On the tenth value distance of the photon field along the maze of high‐energy linear accelerator vaults

Abstract There is a wide range in the reported photon tenth value distance (TVD) in the maze of high‐energy linear accelerator vaults. In order to gain insight into the appropriate use of the TVD value during door design, we performed measurements of the photon dose in the maze of four vaults. In addition, our study represents the first to describe a scenario where an inner borated polyethylene (BPE) door for neutron shielding is installed in the maze downstream to Point A, the point on the maze centerline that is just visible from the isocenter. The measurements were made along the maze centerline at 1 m above the floor. In all cases, the accelerator operated at a nominal energy of 15 MV. Of the four vaults, three were equipped with an inner BPE door at a distance of 1.0–2.1 m downstream to Point A. The door was made of 10.16 cm (4″) BPE sandwiched between two 0.635 cm (1/4″) steel face plates. The photon dose in the maze without a BPE door decreases exponentially with a characteristic TVD of 6 m beyond a distance of 2.5 m from Point A. The presence of a BPE door in an identical vault not only reduces the photon intensity in the maze by about an order of magnitude, but also softens the energy spectrum with a shortened TVD of 4.7 m, significantly lessening the shielding burden at the outer maze entrance. In contrast to the common use of Point A as the reference point to specify distance, the photon dose in the maze with a BPE door located downstream to Point A can be satisfactorily described as exponential functions of the distance measured from the door, which shows good consistency among the three vaults of different room parameters.


Abstract
There is a wide range in the reported photon tenth value distance (TVD) in the maze of high-energy linear accelerator vaults. In order to gain insight into the appropriate use of the TVD value during door design, we performed measurements of the photon dose in the maze of four vaults. In addition, our study represents the first to describe a scenario where an inner borated polyethylene (BPE) door for neutron shielding is vault not only reduces the photon intensity in the maze by about an order of magnitude, but also softens the energy spectrum with a shortened TVD of 4.7 m, significantly lessening the shielding burden at the outer maze entrance. In contrast to the common use of Point A as the reference point to specify distance, the photon dose in the maze with a BPE door located downstream to Point A can be satisfactorily described as exponential functions of the distance measured from the door, which shows good consistency among the three vaults of different room parameters.  4 Consequently, the predominant photon contribution at the outer maze entrance comes from the capture gamma rays when the maze length is greater than three meters. 4 In addition, capture gamma rays are very energetic with an average energy of 3.6 MeV and have a tenth value layer (TVL) of 6.1 cm of lead, which could require significant amount of shielding materials resulting in a massive door. 1 During door design, it is essential to have a reasonably good estimate of the photon dose at the outer maze entrance in order to determine the thickness of the materials, which are usually lead and/or steel (In addition, 5% borated polyethylene or BPE is typically used in the door for neutron shielding). From a clinical point of view, a light door is beneficial because of the opening/closing speed and safety reasons. Therefore, it is desirable to put as little materials as possible in the door while achieving adequate shielding capability. This effort, however, can be largely hindered if large uncertainty exists in estimating the photon dose at the door. It is the authors' experience that this estimate is particularly sensitive to the TVD values, which range from 3.9 to 6.2 m in the literature for a nominal energy of 15 MV. 1,2,5 To better illustrate the sensitivity to TVD, we compare in Fig. 1 the photon doses calculated using a TVD value of 6.2 m (D TVD = 6.2 m ) and 3.9 m (D TVD = 3.9 m ), respectively. Figure 1 shows the ratio (R = D TVD = 6.2 m /D TVD = 3.9 m ) as a function of d 2 , the distance between the outer maze entrance and Point A, which is defined as the point on the maze centerline that is just visible from the isocenter. 1 As can be seen, depending on the choice of TVD values, the calculated photon dose can vary by a factor of seven for a ninemeter-long maze, which would result in a vastly different door design.
In a recent design of a linac vault to house a 15 MV accelerator at our institute, the large range of the reported TVD values has created a great deal of uncertainty in determining the lead thickness to be used in the door. On the one hand, assuming a TVD value of 3.9 m, ¼" of lead-equivalent-thick materials (in addition to 4″ BPE for neutron shielding) will suffice the institutional ALARA (As Low As Reasonably Achievable) goal of 1 mR/week outside the door. On the other hand, an additional 2″ thick lead is required if a TVD value of 6.2 m is assumed, which represents an increase of about 5,000 lbs in weight for the door measuring 87″ 9 68″. Such a heavy door not only slows down the operational speed and increases the cost, but also creates engineering difficulties and potentially leads to safety issues. The lack of more precise data in TVD value in the literature has prompted us to carry out a detailed measurement in the maze once the linac was installed.
McGinley et al. have studied a number of methods that aim to replace the heavy door at the outer maze entrance, including reducing the inner maze opening size and adding neutron absorbing materials at the inner maze entrance. 6 In all of the methods, it was found that the photon dose in the maze can be described by the sum of two exponential functions of the distance along the maze centerline,  6 In addition, two bunkers (one with an inner BPE door and the other without) in the current study have identical dimensions, which offers us unique opportunity to conduct a comparative study as the differences observed can be unambiguously attributed to the presence of the inner BPE door.  The treatment room and maze parameters are summarized in  x ≥ 2.5 m, the measurements can be fitted to an exponential function D = 1.67 9 10 À6 9 10 Àx/6.0 for Vault 1, which is shown as a straight line in Fig. 3. Similarly, the measurements for Vault 2 can be fitted to an exponential function D = 2.93 9 10 À7 9 10 Àx/4.7 . The exponential behavior is consistent with previous reports; 1,2,5 however, the derived TVD for Vault 1, which is 6.0 m, is in closer agreement with the reported 6.2 m in Ref. [ than those suggested in Refs. [1] and [2]. As can be seen in Fig. 3,   to Point A, the use of Point A as the reference point may not be ideal. To the best of our knowledge, our work represents the first to study such a scenario.

2.B | Photon dose measurements in the maze
As can been seen in Fig. 4(a), the photon dose distribution as a function of the distance from Point A shows a rather wide range of variations among Vaults 2 to 4, for which the BPE door is located at a distance between 1.0 and 2.1 m from Point A. When expressed as a function of the distance measured from the BPE door in Fig. 4(b The boron-neutron capture gamma ray has an energy of 478 keV, 1 significantly lower than that from the neutron-concrete interactions. The reduction in the number of neutrons entering the maze greatly lessens the shielding burden at the outer maze entrance. In fact, for a workload of 500 Gy/week for 15 MV, at a distance of 4.5 m from the inner BPE door, the exposure level would result in a weekly dose below our institutional ALARA goal of 1 mR/week for controlled areas without the need of a shielded door at the outer maze entrance. In contrast, a 5.08 cm (2″) lead equivalent thickness is needed (in addition to the 4″ BPE for neutron shielding) for Vault 1 to bring the radiation level outside the door to within the ALARA limit.

| CONCLUSION S
There is a wide range of the reported photon TVD value in the maze of a high-energy linear accelerator vault. Our study has shed light on the importance of appropriate choice of the TVD value during door design. The incorporation of an inner BPE door to limit/prevent the photoneutrons from entering the maze greatly lessens the shielding burden at the outer maze entrance. Our study is the first to describe a scenario where the BPE door is located downstream to Point A.
For such a case, it is found that the photon dose along the maze can be reasonably well described as exponential functions of the distance measured from the inner BPE door and is consistent among vaults of different parameters.

CONFLI CT OF INTEREST
The authors have no conflicts of interest.