MONTE CARLO SIMULATIONS USED TO ESTABLISH A FRENCH NATIONAL HDR BRACHYTERAPY REFERENCE

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1 Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications Palais des Papes, Avignon, France, September 12-15, 2005, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2005) MONTE CARLO SIMULATIONS USED TO ESTABLISH A FRENCH NATIONAL HDR BRACHYTERAPY REFERENCE Gouriou J and Douysset G Laboratoire National Henri Becquerel CEA Saclay Gif-sur-Yvette, France jean.gouriou@cea.fr; guilhem.douysset@cea.fr ABSTRACT The different Monte Carlo computations made to establish a French dosimetric reference for 192 Ir High dose rate (HDR) brachytherapy afterloading are described in this article. Two different components of the air-kerma-rate determination are explained in more details: the attenuation correction factor and the interpolated calibration coefficient. The Monte Carlo codes MCNP and PENELOPE have been used to simulate the different studied elements. The relative combined standard uncertainty associated with the air-kerma-rate is lower than 1 %. EYWORDS: 192 Ir, brachytherapy, source calibration, MCNP, PENELOPE 1. INTRODUCTION Brachytherapy used in medical physics to irradiate tumorous cells consists in placing radioactive material sealed in needles, seeds, wires, or catheters directly into or near the target zone. The name Brachy is borrowed from the Greek, meaning "short", to describe the small or contact distances involved in such therapy. Using this method, high radiation doses can be delivered locally to the tumour with rapid dose fall-off in the surrounding normal tissues. In the past, brachytherapy was carried out mostly with radium or cesium sources. Currently, the use of artificially produced radionuclides such as 192 Ir, 198 Au, 125 I and 103 Pd has rapidly increased for the last 10 years. In the USA, high dose rate (HDR) and pulse dose rate (PDR) brachytherapy has considerable importance with approximately 1000 units in operation. In Europe and especially in France, its development has increased during these last years (about 60 units are now in operation in France). The number of units is expected to increase in coming years to replace 137 Cs afterloaders and 192 Ir implants. According to the International Commission on Radiation Units and Measurements (ICRU) definition, HDR is greater than 12.0 Gy per hour, although the usual dose rate delivered to the tumor by current HDR brachytherapy units is about Gy per hour. According to commonly accepted ICRU recommendations, discrepancies between prescribed and actually delivered doses should not exceed 5 % [1]. More recently, Mijnheer et al. [2] and Brahme et al. [3] formulated for the delivered dose a margin of 3.5 %, expressed as 1 standard deviation (k = 1) from the prescribed dose. Generally, the factors responsible for any uncertainty American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11

2 in the dose delivery can be attributed to one of the following categories: dose calculation, patient setup and radiation source calibration. The potential errors resulting from the first two categories differ for individual patients, contrary to the errors related to the radiation source calibration. The latter might be disclosed as systematic errors in dose delivery and in extreme situations are manifested by clinically observable symptoms. The Laboratoire National Henri Becquerel (LNHB) has recently developed a dosimetric reference for High Dose Rate (HDR) brachyterapy in order to offer to medical physicists a direct traceability to a national reference. To keep the discrepancy between prescribed and delivered doses under about 3 %, the radiation source calibration is determined with a relative standard uncertainty less than 1 % (k = 1). The brachytherapy sources are calibrated in air in terms of reference air-kerma-rate (RAR, symbol : R, see ICRU [4]) in Europe and air-kerma-strength (AS, symbol: S, see Nath et al. [5]) in the USA : d R = ( d ) dref 2 (1a) S 2 = ( d) d (1b) Where (d) is the air-kerma-rate measured at a distance d, and d ref is the reference distance. Both quantities are defined for an air point placed into an infinite volume of vacuum with no attenuation and no scattering. The two terminologies are equivalent since d ref = 100 cm. For reasons of homogeneity in the following paper only the RAR term will be used. The kerma is an acronym for inetic Energy Released per unit Mass. erma is the sum of the initial kinetic energies of all the charged particles liberated by uncharged ionizing radiation (in this article, photons) in a sample of matter, divided by the mass of the sample. The SI unit of kerma is the Gray (Gy), which is equal to one joule per kilogram (J/kg). The RAR of the source is measured with a cavity ionization chamber using a technique originally developed by Goetsch et al. [6]. The calibration coefficient of the ionization chamber for the 192 Ir spectrum is determined indirectly by interpolation from 250 kv x-rays, 137 Cs and/or 60 Co calibrations. According to this method, the RAR of a brachytherapy source is estimated using the following equation: R (Ir) i i ref 2 d = N I k (2) d with : k i = k N katt kscatt. i American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11

3 N (Ir) denotes the interpolated calibration coefficient for the 192 Ir spectrum, I is the current delivered by the ionization chamber (corrected for radioactive decay, atmospheric effects, collection efficiency and polarity effects), k i are correction factors respectively for nonuniformity, attenuation and scattering effects. The radioactive source used by the LNHB is a Nucletron micro Selectron HDR V2 unit fitted with the most recently designed source (manufactured by Mallinckrodt Diagnostica). This source is made out of a pure 192 Ir cylinder (length: 3.60 mm, diameter: 0.65 mm) that is surrounded by an AISI 316L stainless steel encapsulation (radial thickness: 125 µm). The source is attached to a 1.5 m long and 0.9 mm diameter steel cable. In this article, we present the different Monte Carlo computations made to determine several components of the reference air-kerma-rate R. Two different components would be detailed in the following sections: the attenuation correction factor k att and the interpolated calibration coefficient N (Ir). The values of the other correction factors obtained by measurement or by theoretical calculations could be found in another article [7]. 2. RAR COMPONENTS CALCULATED BY MONTE CARLO SIMULATIONS 2.1. Attenuation Correction Factor Method As the RAR is defined in vacuum, the attenuation of the primary beam between the source and the ionization chamber must be taken into account. The attenuation could come from air and from catheter wall absorption. To extrapolate the measured current to the zero absorption configuration, its value is multiplied by the attenuation factor k att. The attenuation factor can be expressed by the following expression: air (vacuum) katt = (3) air (air + jig) where d air = ( air ) (4) dt represents the air-kerma rate and E tr( ) air( m) = µ E φm( E) de (5) 0 ρ air φ m( E ) represents the photon fluence at energy E in the environmental conditions m (vacuum or air+jig), and ( µ tr ( E) ρ ) air stands for the mass energy transfer coefficient in air (see tables established by Hubbell and Seltzer [8]). The MCNP-4C Monte Carlo code [9] has been used to simulate photon fluences in the two following configurations: American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11

4 iridium source alone (including encapsulation) and 15 cm of cable placed into vacuum (m = vacuum); full experimental set-up (source, cable, catheter and jig) placed into standard air (m = air+jig). A picture of the experimental set-up without the source is shown in picture 1. Figure 1. Vertical catheter surrounded by the experimental jig Simulation a Simulated geometry The figure 2a shows the cutting plan of the simulated radioactive source (type Nucletron micro Selectron HDR V2) with the help of MCNP (Mcplot command). The centre of the picture, represented in red color, corresponds to the active region of the 192 Ir radioactive source. Around this element are represented in green the steel cable and the stainless steel encapsulation (AISI 316L, ρ = 7.99 g/cm 3 ) and in yellow the catheter in polystyrene (ρ = g/cm 3 ). The regions colorized in indigo are composed of air. The source, cable included, is aligned with the symmetry axis of the catheter. The upper end of the source is localized at 1 mm distance to the internal surface of the catheter. American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11

5 (a) (b) (c) Figure 2. Two dimensional representations of geometry model used to simulate the 192 Ir source made by the MCNP Monte Carlo code. (a) cutting plan of the source; vertical (b) and horizontal (c) cutting plans of the jig. The figures 2a and 2b show the numerical model employed to simulate the jig. The goal of this element is to maintain the catheter perfectly vertical. Only the upper part of the jig is taken into account in the simulations. The material for this structure is made up of polymethylmetacrylate (PMMA, ρ = 1.19 g/cm 3 ) tinted in grey on the pictures b Initial radioactive emissions The initial 192 Ir photon emissions are taken from the Nucleide 2000 tables [10]. The initial photon lines are taken into account only if the product of their kinetic energy by intensity is sufficiently high. When the relative contribution of the line compared to the full initial theoretical population is less than 1 to 1000, the line is not taken into account. Finally with this criterion, the strongest 21 photon lines are modelized in the 192 Ir simulations. Although 192 Ir is a pure β emitter, this contribution has been neglected. With a mean energy of about 200 kev, few of the emitted electrons succeed to leave the source. Several simulations have been made with MCNP-4C for several initial electrons of different kinetic energies: 100, 200 and 500 kev. The results show that no electrons are detected into a sphere of 2 mm radius localized at 15 cm from the source. For the secondary photons which come from these electrons, their numbers are very small, with about 10 detected photons for 15 millions electrons with an initial kinetic energy of 200 kev. This contribution is also not integrated in our simulations. The radioactive region of the source is simulated so as to have a homogeneous distribution into the initial volume and an isotropic emission c Calculated fluence spectra The photonic fluence spectra are detected into several spheres of 2 mm radius localized respectively at 10, 15 and 20 cm from the centre of the radioactive region of the source. When the contribution of air and the experimental set-up is neglected, the materials of these regions are replaced by vacuum. The experimental set-up includes the catheter and the jig. American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11

6 About 6 billions of histories have been made with MCNP-4C under the mode P E. The fluence spectra have been calculated with the tally F4. The bin-width of the spectra is 1 kev. No variance reduction techniques have been used excepted geometrical rejection outside the simulated geometry (IMP=0) and energy cutoff for the entire geometry (1 kev for photon and 10 kev for electron). To make an accurate simulation of the electron transport, the ITS 3.0 algorithm is made active with the command X18 set equal to Results The simulated fluence spectra are presented on figure 3. One can note that the attenuation of the primary beam is partly compensated by the scattering leading to a relatively low value of k att. Figure 3. Simulated fluence spectra in the two simulated configurations (source alone or with the full experimental set-up). Since the value of k att is almost constant over the cm range (see below table I), an averaged value of (13) has been used. American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11

7 Table I. The value of the attenuation correction factor k att. Distance (cm) k att Equivalent energy a (kev) a Air-kerma-weighted 2.2. Interpolated Calibration Coefficient for the 192 Ir Spectrum Method As indicated in the introduction, the calibration coefficient of the chamber at 192 Ir energy is estimated by interpolation between x-ray, 137 Cs and 60 Co calibration coefficients. Two different ways can be used, between x-rays and 137 Cs or between x-rays and 60 Co. This approach is all the more valid because the NE cm 3 ionizing chamber energy response function is flat across this energy range. The calibration coefficient variation is lower than 0.9 % from x-rays to 60 Co (see table II). This gives more confidence in the interpolated calibration coefficient used for the 192 Ir spectrum. For all calibrations, the chamber is fitted with the build-up cap corresponding to the highest energy. Beam Table II. Calibration coefficients of the NE2571 ionization chamber. Air-erma rate (Gy/h) Average energy a (kev) N (Gy/h) u(n )/ N (%) x-rays b Cs Co a Air-kerma-weighted b HV = 250 kv, HVL(Cu) = 2.5 mm In order to account for chamber wall effect, the calibration coefficients have to be weighted by the appropriate wall attenuation correction factor A wall. This factor corrects the absorbed dose in the gas cavity for the effects of attenuation and scatter in the wall. A wall depends on the incident spectrum and on the wall material and thickness. With these A wall factors, a linear two points interpolation is performed using the following equation: N (Ir) = f w1 A wall (1) N (1) + f A (Ir) wall w2 A wall (2) N (2) (6) American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11

8 where N (i) represents the calibration coefficient for spectrum (i). The weighted interpolation factor f wi can be estimated by the corresponding equations: f w1 EIr E2 = E E 1 2 f w2 EIr E1 = E E The subscripts (1) and (2) represent respectively 137 Cs and x-rays or x-rays and 60 Co. By definition, f + f 1. The E i values are the air-kerma-weighted energies for spectrum (i). w1 w2 = Since the LNHB holds the national reference beams of 60 Co and 137 Cs, the NE2571 chamber has been calibrated with these beams. The Bureau International des Poids et Mesures (BIPM) realized the x-ray calibrations Simulation a. Simulated geometry The A wall factors have been estimated by Monte Carlo simulations using the Penelope 2001 code [11]. A specific user program has been developed for simulating the perturbation correction factor connected with the presence of the wall (chamber and the build-up cap). The following figure 2 show the geometric model used for simulating the Nuclear Enterprise NE2571 chamber and its associated build-up cap made in Delrin. The ionization chamber is supposed to be in vacuum. The method used to calculate the A wall factors is following the approach established by Rogers et al. [12]. 1 2 Figure 2: Two dimensional representation of the NE2571 chamber with its associated build-up cap made by GVIEW2D. The values of the physical simulation parameters C 1, C 2, W cc and W cr have been set equal to 0.10, 0.05, and For all the simulated geometry, the absorption energies (similar to cutoff energies for electron, positron and photon) E abs have been set equal to 5 kev. The maximum transport length DSMAX is set to be smaller than 1/10 th of the smallest dimension of each simulated region. American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11

9 2.2.2.b. Initial spectra The simulations have been made for four different incident spectra. The 250 kv x-rays spectrum came from the BIPM (Burns D.T. private communication). Since the LNHB holds the national reference beams of 60 Co and 137 Cs, the specific geometry of these two irradiators has been simulated with MCNP under the mode P E. The photon spectra have been calculated with the tally F1 at 100 cm from the radioactive source. No variance reduction techniques have been used excepted geometrical rejection outside the simulated geometry (IMP=0) and cutoff energy for the entire geometry (10 kev for photon and 50 kev for electron inside the source and ranging from 100 kev to 800 kev for electron outside the source). To make an accurate simulation of the electron transport, the ITS 3.0 algorithm is made active with the command X18 set equal to 1. For the 192 Ir source, the previous 15 cm source distance fluence spectrum simulated for the k att calculation with the full experimental set-up configuration has been used as the 192 Ir spectrum. The continuous component and the photon lines of the simulated spectrum have been taken into account Results The air-kerma-weighted average energies have been obtained from the previous simulated spectra whereas an experimental spectrum has been used for x-rays. The air-kerma-weighted average energy for 192 Ir is found equal to kev. With these data, the weighted interpolation factors f w1 and f w2 are respectively equal to 0.53 and 0.47 for the x-rays and 137 Cs interpolation whereas f w1 = 0.75 and f w2 = 0.25 are obtained for the x-rays and 60 Co interpolation. The estimated standard uncertainty associated with each fwi is about The calculated Monte Carlo A wall values are summarized in table III. These results for 60 Co, x-rays and 192 Ir are in good agreement with the International Atomic Energy Agency (IAEA) reference report in the domain of brachytherapy metrology [13]. Table III. A wall factors calculated by Monte Carlo for the NE2571 ionization chamber. Beam A wall u(a wall ) x-rays a Cs < Co < Ir a HV = 250 kv, HVL(Cu) = 2.5 mm American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11

10 Then the interpolated calibration coefficients N (Ir) for 192 Ir are calculated. The agreement between the two calculated values is very good (see table IV). The (x-rays Cs) interpolated result has been used for the French dosimetric reference due to its smaller uncertainty. Table IV. The interpolated values of the calibration coefficient at 192 Ir energy (chamber NE2571). (x-rays Cs) (x-rays + 60 Co) N (Ir) (Gy/h) u[n (Ir)]/ N (Ir) 0.50 % 0.68 % 3. CONCLUSION This article described the different Monte Carlo computations made to determine several components of a standard calibration for HDR 192 Ir brachytherapy source. Two different components of the reference air-kerma-rate R have been detailed: the attenuation correction factor k att and the interpolated calibration coefficient N (Ir). These values contributed to establish a national standard calibration in France with a relative combined standard uncertainty less than 1.0 % (k = 1). With this order of magnitude, a medical physicist could keep the discrepancy between prescribed and delivered doses under about 3 %. The uncertainty budget for the determination of the LNHB dosimetric standard is summarized in table V. Table V. Uncertainty budget for the definition of the LNHB dosimetric standard. Relative standard uncertainty (%) Value Type A Type B N (Ir) (Gy/h.A) I (A) k N k att k scatt d (mm) Combined standard uncertainty 0.59 American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11

11 Moreover, a bilateral comparison of national dosimetric standards for HDR brachytherapy has been conducted between the LNHB and the University of Wisconsin Accredited Dosimetry Calibration Laboratory [7]. Two types of well chambers, Nucletron Model and Standard Imaging Model HDR 1000+, have been calibrated in both laboratories and calibration coefficients have been compared. The agreement between the calibration coefficients is very good. In all studied cases, the discrepancy between the two measurements is within 0.3 %. REFERENCES 1. International Commission on Radiation Units and Measurements (ICRU) Determination of absorbed doses in a patient irradiated by beams of X or gamma rays in radiotherapy procedures, Report ICRU No 24, ICRU Washington DC, USA (1976). 2. B.J. Mijnheer, J.J. Batterman, A. Wambersie, What degree of accuracy is required and can be achieved in photon and neutron therapy?, Radioth. Oncol., 8, pp (1987). 3. A. Brahme, J. Chavaudra, T. Landberg, E.C. McCullough, F. Nüssli, A. Rawlinson, G. Svensson and H. Svensson, Accuracy requirements and quality assurance of external beam therapy with photons and electrons, Acta Oncol. (Stockholm), Suppl. 1, pp (1988). 4. International Commission on Radiation Units and Measurements (ICRU) Dose and volume specification for reporting intracavitary therapy in gynecology, Report ICRU No 38, ICRU Washington DC, USA (1985). 5. R.. Nath, L.L. Anderson, G. Luxton,.A. Weaver, J.F. Williamson and A.S. Meigooni, Dosimetry of interstitial brachytherapy sources: recommendations of the AAPM radiation therapy committee task group No 43, Med. Phys., 22, pp (1995). 6. S.J. Goetsch, F.H. Attix, D.W. Pearson and B.R. Thomadsen, Calibration of 192 Ir high-doserate afterloading systems, Med. Phys., 18, pp (1991). 7. G. Douysset, J. Gouriou, F. Delaunay, L. DeWerd,. Stump and J. Micka, Comparison of dosimetric standards of USA and France for HDR brachytherapy, Phys. Med. Bio., 50, pp (2005). 8. J.H. Hubbell and S.M. Seltzer, Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients (Version 1.03), (Gaithersburg, MD: National Institute of Standards and Technology) (Online (2004). 9. J.F. Breismeister, MCNP, A General Monte Carlo N-particle Transport Code Version 4C, Manual LA-13709, Radiation Safety Information Computational Center (RSICC), Oak Ridge USA (2000). 10. M.M. Bé, B. Duchemin, F. Lagoutine, N. Coursol, J. Legrand, E. Schönfeld,. Debertin, Table of radionuclides, Commissariat à l Energie Atomique Saclay, ISBN , (1999). 11. F. Salvat, J.M. Fernández-Varea, E. Acosta and J. Sempau, PENELOPE, A code system for Monte Carlo simulation of Electron and Photon transport, Proceedings of a Workshop/Training Course, OECD/NEA, Issy-les-Moulineaux, France, 5-7 November 2001, Report NEA/NSC/DOC(2001)19, ISBN , (2001). 12. D.W.O. Rogers and A.F. Bielajew, Wall attenuation and scatter corrections for ions chambers: measurements versus calculations, Phys. Med. Biol., 35, pp (1990). 13. International Atomic Energy Agency (IAEA), Calibration of photon and beta ray sources used in brachytherapy, Report IAEA-TECDOC-1274, ISSN , IAEA, Vienna Austria (2002). American Nuclear Society Topical Meeting in Mathematics & Computations, Avignon, France, /11