放射治疗中的最佳剂量校准
Optimal dose calibration in radiotherapy
摘要：
本文将最优试验设计理论提供的工具应用于非线性校正模型。这是出于使用辐射变色胶片用于放射治疗目的来估计辐射剂量的需要。在这种情况下，校准模型是非线性的，并且解释变量不能从模型中明确地计算出来。在这种情况下，必须在因变量上找到试验设计。为此，将使用反函数定理来获得待优化的信息矩阵。从两个不同的角度计算响应变量的最优设计，首先用于拟合模型并估计每个参数，然后用于预测要应用于患者的适当剂量。虽然第一个是一个共同的观点，在一般情况下的最佳试验设计，后者实际上是校准问题的主要目标的从业者和算法计算这些最佳设计也提供。
英文摘要：
In this paper, the tools provided by the theory of Optimal Experimental Design are applied to a nonlinear calibration model. This is motivated by the need of estimating radiation doses using radiochromic films for radiotherapy purposes. The calibration model is in this case nonlinear and the explanatory variable cannot be worked out explicitly from the model. In this case an experimental design has to be found on the dependent variable. For that, the inverse function theorem will be used to obtain an information matrix to be optimized. Optimal designs on the response variable are computed from two different perspectives, first for fitting the model and estimating each of the parameters and then for predicting the proper dose to be applied to the patient. While the first is a common point of view in a general context of the Optimal Experimental Design, the latter is actually the main objective of the calibration problem for the practitioners and algorithms for computing these optimal designs are also provided.
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