Department of Radiation Oncology, Columbia University, New York, NY, USA.
Med Phys. 2012 Apr;39(4):1696-703. doi: 10.1118/1.3691174.
Phase-based and amplitude-based sorting techniques are commonly used in four-dimensional CT (4DCT) reconstruction. However, effect of these sorting techniques on 4D dose calculation has not been explored. In this study, the authors investigated a candidate 4DCT sorting technique by comparing its 4D dose calculation accuracy with that for phase-based and amplitude-based sorting techniques.
An optimization model was formed using organ motion probability density function (PDF) in the 4D dose convolution. The objective function for optimization was defined as the maximum difference between the expected 4D dose in organ of interest and the 4D dose calculated using a 4DCT sorted by a candidate sampling method. Sorting samples, as optimization variables, were selected on the respiratory motion PDF assessed during the CT scanning. Breathing curves obtained from patients' 4DCT scanning, as well as 3D dose distribution from treatment planning, were used in the study. Given the objective function, a residual error analysis was performed, and k-means clustering was found to be an effective sampling scheme to improve the 4D dose calculation accuracy and independent with the patient-specific dose distribution.
Patient data analysis demonstrated that the k-means sampling was superior to the conventional phase-based and amplitude-based sorting and comparable to the optimal sampling results. For phase-based sorting, the residual error in 4D dose calculations may not be further reduced to an acceptable accuracy after a certain number of phases, while for amplitude-based sorting, k-means sampling, and the optimal sampling, the residual error in 4D dose calculations decreased rapidly as the number of 4DCT phases increased to 6.
An innovative phase sorting method (k-means method) is presented in this study. The method is dependent only on tumor motion PDF. It could provide a way to refine the phase sorting in 4DCT reconstruction and is effective for 4D dose accumulation. Optimized sorting techniques could achieve acceptable residuals (less than 0.5% of the prescription dose) using 6 sorting samples, which is much better than amplitude-based or phase-based sorting. Further increase in sorting phase number exceeding 6 or more may not be necessary when using the k-means sampling or optimal sampling points.
在四维 CT（4DCT）重建中，通常使用基于相位和基于幅度的排序技术。然而，这些排序技术对 4D 剂量计算的影响尚未得到探索。在这项研究中，作者通过比较基于相位和基于幅度的排序技术，研究了一种候选的 4DCT 排序技术，以评估其 4D 剂量计算的准确性。
使用器官运动概率密度函数（PDF）在 4D 剂量卷积中建立优化模型。优化的目标函数定义为感兴趣器官的预期 4D 剂量与使用候选采样方法对 4DCT 排序计算的 4D 剂量之间的最大差异。作为优化变量的排序样本，是根据 CT 扫描期间评估的呼吸运动 PDF 选择的。研究中使用了来自患者 4DCT 扫描的呼吸曲线以及治疗计划的 3D 剂量分布。给定目标函数，进行残差分析，发现 K-均值聚类是一种有效的采样方案，可以提高 4D 剂量计算的准确性，并且与患者特定的剂量分布无关。
患者数据分析表明，K-均值采样优于传统的基于相位和基于幅度的排序，并且与最优采样结果相当。对于基于相位的排序，在一定数量的相位之后，4D 剂量计算中的残差可能无法进一步降低到可接受的精度，而对于基于幅度的排序，K-均值采样和最优采样，随着 4DCT 相位数量增加到 6，4D 剂量计算中的残差迅速降低。
本研究提出了一种创新的相位排序方法（K-均值方法）。该方法仅依赖于肿瘤运动 PDF。它可以提供一种改进 4DCT 重建中相位排序的方法，并且对 4D 剂量积累有效。使用 6 个排序样本可以实现优化的排序技术，达到可接受的残差（小于处方剂量的 0.5%），这比基于幅度或相位的排序要好得多。当使用 K-均值采样或最佳采样点时，超过 6 个或更多的排序相位数量的进一步增加可能不是必要的。
