Numerical investigation of treated brain glioma model using a two-stage successive over-relaxation method. (February 2023)

• Record Type: Journal Article
• Authors: Hussain, Abida; Muthuvalu, Mohana Sundaram; Faye, Ibrahima; Zafar, Mudasar; Inc, Mustafa; Afzal, Farkhanda; Iqbal, Muhammad Sajid
• Is Part Of: Computers in biology and medicine. Volume 153(2023)
• Publication Date: 2023-02
• Subjects: Brain tumor modeling -- Two-stage successive over-relaxation -- Two-stage Gauss-Seidel -- Gauss-Seidel -- Glioma; Medicine -- Data processing -- Periodicals; Biology -- Data processing -- Periodicals; 610.285
• DOI: 10.1016/j.compbiomed.2022.106429
• Languages: English
• ISSNs: 0010-4825

Abstract

Abstract: A brain tumor is a dynamic system in which cells develop rapidly and abnormally, as is the case with most cancers. Cancer develops in the brain or inside the skull when aberrant and odd cells proliferate in the brain. By depriving the healthy cells of leisure, nutrition, and oxygen, these aberrant cells eventually cause the healthy cells to perish. This article investigated the development of glioma cells in treating brain tumors. Mathematically, reaction-diffusion models have been developed for brain glioma growth to quantify the diffusion and proliferation of the tumor cells within brain tissues. This study presents the formulation the two-stage successive over-relaxation (TSSOR) algorithm based on the finite difference approximation for solving the treated brain glioma model to predict glioma cells in treating the brain tumor. Also, the performance of TSSOR method is compared to the Gauss-Seidel (GS) and two-stage Gauss-Seidel (TSGS) methods in terms of the number of iterations, the amount of time it takes to process the data, and the rate at which glioma cells grow the fastest. The implementation of the TSSOR, TSGS, and GS methods predicts the growth of tumor cells under the treatment protocol. The results show that the number of glioma cells decreased initially and then increased gradually by the next day. The computational complexity analysis is also used and concludes that the TSSOR method is faster compared to the TSGS and GS methods. According to the results of the treated glioma development model, the TSSOR approach reduced the number of iterations by between 8.0 and 71.95%. In terms of computational time, the TSSOR approach is around 1.18–76.34% faster than the TSGS and GS methods. Highlights: The development of glioma cells was investigated in the treatment of brain tumors. To predict glioma cells in the treatment of brain tumor, the formulation of a two-stage sequential hyperrelaxation algorithm based on the finite difference approach to solve the treated brain glioma model is presented. The performance of the TSSOR method was compared with the Gauss-Seidel (GS) and two-stage Gauss-Seidel methods (TSGS) in terms of the number of iterations, the time taken to process the data, and the data processing speed. The computational complexity analysis is also used and it is concluded that the TSSOR method is faster than the TSGS and GS methods.