A novel free boundary algorithm for the solution of cell population balance models

Kavousanakis, ME; Mantzaris, NV; Boudouvis, AG

dc.contributor.author	Kavousanakis, ME	en
dc.contributor.author	Mantzaris, NV	en
dc.contributor.author	Boudouvis, AG	en
dc.date.accessioned	2014-03-01T01:29:34Z
dc.date.available	2014-03-01T01:29:34Z
dc.date.issued	2009	en
dc.identifier.issn	0009-2509	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19320
dc.subject	Cell heterogeneity	en
dc.subject	lac operon	en
dc.subject	Mathematical modelling	en
dc.subject	Nonlinear dynamics	en
dc.subject	Numerical analysis	en
dc.subject.classification	Engineering, Chemical	en
dc.subject.other	Analytical solutions	en
dc.subject.other	Apriori	en
dc.subject.other	Arc length	en
dc.subject.other	Asymptotic behaviors	en
dc.subject.other	Bi-stability	en
dc.subject.other	Cell populations	en
dc.subject.other	Computational time	en
dc.subject.other	Continuation algorithm	en
dc.subject.other	Daughter cells	en
dc.subject.other	Experimental evidence	en
dc.subject.other	Finite Element	en
dc.subject.other	Finite element algorithms	en
dc.subject.other	First-order	en
dc.subject.other	Free boundary	en
dc.subject.other	Gene regulatory networks	en
dc.subject.other	Heterogeneous systems	en
dc.subject.other	Integral-differential equations	en
dc.subject.other	lac operon	en
dc.subject.other	Mathematical modelling	en
dc.subject.other	Model system	en
dc.subject.other	Multi-physics	en
dc.subject.other	Nonlinear dynamics	en
dc.subject.other	Oscillatory behaviors	en
dc.subject.other	Recent progress	en
dc.subject.other	Single-cell level	en
dc.subject.other	State space	en
dc.subject.other	Two-dimensional	en
dc.subject.other	Algorithms	en
dc.subject.other	Asymptotic analysis	en
dc.subject.other	Cell culture	en
dc.subject.other	Cell membranes	en
dc.subject.other	Cell proliferation	en
dc.subject.other	Computer simulation	en
dc.subject.other	Differential equations	en
dc.subject.other	Nucleic acids	en
dc.subject.other	RNA	en
dc.subject.other	Stainless steel	en
dc.subject.other	Mathematical models	en
dc.title	A novel free boundary algorithm for the solution of cell population balance models	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ces.2009.06.054	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ces.2009.06.054	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	There exists an abundance of experimental evidence in a variety of systems. showing that cell populations are heterogeneous systems in the sense that properties such as size, shape, DNA and RNA content are unevenly distributed amongst the cells of the population. The quantitative understanding of heterogeneity is of great significance, since neglecting its effect can lead to false predictions. Cell population balance models are used to address the implications of heterogeneity and can accurately capture the dynamics of heterogeneous cell populations. They are first-order partial-integral differential equations and due to the complexity of formulation, analytical solutions are hard to obtain in the majority of cases. Despite the recent progress, the efficient solution of cell population balance models remains a challenging task. One of the main challenges stems from the fact that the boundaries of the intracellular state space are typically not known a priori and using fixed-boundary algorithms leads to inaccuracies and increased computational time demands. Motivated by this challenge, we formulated a free boundary finite element algorithm, capable of solving cell population balance equations more efficiently than the traditional fixed-boundary algorithms. The implementation of the algorithm is accommodated, in the finite element based software package COMSOL Multiphysics. We demonstrate the efficiency of this algorithm using the lac operon gene regulatory network as our model system and perform transient and asymptotic behavior analysis. In the latter case, the pseudo-arc-length continuation algorithm is incorporated, in order to investigate the existence of a bistability region, also observed at the single-cell level. Our analysis, revealed the existence of a region of bistability when cell heterogeneity is taken into account; however, its extend shrinks comparing to homogeneous cell populations. The free boundary algorithm can be easily extended for problems of higher dimensionality and we present results for a two-dimensional cell population balance model, which can exhibit an oscillatory behavior. It is shown that oscillations do not persist when the intracellular content is unevenly distributed amongst the daughter cells. (C) 2009 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Chemical Engineering Science	en
dc.identifier.doi	10.1016/j.ces.2009.06.054	en
dc.identifier.isi	ISI:000271299000005	en
dc.identifier.volume	64	en
dc.identifier.issue	20	en
dc.identifier.spage	4247	en
dc.identifier.epage	4261	en