Zaghian Maryam, Lim Gino, Liu Wei, Mohan Radhe
Department of Industrial Engineering, University of Houston, Houston, USA.
Department of Radiation Oncology, Mayo Clinic, Phoenix, USA.
J Cancer Ther. 2014 Feb;5(2):198-207. doi: 10.4236/jct.2014.52025.
Prescriptions for radiation therapy are given in terms of dose-volume constraints (DVCs). Solving the fluence map optimization (FMO) problem while satisfying DVCs often requires a tedious trial-and-error for selecting appropriate dose control parameters on various organs. In this paper, we propose an iterative approach to satisfy DVCs using a multi-objective linear programming (LP) model for solving beamlet intensities. This algorithm, starting from arbitrary initial parameter values, gradually updates the values through an iterative solution process toward optimal solution. This method finds appropriate parameter values through the trade-off between OAR sparing and target coverage to improve the solution. We compared the plan quality and the satisfaction of the DVCs by the proposed algorithm with two nonlinear approaches: a nonlinear FMO model solved by using the L-BFGS algorithm and another approach solved by a commercial treatment planning system (Eclipse 8.9). We retrospectively selected from our institutional database five patients with lung cancer and one patient with prostate cancer for this study. Numerical results show that our approach successfully improved target coverage to meet the DVCs, while trying to keep corresponding OAR DVCs satisfied. The LBFGS algorithm for solving the nonlinear FMO model successfully satisfied the DVCs in three out of five test cases. However, there is no recourse in the nonlinear FMO model for correcting unsatisfied DVCs other than manually changing some parameter values through trial and error to derive a solution that more closely meets the DVC requirements. The LP-based heuristic algorithm outperformed the current treatment planning system in terms of DVC satisfaction. A major strength of the LP-based heuristic approach is that it is not sensitive to the starting condition.
放射治疗的处方是根据剂量体积约束（DVC）给出的。在满足DVC的同时解决注量图优化（FMO）问题，通常需要在各种器官上进行繁琐的试错来选择合适的剂量控制参数。在本文中，我们提出了一种迭代方法，使用多目标线性规划（LP）模型来求解子野强度，以满足DVC。该算法从任意初始参数值开始，通过迭代求解过程逐步更新值，朝着最优解前进。该方法通过在危及器官（OAR）保护和靶区覆盖之间进行权衡来找到合适的参数值，以改进解决方案。我们将所提出算法的计划质量和DVC的满足情况与两种非线性方法进行了比较：一种是使用L-BFGS算法求解的非线性FMO模型，另一种是由商业治疗计划系统（Eclipse 8.9）求解的方法。我们从机构数据库中回顾性地选择了5例肺癌患者和1例前列腺癌患者进行本研究。数值结果表明，我们的方法在试图保持相应OAR的DVC得到满足的同时，成功地提高了靶区覆盖以满足DVC。用于求解非线性FMO模型的LBFGS算法在5个测试案例中的3个中成功满足了DVC。然而，除了通过试错手动更改一些参数值以得出更符合DVC要求的解决方案外，非线性FMO模型中没有其他方法可以纠正未满足的DVC。基于LP的启发式算法在DVC满足方面优于当前的治疗计划系统。基于LP的启发式方法的一个主要优点是它对起始条件不敏感。
