Department of Oncology, University of Alberta, 11560 University Ave, Edmonton, Alberta T6G 1Z2, Canada.
Biomed Phys Eng Express. 2020 Feb 17;6(2):025006. doi: 10.1088/2057-1976/ab6e15.
To develop the enabling algorithmic techniques which allow forward-peaked adaptive angular meshing to be compatible with angular advection of magnetic fields within a deterministic Grid Based Boltzmann Solver (GBBS) for MRI-guided radiotherapy, and establish appropriate energy adaptive meshing schemes which minimize total numerical degrees of freedom while preserving high dosimetric accuracy for parallel and perpendicular magnetic fields.
A framework to independently adapt angular mesh resolution and basis function refinement of forward and backscattering hemispheres is developed, uniquely accommodating angular advection introduced by magnetic fields. Upwind stabilization techniques to accurately transfer fluence between hemispheres having different discretization are established. To facilitate oblique beam and magnetic field orientations, cardinal forward-peaked mesh orientations were devised to balance requirements for acyclic space-angle sweep ordering, while ensuring the beam predominantly overlaps the forward hemisphere. Energy-dependent fluence anisotropy is investigated, leading to adaptive angular meshing schemes for parallel and perpendicular magnetic fields. Calculated dose distributions were validated against GEANT4 Monte Carlo calculations on slab geometry and anthropomorphic phantoms.
Forward-peaked and isotropic energy adaptive angular meshing schemes were developed for parallel and perpendicular magnetic fields respectively, which reduce the number of elements solved by 52.8% and 47.7% respectively compared to static discretization using 32 quadratic elements while retaining over 97% of points passing the gamma 1%/1 mm criterion against Monte Carlo.
Techniques to preserve angular upwind-stabilization between hemispheres of a forward-peaked mesh and establish an acyclic directed space-angle sweep graph enabled energy-adaptive meshing schemes to be developed while accurately solving for magnetic fields. This substantially reduced the numerical degrees of freedom while retaining excellent dosimetric agreement with Monte Carlo. These algorithmic underpinnings contribute towards a fast deterministic GBBS for MRI-guided radiotherapy.
开发使前峰自适应角网格与磁共振引导放射治疗中确定性网格基于玻尔兹曼求解器（GBBS）内的角平流磁场兼容的使能算法技术，并建立适当的能量自适应网格方案，在保持对平行和垂直磁场的高剂量准确性的同时最小化总数值自由度。
开发了一个独立适应前向和后向半球角网格分辨率和基函数细化的框架，独特地适应磁场引入的角平流。建立了在上风向稳定技术，以在具有不同离散化的半球之间准确传输剂量。为了便于斜束和磁场方向，设计了基数前峰网格方向，以平衡非循环空间-角度扫描排序的要求，同时确保束主要重叠前半球。研究了能量相关的剂量各向异性，导致用于平行和垂直磁场的自适应角网格方案。计算剂量分布与 GEANT4 蒙特卡罗在平板几何和人体模型上的计算进行了验证。
为平行和垂直磁场分别开发了前峰和各向同性能量自适应角网格方案，与使用 32 个二次元素的静态离散相比，分别减少了 52.8%和 47.7%的求解元素数量，同时保留了超过 97%的通过蒙特卡罗伽玛 1%/1mm 标准的点。
保留前峰网格半球之间角上风稳定的技术并建立非循环有向空间-角度扫描图，使能量自适应网格方案得以开发，同时准确求解磁场。这大大减少了数值自由度，同时保留了与蒙特卡罗非常好的剂量一致性。这些算法基础为磁共振引导放射治疗的快速确定性 GBBS 做出了贡献。
