Asymptotic behaviour of global solutions to a model of cell invasion
Gabriela Litcanu, Cristian Morales-Rodrigo
在本文中，我们分析了一个数学模型的细胞入侵过程中的关键事件为重点。研究了相应的三个非线性偏微分方程耦合系统的整体适定性和非负解的渐近性态。
In this paper we analyze a mathematical model focusing on key events of the cells invasion process. Global well-possedness and asymptotic behaviour of nonnegative solutions to the corresponding coupled system of three nonlinear partial differential equations are studied.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper, we study the global dynamics of a general reaction-diffusion model based on acid-mediated invasion hypothesis, which is a candidate explanation for the Warburg effect. A key feature of this model is the density-limited tumor diffusion term for tumor cells, which might give rise to the degeneracy of the parabolic equation. Our theoretical results characterize the effects of acid resistance and mutual competition of healthy cells and tumor cells on tumor progression in the long term, i.e., whether the healthy cells and tumor cells coexist or the tumor cells prevail after tumor inv…
Multiscale modelling, analysis and simulation of cancer invasion mediated by bound and soluble enzymes
本文构建了癌细胞通过膜结合型和可溶性基质降解酶降解细胞外基质的微观模型，利用均化理论推导出宏观模型，证明了其适定性，并用有限元方法模拟了酶在癌症侵袭中的作用。
Existence of weak solutions for a volume-filling model of cell invasion into extracellular matrix
该研究针对细胞侵入细胞外基质的体积填充耦合模型，利用部分梯度流结构证明了弱解的存在性，并通过有限差分模拟验证行波解、分析降解率趋于无穷时的渐近行为。
Global existence for a degenerate haptotaxis model of tumor invasion under the go-or-grow dichotomy hypothesis
我们提出并研究了一个强耦合的PDE-ODE-ODE系统建模癌细胞入侵下的去或生长假设，断言癌细胞可以移动或增殖的组织网络。因此，我们的设置功能两个相互作用的细胞群体与他们的相互过渡，并涉及组织依赖的退化扩散和haptotaxis的移动亚群。增殖细胞和组织演变的特征在于通过ODE的方式为各自的密度。我们证明了弱解的整体存在性，并通过二维环境下的数值模拟说明了模型的行为。
Global classical solutions for a metastatic cancer invasion model with negative haptotaxis
本研究针对转移性癌症侵袭的PDE-ODE模型，在参数限制下证明了二维全模型及三维变体的全局经典解存在性，并通过数值模拟展示了肿瘤侵袭与转移过程。
Growth of cancer stem cell driven tumors: staged invasion, linear determinacy, and the tumor invasion paradox
本文研究癌症干细胞与肿瘤细胞相互作用的偏微分方程模型，利用几何奇异摄动理论刻画分阶段侵袭和肿瘤细胞灭绝两种机制，并揭示提高肿瘤细胞死亡率反而可能增加总癌症质量的肿瘤侵袭悖论。
We present and analyze new multi-species phase-field mathematical models of tumor growth and ECM invasion. The local and nonlocal mathematical models describe the evolution of volume fractions of tumor cells, viable cells (proliferative and hypoxic cells), necrotic cells, and the evolution of MDE and ECM, together with chemotaxis, haptotaxis, apoptosis, nutrient distribution, and cell-to-matrix adhesion. We provide a rigorous proof of the existence of solutions of the coupled system with gradient-based and adhesion-based haptotaxis effects. In addition, we discuss finite element discretization…
On a cross-diffusion hybrid model: Cancer Invasion Tissue with Normal Cell Involved
本文提出了一种涉及正常细胞的肿瘤侵袭模型，通过交叉扩散混合系统微分方程研究肿瘤侵袭的数学适定性问题。
Analysis of a model arising from invasion by precursor and differentiated cells
研究了一类退化反应扩散方程组的波动解。我们证明了当波速大于或等于某个数值时，存在一族波，且在该值以下不存在单调波解。我们还研究了波的单调性、唯一性和渐近性。
On a mathematical model for cancer invasion with repellent pH-taxis and nonlocal intraspecific interaction
本文从介观尺度推导出含非局部项及环境酸度偏置的细胞反应-扩散-趋向性方程，证明了耦合系统简化版非负解的全局存在性、唯一性与有界性，并通过一维模式形成研究与数值模拟展示了解的定性行为。
Global existence for a degenerate haptotaxis model of cancer invasion
我们提出并研究了一个强耦合的PDE-ODE系统与组织依赖性的退化扩散和haptotaxis，可以作为癌细胞通过细胞外基质入侵的模型原型。我们证明了弱解的整体存在性，并通过二维环境下的数值模拟说明了模型的行为。
Cell proliferation is typically incorporated into stochastic mathematical models of cell migration by assuming that cell divisions occur after an exponentially distributed waiting time. Experimental observations, however, show that this assumption is often far from the real cell cycle time distribution (CCTD). Recent studies have suggested an alternative approach to modelling cell proliferation based on a multi-stage representation of the CCTD. In order to validate and parametrise these models, it is important to connect them to experimentally measurable quantities. In this paper we investigat…
Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion
本文构建多尺度表型结构趋触性癌症侵袭模型，由基于个体的分支随机游走推导连续耦合系统，并通过行波分析揭示间充质细胞主导前缘、上皮细胞主导后部的空间结构。
We consider a model for the dynamics of growing cell populations with heterogeneous mobility and proliferation rate. The cell phenotypic state is described by a continuous structuring variable and the evolution of the local cell population density function (i.e. the cell phenotypic distribution at each spatial position) is governed by a non-local advection-reaction-diffusion equation. We report on the results of numerical simulations showing that, in the case where the cell mobility is bounded, compactly supported travelling fronts emerge. More mobile phenotypic variants occupy the front edge,…
Survival and invasion dynamics in cell populations: an analytical framework for threshold behaviour in nonlinear age-structured models
本文提出一个分析框架，用于研究细胞群体中年龄依赖的分裂率对侵袭速度和生存阈值的影响。
Travelling waves in a minimal go-or-grow model of cell invasion
该研究针对细胞侵袭的最小go-or-grow模型，通过快速转换情形分析将其总细胞密度简化为单反应扩散方程描述，进而研究行波解，证明其波速受Fisher-KPP方程波速约束。
Existence, regularity and stability in a strongly degenerate nonlinear diffusion and haptotaxis model of cancer invasion
针对耦合 ECM 动力学的强退化非线性扩散—趋触癌症侵袭模型，本文建立相容估计与正则性、紧性结果，证明弱解稳定性及全局存在性。
Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model
我们考虑了一个包括两个癌细胞家族的趋触性癌症侵袭模型。两个家族都在细胞外基质上迁移并增殖。此外，该模型描述了两个家族之间的上皮细胞到间充质样的过渡，以及细胞外基质的降解和自我重建过程。在大初值条件下，证明了该问题的正解和条件整体经典解的存在唯一性。
Global behaviour of solutions stable at infinity for gradient systems in higher space dimension: the no invasion case
本文研究高维抛物型梯度系统在无穷远处稳定解的全局渐近行为，依据解偏离平衡态区域的平均增长速度，给出渐近能量的符号判定，并用于后续径向对称解的分析。
We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different proliferative abilities and mobility, which may vary from part to part of the tissue, as well as by different invasion potentials within the membranes. The original transmission problem, consisting of a set of mass balance equations for the volume fraction of cells of every population complemented with continuity of stresses and mass flux across the surfaces of the m…
We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character. We prove global existenc…
Recovering the initial condition and physical coefficients in a nonlinear PDE model of cell invasion
针对细胞侵袭非线性反应扩散模型，利用Carleman估计建立反应系数全局唯一性与Lipschitz型稳定性，以及初始条件的对数稳定性，并提出两阶段数值算法。
A free boundary analysis of tumor invasion driven by angiogenesis
研究由血管生成驱动的肿瘤侵袭的自由边界模型，通过该模型描述肿瘤细胞扩散等情况，证明肿瘤能长期存活并得出相关表达式，还根据比率κ区分肿瘤发展的两种情况。
Travelling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons
本研究通过对基于智能体的体积填充细胞入侵模型进行粗粒化推导出反应扩散方程组，通过数值和解析方法研究其行波解，并与文献中较简单模型进行系统比较，验证了部分简化模型的适用性，同时揭示了体积填充效应带来的独特性质。
We propose a novel approach to modeling cell migration in an anisotropic environment with biochemical heterogeneity and interspecies interactions, using as a paradigm glioma invasion in brain tissue under the influence of hypoxia-triggered angiogenesis. The multiscale procedure links single-cell and mesoscopic dynamics with population level behavior, leading on the macroscopic scale to flux-limited glioma diffusion and multiple taxis. We verify the non-negativity of regular solutions (provided they exist) to the obtained macroscopic PDE-ODE system and perform numerical simulations to illustrat…
An Analysis of a Mathematical Model Describing Acid-mediated Tumor Invasion
本文研究了描述酸介导肿瘤侵袭的反应扩散模型，分析了该模型在不同边界条件下的解的存在性和唯一性，并通过数值模拟验证了结果。
This paper investigates the large time behaviour of a three species reaction-diffusion system, modelling the spatial invasion of two predators feeding on a single prey species. In addition to the competition for food, the two predators exhibit competitive interactions and under some parameter conditions ($μ>0$), they can also be considered as two mutants. When mutations occur in the predator populations, the spatial spread of invasion takes place at a definite speed, identical for both mutants. When the two predators are not coupled through mutation, the spreading behaviour exhibits a more com…
Wavespeed selection and interstitial gap formation in an acid-mediated cancer invasion model
该研究探讨了酸介导的癌症侵袭模型中波速选择与间隙形成机制，揭示了降解率对间隙大小的影响及Fisher-KPP系统的关联。
Theory of adhesion-driven self-organisation in growing tissues
研究通过多尺度分析揭示了细胞粘附、自扩散和增殖之间的平衡如何控制集体动态，发现粘附强度调节影响组织侵袭的凝聚力与模式形成。
Global existence of classical solutions and numerical simulations of a cancer invasion model
本文从理论和数值两方面研究了一个由三个耦合偏微分方程组成的癌症入侵模型，证明了在缺乏酶扩散的情况下二维和三维有界区域中全局经典解的存在性，并基于Galerkin有限元与不动点迭代算法进行了数值模拟验证。
Estimates on the asymptotic behaviour of solution to linear integro-differential equations are fundamental in understanding the dynamics occuring in many nonlocal evolution problems. They are usually derived by using precise decay estimates on the heat kernel of the considered diffusion process. In this note, we show that for some generic jump diffusion and particular initial data, one can derive a lower bound of the asymptotic behaviour of the solution using a simple PDE argument. This is viewed as an independant preliminary brick to study invasion phenomena in nonlinear reaction diffusion pr…
A Damage-Driven Model for Duchenne Muscular Dystrophy: Early-Stage Dynamics and Invasion Thresholds
本文提出一个基于损伤驱动的数学模型，研究杜兴肌肉营养不良的早期动态和入侵阈值，通过线性化分析证明扩散不引发图灵不稳定性，疾病进展通过入侵过程实现，推导出入侵起始条件和最小传播速度。
Travelling Waves in a Mathematical Model for Oncolytic Virotherapy
该研究通过反应扩散模型分析了溶瘤病毒治疗中行波解的存在性，确定了最小波速并探讨了肿瘤环境中的传播机制。
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive operators we establish new criteria for an asynchronous exponential growth of solutions to such equations. We discuss the question of exponential size growth of cells. We study in detail a constant size growth model and a model with target size division. We also present versions of the model when the population is heterogeneous.
We provide a review of recent advancements in nonlocal continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial nonlocality occurring in advection terms, used to characterise a cell's motility bias according to its interactions with other cellular and acellular components in its vicinity (e.g., cell-cell and cell-tissue adhesions, nonlocal chemotaxis), but we also shortly address spatially nonlocal source terms. Following a brief introduction and motivation, we give a systematic classi…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。