1.Key Laboratory of In-fiber Integrated Optics, Ministry Education of China, Harbin Engineering University, Harbin 150001, China 2.Electronic Engineering College, Ministry Education of China, Heilongjiang University, Harbin 150001, China 3.Optical Fiber Sensors Research Centre, University of Limerick, Limerick, Ireland
Fund Project:Project supported by the Natural Science Foundation of Heilongjiang Province, China (Grant No. ZD2019H003), the Joint Research Fund in Astronomy of the National Natural Science Foundation of China and the Chinese Academy of Sciences, China (Grant Nos. U1631239, U1931206), and the Programme of Introducing Talents of Discipline to Universities (Grant No. B13015)
Received Date:26 June 2020
Accepted Date:30 August 2020
Available Online:12 December 2020
Published Online:05 January 2021
Abstract:A algorithm of obtaining absolute dose at each tissue depth only by the mathematical calculation of formula is reported. The algorithm is based on integrating the energy flux of the electron generated by X-ray in the range of irradiation field, and the energy spectrum of ray and the secondary scattered ray are considered in this process. In this algorithm, the water phantom in the irradiation field is divided into several thin layers, and the energy flux of the electrons generated by interaction between the ray and thin layer reaching the calculation point is calculated. Finally, the absolute dose of the calculation point can be obtained by accumulating the energy flux contribution of all thin layers. For the X-ray with continuous energy spectrum, the expected mass attenuation coefficient is calculated for obtaining the photon flux at each depth in this process. The absolute dose calculated by this algorithm is verified by Monte Carlo simulation, and the difference between the algorithm and simulation is compensated for by a dose function about multiple scattering photons, and the function shows fast descent and then slow ascent. It is found that the ratio of the dose caused by backscatter to the surface dose, and the relationship among forward scatter, backward scatter and primary ray, and the relationship between the dose and the depth of the secondary scattered rays show a trend of first rising and then declining, and the depth of the peak value deviates from the position of the thin layer. Three-dimensional energy spectra of the secondary photon and the secondary electron are also compared with each other, and the spectrum is a function of particle flux about particle energy and particle direction. From the perspective of Compton effect, the physical meanings of different positions in the three-dimensional energy spectrum of the two particles are explained. It is found that the difference between algorithm percentage depth dose and simulation percentage depth dose is similar to the difference between small irradiation field percentage depth dose and big irradiation field percentage depth dose from simulation, and it is verified that the difference between algorithm and simulation comes from the increase of scattered rays. Finally, the algorithm is applied to the dose calculation of non-uniform phantom, which can accurately reflect the dose distribution characteristics and have less error. Keywords:radiotherapy/ model/ absolute dose/ Compton effect
图3所示为真实加速器(型号为Varian IX 3937)测量PDD实验数据(experiment data)与基于蒙特卡罗仿真出来PDD数据(Monte Carlo simulation)的对比, 纵坐标为以最大剂量值为单位的归一化剂量(normalized dose), 横坐标为水模体深度(depth). 实验条件为6 MV的X射线、照射野面积为10 cm × 10 cm, 源皮距为100 cm. 在每个深度处两组数据的差异小于 ± 3.6%. 图 3 蒙特卡罗PDD与真实测量数据的对比 Figure3. Comparison of PDD between Monte Carlo simulation and experimental data.
表1不同肺模体密度ρ对应参数kρ和μ0 Table1.Parameters kρ and μ0 of lung phantom densities ρ.
图11所示为4种不同肺密度的PDD曲线, 对比肺模体密度为0.1, 0.2与1 g/cm3时的结果发现, 横向电子不平衡带来的剂量跌落随着密度的降低而增大. 肺模体密度0.1 g/cm3的PDD在第一个水肺交界处(如图11中深度为5 cm处曲线所示)相对深度为10 cm的剂量跌幅约为17%, 密度0.2 g/cm3的剂量跌幅约为5%, 肺模体密度0.4 g/cm3的PDD曲线在10 cm后剂量增长约为4.5%, 这一结果与文献[23]一致. 但在深度6—10 cm处的计算剂量偏低, 与文献[23]差别最大为3%, 这主要是因为算法未考虑到从第一层水模体中进入肺模体的多次散射带来的剂量贡献, 而更小射野散射带来的剂量贡献会更小, 因此图11的计算结果与更小射野的非均匀模体PDD更加接近[24]. 图 11 不同肺密度的水肺水模体的射野中心轴百分深度剂量 Figure11. Percentage depth dose of the central axis of the field of radiation in water-lung-water phantom with different lung densities.
图 12 不同模体深度处的离轴比曲线 (a) 7 cm; (b) 11 cm Figure12. Off-axis ratio curves at different phantom depths: (a) 7 cm; (b) 11 cm.