Department of Mathematics, Air University, Islamababd, Pakistan. Department of Mathematics, Balauchistan University of Information Technology, Engineering and Management Sciences, Quetta, Pakistan.
Tissue engineering is a preeminent field which aims to regenerate or repair the functions of devastated or damaged organs or tissues due to some accident, disease or age related degeneration. This field provides immense help in saving lives of thousands of patients. Tissues or organs are engineered within the patient’s body or in a laboratory, which is later implanted in the patient’s body. The important challenges for tissue engineers are: appropriate nutrients supply and optimum cell density with uniform distribution of cells in a final construct. Mathematical modeling is the best tool in order to understand the mechanism of cell proliferation and nutrient supply in a bioreactor. Mathematical models not only help to analyze potentially useful results but also enlighten the way of further research. In this work, a simple mathematical model of diffusive nutrient transport and non-linear cell proliferation in a bioreactor is developed. A cell seeded porous scaffold is kept in a bioreactor with a fixed nutrient supply. We model the consumption and transport of nutrients by reaction-diffusion equation and cell proliferation by Fisher Kolmogorove equation. Nutrient delivery to the cell seeded scaffold is purely due to diffusion. The model is solved numerically by commercial finite element solver COMSOL. The results show that all types of constructs, if nutrient supply depends on diffusion, will produce cell proliferated regions near nutrient supply. The results are presented for uniform and non-uniform initial cell seeding strategies. It is also observed that cell proliferation is insensitive to the initial seeding strategy.
Shakeel, M. and Raza, S. (2014) Nonlinear Computational Model of Biological Cell Proliferation and Nutrient Delivery in a Bioreactor. Applied Mathematics, 5, 2284-2298. doi: 10.4236/am.2014.515222.
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