A Survey of Mathematical Models of Cancer Growth and
Therapies

Worrawimol Chareontummasathit

doi:https://doi.org/10.14445/22315373/IJMTT-V69I8P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 8 | Year 2023 | Article Id. IJMTT-V69I8P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I8P507

A Survey of Mathematical Models of Cancer Growth and Therapies

Worrawimol Chareontummasathit

Received	Revised	Accepted	Published
15 Jun 2023	30 Jul 2023	14 Aug 2023	30 Aug 2023

Abstract

Mathematical modeling is a well-known powerful tool for testing hypotheses in deep mechanisms to understand chemistry, physics, and biology research areas. Over the past decades, the number of mathematical models in cancer research has increased development because of the high – performance of computers with high technologies. However, clinical data from cancer laboratories and cancer treatments are still a golden key for cancer modeling. This review article will show compositions from some of the various mathematical models both discrete and continuous dynamical systems to predict cancer growth and therapies.

Keywords

Mathematical model, Cancer growth and treatment model, Ordinary differential equations.

References

[1] H. P. Greenspan, “Models for the Growth of a Solid Tumor by Diffusion,” Studies in Applied Mathematics, vol. 51, no. 4, pp. 317-340, 1972.
[CrossRef] [Google Scholar] [Publisher Link]
[2] J. E. Till, E. A. McCulloch, and L. Siminovitch, “A Stochastic Model of Stem Cell Proliferation, Based on the Growth of Spleen Colony– Forming Cells,” Proceedings of the National Academy of Sciences, vol. 51, no. 1, pp. 29-36, 1964.
[CrossRef] [Google Scholar] [Publisher Link]
[3] An-Shen Qi et al., “A Cellular Automaton Model of Cancerous Growth,” Journal of Theoretical Biology, vol. 161, no. 1, pp. 1-12, 1993.
[CrossRef] [Google Scholar] [Publisher Link]
[4] Ankana Boondirek, and Wannapong Triampo, “Cancer Research: Computer Simulation of Tumor Growth with Immune Response,” Naresuan University Journal: Science and Technology, vol. 17, no. 3, pp. 196-200, 2009.
[Google Scholar] [Publisher Link]
[5] Saowaros Srisuk, and Ankana Boondirek, “A Stochastic Cellular Automata Model for Avascular Tumor Growth with Surveillance of an Immune Response Against the Tumorous Cells: on a Cubic Lattice,” Burapha Science Journal, vol. 25, no. 1, pp. 400-415, 2020.
[Google Scholar] [Publisher Link]
[6] Silvio C. Ferreira, Marcelo Lobato Martins, and M. J. Vilela, “Reaction-Diffusion Model for the Growth of Avascular Tumor,” Physical Review E, vol. 65, 2002.
[CrossRef] [Google Scholar] [Publisher Link]
[7] Silvio C. Ferreira, Marcelo Lobato Martins, and M. J. Vilela, “Morphology Transitions Induced By Chemotherapy in Carcinomas in Situ,” Physical Review E, vol. 67, 2003.
[CrossRef] [Google Scholar] [Publisher Link]
[8] D. G. Mallet, and L. G. De Pillis, “A Cellular Automata Model of Tumor-Immune System Interactions,” Journal of Theoretical Biology, vol. 239, no. 3, pp. 334-350, 2006.
[CrossRef] [Google Scholar] [Publisher Link]
[9] Peter S. Kim et al., “Quantitative Impact of Immunomodulation Versus Oncolysis with Cytokine-Expressing Virus Therapeutics,” Mathematical Biosciences and Engineering, vol. 12, no. 4, pp. 841-858, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Zachary Abernathy, Kristen Abernathy, and Jessica Stevens, “A Mathematical Model for Tumor Growth and Treatment using Virotherapy,” AIMS Mathematics, vol. 5, no. 5, pp. 4136-4150, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Gregory Belostotski, “A Control Theory Model for Cancer Treatment by Radiotherapy” International Journal of Pure and Applied Mathematics, vol. 25, no. 4, pp. 447-480, 2005.
[Google Scholar] [Publisher Link]
[12] Zijian Liu, and Chenxue Yang, “A Mathematical Model of Cancer Treatment by Radiotherapy,” Computational and Mathematical Methods in Medicine, pp. 1-12, 2014.
[CrossRef] [Google Scholar] [Publisher Link]
[13] Ophir Nave, “A Mathematical Model for Treatment using Chemo-Immunotherapy,” Heliyon, vol. 8, no. 4, pp. 1-16, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[14] E. A. Reis, L. B. L. Santos, and S. T. R. Pinho, “A Cellular Automata Model for Avascular Solid Tumor Growth Under the Effect of Therapy,” Physica A: Statistical Mechanics and its Applications, vol. 388, no. 7, pp. 1303-1314, 2009.
[CrossRef] [Google Scholar] [Publisher Link]
[15] Fateme Pourhasanzade, and S. H. Sabzpoushan “A Cellular Automata Model of Chemotherapy Effects on Tumour Growth: Targeting Cancer and Immune Cells,” Mathematical and Computer Modelling of Dynamical Systems, vol. 25, no. 1, pp. 63-89, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[16] Hang Xie et al., “Modelling Three-Dimensional Invasive Solid Tumor Growth in Heterogeneous Microenvironment Under Chemotherapy,” PLOS ONE, vol. 13, no. 10, pp. 1-26, 2018.
[CrossRef] [Google Scholar] [Publisher Link]

Citation :

Worrawimol Chareontummasathit, "A Survey of Mathematical Models of Cancer Growth and Therapies," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 8, pp. 55-61, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I8P507