The role of a bioreactor during the in vitro tissue culture process is important as the cell growth can be significantly enhanced by providing adequate nutrient supply and favorable mechanical stimuli, i.e. shear stress to the cells. Within a certain range, flow-induced shear stress has a positive impact on the cell growth. In the past, bioreactors and scaffold structures were designed based on empirical evidence, e.g. the flow rate inside the bioreactor was selected based on a trial and error method. More recently, mathematical and computational modeling of such complex process has been able to provide insight into the culture process and predict the overall cell and tissue growth. Although a number of computational studies which provide such cell and tissue growth information can be found in the literature, a comprehensive simulation to predict the overall tissue growth based on the supply of multiple nutrients and shear stress level acting on the cells is not yet available. In this study a simultaneous fluid flow and mass transfer analysis has been performed using the lattice Boltzmann method. A cell growth equation which considers the transport of multiple nutrients as well as the shear stress induced on the cells to predict the cell growth rate has been implemented. The overall model integrates the momentum, convection-diffusion and cell growth equations in a coupled fashion to predict the cell growth on a single strand of a scaffold placed inside a perfusion bioreactor. It is found that the maximum shear stress on the strand surface occurs near the strand shoulder. The nutrient supply and cell growth rate at the front of the cylinder is about ten times higher than at the rear of the cylinder. The cell growth rate obtained in the present study compares well with the results of other models documented in the literature.

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