Department of Oncology, University of Alberta, 11560 University Ave, Edmonton, Alberta T6G 1Z2, Canada.
Phys Med Biol. 2019 Sep 19;64(18):185012. doi: 10.1088/1361-6560/ab35bc.
Accurate and efficient patient dose calculations are essential for treatment planning in magnetic resonance imaging guided radiotherapy (MRIgRT). Achieving reasonable performance for a space-angle discontinuous finite element method (DFEM) grid based Boltzmann solver (GBBS) with magnetic fields for clinical MRIgRT applications largely depends on how the transport sweep is orchestrated. Compared to classical Discrete Ordinates, DFEM in angle introduces increased angular degrees of freedom and eliminates ray-effect artifacts. However, the inclusion of magnetic fields introduces additional serial dependencies such that parallelization of the space-angle transport sweeps becomes more challenging. Novel techniques for the transport sweep and right-hand source assembly are developed, predicated on limiting the number of bulk material densities modeled in the transport sweep scatter calculations. Specifically, k-means clustering is used to assign sub-intervals of mass-density for each spatial element to execute the scatter-dose calculations using batched multiplication by pre-inverted transport sweep matrices. This is shown to be two orders of magnitude more efficient than solving each elemental system individually at runtime. Even with discrete material densities used in the transport sweep scatter calculations, accuracy is maintained by optimizing the material density assignments using k-means clustering, and by performing the primary photon fluence calculations (ray-tracing) using the underlying continuous density of the computed tomography (CT) image. In the presence of 0.5 T parallel and 1.5 T perpendicular magnetic fields, this approach demonstrates high levels of accuracy with gamma 1%/1 mm passing rates exceeding 94% across a range of anatomical sites compared to GEANT4 Monte Carlo dose calculations which used continuous densities. This deterministic GBBS approach maintains unconditional stability, produces no ray-effect artifacts, and has the benefit of no statistical uncertainty. Runtime on a non-parallelized Matlab implementation averaged 10 min per beam averaging 80 000 spatial elements, paving way for future development based on this algorithmically efficient paradigm.
准确高效的患者剂量计算对于磁共振引导放射治疗（MRIgRT）的治疗计划至关重要。对于临床 MRIgRT 应用中具有磁场的空间角度不连续有限元方法（DFEM）网格的 Boltzmann 求解器（GBBS），要实现合理的性能，在很大程度上取决于如何协调传输扫描。与经典离散坐标相比，DFEM 在角度上引入了更多的角度自由度，并消除了射线效应伪影。然而，磁场的引入增加了额外的串行依赖性，使得空间角度传输扫描的并行化更加具有挑战性。本文开发了传输扫描和右手源组装的新技术，这些技术基于限制在传输散射计算中建模的体材料密度的数量。具体来说，使用 K-均值聚类为每个空间元素分配质量密度的子区间，以便使用预反转的传输扫描矩阵的批乘法执行散射剂量计算。这比在运行时单独求解每个元素系统的效率高两个数量级。即使在传输散射计算中使用离散材料密度，也可以通过使用 K-均值聚类优化材料密度分配以及使用计算断层摄影术（CT）图像的基础连续密度执行初级光子通量计算（射线追踪）来保持准确性。在 0.5 T 平行和 1.5 T 垂直磁场存在的情况下，与使用连续密度的 GEANT4 蒙特卡罗剂量计算相比，该方法在一系列解剖部位上的伽马 1%/1 mm 通过率超过 94%，显示出很高的准确性。这种确定性 GBBS 方法保持无条件稳定性，不会产生射线效应伪影，并且具有无统计不确定性的优势。在非并行化的 Matlab 实现上的运行时间平均为每束 10 分钟，平均每个光束有 80,000 个空间元素，为基于这种算法高效范例的未来发展铺平了道路。
