Application of Mathematical Model of Cancer Treatment by Radiotherapy

Abstract

The aim of this study is achieve an analysis of the mathematical model governing radiotherapy as well as to achieve the concentration of healthy and cancerous cells to reduce the length of treatment and less damage to cancer treatment by this type of therapy. In order to obtain this, we used the latest mathematical radiotherapy model based on the Lotka-Volterra competitive equations and the Adomian decomposition method that is the one of the most advanced analytical solutions to solve differential equations to attain our goal. The calculation of the Adomian decomposition method was applied to the mathematical model governing radiotherapy, and then the concentration of healthy and cancerous cells was achieved with a very good approximation. Comparison of the behavior of healthy and cancerous cells concentrations based on experimental cases and the behavior of healthy and cancerous cells concentrations based on computations express the correctness of the work. ADM indicates the concentration of healthy and cancerous cells during the treatment stage and the no treatment stage can be effective in improving the modeling based on the competitive model of the Lotka-Volterra equations, which results in the reduction of the use of diagnostic devices, less radiation, the faster treatment process and decreasing the cost of treatment for patients and governments.