Comparative Study on Homogeneous and Inhomogeneous Photon Dose Distribution from a High Dose Rate 192 Ir Brachytherapy Source using MCNP5 S.M. Reda Department of Physics, Faculty of Science, Zagazig University, Zagazig, Egypt E-mail: sonreda@yahoo.com Received: 20/3/2013 Accepted: 20/4/2013 ABSTRACT The purpose of this study is to simulate and analyse the influence of inhomogeneities on the dose rate distribution on brachytherapy and verifying a good tool for dose calculation. The study focused on the evaluation and comparison of dose rate distribution in water phantom using Monte Carlo Code (MCNP5). A simulated High Dose Rate (HDR) 192 Ir brachytherapy source was used. The dose was calculated in a homogenous water phantom at angular cells around the source. For inhomogeneties, cone cells were used to calculate dose distribution around Ir source in water and inhomogeneous medium that includes water, soft tissue, air and skeletal bone. Both the track length energy deposition tally (F6) and pulse height tally (*F8) were used in the isotropic dose calculation. The difference in calculations between the two tallies in the angular anisotropic distribution ranged from 0.0056 to 0.4213% for water and water plus soft tissue phantoms respectively. Impact of soft tissue on dose rate distributions was clear with maximum difference of 5.4%. The maximum differences due to inhomogeneities were 8.157% and 14.779% for F6 and for *F8 respectively. The results indicated that tally F6 is a good tool to calculate the effect of inhomogeneity due to soft tissue, air and bone on brachytherapy in an inhomogeneous medium. Key words: Inhomogeneous photon dose, Dose rate distribution, Brachytherapy, HDR 192 Ir brachytherapy, MCNP-5. INTRODUCTION The advantage of internal radiotherapy (brachytherapy) technique over the external beam radiotherapy (EBRT) is the high conformal delivery of energy to the target tissues and sparing of the healthy tissues. This is due to the inverse square law effect on the dose distribution around the source (1) and due to the low energy photons. Although there are some recent attempts for using deterministic methods, most of the radiation field computations for brachytherapy using Monte Carlo (MC) methods (2). MC has become an accepted dose calculation methodology in brachytherapy treatment planning (3-5). Unlike a deterministic method, which solves the transport equation for the average particle behaviour, Monte Carlo method gives an answer by simulating individual particles, tallying the results and inferring the average behaviour of particles in a physical system from the average behaviour of simulated particles using the central limit theorem (6). 165
MCNP is a Monte Carlo general-purpose N-Particle code that can be used for neutron, photon, electron, or coupled neutron/photon/electron transport within an arbitrary three-dimensional configuration of materials in geometric cells. This code simulates electrons, neutrons and photons in a wide energy range through a stochastic process based on physical and statistical principles of radiation transport and particle interactions (7). Inhomogeneities, such as bone and soft tissues, were not taken into account in clinical usage of brachytherapy. Actually, the presence of less dense dry air and highly dense skeletal bone in the path of radiation, affects the exact dose delivery in brachytherapy (8). There are implant sites where the inhomogeneities may be important, such as implants used to treat head and neck tumors (9). Calculations using Monte Carlo tool reported that large errors inheterogeneities has been validated (10). Inhomogeneities may consist of diverse materials having large differences in physical properties (density, atomic number, etc) in addition to variations of tissue compositions. Over this wide range of energy and materials, the magnitudes of photon interaction coefficients change greatly (11-12). In the clinical environment, inhomogeneities may have an irregular shape, and the surrounding medium is typically bounded by a complex surface. Such circumstances make brachytherapy dose calculation in inhomogeneous media a complicated three-dimensional problem (13-14). The aim of this study is to simulate and analyse the influence of inhomogeneities on the dose rate distribution on brachytherapy and verify a good tool for dose calculation. For this purpose, Monte Carlo Code MCNP-5 was used to simulate the 192 Ir brachytherapy device with typical homogeneous and inhomogeneous (extremely irregular) phantoms. Inhomogeneities effect was performed using inhomogeneous medium that includes water, soft tissue, air and skeletal bone around Ir source. MATERIALS AND METHODS The 192 Ir High Dose Rate (HDR) brachytherapy device used in this study has been designed by Siebert (15) as shown in figure 1.The 192 Ir brachytherapy device is 192 Ir core cylinder with radius 0.0325 cm geometrically centered at the origin. It is capped at both ends by half spheres with the same radii to give a total length of 0.36 cm. The core is encased in a stainless steel cylinder with radius 0.045 cm, and a half sphere cap with radius 0.061 cm at one end. At the other end, a cone is connected to the woven steel cable to give a maximum length of 0.45 cm to the steel encapsulation. The material of the capsule and cable is the same steel but with different densities. A 5 cm-radius sphere filled with pure water (ρ=1.00g cm -3 ) surrounds the device, which also serves as the boundary of the problem. The dose is determined for anisotropic distributions of ten-degree increments from 0 o, which is the axis through the center of the device along the woven steel cable, to 180 o using the above mentioned code as shown in figure 2. Fig. 1. Geometry of 192 Ir brachytherapy device (15). 166
Fig. 2. Side view of anisotropic brachytherapy model. The angular tally cells are wedges of a sphere cut at 10 o increments. The volume of the wedges had to be calculated and the data should be input manually for the tallies in the anisotropic dose determination process. Mass within the cell is calculated using the MCNP program by multiplying the volume of the cell times by the density of the material within the cell (6). MCNP5 code was used to simulate the radiation transport through a stochastic process based on physical and statistical principles of radiation transport and particles interaction. 5x10 8 histories are traced here to perform the simulation for evaluation of the effects of inhomogeneities. For inhomogeneities effect study, the dose was firstly calculated without any inhomogeneity at the irregular conical wedges (volume cells) around the source. The soft tissue (ρ=1.04g cm -3 ) was then positioned among water cells in the water phantom as shown in figure 3a and the dose was then calculated at the same cells around the source. Air (ρ=1.0 x 10-5 g cm -3 ) and skeletal bone (ρ=1.4g cm - 3 ) were positioned among water plus soft tissue cells as shown in figure 3b and the dose was calculated at the same cells around the source. a b Fig. 3a. Side view of anisotropic brachytherapy model. The angular tally cells are water plus soft tissue. Fig. 3b. Side view of anisotropic brachytherapy model. The angular tally cells are water, soft tissue, air and bone. 167
To elucidate the influence of homogeneities and inhomogenities on the dose rate distribution on brachytherapy, either pure water or a combination of water, soft tissue, air and bone phantoms were simulated. Both the track length cell energy deposition tally (F6) and pulse height tally (*F8) were used in the anisotropic dose determinations. F6 is utilized to calculate the deposited energy only by photons. It consists basically of a track length tally multiplied by a reaction rate convolved with an energy-dependent heating function (16). F6 results, which give energy deposition in MeV g -1, were converted to Gray (Gy) with the tally multiplier card (FM card). On the other hand, *F8 tally provides the energy distribution of pulses created in a detector by radiation and is called a pulse height tally. The *F8 tally give results in MeV and were converted into MeV g -1 dividing by the mass within the cell. The resulting values were multiplied by 1.602E-10 to convert the units to J kg -1 (Gy). The results from both F6 and *F8 tallies were compared with relevant published data. RESULTS The angular anisotropic dose distribution normalized to one source particle (photon) for homogeneous water phantom was performed as a quality assurance on the simulation. Comparison between F6 and *F8 tallies results with that reported (17) is shown in figure 4. The percent-difference in the current angular anisotropic distribution between F6 and *F8 results are from 0.0056 to 0.4213%. The percent-differences in the reference angular anisotropic distribution are from 0.0 to 0.28%. The percent-difference between current and reference F6 and *F8 results are from -5.23E-07 to 1.32E- 05%. However, both had significant error associated with the percent-difference. The angular anisotropic dose distribution for inhomogeneous (water plus soft tissue) and (water, soft tissue, air and bone) phantoms were performed. The percent differences between F6 and *F8 tallies values in the angular anisotropic distribution, for water plus soft tissue, are ranged from 0.01 to 0.397%. The angular anisotropic dose distributions for inhomogeneous (water, soft tissue, air and bone) phantom are shown in table 1. The percent differences ranged from -17.8 to 9.54 %. 1.5E-14 1.48E-14 1.46E-14 1.44E-14 1.42E-14 1.38E-14 1.36E-14 1.34E-14 1.32E-14 F6 F6 from reference *F8 *F8 from reference Fig. 4. Comparison between F6 and *F8 angular dose distribution in homogenous water phantom. 168
Table 1: The angular anisotropic dose distributions for inhomogeneous (water, soft tissue, air and bone) phantom. Average angle (degrees) F6 (Gy) Standard Deviation (±) *F8 (Gy) Standard Deviation (±) %Difference between F6 and *F8 5 1.31E-14 3.93E-18 1.31E-14 6.55E-18-0.0177 15 1.45E-14 4.34E-18 1.45E-14 7.25E-18 0.251 25 1.56E-14 3.12E-18 1.46E-14 2.32E-15-6.71 35 1.42E-14 2.84E-18 1.43E-14 5.71E-18 0.303 45 1.44E-14 2.87E-18 1.44E-14 7.20E-18 0.195 55 1.54E-14 3.08E-18 1.55E-14 7.73E-18 0.345 65 1.57E-14 3.14E-18 1.74E-14 2.63E-15 9.54 75 1.46E-14 2.91E-18 1.46E-14 5.85E-18 0.370 85 1.45E-14 2.90E-18 1.45E-14 7.26E-18 0.133 95 1.55E-14 3.10E-18 1.56E-14 7.78E-18 0.272 105 1.57E-14 3.14E-18 1.55E-14 2.43E-15-1.05 115 1.45E-14 2.90E-18 1.46E-14 5.83E-18 0.338 125 1.44E-14 2.89E-18 1.45E-14 7.24E-18 0.252 135 1.54E-14 3.07E-18 1.54E-14 7.71E-18 0.293 145 1.57E-14 3.14E-18 1.33E-14 2.07E-15-17.8 155 2.79E-18 1.40E-14 5.61E-18 0.292 165 1.38E-14 4.13E-18 1.38E-14 6.91E-18 0.321 175 1.39E-14 4.18E-18 1.39E-14 6.97E-18 0.0108 Comparison between F6 and *F8 tallies results for water plus soft tissue phantom and inhomogeneous phantom are shown in figures 5 and 6 respectively. The difference in calculated doses between F6 and *F8 tally results was small as shown in figure 5. On the other hand, there was obvious large difference between the results of the two tallies calculated in an inhomogeneous phantom (figure 6). F6 *F8 1.5E-14 1.3E-14 Fig. 5. Comparison between F6 and *F8 angular dose distribution in inhomogeneous (water and soft tissue) water phantom. 169
2E-14 1.8E-14 F6 *F8 1.2E-14 1E-14 Fig. 6. Comparison between F6 and *F8 Angular dose distribution in inhomogeneous (water, soft tissue, air and bone) water phantom. Comparisons of dose distribution for homogeneous and (water plus soft tissue) phantoms using F6 tally are shown in figure 7. The maximum difference in the calculated doses was found to be 5.395%. By the same pattern, *F8 reported 5.413% as a maximum difference (figure 8). water water + soft tissue 1.5E-14 1.3E-14 Fig. 7. The angular dose distribution by tally F6 (in Gray) for homogeneous and inhomogeneous (water plus soft tissue) water phantom. 170
water watr + soft tissue 1.5E-14 1.3E-14 Fig. 8. The angular dose distribution by Tally *F8, with result modified to Gray, for homogeneous and inhomogeneous (water plus soft tissue) water phantom. As shown in figures 9 and 10, there were large differences when comparing homogeneous and inhomogeneous (water, soft tissue, air and bone) water phantoms using F6 and *F8 tallies. F6 tally results reported 8.157% as a maximum difference and *F8 tally results reported maximum difference of 14.779% as shown in table 2. 1.7E-14 water water, soft tissue, air and bone 1.5E-14 1.3E-14 Fig. 9. The angular dose distribution by tally F6, with result in gray, for homogeneous and inhomogeneous (water, soft tissue, air and bone) water phantom. 171
2E-14 water water, soft tissue, air and bone 1.8E-14 1.2E-14 Fig.10. the angular dose distribution by tally F8, with result modified to gray, for homogeneous and inhomogeneous (water, soft tissue, air and bone) water phantom. Table 2: The comparison between homogeneous and inhomogeneous (water, soft tissue, air and bone) angular anisotropic dose distributions. Averag F6 (Gy) *F8 (Gy) e angle Cell Homogene Inhomogene %Differe Homogene Inhomogene %Differe (degree Materi ous ous nce ous ous nce s) al 5 Water 1.33E-14 1.31E-14-1.43593 1.33E-14 1.31E-14-1.82304 15 Soft tissue 1.39E-14 1.45E-14 3.764504 1.39E-14 1.45E-14-1.40054 25 Air 1.43E-14 1.56E-14 8.15697 1.44E-14 1.46E-14 1.45879 35 Bone 1.45E-14 1.42E-14-2.20146 1.46E-14 1.43E-14-7.78412 45 Water 1.46E-14 1.44E-14-1.87842 1.47E-14 1.44E-14-2.10861 Soft 55 tissue 1.47E-14 1.54E-14 4.530551 1.47E-14 1.55E-14-0.88454 65 Air 1.47E-14 1.57E-14 6.20798 1.48E-14 1.74E-14 14.77939 75 Bone 1.48E-14 1.46E-14-1.32331 1.48E-14 1.46E-14-6.945 85 Water 1.48E-14 1.45E-14-1.88738 1.48E-14 1.45E-14-2.03349 95 Soft tissue 1.48E-14 1.55E-14 4.779824 1.48E-14 1.56E-14-0.635 105 Air 1.48E-14 1.57E-14 6.051075 1.48E-14 1.55E-14 4.526021 115 Bone 1.47E-14 1.45E-14-1.46276 1.48E-14 1.46E-14-7.11155 125 Water 1.47E-14 1.44E-14-1.74716 1.47E-14 1.45E-14-1.96189 135 Soft tissue 1.47E-14 1.54E-14 4.673755 1.47E-14 1.54E-14-0.49166 145 Air 1.45E-14 1.57E-14 7.58222 1.46E-14 1.33E-14-9.51789 155 Bone 1.43E-14-2.56207 1.44E-14-8.15674 165 Water 1.38E-14-1.33492 1.38E-14-1.50002 175 Soft tissue 1.34E-14 1.39E-14 3.888749 1.34E-14 1.39E-14-1.30563 172
DISCUSSION In the present work the MCNP5 code is used to study the dose distribution in both homogeneous and inhomogeneous phantoms during brachytherapy. The results obtained from the input files indicated that the geometry and materials were correctly modeled. Energy deposition over a cell was calculated using F6 tally while * F8 tally was used to calculate the pulse height. The tally volumes were rather complicated and consisted of irregular conical wedges formed by intersecting cones, a spherical surface and a plane just touching the outside longitudinal edge of the source. Tallies extended from the source outside edge to a 5 cm radius and the reported dose was thus a volumeaveraged result integrated over the whole tally volume. In pure water phantom, a good agreement was found between the calculated F6 and *F8 results with the corresponding F6 and *F8 results published (17). It is clear that the dose distribution follows the same trend in both water and soft tissue, with slight difference of about 5.4% (it may be due to the boundary conditions between soft tissue and water). This was expected as the physical densities of water and soft tissue are nearly equal (18). In air, the dose was increased due to its low physical density and decreased attenuation of radiation (18-20). On the other hand, bone shows a clear dose inhomogeneity which may be attributed to the presence of high Z elements in bone tissue (21-22) in addition to the large physical density and electron density values of bone compared to the constitution of other tissues (18). The dose was generally decreased in bone which may be due to increased attenuation of radiation (20). These results are in agreement with literatures data (1, 8). In order to verify the best tool for studying the impact of inhomogenity on brachytherapy dose distribution, the dose was compared using F6 and *F8 tallies. Low differences and low statistical error were recorded between the two used tallies for pure water and water plus soft tissue phantoms. For tally F6 dose calculation, the impact of inhomogeneities (soft tissue, air and bone) on dose rate distribution was very clear with a maximum difference of 8.157% from that of homogeneous phantom. For tally F8 dose calculation, the difference in dose was large (14.779%). However, the *F8 statistical uncertainty and standard deviation were large, especially in air cells, angle 25, 65 and 145, that may be due to the very low air density. The difference between F6 and *F8 for inhomogeneous phantom containing bone and air probably comes from the large uncertainty (15%) in the *F8 value in air cells. Therefore, tally F6 seems to be a good tool to calculate the effect of inhomogeneity on brachytherapy dose distribution. However, there were some disagreements with the result provided (17) about homogeneous water phantom. Author (17) mentioned that the precision of the F6 tally was found to be smaller by about a half an order of magnitude than the *F8 tally. CONCLUSIONS The impact of inhomogeneity on brachytherapy dose distribution caused by different tissues has been calculated. It is clear that different tissues attenuate radiation relayed to different composition. It was found that some difference in dose distribution was found between water and soft tissue in spite of the nearly equal densities. This may give an indication that the boundary conditions have an effect on dose distribution in the real human body. Bone and air tissues showed a clear inhomogeneity values. It is also observed that the tally F6 is a good tool to calculate the effect of inhomogeneity on brachytherapy due to air and bone. 173
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