"An emerging feature of mechanical stimulation tissue engineering are flexible bioreactors that can move together with the actuation system. These have the potential of applying more physiologically relevant movement regimes than conventional systems. The development of such a bioreactor requires the optimal design and operational parameters. A mathematical model was developed to provide better insights into the system, by highlighting heterogeneous nutrient distribution due to the geometry, oxygen permeability, cell distribution, flow velocity or inlet location. Furthermore the aim was to find an optimum flow rate considering residence time, replenishment of nutrients and their effects on cell growth.
The chamber consists of 3D printed parts, a 3cm long filamentous scaffold and a lose membrane fit around it to make the system air-tight. There is one inlet and one outlet located on each opposite end of the chamber, through which media is continuously fed via a peristaltic pump.
We consider fluid flow and mass transport in the bioreactor chamber. The geometry consists of an outer cylinder, representing the scaffold, and a free flow area around it as the space between scaffold and membrane. We operate in a cylindrical coordinate system (r, theta, z) and assume axisymmetry, so that quantities do not vary with theta, and there is no flow in the azimuthal at z=0. The fluid enters the chamber from the inlet at a volumetric flow rate, carrying Glucose and Oxygen, and leaves at the outlet. We model the fluid as incompressible Newtonian of constant viscosity and density. Nutrients are fed via the fluid through the inlet and leave the system at the outlet. Nutrients diffuse through the scaffold and free flow area at different rates, given by individual diffusivity constants. Nutrient consumption and metabolite production is modelled by Michaelis Menten kinetics. Cells are located on the scaffold only, where they can consume nutrients, produce lactate multiply and spread. We assume cells are initially homogeneously distributed through the scaffold. Cell growth is modelled with a Monod-type kinetic equation. The availability of Oxygen and Glucose is needed for cell growth, whereas Lactate concentration slows down growth.
The multiphysics software COMSOLwas used to solve this model by coupling the porous and free flow module to the transport of diluted species in porous media modules.
Different flow rates, and initial cell numbers were modelled in a parametric sweep, to answer the question of what parameters will lead to sustained cell growth. To avoid depriving cells of oxygen too quickly, the introduction of a membrane permeable to gasses is tested.
The resulting simulations showed oxygen depletion and growth inhibiting lactate concentrations at low flow rates, and an optimum cell growth curve at intermediate flow rates. Oxygen delivery was greatly improved upon the introduction of the permeable membrane. There is ongoing experimental work to validate the results of this model."