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On the numerical approximation of drug diffusion in complex cell geometry
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA. (Numerical Analysis)
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.ORCID iD: 0000-0003-4950-6646
Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden.
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.
Keyword [en]
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: urn:nbn:se:kth:diva-32389DOI: 10.1145/1838002.1838021Scopus ID: 2-s2.0-77956295910ISBN: 9781605586427 (print)OAI: oai:DiVA.org:kth-32389DiVA: diva2:410360
Note
QC 20110413Available from: 2011-04-13 Created: 2011-04-13 Last updated: 2012-04-19Bibliographically approved
In thesis
1. Numerical Approximation of Reaction and Diffusion Systems in Complex Cell Geometry
Open this publication in new window or tab >>Numerical Approximation of Reaction and Diffusion Systems in Complex Cell Geometry
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. xi, 38 p.
Series
Trita-CSC-A, ISSN 1653-5723 ; 2010:04
Keyword
Complex Cell Geometry, Reaction and Diffusion System, Metabolism in Biological Cells, Homogenization, Compartment Modelling
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-12099 (URN)978-91-7415-586-0 (ISBN)
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 Enzymology
Available from: 2010-03-05 Created: 2010-03-03 Last updated: 2011-04-13
2. Computational Modeling of Reaction and Diffusion Processes in Mammalian Cell
Open this publication in new window or tab >>Computational Modeling of Reaction and Diffusion Processes in Mammalian Cell
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

PAHs are the reactive toxic chemical compounds which are present as environmental pollutants. These reactive compounds not only diffuse through the membranes of the cell but also partition into the membranes. They react with the DNA of the cell giving rise to toxicity and may cause cancer. To understand the cellular behavior of these foreign compounds, a mathematical model including the reaction-diffusion system and partitioning phenomenon has been developed. In order to reduce the complex structure of the cytoplasm due to the presence of many thin membranes, and to make the model less computationally expensive and numerically treatable, homogenization techniques have been used. The resulting complex system of PDEs generated from the model is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. Then the model was reduced to a system of ODEs, a compartment model (CM). The quantitative analysis of the results of the CM shows that it cannot fully capture the features of metabolic system considered in general. Thus the PDE model affords a more realistic representation. In order to see the influence of cell geometry in drug diffusion, the non-spherical axi-symmetric cell geometry is considered, where we showed that the cellular geometry plays an important role in diffusion through the membranes. For further reduction of complexity of the model, another simplified model was developed. In the simplified model, we used PDEs for the extracellular domain, cytoplasm and nucleus, whereas the plasma and nuclear membranes were taken away, and replaced by the membrane flux, using Fick's Law. We further extended the framework of our previously developed model by benchmarking against the results from four different cell lines. Global optimization techniques are used for the parameters describing the diffusion and reaction to fit the measured data. Numerical results were in good agreement with the in vitro results. For the further development of the model, the process of surface bound reactions were added, thus developing a new cell model. The effective equations were derived using iterative homogenization for this model. The numerical results of some of the species were qualitatively verified against the in vitro results found in literature.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. xiii, 52 p.
Series
Trita-CSC-A, ISSN 1653-5723 ; 2012:03
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-93466 (URN)978-91-7501-315-2 (ISBN)
Public defence
2012-05-15, E2, Lindstedsvägen 3, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20120419Available from: 2012-04-19 Created: 2012-04-17 Last updated: 2012-04-19Bibliographically approved

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