Ionization chamber dosimetry of small photon fields: a Monte Carlo study on stopping-power

Home Search Collections Journals About Contact us My IOPscience Ionization chamber dosimetry of small photon fields: a Monte Carlo study on stopping-power ratios for radiosurgery and IMRT beams This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2003 Phys. Med. Biol. 48 2081 (http://iopscience.iop.org/0031-9155/48/14/304) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 152.92.171.92 The article was downloaded on 15/10/2010 at 15:32 Please note that terms and conditions apply.

INSTITUTE OF PHYSICS PUBLISHING Phys. Med. Biol. 48 (2003) 2081 2099 PHYSICS IN MEDICINE AND BIOLOGY PII: S0031-9155(03)61152-8 Ionization chamber dosimetry of small photon fields: amontecarlo study on stopping-power ratios for radiosurgery and IMRT beams FSánchez-Doblado 1,2,PAndreo 3,RCapote 1,2,ALeal 1,2,MPerucha 2, RArráns 1,LNúñez 4,EMainegra 5,JILagares 1,2 and E Carrasco 1,2 1 Radiofísica, Hospital Univ Virgen Macarena, Avda Dr Fedriani s/n, E-41009 Sevilla, Spain 2 Dpto Fisica Medica y Biofísica, F Medicina, Universidad Sevilla, Spain 3 Division of Medical Radiation Physics, University of Stockholm, Karolinska Institute, PO Box 260, SE-171 76 Stockholm, Sweden 4 Radiofísica, Clínica Puerta de Hierro, Madrid, Spain 5 National Research Council, Ottawa, Canada Received 21 March 2003 Published 1 July 2003 Online at stacks.iop.org/pmb/48/2081 Abstract Absolute dosimetry with ionization chambers of the narrow photon fields used in stereotactic techniques and IMRT beamlets is constrained by lack of electron equilibrium in the radiation field. It is questionable that stopping-power ratio in dosimetry protocols, obtained for broad photon beams and quasielectron equilibrium conditions, can be used in the dosimetry of narrow fields while keeping the uncertainty at the same level as for the broad beams used in accelerator calibrations. Monte Carlo simulations have been performed for two 6 MV clinical accelerators (Elekta SL-18 and Siemens Mevatron Primus), equipped with radiosurgery applicators and MLC. Narrow circular and Z-shaped on-axis and off-axis fields, as well as broad IMRT configured beams, have been simulated together with reference 10 10 cm 2 beams. Phase-space data have been used to generate 3D dose distributions which have been compared satisfactorily with experimental profiles (ion chamber, diodes and film). Photon and electron spectra at various depths in water have been calculated, followed by Spencer-Attix ( = 10 kev) stopping-power ratio calculations which have been compared to those used in the IAEA TRS- 398 code of practice. For water/air and PMMA/air stopping-power ratios, agreements within 0.1% have been obtained for the 10 10 cm 2 fields. For radiosurgery applicators and narrow MLC beams, the calculated s w,air values agree with the reference within ±0.3%, well within the estimated standard uncertainty of the reference stopping-power ratios (0.5%). Ionization chamber dosimetry of narrow beams at the photon qualities used in this work (6 MV) can therefore be based on stopping-power ratios data in dosimetry protocols. For amodulated 6 MV broad beam used in clinical IMRT, s w,air agrees within 0.1% with the value for 10 10 cm 2, confirming that at low energies IMRT 0031-9155/03/142081+19$30.00 2003 IOP Publishing Ltd Printed in the UK 2081

2082 FSánchez-Doblado et al absolute dosimetry can also be based on data for open reference fields. At higher energies (24 MV) the difference in s w,air was up to 1.1%, indicating that the use of protocol data for narrow beams in such cases is less accurate than at low energies, and detailed calculations of the dosimetry parameters involved should be performed if similar accuracy to that of 6 MV is sought. (Some figures in this article are in colour only in the electronic version) 1. Introduction The strong collimation used in stereotactic and intensity modulated radiotherapy (IMRT) techniques to produce the necessary clinical narrow fields modifies significantly the energy spectra of conventional radiotherapy broad beams, at the time that collimator leakage (Kim et al 2001) may increase considerably the integral dose to the patient. The absorbed dose at a reference point in water has to be determined for a beam which differs substantially from the reference 10 10 cm 2 field recommended by most radiotherapy dosimetry protocols (Kubsad et al 1990, Sixel and Faddegon 1995). Initially, the collimation hardens the primary photon beam shifting the spectrum towards higher energies; this is counterbalanced by the build-up of secondary photons and the increased pair production in the collimation system which increases the lower energy component of the spectrum. Depending on the physical configuration of the beam used (size, off-axis position, irregularity shape, combination of beamlets in an IMRT beam, etc) the varying contributions of primary and secondary photon fluence originate a beam with little resemblance to those used in conventional radiotherapy. Their dosimetry poses a considerable challenge to the accuracy of modern radiotherapy treatments. Absolute dosimetry with ionization chambers of the small photon fields used for stereotactic techniques and IMRT beamlets is constrained by the generalized lack of electron equilibrium in the radiation field and the size of the chamber cavity volume. So-called micro ionization chambers have been developed by some manufacturers (PTW, IBA-Wellhöfer) to deal with the limitation in volume, but considerable uncertainty exists with regard to the validity of using existing dosimetry data with such chambers. Such data, notably stoppingpower ratios to convert the absorbed dose in the chamber air cavity into absorbed dose to water, and those entering into the wall perturbation correction factors, have been obtained for broad photon beams, where conditions of quasi-electron equilibrium prevail. It is, therefore, questionable that such data can be used in the dosimetry of narrow fields while keeping the uncertainty at the same level as for the broad beams used in the reference conditions of an accelerator calibration. The situation is even more complicated in IMRT dosimetry when beamlets are not centred (off-axis) as they impinge on the irradiated volume with a certain inclination. As a consequence, small air-filled ionization chambers have mostly been used to perform relative measurements, a task often complemented with different detector types such as diodes, diamonds, radiographic film, radiochromic film, plastic scintillators, polymer gels and liquid ionization chambers (cf Westermark et al 2000, Perucha et al 2003, McJury et al 2000, Sánchez-Doblado et al 2002), etc. The depth-dependence of water/air stopping-power ratios with the photon field size was first analysed by Andreo and Brahme (1986) using Monte Carlo methods where, for a 6 MV experimental spectrum, it was shown that the maximum difference in stopping-power ratios between broad and narrow fields could be up to 1% for a 5 mm diameter beam size;

Ionization chamber dosimetry of small photon fields 2083 differences became practically negligible for slightly larger beams. Studies using the same methodology and yielding similar results, but specific to the field of stereotactic radiosurgery, were conducted by Heydarian et al (1996)for a Siemens Mevatron KD2 accelerator equipped with a stereotactic system using as input published 6 MV non-stereotactic spectral data. However, the stopping-power ratios were calculated as ratios of collision stopping-powers at the Monte Carlo calculated mean electron energy, a methodology which is not used for accurate dosimetry. A detailed study by Verhaegen et al (1998) on 6 MV stereotactic radiosurgery beams proceeded one step further including detailed simulations of a Varian Clinac-600SR accelerator with the BEAM/EGS4 Monte Carlo code (Rogers et al 1995, Nelson et al 1985). For the Varian accelerator simulated, this comprehensive study verified the validity of the general assumption that measured dose ratios were equal to measured detector readings, upon calculations of the electron spectra of narrow fields at d max and 5 cm depth, obtaining a stopping-power ratio dependence consistent with the results of Andreo and Brahme (1986) and Heydarian et al (1996). Many other studies based on the use of Monte Carlo methods have been published, mainly verifying depth and lateral dose distributions obtained with different detectors in radiosurgery and IMRT beams (cf Lovelock et al 1995, De Vlamynck et al 1999, Li et al 2001, Pawlicki and Ma 2001, Aaronson et al 2002, Siebers et al 2002, etc),butthey have not taken into account absolute dose determinations. The field of absolute dosimetry of IMRT beamlets thus remains without answers (Boyer et al 2001). In this work Spencer-Attix ( = 10 kev) stopping-power ratios for ionization chamber dosimetry have been determined for the small photon beams used in radiosurgery and IMRT beamlets, as well as for real IMRT beams, which have been compared with those used by the most recent dosimetry protocols for reference dosimetry based on standards of absorbed dose to water (Almond et al 1999, Andreo et al 2000). For this purpose, detailed simulations of two accelerators equipped, respectively, with radiosurgery and MLC collimators have been made using the BEAM/EGS4 Monte Carlo code to produce phase-space data, which in turn have been used to compute depth-dose and transverse-dose profiles and stopping-power ratios at the reference depths with user codes based on the EGSnrc Monte Carlo system (Kawrakow 2000). To establish the validity of the accelerators simulations, the quality of the calculated phasespace data has been verified comparing Monte Carlo data with experimentally determined percent depth-dose, transverse-dose profiles and isodose distributions measured with various detector types. 2. Material and methods 2.1. Accelerators and collimators The two clinical accelerators simulated in this study have been an Elekta SL-18 and a Siemens Mevatron Primus, both producing 6 MV photons. The Elekta accelerator is equipped with an in-house designed radiosurgical collimator with cylindrical treatment cones that produce beams between 2.9 mm and 50.3 mm diameter at the isocentre. These are made of tungsten surrounded by stainless steel. Various aspects of the design of this collimator have been analysed in a preliminary study (Perucha et al 2003) leading to the final design which was adopted for the calculations presented in this work. The Siemens accelerator is a dual photon linac equipped with a multileaf collimator (MLC) used for IMRT treatments. The MLC has 29 opposed leaf pairs, the outer leaves of each bank project a shadow width of 6.5 cm at the isocentre plane, while the inner 27 leaf pairs project a width of 1 cm. Both leaf end and leaf side match the beam divergence, making the configuration double-focused.

2084 FSánchez-Doblado et al 2.2. Experimental determinations Depth- and transverse-dose and ionization profiles have been measured using film dosimetry, diodes and a small ionization chamber. The radiographic film was of the type Kodak X-OMAT V, sandwiched in slabs of Solid Water TM. One film of each measuring session was calibrated prior to the use of every set; its response (optical density versus dose) was analysed within the range 5 180 cgy. Two different types of densitometers were used, an automatic Scanditronix with a 0.1 cm diameter diaphragm and a CMS 1710 laser densitometer with a 0.025 cm diameter diaphragm. In addition, for the IMRT measurements, Kodak EC-L and EDR2 films were also used together with an Agfa Arcus-1200 scanner. The measured profiles were obtained using home-made software specifically designed for the analysis of scanned x-ray films (Lagares et al 2002); this software allows working with calibration curves sensitive to dose values as low as 2 cgy for the EDR2 film. The diodes used were of the silicon p-type, manufactured by Scanditronix. They have a 0.3 mm 3 sensitive volume, a detection area with a diameter of 2.5 mm and a sensitive thickness of 60 µm. Diodes used in this work were of the electron-type, that is, without the tungsten shielding used in conventional photon-diodes to compensate for the increased diode response to low energy photons; this is consistent with the manufacturer recommendations. The ionization chamber was a Scanditronix RK-05, with avolume of 0.12 cm 3 (4 mm internal diameter and 10 mm length) and Rexolite walls. It was positioned with its longitudinal axis parallel to the beam axis. The diodes and the ionization chamber were used in a Scanditronix RFA-300 computerized water phantom. No corrections were made on the readings of these instruments, and in the comparisons that follow relative ionization measurements were used. 2.3. Monte Carlo calculations The BEAM/EGS4 Monte Carlo code (Rogers et al 1995, Nelson et al 1985) has been used to simulate the radiation transport through the configurations of the two accelerators. The treatment heads and the two types of collimators, radiosurgical and MLC, were modelled using the various geometric modules implemented in the BEAM code. For the various results reported in this work, between 300 and 800 million electrons with initial energies of 5.6 MeV (Siemens) and 6.6 MeV (Elekta) were simulated down to a cut-off of 700 kev (total electron energy); in the case of Z-shaped IMRT fields the electron energy cut-off in the air volumes was 521 kev. The photon energy cut-off was 10 kev in all cases. Various techniques for variance reduction included in the BEAM code were used; these were uniform bremsstrahlung splitting (20), photon splitting (20) and photon forcing (each bremsstrahlung photon was forced to interact once at the bottom of the air slab). The phasespace data characterizing the Siemens beams were obtained first just above the collimators of the accelerator; these were used as input for the subsequent simulations through the collimators, yielding the phase space in air at the position of the phantom surface. For the Elekta accelerator, the first step of the simulation was to obtain phase-space data at 52.9 cm for a 10 10 cm 2 collimator setting; the various radiosurgery collimators were then simulated in subsequent steps. In both cases the data were finally scored in a plane perpendicular to the beam axis, at adistance of 90 cm from the radiation source. The various configurations simulated are shown in figure 1,which serves as reference for the results presented in the following section. Three cases, namely collimator radii of 0.3 cm and 1.0 cm and a reference 10 10 cm 2 field were simulated for the radiosurgery accelerator. Forthe IMRT configuration the fields were 10 10 cm 2, and two on-axis and off-axis irregular fields (both within 2 2cm 2 ). Special small Z-shaped collimated field configured with the

Ionization chamber dosimetry of small photon fields 2085 RADIOSURGERY (a) (b) (c) IMRT (d) (e) (f) (g) (h) (i) Figure 1. Configurations for the radiosurgery ((a) (c)) and multi-leaf collimator (MLC) IMRT ((d) (i)) beams used for the Monte Carlo calculations presented in subsequent figures. Sets (a) and (d) correspond to 10 10 cm 2 reference fields, the latter being produced with a MLC; set (i) corresponds to the cases of transmission leakage through the leafs of the MLC. MLC, as well as broad real IMRT beams, were also simulated to study dose distributions at different depths in water for the Siemens Primus accelerator. The resulting phase-space files contained approximately between 30 and 70 million particles. Asimple analysis on photon spectral variation with field size and position within the beam was made for circular fields and rings. The 6 MV photon spectrum from Mohan et al (1985) was used as input to simulations through configurations similar to those of the radiosurgery applicators, rather than performing the complete accelerator head simulation used in the other cases. These calculations were made with a modified version (Mainegra et al 1998)ofthe well-known EGS4 user-code DOSRZ which scores dose and spectral distributions

2086 FSánchez-Doblado et al in selected regions of interest and allows the separate scoring of primary and scattered photon fluence. Several of the enhancements in the physical data available for the EGS4 package were implemented for the simulations. These were the NIST photon cross section dataset DLC-136/PHOTX (RSIC 1993), implemented in EGS4 by Sakamoto (1993), the lowenergy photon-scattering (LSCAT) package including bound Compton scattering and Doppler broadening (Namito et al 1994, 1995) and molecular form factors for coherent scattering in water (Morin 1982). The phase-space files at the phantom surface were in turn used as input to subsequent in-phantom simulations. For the calculations of depth and transverse profiles, the code DOSXYZ (Ma et al 2000) was used to obtain 3D dose distributions at different depths. The calculated profiles were compared with the experimental data. Electron and photon cut-offs for these calculations were 700 kev (total electron energy) and 10 kev, respectively. The number of histories simulated was chosen so that the statistical standard uncertainty at the depth of maximum absorbed dose was between 1 2%. The codes FLURZ and SPRRZ of the EGSnrc system (Kawrakow 2000, Rogers et al 2000)were used to calculate, respectively, the energy spectra and stopping-power ratios at different depths (5, 10 and 15 cm) in a water phantom. Cylindrical volumes of 0.5 cm height and radii of 3 cm (for the 10 10 cm 2 and off-axis field) and 0.3 cm (for the small centred fields) were employed for the scoring of both quantities. The phantom radius was 20 cm for all cases studied, except for the off-axis IMRT configuration, where a 40 cm phantom radius was used. Electron and photon cutoffs for these calculations were 521 kev (total electron energy) and 1 kev, respectively. The statistical standard uncertainty in all regions of interest was below 0.3% for the stopping-power calculations and below 5% for the spectral data. The CPU time required for the calculations was drastically reduced with the use of a Linux cluster with 47 Pentium III 1.1 GHz PCs, capable of running processes simultaneously using an in-house specific model for the distribution of the simulation tasks (Sánchez-Doblado et al 2000, Leal et al 2003). With this computer configuration not only a significant reduction in processing time was achieved, but also a detailed analysis of every single sub-process was easily analysed and associated with its corresponding simulation fragment. 3. Results and discussion 3.1. Experimental verification In order to verify first the validity of the accelerators simulations and their calculated phasespace data, Monte Carlo calculated depth-dose and transverse-dose profiles were compared with experimentally determined profiles measured with various detector types in the two accelerators simulated. Results for the Elekta SL-18 accelerator are shown in figure 2 for a reference 10 10 cm 2 field and radiosurgery applicators of different diameters. The experimental depth-dose distributions were measured with the RK-05 ionization chamber (10 10 cm 2 field) and diodes (applicators), whereas the transverse-dose profiles were obtained with film dosimetry. In all cases the good agreement found was considered to be suitable for clinical purposes, the agreements being comparable to the results obtained previously by different authors for similar configurations. For the Siemens Primus accelerator equipped with multi-leaf collimator (MLC), figure 3(a) compares Monte Carlo calculated and experimental (diode) depth-dose distributions for a 10 10 cm 2 field, showing excellent agreement. The special cases of MLC irregular Z-shaped small fields (henceforth referred to as Z-field ), both on the central axis and

Ionization chamber dosimetry of small photon fields 2087 Figure 2. Comparison of Monte Carlo calculated (lines) and experimental (dots) depth-dose and transverse-dose profiles at 7 cm depth for a 6 MV 10 10 cm 2 reference field (a) and radiosurgery applicators of diameters 2.25 cm (d), 1.05 cm (b) and 0.3 cm ((c) and (e)) of an Elekta SL-18 linear accelerator. Depth-dose distributions measured with Scanditronix RK-05 ionization chamber (reference field) and diodes (applicators), and transverse-dose profiles with film using a reader aperture diameter of 0.025 cm. The configurations correspond to figures 1(a) (c). off-axis, were considered to be of high interest for clinical dosimetry, as it is well known that the simulation of small MLC-shaped fields poses a significant challenge to the use of the Monte Carlo method in IMRT. Figure 3(b) compares calculated and experimental (diode) depth-doses for a Z-field centred on-axis (configuration in figure 1(g)) whereas figures 3(c) and (d) compare calculated and experimental (film) transverse-dose profiles for Z-fields centred 8cmoff-axis (configuration in figure 1(h)) and on-axis (configuration in figure 1(g)); in the two cases the profiles are at a depth of 10 cm. The almost perfect agreement of the two sets of results shown in the figure provided confidence on the quality of the simulation of these complex MLC geometries. The analysis for the Z-fields was further extended to a comparison of isodose distributions at the depth of 10 cm. Results are shown in figure 4, where the left-hand side corresponds to the on-axis case and the right-hand side to the off-axis. The distributions have been normalized to the maximum dose on the central axis of the calculated and measured depth-dose curves. In these examples, small discrepancies between the Monte Carlo and the experimental distributions can be observed in the shape of the 80 90% isodosis, though at lower isodose values the differences are considered to be minimal. To confirm the possible clinical dosimetry influence of the differences found for the small irregular field above, a final comparison was made for a clinical IMRT beam. The field configuration and the comparison of Monte Carlo results versus film are shown in figure 5, where the left-hand side shows the dose delivered by each of the individual fields that form

2088 FSánchez-Doblado et al 100 (a) 100 (b) 80 80 PDD (%) 60 40 PDD (%) 60 40 20 20 0 0 5 10 15 20 25 30 35 Depth (cm) 0 0 2 4 6 8 10 12 14 16 18 20 22 Depth (cm) 100 (c) 100 (d) Relative Dose (%) 80 60 40 20 Relative Dose (%) 80 60 40 20 0 4 6 8 10 12 Inplane (cm) 0-4 -2 0 2 4 Inplane (cm) Figure 3. Comparison of Monte Carlo calculated (lines) and experimental (dots) depth-dose and transverse-dose profiles at a depth of 10 cm for 6 MV beams generated with the multi-leaf collimator of a Siemens Mevatron Primus linear accelerator. Results are for a 10 10 cm 2 reference field (a), for a Z-field centred on-axis ((b) and (d)), and for a Z-field centred 8 cm off-axis (c). Depth-dose distributions measured with diodes and transverse-dose profiles with film. The configurations correspond to figures 1(d), (g) and (h). the final IMRT modulated beam (lower part of the figure). The comparison of the final doses obtained demonstrates good agreement, showing that the potential differences between Monte Carlo calculated and experimental small fields counterbalance, yielding an overall final result in agreement with widely accepted criteria for the discrepancies between dose calculations in treatment planning (cf Van Dyk et al 1999). 3.2. Photon spectra (air) Relevant examples of Monte Carlo calculated photon spectra in air, at the position of the phantom surface, are presented in this section for the simulated radiosurgery and MLC collimated IMRT beams. As mentioned before, a comparative analysis on spectral differences was made for configurations similar to the radiosurgery applicators used in the Elekta SL-18 linear accelerator, where a well-known 6 MV photon spectrum (Mohan et al 1985) was used as input to simulations through such applicators type. In order to analyse the spectral variation at various positions in the beam, spectra were scored for a reference 10 cm radius beam and for a narrow 0.3 cm beam together with annular regions of constant radial width (0.3 cm) at different positions (varying internal and external radii). Results are shown in figure 6 for

MC On axis Film Off axis Figure 4. Comparison of Monte Carlo calculated and experimental isodose distributions at a depth of 10 cm for the 6 MV MLC Z-shaped IMRT field. The right-hand side shows isodoses for a Z-field centred 8 cm off-axis and the left-hand side for a Z-field centred on-axis. The experimental distributions were obtained with film. The configurations correspond to figures 1(g) and (h). MC Film Ionization chamber dosimetry of small photon fields 2089

2090 FSánchez-Doblado et al 105 M.U. 15 M.U. 60 M.U. 90 M.U. Film MC 15 M.U. 30 M.U. 15 M.U. 50 cgy 45 M.U. 30 M.U. 30 M.U. 75 cgy 100 cgy Figure 5. Comparison of Monte Carlo calculated and experimental isodose distributions of a clinical IMRT beam. The left-hand side shows the configuration delivered by each of the individual fields that conform the final IMRT beam shown in the lower part of the figure. The experimental distributions were obtained with film. various cases, where the corresponding radial dimensions (internal and external radii) are given. The spectra, normalized to the integral fluence, are separated into their primary and scattered components, and the relative percentage of the primary fluence, as well as the mean energy of each spectrum, is indicated in each case. The peak originated by pair production interactions in the applicators can be clearly seen in all the secondary spectra. It can also be observed that, except in the case of the large field, the contribution of photons scattered in the collimators is rather constant, and larger than that of primaries by about 70% in all cases. At the same time their mean energies do not change appreciably even if there is a clear shift of the primary spectra towards high energies. Figure 7 illustrates the results from the full simulation of the accelerators for the calculated photon fluence in air, at the position of the phantom surface, for 6 MV beams produced with the MLC of the Siemens Mevatron Primus (left) and the radiosurgery applicators of the Elekta SL-18 linac (right). The corresponding field sizes are indicated in the figure, as well as the mean energy of the spectra in each case. The upper panels correspond to the relative fluence, normalized to the integral fluence. A substantial difference in the shape of the spectra can be observed in the two types of collimators, MLC and radiosurgery, and in the latter case the dominance of low-energy scattered photons in the collimator walls can easily be seen.

Ionization chamber dosimetry of small photon fields 2091 10 8 Primary/ Total Fluence: 96.5 % R in =0 mm, R out =100 mm, <E ph >=1.86 MeV (a) Primary/Total Fluence: 34.3% R in =0 mm, R out =3 mm, <E ph >=1.90M ev (b) Fluence [normalized to the integral] 10 6 10 4 10 2 10 0 10 6 10 4 Primary/Total Fluence: 29.7% R in =47 mm, R out =50 mm, <E ph >=1.87 MeV (c) Primary/ Total Fluence: 22.3% R in =97 mm, R out =100 mm, <E ph >=1.81M ev (d) 10 2 10 0 0 1 2 3 4 5 6 Energy [MeV] 0 1 2 3 4 5 6 Energy [MeV] Figure 6. Monte Carlo calculated photon fluence in air, at the position of the phantom surface, for a 6 MV spectrum transported through radiosurgery applicators as those in an Elekta SL-18 linear accelerator. Results are for circular beams of 10 cm (a) and 0.3 cm (b), and annular regions 0.3 cm wide at different positions ((c) and (d)). The spectra are normalized to the integral fluence and separated into primary (thick lines) and scattered (thin lines) components. The relative percentages of the primary fluence, as well as the mean energy of each spectrum, are indicated in each case. The peak originated by pair production interactions in the cases of strong collimation can be observed, even in the transmitted leakage spectra of the MLC; although the leakage has intensity much lower than the irregular fields, this is still enough to become important at the time of estimating the integral dose to a patient. As expected, there is a large spectral difference between the open 10 10 cm 2 beams and the narrow irregular or circular fields; the small fields spectra being shifted towards higher energies, even if the mean energies are somewhat softened by the pair production peak. Interestingly enough, the off-axis MLC irregular field, without a direct contribution from photons at the central axis, appears to be very similar in shape to the open 10 10 cm 2 beam even if the pair production peak softens considerably its mean energy. The transmitted leakage spectrum of the MLC, with a large filtration of low-energy photons, is the hardest of all the MLC spectra. 3.3. In-phantom photon and electron spectra: stopping-power ratios As already described, the validated phase-space data of the two accelerators have been used to calculate spectral distributions of photons and electrons in water, and to determine Spencer- Attix ( = 10 kev) water/air, and in some cases PMMA/air, stopping-power ratios. Figure 8 shows Monte Carlo calculated photon and electron spectra at various depths in water for the 6 MV 10 10 cm 2 field and radiosurgery applicators with diameters of 1.0 cm and

2092 FSánchez-Doblado et al Fluence (normalized to the integral) Fluence/incident particle [cm -2 MeV -1 ] 0.06 0.04 0.02 0.00 10-6 10-8 <E ph > [Mev] 1.604 ( 10x10) 1.729 ( on axis) 1.495 ( off-axis) 1.854 ( transmis.) (a) (b) <E ph 1.600 ( 10x10 ) 1.704 ( Φ=1.05) 2.246 ( Φ=0.3) 10-10 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Energy [MeV] Energy [MeV] (c) (d) Figure 7. Monte Carlo calculated photon fluence in air, at the position of the phantom surface, for 6 MV fields produced with the MLC of a Siemens Mevatron Primus ((a) and (b)) and the radiosurgery applicators of an Elekta SL-18 linac ((c) and (d)). The upper panels correspond to the relative fluence, normalized to the integral fluence in each case. The spectra for the Siemens linac (left) correspond to a 10 10 cm 2 field, irregular fields of 2 2cm 2 centred on-axis and 8 cm off-axis, and the transmission leakage (configuration in figures 1(d) (f) and (i)). For the Elekta linac (right) the spectra correspond to a 10 10 cm 2 field and applicator diameters of 1.0 cm and 0.3 cm (configuration in figures 1(a) (c)). The mean energy of the photon spectra is indicated in each case. 0.3 cm in the Elekta SL-18 linear accelerator. The configurations correspond to figures 1(a) (c). The spectra are normalized to the integral fluence in each case. As expected, a light hardening of the photon spectra with depth can be observed in each case, but the changes in the corresponding electron spectra at different depths are rather small. More interestingly, the shape of the electron spectra for the various configurations is very similar. In the case of the MLC fields of the Siemens Mevatron Primus linear accelerator similar results are shown in figure 9. The calculated photon and electron spectra, normalized to the integral fluence, are shown at the same depths as in figure 8 for the 6MV10 10 cm 2 field and irregular fields centred on-axis and 8 cm off-axis. The configurations correspond to figures 1(d) (f), respectively. The shape of the on-axis spectra, both photons and electrons, is very similar to those of broad beams. However, in the off-axis case, where the angular incidence is large, there is a predominance of the low energy part of the spectrum which results in mean energies considerably different from the on-axis spectra. As in the radiosurgery case, the electron spectra are rather similar at all depths and quite similar for all the configurations. Moreover, the overall shape of these spectra does not differ considerably from those for the case of the radiosurgery fields.

Ionization chamber dosimetry of small photon fields 2093 0.03 0.02 PHOTONS <E ph 1.537 (5 cm) 1.527 (10 cm) 1.552 (15 cm) (a) 0.03 0.02 ELECTRONS <E e 1.043 (5 cm) 1.074 (10 cm) 1.119 (15 cm) (d) 0.01 0.01 Fluence (normalized to the integral) 0.00 0.010 0.005 0.000 0.010 <E ph 2.072 (5 cm) 2.202 (10 cm) 2.330 (15 cm) <E ph 2.080 (5 cm) 2.202 (10 cm) 2.322 (15 cm) (b) (c) 0.00 0.02 0.01 0.00 0.02 <E e 1.162 (5 cm) 1.200 (10 cm) 1.241 (15 cm) <E e 1.192 (5 cm) 1.229 (10 cm) 1.299 (15 cm) (e) (f) 0.005 0.01 0.000 0.00 0 2 4 6 0 2 4 6 Energy [MeV] Energy [MeV] Figure 8. Monte Carlo calculated photon (left) and electron (right) spectra, at the depths in water of 5 cm (dotted lines), 10 cm (thick lines) and 15 cm (thin lines), for the 6 MV 10 10 cm 2 field ((a) and (d)) and radiosurgery applicators with diameters of 1.0 ((b) and (e)) and 0.3 cm ((c) and (f)) of an Elekta SL-18 linear accelerator. The spectra are normalized to the integral fluence in each case. The configurations correspond to figures 1(a) (c). Calculated Spencer-Attix ( = 10 kev) stopping-power ratios water/air and PMMA/air at 5 cm depth for different 6 MV radiosurgery and MLC beams are shown in table 1. The s w,air value for the spectrum of transmitted leakage in the MLC is also given. In all cases the type A (statistical) standard uncertainty of the calculated values is lower than 0.1% except in the case of the MLC transmission, where the standard uncertainty is 0.8%. The results for the

2094 FSánchez-Doblado et al 0.03 0.02 PHOTONS <E ph 1.374 (5 cm) 1.394 (10 cm) 1.436 (15 cm) (a) 0.03 0.02 ELECTRONS <E e 0.922 (5 cm) 0.931 (10 cm) 0.950 (15 cm) (d) 0.01 0.01 Fluence (normalized to the integral) 0.00 0.010 0.005 0.000 0.04 <E ph 1.743 (5 cm) 1.852 (10 cm) 1.958 (15 cm) <E ph 1.269 (5 cm) 1.121 (10 cm) 1.037 (15 cm) (b) (c) 0.00 0.02 0.01 0.00 0.02 <E e 0.981 (5 cm) 1.006 (10 cm) 1.037 (15 cm) <E e 0.844 (5 cm) 0.820 (10 cm) 0.811 (15 cm) (e) (f) 0.02 0.01 0.00 0.00 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Energy [MeV] Energy [MeV] Figure 9. Monte Carlo calculated photon (left) and electron (right) spectra, at the depths in water of 5 cm (dotted lines), 10 cm (thick lines) and 15 cm (thin lines), for the 6 MV 10 10 cm 2 field ((a) and (d)) and irregular fields within 2 2cm 2 centred on-axis ((b) and (e)) and 8 cm off-axis ((c) and (f)) produced with the MLC of a Siemens Mevatron Primus linear accelerator. The spectra are normalized to the integral fluence in each case. The configurations correspond to figures 1(d) (f). 10 10 cm 2 fields produced by each accelerator can be compared first with those given by Andreo (1994) which are the basic dataset used in IAEA TRS-398 (Andreo et al 2000). The experimental TPR 20,10 for the radiosurgery and the MLC accelerators are, respectively, 0.690 and 0.677; their corresponding s w,air protocol values are 1.1187 and 1.1213. These can be compared with the values determined in this work by direct simulation, which are 1.1188 and

Ionization chamber dosimetry of small photon fields 2095 Table 1. Spencer-Attix ( = 10 kev) stopping-power ratios water/air, s w,air,andpmma/air, s PMMA,air,at5cm depth in water for various 6 MV radiosurgery and MLC beams, including irregular homogeneous and IMRT fields. The s w,air value for the spectrum of transmitted leakage in the MLC is also given. The type A (statistical) standard uncertainty of the calculated values is lower than 0.1% except in the case of the MLC transmission (0.8%). s w,air s PMMA,air Beam Ratio Ratio quality Andreo This this work/ Andreo This this work/ 6MVbeams (TPR 20,10 ) (1994) a work Andreo (1994) a work Andreo Configuration Elekta SL-18 radiosurgery 10 10 cm 2 0.690 1.1187 1.1188 1.000 1.0853 1.0856 1.000 figure 1(a) 1.0 cm diameter 1.1155 0.997 1.0819 0.997 figure 1(b) 0.3 cm diameter 1.1153 0.997 1.0817 0.997 figure 1(c) Siemens Primus MLC 10 10 cm 2 0.677 1.1213 1.1221 1.001 1.0880 1.0892 1.001 figure 1(d) 2 2cm 2 irregular 1.1203 0.999 1.0870 0.999 figure 1(e) on-axis 2 2cm 2 irregular 1.1250 1.003 1.0922 1.004 figure 1(f ) 8cmoff-axis MLC transmission 1.1300 1.008 figure 1(i) IMRT beam 1.1201 0.999 figure 12 (10 10 cm 2 approx) a These are the values in the IAEA TRS-398 code of practice (Andreo et al 2000). 1.1221, respectively. The agreement between the two independent determinations is within 0.1%, which is considered to be excellent. In the case of s PMMA,air where the values from Andreo (1994) are 1.0853 and 1.0880, the agreement shown in table 1 is also within 0.1%. In the case of radiosurgery applicators and MLC beams, the calculated values of stoppingpower ratios in this work (cf table 1) agree with the 10 10 cm 2 s w,air reference values (protocol data) within ±0.3%. For the s PMMA,air values the corresponding values are within ±0.4%. These differences are well within the estimated standard uncertainty of the reference stoppingpower ratios given in IAEA TRS-398 (0.5%). The values of s PMMA,air have a minimal influence in absolute dosimetry, as these are relevant only in the determination of the perturbation correction factor for the wall effect of a chamber, p wall.inthe case of the transmission leakage of the MLC the difference with the reference s w,air value is of 0.8%; this parameter is mostly of interest for estimates of the integral dose to a patient (see below). It can thus be concluded that the stopping-power ratios of strongly collimated 6 MV beams, both for radiosurgery applicators and MLC beams, agree very well with those used for the reference dosimetry of conventional external radiotherapy beams recommended in dosimetry protocols. At the photon qualities analysed in this work, ionization chamber dosimetry of narrow beams can therefore be based on the same set of dosimetry data (stopping-powers). A final comparison has been made between the s w,air values for the reference 10 10 cm 2 field and a modulated broad beam of similar size used in clinical IMRT, both of 6 MV and for the MLC of the Siemens Mevatron Primus linear accelerator. The calculated photon spectra are compared in figure 10, showing that they almost coincide. The corresponding stoppingpower ratios, determined from the relevant electron spectra, agree within 0.1%, showing that the ionization chamber dosimetry of typical IMRT beams can also be based on protocol stopping-power ratios data for the open reference field. It is interesting to note that the 0.8%

2096 FSánchez-Doblado et al -2-1 Fluence/incident particle (cm MeV ) 1.0x10-5 S w,air 8.0x10-6 6.0x10-6 4.0x10-6 2.0x10-6 1.1221 1.1201 0.0 0 1 2 3 4 5 6 Energy [MeV] Figure 10. Monte Carlo calculated photon spectra, at a depth of 5 cm in water, in the central axis of a 6 MV 10 10 cm 2 field (solid line) and a clinical IMRT field (dotted line) of similar area. The two beams are produced with the MLC of a Siemens Mevatron Primus linear accelerator. The calculated water/air stopping-power ratios for the two fields differ by 0.1%. difference in s w,air for the transmission leakage spectrum, which is present in varying degree in the beamlets of the IMRT beam, does not play a significant role in the dosimetry of the employed IMRT beam. The above conclusions are valid, as emphasized, for photon beams of 6 MV. A careful analysis of the beam qualities involved can demonstrate that the results are not too different from what could be expected for these, rather low, qualities. The determination of the TPR 20,10 beam quality specification for the beams involved in our study yields values within 3 3.5%. Forthis difference in range of qualities, the shape of the s w,air versus TPR 20,10 curve (cf figure 1 in Andreo 2000)shows a very small difference in s w,air, consistent with the differences found in this work. Should higher qualities and larger differences be involved, the expected differences in s w,air would become larger due to the steepness of the s w,air versus TPR 20,10 curve at these energies. To verify this hypothesis, s w,air was calculated for a circular field of 2 mm diameter using the 24 MV photon spectrum from the widely accepted standard set of Mohan et al (1985). For reference, the same calculation was made for the 6 MV spectrum of this set. As expected, the results for the 6 MV narrow beams agree with the reference, protocol-based, value within 0.3%, consistent with our results above. However, for the 24 MV narrow field spectrum the calculated s w,air differs by up to 1.1% from the reference value. These findings allow us to conclude that our statement of using protocol data for the open reference field in the case of narrow or IMRT fields, is confirmed for the low energies most commonly used in radiotherapy treatments, but the discrepancies found for higher energies require performing detailed calculations of the dosimetry parameters involved in order to achieve the same uncertainty as for the previous cases. 4. Conclusions The so far unresolved issue of absolute dosimetry with ionization chambers of the small photon fields used for stereotactic techniques and IMRT beamlets has been addressed using Monte Carlo methods. Simulations of the configurations used in these areas have been performed for

Ionization chamber dosimetry of small photon fields 2097 two clinical accelerators, an Elekta SL-18 and a Siemens Mevatron Primus, both producing 6 MV photons. Radiosurgery applicators (Elekta) and MLC fields, both irregular and IMRT configured (Siemens), have been simulated, together with reference 10 10 cm 2 fields, and their phase-space data at the position of the phantom surface determined. These data have been used first to generate absorbed dose profiles (depth and transverse) and complete 3D dose distributions which have been compared to experimentally determined profiles (measured with ionization chamber, diodes and film) to verify the quality of the Monte Carlo determined data. The results for all the configurations simulated, including Z-shaped small fields, both on-axis and off-axis, have been found to be excellent, providing support for the use of the phase-space data in our subsequent analysis. The phase-space data have been used to compute photon and electron spectra at various depths in water, followed by stopping-power calculations for ionization chamber dosimetry under various configurations. Differences in the various spectra with field size and depth have been analysed. The calculated stopping-power ratios have been compared with those used in recent dosimetry protocols, namely the IAEA TRS-398 Code of Practice based on standards of absorbed dose to water. Agreements within 0.1% have been obtained for 10 10 cm 2 fields between protocol data and the calculations of this work for water/air and PMMA/air stopping-power ratios in the two accelerators simulated, insuring that our calculation methodology and procedures are correct. In the case of radiosurgery applicators and MLC narrow beams, the calculated values of the stopping-power ratios agree with the reference s w,air values within ±0.3% for the most common cases, and with the s PMMA,air values within ±0.4%, which are well within the estimated standard uncertainty of the reference stopping-power ratios (s PMMA,air values are relevant only for the determination of p wall ). At the photon qualities analysed in this work (6 MV), ionization chamber dosimetry of narrow beams can therefore be based on the same set of dosimetry data. Additional calculations have been made for a real IMRT beam. The water/air stopping-power ratio determined in this case agree within 0.1% with the reference data, showing also that the ionization chamber dosimetry of typical IMRT beams can be based on protocol data for the open reference field at low energies. The analysis has been extended to higher energies (24 MV) using a less detailed procedure (published spectra) to derive narrow field data. The difference in water/air stopping-power ratios in this case was found to be up to 1.1%. This allows us to conclude that the use of protocol data for open fields at high energies in narrow beams is less accurate than at low energies, and detailed calculations of the dosimetry parameters involved should be performed if similar accuracy to that of 6 MV is sought. Acknowledgments The authors are indebted to the Spanish Fondo de Investigaciones Sanitarias for a Health Research Grant and to the LOU contract between the University of Seville and the Andalusian Health Service (SAS). PA acknowledges the support provided by the King Gustaf V Jubilee Fund, Stockholm. References Aaronson R F, DeMarco J J, Chetty I J and Solberg T D 2002 A Monte Carlo based phase space model for quality assurance of intensity modulated radiotherapy incorporating leaf specific characteristics Med. Phys. 29 2952 8 Almond P R, Biggs P J, Coursey B M, Hanson W F, Huq M S, Nath R and Rogers D W O 1999 Task Group 51 Protocol for clinical reference dosimetry of high-energy photon and electron beams Med. Phys. 26 1847 70

2098 FSánchez-Doblado et al Andreo P 1994 Improved calculations of stopping-power ratios and their correlation with the quality of therapeutic photon beams Measurement Assurance in Dosimetry (Vienna, 1993) (Vienna: International Atomic Energy Agency) pp 335 59 Andreo P 2000 On the beam quality specification of high-energy photons for radiotherapy dosimetry Med. Phys. 27 434 40 Andreo P and Brahme A 1986 Stopping power data for high energy photon beams Phys. Med. Biol. 31 839 58 Andreo P, Burns D T, Hohlfeld K, Huq M S, Kanai T, Laitano F, Smyth V and Vynckier S 2000 Absorbed dose determination in external beam radiotherapy: an International Code of Practice for dosimetry based on standards of absorbed dose to water IAEA Technical Reports Series no 398 (Vienna: International Atomic Energy Agency) Boyer A L et al 2001 Intensity-modulated radiotherapy: current status and issues of interest Int. J. Radiat. Oncol. Biol. Phys. 51 880 914 De Vlamynck K, Palmans H, Verhaegen F, De Wagter C, De Neve W and Thierens H 1999 Dose measurements compared with Monte Carlo simulations of narrow 6 MV multileaf collimator shaped photon beams Med. Phys. 26 1874 82 Heydarian M, Hoban P W and Beddoe A H 1996 A comparison of dosimetry techniques in stereotactic radiosurgery Phys. Med. Biol. 41 93 110 Kawrakow I 2000 Accurate condensed history Monte Carlo simulation of electron transport. I. EGSnrc, the new EGS4 version Med. Phys. 27 485 98 Kim J O, Siebers J V, Keall P J, Arnfield M R and Mohan R 2001 A Monte Carlo study of radiation transport through multileaf collimators Med. Phys. 28 2497 506 Kubsad S S, Mackie T R, Gehring M A, Misisco D J, Paliwal B R, Mehta M P and Kinsella T J 1990 Monte Carlo and convolution dosimetry for stereotactic radiosurgery Int. J. Radiat. Oncol. Biol. Phys. 19 1027 35 Lagares J I, Sánchez-Doblado F, Rosello J V and Arrans R 2002 IMRT dose distribution by film: optical parameter selection Radioth. Oncol. 64 (Suppl 1) S218 (723) Leal A, Sánchez-Doblado F, Arráns R and Roselló J V 2003 Routine IMRT verification by means of an automatic MC simulation system Int. J. Radiat. Oncol. Biol. Phys. 65 58 68 Li X A, Ma L, Naqvi S, Shih R and Yu C 2001 Monte Carlo dose verification for intensity-modulated arc therapy Phys. Med. Biol. 46 2269 82 Lovelock D M, Chui C S and Mohan R 1995 A Monte Carlo model of photon beams used in radiation therapy Med. Phys. 22 1387 94 Ma C-M, Rogers D W O and Walters B 2000 DOSXYZ00 Users Manual Report PIRS-0509(B) rev E (Ottawa: NRCC) Mainegra E, Capote R and López E 1998 Evaluation of dose rate constant for Pd-103, Ir-192, Yb-169 and I-125 brachytherapy sources: an EGS4 Monte Carlo study Phys. Med. Biol. 43 1557 66 McJury M, Oldham M, Cosgrove V P, Murphy P S, Doran S, Leach M O and Webb S 2000 Radiation dosimetry using polymer gels: methods and applications Br. J. Radiol. 73 919 29 Mohan R, Chui C and Lidofsky L 1985 Energy and angular distributions of photons from medical linear accelerators Med. Phys. 12 592 7 Morin L R M 1982 Molecular form factors and photon coherent scattering cross section of water J. Phys. Chem. Ref. Data. 11 1091 8 Namito Y, Ban S and Hirayama H 1994 Implementation of Doppler broadening of Compton scattered photon into the EGS4 code Nucl. Instrum. Methods A 349 489 94 Namito Y, Ban S and Hirayama H 1995 LSCAT: low-energy photon scattering expansion for the EGS4 code KEK Internal Report 95-10 National Institute for High Energy Physics, Japan Nelson W R, Hirayama H and Rogers D W O 1985 The EGS4 Code System SLAC-265 Stanford Linear Accelerator Center, Stanford, CA Pawlicki T and Ma C M 2001 Monte Carlo simulation for MLC-based intensity-modulated radiotherapy Med. Dosim. 26 157 68 Perucha M, Sánchez-Doblado F, Leal A, Rincón M, Arrans R, Nuñez L and Carrasco E 2003 Investigation of radiosurgical beam profiles using the Monte Carlo method Med. Dosim. 28 1 6 Rogers D W O, Faddegon B A, Ding G X, Ma C-M, We J and Mackie T R 1995 BEAM: a Monte Carlo code to simulate radiotherapy treatment units Med. Phys. 22 503 24 Rogers D W O, Kawrakow I, Seuntjens J P and Walters B R B 2000 NRC User Codes for EGSnrc Report PIRS-702 (Ottawa: NRCC) RSIC 1993 Photon Interaction Cross Section Library RSIC Data Package DLC-136/PHOTOX Radiation Shielding Information Center, Oak Ridge TN Sakamoto Y 1993 Photon cross section data PHOTX for PEGS4 code Proc. 3rd EGS4 User s Meeting in Japan KEK Internal Report 93-15 National Institute for High Energy Physics, Japan

Ionization chamber dosimetry of small photon fields 2099 Sánchez-Doblado F, Capote R, Leal A, Perucha M and Andreo P 2002 Monte Carlo calculations for the dosimetry of narrow photon beams in radiosurgery and IMRT Radioth. Oncol. 64 (Suppl 1) S218 (725) Sánchez-Doblado F, Perucha M, Leal A, Rincón M, Arráns R, Núñez L, Rosello J, Carrasco E, Martín G and Medrano J C 2000 Computational methods for treatment verification: the full Monte Carlo contribution The Use of Computers in Radiation Therapy, XIIIth International Conference, (Heidelberg, Germany) (Berlin: Springer) pp 272 4 Siebers J V, Keall P J, Kim J O and Mohan R 2002 A method for photon beam Monte Carlo multileaf collimator particle transport Phys. Med. Biol. 47 3225 49 Sixel K E and Faddegon B A 1995 Calculation of x-ray spectra for radiosurgical beams Med. Phys. 22 1657 61 Van Dyk J, Barnett R D and Battista J J 1999 Computerized radiation treatment planning systems The Modern Technology Of Radiation Oncology ed J Van Dyk (Madison, WI: Medical Physics Publishing) pp 231 86 Verhaegen F, Das I J and Palmans H 1998 Monte Carlo dosimetry study of a 6 MV stereotactic radiosurgery unit Phys. Med. Biol. 43 2755 68 Westermark M, Arndt J, Nilsson B and Brahme A 2000 Comparative dosimetry in narrow high-energy photon beams Phys. Med. Biol. 45 685 702