Darío Esteban Sanz | PubMed Health

PubMed2004

The separation of the head and phantom scatter components from a phase space description.

The formalism based on phantom and collimator scatter factors for high energy photon beams is deduced using a phase space description. The phantom scatter factors (Sp) depend on the field size and shape at the level of the phantom and are generally considered independent of the collimation details used to form the desired field provided the effect of contaminant electrons can be neglected. As demonstrated in this work, this behaviour leads to the applicability of the Clarkson method in irregular fields. However, for a given field formed with a tertiary collimator it is not a priori clear that the variations of extrafocal radiation due to secondary collimator setting do not affect the phantom scatter correction factors. In fact, the extrafocal radiation has a lower mean energy than that of unscattered photons, and this radiation can reach points well outside the radiation field increasing the irradiated phantom volume. Besides, transmission through the blocks contributes to phantom scatter. Therefore, for a given block-defined field, the associated phantom scatter dose, per unit of fluence in air on the central axis, should in principle increase when enlarging the secondary collimator field. To confirm this, isocentric Sp data for 6 MV photons were measured at 10 cm depth in water, reducing with cerrobend blocks several fields formed with the secondary collimators. In particular, when a 30 x 30 cm2 collimator field is reduced with blocks to a 7 x 7 cm2 field, the dose per unit of fluence in air is 1.4% higher than that of the square collimator field equating the given block field. Our calculations indicate that in this case the block transmission accounts for only 0.2% of this increment, showing that the remaining effect is due to extrafocal radiation. As a concluding remark, this work contributes to a better understanding of the classical Clarkson method for irregular fields giving, additionally, a formal interpretation of the commonly used quantities.

Algorithms↗

PubMed2002

Accuracy limits of the equivalent field method for irregular photon fields.

A mathematical approach is developed to evaluate the accuracy of the equivalent field method using basic clinical photon beam data. This paper presents an analytical calculation of dose errors arising when field equivalencies, calculated at a certain reference depth, are translated to other depths. The phantom scatter summation is expressed as a Riemann-Stieltjes integral and two categories of irregular fields are introduced: uniform and multiform. It is shown that multiform fields produce errors whose magnitudes are nearly twice those corresponding to uniform fields in extreme situations. For uniform field shapes, the maximum, local, relative dose errors, when the equivalencies are calculated at 10 cm depth on the central axis and translated to a depth of 30 cm, are 3.8% and 8.8% for 6 MV and cobalt-60 photon beams, respectively. In terms of maximum dose those errors are within 1-2%. This supports the conclusion that the equivalencies between rectangular fields, which are examples of uniform fields, are applicable to dose ratio functions irrespective of beam energy. However, the magnitude of such errors could be of importance when assessing the exit dose for in vivo monitoring. This work provides a better understanding of the influence of the irregular field shapes on the accuracy of the equivalent field method.

Calibration↗