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Analytical And Numerical Approximation of Effective Diffusivities in The Cytoplasm of Biological Cells
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.ORCID iD: 0000-0003-4950-6646
Chalmers University of Technology, Math. Dept.
2007 (English)Report (Other academic)
Abstract [en]

The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplsma has a very complex geometric structure which cannot be handled by standard discretization techniques. In the present paper we propose a homogenization technique for computing effective diffusion constants. This is accomplished by using a two-step strategy. The first step consists of an analytic homogenization from the smallest to an intermediate scale. The homogenization error is estimated by comparing the analytic diffusion constant with a numerical estimate obtained by using real cell geometries. The second step consists of a random homogenization. Since no analytical solution is known to this homogenization problem, a numerical approximation algorithm is proposed. Although rather expensive this algorithm provides a reasonable estimate of the homogenized diffusion constant.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology , 2007. , 21 p.
Trita-NA, ISSN 0348-2952 ; 2007:4
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-48496OAI: diva2:457760
QC 20111122Available from: 2011-11-22 Created: 2011-11-19 Last updated: 2011-11-22Bibliographically approved

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Hanke, Michael
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