放射生物LQ线性二次模型的数理基础及临床意义

摘要

目的:本文拟从对LQ模型提出的数学、物理、数理统计、放射生物学模型的研究分析LQ模型的数理基础和理论背景,系统阐述LQ模型的理论基础,为更好理解并应用放射生物LQ模型提供理论基础,为临床放疗方案改变作参考.方法:从LQ模型的数学公式研究人手,充分发掘LQ模型计算公式得出的数理依据和放射生物学实验结果,分别从LQ模型的N无穷次贝努力实验的泊松概率模型、低LET射线和高LET射线对DNA双链造成击打原理和模型、笛卡尔坐标系和半对数坐标系的应用、细胞存活曲线的计算和表达等几个方面系统阐述LQ模型的理论基础.并研究了α损伤和β的不同数学背景,从射线和细胞作用过程分析人手重新阐述了α、β值的放射生物学意义,同时研究了早晚反正组织中损伤等效剂量计算公式的应用范围.结果:通过对LQ模型分析得到α损伤其实代表了高LET射线与细胞中靶DNA的作用模式,作用概率和辐射场粒子存在一次正相关关系,β是低LET射线与细胞中靶DNA作用的结果,和辐射场中粒子通量存在二次方正相关关系；早晚反应组织等效剂量除了需要满足f＞/(βt/βN)外还需要满足本文(18)式提出的条件.结论:放射生物学LQ模型不单是一个放射生物学模型,其模型得意提出和应用和辐射剂量学、分析数学、数理统计学、生物物理学等学科息息相关,只有深刻理解以上学科在该模型中意义才能正确理解和应用LQ模型.%Objective: This article aims to provide a in-depth explanation and research of the basic theory of LQ model which may help the radiation physician to get a more complete understanding and correspondingly get suggestion when a radiation-therapy schedule should be changed. Methods: We start our research form the mathematical formula of LQ model, to exploit the mathematical base of LQ model based on radiation biology and experimental results respectively, which contains the LQ model of N infinitely Bernoulli trials ( Poisson probability model), low-LET radiation and high-LET radiation caused dou-ble-stranded DNA damage , the application of Cartesian coordinate system and the semi-logarithmic coordinates, the calculation of cell survival curves and expression system. Meanwhile we also study the radiation biological significance of α and β from the role of interaction between radiation Particle and cell. Results: Through the analysis of the LQ model we found that the a dam-age which represents the reaction between high-LET radiation and the target DNA in the cell, there is a positive correlation be-tween probability of radiation particles and the radiation field. The β damage which represents the reaction between low-LET radiation and the target DNA in the cell, there is a quadratic positive correlation between probability of radiation particles andthe radiation field. The Formula must be satisfied asf> √βt/βN and the boundary condition which is proposed in the equation of (18). Conclusions: LQ model and its calculation equation were proposed by Kellerer and Rossi's Cradwick and Leenheuts, which were widely used in radiation biology research and clinical radiation therapy. The theory of LQ model had a profound im-pact on radiation biology research and clinical applications.