Mathematical oncology

Teorell made preliminary efforts to model in a work published 1937

{{cite journal |last=Teorell |first=T. |year=1937 |title=Kinetics of distribution of substances administered to the body, I: The extravascular modes of administration |url=https://www.diva-portal.org/smash/record.jsf?pid=diva2%3A513484&dswid=2674 |journal=Archives Internationales de Pharmacodynamie et de Thérapie |volume=57 |pages=205-225 |via=Digitala Vetenskapliga Arkivet}}}} because of the problem of the time a drug injected exists within the body was an unknown.{{cite book |last1=Bellman |first1=R. E. |last2=Jacquez |first2=J. A. |last3=Kalaba |first3=R. |editor-last=Neyman |editor-first=Jerzy |date=1961 |chapter=Mathematical models of Chemotherapy|chapter-url=https://books.google.com/books?id=owhwipCllgkC&dq=mathematical+cancer+1951&pg=PA57 |title=Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability |location=Berkeley, Los Angeles, London |publisher=University of California Press, Cambridge University Press |isbn= |pages=57, 65}} Modelling by epidemiological data originated in 1954.

Modeling types:{{cite book|last1=Wodarz |first1=Dominik|last2=Komarova|first2=Natalia |year=2014 |chapter=Mathematical modeling of tumorigenesis|chapter-url=https://books.google.com/books?id=90i7CgAAQBAJ&dq=Mathematical+Oncology&pg=PR7 |title=Dynamics of Cancer: Mathematical Foundations of Oncology|url=https://books.google.com/books?id=90i7CgAAQBAJ&q=Mathematical+Oncology |publication-place=New Jersey, London, Singapore, Beijing, Shanghai, Hong Kong, Taipei, Chennai |publisher=World Scientific |page=19|isbn=978-9814566384}}

• epidemiological data
• mechanistical: tumor growth conceptualized from conceptualization of the tumor matter as a type of mechanism
• cancer cell population evolution

Models use ordinary differential equations{{cite journal |last1=Sachs |first1=R.K. |last2=Hlatky |first2=L.R. |last3=Hahnfeldt |first3=P. |title=Simple ODE models of tumor growth and anti-angiogenic or radiation treatment |journal=Mathematical and Computer Modelling |date=June 2001 |volume=33 |issue=12–13 |pages=1297–1305 |doi=10.1016/S0895-7177(00)00316-2 |doi-access=free }} and partial differential equations{{Cite journal|title=A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice|date=2022 |pmc=9145520 |last1=Mirzaei |first1=N. M. |last2=Tatarova |first2=Z. |last3=Hao |first3=W. |last4=Changizi |first4=N. |last5=Asadpoure |first5=A. |last6=Zervantonakis |first6=I. K. |last7=Hu |first7=Y. |last8=Chang |first8=Y. H. |last9=Shahriyari |first9=L. |journal=Journal of Personalized Medicine |volume=12 |issue=5 |page=807 |doi=10.3390/jpm12050807 |doi-access=free |pmid=35629230 }} to represent tumor growth, angiogenesis,{{Cite journal|title=Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data|date=2021 |pmc=8234316 |last1=Hormuth II |first1=DA |last2=Phillips |first2=C. M. |last3=Wu |first3=C. |last4=Lima |first4=E. A. |last5=Lorenzo |first5=G. |last6=Jha |first6=P. K. |last7=Jarrett |first7=A. M. |last8=Oden |first8=J. T. |last9=Yankeelov |first9=T. E. |journal=Cancers |volume=13 |issue=12 |page=3008 |doi=10.3390/cancers13123008 |doi-access=free |pmid=34208448 }} metastasis development,{{Cite journal|title=A Mathematical Framework for Modelling the Metastatic Spread of Cancer|date=March 22, 2019|journal=Bulletin of Mathematical Biology|volume=81|issue=6|doi=10.1007/s11538-019-00597-x|pmc=6503893 |last1=Franssen |first1=L. C. |last2=Lorenzi |first2=T. |last3=Burgess |first3=A. E. |last4=Chaplain |first4=M. A. |pages=1965–2010 |pmid=30903592 }} and treatment responses.

Simulation of cancer behavior potentially reduces the need for early-phase experimental trials.{{Cite web|url=https://www.mdanderson.org/patients-family/diagnosis-treatment/clinical-trials/phases-of-clinical-trials.html|title=Phases of Clinical Trials|website=MD Anderson Cancer Center|publisher=University of Texas}}{{Cite journal|last1=Chambers |first1=RB|date=October 2000|title=The Role of Mathematical Modeling in Medical Research: "Research Without Patients?"|journal=Ochsner Journal|volume= 2 |issue=4|pages=218–223 |pmid=21765699|pmc=3117507|doi-access=}}

Researchers develop models that describe tumor dynamics, the effects of treatment, to remedy possible non-optimal treatment responses supporting the development of more effective treatment protocols.{{Cite journal|last1= Powathil|first1=Gibin G.|last2= Swat|first2=Maciej|last3=Chaplain|first3=Mark A.J. |date=February 2015 |title=Systems oncology: Towards patient-specific treatment regimes informed by multiscale mathematical modelling|journal=Seminars in Cancer Biology|volume=30|issue=|pages=13–20|doi=10.1016/j.semcancer.2014.02.003|issn=1044-579X|arxiv=|bibcode=|s2cid=|doi-access=|pmid=24607841 |hdl=10023/7713 |hdl-access=free}}

Control theory{{Cite journal|title=Optimal Control Theory for Personalized Therapeutic Regimens in Oncology: Background, History, Challenges, and Opportunities|date=2020 |pmc=7290915 |last1=Jarrett |first1=A. M. |last2=Faghihi |first2=D. |last3=Hormuth Da |first3=I. I. |last4=Lima |first4=E. A. |last5=Virostko |first5=J. |last6=Biros |first6=G. |last7=Patt |first7=D. |last8=Yankeelov |first8=T. E. |journal=Journal of Clinical Medicine |volume=9 |issue=5 |page=1314 |doi=10.3390/jcm9051314 |doi-access=free |pmid=32370195 }} and optimization are applied to treatment planning in cancer therapies, particularly in radiotherapy and chemotherapy. By optimizing dose schedules and timing, mathematical oncology aims to maximize therapeutic efficacy while minimizing adverse effects.{{Cite journal|title=Optimizing the future: how mathematical models inform treatment schedules for cancer|date=2022 |pmc=9117454 |last1=Mathur |first1=D. |last2=Barnett |first2=E. |last3=Scher |first3=H. I. |last4=Xavier |first4=J. B. |journal=Trends in Cancer |volume=8 |issue=6|pages= 506–516|doi=10.1016/j.trecan.2022.02.005 |pmid=35277375 }}

Statistical methods can be important for understanding cancer progression, analyzing treatment outcomes, and identifying significant trends in large data sets. Advances in artificial intelligence (AI){{Cite journal|title=Artificial intelligence in oncology|first1=Hideyuki|last1=Shimizu|first2=Keiichi I|last2=Nakayama|date=March 21, 2020|journal=Cancer Science|volume=111|issue=5|pages=1452–1460 |doi=10.1111/cas.14377|pmid=32133724 |pmc=7226189 }} and machine learning{{Cite journal|title=Machine Learning in Oncology: Methods, Applications, and Challenges|date=2020 |pmc=7608565 |last1=Bertsimas |first1=D. |last2=Wiberg |first2=H. |journal=JCO Clinical Cancer Informatics |volume=4 |issue=4 |pages=885–894 |doi=10.1200/CCI.20.00072 |pmid=33058693 }} have further impacted the field. AI algorithms{{Cite journal|title=Artificial intelligence in healthcare: transforming the practice of medicine|first1=Junaid|last1=Bajwa|first2=Usman|last2=Munir|first3=Aditya|last3=Nori|first4=Bryan|last4=Williams|date=July 21, 2021|journal=Future Healthcare Journal|volume=8|issue=2|pages=e188–e194 |doi=10.7861/fhj.2021-0095|pmid=34286183 |pmc=8285156 }} can process larger amounts of patient data and identify patterns that may predict individual responses to treatment, personalizing therapeutic strategies.{{Cite journal|last1=Hesse|first1=Janina |last2= Nelson|first2=Nina|last3=Relógio|first3=Angela |date=March 2024|title=Shaping the future of precision oncology: Integrating circadian medicine and mathematical models for personalized cancer treatment|journal=Current Opinion in Systems Biology|volume=37 |doi=10.1016/j.coisb.2024.100506|doi-access=free}}

AI allows researchers to predict the behavior of individual cells with greater accuracy by integrating diverse types of patient data. AI-driven models can also identify mathematical equations that more precisely reflect tumor growth dynamics, helping researchers uncover relationships between various biological factors more quickly.{{Cite journal|last1= El Naqa|first1=Issam|last2=Karolak|first2=Aleksandra |last3=Luo|first3=Yi |last4=Folio|first4=Les |last5=Tarhini|first5=Ahmad A. |last6=Rollison|first6=Dana |last7=Parodi|first7=Katia |date=8 September 2023|title=Translation of AI into oncology clinical practice|journal=Oncogene|volume=42 |issue=42 |pages=3089–3097 |doi=10.1038/s41388-023-02826-z |issn=|arxiv=|bibcode=|s2cid=|doi-access=|pmid=37684407 }}{{cite web | url=https://www.cancer.gov/research/infrastructure/artificial-intelligence#:~:text=AI%20Tool%20Helps%20Predict%20Responses,are%20used%20to%20guide%20treatment | title=AI and Cancer| publisher=U.S. Department of Health and Human Services: National Cancer Institute| date=30 May 2024 }}

{{notelist}}

{{Reflist}}

• [https://www.moffitt.org/research-science/divisions-and-departments/quantitative-science/integrated-mathematical-oncology/ Moffitt Cancer Center's Integrated Mathematical Oncology Program]
• [https://mathematical-oncology.org/ mathematical-oncology.org]
• {{Cite journal|last1=Cook |first1=P. J. |last2=Doll|first2=Richard |last3=Fellingham|first3=S. A.|author2-link=Richard Doll|date=15 January 1969|title=A mathematical model for the age distribution of cancer in man|journal=International Journal of Cancer|volume=4 |issue=1|pages=93–112 |doi=10.1002/ijc.2910040113| pmid=5346480 }}
• {{Cite journal|last1=Boeryd |first1=B. |last2= Ganelius|first2=T.|last3= Lundin|first3=P.|last4= Mellgren|first4=J. |date=15 September 1966|title=Counting and sizing of tumor metastases in experimental oncology|journal=International Journal of Cancer|volume=1 |issue=5|pages=497–502|doi=10.1002/ijc.2910010509 |pmid=5912537 }}
• {{Cite journal|last1=Iversen|first1=S |date=December 1954 |title=Human Cancer and Age|journal= British Journal of Cancer|volume=8|issue=4|pages=575–584|doi=10.1038/bjc.1954.62|issn=|arxiv=|bibcode=|s2cid=|doi-access=|pmid=14351598 |pmc=2007970 }}
• {{cite journal |last1=Arley |first1=Niels |last2=Iversen |first2=Simon |title=On the Mechanism of Experimental Carcinogenesis: IX. Application of the Hit Theory to Tumours Produced by Ultraviolet Radiation |journal= Acta Pathologica et Microbiologica Scandinavica|date=September 1953 |volume=33 |issue=2 |pages=133–150 |doi=10.1111/j.1699-0463.1953.tb01503.x |pmid=13123901 }}

• [https://www.smb.org/ Society for Mathematical Biology]

Category:Oncology

Category:Mathematics

Category:Medical research

Category:Mathematical and theoretical biology

Category:Systems biology