Department of Radiation Oncology, Stanford University, Stanford, CA 94305, USA.
Phys Med Biol. 2012 Jul 7;57(13):4139-53. doi: 10.1088/0031-9155/57/13/4139. Epub 2012 Jun 8.
Intensity modulated radiation therapy (IMRT) inverse planning using total-variation (TV) regularization has been proposed to reduce the complexity of fluence maps and facilitate dose delivery. Conventionally, the optimization problem with L-1 norm is solved with quadratic programming (QP), which is time consuming and memory expensive due to the second-order Newton update. This study proposes to use a new algorithm, template for first-order conic solver (TFOCS), for fast and memory-efficient optimization in IMRT inverse planning. The TFOCS utilizes dual-variable updates and first-order approaches for TV minimization without the need to compute and store the enlarged Hessian matrix required for Newton update in the QP technique. To evaluate the effectiveness and efficiency of the proposed method, two clinical cases were used for IMRT inverse planning: a head and neck case and a prostate case. For comparison, the conventional QP-based method for the TV form was adopted to solve the fluence map optimization problem in the above two cases. The convergence criteria and algorithm parameters were selected to achieve similar dose conformity for a fair comparison between the two methods. Compared with conventional QP-based approach, the proposed TFOCS-based method shows a remarkable improvement in computational efficiency for fluence map optimization, while maintaining the conformal dose distribution. Compared with QP-based algorithms, the computational speed using TFOCS for fluence optimization is increased by a factor of 4 to 6, and at the same time the memory requirement is reduced by a factor of 3 to 4. Therefore, TFOCS provides an effective, fast and memory-efficient method for IMRT inverse planning. The unique features of the approach should be particularly important in inverse planning involving a large number of beams, such as in VMAT and dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT).
基于全变差（Total Variation, TV）正则化的强度调制放射治疗（Intensity Modulated Radiation Therapy, IMRT）逆向计划已被提出，以降低通量图的复杂性并促进剂量传递。传统上，使用二次规划（Quadratic Programming, QP）解决 L-1 范数优化问题，由于二阶牛顿更新，该方法耗时且内存昂贵。本研究提出使用新算法，即模板一阶锥规划求解器（Template for First-Order Conic Solver, TFOCS），在 IMRT 逆向计划中实现快速高效的优化。TFOCS 利用对偶变量更新和一阶方法进行 TV 最小化，而无需计算和存储 QP 技术中牛顿更新所需的扩展 Hessian 矩阵。为了评估所提出方法的有效性和效率，使用两个临床病例进行 IMRT 逆向计划：头颈部病例和前列腺病例。为了进行比较，采用基于传统 QP 的方法来解决上述两个病例中的通量图优化问题。选择收敛标准和算法参数，以实现两种方法之间公平比较的相似剂量一致性。与基于传统 QP 的方法相比，所提出的基于 TFOCS 的方法在通量图优化的计算效率方面有显著提高，同时保持了剂量的一致性。与基于 QP 的算法相比，使用 TFOCS 进行通量优化的计算速度提高了 4 到 6 倍，同时内存需求降低了 3 到 4 倍。因此，TFOCS 为 IMRT 逆向计划提供了一种有效、快速和节省内存的方法。该方法的独特特征在涉及大量射束的逆向计划中尤为重要，例如在容积调强弧形治疗（Volumetric Modulated Arc Therapy, VMAT）和密集角采样稀疏强度调制放射治疗（Dense Angularly Sampled and Sparse Intensity Modulated Radiation Therapy, DASSIM-RT）中。
