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Numerical Approximation of Reaction and Diffusion Systems in Complex Cell Geometry
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA. (Numerical Analysis)
2010 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The mathematical modelling of the reaction and diffusion mechanism of lipophilic toxic compounds in the mammalian cell is a challenging task because of its considerable complexity and variation in the architecture of the cell. The heterogeneity of the cell regarding the enzyme distribution participating in the bio-transformation, makes the modelling even more difficult. In order to reduce the complexity of the model, and to make it less computationally expensive and numerically treatable, Homogenization techniques have been used. The resulting complex system of Partial Differential Equations (PDEs), generated from the model in 2-dimensional axi-symmetric setting is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. The model can be extended to more complex reaction systems and also to 3-dimensional space. For the reduction of complexity and computational cost, we have implemented a model of mixed PDEs and Ordinary Differential Equations (ODEs). We call this model as Non-Standard Compartment Model. Then the model is further reduced to a system of ODEs only, which is a Standard Compartment Model. The numerical results of the PDE Model have been qualitatively verified by using the Compartment Modeling approach. The quantitative analysis of the results of the Compartment Model shows that it cannot fully capture the features of metabolic system considered in general. Hence we need a more sophisticated model using PDEs for our homogenized cell model.

Place, publisher, year, edition, pages
Stockholm: KTH , 2010. , p. xi, 38
Series
Trita-CSC-A, ISSN 1653-5723 ; 2010:04
Keywords [en]
Complex Cell Geometry, Reaction and Diffusion System, Metabolism in Biological Cells, Homogenization, Compartment Modelling
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-12099ISBN: 978-91-7415-586-0 (print)OAI: oai:DiVA.org:kth-12099DiVA, id: diva2:301451
Presentation
2010-03-30, E2, KTH Main building, Lindstedtsv. 3, 100 44 Stockholm, 13:00 (English)
Opponent
Supervisors
Projects
Computational Modelling of the Mammalian Cell and Membrane Protein EnzymologyAvailable from: 2010-03-05 Created: 2010-03-03 Last updated: 2011-04-13
List of papers
1. Simulation of transport of lipophilic compounds in complex cell geometry
Open this publication in new window or tab >>Simulation of transport of lipophilic compounds in complex cell geometry
2009 (English)In: Proceedings of the COMSOL Conference, Milan, 2009, 2009Conference paper, Published paper (Refereed)
Keywords
complex cellular architecture, reaction and diffusion system, homogenization, metabolism in biological cells
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-32381 (URN)
Note
QC 20110413Available from: 2011-04-13 Created: 2011-04-13 Last updated: 2011-04-13Bibliographically approved
2. On the numerical approximation of drug diffusion in complex cell geometry
Open this publication in new window or tab >>On the numerical approximation of drug diffusion in complex cell geometry
2009 (English)In: Proceedings of the 6th International Conference on Frontiers of Information Technology, FIT '09, Abbottabad, 2009Conference paper, Published paper (Other academic)
Abstract [en]

The mathematical modeling of a mammalian cell is a very tedious work due to its very complex geometry. Especially, taking into account the spatial distribution and the inclusion of lipophilic toxic compounds greatly increases its complexity. The nonhomogeneity and the different cellular architecture of the cell certainly affect the diffusion of these compounds. The complexity of the whole system can be reduced by a homogenization technique. To see the effect of these compounds on different cell architectures, we have implemented a mathematical model. The work has been done in 2-dimensional space. The simulation results have been qualitatively verified using compartmental modeling approach. This work can be extended with a more complex reaction-diffusion system and to 3-dimensional space as well. Copyright 2009 ACM.

Place, publisher, year, edition, pages
Abbottabad: , 2009
Keywords
Approximation of complex geometry, Homogenization, Metabolism in biological cells, Reaction-Diffusion system, 3-dimensional, Cell architectures, Cell geometries, Cellular architecture, Compartmental modeling, Complex geometries, Complex reactions, Dimensional spaces, Drug diffusion, Homogenization techniques, Mammalian cells, Mathematical modeling, Nonhomogeneity, Numerical approximations, Reaction diffusion systems, Simulation result, Spatial distribution, Toxic compounds, Whole systems, Diffusion in liquids, Dynamic models, Homogenization method, Information technology, Mammals, Metabolism, Computational geometry
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-32389 (URN)10.1145/1838002.1838021 (DOI)2-s2.0-77956295910 (Scopus ID)9781605586427 (ISBN)
Note
QC 20110413Available from: 2011-04-13 Created: 2011-04-13 Last updated: 2012-04-19Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • modern-language-association-8th-edition
  • vancouver
  • Other style
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  • de-DE
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  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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