TITLE:
Nonlinear Computational Model of Biological Cell Proliferation and Nutrient Delivery in a Bioreactor
AUTHORS:
Muhammad Shakeel, Sahar Raza
KEYWORDS:
In Vitro Tissue Engineering, Nutrient Transport, Cell Proliferation
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.15,
August
11,
2014
ABSTRACT:
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.