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 D₉₀, rectum and bladder D_1cc and urethra D_0.1cc. 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.

这项工作的目的是为高剂量率 (HDR) 近距离放射治疗治疗计划问题开发一种有效的二次混合整数规划算法，并将该算法集成到基于蒙特卡洛的开源治疗计划软件 RapidBrachyMCTPS 中。混合整数算法对基于剂量体积直方图 (DVH) 的问题产生全局最优解，并且与其他方法不同，它不易受到局部最小值捕获的影响。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 名前列腺癌患者的治疗计划。使用 RapidBrachyMCTPS 计算每个停留位置的剂量分布，其中 A 型不确定性在计划目标体积 (PTV) 内的体素中小于 0.2%。优化过程分为两部分。第一的，数据经过预处理，通过消除对解决方案影响可忽略不计的体素（例如远离驻留位置）来减小问题规模。其次，找到了获得得分最高的计划的最佳停留时间组合。停留位置和剂量体积约束被用作商业混合整数优化器（Gurobi Optimization，Inc.）的输入。评分采用基于惩罚的标准。体素缩减技术成功地将问题大小平均减少了 91%，而没有损失质量。优化过程的预处理平均需要 4 秒，求解全局最大值平均需要 33 秒。总优化时间平均为 37 秒，与已发表文献中报道的约 15 分钟优化时间相比有了很大的改进。D ₉₀，直肠和膀胱D _{1 cc}和尿道D _{0.1 cc}。总之，对于使用基于 DVH 的指标来解决 HDR 近距离放射治疗计划问题，快速混合整数优化比当前混合整数方法快一个数量级。