CyberKnife® fixed cone and Iris™ defined small radiation fields: Assessment with a high‐resolution solid‐state detector array

Abstract Purpose The challenges of accurate dosimetry for stereotactic radiotherapy (SRT) with small unflattened radiation fields have been widely reported in the literature. In this case, suitable dosimeters would have to offer a submillimeter spatial resolution. The CyberKnife® (Accuray Inc., Sunnyvale, CA, USA) is an SRT‐dedicated linear accelerator (linac), which can deliver treatments with submillimeter positional accuracy using circular fields. Beams are delivered with the desired field size using fixed cones, the InCise™ multileaf collimator or a dynamic variable‐aperture Iris™ collimator. The latter, allowing for field sizes to be varied during treatment delivery, has the potential to decrease treatment time, but its reproducibility in terms of output factors (OFs) and dose profiles (DPs) needs to be verified. Methods A 2D monolithic silicon array detector, the “Octa”, was evaluated for dosimetric quality assurance (QA) for a CyberKnife system. OFs, DPs, percentage depth‐dose (PDD) and tissue maximum ratio (TMR) were investigated, and results were benchmarked against the PTW SRS diode. Cross‐plane, in‐plane and 2 diagonal dose profiles were measured simultaneously with high spatial resolution (0.3 mm). Monte Carlo (MC) simulations with a GEANT4 (GEometry ANd Tracking 4) tool‐kit were added to the study to support the experimental characterization of the detector response. Results For fixed cones and the Iris, for all field sizes investigated in the range between 5 and 60 mm diameter, OFs, PDDs, TMRs, and DPs in terms of FWHM measured by the Octa were accurate within 3% when benchmarked against the SRS diode and MC calculations. Conclusions The Octa was shown to be an accurate dosimeter for measurements with a 6 MV FFF beam delivered with a CyberKnife system. The detector enabled real‐time dosimetric verification for the variable aperture Iris collimator, yielding OFs and DPs consistent with those obtained with alternative methods.


| INTRODUCTION
The CyberKnife ® system can deliver stereotactic radiotherapy (SRT) treatments with high doses in a few fractions using small radiation fields, with submillimeter positional accuracy. 1,2 The linear accelerator (linac), mounted on a robotic arm, is operated without a flattening filter and the treatment beam is shaped using fixed circular cones, the InCise™ multileaf collimator or the variable aperture Iris™ collimator (Fig. 1). 1,3 The latter, allowing for the radiation field size to be varied during treatment delivery, has the potential to decrease the peripheral dose compared to fixed collimators 4 and to reduce treatment time. 3 A CyberKnife system, the first of its kind in Australia, was recently installed at the Sir Charles Gairdner Hospital (SCGH), Nedlands, WA, with promising early clinical results. 5 Small-field dosimetry, known to be challenging due to volume averaging effects and a lack of charged particle equilibrium (CPE), has been extensively discussed in the literature. 6,7 The problems associated with small-field dosimetry for flattened beams are likely to be compounded in flattening filter free (FFF) beams, given their inherently higher dose gradients, not just the penumbral region but also in the central beam, and higher doses per pulse. 8,9 In the context of small-field SRT, the accuracy of treatment planning systems (TPSs) in predicting dose distributions can be significantly limited by uncertainties in underlying dosimetry data. 2 In particular, incorrectly measured output factors (OFs) can result in systematic uncertainties leading to incorrect TPS-derived output. 10 This would be a major concern when a variable aperture collimator such as the Iris is used, for which its mechanical reproducibility would have to be verified.
Dedicated dosimeters are an essential part of a small-field-specific quality assurance (QA) protocol, which has been shown to be clinically justified. 11 These would ideally have a small water-equivalent sensitive volume (SV), allowing for high positioning accuracy, and show negligible energy, dose rate, and directional dependence. 12 Although commercially available detectors do not satisfy all of the above criteria, it has been common practice to perform measurements with at least two types of dosimeters to cross-check the consistency of results, 13 as recently recommended by an ICRU report. 6 For a CyberKnife system, the dosimeter of choice for beam characterization has long been the Gafchromic film, thanks to its small energy dependence and high spatial resolution. 14,15 Films, though, require a postirradiation analysis process with long waiting times.
Film-derived readings may be affected by large uncertainties due to batch-to-batch sensitivity variations, film polarization, nonuniformity, scanning, and handling techniques. 13 Solid-state detectors have stable response, a ratio of signal in dosimeter to dose in water that is nearly energy independent in the megavoltage photon range (while calibrated at a depth in water, the same calibration can be used for other depths), high sensitivity and small SVs. Solid-state detectors thus have the potential to offer comparable performance to Gafchromic film, though with a real-time readout. Their use is recommended by a recent IAEA-AAPM dosimetry protocol, 7 but only single detectors used with various scanning techniques have been shown to offer submillimeter spatial resolution. 6 When used for small-field dosimetry, correction factors need to be applied to account for beam perturbations, due to their SVs and extracameral components. These factors depend on detector design, treatment head design, beam quality, field size, and measurement conditions. 6 Monte Carlo (MC) codes are commonly used for modeling linac beam lines, and have been shown to be an effective tool in characterizing detector response in small radiation fields and their required correction factors. 16 Nevertheless, these remain inconvenient to use in practice, especially for percentage depth dose (PDD), tissue maximum ratio (TMR), and dose profile (DP) measurements because of the multidimensional factor dependencies (field size, depth, and distance). 16 Most importantly, corrections factors from MC simulations require knowledge of the detector construction and deficiencies in information provided by vendors, or manufacturing variability, will lead to inaccurate results. 17 A preferable solution would be to design a "correction-free" detector, or one maintaining a correction factor close to unity. This has been shown to be possible with the addition of low density media to the high density detector components. 18 However, it would still be necessary to verify that these modifications are appropriate under all beam quality and measurement conditions. 19 The Octa is a 2nd generation monolithic silicon-diode array detector designed by the Centre for Medical Radiation Physics a submillimeter resolution, for any given field size. The Octa was previously characterized as an accurate detector for relative dosimetry under irradiation with both flattened and FFF beams, for small radiation fields as defined with photon jaws. 20 In the present study, the potential of the Octa for beam characterization in the particular case of small radiation fields for SRT treatments with the CyberKnife system was evaluated.

2.A | The Octa detector
The Octa is a 2D monolithic silicon array detector based on SVs fabricated on a high resistivity p-type epitaxial layer, 21  The device (Fig. 2) has a submillimeter resolution with diodes having a 0.3 mm pitch along the vertical and horizontal arrays and 0.43 mm pitch along the two diagonal arrays. The diodes are operated in passive mode and are connected to a multichannel readout electronics data acquisition (DAQ) system based on a commercially available analogue front end (AFE0064, Texas Instruments), which was previously described in detail. 22,23 An equalization procedure 24 is used to correct for small differences in each channel response. The Octa is sandwiched between two Perspex plates, each 5 mm thick, with a small air gap on top of its SVs to minimize the number and size of corrections that are required to relate its readings to dose. 25

2.B | Experimental measurements
Experimental measurements described in this study were carried out at the Sir Charles Gairdner Hospital (SCGH), Nedlands, WA, Australia, with an Accuray CyberKnife M6 linac. IBA solid water slabs type RW3 were used to reach the required measurement depths.
Measurements by the Octa were compared with those made using a PTW SRS diode 60018 mounted parallel to be them axis in an IBA 3D water-phantom. The diode was oriented vertically, measuring at the effective point of measurement of 1.3 mm from top surface. Its readings were corrected using the correction factors by Francescon et al. 26

2.C | Output factors and dose profiles
In this study, output factors were defined as the ratio between the detector reading at a specific field size (clin) and that at the machine specific reference field (msr), following the formalism used by Francescon et al. 26 : where M fclin and M fmsr are the corrected detector readings in the f clin and f msr fields respectively. For the CyberKnife system, the reference field was taken as that given by the 60 mm diameter collimator.
The OFs and DPs were measured by the Octa at 15 mm depth in solid water, 800 mm source to detector distance (SDD).
Prior to the measurements, the Octa was aligned with respect to the treatment machine central axis (CAX) by maximizing the response of its central pixel using the smallest available field size (5 mm diameter). Once aligned, for any given field size, OF and DPs (in-plane, cross-plane, and two diagonals) were measured simultaneously.
For OF measurements, the detector reading at each field size was taken as the average response of its central pixel over three repetitions of the same measure. This was followed by normalization of these averages to the average reading at the reference field size.
For DP measurements, the Octa reading at each field size was taken as the reading of each channel averaged over three repetitions of the same measure followed by normalization of the response of each channel to the median response of the pixels within 0.5 mm of the CAX. For a quantitative estimation of the FWHM and penumbra width, all profiles were analysed with MATLAB (Mathworks, Inc., Natick, MA, USA) using a shape preserving interpolant function.
Penumbra width was taken as the distance between the 80% and the 20% isodose levels.
Following the approach recommended by the vendor, 3   Nominal solid water depths were converted to water equivalent depths including accounting for the density of Perspex plates. For a quantitative estimation of the percentage differences, measured values were analysed with MATLAB using a shape preserving interpolant function.

2.E | Monte Carlo GEANT4 application
Calculations with GEANT4 (GEometry ANd Tracking 4), 27 a general purpose MC tool-kit for the simulation of the passage of particles through matter which has been validated for medical applications by different groups, 28,29 were added to the study to support the experimental characterization of the detector response.
The International Atomic Energy Agency (IAEA) phase space (PHSP) files containing the detailed description (position, direction, kinetic energy, statistical weight, type) of the particles scored at the exit of the Iris collimator, for a CyberKnife linac, were downloaded from the online repository (http://www-nds.iaea.org/phsp/ phsp.htmlx). The PHSP files, previously validated by Francescon et al., 30 were read by a GEANT4 application purposely developed in-house for this study using a C++ class adapted from a previous work by Cortés-Giraldo. 31 The PHSP files were in this way used as the primary generator in the GEANT4 application in order to simulate the irradiation of a solid water phantom. The solid water was modeled as the IBA type RW3, to match that used for the experimental measurements with the Octa. The GEANT4 Standard EM physics list option 4 was used in this study, with production cuts set to 0.1 mm for electrons and photons in the phantom.

3.B | Dose profiles
Representative equivalent circular profiles for the Octa and SRS diode are shown in Fig. 4 for fixed cones and in Fig. 5 for Iris collimated radiation fields. In Fig. 6, equivalent profiles measured by the Octa for fixed cones are compared to those measured for the Iris, for the same nominal field size. In Fig. 7 in-plane nonaveraged profiles measured by the Octa are compared before and after a reset of the Iris, defined as setting the aperture of the collimator to the desired size, followed by its complete closure and then a reset of the aperture to the desired size.
Profiles are shown in the figures aligned such that the origin lies at the coordinate corresponding to the 50% response. Error bars, calculated as 3 standard deviations, did not exceed the symbol size. F I G . 7. In-plane dose profiles measured by the Octa before (1) and after (2) a reset of the Iris collimator, for (a) 5 mm, (b) 7.5 mm, and (c) 10 mm diameter circular field sizes. Profiles are aligned to the 50% response. In the DP relative to the 10 mm diameter, a small asymmetry attributed to the non-perfect uniformity of the detector response could be appreciated. Table 1 for fixed cones and in Table 2 for the Iris. Figure 8 shows the depth doses measured by the Octa in solid water, the SRS diode in water tank and MC calculated in solid water for the 60 mm diameter Iris. Figure 9 shows the TMRs measured by the Octa in solid water and SRS diode in water tank for the 5 mm and the 60 mm diameter fixed cones. Error bars, calculated as 3 standard deviations, did not exceed the symbol size for both experimental measurements and MC calculated results.

4.A | Output factors
Silicon diodes are known to require corrections for output factor measurements due to the electron spectra being perturbed in silicon with respect to water, an effect that increases with decreasing field size. This perturbation has been attributed to the atomic number, mean excitation energy (I-value) and density of silicon SVs being different from that of water, with the nonsilicon extra-cameral components of the detector playing a non-negligible role. 32,33 FFF beams, which have a lower average beam energy than corresponding flattened beams, 9 may require a different correction factor.
In this study, the Octa OFs were accurate within 3% with respect to the SRS diode for both fixed cones and the Iris, with a maximum discrepancy of 2.9% found for the 5 mm diameter Iris.
Discrepancies for the Octa with respect to the expected MC T A B L E 1 Summary of FWHM and penumbra values measured by the Octa and the SRS diode for radiation fields defined by fixed cones. Values refer to representative equivalent profiles measured at 15 mm depth, 800 mm SDD. properties of the collimator. Ideally, this would have to be a longterm test.

4.B | Dose profiles
Small irregularities in the profiles measured by the Octa are due the applied equalization procedure not being able to completely correct for the nonuniform sensitivity of the 512 diodes.
Overall, FWHM values for the Octa for in-plane, cross-plane, and diagonal DPs were well within 3% with respect to the SRS diode values. In particular, for the fixed cones, a maximum discrepancy of 2.6% in FWHM was found for the 7.5 mm diameter field, with differences in penumbra within 0.2 mm for all fields investigated. For the Iris, a maximum discrepancy of 2.9% in FWHM was found for the 10 mm diameter aperture, with differences in penumbra within 0.2 mm for all apertures investigated.
When comparing equivalent profiles measured by the Octa for fixed cones against those measured for the Iris, all discrepancies were within the spatial resolution of the device of 0.3 mm. In particular, with DPs analysed with MATLAB using a shape preserving interpolant function, a maximum difference of 4% in FWHM was found for the 5 mm aperture (0.2 mm), along with a 2.7% difference for the 7.5 mm aperture (0.2 mm) and 2% difference for the 10 mm aperture (0.2 mm). Penumbra values were accurate within 0.2 mm.
These results, which were supported by equivalent SRS diode measurements, were consistent with those of a previous investigation in which FWHM and penumbra values for fixed cones and the Iris were found to be in substantial agreement, with a maximum discrepancy of 0.2 mm in penumbra width for the 5 mm diameter. 36 By the vendor's technical specifications, the average penumbra for the Iris is expected to be larger by 0.2 to 0.6 mm than that for the equivalent fixed cone and to increase with field size, a consequence of the stepwise approximation of a divergent collimator shape because of the increase in transmission penumbra. 3 To our knowledge, no other intercomparison between Iris and fixed cones collimator dose profiles exists in the literature.
The Iris collimator is designed to achieve an aperture reproducibility of 0.2 mm at 800 mm SDD, 3 44 It was found that while the ArcCHECK addresses some of the small-field dosimetry challenges (its diodes have real-time response, high sensitivity and sub-mm lateral size of the SVs), the measurement of field sizes with diameter inferior or equal to the SVs pitch should be considered with care.
When considering machine-specific QA applications for the smallest field sizes offered by a CyberKnife (5, 7.5, and 10 mm diameter), the 1000SRS is probably the most obvious choice. The Octa array offers a comparable performance for OFs measurements, without the volume averaging effect of the former, with a superior nominal spatial resolution for DP measurements and most importantly pulse-per-pulse real-time acquisition.

| CONCLUSIONS
In this work, the Octa detector has been investigated for the dosimetry of small radiation fields as used in SRT with the Cyber-Knife system. For any given field size, the Octa allowed for the simultaneous real-time read-out of OFs and dose profiles for crossplane, in-plane, and two diagonal directions. PDD and TMRs were accurate within 3% with respect to both SRS diode and MC simulations, for all field sizes investigated. The Octa was used for a real time high-spatial resolution verification of the Iris variable aperture reproducibility in terms of FWHM and penumbra values of the dose profiles, as well as OFs. The Iris reproducibility was found to be within the vendor's technical specifications.
Overall, the Octa was shown to be a 'correction-free' dosimeter for routine QA for a CyberKnife system, offering a reliable real-time read-out along with unique properties for dosimetry verification, such as a long-term stability evaluation of the Iris collimator.

ACKNOWLEDGMENTS
We acknowledge the Gross Foundation and National Health and the Medical Research Council of Australia grant APP 1123376 for financial support. We thank the Sir Charles Gairdner Hospital for access to their CyberKnife ® .

CONFLI CTS OF INTEREST
The authors have no relevant conflicts of interest to disclose.