Fuchs Hermann, Moser Philipp, Gröschl Martin, Georg Dietmar
Department of Radiation Oncology, Medical University of Vienna/AKH, Vienna, Austria.
Christian Doppler Laboratory for Medical Radiation Research for Radiation Oncology, Medical University of Vienna, Vienna, Austria.
Med Phys. 2017 Mar;44(3):1149-1156. doi: 10.1002/mp.12105. Epub 2017 Feb 28.
To investigate and model effects of magnetic fields on proton and carbon ion beams for dose calculation.
In a first step, Monte Carlo simulations using Gate 7.1/Geant4.10.0.p03 were performed for proton and carbon ion beams in magnetic fields ranging from 0 to 3 T. Initial particle energies ranged from 60 to 250 MeV (protons) and 120 to 400 MeV/u (carbon ions), respectively. The resulting dose distributions were analyzed focusing on beam deflection, dose deformation, as well as the impact of material heterogeneities. In a second step, a numerical algorithm was developed to calculate the lateral beam position. Using the Runge-Kutta method, an iterative solution of the relativistic Lorentz equation, corrected for the changing particle energy during penetration, was performed. For comparison, a γ-index analysis was utilized, using a criteria of 2%/2 mm of the local maximum.
A tilt in the dose distribution within the Bragg peak area was observed, leading to non-negligible dose distribution changes. The magnitude was found to depend on the magnetic field strength as well as on the initial beam energy. Comparison of the 3 T dose distribution with non-B field (nominal) dose distributions, resulted in a γ (mean value of the γ distribution) of 0.6, with 14.4% of the values above 1 and γ % (1% of all points have an equal or higher γ value) of 1.8. The presented numerical algorithm calculated the lateral beam offset with maximum errors of less than 2% with calculation times of less than 5 μs. The impact of tissue interfaces on the proton dose distributions was found to be less than 2% for a dose voxel size of 1 × 1 × 1 mm .
Non-negligible dose deformations at the Bragg peak area were identified for high initial energies and strong magnetic fields. A fast numerical algorithm based on the solution of the energy-corrected relativistic Lorentz equation was able to describe the beam path, taking into account the particle energy, magnetic field, and material.
研究磁场对质子和碳离子束的影响并建立模型用于剂量计算。
第一步，使用Gate 7.1/Geant4.10.0.p03进行蒙特卡罗模拟，针对质子和碳离子束在0至3 T的磁场中。初始粒子能量分别为60至250 MeV（质子）和120至400 MeV/u（碳离子）。分析所得剂量分布，重点关注束流偏转、剂量变形以及材料不均匀性的影响。第二步，开发一种数值算法来计算束流的横向位置。使用龙格 - 库塔方法，对相对论洛伦兹方程进行迭代求解，并针对穿透过程中粒子能量的变化进行修正。为作比较，采用γ指数分析，使用局部最大值的2%/2 mm标准。
在布拉格峰区域内观察到剂量分布倾斜，导致剂量分布变化不可忽略。发现其大小取决于磁场强度以及初始束流能量。将3 T剂量分布与无磁场（标称）剂量分布进行比较，得到γ（γ分布的平均值）为0.6，14.4%的值大于1，γ%（所有点的1%具有相等或更高的γ值）为1.8。所提出的数值算法计算束流横向偏移的最大误差小于2%，计算时间小于5 μs。对于1×1×1 mm的剂量体素大小，发现组织界面对质子剂量分布的影响小于2%。
对于高初始能量和强磁场，在布拉格峰区域发现了不可忽略的剂量变形。一种基于能量修正相对论洛伦兹方程解的快速数值算法能够描述束流路径，同时考虑了粒子能量、磁场和材料。
