ArticleMathematical and computer modelling2011
An Adaptive Multigrid Algorithm for Simulating Solid Tumor Growth Using Mixture Models.
Article in Mathematical and computer modelling, 2011. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 19 papers.
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Who cites it
19 citing papers in PubMed.
- Data-driven spatio-temporal modelling of glioblastoma.Royal Society open science · 2023Review
- Spatial dynamics of feedback and feedforward regulation in cell lineages.PLoS computational biology · 2022Article
- An Explicit Adaptive Finite Difference Method for the Cahn-Hilliard Equation.Journal of nonlinear science · 2022Article
- Simulation of 3D centimeter-scale continuum tumor growth at sub-millimeter resolution via distributed computing.Computers in biology and medicine · 2021Article
- A Visually Apparent and Quantifiable CT Imaging Feature Identifies Biophysical Subtypes of Pancreatic Ductal Adenocarcinoma.Clinical cancer research : an official journal of the American Association for Cancer Research · 2018Article
- Three-Dimensional Spatiotemporal Modeling of Colon Cancer Organoids Reveals that Multimodal Control of Stem Cell Self-Renewal is a Critical Determinant of Size and Shape in Early Stages of Tumor Growth.Bulletin of mathematical biology · 2018Article
- Activation of the HGF/c-Met axis in the tumor microenvironment: A multispecies model.Journal of theoretical biology · 2018Article
- Simulation of Multispecies Desmoplastic Cancer Growth via a Fully Adaptive Non-linear Full Multigrid Algorithm.Frontiers in physiology · 2018Article
- Model of vascular desmoplastic multispecies tumor growth.Journal of theoretical biology · 2017Article
- Multiscale Modeling of Glioblastoma Suggests that the Partial Disruption of Vessel/Cancer Stem Cell Crosstalk Can Promote Tumor Regression Without Increasing Invasiveness.IEEE transactions on bio-medical engineering · 2017Article
- Feedback, Lineages and Self-Organizing Morphogenesis.PLoS computational biology · 2016Article
- Progress Towards Computational 3-D Multicellular Systems Biology.Advances in experimental medicine and biology · 2016Review
- Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems.Cellular and molecular bioengineering · 2015Article
- Tumor growth in complex, evolving microenvironmental geometries: a diffuse domain approach.Journal of theoretical biology · 2014Article
- A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane.International journal for numerical methods in biomedical engineering · 2014Article
- New type continuities via Abel convergence.TheScientificWorldJournal · 2014Article
- Multispecies model of cell lineages and feedback control in solid tumors.Journal of theoretical biology · 2012Article
- Nonlinear modelling of cancer: bridging the gap between cells and tumours.Nonlinearity · 2010Article
- Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method.Journal of theoretical biology · 2008Article
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Authors and funding
3 authors.
Funding
Abstract
In this paper we give the details of the numerical solution of a three-dimensional multispecies diffuse interface model of tumor growth, which was derived in (Wise et al., J. Theor. Biol. 253 (2008)) and used to study the development of glioma in (Frieboes et al., NeuroImage 37 (2007) and tumor invasion in (Bearer et al., Cancer Research, 69 (2009)) and (Frieboes et al., J. Theor. Biol. 264 (2010)). The model has a thermodynamic basis, is related to recently developed mixture models, and is capable of providing a detailed description of tumor progression. It utilizes a diffuse interface approach, whereby sharp tumor boundaries are replaced by narrow transition layers that arise due to differential adhesive forces among the cell-species. The model 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. Numerical solution of the model is challenging because the equations are coupled, highly nonlinear, and numerically stiff. In this paper we describe a fully adaptive, nonlinear multigrid/finite difference method for efficiently solving the equations. We demonstrate the convergence of the algorithm and we present simulations of tumor growth in 2D and 3D that demonstrate the capabilities of the algorithm in accurately and efficiently simulating the progression of tumors with complex morphologies.
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Registered trials
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.