Introduction
Accurate and precise delivery for stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) is done preferably using dedicated machines like GammaKnife (Elekta, Stockholm, Sweden) and CyberKnife (Accuray Incorporated, California, United States). With the advancement of technology and equipment, the SRS and SRT treatment at one time required the use of an invasive frame, and these techniques are now non-invasive and frameless and delivered using a linear accelerator (LINAC). The availability of high definition 2.5 mm multileaf collimator (MLC), 6D couch, KV CBCT, Brainlab Exactrac (Bavaria, Munich, Germany) online imaging system and flattening filter-free (FFF) beam have made it possible to use conventional LINAC for frameless SRS/SRT; Reference Mamballikalam, Senthilkumar, Bos, Basith and Jayadevan1 however, small field dosimetry is still a challenge.
Treatment planning systems are commonly used to simulate radiation delivery to the patient. SRS/SRT treatment plan verification shows more deviation than larger volumes. Any deviation in dosimetric parameters like dosimetric field size, profile, percentage depth dose (PDD) and output factor may affect the simulation results of the treatment planning system. It is the user’s responsibility to feed proper input data and validate the beam model. Hence, the choice of detector plays an important role in beam data measurements.
In this context, the modern LINAC provides an additional feature of FFF beam which has a special advantage in SRS/SRT. The fluence of photons that comes out of an unflattened beam is dosimetrically different from a flattened beam. Beam hardening does not occur since there is no flattening filter, and the fluence of photons contains a larger number of low-energy photons (<1 MeV). Reference Georg, Knöös and Mcclean2,Reference Dalaryd, Kragl and Ceberg3 There is much lower head scatter and contaminant electrons since the flattening filter makes a significant contribution to it. Reference Fogliata, Garcia and Knöös4 The variation of photon spectrum along the off axis is also much reduced in FFF beams.
Challenges in small field dosimetry
The difficulty in small field dosimetry lies in the electron transport created by the photon interaction with the medium. Reference Georg, Knöös and Mcclean2 At small field widths comparable to the lateral range of secondary electrons, the Bragg–Gray cavity theory fails. Hence, the ionisation chamber which has been the backbone of dosimetry in medicine may not be suitable for small fields. Small field dosimetry is strongly influenced by a lack of lateral electronic equilibrium, source occlusion and detector volume averaging. Reference Das, Morales and Francescon5
Lateral charge particle equilibrium
An absence of lateral charge particle equilibrium (LCPE) along the central axis of radiation field occurs in small field sizes. The full-width half-maximum (FWHM) of these small fields is less than the range of the secondary electrons. LCPE range (rLCPE) can be defined as the minimum radius of circular photon field for which the collision kerma in water and dose deposited in water are equal. These values have been obtained by simulating collision kerma and dose at depth 5 cm along the central axis of the beam. Reference Papaconstadopoulos, Tessier and Seuntjens6 The range of LCPE can be calculated with the following formula:
$${\rm{rLCPE}} = 8.369{\rm{\;TP}}{{\rm{R}}_{20,10}}\left( {10} \right) - 4.382$$
Ideally, the range of LCPE should extend to both sides of the detector. The minimum field size required to provide enough LCPE is twice the calculated range LCPE for a detector with infinitesimally small volume.
Partial occlusion of the source
When the field size becomes smaller than 3 × 3 cm2, source occlusion can affect the fluence output. The field would be entirely made up of penumbra region alone. The output along central axis would be much lower than open field output. The size of the source is generally less than 5 mm, and hence the loss of LCPE would occur for radiation beams with a radius less than 5 mm. Reference Donya, Seniwal, Darwesh and Fonseca8 Other literature suggests there is dependence on focal spot size in small field dosimetry; however, such an effect can only be seen for extremely small fields (<5 × 5 mm2). Reference Das, Morales and Francescon5,Reference Francescon, Cora and Satariano9 Moigner et al, Liu et al. and Czarnecki et al. have shown that there is not much dependence on source sizes of different machines for small fields. Reference Moignier, Huet and Makovicka10–Reference Czarnecki, Wulff and Zink12
Apparent field widening
The output for small fields would be much lesser than expected so, and FWHM of the reduced dose would appear to be at an extended distance from the central axis. Hence, the radiation field width obtained from FWHM on either side of the axis would be larger than the collimator setting (geometrical field width) for small fields where lateral electronic particle equilibrium is not satisfied.
There are various detectors commercially available for small field dosimetry. These are miniature ionisation chambers, diodes, synthetic diamonds, radiochromic film, plastic scintillators, metal-oxide-semiconductor field-effect transistors and gel dosimeters. Reference Das, Morales and Francescon5 Choosing a detector for small fields is based on literature with multiple confirmations, especially with Monte Carlo (MC) validation to confirm radiological equivalence to water. Reference Das, Cheng and Watts13 Francescon et al. states that the detector orientation plays an effect on depth dose and profile measurements. Reference Francescon, Beddar, Satariano and Das14
The additional correction factor k was introduced by Alfonso et al. in 2008 to account for necessary adjustments for possible changes in the detector response. It can be taken as an indicator for the suitability of a detector to be used in small field dosimetry. Reference Alfonso, Andreo and Capote15 The k values of the detector are obtained as the ratio of the dose measured with the detector to the dose simulated in MC. An ideal detector for small fields would show minimal variation from unity. Studies performed by Francescon Reference Francescon, Kilby and Satariano16,Reference Francescon, Kilby, Satariano and Cora17 et al. in CyberKnife showed that micro-ionisation chambers under-respond in small fields and diodes over-respond. Chalkley Reference Chalkley and Heyes18 et al. have stated that the PTW 60019 microDiamond detector was very good for relative dosimetry measurements. Benmakhlouf et al. found that the PTW microLiquid ionisation chamber and PTW 60019 microDiamond detectors were most suitable for Gamma knife dosimetry. Reference Benmakhlouf, Sempau and Andreo19 Other publications suggest IBA stereotactic field diode (SFD) and GafChromic as well. kΩ for various detectors in small fields varies from 0.92 to 1.14 in Siemens and Elekta Linacs. Reference Francescon, Cora, Cavedon and Scalchi20–Reference Chibani and Ma22 Bassinet et al. have provided k values for a range of detectors in 6 MV Varian LINAC against Gafchromic and small LiF TLD cubes. Reference Bassinet, Huet and Derreumaux23 Their work observes that the passive dosimeters are within 2% agreement for small fields. MC measurement by Papaconstadopoulus et al. has found that the kΩ value for microdiamond varied upto 1.4% down to 0.5 cm field sizes. Reference Papaconstadopoulos, Tessier and Seuntjens6
MC simulation
The simulations in PRIMO happen in three steps: (a) the particles are simulated in the top portion of the LINAC head; (b) the fluence from the head is transported down to the bottom part of the LINAC just above the phantom surface where a second phase space file is created. The collimator settings and MLC control points may be defined prior to this simulation; (c) the particle interactions are simulated in a defined phantom. The dimensions and the material of the phantom are defined by the user. Alternatively, a CT scan may also be imported into PRIMO.
The geometry of the accelerator must be known in order to simulate a clinically useful beam in MC. A phase space file contains the information of particles (energy, position, direction of flight, etc) traversing through a plane. When the phase space file contains a large number of particles, it can be taken as the source of radiation and the geometry above it can be neglected. 24 The user needs to only define the collimator settings and phantom geometry. The simulation of the collimator and geometry is not tedious. The variance reduction technique used in the phantom was particle splitting with a splitting factor increasing with decreasing field width. The splitting factor used was large enough to match the latence variance of the phase space files used. Gete et al. have validated first-generation phase space files for 6FFF and Belosi et.al have validated second-generation phase space files. Reference Gete, Duzenli and Milette25,Reference Belosi, Rodriguez and Fogliata26 Belosi states that Varian phase space files can be used as an accurate radiation source for MC simulations.
In this study, the dosimetric evaluation of various detectors suitable for small fields is performed. Their relative merit in the measurement of output factors and scan parameters (e.g., depth dose and profile measurements) is compared with that of MC simulation and their response, and suitability is evaluated.
Materials and Methods
All measurements in this study were performed under a 6FFF beam of Varian TrueBeam STx LINAC (Varian Medical Systems, California, United States). The TPR20,10 value of this beam was 0.632. The dose rate for the measurements was set to maximum at 1400 MU/min. The LINAC was calibrated to deliver 1 cGy/MU to water at maximum dose (dmax) for 10 × 10 cm2 at SSD set-up as per the recommendations of TRS 398. 27 The small fields for the study were defined by jaws and MLCs were retracted during the measurements. The field sizes set in the experiment were 0.8 × 0.8, 1 × 1, 2 × 2, 3 × 3 and 4 × 4 cm2. Three detectors were used in this study—IBA CC01 (IBA Dosimetry, Schwarzenbruck, Germany), IBA SFD (IBA Dosimetry, Schwarzenbruck, Germany) and PTW microDiamond (PTW, Freiburg, Germany). The results of these were compared with MC results simulated in PRIMO.
Radiation field width was defined by FWHM of radiation beam obtained along the cross-line profiles at isocenter depth and the penumbral width from 80 to 20% on either side of the off-axis ratio. All measurements with CC01, SFD and microDiamond were performed in an IBA Bluephantom2 radiation field analyser of 48 × 48 × 48 cm3 scanning dimensions. The PDD and profile were measured using OminPro Accept Software. The step sizes used for PDD and profile measurements were 1 mm. CC01 was horizontally mounted, whereas SFD and microDiamond were vertically positioned. The dwell time at each position was 1 second and the electrometer was set to high sensitivity. The required shift to effective point of measurement was performed for CC01, SFD and microDiamond for depth dose measurements. The effective point of measurement of CC01 was 2.3 mm along the axis and 0.75 mm above the central electrode, and of SFD was 0.7 mm below the top surface. The reference chamber used for CC01 was CC13, for SFD, IBA Reference Dosimetry Diode Detector (RFD), and microDiamond was used without reference. The PDD data were taken along the central axis starting from a depth of 25 cm to −0.5 cm above the surface. Cross-axis profile measurements were performed at a depth of 10 cm.
Output factors were measured using the same water tank and an IBA Dose1 electrometer. The chambers were positioned at 10 cm depth. No shift to the effective point was made. Output factor of a given field size was taken as the ratio of meter readings normalised to 10 × 10 cm2 reference field size without applying any correction to account for change in detector response.
MC simulations were performed on PRIMO, which is a PENELOPE-based Graphical User Interface MC, using Varian Truebeam STx Linac phase space files. The phase space files for MC simulation were adopted from MyVarian Website. Simulations of 6FFF were computed in a virtual water phantom with 1 × 1 × 1 mm3 voxel size. Small field sizes defined are 0.8 × 0.8, 1 × 1, 2 × 2, 3 × 3 and 4 × 4 cm2 at 100 cm SSD.
Results and Discussion
Investigation results and discussion of dosimetric field width, depth of dmax, surface dose, beam penumbra, PDD at 10 cm and 20 cm depth and output factor were done in the following sessions. The calculations revealed a rLCPE of 1.23 cm for 6 MV beam of Tissue Phantom Ratio (TPR) value 0.670 and 0.97 cm for 6FFF of TPR value 0.632. The 6FFF beam in this study should have a small field definition of about 2 × 2 cm2.
Dosimetric field width
FWHM of cross-line profile using CC01, SFD and microDiamond are compared with MC simulation at 10 cm depth in water. The results are shown in Table 1. As the geometric field sizes decreases, the dosimetric field defined by FWHM of various detectors deviates from MC simulation results. At 4 × 4 cm2 the difference is less than 0.25 mm for SFD and microDiamond, and 0.41 mm for CC01. As the field sizes decrease to 0.8 × 0.8 cm2, the difference becomes about 1 mm for all detectors. All three detectors are very close to each other, as can be seen clearly from the Figure 1.
Variation of FWHM of cross-line profile measured using CC01, SFD and microDiamond against MC simulation at 10 cm depth in water
(a) FWHM versus geometric field width for CC01, SFD, microDiamond and MC. (b) Difference in cross-line FWHM from MC simulation.
The higher difference in CC01 FWHM from MC simulation is the result of volume averaging effect of the ionisation chamber. The unanimous results from the detectors indicate that there is a considerable difference in small field profile from MC simulations. A possible reason for this may be a variation in the location in the focal spot can become very prominent in smaller field sizes. Another reason for disparity between planned and measured field size could be source occlusion. No field widening as suggested in literature was seen. In fact, the opposite trend of field shortening was observed in this study. Muralidhar et al. has also observed a similar trend of shortening of field width of about 0.5 mm in cross-axis small fields for 6FFF beams. Reference Muralidhar, Rout and Ramesh28
Position of maximum depth dose, dmax
Variation of position of maximum depth dose, dmax with respect to MC simulation for CC01, SFD and microDiamond are shown in Table 2 and trend is represented in Figure 2. All detectors and MC data show that the position of dmax becomes shallower with decreasing field size. The effect is prominent in field width of 0.8 cm and 1 cm which satisfies the condition for small field (<2 cm) for 6FFF beam. microDiamond detector has the closest agreement with MC with CC01 having the highest variation.
Variation of position of maximum depth dose for CC01, SFD and microDiamond against MC simulation
Position of maximum depth dose versus geometric field width.
The general trend in all the measurements and MC simulation is that the depth of dmax decreases as the field size reduces from 2 × 2 cm2. The MC dmax position was seen to drop abruptly below 2 × 2 cm2. This observation may have been due to the lack to electronic equilibrium. When the field sizes are small, the scatter component and electron contamination would be minimal and the fluence may be assumed to be the primary beam alone. However, as the field size reduces, there is a lack of lateral electronic fluence replacing the outgoing electronic fluence from the beam. Consequently, as the field size reduces and the lack of lateral electronic equilibrium becomes more dominant, the electronic fluence is reduced with depth. As an effect, the fluence of electrons penetrating into dmax is reduced, resulting in lower dmax. This effect dominates with reducing field size, resulting in shift of dmax towards the surface. CC01 being an air cavity chamber has a higher sensitive volume than the other two detectors, and hence the variation in dmax position may be due to volume averaging of the chamber. Since the step size used for measurements and voxel size for MC simulations were 1 mm, 1 mm variations could be accounted for random errors. Godson et al. have reported variation in dmax from 1.3 cm to 1.7 cm for a flattened beam in a Varian Clinac DHX accelerator with jaw setting defined small field of 1 × 1 cm2. Reference Godson, Manickam, Saminathan, Ganesh, Ponmalar and Chandraraj29
Surface dose
The surface dose that measured by various detectors and the deviation from MC simulation are shown in Table 3. All detectors used in this study showed over-response at surface in comparison with MC-simulated surface doses. MC-simulated doses were in the range of 35–40% and the detectors over-responded to 50–60%. microDiamond showed the highest values for surface dose and CC01 the least overestimation. In Figure 3, surface dose that measured by various detectors and MC simulation are plotted against field width.
Surface dose obtained from CC01, SFD, microDiamond and MC simulation for small fields
Surface dose versus geometric field width measured by various detectors and MC simulated.
None of the detectors used were suitable for surface dose measurements. Cashmore et al. state that in high-energy X-rays, the lack of charge particle equilibrium causes the percentage depth ionisation to be different from PDD. Reference Cashmore30 The perturbation of the electronic fluence because of the change in medium from water to the wall of the detector and from wall to the sensitive volume causes the chambers to over-respond at the surface. Keivan et al. have shown that the surface ionisation for unflattened beam reduces as the field size reduces until 3 × 3 cm2 and then surface dose increases. Reference Keivan, Shahbazi-Gahrouei and Shanei31 The surface ionisation for 1 × 1 cm2 was around 45% for PTW pinpoint chamber, PTW Diode E and Sun Nuclear EDGE Diode. The surface ionisation obtained in this study for 6FFF beam has similar findings to results from Keivan et al. This clearly showed that small field definition for 6FFF is around 2 × 2 cm2. Damodar et al. has found microDiamond to be suitable for PDD measurements at all points to within 1% variation from MC simulation results, except for the surface. Reference Damodar, Odgers, Pope and Hill32 The higher density of the detector wall may perturb the fluence. CC01 shows the least overestimation of surface, perhaps volume averaging in ion chamber is less effective than the perturbation of fluence due to a denser wall medium of other detectors. The increase in surface dose with decreasing field size is because, as field sizes reduce, the change in the electronic fluence reaching the point of dmax reduces more predominantly than the reduction in dose from fluence backscattered onto the surface. Cashmore et al. suggest the use of extrapolation chamber for accurate measurement of surface dose. Reference Cashmore30 Increase in surface dose was observed as the field size reduced below 2 × 2 cm2 due to loss of charged particle equilibrium.
Beam penumbra
The variation of beam penumbra for small fields by CC01, SFD and microDiamond against MC simulation is shown in Table 4. The penumbra of the SFD and microDiamond are in agreement with each other but deviate from MC simulation result. CC01 can be seen to overestimate penumbra. Radiation penumbra versus geometric field width at 10 cm depth for CC01, SFD, microDiamond and MC simulation is shown (Figure 4).
Variation of beam penumbra versus geometric field width by CC01, SFD, microDiamond against Monte Carlo simulation
Radiation penumbra versus geometric field width at 10 cm depth for CC01, SFD, microDiamond and MC simulation.
The penumbra can be seen to increase with increasing field width in the detector measurements and MC simulation results. As the field size decreases, the penumbra of the microDiamond and SFD can be seen to deviate away from MC results. The microDiamond and SFD are in agreement with each other, indicating that the simulation of the LINAC in MC deviates from the original when field size becomes very small. This could possibly arise from a shift in the focal spot or source occlusion. Another possibility is that the step size and voxel size used are 1 mm and 1 mm could be introducing an error. A similar mismatch could exist in the treatment planning system, where the field width, as seen before, and the penumbra in the planning system need not match the real dosimetric region in the patient in case of small fields. This could lead to under-dosing the outer regions of a small field treatment plan. The ionisation chamber can be seen to overestimate the penumbra when the field size is greater than 2 × 2 cm2 and underestimate when the field size is smaller than 2 × 2 cm2. Similar results are seen in Denia et al, where there is considerable difference between simulation penumbra and measurement penumbra with diode P. Reference Denia, García and García33
PDD at 10 cm and 20 cm depth
The data from small fields show that with increasing field width, the PDD at 10 cm depth and 20 cm depth shows the same pattern of increasing depth dose. (Figure 5) All detectors are within 2% deviation at 10 cm depth. SFD shows the maximum deviation of 1.5% away from MC-simulated PDD10 for 2 × 2 cm2. The maximum deviation for CC01 is −0.7% away from MC PDD10 at 2 × 2 cm2. Maximum deviation for microDiamond is −0.5% for 3 × 3 cm2. microDiamond shows the closest agreement with MC PDD10. All detectors are slightly under-responding to the depth dose at 10 cm. At 20 cm depth, the deviation from MC PDD20 is much lesser than at 10 cm depth. Maximum deviation for CC01 is 0.3%, SFD is −0.7%, and for microDiamond it is 0.4%. For both depths, microDiamond has the closest depth doses to MC-simulated depth doses and SFD shows the largest deviation.
(a) PDD10 versus field width and (b) PDD20 versus field width: for CC01, SFD, microDiamond and MC simulation.
Output factor
The output factors for CC01, SFD and microDiamond are tabulated against MC (Table 5). microDiamond is very consistent with MC values only deviating more than 1% for 0.8 × 0.8 cm2. CC01 is reliable upto 2 × 2 cm2, not deviating above 2%. The sudden variation in output factor due to volume averaging in CC01 below 2 × 2 cm2 (lack of CPE region) can be clearly seen in Figure 6. SFD has consistently under-responded to OF measurements.
Variation of output factor for small fields by CC01, SFD, microDiamond against MC simulation
Output factors versus geometric field width for CC01, SFD, microDiamond and MC simulation.
Output factor measurements revealed a sudden drop below 2 × 2 cm2 for all detectors and MC simulation. This is another clear indication of the definition of small field for 6FFF is around 2 × 2 cm2. The SFD detector is under-responded in this measurement. CC01 was within 2% for field sizes above 2 × 2 cm2. microDiamond is suitable upto 1 × 1 cm2 where maximum deviation is only 1.1 % in output factor. Application of TRS483 chamber corrections could make the output factors of detectors much closer to MC.
This study provides the deviation between the measured data with various detectors and help end users in choosing the right detector for small field dosimetry. Also it is recommended to perform validation of measured data with MC simulation before Treatment Planning System (TPS) commissioning and clinical implementation. This study is limited to comparison of MC simulation with CC01, SFD and microDiamond detector. Further studies can be performed using Gafchromic film and other detector available for small field dosimetry.
Conclusion
All detectors in this study were suitable for measurements above 2 × 2 cm2. When the field size was smaller than 2 × 2 cm2, the effect of loss of charged particle equilibrium can be seen. Below 2 × 2 cm2, care must be taken in choosing a detector for measurements. microDiamond has been performed the best among all three detectors, only showing deviations for 0.8 × 0.8 cm2. CC01 was suitable above 2 × 2 cm2. CC01 was not accurate for penumbra measurements. SFD showed output factor variations throughout. This study has found that PTW 60019 microDiamond 60019 is a suitable detector for small fields above 1 × 1 cm2. No detector was suitable for surface dose measurements, as the perturbation of the electronic fluence by the wall of the detectors made depth dose curve to be different from depth ionisation curve.
It is not clear how different the geometry of Varian Truebeam LINAC in this study is from the phase space file geometry. Any variation in this could have been amplified at 0.8 × 0.8 cm2. For output factor measurement, TRS483 suggested correction factor need to be applied to account for the difference in detector response. CC01 can be used for field sizes above 2 × 2 cm2. microDiamond detector is suitable for above 1 × 1 cm2. Below these field sizes, perturbation corrections and volume averaging corrections need to be applied.
Acknowledgement
Authors sincerely thank Mr. Prashantkumar Shinde and Dr Gautam K Sharan of Inlaks & Budhrani Hospital, Pune for sparing the microDiamond detector to carry out the measurements and Ms. Sandhya Madhvapathi Rao for the support extended in the manuscript preparation.
