Carleton Laboratory for Radiotherapy Physics, Department of Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada.
ViewRay Inc, Cleveland, USA.
Phys Med. 2018 Oct;54:179-188. doi: 10.1016/j.ejmp.2018.06.638. Epub 2018 Jul 13.
Classical trajectory Monte Carlo (MC) simulations modelling radiation-induced damage on subcellular length scales ignore quantum effects that may be non-negligible as electron energy decreases below 1 keV. This work investigates quantum mechanical (QM) treatments of low-energy electron transport in condensed media, comparing with classical MC.
QM calculations involve a simplified model of electron transport in water with a plane wave incident on a cylinder ("droplet") consisting of a cluster of point scatterers (positioned randomly but constrained by a minimum separation, d). The system of coupled equations for the electron wavefield incident on each scatterer is solved numerically and results are averaged over many clusters with different point scatterer positions. Average QM cluster cross sections and scattering event densities are compared with analogues computed within the corresponding classical MC model, and relative errors on MC results are calculated.
Differences between QM and MC results for both cluster cross section and scattering event density are sensitive to electron energy (wavelength), structure (d), and single-scatterer elastic/inelastic cross sections. Relative errors on cluster cross sections generally differ from errors on scattering event densities. The introduction of inelastic scatter generally increases relative errors (compared to calculations with the same single-scatterer elastic cross section) with some exceptions. Accounting for structure (d≠0) enhances differences between QM and MC results.
The quantum wave nature of electrons is non-negligible for simulations of low-energy electron transport within small-scale biological targets. The development of more realistic models of electron transport in condensed media is motivated for future work.
经典轨迹蒙特卡罗（MC）模拟在亚细胞尺度上模拟辐射诱导损伤忽略了量子效应，而当电子能量降低到 1keV 以下时，这些量子效应可能是不可忽略的。这项工作研究了低能电子在凝聚介质中的量子力学（QM）传输处理，与经典 MC 进行了比较。
QM 计算涉及水中电子传输的简化模型，平面波入射到由点散射体（随机定位但受最小分离距离 d 限制的）组成的圆柱体（“液滴”）。入射到每个散射体的电子波场的耦合方程组通过数值求解，并对具有不同点散射体位置的许多簇进行平均。平均 QM 簇截面和散射事件密度与在相应的经典 MC 模型中计算的类似物进行比较，并计算 MC 结果的相对误差。
电子能量（波长）、结构（d）和单散射弹性/非弹性截面都对 QM 和 MC 结果在簇截面和散射事件密度上的差异敏感。与散射事件密度的误差相比，簇截面的相对误差通常不同。非弹性散射的引入通常会增加相对误差（与具有相同单散射弹性截面的计算相比），但也有一些例外。考虑到结构（d≠0）增强了 QM 和 MC 结果之间的差异。
对于小尺度生物靶标内低能电子传输的模拟，电子的量子波性质是不可忽略的。未来的工作需要开发更现实的凝聚态介质中电子传输模型。
