Detectors assessment for stereotactic radiosurgery with cones

Abstract The purpose of this work is to assess eight detectors performance for output factor (OF), percent depth dose (PDD), and beam profiles in a 6‐MV Clinac stereotactic radiosurgery mode for cone irradiation using Monte Carlo simulation as reference. Cones with diameters comprised between 30 and 4 mm have been studied. The evaluated detectors were ionization chambers: pinpoint and pinpoint 3D, diodes: SRS, P and E, Edge, MicroDiamond and EBT3 radiochromic films. The results showed that pinpoints underestimate OF up to −2.3% for cone diameters ≥10 mm and down to −12% for smaller cones. Both nonshielded (SRS and E) and shielded diodes (P and Edge) overestimate the OF respectively up to 3.3% and 5.2% for cone diameters ≥10 mm and in both cases more than 7% for smaller cones. MicroDiamond slightly overestimates the OF, 3.7% for all the cones and EBT3 film is the closest to Monte Carlo with maximum difference of ±1% whatever the cone size is. For the profiles and the PDD, particularly for the small cones, the size of the detector predominates. All diodes and EBT3 agree with the simulation within ±0.2 mm for beam profiles determination. For PDD curve all the active detectors response agree with simulation up to 1% for all the cones. EBT3 is the more accurate detector for beam profiles and OF determinations of stereotactic cones but it is restrictive to use. Due to respectively inappropriate size of the sensitive volume and composition, pinpoints and diodes do not seem appropriate without OF corrective factors below 10 mm diameter cone. MicroDiamond appears to be the best detector for OF determination regardless all cones. For off‐axis measurements, the size of the detector predominates and for PDD all detectors give promising results.


| INTRODUCTION
Effectiveness of Linac-based stereotactic radiosurgery (SRS) with small cone sizes (few millimeters) brings to more and more frequent use, especially for brain treatments (metastases, trigeminal neuralgia, arteriovenous malformation (AVM), and other brain localizations). [1][2][3] To ensure the quality of these treatments with small field sizes, measurements of percentage depth dose (PDD) curves, tissue-phantom ratios, profiles, and output factors (OF) should be well achieved in spite of the size and composition of the detectors. [4][5][6][7] In this study we will focus on some high dosimetry accuracy measurements of OF, PDD, and off-axis measurements for use of small photon fields in SRS cone irradiation with diameters between 30 and 4 mm.
The required determination of OF will not target on correction factors of the OF as mentioned in several research groups. 4,8 Our purpose is to assess the variation in performance of eight detectors for OF, but also to study for some of these detectors their performance for PDD and beam profiles measurements in a clinical 6-MV linear accelerator photon beam using the PENELOPE Monte Carlo (MC) code 9 as reference.

2.A | Conventional Linac-based device
Measurements were performed by means of a linear accelerator Clinac 2100C (Varian Medical System, Pal Alto, CA) at 6-MV photon beam with an energy index (TPR 20,10 ) of 0.669. The Linac is equipped with an accessory slot mounted cone system developed by BrainLAB. The cone set consists of ten cones with diameters of 30, 25, 20, 17.5, 15, 12.5, 10, 7.5, 5, and 4 mm at the isocenter. The field size defined by the jaws behind the cones was set to 4 × 4 cm square. The Linac nominal dose rate was fixed at 600 MU/min.

2.B | List of used detectors
Seven active detectors and a passive one (Radiochromic film EBT3) were used (Table 1).
Diodes and MicroDiamond detectors were used in axial orientation while the ionization chambers were used in both axial and radial positions.

2.D | OF measurements
In this work, the output factor (OF coll ) was defined by Eq. (1): where D coll represents the measured dose by the detector (det) for each collimator and D 30mm the reference dose measured with the 30-mm diameter collimator. The latter was used as a reference instead of the standard 10 × 10 cm field for two reasons: (a) it is closer to the small fields while there is still sufficient electronic equilibrium and good agreement between measurements made with various types of detectors, 11 (b) in this way, it is not necessary to take into account the contribution of backscatter from X-Y jaws to the beam monitor in the Monte Carlo simulation because jaws position was fix whatever the cone diameter studied.

2.D.1 | Active detectors
After each detector or cone changes, in-plane and cross-plane, profiles were done to center the detector. By means of PTW UNIDOS Webline electrometer for all active detectors, dose measurements were achieved with 100 MU and averaged over a series of at least three repeated runs on different days.

2.D.2 | Passive detector
In order to find the beam center of the film and to place automati-  This method allows to work in the ideal dose range for the film and to obtain the same signal to noise ratio and thus the same uncertainty whatever the cone size is. For films, the output factor (OF coll ) was defined by Eq. (2): Where D coll represents the EBT3 measured dose for a given colli-

2.F | Beam profiles measurements
Profiles measurements were achieved with a water phantom for active detectors and a solid water equivalent one for the films.
To analyze the film profiles, we developed a routine which detects the circular field center and makes 18 coaxial profiles, passing through the center, spaced by 10 degrees angle. This method makes a reduction of the statistical noise without creating several parallel profiles and thus increasing the "sensitive volume" of the detector.

2.G | Monte Carlo simulation
The PENELOPE code 9 is one of the several general-purpose MC packages available intended for simulation of particle transport in radiation therapy. This code is reliable mostly due to the advanced physics and algorithms for their electron transport component. Here, the user-code PenEasy 13 was used. PenEasy is a modular, generalpurpose main program for the PENELOPE Monte Carlo system including various source models, tallies and variance-reduction techniques (VRT). The code includes a new geometry model for performing quadratic and voxelized geometries.
The treatment heads of the Clinac 2100C were simulated according to manufacturer specifications. The geometry of the accelerator is composed of: target, primary collimator, beryllium plate, flattening filter, monitor chambers, mirror, jaws, Mylar plate, and collimator cone (see Fig. 1).
Source characteristics of the 6-MV photon beam were determined iteratively by varying the energy of the primary electron beam, its energetic dispersion, and its shape. 14-17 Parameters used for the primary electron beam was based on a monoenergetic 5.95 MeV beam impinging on the target with a Gaussian spatial distribution and a FWHM of 1 mm. With these parameters, PDD and profile comparison between simulation and measurement do not exceed ±1% in homogenous water phantom for field sizes comprised between 2 × 2 cm and 20 × 20 cm.
Interaction forcing variance reduction and phase-space file (PSF) techniques were used in the simulation of the treatment head.
Bremsstrahlung event is forced in target with a factor of 20. It means that the interaction probability of this event will be increased by a factor of 20. The phase space was realized just before collimator cone because the geometry is not modified upstream. PSF is read several times (between two and five times) in order to obtain the desired statistical uncertainty. All the variance reduction techniques applied were tested in order to prove that they do not change the physics of the calculation and they provide an unbiased estimate of any scored quantity.
The transport energy cutoff of photons and charged particles were respectively 10 and 100 keV. The threshold energies for charged radiative particle and inelastic collisions were set equal to 10 keV. The parameters C1 and C2, modulating the limit between detailed and condensed charged particle simulation, were set to 0.05.
The small volumes of water used for the calculation of D coll in Eq. (1) were taken to be a cube with 1 mm side centered in the beam axis.

3.A | Statistical and reproducibility aspects of the OF, PDD and beam profiles determination
For the OF, PDD, and profiles determination with Monte Carlo simulations, the statistical uncertainties (type-A) were lower than 0.8%.
In the case of active detectors (diodes, ionization chambers, and MicroDiamond), all the measurements were repeated three times in a water tanker at three different days. The uncertainty based on the TRS-398 report uncertainties 18  | 91 dosimetry multichannel correction, 10,20,21 we obtained a relative uncertainty less than 1.5%.

3.B.3 | MicroDiamond
The output factor measured with the MicroDiamond detector slightly overestimates the value, in comparison with the MC simulation, up to 3.7% for all the cones (Fig. 2). This overresponse is also observed by Ralston et al. 5 For the smallest cones (4 and 5 mm diameters), this active detector presents promising results.

3.B.4 | Radiochromic EBT3 film
Using radiochromic EBT3 film to determine OF is commonly accepted and validated in the literature. 6,8,23 Then, as expected, the OF measurement with this film, are the closest to MC simulations than those obtained with the active detectors. The maximum difference with MC is ±1% whatever the cone size is. film, the penumbra difference with MC is even less than 0.1 mm.

3.C | Beam profiles results
In   24 Tyler et al., 25 Yarahmadi et al. 26 and many other authors, the ionization chamber size, even the pinpoint type (Fig. 3), is too big and shows the widest penumbra for all the cones. The excellent sensitive volume of the MicroDiamond    EBT3 Gafchromic films are known to have a high spatial resolution 6,25,26 explaining the proximity of these results with those of MC (Fig. 7). This agreement is within ±0.15 mm for all the curves.

| DISCUSSION
According to report 103 of IPEM, 28 MV photon beam was defined as "small field" when the field size is not enough to provide charged particle equilibrium at the position of measurement and the collimation device obstructs part of the direct beam source as viewed from the point of measurement. When the lateral electronic equilibrium is not achieved (field size less than the lateral range of secondary electrons), electrons of lowest energy are missing on the beam axis causing an increase of the electronic spectrum average energy. At the same time, decreasing field size causes photonic spectrum modification ( Fig. 9) that induce in turn spectrum modification of secondary electrons.
These effects will be directly in relation with the nonwater equivalence detectors (density and composition). Indeed, for these detectors, the electron stopping power ratios 24,29 and the absorption coefficient ratios of photons between water and detector material vary according to the electronic energy spectrum.
In addition, the size of the detector used for the OF estimation and beam profiles measurements has a crucial importance to limit the partial volume effect. Figure 10 shows a 1D perpendicular dose profile of a 4-mm diameter cone for a 6-MV photon beam and the size of the different active detectors: MicroDiamond, pinpoints, diodes SRS, P, E, and Edge.
T A B L E 5 FWHM of profiles simulated and calculated with all detectors for different cone size diameters.

FWHM (mm)
Cone diameter (mm)  30 who determines that a field size was "small" when the square is less than 12 mm for a 6-MV beam. For smaller cones, the size of the detectors is the main reason in the underestimation of OF or the disagreement between measured beam profiles and MC-simulated ones: it is the case of the pinpoint ionization chamber due to its largest air cavity volume and the induced partial volume effects. 7,22 Diodes are the smallest detectors and are commonly used for  The MicroDiamond detector which is a synthetic diamond material overestimates the OF with a maximum gap of 3.7%. This detector has a good signal-to-noise ratio and a much better water equivalence than the other studied diode detectors, its size ( The very good results of EBT3 film on OF and beam profiles measurements, confirmed in many publications, 6,8,23 is close to being a perfect detector: dosimetrically water equivalent, high spatial resolution, and minimal energy dependence. 33 However, it is complicated to use, not a real-time dosimeter and can have some uncertainties due to film polarization, scanner non-uniformity and handling techniques. 25 However, for the first OF determination of a new machine (Cyberknife, linear accelerator), radiochromic film is an unavoidable detector with recognized accuracy.

| CONCLUSION
Monte Carlo simulation, as our gold standard, helps us to determine, over the wide range of detectors we used the most appropriate for measuring the OF, beam profiles and PDD. It is confirmed here that the radiochromic film, especially EBT3 film is the more accurate detector for OF and off axis profile determination of stereotactic cones but it is restrictive to use. Due to inappropriate size of sensitive volume and composition of respectively the pinpoints and the diodes, these detectors do not seem to be suitable without OF corrective factors particularly for cones with diameters below 10 mm.  Nevertheless, these diodes are effective and recommended for beam profiles and PDD measurements whatever the cone diameter is.
Finally, despite its sensitive volume size MicroDiamond seems to be a good consensual detector for OF determination for all used cones.

ACKNOWLEDGMENT
We thank the Scientific Center of Monaco (CSM) for its collaboration and financial support in this study.

CONF LICT OF I NTEREST
The authors declare that they have no conflict of interest.