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Monte Carlo design study for in vivo bone aluminum measurement using a low energy accelerator beam
Applied Radiation and Isotopes 53 (2000) 657±664
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Monte Carlo design study for in vivo bone aluminum measurement using a low energy accelerator beam A. PejovicÂ-MilicÂ*, M.L. Arnold, F.E. McNeill, D.R. Chettle Department of Physics and Astronomy, Medical Physics & Radiation Sciences Unit, McMaster University, 1280 Main St West, Hamilton, ON, Canada L85 4M1
Abstract The need for aluminum monitoring exists in occupational medicine, as well as for the clinical monitoring of patients with renal dysfunction. After the development of an appropriate neutron source card, Monte Carlo simulations were made to design moderator/re¯ector assembly consisting of a polyethylene moderator (2 cm) and graphite re¯ector (30 cm), surrounded by a boronated (5%) wax (20 cm) and lead (1 cm) shield. This design should allow for the bone aluminum measurement of healthy subjects, but prior to that detailed microdosimetry is necessary to address a noticed disagreement between theoretical and experimental dose data. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Aluminum; Bone; Neutron activation analysis; Monte Carlo
1. Introduction The clinical motivation to monitor aluminum body burden arises from its toxic eects. The element has been implicated in dialysis dementia and osteodystrophy (Alfrey, 1984; Ellis et al., 1988) and, more controversially, Alzheimer's disease (Martyn et al., 1989; McLachan et al., 1991; O'Mahony et al., 1995). A means of measuring stored levels of aluminum noninvasively would help to resolve debate about its metabolism and toxicity. Skeleton is thought to be the predominant storage organ for aluminum, which has led to eorts to develop its measurement in the bones of the hand (Green and Chettle, 1992; Lewis et al.,
* Corresponding author. Fax: +1-905-546-1252. E-mail address: [email protected] (A. PejovicÂ-MilicÂ).
1997). Normal aluminum levels in a hand are 0.3± 0.5 mg (ICRP, 1975). Aluminum is measured using the thermal neutron reaction 27Al(n, g )28Al (s=(231 2 3) mb). 28Al decays via bÿ emission, with a half-life of 2.25 min, and a 1.78 MeV g-ray (100%) is emitted following each decay. Choice of neutron source is governed by the need to avoid direct interference produced by fast neutron interactions with 31P and 28Si. This requires that all source neutrons have energies lower than 1.95 MeV. The McMaster KN Van de Graa accelerator can produce a suitable neutron source via the 7Li( p, n )7Be reaction (Palerme et al., 1993; PejovicÂ-Milic et al., 1998a). For proton energies of up to 2.25 MeV, neutron energies are 520 keV or less, well below the thresholds for the interfering reactions. In addition, relatively modest neutron energies can result in lower neutron doses than higher energy sources (PejovicÂMilic et al., 1998b).
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In the present study, the Monte Carlo code MCNP (version 4b2) has been used to design an aluminum irradiation cavity. Optimal choice of materials and dimensions for a new moderator/re¯ector assembly might lead to sucient gain in system performance that normal aluminum levels could become measurable. 2. Method In running MCNP, neutron energies were commonly tallied as thermal (E < 0.5 eV), epithermal (0.5 eV < E < 10 keV) and fast (E > 10 keV), following the US National Bureau of Standard recommendation. In some cases, particularly those involving dose calculations, more detailed neutron energy spectra were recorded. The general design aim was to maximize the thermal neutron ¯ux available to activate aluminum while delivering as low a dose as possible. This required that epithermal and fast neutron components be minimized and that photon production, from neutron interaction in the materials used, also be kept to a minimum. Activation was assessed as realistically as possible by modeling an open hand phantom (22.6 12.4 2 cm width) containing 20 mg of aluminum. Other elements were present in the hand as normal physiological concentrations and the density was measured to be 1.2 g cmÿ3. The number of particles run was such that the relative uncertainty was <5%. 2.1. Neutron source card Total and angular yield as a function of proton energy and neutron spectra at speci®c angles for various proton energies were determined for the 7Li( p, n )7Be reaction. These parameters were calculated analytically (Arnold et al., 1999 this conference), based on published cross section data (Liskien and Paulsen, 1975) and stopping powers (Nuclear Data Tables,
1960). Dierent source cards were derived for the seven proton energies between 1.95 and 2.25 MeV shown in Table 1, which also presents the neutron yields. Angular neutron yields (entered in MCNP as a probability function) de®ned the initial direction of the source neutrons. Given a direction, the corresponding neutron spectrum determined the neutron energy. Hence, the source cards modeled the actual spatial and energy distribution of neutrons produced by the KN accelerator. 2.2. Proton energy and positioning of irradiation cavity Since the accelerator produces a small diameter beam that diverges with increasing distance from the target, it was necessary to determine the best distance between the neutron source and the irradiation cavity. For these simulations a small moderator was modeled, which consisted of a polyethylene cylinder (radius 13 cm, thickness 2 cm). For each of the proton energies shown in Table 1, the source to moderator distance was varied from 2 to 30 cm and the spatial distribution of neutron ¯ux inside the hand phantom was tallied. Since MCNP provides tally data per source neutron, yield ®gures (Table 1) were used to permit comparisons to be made per unit time, for a ®xed proton current. 2.3. Moderator Ideal moderator materials for this type of activation based neutron source should have a low atomic number, a large neutron scattering cross section, keep a beam forward directed, be compact and have minimum g-ray production (Yanch et al., 1992). Heavy and light water, polyethylene, graphite and beryllium were tested. In each case cylinders of radius 13 cm were simulated for two thicknesses, 2 and 5 cm, and at two proton energies, 1.95 and 2.25 MeV. Having selected a moderator material, dierent thicknesses (0±8 cm) and ®nally dierent radii (13±20 cm) were tested.
Table 1 Relative and corrected neutron yields produced at dierent proton energies (0±908 only) Proton energy (MeV)
Relative yield to yield at 2.25 MeV
Corrected yield (n/s/mA)
1.95 2.00 2.05 2.10 2.15 2.20 2.25
0.23 0.32 0.40 0.48 0.58 0.74 1.00
7.9E+07 1.2E+08 1.5E+08 1.9E+08 2.4E+08 3.2E+08 4.3E+08
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2.4. Filter for epithermal and fast neutrons Even after moderation the large majority of the total neutron ¯ux was epithermal (45.4%) or fast (41.2%), unnecessarily increasing the hand dose. Yanch and coauthors (1992) tested aluminum, aluminum oxide, sulfur, silicon and iron in designing an accelerator based boron neutron capture therapy facility. In this case, an aluminum ®lter could preferentially diminish aluminum activation in the hand. Each of the other materials was tested as a 13 cm diameter, 2 cm thick cylinder in combination with a polyethylene moderator of the same dimensions. 2.5. Re¯ector Simulations were then performed of the moderator and hand phantom surrounded by a re¯ector, which was a cube of side 50 cm, hollowed out to allow for insertion of hand and moderator. Lead, graphite, light water, heavy water, alumina, beryllium and polyethylene were modeled as materials. Thermal, epithermal and fast neutrons were tallied in a detector (0.5 cm radius) placed at the center of the hand.
659
shielding is required. Dierent thicknesses of boronated (5%) wax around the re¯ector were tested to provide neutron shielding. An additional 1 cm layer of lead was used for g-ray shielding. Dose calculations were performed after all design features of the irradiation facility had been selected. Calculations were performed for the hand, a patient and a technician present in the room (Fig. 9). The patient and technician were modeled as cylinder (175 cm high 11.3 cm radius). The patient was placed adjacent to aperture, which allowed for insertion of the hand. The technician was situated on the opposite side of the irradiation facility. 3. Results and discussion 3.1. Neutron source card Neutron yields as a function of angle and neutron energy spectra at dierent angles are illustrated in Fig. 1 for a proton energy of 2.25 MeV. The beam is forward directed and has a maximum neutron energy of 520 keV.
2.6. Shielding and dose calculations
3.2. Proton energy and positioning of irradiation cavity
Shielding is needed to reduce neutron dose to the patient and activation in the target room. In addition, photons are produced by neutron interactions in moderator and re¯ector materials, so some speci®c g-ray
Aluminum activation in the hand phantom is shown in Fig. 2 for dierent proton energies. Activation is shown both per neutron (raw data) and per unit time for ®xed proton energy (corrected for relative yield).
Fig. 1. A source card information: (A) neutron yield as a function of angle; (B) neutron energy spectra at dierent angles for proton energy of 2.25 MeV.
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3.3. Moderator
Fig. 2. Activation of the 20 mg aluminum hand phantom with dierent proton energies incident on the 7Li target. Raw data are corrected to activation per incident neutron and corrected data correspond to relative aluminum activation. Modeled geometry is shown in the corner.
The maximum (corrected) activation was obtained at 2.25 MeV. Activation fell to 78% and 32% for proton energies 2.20 and 1.95 MeV respectively. On this basis a proton energy of 2.25 MeV was selected. Fig. 3 shows thermal neutron ¯ux distribution within the hand phantom for dierent source to moderator distances. The smaller separation resulted in higher, but less uniform ¯uxes. For example, at 6 cm separation the ¯ux integrated over the hand was 56% that at 2 cm; this ®gure fell to 16% for a 20 cm source to moderator separation. The best compromise between intensity and uniformity will be determined experimentally.
Fig. 3. Spatial distribution of thermal ¯ux inside the hand phantom with increasing distance between the source and the moderator surface. Percentage of thermal neutrons to the thermal neutrons at 2 cm and at the center of phantom (0,0 position). Note that the source distribution is symmetrical, and therefore, only the neutron ¯ux along the longer side of the phantom was sampled.
Aluminum activation is illustrated in Fig. 4 for the dierent moderator materials, using two thicknesses at two proton energies. For both energies, maximum activation was produced by polyethylene (2 cm) or light water (5 cm). Both materials have the disadvantage of inducing g-ray production, namely 2.2 MeV g-rays from the 1H(n, g )2H reaction. This implied the need for speci®c g-ray shielding as part of the overall assembly. Since it produced the highest activation and is easy to work with, polyethylene was chosen as the moderator material. Fig. 5 shows the dierent components of neutron ¯ux at the center of the hand phantom as a function of moderator thickness. Thermal ¯ux as a proportion of the total ¯ux increases with increasing moderator thickness, implying a reduction in dose. However, the absolute value of the thermal ¯ux falls, which would lead to reduced activation and a worse detection limit. Given that the hand does not contain particularly radiosensitive tissues and that the aim of this design study was to produce as low a detection limit as possible, a 2 cm thick polyethylene moderator was chosen. A minimum moderator radius of 13 cm was chosen to ensure that the hand was covered. Fig. 6 indicates that the distribution of neutron ¯ux through the hand was very little aected by varying the moderator radius between 13 and 20 cm. On this basis, the moderator radius was ®xed at 13 cm. 3.4. Filter for epithermal and fast neutrons Fig. 7 illustrates that all ®lter materials reduced both epithermal and fast neutron ¯uxes. However, they all
Fig. 4. Aluminum activation of the 20 mg hand phantom for dierent moderator materials. Data were obtained using either 2 or 5 cm thick cylinders with 13 cm radius for each material. Modeled geometry is shown in the corner.
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Fig. 5. Neutron ¯ux at the center of the hand phantom for dierent moderator thickness with a constant radius of 13 cm. The neutron ¯ux was calculated inside the hand phantom using a point detector with radius of 0.5 cm. The modeled geometry is the same as in Fig. 4, with varied moderator thickness.
also reduced the thermal neutron ¯ux, leading to a reduction in activation. In addition, all ®lter materials resulted in increased photon production, somewhat osetting any dosimetric advantage gained by a reduction in the fast neutron component. On balance, it was concluded that none of these ®lters would confer an advantage on the irradiation system. 3.5. Re¯ector A comparison of re¯ector materials is presented in Fig. 8, from which it is seen that heavy water and beryllium produce the highest thermal neutron ¯ux, closely followed by light water and graphite.
Another consideration was that lead produced the smallest photon ¯ux, followed by graphite, alumina, heavy water, beryllium, polyethylene and ®nally water. Given also the beryllium is toxic and waters inconvenient to handle, graphite emerged as clearly the best overall material for the re¯ector. Next, the dimensions of a graphite re¯ector were determined. The geometry of the model included apertures for the beam line and through which to insert the hand, as well as a cavity for the hand and moderator. The thermal ¯uxes at the center of the hand increased with increasing re¯ector thickness, reaching saturation between 20 and 30 cm of graphite.
Fig. 6. Eect of moderator radius on the thermal neutron ¯ux, with a ®xed moderator thickness of 2 cm. The neutron ¯ux was sampled in the hand phantom using point detectors of radius 0.5 cm.
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Dg
Fig. 7. Neutron ¯ux in the center of the hand phantom with dierent ®lter materials. Each of the materials was tested as a 13 cm diameter, 2 cm thick cylinder in combination with a polyethylene moderator of the same dimensions. The modeled geometry is shown as well.
3.6. Shielding and dose calculations Dose estimation for a 180 s irradiation at a 25 mA proton beam current are presented in Table 2. Neutron energies were recorded according to the bins speci®ed by published ¯uence to kerma conversion factors (Caswell et al., 1982). Full, neutron plus photon, doses were calculated for the hand phantom, a patient and a technician for the dierent shielding arrangements listed in Table 2. The photon dose was calculated as
X men Eg f Eg Eg r g
were Eg is the photon energy, men/r is the mass-absorption coecient (Hubbell and Seitzer, 1996) and F is the photon ¯ux. These modeled data produce an estimated hand dose that is very much higher than the experimentally measured value, for the same proton current and time, of 6 10ÿ3 Sv (PejovicÂ-Milic et al., 1998b). Part of this discrepancy could arise from dierence between predicted and actual yield from the 7Li( p, n )7Be reaction. Weixiang et al. (1998) did observe a signi®cant dierence between predicted and measured neutron yield. It would be necessary to resolve this discrepancy, probably by use of neutron microdosimetry, while remaining aware that neutron dosimetry in the 100 keV energy range can be problematic. The patient dose is similarly much higher than the previous estimation, which was based on direct measurements (PejovicÂ-Milic et al., 1998b). Until this discrepancy is resolved, the present doses should be treated as upper bound estimates. Even so, it should be noted that a technician remaining in the room with a patient during a measurement would receive a dose of 0.1±0.2% of annual natural background.
4. Conclusion The Monte Carlo code, MCNP, was used as a tool to design an improved irradiation facility as presented in Fig. 9. The primary design goal was to increase
Fig. 8. Investigating suitable re¯ector materials by tallying the neutron ¯uxes over a point detector (0.5 cm radius) placed in the center in the hand phantom aligned with the neutron source.
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Table 2 Equivalent dose estimations for the hand, and the eective dose for a patient and a technician during bone aluminum activation Shielding
Hand dose (Sv)
Patient dose (Sv)
Technician dose (Sv)
6 cm of boronated wax 12 cm of boronated wax 20 cm of boronated wax 20 cm of boronated wax and 1 cm of lead
2.93 10ÿ1 2.93 10ÿ1 2.93 10ÿ1 2.93 10ÿ1
2.60 10ÿ3 1.99 10ÿ3 1.46 10ÿ3 1.29 10ÿ3
2.86 10ÿ5 2.09 10ÿ5 1.18 10ÿ5 3.37 10ÿ6
aluminum activation per unit time for a ®xed proton current incident on a lithium target, the design studies resulted in the choice of a polyethylene moderator, a graphite re¯ector and a combined boronated wax and lead shield. Filtration of fast neutrons was rejected as incurring to great loss of thermal neutrons. Exact source to moderator distance involved a compromise,
which is left for experimental optimization. An important discrepancy between modeled and measured doses remains to be resolved. The newly designed irradiation cavity is expected to increase aluminum activation by a little over 50%, which should lead to a consequent reduction in detection limit by 20±25%. This presents a signi®cant contribution towards the goal of reducing
Fig. 9. The ®nal design of an improved irradiation cavity for bone aluminum activation using an accelerator low energy neutron beam.
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the previous experimentally determined detection limit of 0.7 mg in the normal range of 0.3±0.5 mg. Acknowledgements Funding for this research was provided by the Natural Science and Engineering Research Council of Canada in the form of a PGS B Scholarship for M. L. Arnold and research grant for D.R. Chettle, and by the Eugene G. Bolotkin Scholarship in the form of a graduate scholarship for A. PejovicÂ-MilicÂ. References Alfrey, A.C., 1984. Aluminum intoxication. N. Engl. J. Med. 310, 1113±1115. Arnold, M.L., McNeill, F.E., Prestwich, W.V., Chettle, D.R., 1999. Monte Carlo modeling of accelerator based in vivo neutron activation measurements of manganese levels in human brain: system design and detection limit. In: 4th Topical Meeting on Industrial Radiation and Radioisotope Measurement Applications, Raleigh, NC, USA. Caswell, R.S., Coyne, J.J., Randolph, M.L., 1982. Kerma factors of elements and compounds for neutron energies below 30 MeV. Int. J. Appl. Radiat. Isot. 33, 1227± 1262. Ellis, K.J., Kelleher, S., Raciti, A., Savory, J., Wills, M., 1988. In vivo monitoring of skeletal aluminum burden in patients with renal failure. J. Radianalyt. Nucl. Chem. Ar. 124 (1), 85±95. Green, S., Chettle, D.R., 1992. A feasibility of the in vivo measurement of aluminum in peripheral bone. Phys. Med. Biol. 37 (12), 2287±2296. Hubbell, J.H., Seitzer, S.M. 1996. http://physics.nist.gov/ PhysRefData/contents.html. ICRP, 1975. Report of the Task Group on Reference Man, vol. 23. Pergamon Press, Oxford.
Lewis, D.G., Natto, S.S.A., Ryde, S.J.S., Evans, C.J., 1997. Monte Carlo design study of a moderated 252Cf source for in vivo neutron activation analysis of aluminum. Phys. Med. Biol. 42, 625±636. Liskien, H., Paulsen, A., 1975. Neutron production cross sections and energies for the reactions 7Li(p,n)7Be and 7 Li(p,n)7Be. Atomic Data Nucl. Tables 15 (1), 57±84. Martyn, C.N. et al., 1989 Geographical relation between Alzheimer's disease and aluminum in drinking water, The Lancet, 14 January 59±62. McLachan, D.R.C., Kruck, T.P., Lukiw, W.J., Krishnan, S.S., 1991. Would decreased aluminum ingestion reduce the incidence of Alzheimer's disease? Can. Med. Ass. J. 145 (7), 793±804. Nuclear Data Tables, part 3, 1960. National Academy of Science, Washington, DC. O'Mahony, D., Denton, J., Templer, J., O'Hara, M., Day, J.P., Murphy, S., et al., 1995. Bone aluminum content in Alzheimer's disease. Dementia 6, 69±72. Palerme, S., Chettle, D.R., Kennett, T.J., Prestwich, W.V., Webber, C.E., 1993. In: Ellis, K.J., Eastman, J.D. (Eds.), Pilot Study for in vivo Aluminum Measurement. Plenum Press, New York, pp. 303±306. PejovicÂ-MilicÂ, A., McNeill, F.E., Prestwich, W.V., Waker, A.J., Chettle, D.R., 1998a. Development of an accelerator based determination of aluminum burden in peripheral bone by neutron activation analysis. Appl. Radiat. Isot. 49 (5/6), 717±719. PejovicÂ-MilicÂ, A., McNeill, F.E., Chettle, D.R., 1998b. The development of an in vivo procedure for routine aluminum monitoring in human bone by neutron activation analysis. In: COMP & CCPM Conference Proceedings, London, Canada, pp. 222±224. Weixiang, Y., Gang, Y., Xiaogang, H., Tian, B., 1998. Measurements of the neutron yields from 7Li(p,n)7Be reaction (thick target) with incident energies from 1.885 to 2.0 MeV. Med. Phys. 25 (7), 1222±1224. Yanch, J.C., Zhou, X.-L., Shefer, R.E., Klinkowstein, R.E., 1992. Accelerator-based epithermal neutron beam design for neutron capture therapy. Med. Phys. 19 (3), 709± 721.
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Monte Carlo design study for in vivo bone aluminum measurement using a low energy accelerator beam A. PejovicÂ-MilicÂ*, M.L. Arnold, F.E. McNeill, D.R. Chettle Department of Physics and Astronomy, Medical Physics & Radiation Sciences Unit, McMaster University, 1280 Main St West, Hamilton, ON, Canada L85 4M1
Abstract The need for aluminum monitoring exists in occupational medicine, as well as for the clinical monitoring of patients with renal dysfunction. After the development of an appropriate neutron source card, Monte Carlo simulations were made to design moderator/re¯ector assembly consisting of a polyethylene moderator (2 cm) and graphite re¯ector (30 cm), surrounded by a boronated (5%) wax (20 cm) and lead (1 cm) shield. This design should allow for the bone aluminum measurement of healthy subjects, but prior to that detailed microdosimetry is necessary to address a noticed disagreement between theoretical and experimental dose data. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Aluminum; Bone; Neutron activation analysis; Monte Carlo
1. Introduction The clinical motivation to monitor aluminum body burden arises from its toxic eects. The element has been implicated in dialysis dementia and osteodystrophy (Alfrey, 1984; Ellis et al., 1988) and, more controversially, Alzheimer's disease (Martyn et al., 1989; McLachan et al., 1991; O'Mahony et al., 1995). A means of measuring stored levels of aluminum noninvasively would help to resolve debate about its metabolism and toxicity. Skeleton is thought to be the predominant storage organ for aluminum, which has led to eorts to develop its measurement in the bones of the hand (Green and Chettle, 1992; Lewis et al.,
* Corresponding author. Fax: +1-905-546-1252. E-mail address: [email protected] (A. PejovicÂ-MilicÂ).
1997). Normal aluminum levels in a hand are 0.3± 0.5 mg (ICRP, 1975). Aluminum is measured using the thermal neutron reaction 27Al(n, g )28Al (s=(231 2 3) mb). 28Al decays via bÿ emission, with a half-life of 2.25 min, and a 1.78 MeV g-ray (100%) is emitted following each decay. Choice of neutron source is governed by the need to avoid direct interference produced by fast neutron interactions with 31P and 28Si. This requires that all source neutrons have energies lower than 1.95 MeV. The McMaster KN Van de Graa accelerator can produce a suitable neutron source via the 7Li( p, n )7Be reaction (Palerme et al., 1993; PejovicÂ-Milic et al., 1998a). For proton energies of up to 2.25 MeV, neutron energies are 520 keV or less, well below the thresholds for the interfering reactions. In addition, relatively modest neutron energies can result in lower neutron doses than higher energy sources (PejovicÂMilic et al., 1998b).
0969-8043/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 4 3 ( 0 0 ) 0 0 2 0 0 - 1
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In the present study, the Monte Carlo code MCNP (version 4b2) has been used to design an aluminum irradiation cavity. Optimal choice of materials and dimensions for a new moderator/re¯ector assembly might lead to sucient gain in system performance that normal aluminum levels could become measurable. 2. Method In running MCNP, neutron energies were commonly tallied as thermal (E < 0.5 eV), epithermal (0.5 eV < E < 10 keV) and fast (E > 10 keV), following the US National Bureau of Standard recommendation. In some cases, particularly those involving dose calculations, more detailed neutron energy spectra were recorded. The general design aim was to maximize the thermal neutron ¯ux available to activate aluminum while delivering as low a dose as possible. This required that epithermal and fast neutron components be minimized and that photon production, from neutron interaction in the materials used, also be kept to a minimum. Activation was assessed as realistically as possible by modeling an open hand phantom (22.6 12.4 2 cm width) containing 20 mg of aluminum. Other elements were present in the hand as normal physiological concentrations and the density was measured to be 1.2 g cmÿ3. The number of particles run was such that the relative uncertainty was <5%. 2.1. Neutron source card Total and angular yield as a function of proton energy and neutron spectra at speci®c angles for various proton energies were determined for the 7Li( p, n )7Be reaction. These parameters were calculated analytically (Arnold et al., 1999 this conference), based on published cross section data (Liskien and Paulsen, 1975) and stopping powers (Nuclear Data Tables,
1960). Dierent source cards were derived for the seven proton energies between 1.95 and 2.25 MeV shown in Table 1, which also presents the neutron yields. Angular neutron yields (entered in MCNP as a probability function) de®ned the initial direction of the source neutrons. Given a direction, the corresponding neutron spectrum determined the neutron energy. Hence, the source cards modeled the actual spatial and energy distribution of neutrons produced by the KN accelerator. 2.2. Proton energy and positioning of irradiation cavity Since the accelerator produces a small diameter beam that diverges with increasing distance from the target, it was necessary to determine the best distance between the neutron source and the irradiation cavity. For these simulations a small moderator was modeled, which consisted of a polyethylene cylinder (radius 13 cm, thickness 2 cm). For each of the proton energies shown in Table 1, the source to moderator distance was varied from 2 to 30 cm and the spatial distribution of neutron ¯ux inside the hand phantom was tallied. Since MCNP provides tally data per source neutron, yield ®gures (Table 1) were used to permit comparisons to be made per unit time, for a ®xed proton current. 2.3. Moderator Ideal moderator materials for this type of activation based neutron source should have a low atomic number, a large neutron scattering cross section, keep a beam forward directed, be compact and have minimum g-ray production (Yanch et al., 1992). Heavy and light water, polyethylene, graphite and beryllium were tested. In each case cylinders of radius 13 cm were simulated for two thicknesses, 2 and 5 cm, and at two proton energies, 1.95 and 2.25 MeV. Having selected a moderator material, dierent thicknesses (0±8 cm) and ®nally dierent radii (13±20 cm) were tested.
Table 1 Relative and corrected neutron yields produced at dierent proton energies (0±908 only) Proton energy (MeV)
Relative yield to yield at 2.25 MeV
Corrected yield (n/s/mA)
1.95 2.00 2.05 2.10 2.15 2.20 2.25
0.23 0.32 0.40 0.48 0.58 0.74 1.00
7.9E+07 1.2E+08 1.5E+08 1.9E+08 2.4E+08 3.2E+08 4.3E+08
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2.4. Filter for epithermal and fast neutrons Even after moderation the large majority of the total neutron ¯ux was epithermal (45.4%) or fast (41.2%), unnecessarily increasing the hand dose. Yanch and coauthors (1992) tested aluminum, aluminum oxide, sulfur, silicon and iron in designing an accelerator based boron neutron capture therapy facility. In this case, an aluminum ®lter could preferentially diminish aluminum activation in the hand. Each of the other materials was tested as a 13 cm diameter, 2 cm thick cylinder in combination with a polyethylene moderator of the same dimensions. 2.5. Re¯ector Simulations were then performed of the moderator and hand phantom surrounded by a re¯ector, which was a cube of side 50 cm, hollowed out to allow for insertion of hand and moderator. Lead, graphite, light water, heavy water, alumina, beryllium and polyethylene were modeled as materials. Thermal, epithermal and fast neutrons were tallied in a detector (0.5 cm radius) placed at the center of the hand.
659
shielding is required. Dierent thicknesses of boronated (5%) wax around the re¯ector were tested to provide neutron shielding. An additional 1 cm layer of lead was used for g-ray shielding. Dose calculations were performed after all design features of the irradiation facility had been selected. Calculations were performed for the hand, a patient and a technician present in the room (Fig. 9). The patient and technician were modeled as cylinder (175 cm high 11.3 cm radius). The patient was placed adjacent to aperture, which allowed for insertion of the hand. The technician was situated on the opposite side of the irradiation facility. 3. Results and discussion 3.1. Neutron source card Neutron yields as a function of angle and neutron energy spectra at dierent angles are illustrated in Fig. 1 for a proton energy of 2.25 MeV. The beam is forward directed and has a maximum neutron energy of 520 keV.
2.6. Shielding and dose calculations
3.2. Proton energy and positioning of irradiation cavity
Shielding is needed to reduce neutron dose to the patient and activation in the target room. In addition, photons are produced by neutron interactions in moderator and re¯ector materials, so some speci®c g-ray
Aluminum activation in the hand phantom is shown in Fig. 2 for dierent proton energies. Activation is shown both per neutron (raw data) and per unit time for ®xed proton energy (corrected for relative yield).
Fig. 1. A source card information: (A) neutron yield as a function of angle; (B) neutron energy spectra at dierent angles for proton energy of 2.25 MeV.
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3.3. Moderator
Fig. 2. Activation of the 20 mg aluminum hand phantom with dierent proton energies incident on the 7Li target. Raw data are corrected to activation per incident neutron and corrected data correspond to relative aluminum activation. Modeled geometry is shown in the corner.
The maximum (corrected) activation was obtained at 2.25 MeV. Activation fell to 78% and 32% for proton energies 2.20 and 1.95 MeV respectively. On this basis a proton energy of 2.25 MeV was selected. Fig. 3 shows thermal neutron ¯ux distribution within the hand phantom for dierent source to moderator distances. The smaller separation resulted in higher, but less uniform ¯uxes. For example, at 6 cm separation the ¯ux integrated over the hand was 56% that at 2 cm; this ®gure fell to 16% for a 20 cm source to moderator separation. The best compromise between intensity and uniformity will be determined experimentally.
Fig. 3. Spatial distribution of thermal ¯ux inside the hand phantom with increasing distance between the source and the moderator surface. Percentage of thermal neutrons to the thermal neutrons at 2 cm and at the center of phantom (0,0 position). Note that the source distribution is symmetrical, and therefore, only the neutron ¯ux along the longer side of the phantom was sampled.
Aluminum activation is illustrated in Fig. 4 for the dierent moderator materials, using two thicknesses at two proton energies. For both energies, maximum activation was produced by polyethylene (2 cm) or light water (5 cm). Both materials have the disadvantage of inducing g-ray production, namely 2.2 MeV g-rays from the 1H(n, g )2H reaction. This implied the need for speci®c g-ray shielding as part of the overall assembly. Since it produced the highest activation and is easy to work with, polyethylene was chosen as the moderator material. Fig. 5 shows the dierent components of neutron ¯ux at the center of the hand phantom as a function of moderator thickness. Thermal ¯ux as a proportion of the total ¯ux increases with increasing moderator thickness, implying a reduction in dose. However, the absolute value of the thermal ¯ux falls, which would lead to reduced activation and a worse detection limit. Given that the hand does not contain particularly radiosensitive tissues and that the aim of this design study was to produce as low a detection limit as possible, a 2 cm thick polyethylene moderator was chosen. A minimum moderator radius of 13 cm was chosen to ensure that the hand was covered. Fig. 6 indicates that the distribution of neutron ¯ux through the hand was very little aected by varying the moderator radius between 13 and 20 cm. On this basis, the moderator radius was ®xed at 13 cm. 3.4. Filter for epithermal and fast neutrons Fig. 7 illustrates that all ®lter materials reduced both epithermal and fast neutron ¯uxes. However, they all
Fig. 4. Aluminum activation of the 20 mg hand phantom for dierent moderator materials. Data were obtained using either 2 or 5 cm thick cylinders with 13 cm radius for each material. Modeled geometry is shown in the corner.
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Fig. 5. Neutron ¯ux at the center of the hand phantom for dierent moderator thickness with a constant radius of 13 cm. The neutron ¯ux was calculated inside the hand phantom using a point detector with radius of 0.5 cm. The modeled geometry is the same as in Fig. 4, with varied moderator thickness.
also reduced the thermal neutron ¯ux, leading to a reduction in activation. In addition, all ®lter materials resulted in increased photon production, somewhat osetting any dosimetric advantage gained by a reduction in the fast neutron component. On balance, it was concluded that none of these ®lters would confer an advantage on the irradiation system. 3.5. Re¯ector A comparison of re¯ector materials is presented in Fig. 8, from which it is seen that heavy water and beryllium produce the highest thermal neutron ¯ux, closely followed by light water and graphite.
Another consideration was that lead produced the smallest photon ¯ux, followed by graphite, alumina, heavy water, beryllium, polyethylene and ®nally water. Given also the beryllium is toxic and waters inconvenient to handle, graphite emerged as clearly the best overall material for the re¯ector. Next, the dimensions of a graphite re¯ector were determined. The geometry of the model included apertures for the beam line and through which to insert the hand, as well as a cavity for the hand and moderator. The thermal ¯uxes at the center of the hand increased with increasing re¯ector thickness, reaching saturation between 20 and 30 cm of graphite.
Fig. 6. Eect of moderator radius on the thermal neutron ¯ux, with a ®xed moderator thickness of 2 cm. The neutron ¯ux was sampled in the hand phantom using point detectors of radius 0.5 cm.
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Dg
Fig. 7. Neutron ¯ux in the center of the hand phantom with dierent ®lter materials. Each of the materials was tested as a 13 cm diameter, 2 cm thick cylinder in combination with a polyethylene moderator of the same dimensions. The modeled geometry is shown as well.
3.6. Shielding and dose calculations Dose estimation for a 180 s irradiation at a 25 mA proton beam current are presented in Table 2. Neutron energies were recorded according to the bins speci®ed by published ¯uence to kerma conversion factors (Caswell et al., 1982). Full, neutron plus photon, doses were calculated for the hand phantom, a patient and a technician for the dierent shielding arrangements listed in Table 2. The photon dose was calculated as
X men Eg f Eg Eg r g
were Eg is the photon energy, men/r is the mass-absorption coecient (Hubbell and Seitzer, 1996) and F is the photon ¯ux. These modeled data produce an estimated hand dose that is very much higher than the experimentally measured value, for the same proton current and time, of 6 10ÿ3 Sv (PejovicÂ-Milic et al., 1998b). Part of this discrepancy could arise from dierence between predicted and actual yield from the 7Li( p, n )7Be reaction. Weixiang et al. (1998) did observe a signi®cant dierence between predicted and measured neutron yield. It would be necessary to resolve this discrepancy, probably by use of neutron microdosimetry, while remaining aware that neutron dosimetry in the 100 keV energy range can be problematic. The patient dose is similarly much higher than the previous estimation, which was based on direct measurements (PejovicÂ-Milic et al., 1998b). Until this discrepancy is resolved, the present doses should be treated as upper bound estimates. Even so, it should be noted that a technician remaining in the room with a patient during a measurement would receive a dose of 0.1±0.2% of annual natural background.
4. Conclusion The Monte Carlo code, MCNP, was used as a tool to design an improved irradiation facility as presented in Fig. 9. The primary design goal was to increase
Fig. 8. Investigating suitable re¯ector materials by tallying the neutron ¯uxes over a point detector (0.5 cm radius) placed in the center in the hand phantom aligned with the neutron source.
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Table 2 Equivalent dose estimations for the hand, and the eective dose for a patient and a technician during bone aluminum activation Shielding
Hand dose (Sv)
Patient dose (Sv)
Technician dose (Sv)
6 cm of boronated wax 12 cm of boronated wax 20 cm of boronated wax 20 cm of boronated wax and 1 cm of lead
2.93 10ÿ1 2.93 10ÿ1 2.93 10ÿ1 2.93 10ÿ1
2.60 10ÿ3 1.99 10ÿ3 1.46 10ÿ3 1.29 10ÿ3
2.86 10ÿ5 2.09 10ÿ5 1.18 10ÿ5 3.37 10ÿ6
aluminum activation per unit time for a ®xed proton current incident on a lithium target, the design studies resulted in the choice of a polyethylene moderator, a graphite re¯ector and a combined boronated wax and lead shield. Filtration of fast neutrons was rejected as incurring to great loss of thermal neutrons. Exact source to moderator distance involved a compromise,
which is left for experimental optimization. An important discrepancy between modeled and measured doses remains to be resolved. The newly designed irradiation cavity is expected to increase aluminum activation by a little over 50%, which should lead to a consequent reduction in detection limit by 20±25%. This presents a signi®cant contribution towards the goal of reducing
Fig. 9. The ®nal design of an improved irradiation cavity for bone aluminum activation using an accelerator low energy neutron beam.
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the previous experimentally determined detection limit of 0.7 mg in the normal range of 0.3±0.5 mg. Acknowledgements Funding for this research was provided by the Natural Science and Engineering Research Council of Canada in the form of a PGS B Scholarship for M. L. Arnold and research grant for D.R. Chettle, and by the Eugene G. Bolotkin Scholarship in the form of a graduate scholarship for A. PejovicÂ-MilicÂ. References Alfrey, A.C., 1984. Aluminum intoxication. N. Engl. J. Med. 310, 1113±1115. Arnold, M.L., McNeill, F.E., Prestwich, W.V., Chettle, D.R., 1999. Monte Carlo modeling of accelerator based in vivo neutron activation measurements of manganese levels in human brain: system design and detection limit. In: 4th Topical Meeting on Industrial Radiation and Radioisotope Measurement Applications, Raleigh, NC, USA. Caswell, R.S., Coyne, J.J., Randolph, M.L., 1982. Kerma factors of elements and compounds for neutron energies below 30 MeV. Int. J. Appl. Radiat. Isot. 33, 1227± 1262. Ellis, K.J., Kelleher, S., Raciti, A., Savory, J., Wills, M., 1988. In vivo monitoring of skeletal aluminum burden in patients with renal failure. J. Radianalyt. Nucl. Chem. Ar. 124 (1), 85±95. Green, S., Chettle, D.R., 1992. A feasibility of the in vivo measurement of aluminum in peripheral bone. Phys. Med. Biol. 37 (12), 2287±2296. Hubbell, J.H., Seitzer, S.M. 1996. http://physics.nist.gov/ PhysRefData/contents.html. ICRP, 1975. Report of the Task Group on Reference Man, vol. 23. Pergamon Press, Oxford.
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