BRACHYTHERAPY SOURCE USING THE EGSNRC MONTE CARLO CODE

Transcription

1 Bangladesh Journal of Physics, 12, 61-75, 2012 DOSIMETRIC STUDIES OF THE 192 IR-MICROSELECTRON V2 HDR BRACHYTHERAPY SOURCE USING THE EGSNRC MONTE CARLO CODE L. HONG 1, G. A. ZAKARIA 1,2,* AND G. H. HARTMANN 3 1 Biomedical Engineering Master Studies, Department of Electrical, Mechanical and Industrial Engineering, Anhalt University of Applied Sciences, Koethen, Germany 2 Department of Medical Radiation Physics, Gummersbach Hospital, Academic Teaching Hospital of the University of Cologne, Gummersbach, Germany 3 Dept. of Medical Physics in Radiotherapy, German Cancer Research Center, Heidelberg, Germany Received on , Accepted for Publication on ABSTRACT The purpose of this study is to show that more realistic dosimetric parameters of the 192 Ir microselectron v2 HDR brachytherapy source can be obtained from a Monte Carlo (MC) simulation of absorbed dose depositions. The code system EGSnrc has been used to calculate the air-kerma strength, a two-dimensional dose distribution surrounding the source and the dosimetrical parameters according to the updated TG-43 U1 formalism of the AAPM. Results were compared with available data. The simulation of energy deposition also includes the contribution from the 192 Ir beta decay. A description of the materials and geometry taken for the source and for the 192 Ir nuclide (including photon and beta spectrum) is provided. The obtained value of the air-kerma strength of this source well agrees with that of other MC calculations. The two dimensional dose distribution is also very similar to that of existing data for all distances larger than 0.2 cm. However, very close to the source (i.e. for distances less than 0.2 cm), differences are apparent. Differences can be attributed to both, the dose contribution of emitted beta particles and the nonequilibrium effect of the secondary electrons. Therefore, if it is important to know the dose at such small distances, the data of a more realistic MC simulation based on absorbed dose depositions should be used. This recommendation would apply to even larger distances for sources that have higher photon energies. Keywords: Electron transport, Brachytherapy; 192 Ir source, Monte Carlo simulation, AAPM TG 43 protocol 1. INTRODUCTION Monte Carlo (MC) based calculations have been acknowledged as a valuable tool to provide dosimetrical data for HDR sources used in brachytherapy [1-3]. In order to speed up the calculation time, collision kerma is commonly used to approximate the absorbed dose and derived dose parameters. Thus effects of the electron nonequilibrium and beta particle contribution are not taken into account. This applies, for example, also to the recent "Carleton Laboratory for Radiotherapy Physics (CLRP) Database" of TG-43 brachytherapy dosimetry parameters provided by Taylor and Rogers [4]. However, MC codes are now generally well available that offer an improved tracking of the history of secondary electrons and hence a calculation of the deposited energy by electrons in a volume of interest. Although an absorbed dose calculation is certainly more time consuming compared to a kerma calculation if the same level of uncertainty is aimed at, Corresponding Author: ga.zakaria@arcor.de

2 62 L. HONG, G. A. ZAKARIA AND G. H. HARTMANN it appears worth to investigate whether significant changes of the dose rate would result from the transition from kerma calculation to dose calculation. Such changes are expected to occur in particular in the vicinity of the source. Interest in accurate dose distributions in the vicinity of the source (also called near-source-region) has increased in recent years due to intravascular brachytherapy applications. The AAPM Task Group 60 has issued a report on this particular topic [5]. Baltas et al. [6] have studied the nearsource-region by an own MC code and concluded that a potential contribution of beta particles on dose to tissues in close proximity dosimetry for intravascular brachytherapy should not be ignored. Wang and Li [7] have also performed MC based dose calculations in the near-source-region using the code DOSCGC which is a modification of the EGS4 code. They investigated particularly the influence of the nonequilibrium of the secondary electrons. At distances below 2 mm, they obtained significant changes of the dose rate if both effects, the dose contribution of emitted beta particles and the nonequilibrium effect, are taken into account. However, collision kerma scoring remains an accurate approximation of absorbed dose at the distances beyond 2 mm. A similar study predominantly applied to spherical sources was performed by Ballester et al. using the MC codes GEANT4 and PENELOPE [8]. They also concluded that electronic disequilibrium plays an important role in the vicinity of high-energy brachytherapy sources such as 60 Co and 192 Ir and the dose may not be approximated by collision kerma below 2 mm distances. The codes from the EGS4 family are general purpose Monte Carlo radiation transport package, with special emphasis on transport involving photons and electrons for radiological questions. They are now well available and therefore widely used. In particular the new EGSnrc codes have been improved such that they are capable for a more accurate simulation of electron transport history [9]. The cylinder symmetrical standard codes FLURZnrc and DOSRZnrc were therefore used to perform a comparison between kerma calculations and absorbed dose calculation. In this paper, we present calculation results of the photon spectrum in air of the 192 Ir microselectron v2 HDR brachytherapy source and its dose distribution in water surrounding the source. The obtained results are compared with the existing fluence data from Borg and Rogers [10], the dosimetrical data published by Daskalov [1] and with that of the database provided by Taylor and Rogers [4]. In contrast to these authors and in line with Wang and Li [7] as well as Ballester [8], electron transport is performed for this study including the 0.2% contribution to air-kerma strength from bremsstrahlung photons originating in the source and the dose contribution from the beta spectrum of 192 Ir. Dosimetry parameters are given to distances down to less than 0.2 cm from the source encapsulation. The data are presented twofold: as a 2-dimensional lookup table of the dose rate per source strength and in terms of the dosimetric parameters as recommended by the AAPM Radiation Therapy Committee Task Group 43 [11, 12]. 2. MATERIALS AND METHOD Geometry of the radioactive source The same cylindrical geometry as used in the Monte Carlo study of Borg and Rogers [10] was used for the internal construction and dimensions of the microselectron v2 HDR 192 Ir source (Nucletron B.V., The Netherlands, model No , called the new design ). Fig.1a illustrates the geometry of the real microselectron v2 HDR 192 Ir source, whereas the model used in our

3 DOSIMETRIC STUDIES OF THE 192 IR- MICROSELECTRON V2 HDR BRACHYTHERAPY SOURCE 63 Monte Carlo calculations is shown in Fig.1b. Although the design as shown in Fig. 1b is only an approximation neglecting the real rounded edge shape as shown in Fig. 1a, it was used for two reasons: (a) The user-codes FLURZnrc and DOSRZnrc can calculate fluence and absorbed dose for cylindrical geometries only. (b) We are in particular interested in differences between Kerma and absorbed dose as consequence of the codes and not as a consequence of how well the source is modeled. The source consists of a pure iridium metal core cylinder with rounded edges (length 3.6 mm and diameter 0.65 mm). The radioactivity within the source is assumed to be uniformly distributed. Around this active core is a stainless steel (AISI 316L) encapsulation with a total length of 4.5 mm and an outer diameter of 0.9 mm and connected to a 2.0 mm long flexible woven steel cable with a diameter of 0.7 mm. The real distal capsule tip has rounded edges with a curvature radius of 0.4 mm. The half-life of 192 Ir is days, and on average one decay will result in the emission of 1 electron and photons. The relation between the source activity, A, and the number of photons emitted per second, N photon N photon, is then calculated from: A ( %) [photons s -1 ] (1) where the uncertainty of 0.3% is the estimate from the work of Duchemin and Coursol for the 192 Ir spectrum [13]. The materials used in the Monte Carlo calculations and their compositions, densities and effective atomic number are identical to that of Borg and Rogers [10]. Fig. 1. Mechanical design of microselectron-hdr 192 Ir source. (a) the geometry of the real source ; (b) the model used in the Monte Carlo calculations. All dimensions are in cm (convenient for geometry parameter inputs in EGSnrc Monte Carlo codes system). Monte Carlo calculations We used the FLURZnrc code to calculate the air-kerma strength per activity and the DOSRZnrc code to calculate dose-rate and its distribution in water in terms of cgy h -1 U -1 [14].

4 64 L. HONG, G. A. ZAKARIA AND G. H. HARTMANN For the transport of photons, photoelectric absorption, fluorescent emission of K-shell and L-shell characteristic x-ray, as well as pair production, coherent (Rayleigh) and incoherent (bound Compton) scattering have been simulated. For the transport of electron, Positron annihilation in flight and at rest, Bremsstrahlung production, Multiple scattering, as well as Møller (e e ) and Bhabha(e + e ) scattering have been taken into account. The photon cross sections used in the simulations are taken from the PEGS4 cross section library, and mass-energy absorption coefficients are from NIST database [15, 16]. The energy spectra used for the simulation of the 192 Ir source consist of the bare photon spectrum (average energy ~370 kev). The beta spectrum of 192 Ir (average energy ~181 kev) was taken from Duchemin and Coursol [13]. It is shown in Figure 2 for the three major (95.35%) transitions contributing to the spectrum. The last few percent of the transitions are particles with energy less than 82 kev. Fig. 2. The spectrum for 192 Ir nuclide used as input spectrum for the Monte Carlo calculations. Calculation of fluence spectrum In order to check the calculation, the fluence differential in energy was first calculated in vacuum at a distance of 5 cm from the source center in the transverse axis direction at 5 kev bins and compared with that obtained by Borg and Rogers [10]. The spectrum in units of fluence per MeV was normalized to that per decay. The scoring region for the fluence in the transverse axis direction was a 0.01 cm thick air cylinder for the surface and 1 cm distance, and a 0.05 cm thick air cylinder for the greater distances; its length was 0.02 cm centered at the middle of the active length. The main parameters used for the FLURZnrc code: Number of histories = 10 9, ECUT = 2.0 MeV, PCUT = MeV, ESTEPE = Calculation of source strength Using again the code FLURZnrc, the source strength per activity, Sk / A, in terms of U Bq -1 was calculated at the distance of 100 cm from the center of the source at the transverse axis. Calculation was based on the obtained fluence differential in energy per initial particle in 5 kev bins and the mass energy-absorption coefficients for dry air in the middle of each bin, using: E max 10 9 μen ( Ei ) Sk / A ( Ei ) Ei ( ) ΔE ρ [U Bq -1 ] (2) 5 kev

5 DOSIMETRIC STUDIES OF THE 192 IR- MICROSELECTRON V2 HDR BRACHYTHERAPY SOURCE 65 where E is the mid-point of each energy bin (in MeV), ΔE is the bin size. ( ) i E [MeV -1 cm -2 ] is the photon fluence differential in energy within each energy bin, and μ ( E )/ ρ [cm 2 g -1 ] is the mass energy-absorption coefficient at energy E. The factor i en i is required to convert K air from MeV g -1 into Gy, the number constant is N photon given by Eq.1, and the factor is used to convert the unit Gy m 2 s -1 Bq -1 to U Bq -1. The same input parameters and scoring dimensions as for the spectrum calculation were used. Although Borg and Rogers [10] have found that the Bremsstrahlung photons generated in the high atomic number of Ir-192 core by electrons due to the β - decay increase the air-kerma strength only by 0.2%, it was included for consistency. The cut-off energy for these electrons was 10 kev (kinetic energy). Calculation of kerma rate and absorbed dose rate per source strength For these calculations the source was positioned at the center of a water phantom which is a cylinder of 30 mm in radius and 60 cm in height. Both codes, FLURZnrc and DOSRZnrc were used with identical geometry input parameters. The dose was calculated within a matrix at grid points perpendicularly away and along both directions of the source axis at a distance of 0.00, 0.10, 0.25, 0.50, 0.75, 1.00, 1.50, 2.00, 2.50, 3.00, 4.00, 5.00, 6.00 and 7.00 cm from the source center. Scoring regions were selected as follows: 0.1 cm in r at distances less than 3 cm and 0.5 cm at distances between 3cm and 7 cm; 0.02 cm in z-axis at distances less than 3 cm and 0.05 cm at distances between 3cm and 7 cm. The dose component due to β - decay was again included using a relation between photons and electrons based on equation (1). The number of histories was set to in order to maintain the statistical uncertainty under 0.5%. The main parameters used input for the DOSRZnrc code are: ECUT = MeV, PCUT = MeV, ESTEPE = 0.25, BREM SPLITTING = ON, CHARGED PART. RUSSIAN ROULETTE = ON, ELECTRON RANGE REJECTION = ON, ESAVEIN = 1.0. The variance reduction techniques are implemented to allow for more efficient calculations of the bremsstrahlung photons (factor 10 in calculation time in our case). Comparison of dose results with and without variance reduction techniques showed no difference within the statistical uncertainty. Derivation of TG-43 parameters and functions In order to translate the results of the Monte Carlo calculations into the parameters and functions required for the TG-43 equation (A1), the following steps have been performed. Calculation of the dose rate constant The dose rate constant simply refers to the absorbed dose rate per source strength at the reference position, P(r 0,θ 0 ) which is at 1 cm distance from the source center lateral to the axis. is identical to the dose value obtained at the grid point r = 1 cm d z = 0 cm. Calculation of The function Report: L G (r,θ) L G (r,θ) was obtained the same way as described in the AAPM Task Group No.43 i

6 66 L. HONG, G. A. ZAKARIA AND G. H. HARTMANN G L ( r, ) Lr sin if 0 ( r L / 4) if =0 (3) r sin r sin with 2 1 arctan arctan (4) r cos L / 2 r cos L / 2 where L is the length of the active source and is the angle, in radians, subtended by the tips of the hypothetical line source with respect to the calculation point, P( r, ). Calculation of g L(r) The function g (r) was obtained by: L D( r, 0) GL ( r0, 0) gl( r) D( r (, 0) 0, 0) GL r where the dose values were taken from the calculated matrix of the dose rate by interpolation. Calculation of F(r,θ) The anisotropy function F(r,θ) was tabulated at a radius of 0.25, 0.50, 1.0, 2.0, 3.0, and 5.0 cm for comparison with the data of Taylor and Rogers [4], and at 45 polar angles ranging between 0º 180, again using interpolation between the grid points of the calculated matrix using: F( r, ) D( r, ) GL( r, 0) D( r, ) GL ( r, ) 3. RESULTS AND DISCUSSION Photon fluence (Energy spectrum) 0 The EGSnrc Monte Carlo calculated photon spectrum compared with Borg and Rogers work [10] outside the source are shown in Fig. 3. (5) (6)

7 DOSIMETRIC STUDIES OF THE 192 IR- MICROSELECTRON V2 HDR BRACHYTHERAPY SOURCE 67 Fig. 3. Fluence spectra in 5 kev bins for the source at 5 cm distance, a) from Borg and Rogers data, b) from our study. No bremsstrahlung is included. Air-kerma strength The air-kerma strength per unit source activity was found to U Bq -1 on the basis of our FLURZnrc calculations. This value is close to U Bq -1 obtained from Borg and Rogers s work [10] using EGS4 code and simulation techniques published in The average value of the air-kerma strength per unit source activity is based on fluence spectra at distances ranging from 2 to 50 cm. No lower energy cut-off was performed in order to compare our result with Borg and Rogers reported values. The air-kerma strength, calculated in this work, includes the contribution from Bremsstahlung, which increases the S k /A values without Bremsstrahlung by 0.2% for our 192 Ir microselectron-hdr source. The uncertainty is expressed as 1 standard deviation of the statistical uncertainty. Calculation of absorbed dose rate per source strength and the contribution of electron transport Results for the calculated matrix of the absorbed dose rate per source strength including the contribution of electron transport are given in the Tables 1 and Table 2 show explicitly the increase of the absorbed dose rate due to the transition from kerma to dose calculation. Values, that are not given, are located within the source capsulation.

8 68 L. HONG, G. A. ZAKARIA AND G. H. HARTMANN Table 1. Dose rate per unit air-kerma strength [cgy h -1 encapsulation of source that can not be evaluated). U -1 ] (* means position within the

9 DOSIMETRIC STUDIES OF THE 192 IR- MICROSELECTRON V2 HDR BRACHYTHERAPY SOURCE 69 Table 2. Increase of the to dose rate per unit air-kerma strength [cgy h -1 U -1 ] from the transition from kerma to absorbed dose calculation in per mill.

10 70 L. HONG, G. A. ZAKARIA AND G. H. HARTMANN Radial dose function g (r) Values for the radial dose function L g (r) as calculated by equation (5) are shown in figure 4 and L compared with the data from Daskalov [1] and Taylor and Rogers [4]. The steep increase at very small radii is attributed to beta decay g L (r) Taylor &Rogers Daskalov this work radial distance r (cm) Fig. 4. Radial function in this work and comparison with reference data [1, 4]. Values for the anisotropy function F( r, ) at different distances from the source are given in Table 3 and also shown in figure 5 for a radius of 0.25 cm, 0.50 cm, 1.0 cm and 2.0 cm compared to that of Taylor and Rogers [4]. Whereas a good agreement was obtained at radii beyond 1.0 cm, the disagreement at smaller radii can be explained by the effect of the imperfect approximation of the geometry of the source this work Taylor and Rogers F(r, ) a) b) angle (degree) angle (degree) F(r, ) 1.0 Y Data c) d) angle (degree) angle (degree) Fig. 5. Anisotropy functions at different radii: a) 0.25 cm, b) 0.50 cm, c) 1.00 cm and d) 2.00 cm. For comparison, values from Taylor & Rogers [4] are included.

11 DOSIMETRIC STUDIES OF THE 192 IR- MICROSELECTRON V2 HDR BRACHYTHERAPY SOURCE 71 Table 3. Anisotropy function F( r, ) at different distances from the source. (* means value within the encapsulation of source that can not be evaluated or interpolated). Polar angle Distance from active source center (cm) (degree) * * * * * * * * * * * * * * * * * *

12 72 L. HONG, G. A. ZAKARIA AND G. H. HARTMANN 173 * * * * * * In this study the two cylinder symmetrical standard codes of EGSnrc have been used to characterize the air-kerma strength and the dose-rate distribution of the 192 Ir microselectron v2 HDR brachytherapy source. Since no experimental measurements have been performed for conformation, our results were compared with the data set of Daskalov s investigations published in 1998 [1] and with data of the CLRP Database by Taylor and Rogers [4]. Since electron transport is taken into account in our simulations, the dose-rate distribution of table 1 shows significant differences for distances away from the source smaller than 0.25 cm, however, values are very close to that in the range beyond Dose rate constants agree within the uncertainties with the literature data. Also the radial dose function show very good agreement with the data of Daskalov and Taylor & Rogers except for distances below 0.25 cm. The calculated anisotropy functions show good agreement with the data of Taylor & Rogers for radii greater than 0.5 cm. The significant differences of TG-43 parameters occur at short distance from the active source, even including the specific polar angles (<15º and >165º) from the longitudinal axis, which could be mainly attributed to the influence of simplified geometry model (the tips of the source and encapsulation). The uncertainties reported in this study are statistical uncertainties of type A only. There are a numbers of factors affecting the type B uncertainty in these calculations. Based on statements of various authors of publications dealing with MC dose calculations such as Rivard [17], the uncertainties in cross section data (~1%), source geometry (~0.5%), and material definitions (~0.5%) can be roughly summarized to an overall type B uncertainty of 1%. As an alternative to TG-43 dosimetry protocol and MC calculations, convolution/superposition methods can also be used to calculate the doses surrounding brachytherapy source. The primary dose can also act as the source descriptor for scatter dose calculations according to the primary and scatter dose separation (PSS) formalism described by Russell et al. [18] The goal of using superposition methods is to use contributions from primary and scatter doses to account for inhomogeneities or the lack of a full scattering medium, which are ignored by the TG-43 protocol. Therefore further study would be required to derive an accurate estimate of the impact of heterogeneities on dose distributions for clinical implementation using the true dose (not the collision kerma approximation) calculated by superposition methods. Our work is in line with that of other authors investigating the dose distribution of clinically used brachytherapy sources by MC calculations aiming at a more accurate consideration of a number of influence effects. Such effects are the secondary electron transport, the contribution from the beta spectrum of 192 Ir, but also the type of MC simulation. If such effects are taken into account, the results provide more realistic dose-rate distribution and also more realistic dosimetrical parameters

13 DOSIMETRIC STUDIES OF THE 192 IR- MICROSELECTRON V2 HDR BRACHYTHERAPY SOURCE 73 in particularly within the 0.2 cm distance from the source. In this region a significant difference was obtained between absorbed dose and collision kerma as shown in Table 2 and also in Figure 4 and CONCLUSIONS With respect to our study, we recommend that absorbed dose instead of collision kerma should be calculated for all the points located at distances of less than 0.25 cm from the center of active source where electronic disequilibrium exists. Our study has demonstrated that the standard MC code DOSRZnrc is well suited for that. On the other hand, in case of the microselectron v2 HDR 192 Ir source, collision kerma can always be used to approximate the absorbed dose at distances larger than 0.25 cm from the center of the source (i.e. for the great majority of applications). Since electronic equilibrium is achieved, the kerma calculation is adequate and also more effective compared the calculation of absorbed dose. In this case, reduction of statistical uncertainties and computation time and thus requirements on resources are significant and the kerma approximation appears adequate. However, for brachytherapy sources with a higher energy such as from a 60 Co source, the distance where electronic equilibrium exists is larger than 0.25 cm. In such cases, the recommendation to calculate absorbed dose also applies to larger distances. ACKNOWLEDGEMENTS The authors would like to thank Mario Perez of the DKFZ for his useful help on the first author s study of EGSnrc code. REFERENCES [1] G. M. Daskalov, E. Löffler and J. F. Williamson, Med. Phys. 25, pp 2200 (1998). [2] R. E. P. Taylor and D. W. O. Rogers, Med. Phys. 35, pp 4933 (2008). [3] P. Papagiannis, A. Angelopoulos, E. Pantelis, L. Sakellious, D. Baltas, P. Karaikos, P. Sandilos and L. Vlachos, Med. Phys. 29, pp 2239 (2002). [4] R. E. P. Taylor and D. W. O. Rogers, /clrp/seed_database. [5] R. Nath, H. Amols, C. Coffey, D. Duggan, S. Jani, Z. Li, M. Schell, C. Soares, J. Whiting, P. E. Cole, I. Crocker and R. Schwartz, Med. Phys. 26(2), pp 119 (1999). [6] D. Baltas, P. Karaiskos, P. Papagiannis, L. Sakelliou, E. Löffler and N. Zamboglou, Med. Phys. 28, pp 1875 (2001). [7] R. Wang and X. A. Li, Med. Phys. 29, pp 1678 (2002). [8] F. Ballester, D. Granero, J. P. Calatayud, C. S. Melhus and M. J. Rivard, Med. Phys. 36, pp 4250 (2009). [9] I. Kawrakow and D. W. O. Rogers, NRCC Report PIRS-701 (2006). [10] J. Borg and D. W. O. Rogers, NRCC Report PIRS-629r (1999). [11] R. Nath, L. L. Anderson, G. Luxton, K. A. Weaver, J. F. Williamson and A. S. Meigooni, Med. Phys. 22, pp 209 (1995).

14 74 L. HONG, G. A. ZAKARIA AND G. H. HARTMANN [12] M. J. Rivard, B. M. Coursey, L. A. DeWerd, W. F. Hanson, M. S. Huq, G. S. Ibbott, M. G. Mitch, R. Nath and J. F. Williamson, Med. Phys. 31, pp 633 (2004). [13] B. Duchemin and N. Coursol, Technical Note LPRI/90/018 (France: DAMRI, CEA) (1993). [14] D. W. O. Rogers, I. Kawrakow, J. P. Seuntjens, B. R. B. Walters and E. Mainegra-Hing, NRC Report PIRS-702(rev B) (2005). [15] J. H. Hubbell and S. M. Seltzer, Technical Report NISTIR 5632, NIST, Gaithersburg, MD (1995). [16] J. H. Hubbell, NBS Report NSRDS-NBS-29 (1990). [17] M. J. Rivard, Med. Phys. 34, pp 754 (2007). [18] K. R. Russell and A. Ahnesjö, Phys. Med. Biol. 41, pp 1007 (1996). Appendix: TG-43 parameters and functions According to the AAPM Task Group No.43 Report, the dose in water can be obtained in cylindrical coordinates r and θ by: where G (r,θ) (A1) L D(r,θ) SK Λ g L(r) F(r,θ) G L(r 0,θ 0 ) S K G L(r,θ) g L(r) is the air-kerma source strength, is the dose-rate constant in water, defined as is the ratio of dose rate at the reference position, P(r 0,θ 0 ), and S K. has units of cgy h -1 U -1 which reduces to cm -2, is the geometry function for the line source approximation and r denotes the distance (in centimeters) from the center of the active source to the point of interest, r 0 denotes the reference distance which is specified to be 1 cm in this protocol, and denotes the polar angle specifying the point-of-interest, P(r,θ), relative to the source longitudinal axis. The reference angle, θ 0, defines the source transverse plane, and is specified to be 90 or / 2 radians (Figure A1). The subscript L was added to denote the line source approximation used for geometry function, is a dimensionless radial dose function, which accounts for dose fall-off due to photon scattering and attenuation in the medium and in the encapsulation material at any distance on the transverse plane of the source and

15 DOSIMETRIC STUDIES OF THE 192 IR- MICROSELECTRON V2 HDR BRACHYTHERAPY SOURCE 75 F(r,θ) is a 2D anisotropy function, F(r,θ) that describes the variation in dose as a function of polar angle relative to the transverse plane. Fig. A1. Coordinate system used for brachytherapy dosimetry calculation.