Introduction to Population Balance Modeling
Posted 01 Oct, 2008 in Teaching Materials
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| Contributor(s) | Eric Sherer e-Enterprise Center, Purdue University; VA CoE on Implementing Evidence-based Practice |
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| Abstract |
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| credits | Robert Hannemann, Purdue University Ann Rundell, Purdue University Doraiswami Ramkrishna, Purdue University |
| references | Gardner SN, “Modelling multi-drug chemotherapy: Tailoring treatment to individuals.” Journal of Theoretical Biology, 214: 181-207, 2002.
Hillman RS and Finch CA. Red cell manual, Philadelphia, F.A. David, 1996. Hjortsø MA, Population balances in biomedical engineering: Segregation through the distribution of cell states. New York, McGraw-Hill, 2006. Kromenaker SJ and Srienc F, “Cell-cycle-dependent protein accumulation by producer and nonproducer murine hybridoma cell lines: A population analysis.” Biotechnology and Bioengineering, 38(6): 665-677, 1991. Noirot-Gros MF, Dervyn E, Wu LJ, Mervelet P, Errington J, Ehrlich SD, and Noirot P, “An expanded view of bacterial DNA replication.” Proceedings of the National Academy of Sciences, 99(12): 8342-8347, 2002. Novak B and Tyson JJ, “A model for restriction point control of the mammalian cell cycle.” Journal of Theoretical Biology, 230: 563-579, 2004. Ramkrishna D. Population balances: Theory and applications to particulate systems in engineering. San Diego, Academic Press, 2000. Sherer E, Hannemann RE, Rundell A, and Ramkrishna D, “Analysis of resonance chemotherapy in leukemia treatment via multi-staged population balance models.” Journal of Theoretical Biology, 240(4): 648-661, 2006. Sherer E, Tocce E, Hannemann RE, Rundell, AE, and Ramkrishna D, “Identification of age-structured models: Cell cycle phase transitions.” Biotechnology & Bioengineering, 99(4): 960-974, 2007. Sherer E, Hannemann RE, Rundell A, and Ramkrishna D, “Estimation of likely cancer cure using first- and second-order product densities of population balance models.” Annals of Biomedical Engineering, 35: 903-915, 2007. Steel GG. Growth kinetics of tumors: Cell population kinetics in relation to the growth and treatment of cancer. Oxford, Clarendon Press, 1977. |
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This presentation gives an overview of the role and applications of population balance (or structured) models in describing biological phenomenon. These models represent the continuum between purely empirical models and mechanistic models where details are often lumped into the structured parameters and model description. The advantage of this approach is that a descriptive model, that captures key biological features, can be written without explicitly accounting for the exact biological details. Several examples are shown in the presentation such as describing the division rate of cells and accounting for cell cycle dependent processes. In addition, the derivation of the population balance equations is presented along with techniques for measuring the structured parameters. Applications for the optimization and quantitative description of the outcomes of chemotherapy treatment are also discussed.