Medical Physics Unit, McGill University, Montreal, Quebec, H4A 3J1, Canada.
Department of Radiation Oncology, Mayo Clinic, Rochester, MN 55905, United States of America.
Phys Med Biol. 2020 Dec 7;65(21):215005. doi: 10.1088/1361-6560/aba317.
The purpose of this work was to develop an efficient quadratic mixed integer programming algorithm for high dose rate (HDR) brachytherapy treatment planning problems and integrate the algorithm into an open-source Monte Carlo based treatment planning software, RapidBrachyMCTPS. The mixed-integer algorithm yields a globally optimum solution to the dose volume histogram (DVH) based problem and, unlike other methods, is not susceptible to local minimum trapping. A hybrid linear-quadratic penalty model coupled to a mixed integer programming model was used to optimize treatment plans for 10 prostate cancer patients. Dose distributions for each dwell position were calculated with RapidBrachyMCTPS with type A uncertainties less than 0.2% in voxels within the planning target volume (PTV). The optimization process was divided into two parts. First, the data was preprocessed, in which the problem size was reduced by eliminating voxels that had negligible impact on the solution (e.g. far from the dwell position). Second, the best combination of dwell times to obtain a plan with the highest score was found. The dwell positions and dose volume constraints were used as input to a commercial mixed integer optimizer (Gurobi Optimization, Inc.). A penalty-based criterion was adopted for the scoring. The voxel-reduction technique successfully reduced the problem size by an average of 91%, without loss of quality. The preprocessing of the optimization process required on average 4 s and solving for the global maximum required on average 33 s. The total optimization time averaged 37 s, which is a substantial improvement over the ∼15 min optimization time reported in published literature. The plan quality was evaluated by evaluating dose volume metrics, including PTV D, rectum and bladder D and urethra D. In conclusion, fast mixed integer optimization is an order of magnitude faster than current mixed-integer approaches for solving HDR brachytherapy treatment planning problems with DVH based metrics.
这项工作的目的是开发一种高效的二次混合整数规划算法，用于高剂量率（HDR）近距离治疗计划问题，并将该算法集成到一个开源的基于蒙特卡罗的治疗计划软件 RapidBrachyMCTPS 中。混合整数算法为基于剂量体积直方图（DVH）的问题提供了全局最优解，与其他方法不同，它不易受到局部最小陷阱的影响。混合线性二次惩罚模型与混合整数规划模型相结合，用于优化 10 例前列腺癌患者的治疗计划。使用 RapidBrachyMCTPS 计算每个驻留位置的剂量分布，A型不确定性小于 0.2%的体素位于计划靶区（PTV）内。优化过程分为两部分。首先，对数据进行预处理，通过消除对解影响可以忽略不计的体素（例如，远离驻留位置）来减小问题的规模。其次，找到获得最高分数的最佳驻留时间组合。驻留位置和剂量体积约束作为输入提供给商业混合整数优化器（Gurobi Optimization，Inc.）。采用基于惩罚的标准进行评分。基于体素的缩减技术成功地将问题规模平均缩小了 91%，而不会降低质量。优化过程的预处理平均需要 4 秒，全局最大值求解平均需要 33 秒。总优化时间平均为 37 秒，与已发表文献中报告的约 15 分钟优化时间相比有了很大的提高。通过评估剂量体积指标，包括 PTV D、直肠和膀胱 D 和尿道 D，评估计划质量。总之，快速混合整数优化比当前基于混合整数的方法在解决基于 DVH 的 HDR 近距离治疗计划问题时快一个数量级。
