In this work, we present a methodology to analytically determine microdosimetric quantities in radioimmunotherapy and targeted radiotherapy with alpha particles. Monte Carlo simulations using the Geant4-DNA toolkit, which provides interaction models at the microscopic level, are performed for monoenergetic alpha particles traversing spherical sites with diameters of 1, 5 and 10 µm. An analytical function is fitted against the data in each case to model the energy imparted by monoenergetic particles to the site, as well as the variance of the distribution of energy imparted. Those models allow us to obtain the mean and dose-mean values of specific energy (z) and lineal energy (y) for polyenergetic arrangements of alpha particles. The energetic spectrum is estimated by considering the distance that each particle needs to travel to reach the sensitive target. We apply this methodology to a simple case in radioimmunotherapy: a spherical cell that has its membrane uniformly covered by ²¹¹At, an alpha emitter, with a spherical target representing the nucleus, placed at the center of the cell. We compare the results of our analytical method with calculations using Geant4-DNA of this specific setup for three nucleus sizes corresponding to our three functions. For nuclei with diameter of 1 µm and 5 µm, all mean and dose-mean quantities for y and z were in an agreement within 4% to Geant4-DNA calculations. This agreement improves to approximately 1% for dose-mean lineal energy and dose-mean specific energy. For the 10-µm-diameter case, discrepancies scale to approximately 9% for mean values and 3% for dose-mean values. Dose-mean values are within Geant4-DNA uncertainties in all cases. Our method provides accurate analytical calculations of dose-mean quantities that may be further employed to characterize radiobiological effectiveness of targeted radiotherapy. The spatial distributions of sources and targets are required to calculate microdosimetric-relevant quantities.

在这项工作中，我们提出了一种方法来分析确定放射免疫疗法和靶向放射疗法中含α粒子的微量剂量。使用Geant4-DNA工具包进行的Monte Carlo模拟，该工具包提供了微观级别的相互作用模型，用于穿越直径为1、5和10 µm球形位置的单能α粒子。在每种情况下，都针对数据拟合分析函数，以对单能粒子向该位置传递的能量以及所传递的能量分布的变化进行建模。这些模型使我们能够获得α粒子的多能排列的比能（z）和线能量（y）的平均值和剂量平均值。通过考虑每个粒子到达敏感目标所需移动的距离来估计高能谱。我们将此方法应用于放射免疫治疗的一个简单案例：球形细胞的膜被²¹¹在一个α发射器上，将一个球形目标表示核，放置在该单元的中心。我们将我们的分析方法的结果与使用此特定设置的Geant4-DNA进行计算的结果进行了比较，以得出对应于我们三个功能的三个核尺寸。对于直径为1 µm和5 µm的原子核，y和z的所有均值和剂量均值在Geant4-DNA计算的4％之内。对于剂量均值线性能量和剂量均值比能量，该一致性提高到大约1％。对于直径为10 µm的情况，平均值的差异约为9％，而剂量平均值的差异约为3％。在所有情况下，剂量均值均在Geant4-DNA不确定性范围内。我们的方法提供了剂量均值的准确分析计算，可进一步用于表征靶向放疗的放射生物学有效性。计算微剂量相关量需要源和目标的空间分布。