Shielding design of the Mayo Clinic Scottsdale cyclotron vault

Mayo Clinic Scottsdale (Scottsdale, Arizona) is building a cyclotron vault containing a cyclotron with adjacent targets and a beam line leading to an external target. The targets are irradiated by high energy (15 to 16.5 MeV) protons for the production of radioisotopes. We performed Monte Carlo radiation transport simulations to calculate the radiation dose outside of the vault during irradiation of the cyclotron and external targets. We present the Monte Carlo model including the geometry, sources, and variance reduction methods. Mesh tallies surrounding the vault show the external dose rate is within acceptable


Introduction
A cyclotron facility is under construction at the Scottsdale campus of the Mayo Clinic. The General Electric (GE) cyclotron's primary use is for production of 18 F for PET imaging. The PET isotopes are produced in a target adjacent to the accelerator. The proton beam can be directed to an external target in an adjoining room for production of other clinical and research isotopes including 11 C, 13 N, 15 O, 63 Zn, and 68 Ga. We refer to the former as the cyclotron target and the latter as the external target.

Geometry
The geometry model consists of the entrance maze, the cyclotron room containing the cyclotron target and collimator material, and the external target room with the external target. Details of the cyclotron are not included; we assume the shielding supplied by the vendor will reduce the leakage of any internal radiation from the accelerator to values low in comparison to the sources we consider: a fractional loss of the proton beam passing through a collimator, the interaction of the beam with the target, and the photons emitted by 18 F.  Also shown in pink in Figure 1 are the outlines of the targets and the collimator as modeled. The external target is located further from the end of the beam line shown in the drawing. The exact location will not affect the radiation produced and its penetration through the walls.  Figure 1 showing the cyclotron target and collimator block. Figure 2 shows an enlarged section of Figure 1 around the cyclotron target. The blue block offset from the beam line is a graphite cube used to model the beam fraction (assumed to be 10 %) that is lost when passing though the collimator. It is offset from the beam line to prevent any particles that penetrate the block from reaching the target. We refer to this block as the collimator even though it is not a detailed model of that component. The cyclotron and beam line components were not included in the model.  Figure 3 shows the target model. It was adapted from the GE PETTRACE document [1]. The same model is used in both target locations. All components are concentric cylinders centered 36 inches above the floor. The dimensions are in inches. A beam of 16.5 MeV protons is incident on the 75 μM thick Havar foil covering a vacuum (brown in Fig. 3) downstream from the target. The target (magenta) is 18 O enriched water. It is surrounded upstream by a silver backing plate (grey) with cooling water further upstream. These components are encased in aluminum (green) and stainless steel (yellow).

Source terms
The cyclotron emits a beam of 16.5 MeV protons. The maximum current used in the cyclotron room is 130 μA (micro Amperes) after a 10% loss upon passing through the collimator. The 130 μA is split into 65 μA on two targets. For the Monte Carlo model, we use 130 μA on a single target. We also assume a fully irradiated target emitting 2 x 3500 mCi of 0.511 MeV photons. Table 1 summarizes the cyclotron room target source components. The total rate of emission is 8.927 x 10 14 particles / second. Two proton beams are directed towards the target and collimator with a small divergence angle. The beam origins are just downstream of the target and collimator. Figure 5 shows the two beams for the cyclotron room model. The figure is from a test run with no interactions; with interactions, the beams are stopped in the target and collimator. The photons are emitted isotropically. The photon source is distributed uniformly throughout the target water (H2 18 O) volume. The target room model assumes a 80 μA proton beam impinging on the target in the external target room, a 8 μA beam loss on the collimator in the cyclotron room, and single 3500 mCi load of irradiated target material. Table 2 summarizes the source components. The total rate of emission is 5.493 x 10 14 particles / second.

Mesh tallies
The results are shown in the form of mesh tallies where the dose equivalent rate and its statistical error (relative error in Monte Carlo parlance) are calculated in each cell of a mesh overlaid on the geometry. Each mesh cell in the plane of the mesh is approximately 5 cm square and is 50 cm thick. Each mesh tally extends 1 meter outside of the vault. There are separate mesh tallies for the neutron, photon, and proton dose equivalent rates. These three were summed in post processing to give the total dose equivalent rate. Figures 6 and 7 show the mesh tally locations.  The red mesh tally covers the entire model, centered on the height of the targets and collimator. The vertical dark blue tally also passes through the targets and collimator. The red and blue tallies are used by both models (cyclotron targer and external target). The dark green tally is used in the cyclotron room target model and passes through the cyclotron target and collimator. The dark green tally is not used in the external target model. That model uses the yellow mesh tally that passes through the external target.

Monte Carlo items
The transport of protons, neutrons, and photons was calculated with the Monte Carlo code MCNPX version 2.7.0 [2].
Dose response functions are used to convert the calculated flux, in particles/cm 2 /second, to a dose equivalent rate in Sv/hour. The dose equivalent is the absorbed dose at a point in tissue weighted by a distribution of quality factors related to the LET distribution of radiation at that point. For neutrons, the response function is taken from NCRP-38 1971, ANSI/ANS 6.1. . The quality factors in the NCRP-38 dose response function match those listed in 10 CFR Part 20. For photons, the values in ICRP-21 1971 are used. For protons, the values given in a NASA report were used.
Variance reduction, or biasing, is required to calculate penetration of the thick walls and ceiling and to direct the radiation through the entrance maze. We used the technique of importance splitting. When a particle traverses from a region of lower to high importance, it is split into two equivalent particles so that there is a greater chance of one of those particles avoiding absorption. The model uses 26 importance layers through the walls and ceiling and 31 layers between the source and entrance.
A calculation was run for each of the two source configurations. Each followed at least 5 x 10 7 source particles. The cyclotron target model had some large (> 0.1) relative errors in the external target room and far wall. An additional cyclotron target model with biasing adjusted towards the external target room was run to correct those deficiencies. Combined mesh tallies show the mesh cells with the lowest relative error from the two cyclotron target runs.

Vault shielding results
The mesh tally results are presented as color wash figures overlaid with an outline of the geometry. Contours are shown at 1 x 10 -2 , 1 x 10 -3 , 1 x 10 -4 , 1 x 10 -5 , 1 x 10 -6 , 1 x 10 -7 , and 1 x 10 -8 Sv/hour. Values greater than 100 Sv/hr are colored red. Values less than 10 -10 Sv/hr are dark blue. Different color schemes are used for the dose rate and for the relative error. Figures 8, 9, 10, and 11 show the neutron, photon, proton, and total dose equivalent rates, respectively, in the horizontal mesh tally for the cyclotron target model. External to the vault, the neutrons and photons give nearly equal contributions to the total. The only significant proton contribution is near the target and collimator from protons in the beam and protons scattered off components along the beam line. Figure 10 shows the beams are completely stopped in the target and collimator. Additional protons are produced by interactions in the concrete. These secondary protons contribute a very small fraction to the total dose rate.    Figure 12 shows the relative error for the total dose rate. Except for some regions within the walls, the relative error is less than 0.1 in areas of interest, an indication that the results are valid. Figure 13 plots the dose equivalent rates extracted from the mesh tallies of Figures 8 through 10

Maze entrance door
The vault shielding models described above did not include a door at the maze entrance. We made several studies of the attenuation through entrance doors of different thicknesses and compositions. Except for the door and modifications near the door, the geometry, source, and materials are the same as in the cyclotron target model described above. Because the dose rate at the maze entrance is larger using the main cyclotron target, we assumed irradiation of that target for the door calculations.

Surface source calculations
The calculation was made in two stages using the MCNP surface source write (SSW) and surface source read (SSR) features. Without the need to transport particles from the target through the maze, the SSR calculations require much less computation time. The shorter SSR runs permitrd exploration of a number of door designs.
The initial SSW calculation had irradiation of the main target and collimator by the proton beam as the source. All neutrons and protons crossing a surface spanning the air space in the maze coincident with the first inner wall (the green line in Figure 1) were saved to a file. Only outward (upwards in Figure 1) crossings were saved. To reduce calculation time, biasing to enable penetration of the side and rear walls and the ceiling was not included. Biasing through the maze was retained.
The SSW calculation followed 5,761,845 histories, approximately 1/10 of the histories followed in the vault shielding calculations. The small relative errors around the maze entrance found in the previous results justified using the smaller number of histories. The run resulted in a 1.9 GByte surface source file. Comparison of mesh tallies showed that the SSW calculation gave the same results in the cyclotron room and through the maze as the previous shielding calculation.
An SSR run in the same geometry was made to verify that the same results were obtained. Plots of the ratios of the horizontal neutron and photon mesh tallies near the maze entrance showed that the results agree within 20% in the air volumes downstream of the surface source. A vertical mesh tally outside of the door opening was used to examine any vertical variation of the neutron and photon dose rates. No significant variation was seen.

Door model
The door consists of a polyethylene slab sandwiched between steel plates. It fits into recesses in the outer maze entrance. Figure 17 is a horizontal cut through the model. Figure18 is a vertical cut through the door. In the figures, concrete is grey, air is light blue, polyethylene is yellow, and steel is dark blue. A horizontal mesh tally extends 25 feet in front of the door.
The side and top recesses are 6 ⅞ inches deep (in the +X direction in Figures 17 and 18). The east recess (towards the top in Figure 17) extends 9 inches beyond the maze opening. The west recess extends 5 inches beyond the opening. The top overlap is 4 inches high. The door bottom is flush with the concrete floor. The height of the opening is 84 inches, less than the 96 inch height of the maze. Except for the opening through the outer north wall, the height in the maze was kept at 96 inches.
The outer steel layer is ⅜ inch thick; the inner ¼ inch. A 5 inch thick polyethylene layer was used for the initial calculations. For the 3 inch polyethylene model, the inner thinner steel layer remained as shown and the outer steel layer was moved 2 inches inward (+X direction). The SSR door calculations followed neutrons and protons from the surface source. These calculations did not include penetration of the outer wall other than at the maze opening. The full shielding calculations showed some penetration, especially opposite the second turn in the maze.

Polyethylene composition
A model without a door was run to establish a baseline against which to measure the shielding efficacy of the door options. In the No Door model, the polyethylene and steel layers were replaced by air.
Several compositions were used for polyethylene. The Natural Polyethylene model did not contain any dopants, only ⅔ H and ⅓ C by number. The Borated Polyethylene model contained 5% boron by weight added as boric oxide (B2O3). Trace amounts of iron (0.00058% by weight), sulfate (SO4, 0.0051%), and water (1.1%) found in an analysis of the boric oxide were ignored.
In MCNP, a material constituent can be specified as an element or as the fractions of isotopes making up the element. In the element specification, MCNP chooses the isotopes naturally occurring the element. For boron, we compared runs with natural boron (element specification, Natural B in Figure 11) and with explicit fractions for boron 10 and boron 11 (B10_B11). The results were the same within the statistical uncertainty

Maze entrance door results
The curves in the Figures 19 through 22 show the dose equivalent rates along a north-south line passing through the center of the door (240 inches in Figure 18). The peaks at 91.44 cm mark the location of the surface source. The curves to the right (larger X) of the peak should be ignored. The error bars in Figures 19 and 20 are omitted for clarity. Figures 19 and 20 show the neutron and photon contributions to the dose rate with no door (19) and with a 5 inch borated polyethylene door. Figure 21 shows that boron doping does not change the neutron contribution. Figure 22 shows that the difference between 5 and 3 inch doors is small.    A few dozen steel rods were used to hold the concrete forming framework together. These 7/8 inch diameter rods were left in place after the pour. We wanted to ensure that the presence of the rods did not affect the efficacy of the concrete sheilding wall. We prepared a modified model of the cyclotron target room that omitted the entrance maze and the external target room. Eight inches of the wall between the cyclotron room and the external target room and 8 inches of the the opposite wall were retained. The outer walls included 12 rods on each side. Horizontal mesh tallies at the height of the target also covered a row of three rods in each outer wall. Runs with and without the rods showed no difference in the external photon and neutron dose rates.

Conclusion
We have calculated the dose equivalent rates throughout and just outside of the cyclotron vault. The dose rate external to the vault is less than regulatory limits. In particular, we used the pregnant worker limit of 5 mSv over the course of the pregnancy for occupationally controlled areas and the 1 mSv per year limit for nonoccupational areas. These limits factored in a workload (or use factor) of 0.97.
Photon measurements were taken above the cyclotron room during irradiation of the main target. The highest dose rates at the roof surface were 0.9 μSv/hour and 0.4 μSv/hour at 1 meter above the roof. Our calculations predicted 5 and 3 μSv/hour at these locations.