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

Analytical And Numerical Approximation of Effective Diffusivities in The Cytoplasm of Biological Cells