On the numerical approximation of drug diffusion in complex cell geometry

Abstract

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.