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ID: <

10670/1.8sdh0w

>

·

DOI: <

10.26226/morressier.5cb7218fae0a09001583072b

>

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Quantifying robustness and calculating the probability of meaningful error in proton radiotherapy delivery utilizing a dense Dij matrix

Abstract

When conventional intensity modulated proton therapy algorithms calculate optimal beam spot weights, there is no formal consideration of potential systematic errors. Alternatively, robust optimization addresses these uncertainties within its objective function, yielding plans that are less subject to dose fluctuations when errors occur. Despite these advances, quantifying plan u201crobustnessu201d remains challenging and clinicians have little guidance regarding the likelihood that a plan fails to meet constraints. Additionally, many implementations of robust optimization fail to account for both range and setup errors simultaneously. We describe a novel method of quantifying robustness, yielding a nonparametric probabilistic approximation of dose coverage. Rather than creating a Dij matrix limited to those beam spots (BS) intended for use in treatment delivery, we created a u201cdenseu201d Dij matrix (DDM) with finer spot spacing (1 mm X/Y-axis, 1mm Zdepth) and wider margins (2.5u03c3), which is approximately 25-35-fold larger than origina Dij matrixFollowing optimization, 100 error scenarios are created by translating the optimized plan with normal random shifts in the X,Y, and Energy axes, corresponding to the known uncertainty distributions in these respective directions. Since the locations of BS in each error scenario closely approximate locations of BS already included in the DDM, we can calculate dose distributions and Dij matrices for each individual scenario with minimal additional calculation. Review of a composite DVH comprised of all scenario dose distributions allows one to quickly quantify robustness and determine the fraction of error scenarios that fail to meet constraints, thus allowing clinicians to provide safer and more effective treatments. Lastly, incorporation of all error into an optimization framework allows for simultaneous robust optimization for uncertainties in both range and setup.

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