Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Multispecies model of cell lineages and feedback control in solid tumors.

Journal of theoretical biology·2012

Same author

Nonlinear modelling of cancer: bridging the gap between cells and tumours.

Nonlinearity·2010

Same author

Three-dimensional multispecies nonlinear tumor growth--I Model and numerical method.

Journal of theoretical biology·2008

Same author

Prototyping virtual cancer therapist (VCT): a software engineering approach.

Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference·2007

Same author

Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method.

Bulletin of mathematical biology·2005

Same author

Two-dimensional chemotherapy simulations demonstrate fundamental transport and tumor response limitations involving nanoparticles.

Biomedical microdevices·2004

Same journal

Analysis and control of an SEIR epidemic system with nonlinear transmission rate.

Mathematical and computer modelling·2020

Same journal

Periodic solutions and bifurcation in an <math></math> epidemic model with birth pulses.

Mathematical and computer modelling·2020

Same journal

Optimal and sub-optimal quarantine and isolation control in SARS epidemics.

Mathematical and computer modelling·2020

Same journal

A discrete epidemic model for SARS transmission and control in China.

Mathematical and computer modelling·2020

Same journal

BIFURCATING DISTRIBUTIVE SYSTEM USING MONTE CARLO METHOD.

Mathematical and computer modelling·2012

Same journal

Standard Error Computations for Uncertainty Quantification in Inverse Problems: Asymptotic Theory vs. Bootstrapping.

Mathematical and computer modelling·2010

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 6, 2026

Generation of Heterogeneous Drug Gradients Across Cancer Populations on a Microfluidic Evolution Accelerator for Real-Time Observation

Generation of Heterogeneous Drug Gradients Across Cancer Populations on a Microfluidic Evolution Accelerator for Real-Time Observation

Published on: September 19, 2019

An Adaptive Multigrid Algorithm for Simulating Solid Tumor Growth Using Mixture Models.

S M Wise¹, J S Lowengrub, V Cristini

¹Mathematics Department, University of Tennessee, Knoxville, TN 37996-1300, USA.

Mathematical and Computer Modelling

|November 16, 2010

Summary

This summary is machine-generated.

This paper details a numerical method for a diffuse interface tumor growth model. The adaptive multigrid/finite difference approach efficiently simulates complex tumor progression in 2D and 3D.

More Related Videos

Generation of Microtumors Using 3D Human Biogel Culture System and Patient-derived Glioblastoma Cells for Kinomic Profiling and Drug Response Testing

Generation of Microtumors Using 3D Human Biogel Culture System and Patient-derived Glioblastoma Cells for Kinomic Profiling and Drug Response Testing

Published on: June 9, 2016

A Photopolymerizable Hyaluronic Acid-Collagen Model of the Invasive Glioma Microenvironment with Interstitial Flow

A Photopolymerizable Hyaluronic Acid-Collagen Model of the Invasive Glioma Microenvironment with Interstitial Flow

Published on: October 18, 2024

Related Experiment Videos

Last Updated: Jun 6, 2026

Generation of Heterogeneous Drug Gradients Across Cancer Populations on a Microfluidic Evolution Accelerator for Real-Time Observation

Generation of Heterogeneous Drug Gradients Across Cancer Populations on a Microfluidic Evolution Accelerator for Real-Time Observation

Published on: September 19, 2019

Generation of Microtumors Using 3D Human Biogel Culture System and Patient-derived Glioblastoma Cells for Kinomic Profiling and Drug Response Testing

Generation of Microtumors Using 3D Human Biogel Culture System and Patient-derived Glioblastoma Cells for Kinomic Profiling and Drug Response Testing

Published on: June 9, 2016

A Photopolymerizable Hyaluronic Acid-Collagen Model of the Invasive Glioma Microenvironment with Interstitial Flow

A Photopolymerizable Hyaluronic Acid-Collagen Model of the Invasive Glioma Microenvironment with Interstitial Flow

Published on: October 18, 2024

Area of Science:

Computational biology
Mathematical modeling
Biophysics

Background:

Tumor growth and invasion are complex processes.
Existing models may not capture detailed tumor progression.
Diffuse interface models offer a thermodynamic basis for simulating cell-species interactions.

Purpose of the Study:

To present the numerical solution of a three-dimensional multispecies diffuse interface tumor growth model.
To describe an efficient, fully adaptive, nonlinear multigrid/finite difference method for solving the model equations.
To demonstrate the algorithm's capability in simulating tumor progression with complex morphologies.

Main Methods:

Developed a numerical method based on adaptive nonlinear multigrid and finite difference techniques.
Applied the method to solve coupled, nonlinear, stiff fourth-order advection-reaction-diffusion equations.
Simulated tumor growth in both two and three dimensions.

Main Results:

Demonstrated the convergence of the developed numerical algorithm.
Successfully simulated tumor growth with complex morphologies in 2D and 3D.
The method efficiently and accurately captures tumor progression dynamics.

Conclusions:

The presented numerical method is effective for solving complex diffuse interface tumor growth models.
This approach enables accurate and efficient simulation of tumor development.
The findings support the use of diffuse interface models for studying cancer progression.