Collins-Fekete Charles-Antoine, Brousmiche Sébastien, Hansen David C, Beaulieu Luc, Seco Joao
Département de physique, de génie physique et d'optique et Centre de recherche sur le cancer, Université Laval, Québec, Canada. Département de radio-oncologie et CRCHU de Québec, CHU de Québec, QC, Canada. Department of Radiation Oncology, Francis H. Burr Proton Therapy Center Massachusetts General Hospital (MGH), Boston, MA, United States of America.
Phys Med Biol. 2017 Aug 3;62(17):6836-6852. doi: 10.1088/1361-6560/aa7c42.
The relative stopping power (RSP) uncertainty is the largest contributor to the range uncertainty in proton therapy. The purpose of this work was to develop a systematic method that yields accurate and patient-specific RSPs by combining (1) pre-treatment x-ray CT and (2) daily proton radiography of the patient. The method was formulated as a penalized least squares optimization problem (argmin([Formula: see text])). The parameter A represents the cumulative path-length crossed by the proton in each material, separated by thresholding on the HU. The material RSPs (water equivalent thickness/physical thickness) are denoted by x. The parameter b is the list-mode proton radiography produced using Geant4 simulations. The problem was solved using a non-negative linear-solver with [Formula: see text]. A was computed by superposing proton trajectories calculated with a cubic or linear spline approach to the CT. The material's RSP assigned in Geant4 were used for reference while the clinical HU-RSP calibration curve was used for comparison. The Gammex RMI-467 phantom was first investigated. The standard deviation between the estimated material RSP and the calculated RSP is 0.45%. The robustness of the techniques was then assessed as a function of the number of projections and initial proton energy. Optimization with two initial projections yields precise RSP (⩽1.0%) for 330 MeV protons. 250 MeV protons have shown higher uncertainty (⩽2.0%) due to the loss of precision in the path estimate. Anthropomorphic phantoms of the head, pelvis, and lung were subsequently evaluated. Accurate RSP has been obtained for the head ([Formula: see text]), the lung ([Formula: see text]) and the pelvis ([Formula: see text]). The range precision has been optimized using the calibration curves obtained with the algorithm, yielding a mean [Formula: see text] difference to the reference of 0.11 ±0.09%, 0.28 ± 0.34% and [Formula: see text] in the same order. The solution's accuracy is limited by the assumed HU/RSP bijection, neglecting inherent degeneracy. The proposed formulation of the problem with prior knowledge x-ray CT demonstrates potential to increase the accuracy of present RSP estimates.
相对阻止本领（RSP）的不确定性是质子治疗中射程不确定性的最大贡献因素。本研究的目的是开发一种系统方法，通过结合（1）治疗前的X射线CT和（2）患者的每日质子射线照相，得出准确且针对患者的RSP。该方法被公式化为一个惩罚最小二乘优化问题（求最小值（[公式：见原文]））。参数A表示质子在每种材料中穿过的累积路径长度，通过对HU进行阈值分割来分离。材料的RSP（水等效厚度/物理厚度）用x表示。参数b是使用Geant4模拟生成的列表模式质子射线照相。该问题使用具有[公式：见原文]的非负线性求解器求解。A通过将用三次样条或线性样条方法计算的质子轨迹叠加到CT上来计算。在Geant4中分配的材料的RSP用作参考，同时使用临床HU-RSP校准曲线进行比较。首先对Gammex RMI-467体模进行了研究。估计的材料RSP与计算得到的RSP之间的标准偏差为0.45%。然后根据投影数量和初始质子能量评估了该技术的稳健性。对于330 MeV质子，用两个初始投影进行优化可得到精确的RSP（⩽1.0%）。由于路径估计精度的损失，250 MeV质子显示出更高的不确定性（⩽2.0%）。随后对头部、骨盆和肺部的人体模型进行了评估。对于头部（[公式：见原文]）、肺部（[公式：见原文]）和骨盆（[公式：见原文]）已获得了准确的RSP。已使用该算法获得的校准曲线对射程精度进行了优化，在相同顺序下，与参考值的平均[公式：见原文]差异分别为0.11±0.09%、0.28±0.34%和[公式：见原文]。该解决方案的准确性受到假定的HU/RSP双射的限制，忽略了内在的简并性。所提出的具有先验知识X射线CT的问题公式显示出提高当前RSP估计准确性的潜力。
