Abstract
In this paper, the generic problem of the development of a population balance model for those biological systems involving cellular processes is discussed. Such models are of interest for bioreactor optimisation and control, as well as for different biomedical problems including the study of cancer. The generic model and its features are presented, serving partly to consolidate the studies that have been reported in the literature already. The major challenges and issues with this problem are highlighted. One of the challenges is with respect to the solution technique for these complex models, which issue is addressed here. The algorithm proposed for solving these complex models is based on a hierarchical two-tier solution strategy that has been proposed previously (Immanuel and Doyle, III, Chem. Eng. Sci., 2003). The two-tier strategy involves the calculation of the rates of sub-processes that contribute to the population dynamics in the first tier, with the population itself being updated in the second tier. This in turn enables performing a major portion of the calculations off-line (once at the start of the simulation), thereby achieving a major reduction in the computational load. The algorithm is implemented on a six-dimensional population balance bioreactor model.
Published Version
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