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Hybrid Methods in Engineering

ISSN Imprimir: 1099-2391
ISSN On-line: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v1.i4.70
24 pages

EXPLICIT PERTURBATION SOLUTION OF A MASS STRUCTURED CELL POPULATION BALANCE MODEL

F. C. Peixoto
Institute de Pesquisa e Desenvolvimento (IPD), Grupo de Quimica, Rio de Janeiro, Brazil, and Escola de Quimica, Centro de Tecnologia, UFRJ, Cidade Universitdria, Rio de Janeiro, Brazil

RESUMO

Cell cultures can be thought as a continuum of organisms, each of which goes through a cycle that includes birth, aging, reproduction, and death. The properties of each organism change during this cycle and one (or more) of these properties can be used to continuously characterize the individuals present in the culture, using a frequency distribution function. Rigorous models for this kind of mixture are called population balance equations. Due to their integro-partial differential form, these equations are considered difficult to solve analytically, and approximations or numerical approaches are usually employed. In the present work, an explicit solution to this kind of equation is found, with minimum loss of generality, using a perturbational procedure. Once the recurrence is obtained, the terms are expanded in an orthonormal basis to calculate the time evolution of the distributions.