Feasibility study of using Stereotactic Field Diode for field output factors measurement and evaluating three new detectors for small field relative dosimetry of 6 and 10 MV photon beams

Abstract This study assesses the feasibility of using stereotactic field diode (SFD) as an alternate to gaf chromic films for field output factor (FF) measurement and further evaluating three new detectors for small field dosimetry. Varian 21EX linear accelerator was used to generate 6 and 10 MV beams of nominal square fields ranging from 0.5 × 0.5 cm2 to 10 × 10 cm2. One passive (EBT3 films) and five active detectors including IBA RAZOR diode(RD), SFD, RAZOR nanochamber (RNC), pinpoint chamber (PTW31023), and semiflex chamber (PTW31010) were employed. FFs were measured using films and SFD while beam profiles and percentage depth dose (PDD) distribution were acquired with active detectors. Polarity (kpol) and recombination (ks) effects of ion chambers were determined and corrected for output ratio measurement. Correction factors (CF) of RD, RNC, and PTW31023 in axial and radial orientation were also measured. Stereotactic field diode measured FFs have shown good agreement with films (with difference of <1%). RD and RNC measured beam profiles were within 3% deviation from the SFD values. Variation in kpol with field size for RNC and PTW31023 was up to 4% and 0.4% (for fields ≥ 1 × 1 cm2), respectively, while variation in ks of PTW31023 was <0.2 %. The maximum values of CF have been calculated to be 5.2%, 2.0%, 13.6%, and 25.5% for RD, RNC, PTW31023‐axial, and PTW31023‐radial respectively. This study concludes that SFD with appropriate CFs as given in TRS 483 may be used for measuring FFs as an alternate to EBT3 films. Whereas RD and RNC may be used for beam profile and PDD measurement in small fields. Considering the limit of usability of 2%, RNC may be used without CF for FF measurement in the smallfields investigated in this study.


| INTRODUCTION
In recent years, the use of small fields (<4 × 4 cm 2 ) in radiation therapy has increased many folds after the introduction of modern radiotherapy techniques such as intensity modulated radio therapy (IMRT), stereotactic radiosurgery (SRS), stereotactic body radiotherapy (SBRT) etc. Dose measurement in small fields has been a challenge due to various problems such as lack of charged particle equilibrium, source occlusion and penumbra overlapping. [1][2][3] This is further complicated by the perturbations from different components of the detector, as well as the size of the detector comparable or larger than the radiation field. [4][5][6] The last decade has witnessed a lot of effort for identification of suitable detectors and/ or applying appropriate corrections to employ these detectors for accurate dose measurement in small fields. [7][8][9][10][11] Yet, there is no one-size-fits-all solution available for small field dosimetry with each detector having its own pros and cons. 12,13 However, new detectors are being introduced to meet the above-mentioned challenges.
For field output factor (FF) measurement, volume averaging effect (due to the detector size) and fluence perturbation (due to the existence of high-density material in any detector) are the major detector related challenges. Therefore, output correction factors (CF) are required to correct detector response in small fields for the determination of FFs. 14 A detector is recommended for FF measurement with appropriate corrections if its CF is within AE5% for that particular field size. 13 While some studies have suggested that it may be used without any correction if its response is within AE2% of the actual FF. [15][16][17] GAFCHROMIC EBT films due to their very high spatial resolution, weak energy dependence and water-equivalence (z eff = 7.26), have been recommended for use as gold standard for accurate FF measurement. Hence, films can be employed for CF determination of other large volume and high density detectors using detector to detector correction approach. 13,18 However, tedious processing, nonreusability and passive nature of films require exploring other active detectors suitable for use as a reference. In this regard, unshielded diodes, like stereotactic field diode (SFD), could be a good choice due to their reduced perturbation and smaller volume, thus resulting in smaller CFs as reported in literature compared to shielded diodes and small vented air ion chambers (IC).
IAEA and AAPM have jointly published a code of practice (CoP TRS 483) for dosimetry of static small fields. 13 It provides guidelines for the selection of a detector for reference and relative small field  20 Liu et al have determined the CFs in the circular fields range of 5 to 30 mm, employing 30 mm as reference field. 21 Still these published results need to be validated for different beam lines and collimation systems. To the best of our knowledge novel PTW31023 with a new design has not been yet investigated for beam profile and depth dose measurement in small fields. However, It has been characterized for reference and relative dosimetry in the conventional fields by Bushing et al and Bruggmoser et al. 22,23 Recently, it has also been studied by Casar et al for determination of CFs in radial and axial orientations. 24 However, the response has not been corrected for polarity and recombination effects as recommended by TRS483. Similarly, RNC, the smallest commercially available IC, has been characterized for different dosimetric parameters specially the polarity and stem effects. [25][26][27] A couple of authors have reported output ratio measurements using RNC as well. [28][29][30] Casar et al has also determined the CFs for this detector in radial and axial directions without correcting its response for polarity effect. 24 However, before deploying these detectors for small field relative dosimetry further assessment is needed. Furthermore, the measurement setup is not uniform, as per recommendation of TRS 483, in most of the above-mentioned studies. Therefore, it is important to explore the measurement of CFs of these detectors following TRS 483 protocol, while considering polarity and recombination effects.
The present study aims at investigating the application of SFD as reference detector and evaluating three new detectors (RD, RNC, and PTW31023) not included in TRS483, for relative dosimetry of small fields under 6 and 10 MV beams collimated with jaws and multi leaf collimators (MLCs). The CFs of RD, RNC, and PTW31023 would be a valuable addition to the TRS 483 published data. Specific objectives of the study are as follows: • To evaluate the SFD with its corresponding CFs (published in TRS 483), as a substitute of EBT3 films, for determination of FFs of small fields.
• To investigate RD, RNC, and PTW31023 for measuring beam profiles and depth dose distribution in small fields.
• To investigate the effect of polarity and ion recombination for RNC and PTW31023 ICs in small fields.
• To determine the CFs of RD, RNC, and PTW31023 and to investigate the field size limit for each detector for correction less FF measurements in small fields.

2.A | Beam line and detectors
In this study, VARIAN CLINAC 21EX was used to generate 6 and 10 MV photon beams with a dose rate of 300 MU/min. The reference output of linear accelerator was 1 cGy/MU at the depth of maximum dose (d max ) as measured employing the IAEA standard protocol TRS398 for absorbed dose determination. 31 One passive detector, that is, GAFCHROMIC EBT3 films (ASHLAND) and five active detectors were employed. Active detectors included two diodes:Scanditronix IBA stereotactic field diode (SFD) and IBA RAZOR diode (RD) and three ionization chambers (IC) comprising IBA RAZOR nanochamber (RNC), pinpoint chamber PTW31023 and semiflex chamber PTW31010. Specifications of these detectors are presented in Table 1, while their radiographs are shown in Fig. 1.
SFD and RD are unshielded diodes that have demonstrated lesser perturbation for small fields. Both RNC and PTW31023 have the same cavity radius, that is, 1 mm, but the active volume of PTW31023 is larger due to its cylindrical shape unlike RNC which has spherical air cavity. RNC is the smallest commercially available IC. Novel PTW31023 IC is the successor of its old version PTW31014 with improved guard ring and inner electrode design to make it a reference class detector.

Detectors
Active material/additional components  Film analysis was carried out with DD System ver. 14.65 software (R-Tech. Inc. Japan)and central dose was measured in square region of interest (ROI) with size of 0.5 × 0.5 mm 2 drawn in the center of each exposed film employing ROI Analysis routine. The final dose was measured as the average of three films irradiated for each combination of field size, energy, and collimation system. The uncertainty in terms of relative standard deviation (1 rel. SD) was also calculated.

2.B.2 | Effective field size
Effective field size (s eff ) against each nominal field collimated with jaws and MLCs was measured with SFD using the following formula: where x and y are full width half maxima (FWHM) of crossline and inline beam profiles, respectively, measured at 10 cm depth in water phantom at SSD = 90 cm.

2.B.3 | Field output factors (FF)
FFs were measured with SFD and EBT3 films as described under.

A SFD
For SFD, the following two methods were employed to measure the FF.

a Direct method
FFs were determined with direct method for all fields using the formula given as under.
where M fclin,SFD and M fmsr ,SFD are the detector's readings (average of b Intermediate field method (IFM) Field output factors with SFD were also calculated employing IFM as given in Eq. (3). Field size of 3 × 3 cm 2 (the smallest field for which lateral charged particle equilibrium holds for both energies) was chosen as intermediate field 32 whereas semiflex PTW31010 (mentioned as subscript semi) ion chamber was used to limit the effect of energy dependence of SFD.
where CF fint fmsr ,semi is the CF of semiflex chamber for intermediate field with reference to msr field while CF fclin fint,SFD is the CF of SFD for clinical field with reference to intermediate field and can be calculated as follows: The correction factors for SFD and semiflex IC in above stated formulae were taken from TRS 483. Linear interpolation method was used to find CFs where needed as explained above.

c EBT3 films
Field output factors with EBT3 films were calculated employing method proposed by Garnier et al 33 Table 2. Advantages of this method include the irradiation of films in an ideal dose range and getting the same signal to noise ratio and hence the same uncertainty for all field sizes that would be compromised for smaller fields otherwise. 33 Field output factors with EBT films were calculated using Eq. (5).     Beam profiles with all detectors were measured several times (two to five) on at least two different days to estimate the uncertainty (1SD) that has been found to be <0.19 and 0.17 mm for FWHM and penumbra values respectively.

2.B.5 | Polarity and recombination correction factors of ion chambers
Small vented ICs exhibit a significant polarity and ion recombination effect that may vary with field size. Polarity correction factor (k pol ) was calculated for the investigated field sizes of both energies using the following formula: where M À and M þ are IC signals for negative and positive bias voltage (300 V for RNC and 200 V for PTW31023) respectively.
RAZOR nanochamber has previously been reported to show a minimal deviation (<0.3%) in recombination factor for small fields 27 and hence these were not recalculated in this work. However, for PTW31023 these factors need to be investigated for small fields.   Two voltage method, as given in Eq. (7), was used to calculate the recombination correction factor (k s ) as it gives linear relation between 1/M and 1/V in Jaffe plot 22 which is the basic condition for using this method. 13 where M 1 and M 2 are the IC's readings at bias voltage V 1 (200 V) and V 2 (100 V) respectively.
Stability time of at least 5 min and preirradiation of 10 Gy was given to each IC following the change of bias voltage on electrometer.

2.B.6 | Output ratios (OR)
For OR measurement in small fields, as defined in equation, detector''s signal (M) was corrected for influence quantities like temperature, pressure, polarity, and recombination effects.
where M fclin and M fmsr are corrected average signals of detector for clinical and msr fields respectively.
In order to reduce the uncertainty in measurement, signal for individual small fields was measured interleaving the msr field (10 × 10 cm 2 ) measurement as recommended in TRS 483.

2.B.7 | Correction factors
Correction factors (CFs) of RD, RNC, and PTW31023 for small field f clin were calculated using the following formula: where FF fclin is the average of the field factors as calculated from different methods defined in Eqs. Uncertainty (1 rel. SD) in the readings of each detector was calculated and its propagation for all arithmetic calculations was accounted for determining the final uncertainty in the correction factors. Table 3 shows the corresponding S eff (which is the true representative of an irradiation field) for each nominal field defined with jaws and MLCs based on the beam profile employing Eq. (1). It can be seen that the S eff values are somewhat larger than the nominal field size specifically for 10 MV beam energy and MLC collimated fields (except for MLC collimated reference fields). This increase becomes more significant as the field size is reduced, for instance S eff of 0.58 cm against nominal field of 0.5 × 0.5 cm 2 , that is, 0.08 mm increase corresponds to 16% increase while S eff of 4.08 cm against nominal field of 4 × 4 cm 2 shows an increase of only 2%. Difference between the FFs of SFD (for both IFM and direct method) and films has been found to be <1% with maximum difference of 0.92% for 0.5 × 0.5 cm 2 MLCs defined field of 10 MV beam.

3.B | Field factors
FFs measured with SFD (IFM) have been found to be closer to those measured with films for 10 MV jaws fields whereas for 10 MV MLCs fields, SFD (direct method) measured FFs show better agreement with films. The response is mixed for 6 MV fields.

3.D | Polarity and recombination effect of ion chambers
The polarity (k pol ) and recombination (k s ) correction factors of ICs as a function of field size are plotted for 6 and 10 MV photon beams in Fig. 6. It can be seen that the RNC exhibits a strong polarity effect that varies considerably with field size (in the range of 1.01 to 1.05). However, it has been found practically independent of the collimation system and beam energy in the whole range of field sizes. On the other hand, PTW31023 shows a little variation (<0.4%) in k pol for field size ≥ 1.0 × 1.0 cm 2 in radial orientation. Nevertheless, it deviates significantly for smallest fields. A considerable effect of orientation of PTW31023 on polarity effect is also evident in the smaller fields especially for 10 MV beam (Fig. 6 upper panel). Axial placement of PTW31023 gives larger deviation in k pol , that is, up to 5.9% for 10 MV beam compared to 0.9% deviation in radial direction. Figure 6 (lower panel) present k s of PTW31023 for 6 and 10 MV beams. Variation in k s with field size has been found to be <0.2% for both energies. The overall effect of chamber orientation and energy has been found to be insignificant in all fields. measured with RNC are most consistent with FFs, compared to other detectors, which result in CFs closer to unity as shown in Table 5. The maximum difference in OR of RNC and FF has been found to be 2 % for 1 × 1 cm 2 field of 6 MV MLC beam. RD over responds for fields smaller than 2 × 2 cm 2 resulting in the ORs larger than FF with maximum deviation of 5.2% for 6 MV jaws field size of 0.5 × 0.5 cm 2 . PTW31023 measured ORs are considerably smaller than FFs for small fields (with maximum deviation of up to 25% for 6 MV 0.5 × 0.5 cm 2 field). Furthermore, orientation of PTW31023 also affects OR measurement especially for the smallest field size.

3.E | Output ratios and correction factors
It is evident from Table 5  for field sizes down to 1 × 1 cm 2 of both energies while for smallest field its value increases to 5.2% (i.e. 0.948). Variation in CFs of all detectors has been found to be independent of the collimation system (with variation of <1.1% between MLCs and Jaws defined fields) but dependent on the effective field size.

| DISCUSSION
In this work, it is has been found that the effective field sizes of both energies are significantly different from nominal fields particularly for smallest field size (Table 3). Therefore, these are required to be measured for accurate determination of CFs.
For FFs, a good agreement (<1% variation) has been found between EBT3 films and SFD measurements (employing both direct and IFM methods) for all combinations of field size, energy, and collimation system (Fig. 3). This infers that SFD with corresponding CFs field size as large as 10 × 10 cm 2 . 36,38,39 Regarding ICs, RNC shows a strong polarity effect compared to PTW31023, as obvious from Fig. 6, which may be ascribed to its small size. 25 Spherical chamber design of RNC may also be a factor causing the larger polarity effect that may be reduced by increasing the length with smaller diameter of sensitive volume of IC (as in cylindrical shape of PTW31023). 40 Variation in k pol of RNC with field size is significantly high, that is, up to 4% while it is independent of energy and collimation system. On contrary, for PTW31023 it varies  Table 3). Numbers in parenthesis show the uncertainty (1 rel SD). • RD and RNC may be used for measuring beam profiles and PDDs (beyond build up region) in small fields with an accuracy of up to 3%. PTW31023 is not an appropriate detector for beam profiling though it may be used for PDD measurement.
• PTW31023 may be used as reference class IC in radial direction for fields ≥ 1 × 1 cm 2 as its k pol and k s values are within limits described in TRS 483 for these fields. Whereas RNC has considerably higher value of k pol that shows a significant variation with field size.
• CFs of a detector does not depend on collimation system but dependent on the effective field size and energy. In axial orientation, PTW31023 shows considerably smaller CF compared to radial direction.
• RNC may be used in all fields investigated in this study without any CF considering limit of usability of a detector to be 2%. RD and PTW31023 may be used without CF for fields down to 1 × 1 cm 2 and 1.5 × 1.5 cm 2 respectively. While smaller fields need to get appropriate CFs. However, to achieve a higher level of accuracy (>2%), corrections are required for each detector in all field sizes.

ACKNOWLEDGMENTS
We are grateful to Toyo-Medic Co., Ltd. (Japan) for lending us two detectors (RAZOR diode and RAZOR Nanochamber) for this study. We acknowledge the QST hospital for experimental measurements. The first author acknowledge the support of Higher Education Commission (HEC) Pakistan for providing fellowship under its IRSIP program.

CONF LICT OF I NTEREST
There is no conflict of interest.