A multiscale view of nonlinear diffusion in biology: From cells to tissues
A multiscale view of nonlinear diffusion in biology: From cells to tissues
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DOI：
10.1142/s0218202519400062
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发表时间：
2019-04-01
影响因子：
3.5
通讯作者：
Chouhad, N.
中科院分区：
文献类型：
--
作者：
Burini, D.;Chouhad, N.
本文介绍了一个审查的数学工具，推导出宏观模型在生物学中的基础描述细胞的规模，因为它是由一个动力学理论模型。调查之后是研究视角的概述。推导的灵感来自希尔伯特的方法，在经典的动力学理论，这是在这里适用于广泛的一类动力学方程建模多细胞动力学。这类方程相对于经典动力学理论的主要区别在于细胞相互作用的建模，这是由随机博弈论的理论工具，而不是经典力学的定律。综述的重点是非线性扩散和源项的研究。
This paper presents a review on the mathematical tools for the derivation of macroscopic models in biology from the underlying description at the scale of cells as it is delivered by a kinetic theory model. The survey is followed by an overview of research perspectives. The derivation is inspired by the Hilbert's method, known in classic kinetic theory, which is here applied to a broad class of kinetic equations modeling multicellular dynamics. The main difference between this class of equations with respect to the classical kinetic theory consists in the modeling of cell interactions which is developed by theoretical tools of stochastic game theory rather than by laws of classical mechanics. The survey is focused on the study of nonlinear diffusion and source terms.