具有密度依赖速度的细胞迁移非局部动力学模型的稳定性。

IF 0.8 4区 数学 Q4 BIOLOGY Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2021-03-15 DOI:10.1093/imammb/dqaa013
Nadia Loy, Luigi Preziosi
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引用次数: 0

摘要

本文的目的是研究Loy & Preziosi (2020a)提出的非局部动力学模型的稳定性,该模型中细胞速度受非局部测量的细胞种群密度的影响,并根据极化和运动方向的传感核进行加权。我们在d维设置中执行分析。我们研究了一维情况下的色散关系,并表明稳定性取决于两个无维参数:第一个参数代表系统的刚度,与细胞转动速率、平衡时的平均速度和感应半径有关,而第二个参数与平均速度相对于平衡时评估的密度的导数有关。证明了对于以有限距离为中心的Dirac delta传感核,即距离胞心一定距离的传感,其均匀构型对短波是线性不稳定的。另一方面,对于均匀传感核,即对给定距离内收集到的信息进行均匀加权,识别出最不稳定的波长,并与动力学方程的数值解一致匹配。
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Stability of a non-local kinetic model for cell migration with density-dependent speed.

The aim of this article is to study the stability of a non-local kinetic model proposed by Loy & Preziosi (2020a) in which the cell speed is affected by the cell population density non-locally measured and weighted according to a sensing kernel in the direction of polarization and motion. We perform the analysis in a $d$-dimensional setting. We study the dispersion relation in the one-dimensional case and we show that the stability depends on two dimensionless parameters: the first one represents the stiffness of the system related to the cell turning rate, to the mean speed at equilibrium and to the sensing radius, while the second one relates to the derivative of the mean speed with respect to the density evaluated at the equilibrium. It is proved that for Dirac delta sensing kernels centered at a finite distance, corresponding to sensing limited to a given distance from the cell center, the homogeneous configuration is linearly unstable to short waves. On the other hand, for a uniform sensing kernel, corresponding to uniformly weighting the information collected up to a given distance, the most unstable wavelength is identified and consistently matches the numerical solution of the kinetic equation.

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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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