Analysis of elastohydrodynamics and nutrient transport through deformable porous scaffold inside a hollow fiber membrane bioreactor

Hydrodynamics and nutrient transport in a hollow fiber membrane bioreactor is studied by developing a two-dimensional mathematical model in Cartesian coordinates. In a more realistic scenario, the scaffold is considered to be elastic and deformable, which undergoes deformation with the applied pore pressure. A mixture model is used to deal with the scaffold matrix, cells, and the fluid present in the scaffold region. The method of lubrication theory is incorporated when the aspect ratio of the lumen is small. The nutrient transport in the scaffold region is assumed to be governed by advection-diffusion-reaction mass balance due to the presence of cells and by advection-diffusion in the lumen and porous membrane. Analytical solution of the coupled system is presented for a short time scale where the cell growth, death, or differentiation is neglected. The results obtained focus on the effect of various parameters on the fluid flow, solid deformation, and consumption of nutrients due to different kinds of cells. It is observed that the deformation of the scaffold matrix increases monotonically with the flow rate supplied to the bioreactor. This behavior ensures that one can adjust the fluid flux to achieve optimum deformation in favor of cell growth and avoid damage of the scaffold. Moreover, a general criterion for the distribution of adequate nutrient concentration inside the bioreactor is developed to prevent the formation of the necrosis region inside the scaffold. Accordingly, the current investigation helps to arrive at suitable parameter combinations to monitor and control an ongoing experiment for optimum cell growth.