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Department of Medical Physics, Saskatchewan Cancer Agency, Saskatoon, CanadaAcademic Unit of Medical Physics, Faculty of Medicine and Health, University of Leeds, UK
Institute of Medical Physics, School of Physics, University of Sydney, AustraliaAcademic Unit of Medical Physics, Faculty of Medicine and Health, University of Leeds, UK
The goal of this work was to set out a methodology for measuring and reporting small field relative output and to assess the application of published correction factors across a population of linear accelerators.
Methods and materials
Measurements were made at 6 MV on five Varian iX accelerators using two PTW T60017 unshielded diodes. Relative output readings and profile measurements were made for nominal square field sizes of side 0.5 to 1.0 cm. The actual in-plane (A) and cross-plane (B) field widths were taken to be the FWHM at the 50% isodose level. An effective field size, defined as , was calculated and is presented as a field size metric. was used to linearly interpolate between published Monte Carlo (MC) calculated values to correct for the diode over-response in small fields.
Results
The relative output data reported as a function of the nominal field size were different across the accelerator population by up to nearly 10%. However, using the effective field size for reporting showed that the actual output ratios were consistent across the accelerator population to within the experimental uncertainty of ±1.0%. Correcting the measured relative output using at both the nominal and effective field sizes produce output factors that were not identical but differ by much less than the reported experimental and/or MC statistical uncertainties.
Conclusions
In general, the proposed methodology removes much of the ambiguity in reporting and interpreting small field dosimetric quantities and facilitates a clear dosimetric comparison across a population of linacs.
The International Electrotechnical Commission (IEC) recommends using the distance intercepted by a given isodose curve (50% level) on a plane perpendicular to the beam axis, at a stated fixed distance from the source (isocenter), to define the dosimetric field size [
]. Often in clinical practice the definition of field size is more loosely taken to mean the light field projection at a fixed distance from the source. In the somewhat dated ICRU Report 24 [
ICRU. Determination of absorbed dose in a patient irradiated by beams of x or gamma rays in radiotherapy procedures. Report No. 24, U.S. National Bureau of Standards; 1976.
] the light field projection is defined as the geometric field size. For field sizes large enough to ensure no source occlusion and charged particle equilibrium (CPE) the geometric field size may provide an accurate representation of the dosimetric field size, at least to within a given clinical tolerance. However, Das et al. [
] have reported that for field sizes that do not satisfy the CPE or occlusion criteria the dosimetric field size will be greater than the geometric field size and therefore the traditional close agreement between field size definitions breaks down.
Experimental small field dosimetry can be challenging due to the lack of lateral charged particle equilibrium, spectral changes as a function of field size, detector choice and subsequent perturbations of the charged particle fluence [
] have presented a well thought out dosimetry formalism for reporting corrected relative output factors for small and non-standard fields. The formalism makes use of a field factor (Ω) which converts absorbed dose to water for the machine-specific reference field (fmsr) to that of the clinical field of interest (fclin). This field factor is equal to the ratio of experimental detector readings () multiplied by a detector-specific correction factor (). Although the formalism establishes a framework for correcting small field relative output measurements it could be argued that the reporting, and application, of as a function of field size is still somewhat ambiguous.
Commercial diode detectors have been shown to be a reasonably good choice for small field dosimetry applications [
On the output factor measurements of the CyberKnife iris collimator small fields: Experimental determination of the correction factors for microchamber and diode detectors.
], yet care must be taken when selecting between shielded (photon) and unshielded (electron and stereotactic) diodes. In general, the correction factors required for shielded diodes are approximately twice that required for the unshielded diodes [
On the output factor measurements of the CyberKnife iris collimator small fields: Experimental determination of the correction factors for microchamber and diode detectors.
]. The method makes use of an error weighted average of Alanine pellet, thermoluminescent dosimeter (TLD), Gafchromic EBT film and VIP normoxic gel measured relative outputs to derive a water equivalent output factor. The experimental output factor can then be used to correct for the well documented diode over-response in small fields. Ralston et al. [
] used an air-core fiber optic scintillation dosimeter (FOD) for small field relative output dosimetry and showed the FOD can be used to experimentally determine for other detector types. Cranmer-Sargison et al. [
] used the FOD and diodes to characterize small fields collimated with a new 160-leaf MLC. The authors recommend that output ratios and field size be measured concurrently and advocate for the standard experimental uncertainty on both be quoted when reporting experimental results.
Monte Carlo (MC) simulation has proven to be a powerful tool in overcoming the challenges inherent to small field dosimetry [
Aspradakis MM, Byrne JP, Palmans H, et al. IPEM Report Number 103: small field MV photon dosimetry. Published by the Institute of Physics and Engineering in Medicine; 2010.
Monte Carlo modelling of diode detectors for small field MV photon dosimetry: detector model simplification and the sensitivity of correction factors to source parameterization.
Monte Carlo simulated correction factors for machine specific reference field dose calibration and output factor measurement using fixed and iris collimators on the CyberKnife system.
] have presented MC implementations of the proposed formalism and highlight the importance of systematic experimental validation of the combined accelerator and detector models. Both authors also explored the sensitivity of MC calculated small field output ratios and to the choice of source parameterization and show the correction factors to be a function of field size only. Further work by Scott et al. [
] has shown that the ratio of dose-to-water to dose-to-detector-in-water varies significantly as a function of field size. For small field sizes this ratio correlates with the mass density of the detector material relative to that of water. The authors also show that all water dose profiles are very similar to profiles simulated with a small isolated silicon volume in water (also see Francescon et al. [
Regardless of the dosimeter studied, the relative output and corresponding correction factors appear to have been presented as a function of the nominal field size and not the dosimetric field size. The viability of applying small field central axis relative output correction factors to clinically measured data requires standardization in measurement. In addition to experimental standardization a field size metric, which can be used to appropriately correlate relative output to the measured dosimetric field size, is essential. The suitability of applying published correction factors across a population of linacs is also not apparent from the literature nor is it clear how the corrections should be applied to clinical data reported as a function of the measured dosimetric field size. Each aspect is addressed in the work presented here.
Methods and materials
Defining an effective field size for use in small field dosimetry
For small fields collimated with jaws and/or MLCs there can be a difference between the geometric field size and nominal field size as set on the linac console. The difference can be due to collimator calibration and the positional accuracy of the collimation system itself [
]. Add to this the inherent complication of the dosimetric field size being greater than the geometric field and the requirements for a systematic framework for reporting and interpreting small field dosimetric values becomes clear. As such, a simple small field metric which can be used to represent the dosimetric field size would be of value. A number of approaches to this are possible but given the magnitude of the dimensional and scatter component changes which need to be taken into account an effective small field size is suggested as follows,
(1)
where A and B correspond to the in-plane and cross-plane dosimetric field widths defined as the FWHM at the 50% isodose level. Moreover, one can define an equivalent field area such that,
(2)
Defining and provides a simple yet robust methodological framework for comparing small field dosimetric quantities across a population of linacs with different collimation systems (jaws, MLCs and cones, where the of the latter can be represented by the actual measured area and the as the square root of this). We first explore the use of for small nominally square fields and leave the viability of using for comparison between cone, jaw and MLC collimated small fields for another work.
Experimental measurements
Small field 6 MV relative output measurements were made using two PTW T60017 unshielded diodes on five Varian iX linacs located at three different institutions (See Supplementary Materials for details). Detector specific output ratios () were calculated with respect to a square jaw collimated field of side 3.0 cm for nominal square jaw collimated field sizes of side 1.0, 0.9, 0.8, 0.7, 0.6 and 0.5 cm. Measurements were made at a depth of 5.0 cm with the long axis of the diode detector placed parallel to the beam axis such that the active volume was positioned at the isocenter. Positional fine tuning was performed to ensure the active volume of the detector was located at the radiation isocenter and not just centered on the light field. Following this method ensured the detector positional uncertainty was limited only by accuracy of the water tank system quoted by the manufacturer at ±0.1 mm.
The measurements were repeated three times with the water phantom, detector position and collimation reset between each experimental session. During each experimental session five central axis output readings and five in-plane and cross-plane profile measurements were made at each field size. The mean output ratio and field widths were calculated across the three experimental sessions as were the standard experimental errors for each. was calculated using the dosimetric field widths along each axis and values reported as a function of both the nominal and effective field sizes.
Monte Carlo simulations
A previously published BEAMnrc model of a 6 MV Varian iX linear accelerator head [
] was used to create the input phase space data for all subsequent simulations. The baseline electron source parameterization was modeled as a 6.2 MeV mono-energetic Gaussian with a circularly symmetric FWHM = 0.110 cm [
Monte Carlo modelling of diode detectors for small field MV photon dosimetry: detector model simplification and the sensitivity of correction factors to source parameterization.
] such that the statistical dose uncertainty scored to the active volume was approximately ±0.5%. The EGSnrc transport parameters ECUT, PCUT and ESTEP were set to 0.521 and 0.01 MeV and 0.25 respectively. The EXACT boundary crossing algorithm was used in combination with the PRESTA-II condensed history electron step algorithm (ESAVEIN = 2.0 MeV) and the photon cross-section enhancement variance reduction technique. Phase space data for jaw collimated geometric field sizes of side 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, 1.0 and 3.0 were used as DOSRZnrc input. Simulated output ratios were calculated for each field size as follows,
(3)
where , , and represent the dose per incident particle scored to the active volume of the detector model and linac monitor unit chamber for the fclin and fmsr simulations, respectively.
DOSXYZnrc simulations were run using the same phase space data used in the DOSRZnrc simulations. The history number was set to give a statistical uncertainty of less than ±0.5% within a voxel dimension of 0.05 cm × 0.05 cm × 0.25 cm. The in-plane and cross-plane FWHMs at the 50% level were extracted from the data and the dosimetric field widths plotted as a function of the geometric field widths. The sensitivity of to variations in electron energy and FWHM were investigated using the two data sets. The first set of data was calculated for an electron energy fixed at 6.2 MeV with the Gaussian spatial distribution varied as follows: FWHM = 0.100, 0.110, and 0.120 cm. The second set of data was for electron energies at 5.8, 6.0 and 6.2 MeV with the spatial distribution fixed at a FWHM = 0.110 cm. Once again the dosimetric field widths were extracted from the data and plotted as a function of geometric field widths. For each source parameter combination was plotted as a function of both the nominal and effective field size and the results compared to the experimental data.
Interpreting and applying
The PTW T60017 diode factors published by Cranmer-Sargison et al. [
] were used to correct the experimental data in a manner consistent with the Alfonso et al. formalism. It must be noted that Cranmer-Sargison et al. present the data at the geometric field sizes and therefore some question remains as to the appropriateness of applying the corrections (or similar corrections) to data reported at . The experimental data were corrected using the as published at the geometric field sizes and reassigned to the effective field sizes calculated from the DOSXYZnrc simulations. In all cases linear interpolation was used to assign to the corresponding experimental .
Results
Fig. 1 shows the measured data plotted as a function of the nominal field size (as set on the linac console) and the effective field size calculated using the measured in-plane and cross-plane dosimetric field widths. When the data are plotted as a function of the nominal field size there appears to be a significant difference in the relative output across the linac population, which could be incorrectly interpreted as being a real difference in the electron source width incident on the Bremsstrahlung target. However, when the same data are plotted as a function of there is no discernible difference in relative output across the population of linacs. The inference being that the linear accelerators included in this study have electron source distributions that are very nearly indistinguishable.
Fig. 1Measured data plotted as a function of the nominal (left) and effective (right) field sizes. Shown in the Supplementary Materials are the effective field sizes and measured output ratios presented in a table form. SCC-0,-1,-2 and QUT-1,-2 are labels for the five Varian iX linacs used in this study (See Supplementary Materials for details). It should be noted that the output ratio and measured field widths for linac SCC-0 are from Cranmer-Sargison et al.
Fig. 2 shows the DOSXYZnrc simulation data that relate the dosimetric field width to the corresponding geometric field width for the upper and lower jaws. These data reveal a number of interesting characteristics: (1) dosimetric field widths are greater than the geometric field widths for field sizes less than approximately 0.8 cm × 0.8 cm, (2) the effect is greater along the axis collimated by the upper jaw than that collimated by the lower jaw and (3) the effect is independent of source energy but increases as a function of increased source width. The dosimetric field width data can be thought of as measured data from a perfect collimator jaw suffering from no positional error or uncertainty and therefore can be used to elicit the difference between the geometric and dosimetric field widths for this particular accelerator head.
Fig. 2DOSXYZnrc simulation data showing the relationship between the dosimetric field widths plotted as a function of the geometric field width for the upper (left) and lower (right) jaws, incident electron energy (top) and FWHM (bottom).
Shown in Fig. 3 are the data plotted as a function of both the geometric (left) and effective (right) field sizes. Each graph includes the experimental data plotted as a function of the measured effective field sizes (see Fig. 1). The data simulated using a source FWHM = 0.12 cm, and plotted as a function of the geometric field size, agrees best with the experimental data. However, simulated using a source FWHM = 0.10 cm is clearly in better agreement if plotted as a function of the effective field size. In both instances the agreement between the experimental and simulated data is reasonable at a source FWHM = 0.11 cm.
Fig. 3DOSRZnrc simulated data (solid line) plotted as a function of the nominal field size (left) and effective field size (right) calculated for the incident electron FWHM shown in Fig. 2. In all cases experimental data are given as a function of the effective field size. The solid line connecting the MC data points is included as a guide only and does not represent a functional fit.
Data in Fig. 4 show the relative output plotted as a function of the measured effective field size corrected using values at the geometric field size and the same values reassigned to the associated effective field size. Clearly using at the nominal and effective field sizes produce output factors that are not identical but differ by much less than the reported experimental and/or MC statistical uncertainties. The more important criteria for using the proposed methodology is to characterize, correct and report relative output as a function of the effective field size and not the nominal.
Fig. 4Corrected relative output data plotted as a function of the measured effective field size. The dashed lines connect the data points and do not represent a functional fit.
The measured small field relative output data reported as a function of the nominal field size are clearly different across the accelerator population. However, using the effective field size for reporting showed that the actual output ratios were consistent across the accelerator population (see Fig. 1). This indicates that Varian iX accelerators are generally well matched and that any major discrepancies in the literature may be attributed to reporting relative output as a function of the nominal field size. Understanding the differences between the nominal, geometric and dosimetric field sizes is critical and the implications, as they relate to interpreting small field dosimetric data, should not be discounted. For specialized stereotactic collimators, such as cones or micro-MLCs, the difference between the dosimetric and geometric field widths will be less than that for upstream jaw collimators. This alone highlights the importance of establishing a mechanism which facilitates the presentation of relative output data as a function of the measured equivalent field area.
Reporting measured relative output and dosimetric field widths concurrently is comprehensive but somewhat cumbersome. What has been shown here is that using as a small field metric relieves much of the ambiguity in reporting and simplifies the measured dosimetric field widths into one representative value. In addition, adopting a standard experimental methodology that includes reporting uncertainties in both the effective field size and measured output ratios is vital and consistent with the importance given to the expression of uncertainties documented in the IAEA dosimetry code of practice [
The Monte Carlo simulations clearly show that the dosimetric field size is larger than the geometric field size for small fields (as previously reported by Das et al. [
]). In all cases the dosimetric field width defined by the upper jaws was larger than that defined by the lower jaws. The upper jaws are closer to the source when compared to the lower jaws and therefore require a smaller physical separation to collimate the same geometric field width. The result is greater source occlusion across the upper jaw and therefore an increased effective field size. In short, dosimetric field widths increase as a function of increased source occlusion. For the same reason the dosimetric field widths increase as a function of electron spot size increase. The effective field size should therefore be used when tuning the focal spot size of a linear accelerator Monte Carlo model. As evidenced in Fig. 3, using the geometric field size may result in an incorrect spot size being determined.
There was a negligible difference in the output factors when was applied using the geometric field size or the effective field size. This is consistent with the work of Scott et al. [
] which showed that a 1.0 mm field size difference results in a 1.0% difference in . However, it is recommended that the effective field size be used when assigning , as it provides consistency within the proposed methodology and standardizes the application across a population of linacs.
Presenting small field relative output data as a function of the effective field size, as defined is this work, can be well justified when one considers the phantom and head scatter factor characteristics of small fields. McKerracher and Thwaites [
] show that for square field sizes of side <4.0 cm measured phantom scatter factors are independent of collimation and linac design and dependent only on measurement depth and the beam area irradiated. It is therefore quite reasonable to argue for the use of in comparing small field dosimetric quantities across multiple linacs or different collimation systems (jaws, MLCs and cones). Head scatter factors for rectangular field sizes have been shown to be dependent on the collimator exchange effect [
] note, this effect is negligible at field sizes of side <2.0 cm, where source occlusion becomes the dominant effect. Reporting relative output as a function of the , which one will recall is calculated from the measured dosimetric field widths, clearly takes into account differences in source occlusion for millimeter scale changes in field size. The application of as a reporting mechanism for rectangular field sizes with sides <2.0 cm would require additional investigation. Naturally there may be limitations in further application of the concepts presented here and in no way should one apply or without rigorous experimental validation.
Conclusion
It has been shown that adopting this field size metric and the measurement methodology outlined in this study can provide consistency for small field dosimetry across a population of linear accelerators. However, there could be differences between accelerator designs with greater source occlusion due to a larger focal spot size, a collimation system closer to the source, or simply a smaller field size.
Acknowledgements
Gavin Cranmer-Sargison was funded through a Saskatchewan Cancer Agency research grant. Paul Charles was funded by the Australian Research Council in partnership with the Queensland University of Technology (QUT), the Wesley Research Institute and Premion (Linkage Grant No. LP110100401). Paul Charles would like to thank Tanya Kairn, Trent Aland and Nigel Middlebrook from Premion for assistance with the measurements.
ICRU. Determination of absorbed dose in a patient irradiated by beams of x or gamma rays in radiotherapy procedures. Report No. 24, U.S. National Bureau of Standards; 1976.
On the output factor measurements of the CyberKnife iris collimator small fields: Experimental determination of the correction factors for microchamber and diode detectors.
Aspradakis MM, Byrne JP, Palmans H, et al. IPEM Report Number 103: small field MV photon dosimetry. Published by the Institute of Physics and Engineering in Medicine; 2010.
Monte Carlo modelling of diode detectors for small field MV photon dosimetry: detector model simplification and the sensitivity of correction factors to source parameterization.
Monte Carlo simulated correction factors for machine specific reference field dose calibration and output factor measurement using fixed and iris collimators on the CyberKnife system.
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