Wikipedia

User:Isaac Jung/sandbox


1. Introduction

Definition: Overview of what mathematical oncology is, including its role in cancer research and treatment. Mathematical Oncology is a specific branch of oncology[1], the study, diagnosis, and treatment of cancer. Through the use of mathematics, modeling, and simulations, mathematical modeling allows researchers to run experiments about cancer virtually. Computer-based research allows for testing on a number of factors, allowing understanding of how these factors interact with one another.

Scope: The importance and relevance of mathematical approaches in understanding and combating cancer. Mathematical Oncology

Historical Background: A brief history of how mathematical oncology emerged as a distinct field.


2. History of Mathematical Oncology

Early Development: Pioneers in the field, early models, and the integration of mathematics with biology. Ludwig von Bertalanffy studied the organism growth and why the growth eventually stops. He used observations that many metabolic processes correspond to surface area instead of volume with the formula M=kW^⅔. This model could then be applied to tumor growth and helped with the development of mathematical oncology.[2]

Benjamin Gompertz develop a “law of population growth” in which he tried to improve calculations for life annuities. His model of an increasing death rate was taken by biologists to create models of population growth with mechanistic detail.[3]

Richard Sion and Larry Norton suggested that a cancer’s response to therapy is inversely related to the tumor size. This theory is now known as the Norton-Simon hypothesis. It relies upon 1)chemotherapy efficacy is inversely related to per capita growth 2)tumor growth rate decreases in relation to tumor size. The following conclusion from this hypothesis is that cancer treatments should attempt to remove as much of the cancer as quickly as possible so that followup treatments will be increasingly effective. This method was referred to as dose density by Norton and Simon.[4]


Key Milestones: Significant advancements, the evolution of models, and notable contributions to the field.

Notable Researchers: Brief bios of key figures who have significantly impacted mathematical oncology.


3. Core Concepts and Methods

Mathematical Modeling: Overview of deterministic and stochastic models. Differential equations in modeling tumor growth and treatment responses.

Ordinary Differential Equations(ODE)[5] only take the derivative in response to one variable(have one independent variable). For example, an equation that compares the value of an investment over time is an ODE. In this case, time is the independent variable which determines the value of the investment.

Partial Differential Equations(PDE)[6] can have derivatives for multiple variables. In general, these equations are more difficult to solve than ODEs because of the greater number of possible cases. An example of this would be studying population dynamics of a country in relation to the economy and birth/death rate.[7]


Optimization and Control Theory: Application in treatment planning, including radiotherapy and chemotherapy.

Statistical Methods: Use of statistics in understanding cancer progression and treatment outcomes.

Computational Techniques: Algorithms, simulations, and the role of computational power in advancing the field. With recent advancements in Artificial Intelligence, researchers are able to more accurately predict the behavior of individual cells. AI is better at integrating different types of data from patients. In addition, artificial intelligence can be used to find equations that more closely model the behavior of tumor growth. This allows researchers to more quickly identify relationships between different factors.[8]


4. Applications in Cancer Research and Treatment'

Tumor Growth and Progression: Models for tumor growth dynamics, invasion, and metastasis. The Gompertz function[9], originally used to study human populations, was adapted by A.K. Laird to better understand tumor growth.


Treatment Response: Models predicting patient response to various treatments (chemotherapy, immunotherapy, etc.).


Personalized Medicine: The role of mathematical oncology in tailoring treatments to individual patients based on mathematical predictions.

One possible application of mathematical oncology is to personalize cancer treatment for individual patients. By using mathematical models to better understand the biology that influences cancer growth and treatment, physicians may be able to use insert patient data into the model to generate a better treatment plan.


Clinical Trials: How mathematical models are used to design and analyze clinical trials.


5. Interdisciplinary Collaborations

Integration with Biology: Collaboration between mathematicians, biologists, and oncologists. Researchers in Mathematical Oncology will often collaborate with other researchers for data. Scientific research in oncology is an increasingly multidisciplinary effort.[10]


Bioinformatics and Systems Biology: The role of bioinformatics in mathematical oncology.

Medical Physics: Interaction with radiotherapy and imaging techniques.


6. Recent Advances and Current Research

Emerging Trends: New models, techniques, and areas of study (e.g., AI and machine learning in mathematical oncology).

Significant Studies: Overview of recent impactful research papers and findings.

Ongoing Projects: Current large-scale projects and collaborations in the field.


7. Challenges and Future Directions

Modeling Complexity: Challenges in accurately modeling the complexity of cancer.

Translational Barriers: Issues in translating mathematical models into clinical practice. Translating mathematical models to clinical practice is a difficult process. The process of using the data from mathematical models into a FDA approved treatment is difficult, with less than 9% of drugs going from Phase 1 testing to FDA approval.[11] In addition, mathematical models can be swamped by poor quality data which will lead to models that do not represent general oncology trends. When combined with difficulties in identifying significant links between different factors, a lot of research in mathematical oncology goes unused.[12]


Future Research: Potential areas of growth and the future of mathematical oncology.

8. Notable Institutions and Researchers

Leading Research Centers[13]:

Adler Lab - Salt Lake City, UT

Cancitis Research Group - Roskilde, Denmark

Center for Computational Oncology - Austin, TX

Mathematical Oncology and Computational System Biology - Duarte, CA

Department of Evolutionary Theory - Plon, Germany

Fertig Lab - Baltimore, MD

George Research Group - Houston, TX

Hillen Research Group - Edmonton, Canada

Immune biology of MSI cancer - Heidelberg, Germany

In Silico Modeling Group - Nicosia, Cyprus

Innovative Methods of Computing - Dresden, Germany

Janes Lab - Charlottesville, VA

Jenner Lab - Brisbane, Australia

MacLean Lab - LA, CA

MOLAB - Ciudad Real, Spain

Multiscale Modeling of Multicellular Systems - Adu Dhabi, UAE

Noble Group - London, UK

Quantitative and Translational Medicine Laboratory - Montreal, Canada

Quantitative Cancer Control Lab - San Diego, CA

Quantitative Personalized Oncology Lab - Tampa, FL

Theory Division - Cleveland, OH



Prominent Researchers: Profiles of influential researchers and their key publications.


9. Impact on Cancer Treatment

Case Studies: Examples of how mathematical oncology has directly influenced cancer treatment protocols.

Patient Outcomes: Discussion on how mathematical models have impacted patient outcomes.


10. Educational Resources and Training

Academic Programs: Information on educational programs and courses focused on mathematical oncology.

Workshops and Conferences: Overview of key conferences, workshops, and seminars in the field.


11. References

Citations: List of references, including books, journal articles, and reviews. -Rockne, R. C., & Scott, J. G. (2019, April).

-New study shows the rate of drug approvals lower than previously reported. BIO. (n.d.). https://archive.bio.org/media/press-release/new-study-shows-rate-drug-approvals-lower-previously-reported#:~:text=Overall%20success%20rates%20from%20Phase,rate%20of%20one%20in%2030.

-Integrated mathematical oncology. moffitt. (n.d.). https://www.moffitt.org/research-science/divisions-and-departments/quantitative-science/integrated-mathematical-oncology/

-Oncology, M. (n.d.). Mathematical oncology. The Mathematical Oncology Blog. https://mathematical-oncology.org/

-Markowetz, F. (2024, February 28). All models are wrong and yours are useless: Making clinical prediction models impactful for patients. Nature News.

-Eikenberry, S. E. (2016). Introduction to mathematical oncology. Taylor & Francis Inc.

-Adapted for Math 204 at the University of Victoria. (n.d.). Introduction to differential equations. ODEs: Classification of differential equations. https://web.uvic.ca/~tbazett/diffyqs/classification_section.html#:~:text=Ordinary%20differential%20equations%20or%20(ODE,is%20only%20one%20independent%20variable.&text=Partial%20differential%20equations%20or%20(PDE,partial%20derivatives%20of%20several%20variables.

-Ai and cancer. AI and Cancer - NCI. (n.d.). https://www.cancer.gov/research/infrastructure/artificial-intelligence#:~:text=AI%20Tool%20Helps%20Predict%20Responses,are%20used%20to%20guide%20treatment.


12. See Also

Related Topics: Links to related Wikipedia pages (e.g., Cancer Biology, Systems Biology, Bioinformatics, Computational Biology).

Cancer Systems Biology: https://en.wikipedia.org/wiki/Cancer_systems_biology#:~:text=Cancer%20systems%20biology%20encompasses%20the,properties%20at%20multiple%20biological%20scales.

Bioinformatics: https://en.wikipedia.org/wiki/Bioinformatics

Computational Biology: https://en.wikipedia.org/wiki/Computational_biology

Gompertz Function: https://en.wikipedia.org/wiki/Gompertz_function

Ordinary Differential Equation: https://en.wikipedia.org/wiki/Ordinary_differential_equation

Partial Differential Equation: https://en.wikipedia.org/wiki/Partial_differential_equation

Oncology: https://en.wikipedia.org/wiki/Oncology


13. External Links Useful Resources: Links to research centers, online courses, and other relevant websites.




References

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  1. ^ https://en.wikipedia.org/wiki/Oncology
  2. ^ Eikenberry, S. E. (2016). Introduction to mathematical oncology. Taylor & Francis Inc.
  3. ^ Eikenberry, S. E. (2016). Introduction to mathematical oncology. Taylor & Francis Inc.
  4. ^ Eikenberry, S. E. (2016). Introduction to mathematical oncology. Taylor & Francis Inc.
  5. ^ https://en.wikipedia.org/wiki/Ordinary_differential_equation
  6. ^ https://en.wikipedia.org/wiki/Partial_differential_equation
  7. ^ Adapted for Math 204 at the University of Victoria. (n.d.). Introduction to differential equations. ODEs: Classification of differential equations. https://web.uvic.ca/~tbazett/diffyqs/classification_section.html#:~:text=Ordinary%20differential%20equations%20or%20(ODE,is%20only%20one%20independent%20variable.&text=Partial%20differential%20equations%20or%20(PDE,partial%20derivatives%20of%20several%20variables.
  8. ^ https://www.cancer.gov/research/infrastructure/artificial-intelligence#:~:text=AI%20Tool%20Helps%20Predict%20Responses,are%20used%20to%20guide%20treatment.
  9. ^ https://en.wikipedia.org/wiki/Gompertz_function
  10. ^ Integrated mathematical oncology. moffitt. (n.d.). https://www.moffitt.org/research-science/divisions-and-departments/quantitative-science/integrated-mathematical-oncology/
  11. ^ New study shows the rate of drug approvals lower than previously reported. BIO. (n.d.). https://archive.bio.org/media/press-release/new-study-shows-rate-drug-approvals-lower-previously-reported#:~:text=Overall%20success%20rates%20from%20Phase,rate%20of%20one%20in%2030.
  12. ^ Markowetz, F. (2024, February 28). All models are wrong and yours are useless: Making clinical prediction models impactful for patients. Nature News.
  13. ^ -Oncology, M. (n.d.). Mathematical oncology. The Mathematical Oncology Blog. https://mathematical-oncology.org/
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