Daskalov G M, Kirov A S, Williamson J F
Radiation Oncology Center, Mallinckrodt Institute of Radiology, Washington University School of Medicine, St. Louis, Missouri 63110, USA.
Med Phys. 1998 May;25(5):722-35. doi: 10.1118/1.598254.
In brachytherapy treatment planning, the effects of tissue and applicator heterogeneities are commonly neglected due to lack of accurate, general, and fast three-dimensional (3D) dose-computational algorithms. A novel approach, based on analytical calculation of scattered photon fluxes inside and around a disk-shaped heterogeneity, has been developed for use in the three-dimensional scatter-subtraction algorithm. Specifically, our model predicts the central-ray dose distribution for a collimated photon isotropic source or brachytherapy "minibeam" in the presence of a slab of heterogeneous material. The model accounts for the lateral dimensions, location, composition, density, and thickness of the heterogeneity using precalculated scatter-to-primary ratios (SPRs) for the corresponding homogeneous problem. The model is applicable to the entire brachytherapy energy range (25 to 662 keV) and to a broad range of materials having atomic numbers of 13 to 82, densities of 2.7 g.cm-3 (Al) to 21.45 g.cm-3 (Pt) and thicknesses up to 1 mean free path. For this range of heterogeneous materials, the heterogeneity correction factors (HCFs) vary from 0.09 to 0.75. The model underestimates HCF when multiple scattering prevails and overestimates HCF when absorption dominates. However, the analytic model agrees with Monte Carlo photon transport (MCPT) benchmark calculations within 1.8% to 10% for 125I, 169Yb, 192Ir, and 137Cs for a wide variety of materials, with the exception of Ag. For 125I shielded by Ag, where the mean discrepancy can exceed 25%, the error is due to K-edge characteristic x rays originating within the heterogeneity. The proposed approach provides reductions in CPU time required of 5 x 10(4)-10(5) and 100 in comparison with direct MCPT simulation and 1D numerical integration, respectively. The limitations of model applicability, as determined by the physical properties of heterogeneity material and accuracy required, are also discussed.
在近距离放射治疗治疗计划中，由于缺乏准确、通用且快速的三维（3D）剂量计算算法，组织和施源器不均匀性的影响通常被忽略。一种基于对盘状不均匀性内部及周围散射光子通量进行解析计算的新方法已被开发出来，用于三维散射减法算法。具体而言，我们的模型预测了在存在一块异质材料平板的情况下，准直光子各向同性源或近距离放射治疗“微束”的中心射线剂量分布。该模型使用针对相应均匀问题预先计算的散射与原发射线比率（SPR）来考虑不均匀性的横向尺寸、位置、组成、密度和厚度。该模型适用于整个近距离放射治疗能量范围（25至662keV）以及原子序数为13至82、密度为2.7g·cm⁻³（铝）至21.45g·cm⁻³（铂）且厚度达1个平均自由程的广泛材料。对于此范围内的异质材料，不均匀性校正因子（HCF）在0.09至0.75之间变化。当多次散射占主导时，该模型会低估HCF；当吸收占主导时，会高估HCF。然而，对于125I、169Yb、192Ir和137Cs，除了银之外，对于多种材料，该解析模型与蒙特卡罗光子输运（MCPT）基准计算结果的吻合度在1.8%至10%以内。对于由银屏蔽的125I，平均差异可能超过25%，误差是由于在不均匀性内部产生的K边特征x射线所致。与直接MCPT模拟和一维数值积分相比，所提出的方法分别将所需的CPU时间减少了5×10⁴ - 10⁵倍和100倍。还讨论了由不均匀性材料的物理性质和所需精度所决定的模型适用性的局限性。
