Kernel density estimation-based real-time prediction for respiratory motion
Kernel density estimation-based real-time prediction for respiratory motion
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DOI：
10.1088/0031-9155/55/5/004
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发表时间：
2010-03-07
影响因子：
3.5
通讯作者：
Ruan, Dan
中科院分区：
文献类型：
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作者：
Ruan, Dan
自适应放射治疗的有效递送要求以高精度在真实的时间内定位靶。由数据采集、流传输、处理和传输控制引起的系统延迟需要预测。对于高度移动的目标，例如经历呼吸诱导运动的胸部和腹部肿瘤，预测特别具有挑战性。呼吸运动的复杂性使得很难建立和证明显式模型。在这项研究中，我们荣誉呼吸运动的内在不确定性，并提出了一个统计处理的预测问题。而不是要求一个确定性的协变量响应映射和未来目标位置的唯一估计值，我们的目标是获得一个分布的未来目标位置（响应变量）的条件下观察到的历史样本值（协变量）。其核心思想是使用一种有效的核密度估计方法来估计协变量和响应变量的联合概率分布（pdf）。然后，识别未来目标位置分布的问题归结为基于观测协变量识别联合概率分布函数中的部分。随后，基于此估计的条件分布导出估计量。这种概率观点与现有的确定性方案相比具有一些独特的优点：（1）它与潜在不一致的训练样本兼容，即，当接近的协变量对应于显著不同的响应值时;（2）它不受协变量和响应之间映射的任何先验结构假设的限制;（3）两阶段设置允许在选择统计估计时有很大的自由度，并为所得估计的不确定性提供完整的非参数描述。我们评估了10个患者RPM轨迹的预测性能，使用预测值和观察值之间的均方根差，通过观察数据的标准差进行归一化，作为误差度量。此外，我们比较了所提出的方法与两个基准方法：最近的样本和自适应线性滤波器。基于核密度估计的预测结果表明，普遍显着改善的替代品，特别是有价值的前瞻时间长，当替代方法无法产生有用的预测。
Effective delivery of adaptive radiotherapy requires locating the target with high precision in real time. System latency caused by data acquisition, streaming, processing and delivery control necessitates prediction. Prediction is particularly challenging for highly mobile targets such as thoracic and abdominal tumors undergoing respiration-induced motion. The complexity of the respiratory motion makes it difficult to build and justify explicit models. In this study, we honor the intrinsic uncertainties in respiratory motion and propose a statistical treatment of the prediction problem. Instead of asking for a deterministic covariate-response map and a unique estimate value for future target position, we aim to obtain a distribution of the future target position (response variable) conditioned on the observed historical sample values (covariate variable). The key idea is to estimate the joint probability distribution (pdf) of the covariate and response variables using an efficient kernel density estimation method. Then, the problem of identifying the distribution of the future target position reduces to identifying the section in the joint pdf based on the observed covariate. Subsequently, estimators are derived based on this estimated conditional distribution. This probabilistic perspective has some distinctive advantages over existing deterministic schemes: (1) it is compatible with potentially inconsistent training samples, i.e., when close covariate variables correspond to dramatically different response values; (2) it is not restricted by any prior structural assumption on the map between the covariate and the response; (3) the two-stage setup allows much freedom in choosing statistical estimates and provides a full nonparametric description of the uncertainty for the resulting estimate. We evaluated the prediction performance on ten patient RPM traces, using the root mean squared difference between the prediction and the observed value normalized by the standard deviation of the observed data as the error metric. Furthermore, we compared the proposed method with two benchmark methods: most recent sample and an adaptive linear filter. The kernel density estimation-based prediction results demonstrate universally significant improvement over the alternatives and are especially valuable for long lookahead time, when the alternative methods fail to produce useful predictions.