Multiscale analysis and simulation of a signalling process with surface diffusion

Mariya Ptashnyk; Chandrasekhar Venkataraman

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arXiv · 1805.02150

Multiscale analysis and simulation of a signalling process with surface diffusion

Mariya Ptashnyk·Chandrasekhar Venkataraman

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Abstract

We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of two-scale convergence as well the unfolding method, we show convergence of the solutions to the model to solutions of a two-scale macroscopic problem. We also present a two-scale bulk-surface finite element method for the approximation of the macroscopic model. We report on some benchmarking results as well as numerical simulations in a biologically relevant regime that illustrate the influence of cell-scale heterogeneities on macroscopic concentrations.

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Mariya Ptashnyk, Chandrasekhar Venkataraman. 2018-05-06. Multiscale analysis and simulation of a signalling process with surface diffusion. https://arxiv.org/abs/1805.02150

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