Paper TENTH VALUE LAYERS FOR 60Co GAMMA RAYS AND FOR 4, 6, 10, 15, AND 18 MV X RAYS IN CONCRETE FOR BEAMS OF CONE ANGLES BETWEEN 0° AND 14° CALCULATED BY MONTE CARLO SIMULATION Adnan K. Jaradat* and Peter J. Biggs† shielding barriers using the methodology outlined in National Council on Radiation Protection and Measurements (NCRP) Report No. 151 (NCRP 2005). This report supercedes previous reports on this topic (NCRP 1976, 1977, 1984). This report contains the first and subsequent tenth value layer (TVL) values for all energies used in current therapy electron linear accelerators. However, the published data are based on broad beam attenuation; that is, when the jaws of the linear accelerator or 60Co unit are fully open. For a linear accelerator, the typical maximum field size is 40 ⫻ 40 cm2 at 100 cm and for 60Co it is 33 ⫻ 33 cm2 at 80 cm. Broad beam attenuation represents the most conservative shielding assumption because fields up to the maximum size can be and are used. However, analysis of field sizes used in the radiotherapy clinic (Biggs 1991b) indicate that typical clinical field sizes are much less than the maximum field size available from medical linear accelerators. This analysis shows that 50% of field sizes treated are less than 15 ⫻ 15 cm2 and 90% are less than 26 ⫻ 26 cm2. About the only disease site that routinely requires large fields is Hodgkins’ disease where the chest and lower neck is irradiated. However, even the effective field sizes are much reduced by the lung blocks and this patient population, mainly adolescents, is comparatively small. These results clearly depend on a specific clinic and the mix of patients treated, for example, prostate, head and neck, breast, etc., but, on general grounds, it is unlikely that results from a different clinic would be dramatically higher. There has also been a trend in radiation therapy in specific disease sites to reduce the treatment field as much as possible. One of the reasons for this field reduction, made possible, in part, by better imaging for localization in recent years, is to reduce the co-morbidity of the treatment and the possibility of second cancers, given that many patients, in particular pediatric patients, can live for extended periods. For example, in the case of stereotactic radiosurgery and Abstract—The calculation of shielding barrier thicknesses for radiation therapy facilities according to the NCRP formalism is based on the use of broad beams (that is, the maximum possible field sizes). However, in practice, treatment fields used in radiation therapy are, on average, less than half the maximum size. Indeed, many contemporary treatment techniques call for reduced field sizes to reduce co-morbidity and the risk of second cancers. Therefore, published tenth value layers (TVLs) for shielding materials do not apply to these very small fields. There is, hence, a need to determine the TVLs for various beam modalities as a function of field size. The attenuation of 60Co gamma rays and photons of 4, 6, 10, 15, and 18 MV bremsstrahlung x ray beams by concrete has been studied using the Monte Carlo technique (MCNP version 4C2) for beams of half-opening angles of 0°, 3°, 6°, 9°, 12°, and 14°. The distance between the x-ray source and the distal surface of the shielding wall was fixed at 600 cm, a distance that is typical for modern radiation therapy rooms. The maximum concrete thickness varied between 76.5 cm and 151.5 cm for 60Co and 18 MV x rays, respectively. Detectors were placed at 630 cm, 700 cm, and 800 cm from the source. TVLs have been determined down to the third TVL. Energy spectra for 4, 6, 10, 15, and 18 MV x rays for 10 ⴛ 10 cm2 and 40 ⴛ 40 cm2 field sizes were used to generate depth dose curves in water that were compared with experimentally measured values. Health Phys. 92(5):456 – 463; 2007 Key words: shielding; accelerators, medical; Monte Carlo; photons INTRODUCTION RADIATION THERAPY rooms are generally constructed of concrete because of its relatively low cost. To design the shielding, one determines the thickness of the various * Department of Physics, University of Massachusetts Lowell, One University Avenue, Lowell, MA 01854; † Department of Radiation Oncology, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02114. For correspondence contact: P. J. Biggs, Department of Radiation Oncology, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02114, or email at pjbiggs@partners.org. (Manuscript accepted 21 November 2006) 0017-9078/07/0 Copyright © 2007 Health Physics Society 456 Tenth value layers ● A. K. JARADAT stereotactic radiotherapy, both intra- and extra-cranial, the fields are limited to a few cm in diameter, at most. In accelerated partial breast irradiation, it was recognized that, in a select group of patients, the treatment field need only cover the area of the primary disease and not the whole breast to achieve similar outcomes (Schwartz et al. 2005). This has reduced the sizes of the fields considerably. It is now well accepted that Monte Carlo (MC) methods offer the most powerful tool for modeling radiation transport for radiotherapy applications (Verhaegen and Seuntjens 2003). Ding (2002a) used the MC method to simulate radiotherapy photon beams emerging from an accelerator; using the MC beam code, Hartman Siantar et al. (2001) has modeled the treatmentindependent accelerator head, resulting in the identification of primary and scattered photon sources and electron contamination source; Sheikh-Bagheri and Rogers (2002) used the MC technique to determine the energy spectra of different Varian linear accelerators. In radiation shielding applications, where experiments are either very difficult or extremely time consuming, the MC approach has been frequently used to solve difficult problems. Shobe et al. (1999) measured the scatter fractions of 6, 10, 18, and 25 MV x rays, while Nogueira and Biggs (2001) measured the scatter fractions for 4, 6, 10, and 23 MV x rays and also the TVLs in lead for 4, 6, and 10 MV (Nogueira and Biggs 2002). Maruyama et al. (1971) evaluated the broad-beam attenuation coefficients for lead, iron, heavy concrete, and concrete for x-ray beams and compared the results with experimental measurements. Biggs (1991a) used the MC program, ITS, to determine the dose and energy spectrum of radiation at the door for 4 and 10 MV x rays and to determine the attenuation 60Co gamma ray and photons of 4, 10, and 18 MV x-ray beams by concrete, steel, and lead (Biggs 1996). Biggs (1998) also used the MC code to calculate the shielding thickness required for the roof of a single-story building. In a similar vein, Kong et al. (2005) used the MC method to predict skyshine radiation from electron accelerators and compared the results with experimental measurements. Also, Casanova et al. (2004) used the MC method to analyze the shielding requirements for a MT-25 microtron medical accelerator. Taylor et al. (1999) have determined the scatter fractions of dose for a wide range of energies using the MC methodology. More specifically, Nelson and LaRiviere (1984) used the EGS MC code to determine the spectra and transmission properties of 6, 10, and 25 MV bremsstrahlung beams. These transmission data were for incident broad beams (30° opening angle), approximately equivalent to the beam passing through the primary AND P. J. BIGGS 457 collimator in a modern medical linear accelerator, at azimuthal angles of 0° and about 45°, 90°, and 135°. The purpose of this paper is to determine the TVLs in concrete for a range of energies currently used in radiation therapy as a function of half-opening angle of the x-ray beam for the first, second and third TVLs. TVLs for 60Co also were determined because this modality has been well-established in terms of measured data. MC simulations of photon/electron transport in a water phantom were also used to obtain depth dose curves in water. The agreement between the calculation and the measurement was within the statistical uncertainty of the MC simulations and measured data. METHODS AND MATERIALS Monte Carlo code The MCNP Monte Carlo transport code system, developed at Los Alamos and distributed by the Radiation Shielding Information Computational Center at Oak Ridge National Laboratory, was used in this work. MCNP is a general-purpose Monte Carlo N-particle code (version 4C2) that can be used for neutron, photon, and electron, or coupled neutron/photon/electron transport. For photons, the code takes account of incoherent and coherent scattering, the possibility of fluorescent emission after photoelectric absorption, and bremsstrahlung (MCNP 2003). In this study, because of the small number of photoneutrons produced in the interaction of photons with concrete that produce capture gamma rays, only coupled photons and electrons were studied with no neutrons included. In addition, the version of MCNP used in this study did not have the gamma-neutron cross-sections as a secondary source and therefore the process could not be simulated (Casanova et al. 2004). The results in this paper are based on the photon flux, determined using the f4 tally. This permits a direct comparison with the flux striking the barrier and the ratio defines the transmission factor. It can be argued that the spectrum of photons exiting the barrier is considerably different (lower average energy) from the spectrum of photons entering the barrier. However, this is in the spirit of the definition of the transmission factor (Johns and Cunningham 1983). If one were to use an f8 tally, energy deposited or dose, one still has to face the problem of a different energy spectrum before and after the barrier. Additionally, there is probably not electronic equilibrium for the spectrum of photons exiting the barrier, and one has to determine the dose of the incoming beam, which could be arbitrary since it can be defined at different depths in a phantom. 458 Health Physics The electron energy cut-off was set to 50 keV and the photon energy cut-off to the default of 1 keV. These cut-offs could have been set higher in the barrier, for example, without affecting the final result. The runs were, consequentially, longer. Barrier material Concrete was used for the barrier shielding material with an assumed density of 2.35 g cm⫺3. The weight composition of concrete used in this calculation was taken to be hydrogen, 0.55%; oxygen, 49.57%; sodium, 1.7%; magnesium, 0.26%; aluminum, 4.55%; silicon, 31.36%; sulfur, 0.13%; potassium, 1.9%; calcium, 8.26%; and iron, 1.23% (NCRP 1977). Tenth value layer (TVL) In radiation shielding work, it is customary to use the TVL of a material, which is defined as the thickness of the material needed to reduce the intensity of radiation to one tenth of the initial intensity of the beam at the point of measurement. Because of the build-up factor that occurs for broad beams, the first TVL is always greater than the second and third TVLs. By measuring or calculating the attenuation as a function of absorber thickness, one can determine the required thickness of shielding material for the primary barrier in any radiotherapy room. Bremsstrahlung beam The bremsstrahlung spectra for 4, 6, 10, 15, and 18 MV were generated for 10 ⫻ 10 cm2 for Varian machines by Sheikh-Bagheri and Rogers (2002) using the MC BEAM code. The most probable energies for these beams were 1.0, 0.75, 1.125, 1.5, and 1.75 MeV, and the average energies were 1.52, 1.82, 3.19, 3.88, and 4.88 MeV, respectively. Geometry Transmission measurements. The geometry used in this MC simulation consisted of a point source x-ray beam incident on the absorbing material within different coneshaped angles with circular cross sections. Whereas the maximum field size for conventional linear accelerators is square,‡ it is much simpler to generate a field of circular cross-sections in a MC simulation. Table 1 shows a list of the equivalent square fields for each different cone angle field at 1 m from the x-ray target. The layout of this experiment is shown in Fig. 1. The transmitted radiation was detected with a spherical air-filled detector with a 3-cm radius on the beam central axis at distances of 630 cm, 700 cm, and 800 cm from the source and therefore at different distances from the barrier, namely 30 cm, 100 cm, and 200 ‡ Note that this is not strictly correct for most machines since the field is also limited by a circular, fixed primary collimator that projects a field size of 50 cm diameter at isocenter. May 2007, Volume 92, Number 5 Table 1. Equivalent square area at 1 m from the x-ray target. Angle (°) Area (cm2) 0 3 6 9 12 14 0 9.3 ⫻ 9.3 18.6 ⫻ 18.6 28.1 ⫻ 28.1 37.7 ⫻ 37.7 44.2 ⫻ 44.2 Fig. 1. Source, concrete barrier and the three positions of the detector (a, b, c) behind the barrier. Point a is 30 cm behind the barrier, point b 100 cm, and point c 200 cm. cm, respectively. This was done to evaluate the variation of TVL with distance between the detector and the barrier. Air was assumed as the medium for all regions other than the barrier. Depth dose measurements. Depth doses were generated for these beams to ensure that the applied MC methodology was correct. The geometry used to generate the percent depth dose curves consisted of a point source, cylindrical chamber of radius of 1 cm and thickness of 0.2 cm, and a phantom water tank of dimensions 1 ⫻ 1 ⫻ 1 m3. The distance between the source and the water surface was 1 m (i.e., the water surface was at the isocenter), and the chamber had its flat surface parallel to the water surface. The percent depth dose curves were simulated for two field sizes: 10 ⫻ 10 cm2 and 40 ⫻ 40 cm2. Data collection and normalization. The transmitted radiation was sampled by measuring the number of photons per photon emitted at the target for each cone angle and energy. Results were normalized to the case with no shielding material present. The transmission was measured down to ⬍10⫺3 to ensure an adequate measurement of the third TVL. The errors on the transmission points ranged from ⬍⬍1% for shallow thicknesses and small cone opening Tenth value layers ● A. K. JARADAT AND P. J. BIGGS 459 angles, to ⬃5% for transmission factors of ⬍10⫺3 and large cone opening angles. These numbers were essentially independent of beam energy. The overall average error was 2.2% with a standard deviation of 1.0%. RESULTS Figs. 2 and 3 are plots of the percent depth dose derived from the spectra used for simulation vs. experimental measurements for a field size of 40 ⫻ 40 cm2 at 6 MV and 10 ⫻ 10 cm2 at 18 MV, respectively. In each case the data points correspond to the MC calculation, and the line corresponds to measured data. The transmission data consist of 18 plots for various detector distances from the barrier and different energies (3 distances ⫻ 6 energies); each plot contains one contour for each of the six cone angles. It would be impractical to show all plots. Instead, a sample of these plots is shown to illustrate the type of curves generated. For each plot, the transmission is plotted on a log scale against barrier thickness, and the lines simply bridge the data points to aid the eye. Figs. 4 –7 are families of transmission curves through concrete for cone angles between 0° and 14° for 60Co and 18 MV x rays at 30 cm and 200 cm detector-barrier distances, respectively. Note that the curves in Figs. 4 and 5 for 60Co gamma rays, for angles other than 0°, are not purely exponential, but have a convex shape or shoulder at shallow depths, corresponding to the build-up factor (Chilton et al. 1984). Build-up is also visible at 18 MV for the 30 cm data. The effect almost vanishes at 18 MV for 200 cm. Analysis Fig. 3. Percent depth dose curve 18 MV 10 ⫻ 10 cm2 field size (ⴱ) MCNP; (——) experiment. Fig. 4. Transmission curves for 60Co gamma rays in concrete at a 30 cm detector barrier distance. (⫹) 0°; (‚) 3°; (䡺) 6°; (䉬) 9°; (ⴱ) 12°; (Œ) 14°. Fig. 2. Percent depth dose curve for 6 MV 40 ⫻ 40 cm2 field size (ⴱ) MCNP; (——) experiment. of these data show that the build-up is greater for 60Co than for 18 MV, but, to the eye, the effect is small. Also noticeable is that, for both energies, the transmission curve for 0° is widely separated from the other curves for the 30 cm data but not the 200 cm data. The variation of the first and third TVLs, respectively, as a function of energy, is shown in Figs. 8 and 9, respectively, for all cone angles at 30 cm, compared with the first and subsequent TVLs of NCRP Report No. 51 (NCRP 1977) (heavy dashed line) and NCRP Report No. 151 (NCRP 2005) (heavy dotted line). The first TVL for all angles at 200 cm, again as a function of energy, are compared with the first TVL of NCRP Report No. 51 460 Health Physics Fig. 5. Transmission curves for 60Co gamma rays in concrete at a 200 cm detector barrier distance. (⫹) 0°; (‚) 3°; (䡺) 6°; (䉬) 9°; (ⴱ) 12°; (Œ) 14°. May 2007, Volume 92, Number 5 Fig. 7. Transmission curves for 18 MV x rays in concrete at a 200 cm detector to barrier distance. (⫹) 0°; (‚) 3°; (䡺) 6°; (䉬) 9°; (ⴱ) 12°; (Œ) 14°. Fig. 6. Transmission curves for 18 MV x rays in concrete at a 30 cm detector to barrier distance. (⫹) 0°; (‚) 3°; (䡺) 6°; (䉬) 9°; (ⴱ) 12°; (Œ) 14°. (NCRP 1977) and NCRP Report No. 151 (NCRP 2005) in Fig. 10. The NCRP values refer to broad beam transmission values and are assumed to represent the largest field size. Tables 2– 4 provide the first, second, and third TVLs for all energy and opening angle combinations. Using the uncertainties on the individual measurements given earlier, an error analysis was performed on the TVL values. Data were analyzed for all energies at 0°, 6°, and 14°. For the first, second, and third TVLs, the error is negligible (⬃0.1 cm) for the 0° cone angle, and it increases with cone angle and from the first to the third TVLs. Averaged over all distances (30 cm, 100 cm, and 200 cm), the error increased from 0.1 cm to 0.7 cm at 6° and to 1.0 cm at 14°. The error, averaged over all energies and distances, increased from 0.3 cm for the first TVL to 0.6 cm for the second TVL and to 0.8 cm for the third TVL. A histogram of all the points analyzed gives a most probable error of 0.2 cm and an Fig. 8. First TVLs in concrete as a function of energy for a 30 cm barrier to detector distance. (⫹) 0°; (‚) 3°; (䡺) 6°; (䉬) 9°; (ⴱ) 12°; (Œ) 14°; (– – –) NCRP 51; (- - -) NCRP 151. average of 0.5 ⫾ 0.5 cm. If one were to fit the data with a model, one could likely get smaller errors, but these would then be model dependent. The analysis given above therefore represents a safe upper limit. DISCUSSION The good agreement between the MCNP-generated percent depth dose curves and the measured data is demonstrated in Figs. 2 and 3. Note that a full MC simulation of the treatment head was not used in this work since that would be unnecessary, so some discrepancies are to be expected. For example, although photons scattered by the jaws would be included in the simulation, in this study we Tenth value layers ● A. K. JARADAT Fig. 9. Third TVLs in concrete as a function of energy for a 30 cm barrier to detector distance. (⫹) 0°; (‚) 3°; (䡺) 6°; (䉬) 9°; (ⴱ) 12°; (Œ) 14°; (– – –) NCRP 51; (- - -) NCRP 151. Fig. 10. TVLs in concrete as a function of energy for a 200 cm barrier to detector distance. (⫹) 0°; (‚) 3°; (䡺) 6°; (䉬) 9°; (ⴱ) 12°; (Œ) 14°; (– – –) NCRP 51; (- - -) NCRP 151. only used the photon spectra emanating from a point, namely the target. There is a discrepancy between the two sets of data in the build-up region for 18 MV, as expected, since electron contamination is a well-known effect at this energy. The effect is much less at lower energies, which explains the better agreement at 6 MV, despite the larger field size that will increase the effect of contamination. This MC simulation does not model electron contamination from the treatment head, only that generated in the intervening air. There is good agreement beyond the depth of the maximum dose. The discrepancy in the build-up region was AND P. J. BIGGS 461 investigated by Ding (2002b), who was unable to solve the problem. He added a lead filter to reject electrons in the build-up region, but was unable to reconcile the measured data with his MC data. The effect of build-up, for angles of 9° and higher, can be seen in the transmission plots at 30 cm detector-barrier distance. However, at the 200 cm detector-barrier distance, the build-up effect is considerably less, and largely absent at 18 MV because the scattering source in the concrete is farther away from the detector and therefore will make a lower contribution. Note that for 0° the curves for each energy are independent of distance, as expected, since no in-scatter is involved. This also serves as a secondary check on the applied MC methodology. Further, the curves are not purely exponential, having a larger slope (lower TVL) at the beginning compared with greater depths. These curves are akin to those seen in diagnostic radiology and the first part of the curve represents the attenuation of the low energy component of the beam. A general pattern for the TVLs listed in Tables 2, 3, and 4, for all detector-barrier distances, is that they increase with increasing energy and cone angle. The dependence on cone angle is because of the increased scatter contribution, and it shows how the build-up occurs, i.e., no build-up for small field size, but increasing with increasing angle. The first TVL in Fig. 8 at 30 cm detector-barrier distance is higher than those given in NCRP Report Nos. 51 and 151 for cone angles greater than 6°, although there is better agreement with the data from NCRP Report No. 151 at 4 and 6 MV. However, the MC data are in good agreement with the NCRP Report Nos. 51 and 151 data for the third TVL, as shown in Fig. 9. Interestingly, the first TVL data agree well with the NCRP data at a barrierdetector distance of 200 cm (Fig. 10), but less so with the data from NCRP Report No. 151 at 4 and 6 MV. It is unclear why the first TVL calculated by MC is greater than the published values. However, as the footnote in NCRP Report No. 51 states, “curves are empirically drawn through data points” (NCRP 1977),” and it is clear that no data are shown between 2 and 35 MV of the subsequent TVL curve. However, NCRP Report No. 151 provides more recent data for these specific machine energies. On the other hand, the 200 cm data show that the measurements might have been performed at a distance much greater than 30 cm. This is highlighted in the case of 60Co where the difference between the MC and NCRP data is particularly significant for the first TVL, whereas for the third TVL there is excellent agreement between the MC data and that from NCRP Report No. 151. Further analysis of the 60Co data shows that all the second and third TVLs have about the same values, consistent with the NCRP values, with a slow increase from ⬃17.5 cm at 0° to ⬃21 cm at 14°. In contrast, the first TVLs 462 Health Physics May 2007, Volume 92, Number 5 Table 2. First TVL at 0.3, 1.0, and 2.0 m detector-barrier distance for different cone angles. Cone angle (°) Energy (MV) Distance (m) 1.25 1.25 1.25 4.00 4.00 4.00 6.00 6.00 6.00 10.00 10.00 10.00 15.00 15.00 15.00 18.00 18.00 18.00 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0° 3° 6° 9° 12° 14° 17.5 17.2 17.0 18.0 18.0 18.0 20.0 19.5 19.5 25.5 25.7 25.5 28.0 27.5 28.0 31.0 29.4 30.0 28.0 21.0 18.5 29.5 22.5 19.5 32.0 24.5 21.5 40.5 32.0 28.5 44.0 34.5 31.5 48.0 38.2 34.5 32.5 26.2 22.5 33.5 27.6 23.5 37.0 30.3 26.0 45.5 38.7 34.0 50.0 41.7 37.5 54.5 46.2 41.0 33.5 29.8 26.0 35.5 31.5 27.5 38.5 34.3 30.0 47.5 43.0 38.5 52.0 47.0 42.0 56.5 50.6 48.0 34.5 31.6 29.0 36.5 33.6 30.5 40.0 36.0 33.0 50.5 46.0 42.0 53.0 48.7 45.0 58.0 53.6 50.0 34.5 32.5 29.5 36.5 33.8 31.0 40.0 37.5 34.5 50.5 47.0 43.5 53.0 49.5 46.0 58.5 54.6 51.0 Table 3. Second TVL at 0.3, 1.0, and 2.0 m detector-barrier distance for different cone angles. Cone angle (°) Energy (MV) Distance (m) 1.25 1.25 1.25 4.00 4.00 4.00 6.00 6.00 6.00 10.00 10.00 10.00 15.00 15.00 15.00 18.00 18.00 18.00 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0° 3° 6° 9° 12° 14° 17.0 17.2 17.5 20.5 20.4 20.0 24.5 24.8 24.5 32.0 31.8 31.5 34.0 34.0 33.5 36.0 38.2 36.5 20.5 20.6 19.0 25.5 24.0 22.5 31.0 28.8 27.0 39.5 37.0 34.5 40.5 39.5 36.0 42.5 42.2 40.0 21.5 21.6 20.0 26.0 26.5 25.5 31.5 30.7 29.5 41.0 39.6 38.0 42.0 42.0 40.0 43.5 43.8 42.0 22.0 21.8 21.5 26.0 26.5 25.5 31.5 31.4 30.0 40.0 39.5 39.5 43.0 42.0 41.0 43.5 44.4 42.5 22.0 21.9 21.0 26.5 26.6 26.0 31.5 32.5 30.5 39.0 40.0 38.5 43.0 42.8 41.0 44.0 44.0 42.5 22.0 22.0 21.5 26.5 26.6 27.0 31.5 32.5 31.0 40.0 40.0 38.5 43.0 43.0 41.0 44.0 44.0 43.0 Table 4. Third TVL at 0.3, 1.0, and 2.0 m detector-barrier distance for different cone angles. Cone angle (°) Energy (MV) Distance (m) 1.25 1.25 1.25 4.00 4.00 4.00 6.00 6.00 6.00 10.00 10.00 10.00 15.00 15.00 15.00 18.00 18.00 18.00 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0.3 1.0 2.0 0° 3° 6° 9° 12° 14° 18.0 17.4 17.5 23.5 23.0 23.0 28.0 28.0 28.0 36.0 35.5 35.5 38.0 37.5 37.5 40.0 39.4 40.0 19.0 19.6 19.0 26.0 25.2 25.0 31.5 31.5 30.5 38.0 38.5 39.0 41.5 41.8 41.5 45.5 43.2 42.5 19.5 20.8 20.5 27.0 26.2 26.0 33.5 33.0 32.5 39.0 40.2 40.5 42.0 42.0 41.5 46.0 45.0 45.5 20.5 20.6 21.5 27.5 26.5 28.0 34.0 33.0 34.5 40.5 40.5 42.0 42.5 42.3 42.0 46.0 45.2 46.0 20.5 20.5 21.0 27.5 27.3 28.0 34.5 33.5 34.5 40.0 40.5 41.0 44.0 42.5 43.0 48.0 47.4 46.5 21.0 20.5 20.5 27.5 28.0 28.0 34.5 33.5 36.5 40.0 41.3 40.5 45.0 44.0 43.0 49.0 47.4 47.0 Tenth value layers ● A. K. JARADAT have a much larger TVL for large angles, irrespective of distance. CONCLUSION The MCNP program has been used to study the TVLs for energies between 60Co gamma rays and 18 MV bremsstrahlung incident on concrete at various cone angles up to 14°. The data at large angles agree with NCRP Report No. 151. For smaller angles, the TVL values are significantly less. The results, for cone angles less than the maximum, show that the TVLs are lower than for broad beams. Since average field sizes in radiation therapy are considerably less than the 40 ⫻ 40 cm2 that the machines allow, thinner shielding walls than calculated using the standard NCRP values could be used. For machines that are dedicated to specific procedures, such as stereotactic radiotherapy, this change could be quite significant in view of the small field sizes used in that procedure. Even a machine dedicated to breast cancer, as in our institution, would use considerably smaller field sizes. As an aside, field size reduction would also reduce the scatter dose considerably since it varies as the area of the field (Shobe et al. 1999). REFERENCES Biggs PJ. Calculation of shielding door thicknesses for radiation therapy facilities using the ITS Monte Carlo program. Health Phys 61:465– 472; 1991a. Biggs PJ. Analysis of field and custom block sizes used in radiation therapy—implications for multileaf collimator design. Med Dosim 16:169 –172; 1991b. Biggs PJ. Obliquity factors for Co-60, and 4, 10, and 18 MV x rays for concrete, steel, and lead and angles of incidence between 0° and 70°. Health Phys 70:527–536; 1996. Biggs PJ. Determination of shielding for an unoccupied roof of a radiation therapy facility to account for adjacent buildings—modification of a computer program. Health Phys 75:431– 434; 1998. Casanova AO, Lopez N, Gelen A, Guevaro MV, Diaz O, Cimino L, D’Alessandro K, Melo JC. Shielding analysis of the microtron MT-25 using the MCNP 4C code and NCRP Report No. 51. Radiat Protect Dosim 109:189 –195; 2004. Chilton, AB, Shultis JK, Faw RE. Principles of radiation shielding. Englewood Cliffs, NJ: Prentice-Hall, Inc.; 1984. Ding GX. Energy spectra, angular spread, fluence profiles and dose distributions of 6 and 18 MV photon beams: results of Monte Carlo simulations for a Varian 2100EX accelerator. Phys Med Biol 47:1025–1046; 2002a. Ding GX. Dose discrepancies between Monte Carlo calculations and measurements in the buildup region for a high energy photon beam. Med Phys 29:2459 –2463; 2002b. AND P. J. BIGGS 463 Hartman Siantar CL, Walling RS, Daly TP, Faddegon B, Albright N, Bergstrom P, Bielajew AF, Chuang C, Garrett D, House RK, Knapp D, Wieczorek DJ, Verhey LJ. Description and dosimetric verification of the PEREGRINE Monte Carlo dose calculation system for photon beams incident on a water phantom. Med Phys 28:1322–1337; 2001. Johns HE, Cunningham JR. Physics of radiology. Springfield, IL: Charles C. Thomas; 1983. Kong C, Li Q, Chen H, Du T, Cheng C, Tang C, Li Z, Zhang H, Pei Z, Ming S. Monte Carlo method for calculating the radiation skyshine produced by electron accelerators. Nucl Instr Meth Phys Res B 234:269 –274; 2005. Maruyama T, Kumamoto Y, Kato Y, Hashizume T, Yamamoto M. Attenuation of 4 –32 MV x-rays in ordinary concrete, heavy concrete, iron, and lead. Health Phys 20:277–284; 1971. MCNP. A general Monte Carlo N-particle transport code, version 4C2. Los Alamos: Los Alamos National Laboratory; Report LA-UR-03-1987; 2003. National Council on Radiation Protection and Measurements. Structural shielding design and evaluation for medical use of x-rays and gamma rays of energies up to 10 MV. Bethesda, MD: NCRP; NCRP Report No. 49; 1976. National Council on Radiation Protection and Measurements. Structural shielding design and evaluation for medical use of x-rays and gamma rays of energies up to 10 MV. Bethesda, MD: NCRP; NCRP Report No. 51; 1977. National Council on Radiation Protection and Measurements. Neutron contamination from medical electron accelerators. Bethesda, MD: NCRP; NCRP Report No. 79; 1984. National Council on Radiation Protection and Measurements. Structural shielding design and evaluation for megavoltage x- and gamma-ray radiotherapy facilities. Bethesda, MD: NCRP; NCRP Report No. 151; 2005. Nelson WR, LaRiviere PD. Primary and leakage radiation calculations at 6, 10 and 25 MV. Health Phys 47:811– 818; 1984. Nogueira IP, Biggs PJ. Measurement of scatter factors for 4, 6, 10 and 23 MV x rays at scattering angles between 30° and 135°. Health Phys 81:330 –340; 2001. Nogueira IP, Biggs PJ. Measurement of TVLs in lead for 4, 6 and 10 MV bremsstrahlung x-ray beams at scattering angles between 30° and 135°. Health Phys 83:255–260; 2002. Schwartz GF, Veronesi U, Clough K, Dixon JM, Fentiman IS, Heywang-Köbrunner SH, Holland R, Hughes KS, Mansel RE, Margolese EB, Olivotto IA, Palazzo JP, Solin LJ. Consensus conference on breast conservation. J Am Coll Surgeons 203:198 –207; 2005. Sheikh-Bagheri D, Rogers DWO. Monte Carlo calculation of nine megavoltage photon beam spectra using the BEAM code. Med Phys 29:391– 402; 2002. Shobe J, Rodgers JE, Taylor PL. Scattered fractions from 6, 10, 18 and 25 MV linear accelerator x-rays in radiotherapy facilities. Health Phys 76:27–35; 1999. Taylor PL, Rogers JE, Shobe J. Scatter fractions from linear accelerators from 6 to 24 MV. Med Phys 26:1442–1446; 1999. Verhaegen F, Seuntjens J. Monte Carlo modeling of external radiotherapy photon beams. Phys Med Biol 48:R107–164; 2003. f f