Multiscale Modeling &Simulation, Volume 18, Issue 2, Page 851-886, January 2020.
We present and analyze a model for cell signaling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces and both inter- and intracellular signaling. 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.

中文翻译：

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表面扩散信号过程的多尺度分析与仿真

《多尺度建模与仿真》，第18卷，第2期，第851-886页，2020年1月。
我们介绍并分析了生物组织中细胞信号传导过程的模型。该模型包括细胞表面的扩散和非线性反应以及细胞间和细胞内信号传导。使用两级收敛理论和展开方法中的技术，我们证明了该模型解的收敛性是两级宏观问题的解。我们还提出了一种用于宏观模型逼近的两尺度体面有限元方法。我们报告了一些基准测试结果以及在生物学上相关的方案中的数值模拟，这些方案说明了细胞规模异质性对宏观浓度的影响。