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

Cancer Survival Analysis

Cancer Survival Analysis

Cancer survival analysis focuses on quantifying and interpreting the time from a key starting point, such as diagnosis or the initiation of treatment, to a specific endpoint, such as remission or death. This analysis provides critical insights into treatment effectiveness and factors that influence patient outcomes, helping to shape clinical decisions and guide prognostic evaluations. A cornerstone of oncology research, survival analysis tackles the challenges of skewed, non-normally...

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 the relative...

Tumor Progression

Tumor Progression

Tumor progression is a phenomenon where the pre-formed tumor acquires successive mutations to become clinically more aggressive and malignant. In the 1950s, Foulds first described the stepwise progression of cancer cells through successive stages.
Colon cancer is one of the best-documented examples of tumor progression. Early mutation in the APC gene in colon cells causes a small growth on the colon wall called a polyp. With time, this polyp grows into a benign, pre-cancerous tumor. Further...

Modeling with Differential Equations

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

You might also read

Related Articles

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

Sort by

Same journal

Stability and Robustness of a Generalized Pump-Leak Model for Epithelial Vesicles.

Bulletin of mathematical biology·2026

Same journal

Personalized Spatiotemporal Radiotherapy for GBM: A PDE-Constrained Optimization Study.

Bulletin of mathematical biology·2026

Same journal

Global Stability Analysis of a Mathematical Model for the "Shock-and-Kill" Strategy in HIV-1/SIV Brain Infection.

Bulletin of mathematical biology·2026

Same journal

Phylogenetic Network Models as Graphical Models.

Bulletin of mathematical biology·2026

Same journal

Mathematical Modeling Shows that Overall Infection Burden is Reduced More by Vaccines that Decrease Spread or Accelerate Recovery than those that Lower Severe Infections or Death.

Bulletin of mathematical biology·2026

Same journal

Effects of Seasonal Births and Predation on Disease Spread.

Bulletin of mathematical biology·2026

Search research articles

Related Experiment Video

Updated: Jun 24, 2026

Patient-derived Orthotopic Xenograft Models for Human Urothelial Cell Carcinoma and Colorectal Cancer Tumor Growth and Spontaneous Metastasis

Patient-derived Orthotopic Xenograft Models for Human Urothelial Cell Carcinoma and Colorectal Cancer Tumor Growth and Spontaneous Metastasis

Published on: May 12, 2019

A Mathematical Model to Predict Growth and Treatment for UPS Cancer.

¹Stat-Math Unit, Indian Statistical Institute, 203 B.T. Road, 700 108, Kolkata, India. sumitroy_r@isical.ac.in.

Bulletin of Mathematical Biology

|June 23, 2026

Summary

This study introduces a mathematical model for Undifferentiated Pleomorphic Sarcoma (UPS) growth and treatment. The model reveals that tumor recurrence depends on multiple factors including residual disease, immune response, and treatment timing.

Keywords:

Hybrid Systems Mathematical Oncology Optimal Control Surgery Modeling Tumor-Immune Dynamics Undifferentiated Pleomorphic Sarcoma (UPS)

More Related Videos

Competing-Risk Nomogram for Predicting Cancer-Specific Survival in Multiple Primary Colorectal Cancer Patients after Surgery

Competing-Risk Nomogram for Predicting Cancer-Specific Survival in Multiple Primary Colorectal Cancer Patients after Surgery

Published on: September 27, 2024

Related Experiment Videos

Last Updated: Jun 24, 2026

Patient-derived Orthotopic Xenograft Models for Human Urothelial Cell Carcinoma and Colorectal Cancer Tumor Growth and Spontaneous Metastasis

Patient-derived Orthotopic Xenograft Models for Human Urothelial Cell Carcinoma and Colorectal Cancer Tumor Growth and Spontaneous Metastasis

Published on: May 12, 2019

Competing-Risk Nomogram for Predicting Cancer-Specific Survival in Multiple Primary Colorectal Cancer Patients after Surgery

Competing-Risk Nomogram for Predicting Cancer-Specific Survival in Multiple Primary Colorectal Cancer Patients after Surgery

Published on: September 27, 2024

Area of Science:

Mathematical Oncology
Computational Biology
Differential Equations

Background:

Undifferentiated Pleomorphic Sarcoma (UPS) is an aggressive soft tissue sarcoma.
Understanding the dynamics of UPS growth and response to treatment is crucial for improving patient outcomes.

Purpose of the Study:

To develop a comprehensive mathematical model for UPS growth and treatment.
To analyze the model's properties and identify key factors influencing tumor behavior and recurrence.

Main Methods:

A system of nonlinear differential equations was formulated to simulate UPS.
The model incorporates tumor growth, necrosis, surgical resection, postoperative recovery, immune interaction, and radiation therapy.
Optimal control theory was applied to radiation treatment scheduling.

Main Results:

A critical threshold for tumor survival was identified.
The model predicts an inflammatory and proliferative phase during postoperative recovery.
Tumor-immune subsystem equilibrium states and stability were determined.
An optimal "bang-bang" radiation strategy was found.

Conclusions:

Tumor recurrence in UPS is multifactorial, influenced by residual disease, immune status, and treatment timing.
The mathematical model provides insights into UPS dynamics and treatment optimization.
Further research can refine the model for clinical application.