An analytical model for the prediction of a set of percentage depth dose curves

Abstract

Objective: in the present paper a method for the determination of the percentage depth-dose distributions (PDD) as a function of depth (z) and field size (S) is presented.

Methods and material: field sizes used range from 6 × 6 mm² to 100 × 100 mm². Measurements of PDD  functions were carried out for different values of S employing three distinct detectors. So as to determine the model parameters for each detector it was fitted to experimental data. In addition to that, an expression for the dependence of the maximum depth (zmax) on S is obtained. To analyze the goodness of the model predictions the model results were compared to experimental data for each detector. As a direct application of the model proposed all experimental PDD curves were calculated measuring only three and five field sizes, respectively.

Results and discussion: discrepancies obtained are lesser than 3% (general analysis) and lesser than 5% (partial analysis). Regarding zmax predictions, differences with respect to experimental data do not exceed 1 mm. Discrepancies obtained when utilizing 3 and 5 field sizes were of the same order as those yielded by the full model (11 field sizes). The model parameters variation when distinct field sizes are utilized is lower than 2%.

Conclusion: the model proposed satisfactorily agrees with experimental data. It could be used for quality assurance purposes, secondary monitor unit calculations and might help reducing the number of measurements needed to determine a full set of PDD curves.