# Modeling and simulation of the effect of radiotherapy on nasopharyngeal tumor volume with the fourth order Runge-Kutta Method

Kartika, Devi and Samsu, Farid and Yakin, Khusnul (2021) Modeling and simulation of the effect of radiotherapy on nasopharyngeal tumor volume with the fourth order Runge-Kutta Method. Presented at The International Conference on Engineering, Technology and Social Science (ICONETOS 2020), 31 Oct 2020, Malang, Indonesia.

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## Abstract

Cancer that is benign is often known as a tumor. Currently cancer is a disease that causes death in the world. Cancer
can attack all human organs including the nasopharynx. Nasopharyngeal cancer occupies the top 10 most cancers in
Indonesia. Various methods have been used to treat cancer, one of which is radiotherapy. The dose of radiotherapy
using a fractionated dose and a dose fraction for nasopharyngeal cancer of 1.6 Gy-2.2 Gy. The dosing must consider many things, such as the patient's condition, the duration of treatment and the dose of therapy. Due to the complexity of the metabolic processes of tumor cells, so far it has not been able to reveal the changes in detail. In this research, using mathematical modeling for clinical treatment including cancer treatment. In this study, the modeling used was Gompertz tumor growth and Linear Quadratic (LQ) radiotherapy model. Modeling uses the Rungge-Kutta Order 4 method to solve differential equations and has a higher accuracy than the Heun method. The model was applied to 13 clinical data of nasopharyngeal cancer patients. The results of this study indicate validation with a high level of accuracy using the analysis of the Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). RMSE and MAPE were best in 12 patients with values of 0.96 and 2.31%. All models of the 13 patients were consistent with clinical data. Therefore, this mathematical model can be used as a reference for radiotherapy planning models in hospitals.

Item Type: Conference (Paper) Cancer, Tumor, Radiotherapy, Runge Kutta Order-4, Dose 02 PHYSICAL SCIENCES > 0299 Other Physical Sciences > 029901 Biological Physics02 PHYSICAL SCIENCES > 0299 Other Physical Sciences > 029902 Complex Physical Systems01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics01 MATHEMATICAL SCIENCES > 0103 Numerical and Computational mathematics02 PHYSICAL SCIENCES > 0299 Other Physical Sciences Faculty of Mathematics and Sciences > Department of Physics Khusnul Yakin 08 Jul 2021 12:15