On the field size definition and field output factors in small field dosimetry

BACKGROUND

There is a major conceptual difference between small-field and large field dosimetry that is, different definition of the field size. The dosimetry protocol IAEA TRS-483 recommends the use of the field size defined by measured dose profiles (full-width half maximum, FWHM) that is significantly different from conventional field size definition by the geometric field opening of MLC/Jaw at the isocenter. The application of the effective field size concept, S_clin , was introduced by Cranmer-Sargison et al. (DOI:10.1016/j.radonc.2013.10.002) as a reporting mechanism for field output factors of rectangular fields. The study by Das et al. (DOI:10.1002/mp.15624) indicated the limitations of obtaining the field size by experimentally measuring FWHM, for example, the measured FWHM is smaller than beam geometric size, which is contradictory to what is expected as a result of partial occlusion of the primary photon source by the collimating devices. Cranmer-Sargison et al. and Das et al suggested that additional investigations are needed to evaluate its limitations.

PURPOSE

This study investigates the validity of the field size definition by FWHM and by MLC/Jaw opening and finds the pros and cons between these two methods to resolve the controversial issue.

METHODS

The FWHM can be obtained by measuring or calculating dose profiles. Using Monte Carlo simulations this study compares the field size obtained by FWHM and by field geometric field opening. The EGSnrc system is used to simulate 6 MV beam to generate square and rectangular fields from 5-30 mm with every possible permutation (keeping one jaw fixed and varying other jaw from 5 to 30 mm). The calculated FWHM and output factors are compared with measurements obtained by a microSilicon detector.

RESULTS

The results show that field width (FWHM) derived from MC calculations generally agrees with machine geometric field width within 0.5 mm for square or rectangular fields with a minimum field width of ≥8 mm. For the extremely small fields with a minimum field width of 5 mm the discrepancies are up to 1.6 mm. The field width (FWHM) obtained by measuring dose profiles are unreliable for small fields due to the measurement uncertainties for an extremely small field. The effect of partial occlusion of the primary photon source by the jaws on the beam axis is clearly observed in the calculated dose profiles. For the extremely small field width of 5 mm, Monte Carlo predicted up to 10% exchange factor differences which are confirmed by the measurements.

CONCLUSION

The field size defined by the geometric opening of the beam-defining system, is still valid for small fields. The field size defined by geometric opening is independent of measurement uncertainties, independent of machine design, and highly reproducible. It is feasible to accurately tabulate the output factors as a function of geometric field opening thus eliminating user and detector choice for FWHM measurements. The field output factor of a small rectangular field cannot be related to an equivalent field size without considering the exchange factor due to partial occlusion of the photon source.

Technical note: Determining equivalent squares of high-energetic photon fields

PURPOSE

We developed a method based on a physical pencil beam model for accurate equivalent square calculations for rectangular and irregular fields, for different definitions of equivalent squares, for beams with and without flattening filter, different photon energies, and depths in water.

METHODS

We considered two equivalent square definitions: equal dose at a point on the beam axis and equal depth dose, measured as tissue phantom ratio at 20 and 10 cm depth ( TPR 20 , 10 $\text{TPR}_{20,10}$ ). As dose engine, we used an analytical pencil beam model. By integrating the pencil beam kernels, we assigned square fields to rectangular fields minimizing the dose, respectively, the TPR 20 , 10 $\text{TPR}_{20,10}$ difference. The results were compared with measurements at 100 mm depth for nominal beam energies of 6 and 18 MV, the Sterling equation, the geometric mean, and data from BJR Suppl 25 (British Institute of Radiology, 1996).

RESULTS

Pencil beam results were closest to the measurements. An energy dependence of several millimeters for small field dimensions and depth dependencies for very elongated fields were observed. For the assignment of WFF square to FFF rectangular fields, using the equal- TPR 20 , 10 $\text{TPR}_{20,10}$ definition, our method agrees with previously published results. For circular fields approximated by leaves, we found deviations to the data from BJR Suppl. 25 below 1 mm for diameters smaller than 200 mm.

CONCLUSIONS

Our study shows that the validity range for geometric mean and Sterling equation is limited. Ergo, instead of specifying specific validity ranges, we suggest using the pencil beam method, valid for all aspect ratios, including elongated fields in the primary dose dominated regime. We published our method as python library and graphical user interface on GitHub. Users can choose between two definitions of equivalent square and between WFF and FFF fields. The implemented pencil beam method for irregular fields is also usable for quality assurance such as monitor unit checks.

Validity of equivalent square field concept in small field dosimetry

PURPOSE

The equivalent Square (ES) concept has been used for traditional radiation fields defined by the machine collimating system. For small fields, the concept S_clin was introduced based on measuring dosimetric field width (full-width half maximum, FWHM) of the cardinal axis of the beam profiles. The pros and cons of this concept are evaluated in small fields and compared with the traditional ES using area and perimeter (4A/P) method based on geometric field size settings e.g. light field settings.

METHODS

One hundred thirty-seven square and rectangular fields from 5-50 mm with every possible permutation (keeping one jaw fixed and varying other jaw from 5 mm to 50 mm) were utilized to measure FWHM for the validation of S_clin . Using a microSilicon detector and a scanning water tank, measurements were performed on an Elekta (Versa) machine with Agility head and a Varian TrueBeam with different MLC/Jaw design to evaluate the S_clin concept and to understand the effect of exchange factor in small fields. Field output factors were also measured for all 137 fields.

RESULTS

The data fitting for fields ranging from 5-50 mm between the traditional 4A/P method and S_clin shows differences and indicates a linear relationship with distinct separation of slope for Elekta and Varian machines. As Elekta does not have y jaws, the ES based on 4A/P < S_clin but for the Varian linac 4A/P > S_clin for square fields. Our measured data shows that both methods are equally valid but does vary by the machine design. The field output factor is dependent on the elongation factor as well as machine design. For fields with sides ≥10 mm, the exchange factor is nearly identical in both machines with magnitude up to 4% which is close to measurement uncertainty (±3%) but for small fields (<10 mm) the Elekta machine has higher exchange factors compared to the Varian machine.

CONCLUSION

The results demonstrate that the two concepts for defining equivalent field (S_clin and 4A/P) are equivalent and can be directly related through an empirical equation. This study confirms that 4A/P is still valid for small fields except for very small fields (≤10 mm) where source occlusion is a dominating factor. The S_clin method is potentially sensitive to measurement uncertainty due to measurement of FWHM which is machine, detector and user dependent, while the 4A/P method relies mainly on geometry of the machine and has less dependency on type of machine, detector and user. The exchange factors are comparable for both types of machines. The conclusion is based on data from an Elekta with Agility head and a Varian TrueBeam machine that may have potential for bias due to light field/collimator set up and alignment. Care should be taken in extrapolating these data to any other machine. This article is protected by copyright. All rights reserved.

Using weighted power mean for equivalent square estimation

PURPOSE

Equivalent Square (ES) enables the calculation of many radiation quantities for rectangular treatment fields, based only on measurements from square fields. While it is widely applied in radiotherapy, its accuracy, especially for extremely elongated fields, still leaves room for improvement. In this study, we introduce a novel explicit ES formula based on Weighted Power Mean (WPM) function and compare its performance with the Sterling formula and Vadash/Bjärngard's formula.

METHODS

The proposed WPM formula is ESWPMa,b=waα+1-wbα1/α for a rectangular photon field with sides a and b. The formula performance was evaluated by three methods: standard deviation of model fitting residual error, maximum relative model prediction error, and model's Akaike Information Criterion (AIC). Testing datasets included the ES table from British Journal of Radiology (BJR), photon output factors (S_cp ) from the Varian TrueBeam Representative Beam Data (Med Phys. 2012;39:6981-7018), and published S_cp data for Varian TrueBeam Edge (J Appl Clin Med Phys. 2015;16:125-148).

RESULTS

For the BJR dataset, the best-fit parameter value α = -1.25 achieved a 20% reduction in standard deviation in ES estimation residual error compared with the two established formulae. For the two Varian datasets, employing WPM reduced the maximum relative error from 3.5% (Sterling) or 2% (Vadash/Bjärngard) to 0.7% for open field sizes ranging from 3 cm to 40 cm, and the reduction was even more prominent for 1 cm field sizes on Edge (J Appl Clin Med Phys. 2015;16:125-148). The AIC value of the WPM formula was consistently lower than its counterparts from the traditional formulae on photon output factors, most prominent on very elongated small fields.

CONCLUSION

The WPM formula outperformed the traditional formulae on three testing datasets. With increasing utilization of very elongated, small rectangular fields in modern radiotherapy, improved photon output factor estimation is expected by adopting the WPM formula in treatment planning and secondary MU check.