A Monte Carlo method to evaluate the impact of positioning errors on detector response and quality correction factors in nonstandard beams

During experimental procedures, an adequate evaluation of all sources of uncertainty is necessary to obtain an overall uncertainty budget. In specific radiation dosimetry applications where a single detector is used, common methods to evaluate uncertainties caused by setup positioning errors are not applicable when the dose gradient is not known a priori. This study describes a method to compute these uncertainties using the Monte Carlo method. A mathematical formalism is developed to calculate unbiased estimates of the uncertainties. The method is implemented in egs_chamber, an EGSnrc-based code that allows for the efficient calculation of detector doses and dose ratios. The correct implementation of the method into the egs_chamber code is validated with an extensive series of tests. The accuracy of the developed mathematical formalism is verified by comparing egs_chamber simulation results to the theoretical expectation in an ideal situation where the uncertainty can be computed analytically. Three examples of uncertainties are considered for realistic models of an Exradin A12 ionization chamber and a PTW 60012 diode, and results are computed for parameters representing nearly realistic positioning error probability distributions. Results of practical examples show that uncertainties caused by positioning errors can be significant during IMRT reference dosimetry as well as small field output factor measurements. The method described in this paper is of interest in the study of single-detector response uncertainties during nonstandard beam measurements, both in the scope of daily routine as well as when developing new dosimetry protocols. It is pointed out that such uncertainties should be considered in new protocols devoted to single-detector measurements in regions with unpredictable dose gradients. The method is available within the egs_chamber code in the latest official release of the EGSnrc system.