CN112326708B - 基于瞬发伽马光谱的人体组织密度和元素组成重建算法 - Google Patents
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Abstract
本发明系统研究了不同元素的光谱组成,从理论上推出了组织密度和元素重建的新算法,解决了氢元素的非线性问题。并验证了三种常见碳氢氧不同组合材料的元素组成和密度,它们是聚甲基丙烯酸甲酯,戊二醇和乙二醇。分子的伽马光谱结构可以分解成其组成元素的伽马光谱的线性和非线性的组合,其组合参数可以通过伽马计数的峰值通过最小二乘法求解,进而确定元素组成以及其密度。
Description
技术领域
粒子治疗,核技术,医学成像,蒙特卡洛技术。
背景技术
由于瞬发伽马是射程验证最有前景的方法,它得以广泛的研究。世界各地的研究组研发了不同的伽马相机,有的可以测量一维的束流射程,有的也可以用来三维成像。有些还进行了临床验证测试。
同时蒙特卡洛方法是研究粒子相互作用的有力工具,新的理论方法或者结构设计都可以用蒙特卡洛程序进行模拟验证。
瞬发伽马光谱还可以用来测量人体组织的元素,但这方面的研究还很少,对碳元素和氧元素的初步研究发现具有很好的线性关系。由于氢元素的中子俘获辐射造成的非线性难题,鲜有对氢元素的研究。
氢原子核的中子俘获辐射
本发明系统研究了不同元素的光谱组成,从理论上推出了组织密度和元素重建的新算法,解决了氢元素的非线性问题。并验证了三种常见碳氢氧不同组合材料的元素组成和密度,它们是聚甲基丙烯酸甲酯,戊二醇和乙二醇,分子结构如图1所示。
发明内容
聚甲基丙烯酸甲酯的缩写是PMMA,它的分子式是C5H8O2,当具有一定能量的质子或离子轰击一个PMMA分子,得到伽马光谱同时如果用质子轰击单个元素的原子核,得到光谱/>和/>那么分子的伽马光谱和元素的光谱有方程(2)所示的关系。
氢原子核的中子俘获辐射有部分的中子是碳元素产生的,有部分是氧元素产生的,因此方程(2)进一步分解成方程(3)的形式。其中的系数表达式如方程(4)和(5)所示。
其中和/>代表碳和氧的中子产生贡献率,/>是氢的增强因子。由于氢的中子俘获只产生2.23MeV的伽马光子,因此可以单独列出。为数学上方便处理,把方程(3)分裂成一个方程组(6)。其中/>表示样品x的伽马光谱,/>表示该光谱在2.23MeV处的计数。
当样品中有M摩尔的分子,则元素的摩尔含量为:MC=M*NC,
MO=M*NO和MH=M*NH。方程(6)两边都乘以摩尔数,得到方程组(7a)
(7b)。
其中对应的系数方程变为(8)和(9)。和/>是每摩尔元素的伽马光谱,/>是每摩尔氢由于碳中子产生的2.23MeV计数,/>是每摩尔氢由于氧中子产生的2.23MeV计数。
由于光谱是连续性的,为了得到数值解,我们取其中的一些特征峰来求解方程(7),特征峰如图2所示。因此需要对(7a)进行离散化,得到矩阵方程(10),优化目标是min(Am-B)。
其中是每摩尔碳和氧的伽马光谱,/>是样品测量得到伽马光谱特征峰计数。用最小二乘法就可以求得元素的摩尔含量/>最后通过方程(7b)求解氢的摩尔含量。
进一步通过测量束流的射程R,得到体积,还可以求解样品的密度。
V=S*R (14)。
如果样品中还有别的元素比如钙,则重复碳和氧的分析,如果增加的元素可以发生中子俘获反应,则重复氢的非线性分析。
算法验证
这里将通过一系列蒙特卡洛仿真实验来验证上述算法。用150MeV的质子轰击一个细长的靶体,长度要比高能量的射程大,一般18cm,半径为2cm。然后用虚拟探测器测量从靶体中出射的所有伽马光子,能量从0-10MeV,能量分辨设置为0.01MeV。如图4所示。
为得到单质的摩尔谱,先用质子轰击一系列碳氢材料组合,得到伽马光谱如图5所示,再除以射程内分子的摩尔数,得到碳元素的摩尔谱,如图6所示。
再用质子轰击一系列氢氧材料组合,得到伽马光子谱如图7所示,再除以射程内分子的摩尔数,得到氧元素的摩尔谱,如图8所示。
从图6和图8的摩尔谱中提取氢的中子俘获辐射伽马峰2.23MeV的摩尔计数,如图9所示,它随着氢含量的增加而非线性增加,然后当氢超过10-12又开始减少。因此可以认为氢含量是2.23MeV光子的增强剂。体现在方程(4)和(5)的增强因子。
最后用质子轰击样品材料聚甲基丙烯酸甲酯,戊二醇和乙二醇,得到相应的伽马光谱和特征峰,如图10所示。这里把特征峰按能量分成几组:全能段包含1.5~7MeV的特征峰;低能段包含1.5~4MeV的特征峰;高能段包含4~7MeV的特征峰;中高能段包含2~7MeV的特征峰。通过求解方程(10),每一组都可以求得元素相应的摩尔含量。
三种样品求解的结果汇总到表1-表3中。可以看到中高能段求得的碳氧比和真实值偏差较小。因此建议用中高能段的特征峰来求解。
表1聚甲基丙烯酸甲酯的碳氧含量
表2戊二醇的碳氧含量
表3乙二醇的碳氧含量
通过求解方程(13)和(15)可以得到氢含量以及样品密度。如表4所示。氢含量由于其非线性难题,最后的偏差还是稍大,但对于氢含量较低的分子,结果符合的比较好。对于三个样品材料,求解的密度都符合的比较好。
表4氢含量求解
用重建算法重新绘制伽马光谱,如图11和图12所示。在各个特征峰处符合的都比较好。因此验证本发明的重建算法的有效性。
附图说明
图1是分子结构图
图2是原理图
图3是PMMA峰值点图
图4是实验几何设置图
图5是碳氢材料组合的伽马光谱图
图6是碳氢材料组合的每摩尔伽马光谱图
图7是氢氧材料组合的伽马光谱图
图8是氢氧材料组合的每摩尔伽马光谱图
图9是氢2.23MeV计数的非线性图
图10是样品材料的伽马光谱以及特征峰图
图11是重建算法得到的伽马光谱0-4MeV图
图12是重建算法得到的伽马光谱4-7MeV图。
Claims (2)
1.基于瞬发伽马光谱的人体组织密度和元素组成重建算法,其特征在于,所述算法的数值求解分子伽马光谱和元素摩尔光谱关系方程(1):
左边第一项是分子伽马光谱,右边第一项是具有线性关系的元素总和伽马谱,右边第二项是具有非线性关系的元素总和伽马谱;光谱关系方程(1)中右边的线性项系数Nk是第k种元素的正实数系数,该种元素不发生中子俘获辐射;非线性项是由于这部分元素发生中子俘获辐射,系数f(x,n)是分子结构和含氢量的非线性函数;氢原子核的中子俘获辐射反应式是
求解方程(1)由以下步骤组成:
步骤1:氢原子核的中子俘获辐射有部分中子是碳元素产生的,有部分是氧元素产生的,因此方程(1)进一步分解成方程(3)的形式;其中的系数表达式是方程(4)和(5)所示:
其中和/>代表碳和氧的中子产生贡献率,/>是氢的增强因子;
步骤2:由于氢的中子俘获只产生2.23MeV的伽马光子,因此可以单独列出;把方程(3)分裂成一个方程组(6):
其中表示样品x的伽马光谱,/>表示该光谱在2.23MeV处的计数;
步骤3:当样品中有M摩尔的分子,则元素的摩尔含量为:MC=M*NC,MO=M*NO和MH=M*NH;方程(6)两边都乘以摩尔数,得到方程组(7a)(7b):
其中对应的系数方程变为(8)和(9);和/>是每摩尔元素的伽马光谱,/>是每摩尔氢由于碳中子产生的2.23MeV计数,/>是每摩尔氢由于氧中子产生的2.23MeV计数;
步骤4:由于光谱是连续性的,为了得到数值解,本发明取其中的一些特征峰来求解方程(7);因此需要对(7a)进行离散化,得到矩阵方程(10),优化目标是min(Am-B):
其中是每摩尔碳和氧的伽马光谱,/>是样品测量得到伽马光谱特征峰计数;用最小二乘法就可以求得元素的摩尔含量/>
步骤5:最后通过方程(7b)求解氢的摩尔含量;
步骤6:进一步通过测量束流的射程R,得到体积,还可以求解样品的密度:
V=S*R (14);
2.根据权利要求1所述的重建算法,其特征在于,如果样品中还有别的元素,这些元素不发生中子俘获,则重复权利要求1中步骤1到步骤4以及步骤6碳和氧的分析求解过程,如果增加的元素可以发生中子俘获反应,则重复权利要求1中步骤1到步骤6中氢的非线性分析求解过程。
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