Evaluation approach for whole dose distribution in clinical cases using spherical projection and spherical harmonics expansion: spherical coefficient tensor and score method
Evaluation approach for whole dose distribution in clinical cases using spherical projection and spherical harmonics expansion: spherical coefficient tensor and score method
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DOI：
10.1093/jrr/rrab081
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发表时间：
2021-09-29
影响因子：
2
通讯作者：
Tanigawa, Noboru
中科院分区：
文献类型：
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作者：
Anetai, Yusuke;Koike, Yuhei;Tanigawa, Noboru
整个剂量分布由精心设计的治疗计划产生，包括患者具体情况(肿瘤的位置、大小和形状等)。和特定设施(临床政策和目标、设备等)信息。为了有效地评估整个剂量分布，我们提出了一种应用球面投影和实球面调和(SH)展开的方法，从而将展开系数作为秩2张量，即SH系数张量，用于每个患者特定的剂量分布。为了验证这一张量的性质，我们从流形学习方法和多维尺度(MDS)中引入了ISOMAP。随后，我们得到了表示相似性的MDS距离ETA和SH得分Zeta，Zeta是SH系数张量的Frobenius范数。然后在强度调制放射治疗(IMRT)数据集中得到验证：(I)375个混合治疗区域，(Ii)135个头颈部(HN)和(Iii)132个前列腺癌病例。MDS图表明，SH系数张量能够对整个剂量分布进行定量特征提取。特别是，SH评分系统地检测到与平均病例的偏差大于+1.5标准差(SD)的不规则病例，这与需要非常复杂的剂量分布的临床不规则病例相匹配。综上所述，所提出的SH系数张量是整个剂量分布的有用表示。由SH系数张量得到的SH分数是一种方便而简单的判据，用于表征整个剂量分布，它不依赖于数据集。
Whole dose distribution results from well-conceived treatment plans including patient-specific (location, size and shape of tumor, etc.) and facility-specific (clinical policy and goal, equipment, etc.) information. To evaluate the whole dose distribution efficiently and effectively, we propose a method to apply spherical projection and real spherical harmonics (SH) expansion, thus leading to the expanded coefficients as a rank-2 tensor, SH coefficient tensor, for every patient-specific dose distribution. To verify the feature of this tensor, we introduce Isomap from the manifold learning method and multi-dimensional scaling (MDS). Subsequently, we obtained the MDS distance representing similarity, eta, and the SH score, zeta, which is a Frobenius norm of the SH coefficient tensor. These were then validated in the intensity-modulated radiation therapy (IMRT) data sets of: (i) 375 mixing treated regions, (ii) 135 head and neck (HN), and (iii) 132 prostate cases, respectively. The MDS map indicated that the SH coefficient tensor enabled a quantitative feature extraction of whole dose distributions. In particular, the SH score systematically detected irregular cases as the deviation higher than +1.5 standard deviations (SD) from the average case, which matched up with clinically irregular case that required very complicated dose distributions. In summary, the proposed SH coefficient tensor is a useful representation of the whole dose distribution. The SH score from the SH coefficient tensor is a convenient and simple criterion used to characterize the entire dose distributions, which is not dependent on the data set.