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相关概念视频

Cell Migration01:09

Cell Migration

Cell migration, the process by which cells move from one location to another, is essential for the proper development and viability of organisms throughout their life. When cells are not able to migrate properly to their ordained locations, various disorders may occur. For example, disruption in cell migration causes chronic inflammatory diseases such as arthritis.
Cell Migration01:19

Cell Migration

Cell migration is a process by which the cells move from one location to another, playing an essential role in embryological development, repair and regeneration, immune response, and metastasis. Cells migrate in response to chemical or mechanical signals generated by specific organs or tissues. The overall mechanism includes three steps - polarization, protrusion, and release. Polarization involves the formation of a distinct cell front and rear, which determines the direction of movement.
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

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相关实验视频

Updated: May 15, 2026

Modeling and Imaging 3-Dimensional Collective Cell Invasion
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Modeling and Imaging 3-Dimensional Collective Cell Invasion

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在集体细胞迁移中的表型结构:数学模型和方法的教程.

Tommaso Lorenzi1, Kevin J Painter2, Chiara Villa3,4

  • 1Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy.

Journal of mathematical biology
|May 16, 2025
PubMed
概括

表型多样性显著影响人口动态. 本综述介绍了表型结构的部分微分方程 (PS-PDEs),以建模细胞系统和集体细胞迁移中的这种多样性.

关键词:
细胞运动 细胞运动集体细胞动态 集体细胞动态集中现象是一种集中现象.非地方的PDE.根据表型结构的种群.旅行波浪的旅行.

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科学领域:

  • 数学生物学 数学生物学
  • 计算生物学 计算生物学
  • 人口动态 人口动态

背景情况:

  • 现型多样性,人口内的特征范围,极大地影响了人口层面的动态.
  • 信号传递,运动和生长等特征的细胞异质性影响癌症的进展和治疗反应.

研究的目的:

  • 审查和扩展经典的部分微分方程 (PDE) 模型,以纳入表型结构.
  • 引入表型结构的部分微分方程 (PS-PDEs) 用于建模复杂的人口动态.

主要方法:

  • 审查将经典模型 (费舍尔-KPP,凯勒-塞格尔) 扩展到PS-PDEs.
  • 介绍了从基于代理的模型中推导PS-PDEs的方法.
  • 在PS-PDEs中分析移动波和度现象.
  • 讨论PS-PDEs的数值模拟技术.

主要成果:

  • PS-PDEs提供了一个复杂的框架,用于模拟具有表型多样性的种群.
  • 现型结构可以在PS-PDE模型中通过移动波来推断.
  • 数字方法,就像线的方法一样,可以模拟PS-PDEs.

结论:

  • PS-PDEs为了解表型多样性如何塑造人口动态提供了一个强大的工具.
  • 突出了未来的研究方向和PS-PDE建模中的数学挑战.