ArticleJournal of theoretical biology2008
Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method.
Article in Journal of theoretical biology, 2008. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 80 papers.
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Who cites it
80 citing papers in PubMed.
- Stabilized Radial Basis Function Finite Difference Schemes with Mass Conservation for the Cahn-Hilliard Equation on Surfaces.Entropy (Basel, Switzerland) · 2025Article
- Validating the predictions of mathematical models describing tumor growth and treatment response.ArXiv · 2025Article
- Carotenoids as modulators of the PI3K/Akt/mTOR pathway: innovative strategies in cancer therapy.Medical oncology (Northwood, London, England) · 2024Review
- Dynamic cluster field modeling of collective chemotaxis.Scientific reports · 2024Article
- Efficient numerical approaches with accelerated graphics processing unit (GPU) computations for Poisson problems and Cahn-Hilliard equations.AIMS mathematics · 2024Article
- A multiscale chemical-mechanical model predicts impact of morphogen spreading on tissue growth.NPJ systems biology and applications · 2023Article
- Data-driven spatio-temporal modelling of glioblastoma.Royal Society open science · 2023Review
- Tumor growth towards lower extracellular matrix conductivity regions under Darcy's Law and steady morphology.Journal of mathematical biology · 2022Article
- A continuum mechanical framework for modeling tumor growth and treatment in two- and three-phase systems.Archive of applied mechanics = Ingenieur-Archiv · 2022Article
- Simulation of 3D centimeter-scale continuum tumor growth at sub-millimeter resolution via distributed computing.Computers in biology and medicine · 2021Article
- Mathematical simulation of tumour angiogenesis: angiopoietin balance is a key factor in vessel growth and regression.Scientific reports · 2021Article
- Mathematical Modeling and Numerical Simulation of Atherosclerosis Based on a Novel Surgeon's View.Archives of computational methods in engineering : state of the art reviews · 2021Article
- A Coupled Mass Transport and Deformation Theory of Multi-constituent Tumor Growth.Journal of the mechanics and physics of solids · 2020Article
- Optimal Control Theory for Personalized Therapeutic Regimens in Oncology: Background, History, Challenges, and Opportunities.Journal of clinical medicine · 2020Review
- Mathematical Modelling for the Role of CD4Computational and mathematical methods in medicine · 2020Article
- Radiation protraction schedules for low-grade gliomas: a comparison between different mathematical models.Journal of the Royal Society, Interface · 2019Article
- Three-dimensional tumor growth in time-varying chemical fields: a modeling framework and theoretical study.BMC bioinformatics · 2019Article
- Towards a Physiological Scale of Vocal Fold Agent-Based Models of Surgical Injury and Repair: Sensitivity Analysis, Calibration and Verification.Applied sciences (Basel, Switzerland) · 2019Article
- A 3D Multiscale Model to Explore the Role of EGFR Overexpression in Tumourigenesis.Bulletin of mathematical biology · 2019Article
- Tumor growth and calcification in evolving microenvironmental geometries.Journal of theoretical biology · 2019Article
20 more citing papers are in PubMed but not listed here.
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4 authors.
Funding
Abstract
This is the first paper in a two-part series in which we develop, analyze, and simulate a diffuse interface continuum model of multispecies tumor growth and tumor-induced angiogenesis in two and three dimensions. Three-dimensional simulations of nonlinear tumor growth and neovascularization using this diffuse interface model were recently presented in Frieboes et al. [2007. Computer simulation of glioma growth and morphology. NeuroImage S59-S70], but that paper did not describe the details of the model or the numerical algorithm. This is done here. In this diffuse interface approach, sharp interfaces are replaced by narrow transition layers that arise due to differential adhesive forces among the cell species. Accordingly, a continuum model of adhesion is introduced. The model is thermodynamically consistent, is related to recently developed mixture models, and thus is capable of providing a detailed description of tumor progression. The model is well-posed and consists of fourth-order nonlinear advection-reaction-diffusion equations (of Cahn-Hilliard-type) for the cell species coupled with reaction-diffusion equations for the substrate components. We demonstrate analytically and numerically that when the diffuse interface thickness tends to zero, the system reduces to a classical sharp interface model. Using a new fully adaptive and nonlinear multigrid/finite difference method, the system is simulated efficiently. In this first paper, we present simulations of unstable avascular tumor growth in two and three dimensions and demonstrate that our techniques now make large-scale three-dimensional simulations of tumors with complex morphologies computationally feasible. In part II of this study, we will investigate multispecies tumor invasion, tumor-induced angiogenesis, and focus on the morphological instabilities that may underlie invasive phenotypes.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.