Department of Radiation Oncology, Hospital of The University of Pennsylvania, Philadelphia, PA, USA.
Department of Atomic, Molecular and Nuclear Physics, Universidad de Sevilla, Seville, Spain.
Med Phys. 2019 Sep;46(9):4204-4214. doi: 10.1002/mp.13673. Epub 2019 Jul 20.
This work introduces the concept of segment-averaged linear energy transfer (LET) as a new approach to average distributions of LET of proton beams based on a revisiting of microdosimetry theory. The concept of segment-averaged LET is then used to generate an analytical model from Monte Carlo simulations data to perform fast and accurate calculations of LET distributions for proton beams.
The distribution of energy imparted by a proton beam into a representative biological structure or site is influenced by the distributions of (a) LET, (b) segment length, which is the section of the proton track in the site, and (c) energy straggling of the proton beam. The distribution of LET is thus generated by the LET of each component of the beam in the site. However, the situation when the LET of each single proton varies appreciably along its path in the site is not defined. Therefore, a new distribution can be obtained if the particle track segment is decomposed into smaller portions in which LET is roughly constant. We have called "segment distribution" of LET the one generated by the contribution of each portion. The average of that distribution is called segment-averaged LET. This quantity is obtained in the microdosimetry theory from the average and standard deviation of the distributions of energy imparted to the site, segment length, and energy imparted per collision. All this information is calculated for protons of clinically relevant energies by means of Geant4-DNA microdosimetric simulations. Finally, a set of analytical functions is proposed for each one of the previous quantities. The presented model functions are fitted to data from Geant4-DNA simulations for monoenergetic beams from 100 keV to 100 MeV and for spherical sites of 1, 5, and 10 μm in diameter.
The average differences along the considered energy range between calculations based on our analytical models and MC for segment-averaged dose-averaged restricted LET are -0.2 ± 0.7 keV/μm for the 1 μm case, 0.0 ± 0.9 keV/μm for the 5 μm case, and -0.3 ± 1.1 keV/μm for the 10 μm case, respectively. All average differences are below the average standard deviation (1σ) of the MC calculations.
A new way of averaging LET for a proton beam is performed to incorporate the effects produced by the variation of stopping power of each individual proton along microscopic biological structures. An analytical model based on MC simulations allows for fast and accurate calculations of segment-averaged dose-averaged restricted LET for proton beams, which otherwise would need to be calculated from exhaustive MC simulations of clinical plans.
本研究通过重新审视微剂量学理论，提出了一种基于分段平均线性能量传递（LET）的新方法，用于平均质子束的 LET 分布。然后，我们使用分段平均 LET 的概念从蒙特卡罗模拟数据中生成一个分析模型，以快速准确地计算质子束的 LET 分布。
质子束在代表性生物结构或部位中传递的能量分布受到以下三个分布的影响：（a）LET，（b）段长度，即质子在部位中的轨迹段，以及（c）质子束的能量离散度。因此，LET 分布是由束中每个成分的 LET 生成的。然而，当质子在部位中的路径上的 LET 变化显著时，情况并不明确。因此，如果将粒子轨迹段分解为 LET 大致恒定的较小部分，可以得到新的分布。我们将 LET 的“分段分布”称为由每个部分的贡献生成的分布。该分布的平均值称为分段平均 LET。在微剂量学理论中，该量是通过对赋予部位的能量分布、段长度和每次碰撞赋予的能量的平均值和标准偏差来获得的。所有这些信息都是通过 Geant4-DNA 微剂量模拟计算得到的，用于临床相关能量的质子。最后，为每个先前的量提出了一组分析函数。为从 100keV 到 100MeV 的单能束和直径为 1、5 和 10μm 的球形部位，提出了基于蒙特卡罗模拟的模型函数。
在考虑的能量范围内，基于我们的分析模型和 MC 计算的分段平均剂量平均受限 LET 的平均差异分别为 1μm 情况下为-0.2±0.7keV/μm，5μm 情况下为 0.0±0.9keV/μm，10μm 情况下为-0.3±1.1keV/μm。所有平均差异均低于 MC 计算的平均标准偏差（1σ）。
为了纳入每个质子在微观生物结构中停止能力变化产生的影响，对质子束的 LET 进行了新的平均处理。基于 MC 模拟的分析模型允许快速准确地计算质子束的分段平均剂量平均受限 LET，否则需要从临床计划的详尽 MC 模拟中计算。
