Enhancement of cell growth in tissue-engineering constructs under direct perfusion: Modeling and simulation

Perfusion bioreactors improve mass transfer in cell-scaffold constructs. We developed a mathematical model to simulate nutrient flow through cellular constructs. Interactions among cell proliferation, nutrient consumption, and culture medium circulation were investigated. The model incorporated modified Contois cell-growth kinetics that includes effects of nutrient saturation and limited cell growth. Nutrient uptake was depicted through the Michaelis-Menton kinetics. To describe the culture medium convection, the fluid flow outside the cell-scaffold construct was described by the Navier-Stokes equations, while the fluid dynamics within the construct was modeled by Brinkman's equation for porous media flow. Effects of the media perfusion were examined by including time-dependant porosity and permeability changes due to cell growth. The overall cell volume was considered to consist of cells and extracellular matrices (ECM) as a whole without treating ECM separately. Numerical simulations show when cells were cultured subjected to direct perfusion, they penetrated to a greater extent into the scaffold and resulted in a more uniform spatial distribution. The cell amount was increased by perfusion and ultimately approached an asymptotic value as the perfusion rates increased in terms of the dimensionless Peclet number that accounts for the ratio of nutrient perfusion to diffusion. In addition to enhancing the nutrient delivery, perfusion simultaneously imposes flow-mediated shear stress to the engineered cells. Shear stresses were found to increase with cell growth as the scaffold void space was occupied by the cell and ECM volumes. The macro average stresses increased from 0.2 mPa to 1 mPa at a perfusion rate of 20 microm/s with the overall cell volume fraction growing from 0.4 to 0.7, which made the overall permeability value decrease from 1.35 x 10(-2)cm(2) to 5.51 x 10(-4)cm(2). Relating the simulation results with perfusion experiments in literature, the average shear stresses were below the critical value that would induce the chondrocyte necrosis.