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

Mathematical Modeling: Problem Solving01:29

Mathematical Modeling: Problem Solving

400
Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
400
Modeling in Therapy01:26

Modeling in Therapy

520
Modeling, a key technique in therapy, uses observational learning to help clients acquire and practice new skills by watching therapists demonstrate desired behaviors. This approach, rooted in Albert Bandura's concept of vicarious learning, plays a significant role in therapeutic interventions for various psychological conditions, including social anxiety, ADHD, and depression.
Participant Modeling
Participant modeling involves therapists demonstrating calm and effective behaviors in...
520
Mathematical Induction01:29

Mathematical Induction

297
Mathematical induction is a structured method of proof used to confirm the truth of statements involving natural numbers. Consider the sum of the first n natural numbers:This formula describes a pattern that appears to hold true as more terms are added. To verify that it is valid for all natural numbers, mathematical induction proceeds in two essential steps. The first is the base case, where the formula is tested for the initial value, typically n = 1. Substituting into both sides confirms the...
297
Fundamental Mathematical Principles in Pharmacokinetics: Mathematical Expressions and Units01:19

Fundamental Mathematical Principles in Pharmacokinetics: Mathematical Expressions and Units

1.6K
Mathematical principles play a crucial role in pharmacokinetics, providing a framework for understanding and quantifying drug distribution and elimination dynamics in the body. By utilizing mathematical expressions and units, pharmacologists can accurately characterize the behavior of drugs, optimize dosing regimens, and predict therapeutic outcomes.
One significant application of mathematics in pharmacokinetics is the characterization of drug distribution through the volume of distribution...
1.6K
Pharmacokinetic Models: Comparison and Selection Criterion01:26

Pharmacokinetic Models: Comparison and Selection Criterion

387
Physiological and compartmental models are valuable tools used in studying biological systems. These models rely on differential equations to maintain mass balance within the system, ensuring an accurate representation of the dynamic processes at play.
Physiological models take a detailed approach by considering specific molecular processes. They can predict drug distribution, metabolism, and elimination changes, providing a comprehensive understanding of how drugs interact with the body.
387
Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs01:21

Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs

3.2K
The fundamental mathematical principles, such as calculus and graphs, play crucial roles in analyzing drug movement and determining pharmacokinetic parameters. Differential calculus examines rates of change and helps to determine the dissolution rate of drugs in biofluids, as well as how drug concentrations change over time. For instance, it can help calculate the rate of elimination of a drug from the body based on its concentration-time profile.
On the other hand, integral calculus focuses on...
3.2K

You might also read

Related Articles

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

Sort by
Same author

The Use of Radiotherapy in the Cure of Different Cancers - Further Results From the FORTY (Favourable Outcomes From RadioTherapY) Project.

Clinical oncology (Royal College of Radiologists (Great Britain))·2025
Same author

Patient Experiences of Using Wearable Health Monitors During Cancer Treatment: A Qualitative Study.

Clinical oncology (Royal College of Radiologists (Great Britain))·2024
Same author

Characterisation of the UK high energy proton research beamline for high and ultra-high dose rate (FLASH) irradiation.

Biomedical physics & engineering express·2023
Same author

Assessing Equity of Access to Proton Beam Therapy: A Literature Review.

Clinical oncology (Royal College of Radiologists (Great Britain))·2023
Same author

An Update to the Malthus Model for Radiotherapy Utilisation in England.

Clinical oncology (Royal College of Radiologists (Great Britain))·2022
Same author

Clinically relevant nanodosimetric simulation of DNA damage complexity from photons and protons.

RSC advances·2022
Same journal

Research Trends in Physical Activity and Breast Cancer: A 25-Year Bibliometric Analysis (2000-2025).

Clinical oncology (Royal College of Radiologists (Great Britain))·2026
Same journal

Concordance Between Planned and Delivered treatment for Head and Neck Cancer Patients Treated With Curative Intent: A Real-World Comparison of Under 70-year-olds With 70-year-olds and Over.

Clinical oncology (Royal College of Radiologists (Great Britain))·2026
Same journal

A Novel Technique for Pain Management to Deliver a Course of Palliative Radiotherapy.

Clinical oncology (Royal College of Radiologists (Great Britain))·2026
Same journal

Broad-Spectrum Antibiotics are Associated with worse Survival After Radical Treatment for Glioblastoma Multiforme: A Multicentre Study.

Clinical oncology (Royal College of Radiologists (Great Britain))·2026
Same journal

Exploring the Need for Plan Adaptation in Robustly Optimised Head and Neck Intensity Modulated Proton Therapy: A Dosimetric Perspective From Initial Institutional Experience.

Clinical oncology (Royal College of Radiologists (Great Britain))·2026
Same journal

Lifting the Lid on Best Practice in a Case of Oligometastatic Breast Cancer.

Clinical oncology (Royal College of Radiologists (Great Britain))·2026
See all related articles

Related Experiment Video

Updated: Feb 14, 2026

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies
08:34

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies

Published on: February 6, 2019

21.2K

Mathematical Modelling for Patient Selection in Proton Therapy.

T Mee1, N F Kirkby2, K J Kirkby2

  • 1Division of Cancer Sciences, School of Medical Sciences, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, UK; NIHR Manchester Biomedical Research Centre, Manchester University, Manchester Academic Health Science Centre, Manchester, UK; The Christie NHS Foundation Trust, Manchester, UK.

Clinical Oncology (Royal College of Radiologists (Great Britain))
|February 18, 2018
PubMed
Summary
This summary is machine-generated.

Mathematical modeling aids in patient selection and service demand prediction for proton beam therapy (PBT), a new cancer treatment with limited clinical evidence. Various techniques are used, with comprehensive models expected as more PBT data emerges.

Keywords:
Discrete event simulationNTCPmathematical modellingpatient selectionproton therapy

More Related Videos

Functional Characterization of Na+/H+ Exchangers of Intracellular Compartments Using Proton-killing Selection to Express Them at the Plasma Membrane
07:38

Functional Characterization of Na+/H+ Exchangers of Intracellular Compartments Using Proton-killing Selection to Express Them at the Plasma Membrane

Published on: March 30, 2015

9.7K
Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
20:36

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

9.2K

Related Experiment Videos

Last Updated: Feb 14, 2026

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies
08:34

Proton Therapy Delivery and Its Clinical Application in Select Solid Tumor Malignancies

Published on: February 6, 2019

21.2K
Functional Characterization of Na+/H+ Exchangers of Intracellular Compartments Using Proton-killing Selection to Express Them at the Plasma Membrane
07:38

Functional Characterization of Na+/H+ Exchangers of Intracellular Compartments Using Proton-killing Selection to Express Them at the Plasma Membrane

Published on: March 30, 2015

9.7K
Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
20:36

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

Published on: July 4, 2007

9.2K

Area of Science:

  • Oncology
  • Medical Physics
  • Health Services Research

Background:

  • Proton beam therapy (PBT) is an emerging cancer treatment modality.
  • The clinical evidence base for PBT is currently limited.
  • Predicting patient eligibility and service demand for PBT is challenging.

Purpose of the Study:

  • To explore the role of mathematical modeling in PBT.
  • To identify current modeling techniques used in PBT.
  • To forecast future developments in PBT modeling.

Main Methods:

  • Review of mathematical and statistical modeling techniques.
  • Discussion of discrete event simulation, normal tissue complication probability (NTCP), quality-adjusted life-years (QALYs), and Markov Chain models.
  • Analysis of the current landscape of PBT modeling approaches.

Main Results:

  • Mathematical modeling assists in patient selection for PBT.
  • Modeling techniques help predict the demand for PBT services.
  • No single modeling technique currently dominates the field.

Conclusions:

  • Mathematical models are valuable tools for optimizing PBT implementation.
  • The development of comprehensive PBT models is ongoing.
  • Future models will likely be less reliant on specific radiotherapy technologies as PBT evidence grows.