CELIA & IMB Laboratories, Bordeaux University, Talence, France.
Phys Med Biol. 2010 Jul 7;55(13):3843-57. doi: 10.1088/0031-9155/55/13/018.
High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g.Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung, Compton scattering and the production of delta electrons are added to our model, the computation time will only slightly increase. Its margin of error, on the other hand, will decrease and should be within a few per cent of the actual dose. Therefore, the new model has the potential to become useful for dose calculations in clinical practice.
高能电离辐射是治疗许多癌症的重要手段。电子剂量计算方法可分为半经验模型(如 Fermi-Eyges、卷积叠加)和概率方法(如蒙特卡罗)。第三种剂量计算方法最近才引起医学物理学界的关注。这种方法基于辐射转移的确定性动力学方程。我们推导出一种用于组织中电子输运的宏观偏微分方程模型。该模型在相空间中采用角封闭。对于自由流和各向同性状态,它是精确的。我们通过基于 Berthon 等人(2007 年 J. Sci. Comput. 31 347-89)的新开发的 HLLC 方案对其进行数值求解,该方案在离散水平上精确地保留了分析解的关键特性。我们讨论了来自医学物理学文献的几个测试案例。考虑了具有学术性 Henyey-Greenstein 散射核的测试案例。我们将我们的模型与基准离散坐标解进行了比较。采用简化的电子与组织相互作用模型来计算水模中电子束的剂量,并对脊柱照射进行了计算。在这里,我们的模型与 PENELOPE 蒙特卡罗代码进行了比较。在学术示例中,使用新模型和基准结果计算的通量差异小于 1%。半最大值深度差异小于 0.6%。在与蒙特卡罗的两次比较中,我们的模型给出了定性合理的剂量分布。由于粗糙的相互作用模型,这些迄今为止还没有达到临床实践所需的精度。然而,新模型的计算成本不到蒙特卡罗模拟的十分之一。此外,模拟可以以类似于蒙特卡罗模拟的方式设置。如果向我们的模型添加更详细的效果,例如电子-光子耦合输运、韧致辐射、康普顿散射和 delta 电子的产生,计算时间只会略有增加。另一方面,其误差幅度将减小,应在实际剂量的几个百分点以内。因此,新模型有可能成为临床实践中剂量计算的有用工具。