Simplified 2D-Axisymmetric Model for Reaction-Diffusion Mechanism of PAHs in a Mammalian Cell

M. Qaiser, Q. A. Chaudhry, S. Zainab, A. Shuaib

Abstract


This paper illustrates a mathematical model for reaction and diffusion of harmful lipophilic chemical compounds in a V79 mammalian cell. Since modeling of a mammalian cell is itself a hard slog due to its complex geometry, heterogeneity and variation of cellular architecture and it becomes even more difficult with the presence of plasma/nuclear membranes. A detailed mathematical model was developed earlier that gave rise to a system of PDEs which was handled numerically. Homogenization technique was applied for the numerical treatment of cytoplasm. For the reduction of complexity and computational labor of the detailed model, a simplified model with the inclusion of nuclear envelope is developed in this paper. This was done by replacing plasma/nuclear membranes by defining membrane flux, using Fick’s law of diffusion. Results of newly developed simplified model are compared with the results of detailed model, where they show a nice agreement.

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