基于多参数泊松分布的碘粒子放射性计数模型  

A Method of Iodine Particles Radioactivity Counting Based on Multi-parameter Poisson Distribution

作　　者：张敏 王浩聪 王从晓 谷浩 李刚 陈明 胡效坤[2] ZHANG Min;WANG Haocong;WANG Congxiao;GU Hao;LI Gang;CHEN Ming;HU Xiaokun(College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao,Shandong 266590,China;Department of Interventional Radiology,the Affiliated Hospital of Qingdao University,Qingdao,Shandong 266555,China)

机构地区：[1]山东科技大学数学与系统科学学院,山东青岛266590 [2]青岛大学附属医院介入医学中心,山东青岛266555

出　　处：《数学建模及其应用》2022年第3期27-33,共7页Mathematical Modeling and Its Applications

基　　金：山东省自然科学基金(ZR2020MF016,ZR2021MF038);国家重点研发计划-政府间国际科技创新合作-中国和美国政府间合作项目(2019YFE0120100)。

摘　　要：放射性碘125粒子常用于脑部肿瘤的介入治疗,其植入病灶后,利用放射的γ射线破坏病灶部位组织细胞,损坏组织功能,达到杀死肿瘤细胞的目的.如何根据病灶的几何信息和肿瘤恶性程度分级,精准计算植入粒子信息以及它们在肿瘤靶区的放射强度是临床治疗的关键.本文模拟多个碘125粒子在体内的放射性计数值情况,设计多参数可控的泊松分布进行函数拟合计数,基于最小二乘逼近思想,利用L-M方法求解有关参数.数值实验中,通过C++进行程序设计,计算不同活度、数量和位置的放射性粒子的计数值,采用Matlab将数值可视化.研究结果表明可以通过设计粒子分布和数量使其达到模拟治疗的最优效果.Extensive research suggests that radioactive iodine-125(^(125)I)particles are often used in the interventional treatment of brain tumors.After being implanted into the lesions,they can destroy the tissue cells at the lesion site and damage the tissue function to achieve the purpose of killing the tumor cells.A key aspect of clinical treatment is to accurately calculate the information and radioactive intensity of implanted ^(125)I particles according to the nature of the tumor.In this paper,we simulate the radioactive count value of multiple ^(125)I particles in the body and design a multi-parameter controllable Poisson distribution based on the idea of least square approximation for function fitting counting,and then use the L-M method to solve the related parameters.Using C++we are able to calculate the count values of radioactive particles with different activities,numbers and locations,and their values are visualized using Matlab.The results show that the optimal effect of simulated treatment could be achieved by designing the distribution and number of particles.

关 键 词：碘粒子放射性计数 泊松分布 计数建模 可视化模型 

分 类 号：O29[理学—应用数学] R931.5[理学—数学]