Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

The Fluid Mosaic Model01:34

The Fluid Mosaic Model

179.8K
The fluid mosaic model was first proposed as a visual representation of research observations. The model comprises the composition and dynamics of membranes and serves as a foundation for future membrane-related studies. The model depicts the structure of the plasma membrane with a variety of components, which include phospholipids, proteins, and carbohydrates. These integral molecules are loosely bound, defining the cell’s border and providing fluidity for optimal function.
179.8K
Nonlinear Pharmacokinetics: Causes of Nonlinearity01:22

Nonlinear Pharmacokinetics: Causes of Nonlinearity

745
Nonlinearity in drug pharmacokinetics is caused by various factors influencing how a drug is absorbed, distributed, metabolized, and excreted. Understanding these nonlinear processes is crucial for predicting drug behavior in the body and optimizing drug dosing regimens.
Nonlinear drug absorption can occur when the process is rate-limited by solubility, carrier-mediated transport systems, or saturation of the presystemic gut wall or hepatic metabolism. For instance, high doses of riboflavin...
745
Steady Flow of a Fluid Stream01:27

Steady Flow of a Fluid Stream

773
Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...
773
Fluid Mosaic Model01:19

Fluid Mosaic Model

17.5K
Scientists identified the plasma membrane in the 1890s and its principal chemical components (lipids and proteins) by 1915. The model for plasma membrane structure, proposed in 1935 by Hugh Davson and James Danielli, was the first model to be widely accepted in the scientific community. The model was based on the plasma membrane's "railroad track" appearance in early electron micrographs. Davson and Danielli theorized that the plasma membrane's structure resembled a sandwich...
17.5K
Nuclear Stability03:18

Nuclear Stability

23.4K
Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
To hold positively charged protons together...
23.4K
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

322
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
322

You might also read

Related Articles

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

Sort by
Same author

A phase-field model for viscoelastic compressible tumor growth.

ArXiv·2026
Same author

Wrinkling dynamics accelerate due to sudden changes in boundary conditions.

Physical review. E·2026
Same author

Chemomechanical regulation of growing tissues from a thermodynamically-consistent framework and its application to tumor spheroid growth.

Journal of mathematical biology·2025
Same author

Chemomechanical regulation of growing tissues from a thermodynamically-consistent framework and its application to tumor spheroid growth.

ArXiv·2024
Same author

tauFisher predicts circadian time from a single sample of bulk and single-cell pseudobulk transcriptomic data.

Nature communications·2024
Same author

Mathematical modeling of cancer immunotherapy for personalized clinical translation.

Nature computational science·2023

Related Experiment Video

Updated: Feb 13, 2026

Three-dimensional Cell Culture Model for Measuring the Effects of Interstitial Fluid Flow on Tumor Cell Invasion
07:41

Three-dimensional Cell Culture Model for Measuring the Effects of Interstitial Fluid Flow on Tumor Cell Invasion

Published on: July 25, 2012

17.1K

Nonlinear studies of tumor morphological stability using a two-fluid flow model.

Kara Pham1,2, Emma Turian3,4, Kai Liu1

  • 1Department of Mathematics, University of California at Irvine, Irvine, CA, 92697-3875, USA.

Journal of Mathematical Biology
|March 17, 2018
PubMed
Summary

Tumor shape and aggressiveness depend on viscosity. More viscous tumors form invasive fingers, while less viscous ones develop compact shapes with invaginations, correlating stiffness with aggressiveness.

Keywords:
Boundary integral methodMoving boundary problemsSolid tumor growthStokes flow

More Related Videos

Human Neuroendocrine Tumor Cell Lines as a Three-Dimensional Model for the Study of Human Neuroendocrine Tumor Therapy
12:04

Human Neuroendocrine Tumor Cell Lines as a Three-Dimensional Model for the Study of Human Neuroendocrine Tumor Therapy

Published on: August 14, 2012

29.5K
Brain Morphology of Cannabis Users With or Without Psychosis: A Pilot MRI Study
07:30

Brain Morphology of Cannabis Users With or Without Psychosis: A Pilot MRI Study

Published on: August 18, 2020

7.8K

Related Experiment Videos

Last Updated: Feb 13, 2026

Three-dimensional Cell Culture Model for Measuring the Effects of Interstitial Fluid Flow on Tumor Cell Invasion
07:41

Three-dimensional Cell Culture Model for Measuring the Effects of Interstitial Fluid Flow on Tumor Cell Invasion

Published on: July 25, 2012

17.1K
Human Neuroendocrine Tumor Cell Lines as a Three-Dimensional Model for the Study of Human Neuroendocrine Tumor Therapy
12:04

Human Neuroendocrine Tumor Cell Lines as a Three-Dimensional Model for the Study of Human Neuroendocrine Tumor Therapy

Published on: August 14, 2012

29.5K
Brain Morphology of Cannabis Users With or Without Psychosis: A Pilot MRI Study
07:30

Brain Morphology of Cannabis Users With or Without Psychosis: A Pilot MRI Study

Published on: August 18, 2020

7.8K

Area of Science:

  • Biophysics
  • Mathematical Biology
  • Cancer Research

Background:

  • Avascular tumor growth dynamics at the tissue scale are complex.
  • Understanding the biomechanical factors influencing tumor morphology is crucial for predicting aggressiveness.

Purpose of the Study:

  • To model and analyze the nonlinear dynamics of avascular tumor growth using a two-fluid flow Stokes model.
  • To investigate the role of viscosity, apoptosis, adhesion, and vascularization in regulating tumor evolution and shape.

Main Methods:

  • Employed a two-fluid flow Stokes model for avascular tumors.
  • Utilized linear morphological stability analysis and 2D boundary-integral simulations.
  • Developed a novel reformulation for efficient numerical solutions.

Main Results:

  • Tumor evolution is governed by parameters including apoptosis, adhesion, vascularization, and viscosity ratio.
  • Nonlinear simulations revealed two distinct tumor shapes based on viscosity: invasive fingers (higher tumor viscosity) and compact invaginations (lower tumor viscosity).
  • Linear theory underpredicts perturbation growth compared to nonlinear simulations.

Conclusions:

  • Tumor biomechanics, particularly viscosity, significantly dictates tumor shape and invasive potential.
  • A positive correlation exists between tumor stiffness (viscosity) and aggressiveness, consistent with experimental observations.
  • The model provides insights into the physical mechanisms driving tumor morphology and progression.