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The evaluation of the neutron dose equivalent in the two-bend maze
Physica Medica 36 (2017) 119–125
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Original paper
The evaluation of the neutron dose equivalent in the two-bend maze Á.Á. Tóth a,⇑, B. Petrovic´ a,b, N. Jovancˇevic´ a, M. Krmar a, L. Rutonjski b, O. Cˇudic´ b a b
Physics Department, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia Institute of Oncology Vojvodina, Sremska Kamenica, Serbia
a r t i c l e
i n f o
Article history: Received 10 August 2016 Received in Revised form 13 February 2017 Accepted 20 March 2017 Available online 4 April 2017 Keywords: Neutron dose Two-bend maze Tenth-value distance
a b s t r a c t The purpose of this study was to explore the effect of the second bend of the maze, on the neutron dose equivalent, in the 15 MV linear accelerator vault, with two bend maze. These two bends of the maze were covered by 32 points where the neutron dose equivalent was measured. There is one available method for estimation of the neutron dose equivalent at the entrance door of the two bend maze which was tested using the results of the measurements. The results of this study show that the neutron equivalent dose at the door of the two bend maze was reduced almost three orders of magnitude. The measured TVD in the first bend (closer to the inner maze entrance) is about 5 m. The measured TVD result is close to the TVD values usually used in the proposed models for estimation of neutron dose equivalent at the entrance door of the single bend maze. The results also determined that the TVD in the second bend (next to the maze entrance door) is significantly lower than the TVD values found in the first maze bend. Ó 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
1. Introduction Medical therapy accelerators working at energies higher than energy threshold for (c, n) nuclear reaction of some materials irradiated by the photon beam, produce measurable number of neutrons. Lead is one of the materials commonly used in accelerator heads, and energy threshold for (c, n) reaction for isotope 208Pb (52.4% in natural lead) is 6.7 MeV. To protect staff at radiotherapy departments, maze designed bunkers having thick primary and secondary shielding walls, massive shielding doors and wall covers which are good neutron moderators (plastic, paraffin) are usually applied as a cost-effective solution. Neutron dose at the entrance door of one bend maze is considered in a number of publications [1–5], but two bend maze publications are quite rare [6,7]. Recommendations for the design of the entrance maze door which can provide proper shielding for both photon and neutron radiation can be found in NCRP protocol [8]. Two methods for the estimation of the neutron dose equivalent at the place of the door are generally accepted: Kersey’s and Wu and McGinley’s [8,9]. Both these methods provide neutron dose equivalent estimation for standard one bend maze geometry of the linac’s vault. The IAEA publication [10] provides methodology for the estimation of neutron dose equivalent in the two bend maze. According to this document, neutron dose in the second bend decreases following the exponential ⇑ Corresponding author at: Department of Physics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovic´a 4, 21000 Novi Sad, Serbia. E-mail address: [email protected] (Á.Á. Tóth).
trend. For a proper estimation of the dose at the maze door, it is acceptable to use total length of the corridor – a sum of lengths of two maze bends and reduce this number by a factor of 1/3. The objective of this work is to present detailed measurements of the neutron dose equivalent in the two bend maze. These measurements can be used to establish accurate values of the tenth value distance (TVD) in the first bend of the maze and compare it with values predicted by models [9]. TVD for the second maze bend can be different from TVD in the first bend, since the mean energy of neutrons should be significantly lower due to the large number of scatterings. One of the goals of this work is to estimate TVD in both bends of the maze. The neutron source strength or the neutron dose equivalent at the reference point cannot be found, unfortunately in relevant literature for new Elekta Versa HD linear accelerator. Only one available neutron source strength data [11] for accelerators is related to the neutrons created in the regime in which an electron beam is used. In this regime, the accelerator produces two orders of magnitude lower number of neutrons than in the regime when the photon beam is used. To overcome this problem, the neutron source strength for the Elekta Versa HD accelerator was estimated using a technique similar to that described in the reference Followill et al. [12]. By a simple comparison of activity induced in activation detectors made from natural Indium, which were exposed under the same conditions in the vicinity of a Versa HD or a Varian 2100 C accelerator the neutron source strength was estimated. This led to the usage of the proposed methods for the neutron dose calculation and to the comparison
http://dx.doi.org/10.1016/j.ejmp.2017.03.017 1120-1797/Ó 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. a) Scheme of therapy vault. b) Magnified maze area. Lines represent directions of activation detectors alignments.
of the obtained results with the measurements. One of the most important objectives of this work is to verify the trends of the neutron dose equivalent decrease along the both bends of the
maze corridors. Special attention was paid to the comparison of the neutron dose equivalent measured in the second maze bend and the results of the model given in IAEA report [10].
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2. Materials and methods Neutron dose equivalent was measured in the vault of the therapy bunker at the Radiotherapy department, Institute of Oncology Vojvodina, Sremska Kamenica, Serbia. The accelerators installed inside were manufactured by Elekta, type Versa HD, producing 6 MV, 10 MV and 15 MV photon energies. The schematic drawing of mazes of the linear accelerator vault is presented in Fig. 1. Two Versa HD accelerators are operating in identical and mirrorsymmetric rooms. Fig. 1a) shows the position of the accelerator in one room, while the characteristic dimensions are depicted in second room. The height of the vault is 3.95 m. It can be seen that the maze is designed to have two bends oriented orthogonally. The complete surface of inner bunker walls is covered by decorative wooden plates, 2 cm thick. The part of the wall, which is directly irradiated by neutrons from the accelerator head, positioned at the end of the maze, is covered by 2 cm thick layer of PVC material (polyvinyl chloride), to slow down neutrons reflected in the maze path. The position of PVC plates is given in Fig. 1a. PVC plates were fixed between concrete walls and decorative wooden plates. The area covered by PVC plates is 20.3 m2. Fig. 1b represents a magnified maze area, with several characteristic measurement points and the straight-line distance between most significant points. All measurements of neutron dose equivalent were performed at 15 MV photon beam energy. Gantry was positioned at 0°. Field size at 1 m focal distance (isocenter) was 10 10 cm2. Water phantom was used as scatter material, to mimic general radiation therapy conditions. The delivered dose to the build up, under isocentric setup was 3 Gy, for each measurement of neutron dose in the maze. Considering that Versa HD accelerator operating at 15 MV delivers 6 Gy/min at the changing output dose rate of 600 MU/min (Elekta Versa HD automatic dose rate), measuring time at each of 32 points was 30 s. The neutron dose equivalent was measured using Meridian model 5085 neutron survey meter. The detector assembly is based upon standard Anderson Braun design containing He-3 proportional counter (5 cm length) operating at 1250 V inside the polyethylene cylinder (22 cm diameter, 24 cm length). Dosimeter was positioned 1 m above the floor with long axis of He-3 counter horizontal and oriented normally to the AB and BC direction. It was previously determined that in this particular position, the dosimeter shows maximum reading of neutron dose equivalent. Relatively high count rate of 50,000 counts per mrem provides a high sensitivity for the neutron survey (of 0.2 nSv per count). Natural neutron background in therapy vaults is significantly lower than the instrument threshold and can be neglected. Manufacturer (Health Physics Instruments, Goleta, CA) declares in manuel up to 15% accuracy for the detector. Calibration factor was checked in our laboratory using 252Cf source, before any use of neutron survey meter. Measurements were performed along the central maze line (mid-line of corridors, direction ABC) and along the lines parallel to the mid-line of the maze, 30 cm away of the left and right wall, following the structure of the maze corridor. The distance between two measurement points was 1 m. Same sets of measurements were performed in both bends of the maze. The most important result of all measurements performed along three lines, (mid-line and 30 cm away of both left and right maze wall as outlined in Fig. 1b) was to get a rough information on spatial distribution of neutron dose equivalent in both maze bends. No additional technique (like passive detectors) were applied in this phase of the research. Monte Carlo calculations can be used to confirm results of measurements [13,14], however no results of MC simulations will be presented in this manuscript. There are two widely accepted methods for neutron dose equivalent calculations for the one bend therapy vaults. Kersey’s method
Fig. 2. Neutron dose equivalent measured along A-B-C direction. Last four points belong to the second bend.
[10] gives the neutron dose equivalent at the maze entrance (it should be point H in Fig. 1 in one bend maze geometry) as follows:
Dn ¼ H1 103 ðAr =Sl Þ ð1=d1 Þ ð10d2 =5 Þ 2
ð1Þ
where H1 is neutron dose equivalent at 1 m from the accelerator target in mSv per unit photon dose in isocentre, Ar is crosssectional area of inner maze entrance, Sl is cross-sectional area of maze, d1 is a distance from the isocenter to the inner maze point A and d2 is distance between point A and maze entrance door. Wu and McGinley’s (Modified Kersey’s) [10] method for estimation of neutron dose equivalent at the maze entrance is given as:
Dn ¼ 2:4 1015 uA
d d pffiffiffiffiffiffiffiffiffiffiffi 2 2 Ar =Sl 1:64 10 1:9 þ 10 TVD
ð2Þ
where uA is the total neutron fluence at the inner maze point A given as:
uA ¼
Qn 4p
2 d1
þ
5:4Q n 1:3Q n þ 2p S 2p S
ð3Þ
where Q n is the neutron source strength, S is the surface area of the treatment room and TVD is the tenth value distance given by:
TVD ¼ 2:06
pffiffiffiffi Sl
ð4Þ
Based on the Kersey’s model, the neutron dose equivalent at two bend maze entrance (point C, Fig. 2), according to the IAEA Report [10], can be estimated as:
Dn ¼ H1 103 ðAr =Sl Þ ð1=d2 Þ ð10d2 =5 Þ ð10d3 =5 Þ ð1=3Þ 2
ð5Þ
d3 is distance from point B to point C (length of additional bend). It can be seen, from Eqs. (1) and (5), that the neutron dose equivalent for two maze bend can be estimated as neutron dose for the maze length equal to the sum of both bends (distance AB + BC), reduced by factor 1/3. Similar results can be found in Ref. [16]. In this study it is concluded that the presence of the second maze bend gives results which are at least 2.5 times lower than the estimation of Kersey’s equation. It is stated in Refs. [10,15] that 1/3 reduction can be applied in cases when both of the maze bends are long enough and when cross-sectional area of maze or maze entrances are not too large. Considering that both maze bends and cross-section areas satisfy the mentioned requirements, Eq. (5) can be used for neutron dose equivalent estimation for vault presented in Fig. 1. It should be emphasized that in Kersey’s model for estimation of neutron dose equivalent, that TVD = 5 m is already presumed. This TVD is the same for both bends of the
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maze. One of the most important goals of this study is to confirm by measurements of the neutron dose equivalent if TVD = 5 m is a good approximation, and whether it is possible to use the same value of the TVD for both bends of the maze. Considering that the neutron source strength or neutron dose equivalent for Elekta Versa HD accelerators cannot be found in the literature, simple measurements were performed to estimate the values of the mentioned parameters. The Institute of Oncology is equipped with one Varian 2100 C linear accelerator and an Elekta Versa HD linear accelerator (the third one), both of them operating at 15 MV. Both accelerators are located in standard one bend vaults, which have the very same design. The scheme for the vaults can be seen in Ref. [17]. The only difference between the two bunkers is that the inner walls of the Varian vault are covered by wood and that the vault where the Electa accelerator is located is covered with PVC plates. Simple estimation of neutron presence in the vicinity of the Electa Versa HD accelerator can be obtained by a comparison of the activity produced in the activation detectors exposed under identical conditions to photo neutrons originating from heads of both accelerators. It is similar to the approach described in the Ref. [12]. In this experiment the Varian Linac is considered to be a ‘‘known neutron source” because the neutron source strength and neutron dose equivalent of the Varian 2100 therapy machine are already known [8]. It can be expected that that the ratio of neutron source strengths should be equal to the ratio of the saturation activities
Q Vn Q En
R 15
rðEÞ/V ðEÞdE rðEÞ/E ðEÞdE ECd
E
ð6Þ
Cd ¼ R 15
By Q Vn and Q En are denoted neutron strengths of Varian and Elekta accelerators, r(E) is the cross section for neutron capture, in the energy region from the cadmium cut-off (ECd) to the 15 MeV endpoint energy. With UV(E) and UE(E) are signed neutron fluencies for the Varian and Elekta accelerators respectively. The standard way to determine saturation activity is to expose some activation detector to the neutron fluence and to measure the gamma spectra emitted by the radioactive product of the neutron capture. Measured intensities of detected gamma lines can be used to calculate the saturation activity. The ratio of the saturation activities can be expressed as:
R 15 ECd R 15 ECd
E
E rðEÞ/V ðEÞdE NVd ekDtE 1 ektirr 1 ektm ¼ E kDtV E V 1 ektm rðEÞ/E ðEÞdE Nd e 1 ektirr
ð7Þ
N Vd and N Ed are total areas under peaks of the chosen energy in the gamma spectra of the activated detectors. Superscripts V and E denote that the peaks belong to the spectra of In coin exposed in vaults of the Varian and Elekta accelerators respectively. Cooling times (time between the end of exposition and beginning of the measurement) are denoted by Dt V and DtE for activation detectors exposed to neutrons in the vicinity of the Varian and Elekta accelerators respectively. Times of irradiation are tVirr and t Eirr and by tVm and tEm are denoted the durations of the measurements. For all mentioned quantities, durations of irradiations and durations of measurements, superscripts V and E have the same meanings as for the areas under peaks. 3. Results and discussion In order to get the estimation of the neutron source strength for Elekta Versa HD accelerator, two coins made from natural indium metal (2 cm diameter, 8.71 g) enveloped by 1 mm thick cadmium filter were exposed to fast neutrons in both vaults. Activation detectors were placed on the treatment couch 141 cm from focus
(focus to couch distance was 100 cm and distance between beam axis and the activation detector was 100 cm). In both cases the field was 10 10 cm2, and photon dose was 4 Gy at build-up thickness. This means that the beam time was 60 s for Varian accelerator (t Virr ) and 40 s for Elekta Versa HD accelerator (t Eirr ). Gamma radiation of 116In produced by neutron capture on 115In was measured in low-background HPGe detector shielded by 25 cm of pre WWII iron. Relative efficiency of the detector is 32%. Cooling times (time between end of exposition and beginning of measurement) were DtV ¼ 31 minutes and DtE ¼ 42 minutes. Three most prominent peaks of 116In at 417 keV, 1097 keV and 1293 keV were used in this analysis. Measurement times (tVm and tEm for coins exposed at Varian and Elekta accelerators respectively) were determined to get statistical uncertainty of the area under all three peaks recorded in gamma spectra of 116In less than 2%. For the first coin tVm was 1000 s and for the second one t Em was 2500 s. The ratio of saturation activities, presented in Eq. (7), was calculated for all three energies, and the mean value was found. It was obtained that neutron source strength for Elekta Versa HD accelerator is:
Q En ¼ 0:55ð1ÞQ Vn This means that neutron source strength of Elekta Versa HD linear therapy accelerator is 0.4181012 n/Gy. If we compare known values of neutron source strengths for different types for same energies of Varian and Elekta accelerators [8,11], it can be seen that Elekta accelerators produce about two times lower number of neutrons than Varian ones. Our estimation is in good correlation with the existing values of Qn obtained for Varian and Elekta therapy machines. Furthermore, it can be considered that neutron dose equivalent H0 for 15 MV Elekta Versa HD accelerator is 55% of the neutron dose equivalent of Varian 2100 C accelerator. This implies that the neutron dose equivalent for the Versa HD accelerator should be H0 = 0.715 mSv/Gy. Now it is possible to make an estimation of the neutron dose equivalent at the end of the first maze corridor using both proposed methods [8]. If we focus our attention to the first corridor only, it is possible to compare values of the neutron dose equivalent estimated using both proposed models (Eqs. (1) and (2)) and the measured ones. Some of the results are presented in Table 1. Point H is located at the end of the first corridor, at the place where doors in the first bend of the maze should be located. It can be seen that the conservative Kersey model (Eq. (1)) gives more than four times larger estimation than the model described in Eq. (2), as usual. The measured value is almost 24 times lower than the Kersey estimation and 5.5 times lower than the result of the modified Kersey model. Both models are designed to estimate the neutron dose equivalent in vaults composed of standard concrete walls. In the studied vault, a relatively large area (of more than 20 m2) exposed to direct neutrons from the accelerator head is covered by a 2 cm thick PVC layer and walls that are coated by wooden plates. This can be a reason of the relatively large discrepancy between the measured and calculated values of the neutron dose equivalent at point H. It can be seen in Ref. [9] that a layer of borated polyethylene which covers only a part of the maze wall can reduce the neutron dose equivalent two times. Similar measurements [17] showed that for the Varian 2100 C accelerator measured value of the neutron dose
Table 1 Measured and calculated neutron dose equivalent. Neutron dose equivalent D (lSv)
Point B
Point H
Point C
Kersey Modified Kersey Measured
2.91 0.67 0.1
1.84 0.42 0.077
0.153 – 0.0027
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equivalent differs from the calculated one 11 times (Kersey method) and 3.2 times (the modified Kersey method). The Varian vault analyzed in publication [17] is covered by the same type of wooden plates, however there is no plastic neutron moderator inserted at the place where the direct and scattered neutrons from the accelerator head strike the wall of the first corridor. Another possibility could be that our value of the neutron source strength is slightly overestimated and it should be evaluated by some new measurements. Measurements show that values of the neutron dose equivalent in the maze vary in a relatively broad range. In point A the value of 2.17 lSv per 1 Gy of photon dose (in the isocenter) was obtained, while 2.7 nSv per 1 Gy of photon dose was detected in point C, at the outer maze entrance. The most important function of the second bend of the maze, is to reduce the neutron dose at the maze entrance and avoid the use of standard heavy doors. This objective was obviously accomplished, as proved by our measurements. Neutron dose equivalent measured at points E, H and G are 73 nSv, 77 nSv and 78 nSv per 1 Gy of photon dose, respectively. This is a place where entrance doors in the standard one bend maze should be located. The neutron dose is reduced by a factor of 28 along the direction between points A and H. In the model described in the Ref. [10] the point B is the beginning of the second bend in the maze. The neutron dose equivalent measured at point B is 0.10 lSv per 1 Gy of photon dose. Neutron dose equivalent measured at point C is 2.7 nSv per unit photon dose. According to this, it can be concluded that an additional length of 4.5 m of the second maze bend reduces neutron dose equivalent by the factor of 37. According to the IAEA suggestions, the second maze bend should be treated in calculations as a continuation of the first maze corridor. It means that the neutron doses in the second bend should follow an exponential decreasing trend along the maze. Measurements of the neutron dose equivalent along the central line (A-B-C) are presented in Fig. 2, as well as an estimation of the neutron dose equivalent obtained using Eqs. (1) and (5). It can be seen that the conservative Kersey’s model predicts higher neutron dose, however it is evident that the decrease of both measured and calculated neutron dose equivalent along the first maze bend follow almost the same exponential trend. Fig. 2 depicts that neutron dose measured in the second bend has an exponential decreasing trend too, however the slopes of the two segments (A-B and B-C) are different. Moreover, the slopes of lines presenting measured and calculated values in the second bend of the maze differ significantly. It can be easily calculated that in the first bend of the maze TVD is 4.85 m and in the second bend the TVD is 2.83 m. Kersey’s model, where TVD is 5 m, is a relatively good approximation for the first maze bend. According to the other [9] estimation pffiffiffiffi (TVD ¼ 2:06 Sl ), for the maze shown in Fig. 1, TVD should be 6.47 m. It is evident that the measured value is lower than the predicted one. Considering that the inner walls of the vault are covered by 2 cm thick wooden plates, their influence on neutron slowing-down and absorption should not be neglected. If the attenuation properties of 2 cm of wood are equivalent to 0.5 cm of polyethylene [8], it can be expected that the TVD in our vault should be in some degree lower than the predicted one. However, it is apparent that the neutron dose equivalent decreases much faster in the second bend. This result could be expected because neutrons entering the second bend have energies significantly reduced after a number of scatterings during propagation through the first maze bend. Neutron dose equivalent (Dn ðBÞÞ in point B (Eq. (1)) should differ from dose (Dn ðCÞÞ expected in point C (Eq. (5)) for a factor
Dn ðBÞ 1 ¼ Dn ðCÞ ð10d3 =5 Þ ð1=3Þ
ð8Þ
Distance d3 between points B and C is 4.5 m and it can be calculated that the dose in point C should be 24 times lower than neutron dose equivalent in point B. However, measurements of neutron dose equivalent show that the neutron dose equivalent in point C is 37 times lower than the dose measured in point B. The reasons for such high differences between measured and estimated ratios, could be found in the fact that the TVD = 5 m assumption is used for the second bend. The presented results of the measurements show that the TVD values for the two bends can differ significantly. A more accurate approach in neutron dose estimation can be obtained if we slightly modify Eq. (5) to be:
Dn ¼ H1 103 ðAr =Sl Þ ð1=d2 Þ ð10d2 =TVD1 Þ ð10d3 =TVD2 Þ 2
ð9Þ
where TVD1 and TVD2 represent tenth value distance for first and second bend respectively. TVD values are not known in the phase of projecting and building the vault, and they can be estimated from pffiffiffiffi equation TVD ¼ 2:06 Sl , as suggested in Ref. [9]. The TVD approximation of 5 m, in Kersey’s method works well in this case. If two different TVD values (as proposed by Eq. (9)) can be used in the estimation of the neutron dose equivalent, then Eq. (8) turns into Eq. (10) below:
Dn ðBÞ 1 ¼ Dn ðCÞ ð10d3 =TVD2 Þ
ð10Þ
Using TVD2 ¼ 2:83 m, it can be calculated that the dose in point C should be 39 times lower than neutron dose equivalent in point B. This estimation is closer to the ratio of doses measured in points B and C than the result obtained using 5 m for TVD. Since the TVD2 value is not known at the initial phase of building and projecting, the following estimation of TVD2 can be used
TVD2
TVD1 2
ð11Þ
However, it is still difficult to make conclusion according to one case study presented in this work. The measurements in different vaults with two-bend mazes, could confirm this assumption. It can be informative to analyze Eq. (5) in the light of the assumption that in second corridor neutron TVD can have considerably different values than in the first one. Model described in Eq. (5) presume same neutron TVD in both corridors, however factor 1/3 is added to take in consideration the influence of an additional bend in the maze. According to this model, dose on the maze entrance should be 1/3 of the neutron dose equivalent at the end of the single bend corridor having length equal to the sum of the lengths of both corridors in the two bend maze. In the case of two different TVD values the neutron dose equivalent can be estimated using Eq. (9). It can be seen that factor 1/3 in this approach is omitted. Now it is possible to check when Eqs. (5) and (9) will give us the same estimation of neutron dose equivalent. After simple mathematics we’ve got:
ð10d2 =5 Þ ð10d3 =5 Þ ð1=3Þ ¼ ð10d2 =TVD1 Þ ð10d3 =TVD2 Þ
ð12Þ
In some simplified approach we can suppose that TVD1 is 5 m and TVD2 is half of that, which means 2.5 m. Eq. (12) gives us the estimation that both approaches will give the same result for the neutron dose equivalent if the length of the second corridor is 2.4 m. In vaults having two bends described in Refs. [6,7,9,16] the length of the second corridor is much lower than the length of the first one. The length of the second corridor is half of the width of the first corridor and the thickness of the vault wall (distance KC in Fig. 1b). In this geometry it is highly possible that Eq. (5) yields a good estimation of the neutron dose equivalent at the maze door. However, in this case, the second corridor is much longer. The distance between point K and the point C (both points presented in Fig. 1b) equals
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4.5 m. This can be one of the reasons why our estimation of neutron dose equivalent at the maze entrance differs significantly from the model proposed by Eq. (5). It is interesting to compare the neutron dose equivalent measured at one cross-section of the maze corridor. As mentioned before, at one chosen cross-section of the maze, the neutron dose was measured at three points, 30 cm from both walls and in the mid-line of the corridor. Results obtained for four selected cross sections (as shown in Fig. 1) are presented in Fig. 3. It can be seen that neutron dose equivalent measured next to the maze wall is higher than doses measured at two other points. This difference is larger for cross sections closer to the inner maze entrance. Doses measured at cross-section containing point D, at the end of the maze wall (not presented in Fig. 3) are 1.31 lSv, 0.63 lSv and 0.55 lSv per unit photon dose at isocenter. This means that the dose measured in point D near the maze wall is almost 2.4 times larger than the dose measured at the opposite wall of the maze corridor. This fact could be explained by the neutron reflection from the surface directly irradiated by neutrons from the accelerator head. The geometry of the maze allows that a higher number of direct neutrons can be scattered toward point D and the maze wall than to the point located on the other side of the corridor. As it can be seen from Fig. 3, the difference between the dose measured next to the maze wall and other points at the same cross-section become lower and eventually, at the end of the first corridor (cross-section 4), all three doses are the same. A large number of neutron scatterings made a spatial distribution of neutron dose
(a)
(b)
Fig. 3. Neutron dose equivalent measured at several cross sections a) in the first bend and b) in the second bend of the maze.
equivalent more uniform at the end of corridor. It is very interesting to note that at cross-section 3, the decrease of neutron dose equivalent measured at the point opposite from the maze wall is detected. Such a decrease in neutron dose equivalent was not recorded along other cross-sections in the maze corridor. It is possible that the entrance of the second maze bend opens a large room for the expansion of neutrons. There is no wall to enable multiple scattering of neutrons and keep them in same area. By the expansion of neutrons in the second bend, the dose becomes slightly lower. The same analysis was done for two cross-sections in the second bend. Unfortunately, it was not possible to measure the neutron dose equivalent next to both walls near the entrance because the vault is equipped with double-wing doors opening to the inside, as can be seen in Fig. 1a. It can be seen from Fig. 3b, that near the left wall, the measured neutron dose equivalents are slightly higher than at the other measuring points within the same cross-section. It is highly probable that a larger number of neutrons from the first bend is directed toward the left wall of the second bend. In the direction toward the maze end, this difference disappears, as in the first bend. After multiple scattering, a number of neutrons at the end of the corridor, becomes more uniform.
4. Conclusion The most important result obtained in this study is that the second bend of the maze can make a significant reduction of neutron dose equivalent. The measurements confirmed that the second maze bend, 4.5 m long, can reduce the neutron dose equivalent for a factor of more than 30. Considering that similar reduction is measured in the first maze bend, total reduction of neutron dose equivalent is almost three orders of magnitude. Using estimated values of the neutron source strength it was possible to evaluate the neutron dose equivalent at the end of the first corridor by two proposed models. Kersey method, already known as conservative, gives more than 20 times higher value than the measured one at the place where doors should be located in one bend maze. Modified Kersey model overestimates measured dose value more than 5 times. Considering that both methods are designed for vaults composed of concrete, it is possible that additional plastic moderators, as well as wooden plates covering walls, significantly reduce neutron energy and make a large discrepancy between measured and calculated values of the neutron dose equivalent. It is obtained that the measured neutron dose at the maze entrance is 65 times lower than the neutron dose equivalent estimated using the model proposed for the two bend maze [10]. Our measurements showed that initial estimation TVD = 5 m, used in Kersey’s method is relatively good, since the results obtained show TVD1 ¼ 4:45 m in the first maze bend. TVD in the second maze bend, as confirmed by the measurements, is significantly lower. It is obtained in measurements that TVD2 ¼ 2:83 m. The single available method for estimation of neutron dose equivalent for a two-bend maze suggests the use of the same TVD for both bends, introducing some correction parameter equal 1/3. According to the measured neutron dose equivalent, one can assume that TVD in the second maze bend is approximately half of the TVD in the first maze bend. Certainly, this relationship must be confirmed by measurements in more two-bend mazes, which could be a task for other researchers having access to the twobend mazes of medical linear accelerators. Under the assumption that the TVD in the second bend is half of the TVD in the first one, it can be evaluated that the model proposed for a two-bend maze [10] can give similar results as the model using two TVD values, however just if the length of second corridor is about 2.5 m.
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Additional information obtained in the presented work is that the neutron dose equivalent can be higher at one side of maze corridor. For instance, at a cross-section of the corridor close to the inner maze entrance, neutron dose at the maze wall is more than two times higher than the dose measured on the opposite wall. This difference is smaller at distant cross-sections, and if the maze corridor is long enough, the neutron dose becomes uniform. Acknowledgement The work done in this paper was supported by the project ‘‘Studying climate change and its influence on the environment: impacts, adaptation and mitigation” (43007) financed by the Ministry of Education and Science of the Republic of Serbia within the framework of integrated and interdisciplinary research for the period 2011–2014. References [1] Kim HS, Jang KW, Park YH, Kwon JW, Choi HS, Lee JK, Kim JK. New empirical formula for neutron dose level at the maze entrance of 15 MeV medical accelerator facilities. Med Phys 2009;36(5):1512–20. [2] Kersey RW. Estimation of neutron and gamma radiation doses in the entrance maze of SL75-20 linear accelerator treatment rooms. Med Mundi 1979;24:151–5. [3] McGinley PH, Huffman KE. Photon and neutron dose equivalent in the maze of high-energy medical accelerator facility. Radiat Prot Manage 2000;17:43–6. [4] Krmar M, Nikolic´ D, Kuzmanovic´ A, Kuzmanovic´ Z, Ganezer K. The effect of paraffin screen on the neutron dose at the maze door of 15 MeV linear accelerator. Med Phys 2013;40:0833902.
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[5] Christ D, Ding G. SU-F-T-657: in room neutron dose from high energy photon beams. Med Phys 2016;43:3615. [6] Dawson DJ, Wissing WWFM, Tonks RE. A doorless entry system for highenergy radiation therapy rooms. Med Phys 1998;25:199–201. [7] Bichay T, Rogow R, Meadows J, Chen C. Dosimetric characterization of a compact doorless high energy linear accelerator vault. IFMBE Proce 2006;14 (3):1980–3. [8] National Council on Radiation Protection and Measurements. Structural shielding design and evaluation for megavoltage X- and gamma-ray radiotherapy facilities, 2005 [Bethesda: NCRP Report 151]. [9] Wu RK, McGinley PH. Neutron and capture gamma along the mazes of linear accelerator vaults. J Appl Clin Med Phys 2003;4(2):162–72. [10] International Atomic Energy Agency. Radiation protection in the design of radiotherapy facilities. Vienna: IAEA; 2006 [Safety Reports Series No. 47]. [11] Cardenas CE, Nitsch PL, Kudchadker RJ, Howell RM, Kry SF. Out-of-field doses and neutron dose equivalents for electron beams from modern Varian and Elekta linear accelerators. J Appl Clin Med Phys 2016;4:442–55. [12] Followill DS, Stovall MS, Kry SF, Ibbott GS. Neutron source strength measurements for Varian, Siemens, Elekta, and General Electric linear accelerators. J Appl Clin Med Phys 2003;3(4):189–94. [13] McGinley PH, Dhaba’an AH, Reft CS. Evaluation of the contribution of capture gamma rays, X-ray leakage, and scatter to the photon dose at the maze door for a high energy medical electron accelerator using a Monte Carlo particle transport code. Med Phys 2000;27:225–30. [14] Silva HR, Rebello WF, Silva AX, Silva MG. Evaluation using Monte Carlo simulations, of the effect of a shielding, called external shielding, for fotoneutrons generated in linear accelerators, using the computational model of Varian accelerator 2300 C/D operating in eight rotation angles of the GA. In: INAC 2011. [15] McGinley PH. Shielding techniques for radiation oncology facilities. Madison: Medical Physics Publishing; 2002. [16] McGinley PH, Butker EK. Evaluation of neutron dose equivalent levels at the maze entrance of medical accelerator treatments rooms. Med Phys 1991;18:279–81. [17] Krmar M, Baucal M, Bozˇic´ N, Jovancˇevic´ N, Ciraj-Bjelac O. Neutron dose equivalent measured at the maze door with various openings for the jaws and MLC. Med Phys 2012;39(3):1278–81.
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Original paper
The evaluation of the neutron dose equivalent in the two-bend maze Á.Á. Tóth a,⇑, B. Petrovic´ a,b, N. Jovancˇevic´ a, M. Krmar a, L. Rutonjski b, O. Cˇudic´ b a b
Physics Department, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia Institute of Oncology Vojvodina, Sremska Kamenica, Serbia
a r t i c l e
i n f o
Article history: Received 10 August 2016 Received in Revised form 13 February 2017 Accepted 20 March 2017 Available online 4 April 2017 Keywords: Neutron dose Two-bend maze Tenth-value distance
a b s t r a c t The purpose of this study was to explore the effect of the second bend of the maze, on the neutron dose equivalent, in the 15 MV linear accelerator vault, with two bend maze. These two bends of the maze were covered by 32 points where the neutron dose equivalent was measured. There is one available method for estimation of the neutron dose equivalent at the entrance door of the two bend maze which was tested using the results of the measurements. The results of this study show that the neutron equivalent dose at the door of the two bend maze was reduced almost three orders of magnitude. The measured TVD in the first bend (closer to the inner maze entrance) is about 5 m. The measured TVD result is close to the TVD values usually used in the proposed models for estimation of neutron dose equivalent at the entrance door of the single bend maze. The results also determined that the TVD in the second bend (next to the maze entrance door) is significantly lower than the TVD values found in the first maze bend. Ó 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
1. Introduction Medical therapy accelerators working at energies higher than energy threshold for (c, n) nuclear reaction of some materials irradiated by the photon beam, produce measurable number of neutrons. Lead is one of the materials commonly used in accelerator heads, and energy threshold for (c, n) reaction for isotope 208Pb (52.4% in natural lead) is 6.7 MeV. To protect staff at radiotherapy departments, maze designed bunkers having thick primary and secondary shielding walls, massive shielding doors and wall covers which are good neutron moderators (plastic, paraffin) are usually applied as a cost-effective solution. Neutron dose at the entrance door of one bend maze is considered in a number of publications [1–5], but two bend maze publications are quite rare [6,7]. Recommendations for the design of the entrance maze door which can provide proper shielding for both photon and neutron radiation can be found in NCRP protocol [8]. Two methods for the estimation of the neutron dose equivalent at the place of the door are generally accepted: Kersey’s and Wu and McGinley’s [8,9]. Both these methods provide neutron dose equivalent estimation for standard one bend maze geometry of the linac’s vault. The IAEA publication [10] provides methodology for the estimation of neutron dose equivalent in the two bend maze. According to this document, neutron dose in the second bend decreases following the exponential ⇑ Corresponding author at: Department of Physics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovic´a 4, 21000 Novi Sad, Serbia. E-mail address: [email protected] (Á.Á. Tóth).
trend. For a proper estimation of the dose at the maze door, it is acceptable to use total length of the corridor – a sum of lengths of two maze bends and reduce this number by a factor of 1/3. The objective of this work is to present detailed measurements of the neutron dose equivalent in the two bend maze. These measurements can be used to establish accurate values of the tenth value distance (TVD) in the first bend of the maze and compare it with values predicted by models [9]. TVD for the second maze bend can be different from TVD in the first bend, since the mean energy of neutrons should be significantly lower due to the large number of scatterings. One of the goals of this work is to estimate TVD in both bends of the maze. The neutron source strength or the neutron dose equivalent at the reference point cannot be found, unfortunately in relevant literature for new Elekta Versa HD linear accelerator. Only one available neutron source strength data [11] for accelerators is related to the neutrons created in the regime in which an electron beam is used. In this regime, the accelerator produces two orders of magnitude lower number of neutrons than in the regime when the photon beam is used. To overcome this problem, the neutron source strength for the Elekta Versa HD accelerator was estimated using a technique similar to that described in the reference Followill et al. [12]. By a simple comparison of activity induced in activation detectors made from natural Indium, which were exposed under the same conditions in the vicinity of a Versa HD or a Varian 2100 C accelerator the neutron source strength was estimated. This led to the usage of the proposed methods for the neutron dose calculation and to the comparison
http://dx.doi.org/10.1016/j.ejmp.2017.03.017 1120-1797/Ó 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. a) Scheme of therapy vault. b) Magnified maze area. Lines represent directions of activation detectors alignments.
of the obtained results with the measurements. One of the most important objectives of this work is to verify the trends of the neutron dose equivalent decrease along the both bends of the
maze corridors. Special attention was paid to the comparison of the neutron dose equivalent measured in the second maze bend and the results of the model given in IAEA report [10].
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2. Materials and methods Neutron dose equivalent was measured in the vault of the therapy bunker at the Radiotherapy department, Institute of Oncology Vojvodina, Sremska Kamenica, Serbia. The accelerators installed inside were manufactured by Elekta, type Versa HD, producing 6 MV, 10 MV and 15 MV photon energies. The schematic drawing of mazes of the linear accelerator vault is presented in Fig. 1. Two Versa HD accelerators are operating in identical and mirrorsymmetric rooms. Fig. 1a) shows the position of the accelerator in one room, while the characteristic dimensions are depicted in second room. The height of the vault is 3.95 m. It can be seen that the maze is designed to have two bends oriented orthogonally. The complete surface of inner bunker walls is covered by decorative wooden plates, 2 cm thick. The part of the wall, which is directly irradiated by neutrons from the accelerator head, positioned at the end of the maze, is covered by 2 cm thick layer of PVC material (polyvinyl chloride), to slow down neutrons reflected in the maze path. The position of PVC plates is given in Fig. 1a. PVC plates were fixed between concrete walls and decorative wooden plates. The area covered by PVC plates is 20.3 m2. Fig. 1b represents a magnified maze area, with several characteristic measurement points and the straight-line distance between most significant points. All measurements of neutron dose equivalent were performed at 15 MV photon beam energy. Gantry was positioned at 0°. Field size at 1 m focal distance (isocenter) was 10 10 cm2. Water phantom was used as scatter material, to mimic general radiation therapy conditions. The delivered dose to the build up, under isocentric setup was 3 Gy, for each measurement of neutron dose in the maze. Considering that Versa HD accelerator operating at 15 MV delivers 6 Gy/min at the changing output dose rate of 600 MU/min (Elekta Versa HD automatic dose rate), measuring time at each of 32 points was 30 s. The neutron dose equivalent was measured using Meridian model 5085 neutron survey meter. The detector assembly is based upon standard Anderson Braun design containing He-3 proportional counter (5 cm length) operating at 1250 V inside the polyethylene cylinder (22 cm diameter, 24 cm length). Dosimeter was positioned 1 m above the floor with long axis of He-3 counter horizontal and oriented normally to the AB and BC direction. It was previously determined that in this particular position, the dosimeter shows maximum reading of neutron dose equivalent. Relatively high count rate of 50,000 counts per mrem provides a high sensitivity for the neutron survey (of 0.2 nSv per count). Natural neutron background in therapy vaults is significantly lower than the instrument threshold and can be neglected. Manufacturer (Health Physics Instruments, Goleta, CA) declares in manuel up to 15% accuracy for the detector. Calibration factor was checked in our laboratory using 252Cf source, before any use of neutron survey meter. Measurements were performed along the central maze line (mid-line of corridors, direction ABC) and along the lines parallel to the mid-line of the maze, 30 cm away of the left and right wall, following the structure of the maze corridor. The distance between two measurement points was 1 m. Same sets of measurements were performed in both bends of the maze. The most important result of all measurements performed along three lines, (mid-line and 30 cm away of both left and right maze wall as outlined in Fig. 1b) was to get a rough information on spatial distribution of neutron dose equivalent in both maze bends. No additional technique (like passive detectors) were applied in this phase of the research. Monte Carlo calculations can be used to confirm results of measurements [13,14], however no results of MC simulations will be presented in this manuscript. There are two widely accepted methods for neutron dose equivalent calculations for the one bend therapy vaults. Kersey’s method
Fig. 2. Neutron dose equivalent measured along A-B-C direction. Last four points belong to the second bend.
[10] gives the neutron dose equivalent at the maze entrance (it should be point H in Fig. 1 in one bend maze geometry) as follows:
Dn ¼ H1 103 ðAr =Sl Þ ð1=d1 Þ ð10d2 =5 Þ 2
ð1Þ
where H1 is neutron dose equivalent at 1 m from the accelerator target in mSv per unit photon dose in isocentre, Ar is crosssectional area of inner maze entrance, Sl is cross-sectional area of maze, d1 is a distance from the isocenter to the inner maze point A and d2 is distance between point A and maze entrance door. Wu and McGinley’s (Modified Kersey’s) [10] method for estimation of neutron dose equivalent at the maze entrance is given as:
Dn ¼ 2:4 1015 uA
d d pffiffiffiffiffiffiffiffiffiffiffi 2 2 Ar =Sl 1:64 10 1:9 þ 10 TVD
ð2Þ
where uA is the total neutron fluence at the inner maze point A given as:
uA ¼
Qn 4p
2 d1
þ
5:4Q n 1:3Q n þ 2p S 2p S
ð3Þ
where Q n is the neutron source strength, S is the surface area of the treatment room and TVD is the tenth value distance given by:
TVD ¼ 2:06
pffiffiffiffi Sl
ð4Þ
Based on the Kersey’s model, the neutron dose equivalent at two bend maze entrance (point C, Fig. 2), according to the IAEA Report [10], can be estimated as:
Dn ¼ H1 103 ðAr =Sl Þ ð1=d2 Þ ð10d2 =5 Þ ð10d3 =5 Þ ð1=3Þ 2
ð5Þ
d3 is distance from point B to point C (length of additional bend). It can be seen, from Eqs. (1) and (5), that the neutron dose equivalent for two maze bend can be estimated as neutron dose for the maze length equal to the sum of both bends (distance AB + BC), reduced by factor 1/3. Similar results can be found in Ref. [16]. In this study it is concluded that the presence of the second maze bend gives results which are at least 2.5 times lower than the estimation of Kersey’s equation. It is stated in Refs. [10,15] that 1/3 reduction can be applied in cases when both of the maze bends are long enough and when cross-sectional area of maze or maze entrances are not too large. Considering that both maze bends and cross-section areas satisfy the mentioned requirements, Eq. (5) can be used for neutron dose equivalent estimation for vault presented in Fig. 1. It should be emphasized that in Kersey’s model for estimation of neutron dose equivalent, that TVD = 5 m is already presumed. This TVD is the same for both bends of the
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maze. One of the most important goals of this study is to confirm by measurements of the neutron dose equivalent if TVD = 5 m is a good approximation, and whether it is possible to use the same value of the TVD for both bends of the maze. Considering that the neutron source strength or neutron dose equivalent for Elekta Versa HD accelerators cannot be found in the literature, simple measurements were performed to estimate the values of the mentioned parameters. The Institute of Oncology is equipped with one Varian 2100 C linear accelerator and an Elekta Versa HD linear accelerator (the third one), both of them operating at 15 MV. Both accelerators are located in standard one bend vaults, which have the very same design. The scheme for the vaults can be seen in Ref. [17]. The only difference between the two bunkers is that the inner walls of the Varian vault are covered by wood and that the vault where the Electa accelerator is located is covered with PVC plates. Simple estimation of neutron presence in the vicinity of the Electa Versa HD accelerator can be obtained by a comparison of the activity produced in the activation detectors exposed under identical conditions to photo neutrons originating from heads of both accelerators. It is similar to the approach described in the Ref. [12]. In this experiment the Varian Linac is considered to be a ‘‘known neutron source” because the neutron source strength and neutron dose equivalent of the Varian 2100 therapy machine are already known [8]. It can be expected that that the ratio of neutron source strengths should be equal to the ratio of the saturation activities
Q Vn Q En
R 15
rðEÞ/V ðEÞdE rðEÞ/E ðEÞdE ECd
E
ð6Þ
Cd ¼ R 15
By Q Vn and Q En are denoted neutron strengths of Varian and Elekta accelerators, r(E) is the cross section for neutron capture, in the energy region from the cadmium cut-off (ECd) to the 15 MeV endpoint energy. With UV(E) and UE(E) are signed neutron fluencies for the Varian and Elekta accelerators respectively. The standard way to determine saturation activity is to expose some activation detector to the neutron fluence and to measure the gamma spectra emitted by the radioactive product of the neutron capture. Measured intensities of detected gamma lines can be used to calculate the saturation activity. The ratio of the saturation activities can be expressed as:
R 15 ECd R 15 ECd
E
E rðEÞ/V ðEÞdE NVd ekDtE 1 ektirr 1 ektm ¼ E kDtV E V 1 ektm rðEÞ/E ðEÞdE Nd e 1 ektirr
ð7Þ
N Vd and N Ed are total areas under peaks of the chosen energy in the gamma spectra of the activated detectors. Superscripts V and E denote that the peaks belong to the spectra of In coin exposed in vaults of the Varian and Elekta accelerators respectively. Cooling times (time between the end of exposition and beginning of the measurement) are denoted by Dt V and DtE for activation detectors exposed to neutrons in the vicinity of the Varian and Elekta accelerators respectively. Times of irradiation are tVirr and t Eirr and by tVm and tEm are denoted the durations of the measurements. For all mentioned quantities, durations of irradiations and durations of measurements, superscripts V and E have the same meanings as for the areas under peaks. 3. Results and discussion In order to get the estimation of the neutron source strength for Elekta Versa HD accelerator, two coins made from natural indium metal (2 cm diameter, 8.71 g) enveloped by 1 mm thick cadmium filter were exposed to fast neutrons in both vaults. Activation detectors were placed on the treatment couch 141 cm from focus
(focus to couch distance was 100 cm and distance between beam axis and the activation detector was 100 cm). In both cases the field was 10 10 cm2, and photon dose was 4 Gy at build-up thickness. This means that the beam time was 60 s for Varian accelerator (t Virr ) and 40 s for Elekta Versa HD accelerator (t Eirr ). Gamma radiation of 116In produced by neutron capture on 115In was measured in low-background HPGe detector shielded by 25 cm of pre WWII iron. Relative efficiency of the detector is 32%. Cooling times (time between end of exposition and beginning of measurement) were DtV ¼ 31 minutes and DtE ¼ 42 minutes. Three most prominent peaks of 116In at 417 keV, 1097 keV and 1293 keV were used in this analysis. Measurement times (tVm and tEm for coins exposed at Varian and Elekta accelerators respectively) were determined to get statistical uncertainty of the area under all three peaks recorded in gamma spectra of 116In less than 2%. For the first coin tVm was 1000 s and for the second one t Em was 2500 s. The ratio of saturation activities, presented in Eq. (7), was calculated for all three energies, and the mean value was found. It was obtained that neutron source strength for Elekta Versa HD accelerator is:
Q En ¼ 0:55ð1ÞQ Vn This means that neutron source strength of Elekta Versa HD linear therapy accelerator is 0.4181012 n/Gy. If we compare known values of neutron source strengths for different types for same energies of Varian and Elekta accelerators [8,11], it can be seen that Elekta accelerators produce about two times lower number of neutrons than Varian ones. Our estimation is in good correlation with the existing values of Qn obtained for Varian and Elekta therapy machines. Furthermore, it can be considered that neutron dose equivalent H0 for 15 MV Elekta Versa HD accelerator is 55% of the neutron dose equivalent of Varian 2100 C accelerator. This implies that the neutron dose equivalent for the Versa HD accelerator should be H0 = 0.715 mSv/Gy. Now it is possible to make an estimation of the neutron dose equivalent at the end of the first maze corridor using both proposed methods [8]. If we focus our attention to the first corridor only, it is possible to compare values of the neutron dose equivalent estimated using both proposed models (Eqs. (1) and (2)) and the measured ones. Some of the results are presented in Table 1. Point H is located at the end of the first corridor, at the place where doors in the first bend of the maze should be located. It can be seen that the conservative Kersey model (Eq. (1)) gives more than four times larger estimation than the model described in Eq. (2), as usual. The measured value is almost 24 times lower than the Kersey estimation and 5.5 times lower than the result of the modified Kersey model. Both models are designed to estimate the neutron dose equivalent in vaults composed of standard concrete walls. In the studied vault, a relatively large area (of more than 20 m2) exposed to direct neutrons from the accelerator head is covered by a 2 cm thick PVC layer and walls that are coated by wooden plates. This can be a reason of the relatively large discrepancy between the measured and calculated values of the neutron dose equivalent at point H. It can be seen in Ref. [9] that a layer of borated polyethylene which covers only a part of the maze wall can reduce the neutron dose equivalent two times. Similar measurements [17] showed that for the Varian 2100 C accelerator measured value of the neutron dose
Table 1 Measured and calculated neutron dose equivalent. Neutron dose equivalent D (lSv)
Point B
Point H
Point C
Kersey Modified Kersey Measured
2.91 0.67 0.1
1.84 0.42 0.077
0.153 – 0.0027
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equivalent differs from the calculated one 11 times (Kersey method) and 3.2 times (the modified Kersey method). The Varian vault analyzed in publication [17] is covered by the same type of wooden plates, however there is no plastic neutron moderator inserted at the place where the direct and scattered neutrons from the accelerator head strike the wall of the first corridor. Another possibility could be that our value of the neutron source strength is slightly overestimated and it should be evaluated by some new measurements. Measurements show that values of the neutron dose equivalent in the maze vary in a relatively broad range. In point A the value of 2.17 lSv per 1 Gy of photon dose (in the isocenter) was obtained, while 2.7 nSv per 1 Gy of photon dose was detected in point C, at the outer maze entrance. The most important function of the second bend of the maze, is to reduce the neutron dose at the maze entrance and avoid the use of standard heavy doors. This objective was obviously accomplished, as proved by our measurements. Neutron dose equivalent measured at points E, H and G are 73 nSv, 77 nSv and 78 nSv per 1 Gy of photon dose, respectively. This is a place where entrance doors in the standard one bend maze should be located. The neutron dose is reduced by a factor of 28 along the direction between points A and H. In the model described in the Ref. [10] the point B is the beginning of the second bend in the maze. The neutron dose equivalent measured at point B is 0.10 lSv per 1 Gy of photon dose. Neutron dose equivalent measured at point C is 2.7 nSv per unit photon dose. According to this, it can be concluded that an additional length of 4.5 m of the second maze bend reduces neutron dose equivalent by the factor of 37. According to the IAEA suggestions, the second maze bend should be treated in calculations as a continuation of the first maze corridor. It means that the neutron doses in the second bend should follow an exponential decreasing trend along the maze. Measurements of the neutron dose equivalent along the central line (A-B-C) are presented in Fig. 2, as well as an estimation of the neutron dose equivalent obtained using Eqs. (1) and (5). It can be seen that the conservative Kersey’s model predicts higher neutron dose, however it is evident that the decrease of both measured and calculated neutron dose equivalent along the first maze bend follow almost the same exponential trend. Fig. 2 depicts that neutron dose measured in the second bend has an exponential decreasing trend too, however the slopes of the two segments (A-B and B-C) are different. Moreover, the slopes of lines presenting measured and calculated values in the second bend of the maze differ significantly. It can be easily calculated that in the first bend of the maze TVD is 4.85 m and in the second bend the TVD is 2.83 m. Kersey’s model, where TVD is 5 m, is a relatively good approximation for the first maze bend. According to the other [9] estimation pffiffiffiffi (TVD ¼ 2:06 Sl ), for the maze shown in Fig. 1, TVD should be 6.47 m. It is evident that the measured value is lower than the predicted one. Considering that the inner walls of the vault are covered by 2 cm thick wooden plates, their influence on neutron slowing-down and absorption should not be neglected. If the attenuation properties of 2 cm of wood are equivalent to 0.5 cm of polyethylene [8], it can be expected that the TVD in our vault should be in some degree lower than the predicted one. However, it is apparent that the neutron dose equivalent decreases much faster in the second bend. This result could be expected because neutrons entering the second bend have energies significantly reduced after a number of scatterings during propagation through the first maze bend. Neutron dose equivalent (Dn ðBÞÞ in point B (Eq. (1)) should differ from dose (Dn ðCÞÞ expected in point C (Eq. (5)) for a factor
Dn ðBÞ 1 ¼ Dn ðCÞ ð10d3 =5 Þ ð1=3Þ
ð8Þ
Distance d3 between points B and C is 4.5 m and it can be calculated that the dose in point C should be 24 times lower than neutron dose equivalent in point B. However, measurements of neutron dose equivalent show that the neutron dose equivalent in point C is 37 times lower than the dose measured in point B. The reasons for such high differences between measured and estimated ratios, could be found in the fact that the TVD = 5 m assumption is used for the second bend. The presented results of the measurements show that the TVD values for the two bends can differ significantly. A more accurate approach in neutron dose estimation can be obtained if we slightly modify Eq. (5) to be:
Dn ¼ H1 103 ðAr =Sl Þ ð1=d2 Þ ð10d2 =TVD1 Þ ð10d3 =TVD2 Þ 2
ð9Þ
where TVD1 and TVD2 represent tenth value distance for first and second bend respectively. TVD values are not known in the phase of projecting and building the vault, and they can be estimated from pffiffiffiffi equation TVD ¼ 2:06 Sl , as suggested in Ref. [9]. The TVD approximation of 5 m, in Kersey’s method works well in this case. If two different TVD values (as proposed by Eq. (9)) can be used in the estimation of the neutron dose equivalent, then Eq. (8) turns into Eq. (10) below:
Dn ðBÞ 1 ¼ Dn ðCÞ ð10d3 =TVD2 Þ
ð10Þ
Using TVD2 ¼ 2:83 m, it can be calculated that the dose in point C should be 39 times lower than neutron dose equivalent in point B. This estimation is closer to the ratio of doses measured in points B and C than the result obtained using 5 m for TVD. Since the TVD2 value is not known at the initial phase of building and projecting, the following estimation of TVD2 can be used
TVD2
TVD1 2
ð11Þ
However, it is still difficult to make conclusion according to one case study presented in this work. The measurements in different vaults with two-bend mazes, could confirm this assumption. It can be informative to analyze Eq. (5) in the light of the assumption that in second corridor neutron TVD can have considerably different values than in the first one. Model described in Eq. (5) presume same neutron TVD in both corridors, however factor 1/3 is added to take in consideration the influence of an additional bend in the maze. According to this model, dose on the maze entrance should be 1/3 of the neutron dose equivalent at the end of the single bend corridor having length equal to the sum of the lengths of both corridors in the two bend maze. In the case of two different TVD values the neutron dose equivalent can be estimated using Eq. (9). It can be seen that factor 1/3 in this approach is omitted. Now it is possible to check when Eqs. (5) and (9) will give us the same estimation of neutron dose equivalent. After simple mathematics we’ve got:
ð10d2 =5 Þ ð10d3 =5 Þ ð1=3Þ ¼ ð10d2 =TVD1 Þ ð10d3 =TVD2 Þ
ð12Þ
In some simplified approach we can suppose that TVD1 is 5 m and TVD2 is half of that, which means 2.5 m. Eq. (12) gives us the estimation that both approaches will give the same result for the neutron dose equivalent if the length of the second corridor is 2.4 m. In vaults having two bends described in Refs. [6,7,9,16] the length of the second corridor is much lower than the length of the first one. The length of the second corridor is half of the width of the first corridor and the thickness of the vault wall (distance KC in Fig. 1b). In this geometry it is highly possible that Eq. (5) yields a good estimation of the neutron dose equivalent at the maze door. However, in this case, the second corridor is much longer. The distance between point K and the point C (both points presented in Fig. 1b) equals
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4.5 m. This can be one of the reasons why our estimation of neutron dose equivalent at the maze entrance differs significantly from the model proposed by Eq. (5). It is interesting to compare the neutron dose equivalent measured at one cross-section of the maze corridor. As mentioned before, at one chosen cross-section of the maze, the neutron dose was measured at three points, 30 cm from both walls and in the mid-line of the corridor. Results obtained for four selected cross sections (as shown in Fig. 1) are presented in Fig. 3. It can be seen that neutron dose equivalent measured next to the maze wall is higher than doses measured at two other points. This difference is larger for cross sections closer to the inner maze entrance. Doses measured at cross-section containing point D, at the end of the maze wall (not presented in Fig. 3) are 1.31 lSv, 0.63 lSv and 0.55 lSv per unit photon dose at isocenter. This means that the dose measured in point D near the maze wall is almost 2.4 times larger than the dose measured at the opposite wall of the maze corridor. This fact could be explained by the neutron reflection from the surface directly irradiated by neutrons from the accelerator head. The geometry of the maze allows that a higher number of direct neutrons can be scattered toward point D and the maze wall than to the point located on the other side of the corridor. As it can be seen from Fig. 3, the difference between the dose measured next to the maze wall and other points at the same cross-section become lower and eventually, at the end of the first corridor (cross-section 4), all three doses are the same. A large number of neutron scatterings made a spatial distribution of neutron dose
(a)
(b)
Fig. 3. Neutron dose equivalent measured at several cross sections a) in the first bend and b) in the second bend of the maze.
equivalent more uniform at the end of corridor. It is very interesting to note that at cross-section 3, the decrease of neutron dose equivalent measured at the point opposite from the maze wall is detected. Such a decrease in neutron dose equivalent was not recorded along other cross-sections in the maze corridor. It is possible that the entrance of the second maze bend opens a large room for the expansion of neutrons. There is no wall to enable multiple scattering of neutrons and keep them in same area. By the expansion of neutrons in the second bend, the dose becomes slightly lower. The same analysis was done for two cross-sections in the second bend. Unfortunately, it was not possible to measure the neutron dose equivalent next to both walls near the entrance because the vault is equipped with double-wing doors opening to the inside, as can be seen in Fig. 1a. It can be seen from Fig. 3b, that near the left wall, the measured neutron dose equivalents are slightly higher than at the other measuring points within the same cross-section. It is highly probable that a larger number of neutrons from the first bend is directed toward the left wall of the second bend. In the direction toward the maze end, this difference disappears, as in the first bend. After multiple scattering, a number of neutrons at the end of the corridor, becomes more uniform.
4. Conclusion The most important result obtained in this study is that the second bend of the maze can make a significant reduction of neutron dose equivalent. The measurements confirmed that the second maze bend, 4.5 m long, can reduce the neutron dose equivalent for a factor of more than 30. Considering that similar reduction is measured in the first maze bend, total reduction of neutron dose equivalent is almost three orders of magnitude. Using estimated values of the neutron source strength it was possible to evaluate the neutron dose equivalent at the end of the first corridor by two proposed models. Kersey method, already known as conservative, gives more than 20 times higher value than the measured one at the place where doors should be located in one bend maze. Modified Kersey model overestimates measured dose value more than 5 times. Considering that both methods are designed for vaults composed of concrete, it is possible that additional plastic moderators, as well as wooden plates covering walls, significantly reduce neutron energy and make a large discrepancy between measured and calculated values of the neutron dose equivalent. It is obtained that the measured neutron dose at the maze entrance is 65 times lower than the neutron dose equivalent estimated using the model proposed for the two bend maze [10]. Our measurements showed that initial estimation TVD = 5 m, used in Kersey’s method is relatively good, since the results obtained show TVD1 ¼ 4:45 m in the first maze bend. TVD in the second maze bend, as confirmed by the measurements, is significantly lower. It is obtained in measurements that TVD2 ¼ 2:83 m. The single available method for estimation of neutron dose equivalent for a two-bend maze suggests the use of the same TVD for both bends, introducing some correction parameter equal 1/3. According to the measured neutron dose equivalent, one can assume that TVD in the second maze bend is approximately half of the TVD in the first maze bend. Certainly, this relationship must be confirmed by measurements in more two-bend mazes, which could be a task for other researchers having access to the twobend mazes of medical linear accelerators. Under the assumption that the TVD in the second bend is half of the TVD in the first one, it can be evaluated that the model proposed for a two-bend maze [10] can give similar results as the model using two TVD values, however just if the length of second corridor is about 2.5 m.
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