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Radiation Protection Dosimetry
, Volume 178 (4) – Mar 1, 2018

11 pages

/lp/ou_press/fluka-based-monte-carlo-investigation-of-microdosimetric-distributions-rzKlrk0w2n

- Publisher
- Oxford University Press
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- © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com
- ISSN
- 0144-8420
- eISSN
- 1742-3406
- D.O.I.
- 10.1093/rpd/ncx182
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- See Article on Publisher Site

Abstract FLUKA-based Monte Carlo calculations of microdosimetric distributions in water phantom involving a walled spherical Tissue-Equivalent Proportional Counter filled with tissue-equivalent propane gas have been studied for an indigenously developed telecobalt machine. The simulated site size considered in the study was 2 μm. In the Monte Carlo calculations, field size was varied from 10 cm × 10 cm to 35 cm × 35 cm and the depth was varied as 5–20 cm. The study also includes calculation of microdosimetric distributions with a 30° wedge filter. The efficiency of the calculations was improved up to a factor of 26 by choosing appropriate cut off values for production and transport of electrons. The calculated microdosimetric distributions of telecobalt machine is distinctly different from that of a bare 60Co source which is attributed to the influence of scattered photons from the machine head and the water phantom. INTRODUCTION The property of ionizing radiation in inducing biological effects is related to physical energy depositions at the cellular and sub-cellular structures. Microdosimetry addresses stochastic nature of interactions and energy depositions by the ionizing radiations in such structures. In microdosimetry, a lineal energy distribution is related to Relative Biological Effectiveness. Distribution of energy deposited by ionizing radiations in the microscopic region(1, 2) causes damage to DNA resulting in radiation-induced cell death. Thus, lineal energy is an important quantity for evaluation of radiation quality and its distribution can be measured by using a Tissue-Equivalent Proportional Counter (TEPC) and can be also calculated with Monte Carlo simulations. Generally, TEPC is filled with tissue-equivalent (TE) gas mixtures such as TE methane or TE propane, at low gas pressure, to simulate tissue site sizes similar to the cell nucleus (1 or 2 μm). In microdosimetry, the lineal energy, y, is defined as follows: y=εl¯ (1)where ε is the energy imparted by an event in a specified volume of mean chord length, l¯. An event is the energy deposited in a specific volume by a single charged particle and/or its delta rays and associated charged particles. For a spherical target of diameter, d, l¯=(2/3)d. The number of events with event size between y and y + dy is denoted by f(y). The expectation value of y is known as frequency mean lineal energy, y¯F, and can be defined as follows: y¯F=∫0∞yf(y)dy (2) It is useful to consider the dose distribution of y. The dose probability density, d(y), of y is defined as follows: d(y)=yf(y)/y¯F (3) The dose mean lineal energy, y¯D, is defined as follows: y¯D=∫0∞yd(y)dy=1y¯F∫0∞y2f(y)dy (4) Many published microdosimetric studies described below involved a bare 60Co source(3–15). Biavati and Boer(3) measured microdisometric distributions at 60Co gamma energies for site diameters of 1 and 2 μm. Jessen(8) performed measurements of single-event distributions with a wall-less dipole proportional counter in 0.5 mCi 60Co gamma ray fields from a point source for simulated site diameters of 0.5, 1 and 2 μm. An article by Kliauga and Dvorak(9) reported experimental measurements of microdosimetric event distributions for different monoenergetic photons including 60Co at different site sizes (0.24–7.7 μm) using a wall-less proportional counter. The experimental work by Varma et al.(10) was on determination of microdosimetric event distributions in air and at depths of 2, 5 and 10 cm in a water phantom (30 cm × 30 cm × 30 cm) at three primary photon energies 60 and 660 keV and 60Co (1.25 MeV) using a walled spherical Rossi-type proportional counter (1.27 cm diameter filled with TE propane gas). The site diameters considered in their study were 0.5, 1 and 2 μm. Rollet et al.(13) studied microdosimetric distributions of 60Co and 137Cs sources using a TEPC (HAWK assembly) including FLUKA-based modeling of this TEPC (pure propane gas). Their study also included investigation of influence of single scattering algorithm of electrons on microdosimetric distributions for 1 and 2 μm simulated site diameters. Rollet et al.(14) also studied the microdosimetric distributions of 60Co and 137Cs sources using a mini-cylindrical TEPC and compared against the FLUKA-based Monte Carlo calculations. Chiriotti et al.(15) compared experimental microdosimetric distributions of 60Co (409 kBq) and 137Cs (1.11 GBq) sources at different simulated site sizes (1–3 μm) in pure propane gas-based spherical TEPC against the simulated distributions obtained with two general purpose codes FLUKA(16) and PENELOPE(17). Recently, Moro and Chiriotti(18) carried out measurements against 60Co (409 kBq), 137Cs and 241Am–Be(α,n) gamma and neutron fields with the European TEPC (EuTEPC) filled with pure propane gas, by scaling its density by a factor of 0.75 to get the same equivalent site size in TE propane gas. For the 60Co source, the site diameters considered in their measurements were 0.7, 1.3 and 2.7 μm. A limited number of published studies on microdosimetry are reported in the literature involving a telecobalt machine(19–23). Tilikidis et al.(19) studied the influence of radiation quality changes on microdosimetric variance and depth–dose relations for therapeutic 60Co and 15 MV beams and 21 MeV electron beam. Grindborg et al.(20) performed variance–covariance microdosimetric measurements by using spherical ionization chambers (Extradin A3 and A4 models) against a collimated 60Co gamma ray beam (a therapy unit with a kerma rate of 9 mGy/s at 0.5 m) for determining y¯D. The site diameters studied were 6.1–1680 nm. Grindborg and Olko(21) in their study on collimated 100 kV x-ray and telecobalt beams compared measured and calculated values of y¯D in the nanometer regions. In their study, the measurements were performed against a telecobalt beam and the calculations were based on dose distributions of ionization scored in spherical volumes of 5–2000 nm at 60Co primary photon energies of 1.17 and 1.33 MeV. The authors reported that the measured and calculated y¯D values differed by a factor of 1.2 for the simulated site diameters between 9 nm and 2 μm. Lillhök et al.(22) measured microdosimetric distributions from a Siemens 60Co therapy unit in site diameters of 10 nm–1.5 μm by using the wall-less TEPCs. They utilized variance–covariance method to determine y¯D. Recently, Lindborg et al.(23) simulated Siemens Gammatron 1 60Co gamma therapy unit and reported y¯D values for site sizes of 5–1000 nm and compared the same against the previously published measured values by Grindborg and Olko(21). The authors reported y¯D value of 1.4 keV/μm for the site diameter of 1 μm. As there are no detailed published studies on microdosimetric distributions from a telecobalt radiotherapy beam, the present study is aimed at calculating microdosimetric lineal energy distributions, y¯F and y¯D from the telecobalt radiotherapy beam involving a walled spherical TEPC filled with TE propane gas. The simulated site size considered in the calculations was 2 μm. The influence of field size, depth in water and the presence of wedge filter on the microdosimetric distributions were also investigated. In the study an indigenously developed Bhabhatron II telecobalt machine(24) was simulated using the FLUKA code (version 2011.2c)(16, 25). The study also includes simulation of a bare point 60Co source for comparison of y¯F and y¯D values against the published data(3, 8-10, 14, 15). In addition, efforts were made to improve the efficiency of the Monte Carlo calculations. MATERIALS AND METHODS FLUKA is general purpose code capable of transporting about 60 different particles in matter including photons and electrons from 1 keV to thousands of TeV(16, 25). FLUKA has the capability to handle complex geometries using an improved version of the Combinatorial Geometry package. FLUKA can be used in a biased mode as well as a fully analogue mode. This implies that in order to predict fluctuations, signal coincidence and the correlated events, a wide choice of statistical techniques are available to investigate punch through or other rare events in addition to attenuations by many orders of magnitude. In the present study, FLUKA-based microdosimetric distributions in a sealed spherical TEPC (5 cm diameter) were studied for both bare 60Co source and the indigenously developed telecobalt machine. The TEPC modeled in the study consists of a spherical cavity of diameter 5 cm, surrounded by 3-mm-thick TE A-150 plastic material (density 1.127 g/cm3). The geometric details of this detector were taken from the literature(15, 18). In the Monte Carlo calculations, the spherical cavity of the TEPC is filled with either pure propane gas or TE propane gas. For the TEPC filled with TE propane gas, density of gas in the TEPC, ρg (g/cm3), set in the Monte Carlo calculations for the site size of 2 μm is based on the following equation: ρg=ρtdt/dg (5)where, dt is the site diameter (in cm), dg is the physical cavity diameter (in cm) of the TEPC and ρt is density of tissue (1 g/cm3). Here, the mass collision stopping powers of TE gas and tissue are considered to be identical according to the condition of tissue equivalence. The value of ρg set in the Monte Carlo calculations for the simulated site size of 2 μm is 4 × 10−5 g/cm3. Guided by Chiriotti et al.(26) for the pure propane gas, density of TE propane gas (ρg = 4 × 10−5 g/cm3) was scaled by a factor of 0.75, to get the same equivalent size of 2 μm. Microdosimetric study of bare 60Co source In this simulation, the center of TEPC (5 cm dia) was positioned at 80 cm from a point 60Co source (emission restricted to half-angle θ = 2.1°). This study was considered to compare the FLUKA-calculated microdosimetric distribution against the published distribution by Chiriotti et al.(15) in which TEPC was filled with pure propane. In the present study, we carried out simulations by filling the sensitive region of the TEPC with pure propane gas and TE propane gas for comparison. In the calculations, two energy lines of 60Co, 1.17 and 1.33 MeV were considered. In these simulations, the production threshold for bremmsstrahlung photons generated by the secondary electrons (Pth) and secondary delta-ray electrons (Eth) were set at 1 keV in the detector materials (wall and sensitive gas). The values of transport cut off for photons (Pcut) and electrons (Ecut) were also set at 1 keV. Microdosimetric study of telecobalt machine In the Monte Carlo calculations, the different components of the indigenously developed telecobalt machine such as source capsule, primary collimator and secondary collimators, trimmers were simulated. A schematic diagram of the telecobalt machine (with cylindrical 60Co source), water phantom and TEPC simulated in the Monte Carlo calculations is shown in Figure 1. In the Monte Carlo simulations, water phantom (50 cm × 50 cm × 50 cm) was positioned at Source-to-Surface Distance (SSD) = 80 cm. All the Monte Carlo calculations involving the telecobalt machine utilized TEPC filled with TE propane gas. Figure 1. View largeDownload slide Schematic diagram of telecobalt machine, water phantom and TEPC simulated in the FLUKA Monte Carlo Calculations. In the Monte Carlo calculations, the source geometries such as cylindrical 60Co capsule and a point diverging 60Co source with restricted angular emission (half-angle θ = 14.1°) were considered. Figure not to scale. Figure 1. View largeDownload slide Schematic diagram of telecobalt machine, water phantom and TEPC simulated in the FLUKA Monte Carlo Calculations. In the Monte Carlo calculations, the source geometries such as cylindrical 60Co capsule and a point diverging 60Co source with restricted angular emission (half-angle θ = 14.1°) were considered. Figure not to scale. Before initiating the full-fledged Monte Carlo calculations of microdosimetric lineal energy distribution for different field sizes and depths, following detailed simulation was carried out for 10 cm × 10 cm field size at SSD = 80 cm. In this simulation, the TEPC (5 cm diameter) was positioned at 5 cm depth along the central axis of the water phantom. The parameters Eth, Ecut, Pth and Pcut were also set at 1 keV. In the Monte Carlo calculations, source photons (1.17 and 1.33 MeV) were sampled randomly from the cylindrical 60Co source (2 cm diameter × 2 cm height). Influence of geometry of the 60Co source on the calculated microdosimetric distributions and efficiency of the calculations was also investigated. In this investigation, the cylindrical 60Co source was replaced with a point isotropic 60Co source with a restricted angular emission. We considered a polar angle of θ = 14.1° (half-angle) which opens a circular radiation field of diameter 40 cm at SSD = 80 cm. The values of Pth, Eth, Pcut and Ecut were all set at 1 keV everywhere. This approach has resulted in improvement in the efficiency of the calculation by a factor of ~6 without affecting the values of y¯F and y¯D values (Table 1). Table 1. Monte Carlo-calculated values of y¯F and y¯D (in keV/μm) at 5 cm depth in water phantom for 10 cm × 10 cm field size from telecobalt machine. The calculations are based on cylindrical 60Co source and a point 60Co source with divergence of θ = 14.1°. The transport and production cut off values for both photons and electrons were set 1 keV everywhere. The TEPC modeled in these calculations has 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Source type y¯F y¯D Efficiency Cylindrical isotropic 0.463 ± 0.003 1.748 ± 0.030 — Point diverging 0.464 ± 0.003 1.752 ± 0.030 6 Source type y¯F y¯D Efficiency Cylindrical isotropic 0.463 ± 0.003 1.748 ± 0.030 — Point diverging 0.464 ± 0.003 1.752 ± 0.030 6 The parameters Ecut and Eth play an important role on efficiency of the Monte Carlo calculations. Hence, in order to further improve the efficiency of the calculations, simulations were carried out for 10 cm × 10 cm field at 5 cm depth in water, by varying the values of Eth and Ecut in the machine components and in the water phantom. In these simulations, the point divergent 60Co source (half-angle θ = 14.1°) was considered. As the parameter Pth may not improve the efficiency of the calculations significantly, for all the simulations, value of this parameter was set at 10 keV in the machine head and phantom. However, Pcut was varied as 1, 10 and 100 keV in the machine head and in the phantom. Note that in the TEPC materials (wall and sensitive gas region), the values of Pth, Eth, Pcut and Ecut were set at 1 keV. Table 2 summarizes the above discussion which demonstrates that the calculated values of y¯F and y¯D are not affected while changing the values of cut off parameters. However, there is a significant improvement in the efficiency of the calculations up to a factor of 26 while setting Ecut = 1.25 MeV and 800 keV in the machine head and water phantom, respectively; and Eth = 1.25 MeV and 800 keV in the machine head and water phantom, respectively. The selection of Eth = Ecut = 800 keV in the water phantom was based on the fact that the ESTAR-based(27) Continuously Slowing Down Approximation (CSDA) range of 800 keV electron (kinetic energy) in A150 plastic (wall material of the TEPC) is 0.33 g/cm2. This implies that those electrons having kinetic energy >800 keV can only manage to enter into the sensitive gas region of the TEPC as the 3-mm-thick of wall material of the TEPC corresponds to 0.35 g/cm2. The highest electron energy that would be generated in the machine head is expected to be ~1.25 MeV. As these electrons cannot reach the sensitive region of the TEPC due to the presence of water above the TEPC, we set Ecut = Eth = 1.25 MeV for the machine head. Table 2. Monte Carlo-calculated values of y¯F and y¯D (in keV/μm) at 5 cm depth in water phantom for 10 cm × 10 cm field size from the telecobalt machine. The calculations are based on a point 60Co source with divergence of θ = 14.1° (half-angle). The sensitive volume of the TEPC modeled in these calculations has 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. The transport and production cut off values for electron and transport cut off for the photon in the telecobalt machine head and the water phantom were varied in the calculations. The transport and production cut off for both electron and photon in the TEPC materials were set at 1 keV. The production cut off for photon was set at 10 keV. Transport cut off for photon Transport cut off for electron Production cut off for electron y¯F y¯D Efficiency Machine head: 1 keV; Phantom: 1 keV Machine head: 1 keV; Phantom: 1 keV Machine head: 1 keV; Phantom: 1 keV 0.464 ± 0.003 1.752 ± 0.030 — Machine head: 10 keV; Phantom: 10 keV Machine head: 1 MeV; Phantom: 10 keV Machine head: 50 keV; Phantom: 10 keV 0.460 ± 0.002 1.754 ± 0.021 19 Machine head: 100 keV; Phantom: 10 keV Machine head: 1.25 MeV; Phantom: 800 keV Machine head: 1.25 MeV; Phantom: 800 keV 0.463 ± 0.002 1.757 ± 0.023 26 Transport cut off for photon Transport cut off for electron Production cut off for electron y¯F y¯D Efficiency Machine head: 1 keV; Phantom: 1 keV Machine head: 1 keV; Phantom: 1 keV Machine head: 1 keV; Phantom: 1 keV 0.464 ± 0.003 1.752 ± 0.030 — Machine head: 10 keV; Phantom: 10 keV Machine head: 1 MeV; Phantom: 10 keV Machine head: 50 keV; Phantom: 10 keV 0.460 ± 0.002 1.754 ± 0.021 19 Machine head: 100 keV; Phantom: 10 keV Machine head: 1.25 MeV; Phantom: 800 keV Machine head: 1.25 MeV; Phantom: 800 keV 0.463 ± 0.002 1.757 ± 0.023 26 Guided by the above findings on improvement in the efficiency of the calculations, further simulations for different field sizes (15 cm × 15 cm, 30 cm × 30 cm and 35 cm × 35 cm) and depths (10 and 20 cm) utilized the point divergent 60Co source (half-angle θ = 14.1°) and the above-described cut off parameters (see first three columns of third row of Table 2). Calculations for a 30° wedge filter (introduced below the trimmers) for 10 cm × 10 cm field size also utilized the above settings. When the TEPC was placed in air (without water phantom), the value of Ecut and Eth set in the machine head was 800 keV as secondary electrons produced from the machine below 800 keV will not be able to enter into the gas cavity. All the Monte Carlo calculations utilized the DETECT option for calculating pulse-height spectra in the sensitive volume of the TEPC. DETECT card scores energy deposition on an event by event basis over 1024 number of channels in a linear scale. A distribution of energy deposited per event in the sensitive volume of TEPC was scored using a single scattering mode activated everywhere. All the simulations were run in fully analogue mode. PRECISION DEFAULTs card was used for all simulations. Up to 2 × 1010 primary particles were simulated in five cycles in order to reduce statistical uncertainty <0.3% at the absorbed dose level. The energy frequency spectra obtained through the calculations were converted to lineal energy distributions by dividing the mean energy deposited in each channel with the mean chord length of the spherical cavity. Values of y¯F and y¯D were calculated from these lineal energy distributions. The uncertainty on y¯F and y¯D were calculated using the standard error propagation formula at 1σ level. ENERGY DEPOSITION MECHANISMS IN THE TEPC When the TEPC is exposed to gamma radiation, energy is imparted to the sensitive volume of the TEPC by the secondary electrons produced in the wall material and the sensitive gas. There are four classes of tracks in the gas cavity of a TEPC: crossers, insiders, starters and stoppers(1). Crossers are the charged particles produced in the wall material of the TEPC which have enough energy to cross the gas cavity. Insiders are the charged particles which are generated by interactions with the gas but they lose all their energy in the gas. Starters are also produced in the gas but they leave gas cavity. Charged particles that are classified under stoppers category are those produced in the wall material and lose all their energy in the gas cavity. In the present study, it is expected that contributions from ‘Insiders’ and ‘Starters’ to energy deposition in the sensitive volume of the detector are less significant as compared to contributions from ‘Stoppers’ and ‘Crossers’. This is due to the fact that sensitive volume of the detector is filled with the gas material of low density. Hence, as discussed by Rollet et al.(14) the number of photon-interaction events taking place in the gas cavity is negligible. Therefore, the energy deposited inside the gas cavity is mainly due to electrons created in the detector wall material. When the gas density corresponds to a site diameter 2 μm, electrons having kinetic energy less than ~8 keV are, on average, fully absorbed(14). RESULTS AND DISCUSSIONS The microdosimetric distributions presented below are plot of yd(y) on a linear scale vs. y on a log scale. In this type of plot equal areas under the curve represent equal doses delivered at the intervals of y values considered. For plotting microdosimetric distributions, we have used 25 bins per decade. Figure 2 compares microdosimetric lineal energy distribution in TEPC filled with pure propane gas and TE propane gas for a bare 60Co source. The lineal energy distribution obtained in the present study for pure propane gas compares reasonably well with the FLUKA-based published work by Chiriotti et al.(15) including the peak observed in the region around 0.30 keV/μm. The shape of the lineal energy distribution of TE propane gas is comparable to that of the pure propane gas for the region beyond y = 0.1 keV/μm. However, pure propane gas shows smaller yield in the region y = 0.25–0.4 keV/μm when compared to the TE propane gas. In the FLUKA-based study by Rollet et al.(14) involving a parallel beam of 60Co on a mini-TEPC cylindrical detector (TE propane gas), the peak was observed around 0.3 keV/μm for the site diameter of 2 μm. The FLUKA-based microdosimetric distribution for 60Co involving a HAWK TEPC (pure propane gas; sensitive diameter 12.5 cm) for site diameter of 2 μm published by Rollet et al.(13) shows the peak at ~0.3 keV/μm. Figure 2. View largeDownload slide Comparison of Monte Carlo-calculated microdosimetric distributions in TEPC (5 cm diameter) filled with pure propane and TE propane gas. The bare 60Co source is at 80 cm from the TEPC. The simulated site size is 2 μm. Figure 2. View largeDownload slide Comparison of Monte Carlo-calculated microdosimetric distributions in TEPC (5 cm diameter) filled with pure propane and TE propane gas. The bare 60Co source is at 80 cm from the TEPC. The simulated site size is 2 μm. The published values of y¯F and y¯D for the bare 60Co source for the simulated site size of 2 μm and that from the present study are shown in Table 3. The values of y¯F and y¯D obtained in the present study for pure propane gas compare well with the published values reported by Chiriotti et al.(15) and Varma et al.(10). Considering larger uncertainty on the y¯D value as reported by Rollet et al.(14), the comparison is reasonably good with the corresponding published values of y¯D including the value obtained in the present study. The measured and calculated values of y¯F as reported by Rollet et al.(14) show a difference of ~10–30%, when compared to the corresponding published values and the value obtained in the present study. However, the y¯F and y¯D values reported by Jessen(8), Kliauga and Dvorak(9) and Biavati and Boer(3) are significantly lower than the corresponding values obtained in the present study. Table 3. Comparison of published values of y¯F and y¯D (in keV/μm) for bare 60Co source for the simulated site size of 2 μm. Study y¯F y¯D aChiriotti et al.(15) Experimental (TEPC 5 cm diameter) 0.33 ± 0.02 1.57 ± 0.10 PENELOPE 0.32 ± 0.02 1.35 ± 0.20 FLUKA 0.36 ± 0.02 1.58 ± 0.22 bRollet et al.(14) Experimental (mini-cylindrical TEPC) 0.28 ± 0.02 1.40 ± 0.10 FLUKA 0.27 ± 0.02 1.40 ± 0.10 aVarma et al.(10) Experimental (TEPC 1.27 cm diameter) c0.368 d1.50 Jessen et al.(8) Wall-less dipole Proportional Counter 0.24 1 Biavati and Boer(3) Experimental 0.23 0.982 eKliauga and Dvorak(9) Wall-less Proportional Counter 0.255 1.22 Present study (bare 60Co source) TEPC (5 cm dia) TE Propane gas 0.347 ± 0.002 1.457 ± 0.003 Pure propane gas 0.342 ± 0.003 1.540 ± 0.002 Study y¯F y¯D aChiriotti et al.(15) Experimental (TEPC 5 cm diameter) 0.33 ± 0.02 1.57 ± 0.10 PENELOPE 0.32 ± 0.02 1.35 ± 0.20 FLUKA 0.36 ± 0.02 1.58 ± 0.22 bRollet et al.(14) Experimental (mini-cylindrical TEPC) 0.28 ± 0.02 1.40 ± 0.10 FLUKA 0.27 ± 0.02 1.40 ± 0.10 aVarma et al.(10) Experimental (TEPC 1.27 cm diameter) c0.368 d1.50 Jessen et al.(8) Wall-less dipole Proportional Counter 0.24 1 Biavati and Boer(3) Experimental 0.23 0.982 eKliauga and Dvorak(9) Wall-less Proportional Counter 0.255 1.22 Present study (bare 60Co source) TEPC (5 cm dia) TE Propane gas 0.347 ± 0.002 1.457 ± 0.003 Pure propane gas 0.342 ± 0.003 1.540 ± 0.002 aPure propane gas. bTE propane gas. cUncertainty is ±3%. dUncertainty is ±1.5%. eSimulated site size is 1.9 μm. For telecobalt machine, when the TEPC is positioned in air (field size 10 cm × 10 cm) the values of y¯F and y¯D obtained are 0.439 ± 0.001 keV/μm and 1.632 ± 0.016 keV/μm, respectively. A comparison these values to the bare 60Co source data (Table 3) suggests that y¯F is higher by a factor of 1.26 and y¯D by 1.12. Table 4 presents the values of y¯F and y¯D at different depths in water phantom for various field sizes. The table demonstrates that: (a) for a given field size as the depth increases, the values of y¯F increase gradually (0.482 ± 0.002–0.541 ± 0.003 keV/μm for 35 cm × 35 cm), (b) for a given depth as the field size increases from 10 cm × 10 cm to 30 cm × 30 cm, there is a gradual increase in y¯F (0.463 ± 0.002–0.476 ± 0.002 keV/μm for 5 cm depth and 0.484 ± 0.002–0.539 ± 0.002 keV/μm for 20 cm depth) and beyond 30 cm × 30 cm, y¯F is constant (c) for a given field size y¯D increases with depth (1.757 ± 0.023–1.875 ± 0.025 keV/μm for 10 cm × 10 cm and 1.948 ± 0.027–2.232 ± 0.030 keV/μm for 35 cm × 35 cm) and (d) for a given depth as the field size increases from 10 cm × 10 cm to 30 cm × 30 cm, there is a gradual increase in y¯D (1.757 ± 0.023–1.947 ± 0.030 keV/μm for 5 cm depth and 1.875 ± 0.025–2.265 ± 0.030 keV/μm for 20 cm depth) and beyond 30 cm × 30 cm, y¯D is constant. Above listed points can be explained as follows. In the case of radiotherapy photon beam (e.g. telecobalt beam), for a given field size, when the depth increases: (a) dose due to primary component of photons decreases (due to exponential attenuation of photons in water and inverse square fall off in the primary photon fluence), and (b) the relative contribution of in-phantom scatter to the dose initially increases and then gradually decreases(28, 29). Similarly, for a given depth in phantom, as the field size increase, the dose due to primary component of photons is constant. However, the in-phantom scatter increases up to a field size of about 25 cm × 25 cm, and thereafter, it is nearly constant(28, 29). In micorodosimetry, the scatter component plays an important role on both y¯F and y¯D. The secondary electrons produced by the scattered photons have comparatively shorter range than those produced by the primary photons. As a result, the contributions from stoppers and crossers to the energy deposition in the sensitive volume of the detector will change with depth or field size. Such phenomenon will affect both y¯F and y¯D. For example, for smaller fields (10 cm × 10 cm and 15 cm × 15 cm), y¯D increases with depth (~7–15% increase at 20 cm as compared to 5 cm depth). Whereas y¯F increases by ~5 and 10%, respectively, for 10 cm × 10 cm and 15 cm × 15 cm field sizes, when the depth is increased from 5 to 20 cm. Table 4. Monte Carlo-calculated values of y¯F and y¯D (in keV/μm) presented as a function of depth in water for various field sizes from the telecobalt machine. The calculations are based on a point 60Co source with a divergence of θ = 14.1° (half-angle). The sensitive volume of the TEPC modeled in these calculations has 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Depth (cm) 10 cm × 10 cm 15 cm × 15 cm 30 cm × 30 cm 35 cm × 35 cm y¯F y¯D y¯F y¯D y¯F y¯D y¯F y¯D 5 0.463 ± 0.002 1.757 ± 0.023 0.469 ± 0.002 1.863 ± 0.030 0.476 ± 0.002 1.947 ± 0.030 0.482 ± 0.002 1.948 ± 0.027 10 0.472 ± 0.002 1.822 ± 0.027 0.487 ± 0.001 1.958 ± 0.021 0.501 ± 0.001 2.049 ± 0.020 0.501 ± 0.003 2.061 ± 0.030 20 0.484 ± 0.002 1.875 ± 0.025 0.515 ± 0.002 2.134 ± 0.030 0.539 ± 0.002 2.265 ± 0.030 0.541 ± 0.003 2.232 ± 0.030 Depth (cm) 10 cm × 10 cm 15 cm × 15 cm 30 cm × 30 cm 35 cm × 35 cm y¯F y¯D y¯F y¯D y¯F y¯D y¯F y¯D 5 0.463 ± 0.002 1.757 ± 0.023 0.469 ± 0.002 1.863 ± 0.030 0.476 ± 0.002 1.947 ± 0.030 0.482 ± 0.002 1.948 ± 0.027 10 0.472 ± 0.002 1.822 ± 0.027 0.487 ± 0.001 1.958 ± 0.021 0.501 ± 0.001 2.049 ± 0.020 0.501 ± 0.003 2.061 ± 0.030 20 0.484 ± 0.002 1.875 ± 0.025 0.515 ± 0.002 2.134 ± 0.030 0.539 ± 0.002 2.265 ± 0.030 0.541 ± 0.003 2.232 ± 0.030 Figure 3 presents central axis microdosimetric lineal energy distribution at 5 cm in water phantom for 10 cm × 10 cm field size. In this figure, results obtained based on modeling the cylindrical 60Co source and the one with a point source with a divergence of θ = 14.1° (half-angle) are presented. The figure demonstrates that choice of geometry of the source does not appear to affect the microdosimetric distribution. Figure 3. View largeDownload slide Monte Carlo-calculated on-axis microdosimetric lineal energy spectra at 5 cm depth in water phantom for field size of 10 cm × 10 cm from a telecobalt machine. The distributions are presented for two source geometries, namely, 60Co cylindrical capsule and a point 60Co source with a divergence of θ = 14.1° (half-angle). The TEPC simulated is spherical in shape with 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Figure 3. View largeDownload slide Monte Carlo-calculated on-axis microdosimetric lineal energy spectra at 5 cm depth in water phantom for field size of 10 cm × 10 cm from a telecobalt machine. The distributions are presented for two source geometries, namely, 60Co cylindrical capsule and a point 60Co source with a divergence of θ = 14.1° (half-angle). The TEPC simulated is spherical in shape with 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Figure 4 compares the lineal energy distributions for the cases: (a) bare 60Co source with TEPC in air, (b) telecobalt machine with TEPC in air (10 cm × 10 cm field size) and (c) telecobalt machine with TEPC at 5 cm depth in water (10 cm × 10 cm field size). The figure demonstrates the influence of different components such as machine head and water phantom on the microdosimetric distributions. In the case of bare 60Co source (TEPC filled with TE propane gas) the peak is observed in the region 0.26–0.29 keV/μm (Figure 2) and there is a flat region in the range 1.5–5 keV/μm. Such a flat region is not observed in the case of telecobalt machine with or without the water phantom. In the case of telecobalt machine with or without water phantom, the peak is observed in the region 0.40–0.45 keV/μm. The differences in the lineal energy distributions observed for these cases are attributed to the presence of secondary photons produced from machine head and water phantom. In the case of telecobalt machine with or without water phantom, the electron edge position is slightly shifted to higher y value when compared to the bare 60Co. Figure 4. View largeDownload slide Comparison of Monte Carlo-calculated microdosimetric lineal energy spectra for bare 60Co with TEPC in air, telecobalt machine with TEPC in air (10 cm × 10 cm field size) and telecobalt machine with TEPC at 5 cm depth in water (10 cm × 10 cm field size). The TEPC simulated is spherical in shape with 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Figure 4. View largeDownload slide Comparison of Monte Carlo-calculated microdosimetric lineal energy spectra for bare 60Co with TEPC in air, telecobalt machine with TEPC in air (10 cm × 10 cm field size) and telecobalt machine with TEPC at 5 cm depth in water (10 cm × 10 cm field size). The TEPC simulated is spherical in shape with 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Figure 5 presents the lineal energy distributions at depths 5, 10 and 20 cm in water (10 cm × 10 cm field size) and the shape of the distributions is comparable. For each depth, the peak is observed in the region 0.40–0.45 keV/μm. Figure 5. View largeDownload slide Monte Carlo-calculated on-axis microdosimetric lineal energy spectra at different depths in water phantom for field size of 10 cm × 10 cm from a telecobalt machine. The TEPC simulated is spherical in shape with 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Figure 5. View largeDownload slide Monte Carlo-calculated on-axis microdosimetric lineal energy spectra at different depths in water phantom for field size of 10 cm × 10 cm from a telecobalt machine. The TEPC simulated is spherical in shape with 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Figure 6 compares the lineal energy distributions obtained at 10 cm depth in water for 10 cm × 10 cm field size with and without a 30° wedge filter. The figure demonstrates that the shape of the distributions is same for both the cases. The yield in the individual lineal energy bins is statistically comparable except in the bins 16.61–18.21 and 18.21–19.97 keV/μm where the yield is higher for the case with wedge filter (up to a factor of 2). Table 5 presents the values of y¯F and y¯D as a function of depth in water for 10 cm × 10 cm field, when a 30° wedge filter is introduced between the phantom and the trimmers. A comparison of these results with those in open field (Table 4) shows that the presence of wedge has enhanced the value of y¯F marginally whereas y¯D values have increased considerably. For example, for 10 cm × 10 cm field size, the values of y¯D with and without the wedge filter at 5 cm depth are 2.104 ± 0.020 and 1.757 ± 0.023, respectively. This is due to the fact that relative contribution of scattered photons increases in the presence of wedge filter as the primary photons undergo additional exponential attenuation by the filter. Table 5. Monte Carlo-calculated values of y¯F and y¯D (in keV/μm) presented as a function of depth in water for 10 cm × 10 cm field size from the telecobalt machine, when a 30° wedge is positioned below the trimmers. The calculations are based on a point 60Co source with a divergence of θ = 14.1° (half-angle). The sensitive volume of the TEPC modeled in these calculations has 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Depth (cm) y¯F y¯D 5 0.487 ± 0.001 2.104 ± 0.020 10 0.488 ± 0.001 2.112 ± 0.023 20 0.501 ± 0.001 2.187 ± 0.024 Depth (cm) y¯F y¯D 5 0.487 ± 0.001 2.104 ± 0.020 10 0.488 ± 0.001 2.112 ± 0.023 20 0.501 ± 0.001 2.187 ± 0.024 Figure 6. View largeDownload slide Monte Carlo-calculated on-axis microdosimetric lineal energy spectra at 10 cm depth in water phantom from a telecobalt machine (field size 10 cm × 10 cm) with and without a 30° wedge filter. The TEPC simulated is spherical in shape with 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Figure 6. View largeDownload slide Monte Carlo-calculated on-axis microdosimetric lineal energy spectra at 10 cm depth in water phantom from a telecobalt machine (field size 10 cm × 10 cm) with and without a 30° wedge filter. The TEPC simulated is spherical in shape with 5 cm diameter filled with TE propane gas. The simulated site size is 2 μm. Varma et al.(10) studied the influence of water phantom on the measured values of y¯F and y¯D at different depths (2, 5 and 10 cm) for site diameters 0.5, 1 and 2 μm from a bare 60Co source by comparing against the values when the TEPC is in air (without the water phantom). Table 6 compares the ratios y¯F (water)/ y¯F (air) and y¯D (water)/ y¯D (air) at different depths in water for bare 60Co source and telecobalt machine for the site size of 2 μm. As the depth increases both the ratios increase for bare 60Co source and the telecobalt machine. The ratios obtained in the present study for the bare 60Co compare well with the published values by Varma et al.(10) The ratios y¯F (water)/ y¯F (air) and y¯D (water)/ y¯D (air) for telecobalt machine also compare well with the bare source results. Table 6. Comparison of y¯F (water)/ y¯F (air) and y¯D (water)/ y¯D (air) at depths in water for bare 60Co source and telecobalt machine (10 cm × 10 cm field size). The simulated site size is 2 μm. Ratio Depth (cm) Varma et al.(10) bare60Co Present study Bare60Co Telecobalt machine y¯F (water)/ y¯F (air) 5 1.06 1.05 1.05 10 1.10 1.10 1.08 20 — — 1.10 y¯D (water)/ y¯D (air) 5 1.10 1.08 1.08 10 1.14 1.12 1.12 20 — — 1.15 Ratio Depth (cm) Varma et al.(10) bare60Co Present study Bare60Co Telecobalt machine y¯F (water)/ y¯F (air) 5 1.06 1.05 1.05 10 1.10 1.10 1.08 20 — — 1.10 y¯D (water)/ y¯D (air) 5 1.10 1.08 1.08 10 1.14 1.12 1.12 20 — — 1.15 Okamoto et al.(30) reported measured (TEPC—1.27 cm diameter filled with TE propane gas) and GEANT4-based Monte Carlo values of y¯D=2.34±0.03 and 2.24 ± 0.01, respectively, at SSD = 80 cm from a custom-made 60Co irradiator for site diameter of 1 μm. In the present study, an auxiliary simulation involving the telecobalt machine head and TEPC (5 cm diameter) resulted in y¯D=2.302±0.050 for the site diameter 1 μm. CONCLUSIONS An indigenously developed telecobalt machine was simulated using the FLUKA code to study the microdosimetric distributions in a sealed spherical TEPC filled with TE propane gas. The simulated site size considered in the study was 2 μm. In addition, microdosimetric distributions due to a bare 60Co source was also studied. The lineal energy distribution of bare 60Co source was distinctly different from that obtained for the telecobalt machine. The Monte Carlo calculations involving a cylindrical 60Co capsule vs. point divergent 60Co source (θ = 14.1°) did not affect the microdosimetric distributions including y¯F and y¯D of the telecobalt machine, rather improved the efficiency by a factor of 6. In addition, selection of appropriate values of transport and production cut off for electrons improved the efficiency up to a factor of 26. The values of y¯F and y¯D for the telecobalt machine (10 cm × 10 cm field size) when TEPC was in air are 0.439 ± 0.001 and 1.632 ± 0.016, respectively. Whereas these values for the bare 60Co source are 0.347 ± 0.002 and 1.457 ± 0.003 keV/μm. The study reveals that for a given field size, depth at which the TEPC is positioned in water phantom has an influence on the values of y¯F and y¯D. For example, for 35 cm × 35 cm field size, at 20 cm depth in water, the values of y¯F and y¯D are 0.541 ± 0.003 and 2.232 ± 0.030 keV/μm, respectively. Whereas for this field size, at 5 cm depth, the values y¯F and y¯D are 0.482 ± 0.002 and 1.948 ± 0.027 keV/μm, respectively. Introduction of a 30° wedge filter below the trimmers of the telecobalt machine further enhanced the values of y¯F and y¯D. When this filter is in place, the values of y¯F and y¯D at 10 cm depth are 0.488 ± 0.001 and 2.112 ± 0.023 keV/μm, respectively. Whereas the corresponding values for 10 cm × 10 cm field size without the wedge filter are 0.472 ± 0.002 and 1.822 ± 0.027 keV/μm. ACKNOWLEDGMENTS The authors thank Dr Pradeepkumar, K.S., Associate Director, Health, Safety & Environment Group, Bhabha Atomic Research Centre (BARC), Mumbai for his encouragement and support for this study. The authors also thank Dr D.C. Kar, Division of Remote Handling & Robotics, BARC for providing the mechanical details of the Bhabhatron-II telecobalt machine. REFERENCES 1 International Commission on Radiation Units and Measurements. Microdosimetry. (Bethesda, MD: ICRU Publications) ICRU Report 36 ( 1983). 2 Rossi, H. H. and Zaider, M. Microdosimetry and its Applications ( Berlin, New York: Springer-Verlag) ( 1996). Google Scholar CrossRef Search ADS 3 Biavati, M. H. and Bore, E. D(Y) spectra gamma-rays. Report NYO-2740-3, Radiological Research Laboratory, Columbia University, New York ( 1966). 4 Ellett, W. H. and Braby, L. A. The microdosimetry of 250 kVp and 65 kVp x-rays, 60Co gamma rays, and tritium beta particles. Radiat. Res. 51( 2), 229– 243 ( 1972). Google Scholar CrossRef Search ADS PubMed 5 Bengtsson, L. G. and Lindborg, L. Comparison of pulse height analysis and variance measurements for the determination of dose mean specific energy. In: Proceedings of the Fourth Symposium on Microdosimetry. pp. 832–842. Eur-5122 d-e-f ( 1974). 6 Lindborg, U. L. R. Microdosiinetry measurements in beams of high energy electrons and photons. Doctoral thesis, University of Stockholm, 1975. 7 Eickel, R. and Booz, J. The influence of the counter wall and the counter shape on the spectral energy deposition in small volumes by 60Co gamma-rays and 200 kV X-rays. Radiat. Environ. Biophys. 13, 145– 165 ( 1976). Google Scholar CrossRef Search ADS PubMed 8 Jessen, K. A. Measurements of single event spectra With a wall-less proportional counter In low let radiation fields. Acta Radiol. Ther. Phys. 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Nanodosimetry in a clinical neutron therapy beam using the variance–covariance method and Monte Carlo simulations. Phys. Med. Biol. 52( 16), 4953– 4966 ( 2007). Google Scholar CrossRef Search ADS PubMed 23 Lindborg, L., Hultqvist, M., Carlsson, T. A. and Nikjoo, H. Lineal energy and radiation quality in radiation therapy: model calculations and comparison with experiment. Phys. Med. Biol. 58( 10), 3089– 3105 ( 2013). Google Scholar CrossRef Search ADS PubMed 24 Kumar, R., Kar, D. C., Sharma, S. D. and Mayya, Y. S. Design, implementation and validation of motorized wedge filter for the telecobalt machine (Bhabhatron-II). Phys. Med. 28( 1), 54– 60 ( 2012). Google Scholar CrossRef Search ADS PubMed 25 Fasso, A., Ferrari, A., Sala, P. R. and Ranft, J. FLUKA: status and prospective for hadronic applications. 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Radiation Protection Dosimetry – Oxford University Press

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