TITLE:
Central Upwind Scheme for Solving Multivariate Cell Population Balance Models
AUTHORS:
Shahzadi Mubeen ur Rehman, Nadia Kiran, Shamsul Qamar
KEYWORDS:
Cell Population Balance, Cell Growth, Substrate Consumption, Central Upwind Scheme, Equal and Unequal Partitioning of Cells
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.8,
May
5,
2014
ABSTRACT: Microbial cultures
are comprised of heterogeneous cells that differ according to their size and
intracellular concentrations of DNA, proteins and other constituents. Because
of the included level of details, multi-variable cell population balance models
(PBMs) offer the most general way to describe the complicated phenomena
associated with cell growth, substrate consumption and product formation. For
that reason, solving and understanding of such models are essential to predict
and control cell growth in the processes of biotechnological interest. Such
models typically consist of a partial integro-differential equation for
describing cell growth and an ordinary integro-differential equation for
representing substrate consumption. However, the involved mathematical
complexities make their numerical solutions challenging for the given numerical
scheme. In this article, the central upwind scheme is applied to solve the
single-variate and bivariate cell population balance models considering equal
and unequal partitioning of cellular materials. The validity of the developed
algorithms is verified through several case studies. It was found that the suggested
scheme is more reliable and effective.