Application of Mathematical Model of Cancer Treatment by Radiotherapy

Seyed Mehdi Hosseini Motlagh, Faeze Lari Motefaker
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引用次数: 0

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.
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肿瘤放疗治疗数学模型的应用
本研究的目的是实现对控制放射治疗的数学模型的分析,以及实现健康细胞和癌细胞的浓度,以减少治疗时间和减少这种类型治疗对癌症治疗的损害。为了达到这个目的,我们使用了最新的基于Lotka-Volterra竞争方程的放射治疗数学模型和最先进的求解微分方程的解析解之一Adomian分解方法来实现我们的目标。将Adomian分解法的计算应用于控制放射治疗的数学模型中,然后以很好的近似值获得健康细胞和癌细胞的浓度。基于实验案例的健康细胞和癌细胞浓度行为的比较以及基于计算的健康细胞和癌细胞浓度行为的比较表明了工作的正确性。ADM表明,健康细胞和癌细胞在治疗阶段和未治疗阶段的浓度可以有效地改进基于Lotka-Volterra方程的竞争模型的建模,从而减少诊断设备的使用,减少辐射,加快治疗过程,降低患者和政府的治疗成本。
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16
审稿时长
12 weeks
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