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.
Highlights
In mammalian cell culture, individual cells exhibit heterogeneity due to differences in their cellular metabolism and cell-cycle dynamics [1]
Cell division is an exponential process, the two daughter cells further divide into four daughter cells, four into eight and so on [2]
At any point in time t, in heterogeneous population different cells exist at different stages of the cell cycle
Summary
Individual cells exhibit heterogeneity due to differences in their cellular metabolism and cell-cycle dynamics [1]. They have capability to effectively describe the internal chemical structure of the single cell by incorporating intracellular chemical reactions involving multiple chemical species These models provide the most accurate way of describing the complicated phenomena associated with cell growth, nutrient uptake and/or product formation in microbial populations. They typically consist of multidimensional integrto-partial differential equations for describing the dynamics of the state distribution function, nonlinearly coupled with integro-ordinary differential equations accounting for substrate consumption and (or) product formation. Several case studies are carried out and the results of central-upwind scheme are compared with those obtained from the first order upwind scheme
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