Perturbative analysis of biological parameters for simulating glioblastoma multiforme using Swanson’s model by the method of symmetries

Authors

DOI:

https://doi.org/10.5902/2179460X87204

Keywords:

Swanson model, Exact solution, Split, Symmetries

Abstract

The present work aims to propose an exact solution through split and symmetries for a model used to simulate the growth rate of cancer cells in a specific region of the human body, it also intends to study the behavior of the tumor cell concentration rate by varying the diffusion and proliferation coefficients randomly within a specified interval. The model utilized to simulate the cell
growth rate is the Swanson model, disregarding the term that follows the treatment and considering a constant diffusion coefficient per region. Attaining the exact solution of the Swanson model can aid in the treatment of specific cancer types, as implementing a more accurate model leads to a decrease in the destruction rate of healthy cells neighboring the cancerous cells.

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Author Biographies

Jorge Luiz de Mello Caurio Junior, Universidade Federal de Pelotas

Holds a degree in Mathematics (2022) from the Federal University of Pelotas, currently studying for a master's degree in the Graduate Program in Mathematical Modeling (PPGMMat) at the Federal University of Pelotas.

Aquiles Almeida Ribeiro, Universidade Federal de Pelotas

Graduated in Mathematics from the Federal University of Pelotas (UFPel).
Master's student in the Graduate Program in Mathematical Modeling (PPGMMAT) at UFPel.

Claudio Zen Petersen, Universidade Federal de Pelotas

Holds a degree in Mathematics (Emphasis on Applied and Computational Mathematics) (2005) from the Federal University of Rio Grande do Sul, a master's degree in Mechanical Engineering from the Federal University of Rio Grande do Sul (2008) in the area of Transport Phenomena and a PhD in Mechanical Engineering from the Federal University of Rio Grande do Sul in the area of Transport Phenomena. He has experience in the area of Applied Mathematics and Physics of Nuclear Reactors, with emphasis on analytical and hybrid solutions, working mainly on the following topics: Neutron Diffusion Equation; Point Kinetics and Neutron Space Kinetics.

Fernanda Tumelero, Universidade Federal do Rio Grande

Professor at the Institute of Mathematics, Statistics and Physics - IMEF, Federal University of Rio Grande - FURG. Post-Doctorate in Mathematical Modeling at UFPel (2023). Postdoctoral Fellow in Engineering at the Graduate Program in Mechanical Engineering at UFRGS (2021). Post-Doctorate in Mathematical Modeling at UFPel (2020). PhD in Mechanical Engineering at the Federal University of Rio Grande do Sul (2019). MSc in Mathematical Modeling at the Federal University of Pelotas (2015). Bachelor's Degree in Mathematics from the Federal Institute of Education, Science and Technology of Rio Grande do Sul - Bento Gonçalves Campus (2013).

References

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Hatzikirou, H., Deutsch, A., Schaller, C., Simon, A., Swanson, K. (2005). Mathematical modelling of glioblastoma tumour development: A review. Mathematical Models and Methods in Applied Sciences, 15, 1779–1794.

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INCA (2023). Como se comportam as células cancerosas?

Rockne, R., Swanson, K. R., Alvord Jr, E. C., Rockhill, J. K. (2009). A mathematical model for brain tumor response to radiation therapy. J Math Biol, 58, 561–578.

Sperotto, F. A. (2007). Soluções de equações advectivo-difusivas utilizando split, série geométrica e transformação de bäcklund. Tese de Doutorado, Universidade Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul.

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Published

2024-11-07

How to Cite

Caurio Junior, J. L. de M., Ribeiro, A. A., Petersen, C. Z., & Tumelero, F. (2024). Perturbative analysis of biological parameters for simulating glioblastoma multiforme using Swanson’s model by the method of symmetries. Ciência E Natura, 46(esp. 1), e87204. https://doi.org/10.5902/2179460X87204

Issue

Vol. 46 No. esp. 1 (2024): ERMAC e ENMC

Section

Special Edition 1

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