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SHIELDING DESIGN FOR MULTIPLE-ENERGY LINEAR ACCELERATORS Robert J. Barish* AbstractVThe introduction of medical linear accelerators (linacs) capable of producing three different x-ray energies has complicated the process of designing shielding for these units. The conventional approach for the previous generation of dual-energy linacs relied on the addition of some amount of supplementary shielding to that calculated for the higher-energy beam, where the amount of that supplement followed the historical ‘‘two-source’’ rule, also known as the ‘‘add one HVL rule,’’ a practice derived from other two-source shielding considerations. The author describes an iterative approach that calculates shielding requirements accurately for any number of multiple beam energies assuming the workload at each energy can be specified at the outset. This method is particularly useful when considering the requirements for possible modifications to an existing vault when new equipment is to be installed as a replacement for a previous unit. Health Phys. 106(5):614Y617; 2014 Key words: medical radiation; radiation protection; radiotherapy; shielding

INTRODUCTION HISTORICALLY, MEDICAL linear accelerator technology has evolved from single-photon-energy units in the 1970s, through dual-energy units in the 1980s and 90s, to a present generation where it is possible to acquire three x-ray beam energies as a standard configuration. Examples of this are the Varian TrueBeam (Varian Medical Systems, Palo Alto, CA, USA) and Elekta Precise (Elekta AB, Stockholm, Sweden) treatment systems. When the National Council on Radiation Protection and Measurements (NCRP) published its most recent report on shielding design for radiotherapy facilities, Report No. 151 (NCRP 2005), they addressed the issue of dualenergy linear accelerators (linacs) by suggesting that the design physicist calculate the shielding requirements using *211 E 70th Street, Apt. 12G, New York, NY 10021. The author declares no conflicts of interest. For correspondence or reprints contact the author at the above address or email at [email protected]. (Manuscript accepted 12 September 2013) 0017-9078/14/0 Copyright * 2014 Health Physics Society DOI: 10.1097/HP.0000000000000036

both the high-energy and the low-energy workloads and then add an additional amount to that calculated for the high energy. However, their approach was not completely analytical in this regard, as they only suggested that an examination be made of the relative magnitude of the lowenergy contribution and that the supplementation be one half-value layer depending on whether the calculated values of shielding for the two energies differed by more or less than one tenth-value layer; i.e, the ‘‘two-source rule’’ that had been previously established for other dual-source shielding problems (NCRP 1976). The most relevant IAEA document, Safety Report Series No. 47, does not address dual-energy units (IAEA 2006). With three beam-energies generally quite different in their penetrating ability, the problem of accurately specifying shielding in a cost-effective manner becomes more complicated than for the two-source situation. Recognizing that much of radiotherapy shielding design requires an iterative approach to determine the required barrier thickness, the author has derived a method to calculate the shielding requirements for multiple-beam-energy linacs accurately, assuming the workload at each energy can be specified at the outset. This is often the case for established clinical practices where their existing patterns of care can reasonably dictate the use of the x-ray beams for new facilities they construct or for the replacement of earlier-generation machines when new equipment is to be installed in an existing vault. Changing patterns of usage from Intensity Modulated Radiotherapy (IMRT) to Volumetric Modulated Arc Therapy (VMAT) are, fortunately, adding an additional safety factor to previously calculated shielding values because of the reduced number of monitor units required with the latter technique. ITERATIVE CALCULATIONS IN SHIELDING DESIGN A fundamental requirement in calculating radiation shielding for either diagnostic or therapeutic sources is obtaining the distance from the radiation source to the point that will be shielded. For diagnostic radiology, when considering a barrier such as a wall of the procedure room, the geometry is well established up-front, since the point of

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calculation (occupancy) is not particularly influenced by the few millimeters of shielding that are typically required. For the high-energy sources used in radiotherapy where the cost of shielding can be quite expensive, one often designs a vault in a way that minimizes the interior distances such that the equipment and ancillary patient items will be accommodated in this minimum space rather than relying on a previously assumed exterior footprint. So rather than the shielding being specified inward from the external perimeter, the exact exterior position of the room’s walls will often be dictated by the required thickness of the barrier. For new facilities, this approach allows for a minimum room size with associated cost savings in its construction. For example, if the clearance of the patient couch of a linear accelerator requires a distance of 3 m to the side wall of the vault, the exact distance to the exterior of that wall can only be determined once the required wall thickness is known. Similarly, if the distance from the rear wall to the isocenter is required by the equipment vendor to be 3.8 m, the thickness of that wall and, therefore, the distance to the other side of that wall, are also not independent of one another. The required computational process, performed by an experienced person, generally only requires a couple of iterations of the calculation to determine the required barrier thickness accurately. Clearly, given the expense associated with constructing a typically massive radiotherapy vault, it is desirable to achieve the thinnest possible structure consistent with the required permissible exposure outside the barrier, and that approach is generally taken by experienced planners. THE METHOD FOR MULTI-SOURCE ACCELERATORS One of the fundamental quantities needed in designing shielding is, of course, the workload. In radiotherapy, this is generally expressed as dose (Gy) at isocenter per unit time, where the value of time might vary depending on whether the required shielding conforms to established standards in the United States or in other jurisdictions. Specifically, in the U.S., there is no requirement for instantaneous dose-rate limits (IDR), and shielding is generally calculated for weekly workloads. In some countries, there are IDR requirements as well as daily limits (TADR) that must be adhered to (IPEM 2002). The approach described here is modified easily for any required dose limit, but it is presented here for the typical annual limit (TADR2000) that is most usually narrowed to a single week of operation. In most of the United States, those weekly limits are either 100 mSv for restricted areas or 20 mSv for public areas where full-occupancy can be assumed, although there are some places (such as Massachusetts) where more restrictive dose limits apply. For the shielding

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of public areas, regulations also require conformity with the ‘‘20 mSv in any hour’’ restriction, and this limit must always be considered when high-dose special procedures such as radiosurgery are to be undertaken. The starting point for these calculations is the primary beam workload at each photon energy. Usually this workload will be split also into a workload for conventional Ethree-dimensional (3-D)^ treatments and those that use intensity-modulated techniques (IMRT and/or VMAT). In addition to the primary radiation, for highenergy linacs, secondary barriers are usually derived adequately using a value of 0.1% leakage, since this typically overestimates the actual value and in so doing accounts for low-angle scatter at the periphery of adequately sized primary barriers for all accelerators except those operated with a large high-energy workload Ei.e., 18 MV or greater (Taylor et al. 1999; Nogueira and Biggs 2001)^, energies that are now sparingly used for modern IMRT and VMAT treatments. If an atypical workload distribution weighted toward the high-energy x-rays is expected and the computed barrier thicknesses are also modified by considering slant-distances at the angles of penetration, then the secondary barriers immediately adjacent to the periphery of the primary may require supplementation for the scattered radiation in a manner that has been well described previously (NCRP 2005). The equation used for each individual primary workload in determining a primary barrier thickness is Di = Wi  U  dj2  10jt/TVL where Di is the dose contribution from that energy at the point of calculation, Wi is the workload for that particular beam energy, U is the use factor for the barrier, d is the distance to the calculation point, t is the barrier thickness, and TVL is the shielding material’s tenth-value layer for that energy. This equation, with the same values of d and t, is used for each of the beam energies, changing only the value of Wi and TVL. Summing the results from each separate calculation gives the total expected dose. At first glance, it appears that it is not possible to perform the calculation because both d and t are not known a priori. However, it is obvious that since d depends on t, when the inner surface of the barrier is at a known position, it is possible for an individual with some prior experience at shielding design to start with a reasonable value of both variables. This is really no different than the situation encountered when performing the usual iterative computations described earlier. Given practice, it is possible to converge on the correct value very quickly. It is not necessary to work these values out to a fraction of a millimeter; getting thickness values within a centimeter or two is certainly adequate, particularly if they lead to dose values a bit below the required values. Appendix A shows a calculation for a primary barrier. In this example, the facility

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completely specified the workload for both conventional and IMRT/VMAT treatments with typical fractionated doses and also specified stereotactic radiosurgery (SRS) and stereotactic body radiotherapy (SBRT) for both conventional and IMRT/VMAT techniques. Appendix B shows the calculation for a secondary barrier at the same facility. In these example calculations, the values of TVL are those published in the installation data manual for the Varian TrueBeam accelerator cited earlier. For the upgrade of an existing vault that will receive new equipment, this calculation method is ideal since the values of both d and t are known quantities, which are readily obtained by examining the architectural prints of the existing construction. In this case, it only requires a single pass of the calculations to determine if the total expected dose from the new equipment requires any supplementary shielding in the vault. If this is the case, it is likely that the shielding will be placed internally, so the value of d will remain unchanged and a new value of t can be derived. If the supplementary material is not the same as that originally used (e.g., supplementary Pb or steel to be added to existing concrete), the equation is slightly modified to Wi  U  dj2  10jt1/TVL1  10jt2/TVL2 where the thickness and TVL values of the two different shielding materials are specified separately. CONCLUSION Iterative calculations are required commonly in designing shielding for radiation treatment machines where obtaining a minimum footprint (and a lower overall cost of these massive structures) dictates that the actual positions of personnel occupancy are determined by the required thickness of the shielding barrier, rather than being established in advance of the calculations. This same calculation approach can be used to calculate barriers accurately for multi-modality linear accelerators with any number of x-ray beam energies if the workloads at each energy are stated in advance. This method is particularly useful when evaluating existing vaults for the installation of replacement treatment machines where the as-built barrier dimensions are already established and patterns of usage at differing beam energies may be reasonably predicted. REFERENCES Institute of Physics and Engineering in Medicine. Medical and dental guidance notes. York, England: The IPEM; 2002. International Atomic Energy Agency. Radiation protection in the design of radiotherapy facilities. Vienna: IAEA; Safety Report Series No. 47; 2006. 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 MeV. Bethesda, MD: NCRP; NCRP Report No. 49; 1976.

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National Council on Radiation Protection and Measurements. Structural shielding design and evaluation from megavoltage x- and gamma-ray radiotherapy facilities. Bethesda, MD: NCRP; NCRP Report No. 151; 2005. Nogueira IP, Biggs PJ. Measurement of scatter factors for 4, 6, 10 and 23 MV x-rays at scattering angles between 30 degrees and 135 degrees. Health Phys 81:330Y340; 2001. Taylor PL, Rodgers JE, Shobe J. Scatter fractions from linear accelerators with x-ray energies from 6 to 24 MV. Med Phys 26:1442Y1446; 1999.

APPENDIX A: EXAMPLE PRIMARY BEAM CALCULATION X-ray energies: 6 MV, 10 MV, and 15 MV; Wtot = 60,000 cGy wkj1 at 1 m Workload at 15 MV = 8,000 cGy 1 TVL = 0.432 m concrete (15 MV) Workload at 10 MV = 12,000 cGy 1 TVL = 0.389 m concrete (10 MV) Workload at 6 MV = 40,000 cGy 1 TVL = 0.343 m concrete (6 MV) IMRT factor = 4 In addition to the workload/energy distribution, relative use of the three beam energies for IMRT/VMAT, conventional 3-D, and SRS/SBRT treatments have also been provided by the end-user of the linear accelerator. The values shown for U and P are typical for primary radiation directed at a wall where there is restricted occupancy on the far side. Also, the dose that ‘‘is allowed’’ in the example can be expressed in conventional units as PTj1, where P is the design-goal dose and T is the occupancy factor.

Primary @ 6 MVIMRT/VMAT = 40,000  35% = 14,000 cGy Primary @ 6 MVCONVENTIONAL = 40,000  10% = 4,000 cGy Primary @ 6 MVSRS/SBRT/CONVENTIONAL = 40,000  30% = 12,000 cGy Primary @ 6MVSRS/SBRT/(IMRT/VMAT) = 40,000  25% = 10,000 cGy Total Primary @ 6 MV = 40,000 cGy Primary @10 MVIMRT = 12,000  = 7,200 cGy Primary @10 MVCONVENTIONAL = 12,000  = 1,800 cGy Primary@10 MVSRS/SBRT/CONVENTIONAL = 12,000  0.218  0.188 = 2,700 cGy Primary @10 MV SRS/SBRT/(IMRT/VMAT) = 12,000  0.218  0.188 = 2,700 cGy Total Primary @ 10 MV = 12,000 cGy Primary @15 MVIMRT = 8,000  20% = 1,600 cGy Primary @15 MVCONVENTIONAL = 8,000  50% = 4,000 cGy Primary @15 MVSRS/SBRT/CONVENTIONAL = 8,000  15% = 1,200 cGy

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Primary @ 15 MVSRS/SBRT/(IMRT/VMAT) = 8,000  15% = 1,200 cGy Total Primary @ 15 MV = 8,000 cGy Barrier calculation for wall at West West (primary; restricted; adjacent linac vault #2) d = 6.58 m, U = 3, T = 1, P = 0.10 mGy. Assume a barrier thickness of 1.73 m. Primary @ 6 MV = 40,000 cGy  3  1/(6.58) 2  10j1.73/0.343 = 21 mSv Primary @ 10 MV = 12,000 cGy  3  1/(6.58)2  10j1.73/0.389 = 25 mSv Primary @ 15 MV = 8,000 cGy  3  1/(6.58)2  10j1.73/0.432 = 46 mSv Total = 92 mSv. 100 mSv is allowed. Barrier = 1.73 m concrete. APPENDIX B: EXAMPLE SECONDARY RADIATION CALCULATION Leakage radiation is assumed to be 0.1% of the primary beam dose at isocenter The values shown for U and P are typical for leakage radiation directed at a wall where there is unrestricted occupancy on the far side. Leakage @ 6 MVIMRT/VMAT = 14,000  0.001  4 = 56 cGy Leakage @ 6 MVCONVENTIONAL = 4,000  0.001 = 4 cGy Leakage @ 6 MVSRS/SBRT/CONVENTIONAL = 12,000  0.001 = 12 cGy Leakage @ 6 MV SRS/SBRT’/(IMRT/VMAT) = 10,000  0.001  4 = 40 cGy Total Leakage @ 6 MV = 112 cGy

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Leakage @ 10 MVIMRT = 7,200  0.001  4 = 28.8 cGy Leakage @ 10 MVCONVENTIONAL = 1,800  0.001 = 1.8 cGy Leakage @ 10 MV SRS/SBRT/CONVENTIONAL = 2,700  0.001 = 2.7 cGy Leakage @10 MV SRS/SBRT/(IMRT/VMAT) = 2,700  0.001  4 = 10.8 cGy Total Leakage @ 10 MV = 44.1 cGy Leakage @ 15 MVIMRT = 1,600  0.001  4 = 6.4 cGy Leakage @ 15 MVCONVENTIONAL = 4,000  0.001 = 4 cGy Leakage @ 15 MVSRS/SBRT/CONVENTIONAL = 1,200  0.001 = 1.2 cGy Leakage @ 15 MVSRS/SBRT/(IMRT/VMAT) = 1,200  0.001  4 = 4.8 cGy Total Leakage @ 15 MV = 16.4 cGy Barrier calculation for secondary wall at East Direct leakage toward hospital building at East d = 7.03 m, U = 1, T = 1, P = 0.02 mSv. Assume a barrier thickness of 1.22 m. Leakage @ 6 MV = 112 cGy  1/(7.03)2  10j1.22/0.343 = 7 mSv Leakage @ 10 MV = 44.1 cGy  1/(7.03)2  10j1.22/0.389 = 7 mSv Leakage @ 15 MV = 16.4 cGy  1/(7.03)2  10j1.22/0.432 = 5 mSv Total = 19 mSv. 20 mSv is allowed. Barrier = 1.22 m concrete.

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Shielding design for multiple-energy linear accelerators.

The introduction of medical linear accelerators (linacs) capable of producing three different x-ray energies has complicated the process of designing ...
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