Solução do modelo de reação-difusão de Swanson via Split e simetrias para simulação da concentração celular do glioblastoma multiforme

Abstract

The present work intends to propose an exact solution via Split and symmetries for a model used to simulate the growth rate of cancer cells in a specific region of the human body. The model employed is Swanson’s model, considering a constant diffusion coefficient and with the term related to attenuation resulting from therapies. This model has predominantly been solved numerically. Obtaining the exact solution of the Swanson model can assist in treating certain types of cancer, as implementing a more precise model allows for simulating different real scenarios, thereby aiding in tumor treatment. The proposed solution is free from any errors inherent in numerical methods, operator approximations, residues resulting from series approximations, and does not require verifying its convergence. It is also noted that due to the nature of the solution, computational implementation is simple and consequently low computational cost. Additionally, it is observed that the superposition of solutions demonstrates adaptability to various boundary conditions. Finally, a qualitative and quantitative analysis of the obtained results is conducted, demonstrating the influence of the treatment on tumor cell concentration.