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

Exponential Equations for Modeling Growth

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...

You might also read

Related Articles

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

Sort by

Same author

Mathematical Assessment of the Roles of Vaccination and Pap Screening on the Burden of HPV and Related Cancers in Korea.

Bulletin of mathematical biology·2025

Same author

A Mathematical Model of TCR-T Cell Therapy for Cervical Cancer.

Bulletin of mathematical biology·2024

Same author

Topographic comparison of the retinal microvascular changes between patients with compressive and glaucomatous optic neuropathies.

Scientific reports·2023

Same author

Refractive Predictability between Standard and Total Keratometry during the Femtosecond Laser-Assisted Cataract Surgery with Monofocal Intraocular Lens with Enhanced Intermediate Function.

Korean journal of ophthalmology : KJO·2023

Same author

Modeling LSD1-Mediated Tumor Stagnation.

Bulletin of mathematical biology·2021

Same author

Modeling the Effect of Memory in the Adaptive Immune Response.

Bulletin of mathematical biology·2020

Search research articles

Related Experiment Video

Updated: Apr 8, 2026

Longitudinal Measurement of Extracellular Matrix Rigidity in 3D Tumor Models Using Particle-tracking Microrheology

Longitudinal Measurement of Extracellular Matrix Rigidity in 3D Tumor Models Using Particle-tracking Microrheology

Published on: June 10, 2014

Age-structured mechanical models for tumor growth.

Doron Levy¹, Hyunah Lim¹, Antoine Mellet²

¹Department of Mathematics, University of Maryland College Park, College Park, MD, 20742, USA.

Journal of Mathematical Biology

|April 6, 2026

Summary

This summary is machine-generated.

This study presents a new mechanical model for tumor growth incorporating cell life cycles. The model reveals a death rate threshold influencing tumor expansion or regression, offering insights into tumor dynamics.

Keywords:

Age-structured model Cross-diffusion Existence of solutions Nonlinear Darcy’s law Tumor growth

More Related Videos

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

Author Spotlight: Patient-Informed 3D Model for Studying Glioblastoma Invasion via Interstitial Fluid Flow

Author Spotlight: Patient-Informed 3D Model for Studying Glioblastoma Invasion via Interstitial Fluid Flow

Published on: October 18, 2024

Related Experiment Videos

Last Updated: Apr 8, 2026

Longitudinal Measurement of Extracellular Matrix Rigidity in 3D Tumor Models Using Particle-tracking Microrheology

Longitudinal Measurement of Extracellular Matrix Rigidity in 3D Tumor Models Using Particle-tracking Microrheology

Published on: June 10, 2014

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

Author Spotlight: Patient-Informed 3D Model for Studying Glioblastoma Invasion via Interstitial Fluid Flow

Author Spotlight: Patient-Informed 3D Model for Studying Glioblastoma Invasion via Interstitial Fluid Flow

Published on: October 18, 2024

Area of Science:

Mathematical Biology
Biophysics
Computational Biology

Background:

Classical mechanical models describe tumor growth via cell proliferation limited by internal pressure.
Cellular incompressibility drives outward movement from high-pressure zones, modeled using nonlinear Darcy's law.

Purpose of the Study:

To introduce and analyze a novel mechanical model for tumor growth.
To incorporate the complete life cycle of tumor cells, including age-dependent phases.
To investigate the impact of cell age on tumor expansion and regression dynamics.

Main Methods:

Development of a mechanical model for tumor growth.
Inclusion of cell age as a key variable influencing cell life cycle phases (growth, mitosis, death).
Mathematical analysis to prove the existence of weak solutions and numerical simulations to study tumor behavior.

Main Results:

The model demonstrates that cell age significantly influences tumor cell dynamics.
Numerical investigations focus on age distribution, convergence to traveling wave solutions, and the critical role of the death rate.
A specific threshold for the death rate was identified as a determinant for tumor expansion or regression.

Conclusions:

The age-dependent mechanical model provides a more comprehensive understanding of tumor growth.
The identified death rate threshold is a critical factor in predicting tumor fate.
This model offers potential for developing new therapeutic strategies targeting tumor cell life cycles.