细胞迁移中定义平均首过时间的若干边界值问题综述

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-08-08 DOI:10.3390/axioms13080537
Hélia Serrano, Ramón F. Álvarez-Estrada
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引用次数: 0

摘要

平均首次通过时间是指在环境中迁移的细胞从某一位置出发,首次到达特定位置或目标的平均时间。在这篇专题文章中,我们通过所谓的邻接扩散方程,概述了在二维或三维领域内移动的细胞在各种边界条件(狄里希特、诺伊曼、罗宾或混合)下的平均首次通过时间的特征。我们的重点是将后者简化为边界上某些密度函数的非均质线性积分方程。积分方程可以精确地得出非常简单的边界集合的平均首次通过时间。对于各种边界曲面(包括可精确求解边界的微小变形),积分方程提供了近似解。此外,该方法还可以近似处理混合边界条件,而混合边界条件确实是一个长期悬而未决的问题。本文还提供了新的图表、数字和讨论,旨在阐明分析。
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Review on Some Boundary Value Problems Defining the Mean First-Passage Time in Cell Migration
The mean first-passage time represents the average time for a migrating cell within its environment, starting from a certain position, to reach a specific location or target for the first time. In this feature article, we provide an overview of the characterization of the mean first-passage time of cells moving inside two- or three-dimensional domains, subject to various boundary conditions (Dirichlet, Neumann, Robin, or mixed), through the so-called adjoint diffusion equation. We concentrate on reducing the latter to inhomogeneous linear integral equations for certain density functions on the boundaries. The integral equations yield the mean first-passage time exactly for a very reduced set of boundaries. For various boundary surfaces, which include small deformations of the exactly solvable boundaries, the integral equations provide approximate solutions. Moreover, the method also allows to deal approximately with mixed boundary conditions, which constitute a genuine long-standing and open problem. New plots, figures, and discussions are presented, aimed at clarifying the analysis.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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