Numerical Simulation of a Multiscale Cell Motility Model Based on the Kinetic Theory of Active Particles

Knopoff, Damián; Nieto, Juan J.; Urrutia, L.

doi:10.3390/sym11081003

Cited by 10 publications

(4 citation statements)

References 48 publications

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“…The contributions available in the literature still need additional work which cannot skip over the need of sophisticated analytic tools to achieve this result. A deep analysis of the complex behaviors at the microscopic scale [33][34][35] which can include non symmetrical behaviors [36], can contribute to model the link between individual and collective behaviors.…”

Section: Critical Analysis Towards Safety Problemsmentioning

confidence: 99%

Particle Methods Simulations by Kinetic Theory Models of Human Crowds Accounting for Stress Conditions

Ełaiw

Al‐Turki

2019

Symmetry

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This paper tackles the problem of simulating the dynamics of human crowds in high density conditions on venues which include internal obstacles and in the interaction between two crowd streams moving in two opposite directions. The role of stress condition is taken into account as simulations aim at providing a support to crisis managers in charge of reducing the risk of incidents. The rationale of the modeling approach is that kinetic theory approach, where individual interactions, which might be nonlinearly additive, non symmetric, and non nonlocal, lead to collective behaviors to be examined towards safety problems. Author Contributions: Conceptualization, A.E. and Y.A.-T.; methodology, A.E.; formal analysis, Y.A.-T.; investigation, A.E.; writing original draft preparation, Y.A.-T.; writing review and editing, A.E. and Y.A.-T.; project administration, A.E. All authors have read and agreed to the published version of the manuscript.

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Section: Critical Analysis Towards Safety Problemsmentioning

confidence: 99%

Particle Methods Simulations by Kinetic Theory Models of Human Crowds Accounting for Stress Conditions

Ełaiw

Al‐Turki

2019

Symmetry

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“…Yet another class of multiscale models with chemo-and haptotaxis was proposed and studied in [42,43] and readdressed in terms of numerical simulations in [47] and of well-posedness under more or less restrictive assumptions in [59,70]. The models therein connect macroscopic descriptions of chemoattractant dynamics (reaction-diffusion equations) with mesoscopic kinetic transport equations for the evolution of cell and tissue density functions and can be seen to belong to the kinetic theory of active particles (KTAP) developed by Bellomo et al [1].…”

Section: Introductionmentioning

confidence: 99%

Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence

Kolbe¹,

Sfakianakis²,

Stinner³

et al. 2020

Preprint

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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 existence of weak solutions to a simplified model version and perform numerical simulations for the full setting under several phenotype switching and motility scenarios. We also compare (via simulations) this model with the corresponding haptotaxis-chemotaxis one featuring indirect chemorepellent production and provide a discussion about possible model extensions and mathematical challenges.

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“…Yet another class of multiscale models with chemo-and haptotaxis was proposed and studied in [42,43] and readdressed in terms of numerical simulations in [47] and of well-posedness under more or less restrictive assumptions in [59,70]. The models therein connect macroscopic descriptions of chemoattractant dynamics (reactiondiffusion equations) with mesoscopic kinetic transport equations for the evolution of cell and tissue density functions and can be seen to belong to the kinetic theory of active particles (KTAP) developed by Bellomo et al [1].…”

mentioning

confidence: 99%

Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence

Kolbe¹,

Sfakianakis²,

Stinner³

et al. 2021

Discrete &Amp; Continuous Dynamical Systems - B

View full text Add to dashboard Cite

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 existence of weak solutions to a simplified model version and perform numerical simulations for the full setting under several phenotype switching and motility scenarios. We also compare (via simulations) this model with the corresponding haptotaxis-chemotaxis one featuring indirect chemorepellent production and provide a discussion about possible model extensions and mathematical challenges.

show abstract

Numerical Simulation of a Multiscale Cell Motility Model Based on the Kinetic Theory of Active Particles

Cited by 10 publications

References 48 publications

Particle Methods Simulations by Kinetic Theory Models of Human Crowds Accounting for Stress Conditions

Particle Methods Simulations by Kinetic Theory Models of Human Crowds Accounting for Stress Conditions

Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence

Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence

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