Determination of the tissue attenuation factor along two major axes of a high dose rate HDR 192 Ir source

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1 Determination of the tissue attenuation factor along two major axes of a high dose rate HDR 192 Ir source Sang Hyun Cho a) Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center, Houston, Texas Renate Muller-Runkel Radiation Oncology Center, St. Margaret Mercy Healthcare Centers, Hammond, Indiana William F. Hanson Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center, Houston, Texas Received 9 September 1998; accepted for publication 20 May 1999 Quantitative information on photon scattering around brachytherapy sources is needed to develop dose calculation formalisms capable of predicting dosimetric parameters with minimal empiricism. Photon absorption and scatter around brachytherapy sources can be characterized using the tissue attenuation factor, defined as the ratio of dose in water to water kerma in free space. In this study, the tissue attenuation factor along two major axes of a high dose rate HDR 192 Ir source was determined by TLD measurements and MCNP Monte Carlo calculations. A calculational method is also suggested to derive the tissue attenuation factor along the longitudinal source axis from the factor along the transverse axis, using published anisotropy data as input. TLD and Monte Carlo results agreed with each other for both source axes within the statistical uncertainty 5% of Monte Carlo calculations. Comparison with published data, available only for the transverse source axis, also showed good agreement within 5%. The shape and magnitude of the tissue attenuation factor are found to be remarkably different between the two axes. The tissue attenuation factor reaches a maximum value of about 1.4 at 8 cm from the source along the longitudinal source axis, while a maximum value of about 1.04 occurs at 3 4 cm from the source along the transverse axis. The calculated tissue attenuation factor along the longitudinal source axis generally reproduced the TLD and Monte Carlo results within 5% at most radial distances American Association of Physicists in Medicine. S Key words: Tissue attenuation factor, HDR 192 Ir source, Monte Carlo calculation, TLD I. INTRODUCTION The tissue attenuation factor, also known as the dose ratio function, can be defined as the ratio of dose in water to water kerma in air or free space at the same point in space. 1 Accordingly, it can directly yield the dose in water when multiplied by the water kerma in air. It is also a useful physical quantity that can explicitly show the effects of photon absorption and scatter around brachytherapy sources. For cylindrical brachytherapy sources, it is expected to be dependent on angle, partially because the photon energy spectrum may vary with angle as a result of oblique filtration and source self-absorption. Considering the definition of the tissue attenuation factor, characterizing the angular dependence of the tissue attenuation factor could be a more direct way to calculate the anisotropic dose distribution than using the anisotropy function in a particular medium e.g., water and other dosimetric quantities. However, it is more cumbersome than directly determining the anisotropy function in a medium and the applicability of two dimensional tissue attenuation factor may be very limited within the scope of currently recommended formalisms e.g., AAPM TG-43 formalism 1. Therefore, the tissue attenuation factor has typically been determined around point sources and along the transverse axis of cylindrical sources. On the other hand, better insight into photon absorption and scatter around the source may be obtained from investigating the angular dependence of the tissue attenuation factor. For example, the contribution of primary and scattered photons to radiation dose in water may be analyzed from the tissue attenuation factor if we assume the absorption and scattering in air are negligible. This could be potentially helpful for developing future brachytherapy dose calculation formalisms requiring less empirical data than required by the AAPM TG-43 formalism. 1 In fact, some recent studies 2,3,4 suggest that accurate non-monte Carlo formalisms for low energy photon sources may be developed from the separation of primary and scattered photons in terms of their contribution to radiation dose. Therefore, investigation of the angular dependence of the tissue attenuation factor, at least at both extremes i.e., longitudinal and transverse axes of a filtered cylindrical source, is worth conducting in spite of its limited impact on currently recommended formalism. Furthermore, the two dimensional tissue attenuation factor could serve as 1492 Med. Phys. 26 8, August /99/26 8 /1492/6/$ Am. Assoc. Phys. Med. 1492

2 1493 Cho, Muller-Runkel. and Hanson: Determination of the tissue attenuation 1493 good bench mark data for independent validation of new formalisms. The primary goal of this study was to quantitatively show that photon absorption and scatter are significantly different along the two major axes of a HDR 192 Ir source. For many years, investigators have studied the tissue attenuation factor along the transverse axis of a HDR 192 Ir source, 5 which is an essential input parameter to most calculational formalisms. According to our current knowledge, however, no study has been conducted to determine the tissue attenuation factor along the longitudinal axis. In our work, the tissue attenuation factor along the transverse and longitudinal axes of a HDR 192 Ir source was determined by Monte Carlo calculations and TLD measurements. Also, it was calculated by a simple formalism, based on the AAPM TG-43 protocol, 1 using published anisotropy data 6 as input. II. METHODS AND MATERIALS A. Definitions 1. Tissue attenuation factor The tissue attenuation factor can be determined from measurements or Monte Carlo calculations by taking the ratio of the dose rate in water to water kerma rate in air or free space. For an isotropic point source, it can be defined as T r Ḋ water r Ḋ air r, 1 where Ḋ water and Ḋ air are the dose rates in water and in air, respectively; and r is the distance from the radiation source. Note Ḋ air is an approximate representation of water kerma in air assuming charged particle equilibrium. For a cylindrical source, the two dimensional tissue attenuation factor at radial distance r and angle, T(r, ) may be defined as T r, Ḋ water r, Ḋ air r,, 2 where r is measured from the center of the active source core; and is defined as 0 along the longitudinal source axis and 90 along the transverse source axis. Using the TG-43 formalism, 1 T(r, ) can be related to the anisotropy function, F(r, ), by the following expression: T r, Ḋ water r,90 F water r, T r,90 F water r, Ḋ air r,90 F air r, F air r,, 3 where F water and F air are the anisotropy functions in water and in air, respectively. 2. Anisotropy function The anisotropy function at (r, ) is generally defined as 1 F r, Ḋ r, G r, 0 Ḋ r, 0 G r,, 4 where 0 is the angle corresponding to the reference point i.e., 90 in this study and G is the geometry factor e.g., FIG. 1. Source model for a Nucletron HDR 192 Ir source used in the Monte Carlo calculations a cross-sectional view along the longitudinal source axis. This figure is not drawn to scale. 1/r 2 for point source approximation. For spatially extended sources, the geometry factor accounts for the variation of relative dose due to the spatial distribution of radioactivity within the source, ignoring photon absorption and scattering in the source structure. 1 More details about the geometry factor can be found in the TG-43 report. 1 B. Description of source A HDR 192 Ir source Nucletron Corporation, Columbia, Maryland, model year 1991 served as the basis for calculations and measurements. The source is encapsulated in AISI 316L stainless steel and welded to a steel cable. A more detailed description of the source is given by Williamson and Li. 7 For the Monte Carlo calculations, it was modeled as a seed source composed of two concentric cylinders sandwiched between a flat steel top and bottom Fig. 1. The rounded source tip, as well as the presence of the stainless steel cable connected to the source bottom, was ignored. The effect of this simplification on the results was assumed to be minimal i.e., less than the statistical uncertainty of the Monte Carlo calculations because any possible effect can approximately be canceled out by taking the ratio between D water and D air obtained at the same point in space. Furthermore, a previous study, 8 which dealt with the same source model used here, estimated that the simplification in modeling the source tip resulted in negligible error for the detector sites considered in this work i.e., along the longitudinal and transverse axes. The composition of the stainless steel capsule was chosen to be the same as that used by Williamson and Li, 7 i.e., AISI 304 2% Mn, 1% Si, 19% Cr, 10% Ni, and 68% Fe by weight, and a physical density of 8.02 g cm 3 ). The source core was assumed to consist of pure iridium metal. C. Monte Carlo calculations The code MCNP Monte Carlo N-Particle version 4A, 9 which was developed at Los Alamos National Laboratory and released in July 1990, was used for the Monte Carlo calculations. MCNP is a general purpose Monte Carlo code for performing the transport of neutrons, photons, and/or electrons in various geometries. MCNP offers many convenient features including a powerful geometry modeling tool and various tallies related to particle current, particle flux, and energy deposition. Unlike the EGS4 Electron Gamma Shower version 4 code, 10 simulations are based on a set of few input statements and programming is not needed. The

3 1494 Cho, Muller-Runkel. and Hanson: Determination of the tissue attenuation 1494 TABLE I. Photon energy spectrum of 192 Ir from Radioactive Decay Tables. a Energy kev Fractional intensity/disintegration a Reference FIG. 2. Schematic drawing of experimental setup. This figure is not drawn to scale. photon and electron regimes are from 1 kev to 1000 MeV. The photon interaction data covering the materials and energies used in this work are based on the tables from Hubbell et al. 11 Photon interactions simulated are Compton scattering, coherent scattering, photoelectric absorption, and pair production. Electron transport is simulated using the following physical processes: a collision stopping power, b multiple scattering, c energy straggling, d bremsstrahlung production, and e knock-on electrons. More details about the MCNP code system can be found elsewhere. 9 The 192 Ir photon spectrum used for MCNP calculations included 26 different energies from Radioactive Decay Tables 12 as presented in Table I. Each photon history originated at a random position and direction inside the source core. For the determination of the tissue attenuation factor, energy deposition along both axes of the source was scored by a series of water-filled spherical volumes centered at r 1 13 cm in air and in water. For in-air simulation, calculations were performed for each radial distance at a time to avoid the interdetector attenuation. The simulated water phantom was a sphere of radius 30 cm, adequate to provide full-scatter condition at all detector sites. The radii of the water-filled spherical volumes were 0.05 cm both in air and in water. The radius i.e., 0.05 cm was chosen, after some pilot calculations, in such a way that each detector could provide a good spatial resolution, especially along the longitudinal source axis, while maintaining a reasonable statistical uncertainty 5% in the results in spite of a small scoring volume. Only the photon transport mode was used for this simulation assuming charged particle equilibrium at all detector sites. As reported previously, 13 the error from this simplification was found to be insignificant compared to the statistical error 5% of the simulation. Each photon history was traced down to 1 kev, a default cutoff energy set by MCNP. After 25 million histories, the statistical uncertainty in the results was about 4% obtained for in-water simulation, and about 5% for in-air simulation. D. TLD measurements TLD rods LiF, 1 mm diam, 6 mm long of similar sensitivity 3% were placed at distances between 1 and 13 cm from the source center along both, transverse and longitudinal source axes Fig. 2. The transverse bisector of the TLD rods lay in the plane containing the source axes. Irradiation was performed in polystyrene and air. Polystyrene was chosen for the measurements because a previous study 14 showed the equivalence between polystyrene and water for measurements with 192 Ir sources. To provide full scatter condition in polystyrene, the milled phantom was surrounded with additional polystyrene and solid water so that each measurement point had at least 10 cm of scatter material on all sides. For in-air measurements, a 7.5 cm thick styrofoam block served as phantom. To minimize backscatter from nearby hard surfaces during in-air measurements, the phantom was placed on the tennis racket of an accelerator table top which had been fully extended, turned 90 to the table base, and was raised 1 m above the floor. The location of the HDR source center was verified radiographically before each measurement series. The estimated uncertainty in source position and TLD placement was less than 1 mm. TLD rods were exposed to doses ranging from 10 cgy for the larger distances, to 300 cgy for distances close to the source. Within this dose range, the variation in TLD response is small 5%, 6 the source dwell time was at least 10 times larger than the source travel time, and the TLD signal exceeded the background noise of the reading instrument by at least a factor of 40. One day after exposure, the TLDs were read on a Harshaw 4000 TLD reader, and then annealed at 400 C for 1 h. Further details about TLD processing have been reported previously. 6

4 1495 Cho, Muller-Runkel. and Hanson: Determination of the tissue attenuation 1495 According to Meigooni et al., 15 the TLD signal may be converted to absorbed dose-rate in water in the surrounding medium, as TL av Ḋ r, 5 ts k d t E r F lin where TL av average TLD signal, corrected for background and individual TLD sensitivity, t exposure time, S k air kerma strength of the source cgy m 2 h 1 at start of exposure, d(t) (1 e t )/ t corrects for source decay during exposure, TLD sensitivity ncoul/cgy to a reference energy, E(r) correction to scale TLD response from reference energy to source energy, F lin correction for nonlinearity in TLD response as a function of dose. The tissue attenuation factor is then obtained as the ratio, Ḋ(r) poly /Ḋ(r) air, for each axis. To minimize the need for correction factors, and avoid inter-rod attenuation effects, separate measurements were made for each point (r, ): TLDs from one batch 3% sensitivity variation were exposed on the same day within 5 h for identical times in air and in polystyrene, and these exposures were repeated as often as the number of TLDs in the respective batch allowed. The correction factors to the average TLD response in the denominator of Eq. 5 are therefore identical, or almost identical, for each exposure series in air and in polystyrene, and the ratio becomes Ḋ r poly /Ḋ r air TL av poly /TL av air E r air /E r poly F lin air /F lin poly. 6 Based on work by Karaiskos et al. 16 who used weighted Monte Carlo calculated photon spectra for the Nucletron HDR source to evaluate the variation in energy dependent TLD response as a function of distance in polystyrene, we estimate that E(r) air /E(r) poly 3%for distances up to 13 cm. Thomason and Higgins 17 reported variations of 1% up to 10 cm distance in water, whereas Meigooni et al. 18 reported as much as 8.5% increase in TLD response over this distance in polystyrene. From previously published data, 6 we estimate that F lin air /F lin poly 1%. Since our estimates of both corrections are smaller than the statistical uncertainty, no correction was applied for variation in TLD response with dose or photon energy. This is further justified by the unchanged agreement between Monte Carlo calculations and TLD measurements over the entire distance range. The influence of the finite physical dimension of the TLD was also ignored. 6 The tissue attenuation factor reported here, is the uncorrected ratio of the TLD signal in polystyrene to that in air. All data presented are the average of at least five measurements. III. RESULTS In Figs. 3 and 4, the tissue attenuation factors along the transverse and longitudinal axes of a HDR 192 Ir source are plotted against distance from the source center. As seen in Fig. 3, our TLD measurements and Monte Carlo calculations FIG. 3. The tissue attenuation factor along the transverse source axis, MCNP Monte Carlo calculations;, TLD rod measurements,, Park and Almond Ref. 5, solid curve, Meisberger et al. Ref. 19. Note error bars in Figs. 3 and 4 represent the minimum and maximum statistical errors associated with TLD data, respectively. from this study agree well with published data from the literature. This demonstrates that the MCNP 4A code can accurately predict the dosimetric parameters around a HDR 192 Ir source. According to these results, the Meisberger polynomial 19 used for low dose rate 192 Ir seed sources can be used as a fair representation within 4% of the tissue attenuation factor along the transverse axis of a HDR 192 Ir source, as Park and Almond 5 previously argued. However, the tissue attenuation factor along the longitudinal axis as seen in Fig. 4 is remarkably different from that along the transverse axis. Monte Carlo results are in agreement with the measured data within 5%. The coefficients of the third order polynomial fit to the combined TLD and MCNP data shown in Fig. 4 are given in Table II. The tissue attenuation factor along the longitudinal axis reaches the maximum value of about 1.4 at 8 cm from the source while, along the transverse axis, the maximum value of 1.04 occurs at 3 4 cm from the source. This suggests that dose due to scattered mostly in-scattered photons increases with distance up to 8 cm from the source along the longitudinal axis and decreases thereafter. On the other hand, the primary photon dose is significantly reduced along this axis, mostly due to the following factors: source self-absorption inside the source and narrower solid angles seen by detectors compared to those along the transverse axis. Therefore, compensation between primary and scattered photons does not occur over clinically important distances 10 cm along this axis except at radial distances near to the source. Note, here, primary and scattered mean effective primary and effective scattered, respectively, as explained in Kirov and Williamson 3 where they defined all photons coming out of the source capsule including scattered photons generated inside it as effective primary, and all photons that are pro-

5 1496 Cho, Muller-Runkel. and Hanson: Determination of the tissue attenuation 1496 FIG. 4. The tissue attenuation factor along the longitudinal source axis, MCNP Monte Carlo calculations;, TLD rod measurements;, calculations using Eq. 3 and TLD data from Muller Runkel and Cho Ref. 6. Note the solid curve represents the third order polynomial fit to the combined TLD and MCNP data. duced in the medium surrounding the capsule as effective scattered. Included in Fig. 4 is also the tissue attenuation factor along the longitudinal source axis calculated using Eq. 3. Input data were derived from the respective linear fit values from measured anisotropy data 6 in air and in polystyrene, and the tissue attenuation factor along the transverse axis reported in this study TLD data. The fits for anisotropy data 6 were given by F water r, r for 1 r 13 cm, 7 F air r,0 constant Calculation generally reproduces TLD and MCNP data from this study within 5% at most radial distances although it results in a less bent curve and a lower maximum value than either measured data or Monte Carlo calculations. Some discrepancies are attributed to the inherent uncertainty in input data 6 e.g., 7% at 1 cm and data fitting correlation coefficient R 0.95). TABLE II. Coefficients of the third order polynomial fit for tissue attenuation factor along the longitudinal source axis, T(r) C 0 C 1 r C 2 r 2 C 3 r 3. Coefficient TLD and MCNP C C C C IV. DISCUSSION In this study, we present the tissue attenuation factor along the two major axes of a HDR 192 Ir source. As seen above, they are remarkably different from each other in terms of their shape and magnitude. This difference is mainly due to scatter, as can be seen from Eq. 3 ; the tissue attenuation factor on the transverse axis, T(r,90 ), is modulated on the longitudinal axis by the ratio of anisotropy factors in water over air, F water (r, )/F air (r, ).While the anisotropy in air does not change with distance up to r 10 cm, as we have shown previously, 6 the anisotropy in water becomes less pronounced with distance from the source, due to scatter. 6 The ratio, F water (r, )/F air (r, ), therefore increases significantly with distance. This leads to a shift in the maximum towards larger distances and an increase in its height. As demonstrated so far, photon absorption and scatter around HDR 192 Ir source may be analyzed at several other angles e.g., 15, 30, and 45 using published in-air and inpolystyrene anisotropy data. 6 The AAPM TG-43 formalism 1 can generally result in more accurate dose estimation around low energy brachytherapy sources when input dosimetric parameters are obtained from measurements and/or Monte Carlo calculations. However, since the TG-43 formalism 1 is unable to predict dosimetric parameters themselves, it would not be suitable to handle situations such as dimension change in existing sources, introduction of new sources, etc. unless new input data are provided. Therefore, it may be desirable to develop formalisms that are capable of predicting dosimetric parameters with minimal empiricism, compared to TG-43 type formalisms. Recent studies 2,3,4 demonstrated that an accurate brachytherapy dose calculation formalism requiring minimal empiricism might be developed by separating the contribution of primary and scattered photons to radiation dose. Clearly, a good understanding of photon absorption and scattering property around the source will be essential to further refine such an algorithm. In this regard, the data and calculational method presented in this study could be valuable for developing and independently testing a new algorithm. In principle, any new formalism based on the separation of primary and scattered photon components is expected to be able to predict the tissue attenuation factor along the longitudinal source axis presented in this study. Therefore, we suggest that some preliminary testing of new formalisms could be

6 1497 Cho, Muller-Runkel. and Hanson: Determination of the tissue attenuation 1497 performed using the data provided in this study at least at the extreme, and possibly at other intermediate polar angles using Eq. 3 and published anisotropy data, 6 rather than performing extensive measurements or Monte Carlo calculations. We may infer from the results of this study that the energy spectra along both source axes are significantly different, although quantitative information is unavailable from our data. Further analysis of energy spectra may be beneficial not only for the development of new algorithms but also for the determination of absolute dose from measurements with energy-dependent detectors such as TLD. Accurate information about energy spectra along both source axes might provide upper and lower bounds for possible error in determining absolute dose from TLD readings. Especially, it is worth noting that there is no consensus at the present time about energy-dependent correction factor for TLD measurements with 192 Ir sources due to lack of information. 20,21 V. CONCLUSIONS In this study, the tissue attenuation factor of a HDR 192 Ir source was determined along the transverse and longitudinal source axes by TLD measurements and MCNP Monte Carlo calculations. Also, the tissue attenuation factor along the longitudinal source axis was calculated by the method suggested in this study in which published anisotropy data were used as input. Measured and Monte Carlo data agreed with each other for both axes within the statistical and experimental uncertainty 5%, which demonstrates that the MCNP 4A code can accurately predict the dosimetric parameters around a HDR 192 Ir source. The tissue attenuation factor calculated from published anisotropy data generally reproduced the TLD and Monte Carlo results within 5% at most radial distances. The shape and magnitude of the tissue attenuation factor are found to be remarkably different along the two axes. The tissue attenuation factor reaches a maximum value of about 1.4 at 8 cm from the source along the longitudinal source axis while the maximum value of about 1.04 occurs at 3 4 cm from the source along the transverse source axis. The results of this study also suggest that considerable change in the energy spectrum with angle may occur depending on the degree of source self-absorption and filtration. The data and calculation method presented in this study could be used for developing and independently testing new brachytherapy dose calculation formalisms based on the separation of primary and scattered photon components in terms of their respective contribution to radiation dose. ACKNOWLEDGMENT This investigation was supported in part by Public Health Service Grant No. CA awarded by the National Cancer Institute, Department of Health and Human Services. a Author to whom all correspondence should be addressed; electronic mail: scho@mdanderson.org 1 R. Nath, L. L. Anderson, G. Luxton, K. A. Weaver, J. F. Williamson, and A. S. Meigooni, Dosimetry of interstitial brachytherapy sources: Recommendation of the AAPM Radiation Therapy Committee Task Group No. 43, Med. Phys. 22, J. F. Williamson, The Sievert Integral revisited: Evaluation and extension to 125 I, 169 Yb, and 192 Ir brachytherapy sources, Int. J. Radiat. Oncol., Biol., Phys. 36, A. S. Kirov and J. F. Williamson, Two-dimensional scatter integration method for brachytherapy dose calculations in 3D geometry, Phys. Med. Biol. 42, G. M. Daskalov, A. S. Kirov, and J. F. Williamson, Analytical approach to heterogeneity correction factor calculation for brachytherapy, Med. Phys. 25, H. C. Park and P. R. 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