We consider a mathematical model of the physical and biological processes involved in the bioreactors for cultivating tissues. In a laminar flow duct bioreactor, the Navier-Stokes and convective-diffusion equations are solved to obtain the concentration distribution of chemoattractant secreted from the stromal cells. Then, it is concoitmently used to solve the proposed chemotactic model and stem cell growth kinetics. The simulation results elucidate the spatio-temporal distribution of cells is governed by the interaction of cell chemotactic migration and cell mitosis. A dimensionless number that balances these two effects predicts the extent of non-uniformity in duct chambers. That is, if the directed cell migration rate is much larger than the cell growth rate, the cells will have enough time to move toward the side walls and proliferate rapidly causing prominent non-uniform growth. On the contrary, if the directed cell migration rate is much smaller than the cell growth rate, the cell growth on the cell bed is in comparison more uniform.

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