a Departamento de Física - Centro de Investigación en Óptica y Nanofísica, Regional Campus of International Excellence "Campus Mare Nostrum", Universidad de Murcia, E-30100 Murcia, Spain.
b Departament de Física Aplicada, Universitat d'Alacant, E-03080 Alacant, Spain.
Radiat Res. 2018 Sep;190(3):282-297. doi: 10.1667/RR14988.1. Epub 2018 Jul 11.
The number and energy of secondary electrons generated around the trajectories of swift protons interacting with biological materials are highly relevant in proton therapy, due to the prominent role of low-energy electrons in the production of biodamage. For a given material, electron energy distributions are determined by the proton energy; and it is imperative that the distribution of proton energy at depths around the Bragg peak region be described as accurately as possible. With this objective, we simulated the energy distributions of proton beams of clinically relevant energies (50-300 MeV) at depths around the Bragg peak in liquid water and the water-equivalent polymer poly(methyl methacrylate) (PMMA). By using a simple model, this simulation has been conveniently extended to account for nuclear fragmentation reactions, providing depth-dose curves in excellent agreement with available experimental data. Special care has been taken to describe the electronic excitation spectrum of the target, taking into account its condensed phase nature. A predictive formula has been obtained for the mean value and the width of the proton energy distribution at the Bragg peak depth, quantities which are found to grow linearly with the initial energy of the beam, in good agreement with available data. To accurately characterize (in number and energy) the electrons generated around the proton paths, the energy distributions of the latter at each depth have been convoluted with the energy-dependent ionization inverse mean free paths. This results in a number of low-energy electrons around the Bragg peak larger than when only the proton beam average energy at the given depths is considered. The convoluted ionization inverse mean free path closely resembles the Bragg curve shape. The average energy of the secondary electrons is nearly constant (∼55 eV for liquid water and ∼43 eV for PMMA) in the plateau of the Bragg curve, independent of the proton incident energy and suddenly decaying once the Bragg peak is reached. These findings highlight the importance of a precise calculation of the proton beam energy distribution as a function of the target depth to reliably characterize the secondary electrons generated around the Bragg peak region.
在质子治疗中，与生物材料相互作用的快速质子周围轨迹产生的二次电子的数量和能量非常重要，因为低能电子在生物损伤的产生中起着重要作用。对于给定的材料，电子能量分布取决于质子能量；因此，必须尽可能准确地描述布拉格峰区域周围深度处质子能量的分布。出于这个目的，我们模拟了临床上相关能量（50-300 MeV）的质子束在液体水和水等效聚合物聚甲基丙烯酸甲酯（PMMA）中的布拉格峰周围深度处的能量分布。通过使用简单的模型，这种模拟方便地扩展到了核碎裂反应，提供了与现有实验数据非常吻合的深度剂量曲线。特别注意描述目标的电子激发谱，考虑到其凝聚相性质。得到了布拉格峰深度处质子能量分布的平均值和宽度的预测公式，这些值被发现与束的初始能量线性增长，与现有数据非常吻合。为了准确地描述（数量和能量）质子路径周围产生的电子，将后者在每个深度的能量分布与能量相关的电离逆平均自由程进行卷积。这导致在布拉格峰周围产生的低能电子数量大于仅考虑给定深度处质子束平均能量时的数量。卷积的电离逆平均自由程与布拉格曲线形状非常相似。二次电子的平均能量在布拉格曲线的平台区几乎保持不变（对于液体水约为 55 eV，对于 PMMA 约为 43 eV），与质子入射能量无关，一旦达到布拉格峰，就会突然衰减。这些发现强调了精确计算作为目标深度函数的质子束能量分布以可靠地描述布拉格峰区域周围产生的二次电子的重要性。
