A level-set approach for a multi-scale cancer invasion model

DOI10.5206/mase/11087zbMath1498.92055arXiv1805.07485OpenAlexW3158513904WikidataQ111489579 ScholiaQ111489579MaRDI QIDQ5040326

Dumitru Trucu, Ana Victoria Ponce Bobadilla, Thomas Carraro, Sven E. Wetterauer

Publication date: 11 October 2022

Published in: Mathematics in Applied Sciences and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.07485

zbMATH Keywords

FEMcancer invasionmultiscale modellinglevel-setcut-cells

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Pathology, pathophysiology (92C32)

Uses Software

• UMFPACK

Cites Work

• Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method
• Mathematical modelling of cancer invasion: implications of cell adhesion variability for tumour infiltrative growth patterns
• An adaptive multigrid algorithm for simulating solid tumor growth using mixture models
• Ghost penalty
• A new ghost cell/level set method for moving boundary problems: application to tumor growth
• Multiphase modeling of tumor growth with matrix remodeling and fibrosis
• Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation
• Evolving interfaces via gradients of geometry-dependent interior Poisson problems: application to tumor growth
• The heterogeneous multiscale methods
• On the design of algebraic flux correction schemes for quadratic finite elements
• A simplified mathematical model of tumor growth
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• The fast construction of extension velocities in level set methods
• Modelling the role of cell-cell adhesion in the growth and development of carcinomas
• Model of vascular desmoplastic multispecies tumor growth
• Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis
• Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion
• Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
• A positivity-preserving finite element method for chemotaxis problems in 3D
• Multiscale modelling of fibres dynamics and cell adhesion within moving boundary cancer invasion
• A multiscale mathematical model of tumour invasive growth
• Multiscale moving boundary modelling of cancer interactions with a fusogenic oncolytic virus: the impact of syncytia dynamics
• Cell-scale degradation of peritumoural extracellular matrix fibre network and its role within tissue-scale cancer invasion
• A continuum approach to modelling cell-cell adhesion
• Nonlinear simulation of the effect of microenvironment on tumor growth
• Directionality of macrophages movement in tumour invasion: a multiscale moving-boundary approach
• Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix
• Multiscale modelling of cancer response to oncolytic viral therapy
• Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications
• Multiscale modelling and nonlinear simulation of vascular tumour growth
• The deal.II library, version 8.5
• An improved geometry-aware curvature discretization for level set methods: Application to tumor growth
• MATHEMATICAL MODELLING OF CANCER INVASION: THE IMPORTANCE OF CELL–CELL ADHESION AND CELL–MATRIX ADHESION
• Another Look at Velocity Extensions in the Level Set Method
• The heterogeneous multiscale method
• Multiscale Computational Modelling and Analysis of Cancer Invasion
• Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development
• MATHEMATICAL MODELLING OF CANCER INVASION OF TISSUE: THE ROLE AND EFFECT OF NONLOCAL INTERACTIONS
• Mathematical Modelling of Tumour Invasion and Metastasis
• Modelling solid tumour growth using the theory of mixtures
• CONVERGENCE OF A CANCER INVASION MODEL TO A LOGISTIC CHEMOTAXIS MODEL
• Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source
• Non-local multiscale approaches for tumour-oncolytic viruses interactions
• Efficient Approximation of Flow Problems With Multiple Scales in Time
• A Multiscale Moving Boundary Model Arising in Cancer Invasion
• Algorithm 832
• How accurate is the streamline diffusion finite element method?
• A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion
• MATHEMATICAL MODELLING OF CANCER CELL INVASION OF TISSUE: THE ROLE OF THE UROKINASE PLASMINOGEN ACTIVATION SYSTEM
• An analysis of a mathematical model of trophoblast invasion
• Unnamed Item
• Unnamed Item

This page was built for publication: A level-set approach for a multi-scale cancer invasion model