Analytical probabilistic proton dose calculation and range uncertainties

17th International Conference on the Use of Computers in Radiation Therapy

物理学;计算机科学

Bangert, M.^1 ; Hennig, P.^2 ; Oelfke, U.^1

German Cancer Research Center, DKFZ, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany^1

Max Planck Institute for Intelligent Systems, Spemannstraße 38, 72076 Tübingen, Germany^2

关键词: Arbitrary correlation;    Fractionated radiation;    Intensity-modulated;    Multi-variate normal distributions;    Pencil beam algorithms;    Probabilistic modeling;    Proton dose distributions;    Two-dimensional tests;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/489/1/012002/pdf
DOI  :  10.1088/1742-6596/489/1/012002

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

We introduce the concept of analytical probabilistic modeling (APM) to calculate the mean and the standard deviation of intensity-modulated proton dose distributions under the influence of range uncertainties in closed form. For APM, range uncertainties are modeled with a multivariate Normal distribution p(z) over the radiological depths z. A pencil beam algorithm that parameterizes the proton depth dose d(z) with a weighted superposition of ten Gaussians is used. Hence, the integrals ∫ dz p(z) d(z) and ∫ dz p(z) d(z)2required for the calculation of the expected value and standard deviation of the dose remain analytically tractable and can be efficiently evaluated. The means μk, widths δk, and weights ωkof the Gaussian components parameterizing the depth dose curves are found with least squares fits for all available proton ranges. We observe less than 0.3% average deviation of the Gaussian parameterizations from the original proton depth dose curves. Consequently, APM yields high accuracy estimates for the expected value and standard deviation of intensity-modulated proton dose distributions for two dimensional test cases. APM can accommodate arbitrary correlation models and account for the different nature of random and systematic errors in fractionated radiation therapy. Beneficial applications of APM in robust planning are feasible.