for a long-term culture process within the scaffold region.…”

“…The roles of a dimensionless group of variables such as Pe and Da in determining the nutrient transport behaviour in the HFMB has been discussed in length in our earlier paper [ 29 ]. As the glucose transport in the lumen region of HFMB is governed by the Péclet number, varying this dimensionless number corresponds to varying the length of the bioreactor, or vice versa, provided all other factors remain the same.…”

“…Non-dimensionalisation is very helpful in finding a group of parameters that are needed for the modelling process [ 29 ]. To reduce the number of parameters and simplify the model, the glucose transport equations are defined in terms of non-dimensionalised parameters with the parameters shown in Table 3 .…”

“… Dimensionless governing equations and boundary conditions in lumen, membrane, and extracapillary space (ECS) regions (adopted from [ 29 ]). …”