2018/05/06 by Mariya Ptashnyk, Chandrasekhar Venkataraman, Ptashnyk, Mariya +1 · 1 citation
Computer Science · Engineering · #35B27 #35Kxx #65M60 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1805.02150
openalex publication_date 2018/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.