Journal of Cancer Research and Therapeutics Medknow Publications on behalf of the Association of Radiation Oncologists of India (AROI) ISSN: 0973-1482 EISSN: 1998-4138 Vol. 6, Num. 4, 2010, pp. 421-426

Journal of Cancer Research and Therapeutics, Vol. 6, No. 4, October-December, 2010, pp. 421-426

Review Article

Monte Carlo and experimental dosimetric study of the mHDR-v2 brachytherapy source

Rakesh M Chandola¹, Samit Tiwari², Manoj K Kowar², Vivek Choudhary¹

¹ Department of Radiotherapy, Pt. J.N.M. Medical College and Dr. B.R.A.M. Hospital, Raipur, Chhattisgarh, India
² Department of Applied Physics, Bhilai Institute of Technology, Durg, Chhattisgarh, India

Correspondence Address: Rakesh M Chandola, Department of Radiotherapy, Pt. J.N.M. Medical College and Dr. B.R.A.M. Hospital, Raipur, Chhattisgarh, India, rakemohachan@rediffmail.com

Code Number: cr10110

PMID: 21358074

DOI: 10.4103/0973-1482.77068

Abstract

Keywords: Dose rate constant, Monte Carlo simulation, radial dose function, 2D anisotropy function

Introduction

A general introduction to brachytherapy and MC

Today, in clinical brachytherapy, the application of ¹⁹² Ir in HDR afterloading brachytherapy equipment is common. Due to the steep dose gradients, which in turn determines the energy deposition near the source, MC has become an accepted dose calculation methodology in brachytherapy. ^[1],[2],[3] MC simulation is used to solve various physical problems other than radiation- tissue interaction. There is no established method for the use of MC in brachytherapy dosimetry. As per definition by Lux et al., ^[4] "In all applications of the Monte Carlo method, a stochastic model is constructed in which the expected value of a certain random variable (or a combination of several variables) is equivalent to the value of a physical quantity to be determined."

The Role of the TG-43 U1 Formalism

It is recommended in the American Association of Medical Physicists in Medicine (AAPM) task group-43 (TG-43 U1 and TG-43) ^[5],[6] that dose distribution data of the brachytherapy sources in use should be obtained either by experiment or by MC simulation, which is then to be used as input in the HDR treatment planning system (TPS) for planning of exact dose delivery to the patient.

The AAPM introduces several dose distribution parameters based on direct dose distribution in water medium. These parameters are: the dose rate constant (∧), the geometry factor G(r,θ), the radial dose function g(r), and the 2D anisotropy function F(r, θ). With the exception of the geometry factor, all others are measured. Moreover, for low energy radioactive sources e.g. ¹²⁵ I and ¹⁰³ Pd seeds, the AAPM recommends that independent investigations involving experimental and Monte Carlo methods must be made available for a source prior to its clinical use. ^[7]

The Previous Studies Done

Stump et al. ^[8] did calibration of a some new high dose rate ¹⁹² Ir source using a spherical ionization chamber of volume 3.6 cc. They performed a multiple-distance measurement to estimate the room-scatter radiation. Selvam et al. ^[9] made a Monte Carlo-aided study of primary air kerma strength standardization of a remote afterloading ¹⁹² Ir HDR source. Williamson and Li ^[10] used the Monte Carlo method to calculate complete two-dimensional dose rate distributions about the most widely used HDR source design. A similar Monte Carlo study was performed by Daskalov et al. ^[11]

Materials and Methods

The design of the Nucletron mHDR-v2 ¹⁹² Ir brachytherapy source is taken from Daskalov et al., ^[11] and is illustrated in [Figure - 1].

The ¹⁹² Ir active core of the source has an effective density of 22.42 g/cm ³ . The active length of the active core is 3.6 mm with an active diameter 0.65 mm. The activity of the source is assumed to be uniformly distributed. The active core is covered by the stainless steel AISI 316L encapsulation of density 8.02 g/cm ³ a composition by weight: Fe 68%, Cr 17%, Ni 12%, Mn 2% and Si 1% leading to total length of 4.5 mm and total diameter of 0.9 mm. The distal capsule tip has rounded borders with a curvature radius of 0.4 mm. The source is welded on a flexible woven stainless steel cable with a diameter of 0.7 mm. As the portion of the cable near the source remains in straight line, 5 mm of cable were simulated in addition to the source itself.

The needle used as an applicator was made of stainless steel 1.440I (equivalent to AISI/SAE 316) of density 8.0 g/cm ³ and with a wall thickness of 0.15 mm. The inner and outer diameters of the applicator were 1.35 ± 0.02 mm and 1.65 ± 0.02 mm, respectively. The value of effective attenuation co-efficient was taken as 0.030 ± 0.002 [ANSI 303/304]. ^[12] The unit of the effective attenuation co-efficient was taken as cm ² /g.

The in-air ion chamber used in this study was a 0.1 cc model PTWM-23322 Freiburg with an active length of 1.2 cm and effective diameter of 0.35 cm. The wall material was made of PMMA with a thickness 0.12 g/cm ³ and no cap. The calibration factor was 3.597 E ± 08 Gy/C for ⁶⁰ Co beam. The ionization chamber must have a wall thickness of about 0.31 g/cm ² to provide charge particle equilibrium for the ¹⁹² Ir source emitting a photon spectrum in the energy range from 9 to 885 keV. ^[13] If the wall thickness of the chamber used in measurement differs from the recommended thickness, an appropriate correction should be applied for scattering and attenuation of photons. ^[13] The wall thickness correction factor (A _w) was determined using a formula A _w = 1- γ t : where, ′γ′ is the attenuation and scattering fraction per wall thickness (cm ² /g) and ′t′ is the total thickness (g/cm ² ) of the wall material. ^[12] By calculation, the A _w value equals 1.072. Further, the beam quality correction factor K _Q, which accounts for the difference in the energy spectrum of the photon beam (usually ⁶⁰ Co) for which chamber has been calibrated, was determined for the ¹⁹² Ir source (average energy = 390 keV) by the interpolation method. The charge of the chamber was measured and corrected for non-uniformity, displacement, temperature, and pressure.

The gamma spectrum of the ¹⁹² Ir HDR radioactive source used in this study has been obtained from NuDat database. ^[14] The gamma rays have been simulated considering that ¹⁹² Ir is uniformly distributed in the source core. The beta spectrum has not been considered in simulation since its contribution to the dose rate distribution for distances greater than 1 mm from the source is negligible due to the encapsulation of the source and the catheter in which the source is introduced. ^[15] However, the models for the processes of Compton scattering, photoelectric effect, and Rayleigh scattering have been used simulated in the low energy package of EGSnrc. The cross-section tabulation with uncertainty was taken from the EPDL 97. ^[16]

The source was placed in the center of the water phantom of dimensions 40 Χ 40 Χ 40 cm. ^[17] The density of the water used in the simulation was 0.997 g/cm ³ at 22° C, as is recommended in TG-43 U1. In the simulation in water, the 10 ⁹ primary photons were generated.

The source was kept fixed in the center of a water phantom along the Y axis with the tip of the source toward the + Y axis. The center of the source act as the center of the co-ordinate axes. The chamber was put along the Z axis with the tip toward the + Z axis. The center of the active length of chamber was put at the point of each measurement. For the radial dose function, the chamber was moved along the axis of the source i.e. along the X axis from 1 cm to 15 cm and the values at different distances were normalized to the value at 1 cm. For the 2D anisotropy function, the chamber was moved at a radial distance of r = 5 cm and at polar angles of θ = 0° to 180°. The measured and calculated results of the 2D anisotropy function were normalized to the result at polar co-ordinate (r = 5 cm, θ = 90°). To obtain the dose rate in the form D (X, Y), a grid system having 0.04 cm thick and 0.04 cm high cylindrical rings concentric to the longitudinal axis of the source has been used. To obtain the dose rate in the polar co-ordinate D (r,θ), a grid system composed of 0.04 cm thick concentric sections with an angular width of 5° in 0° to 30° range and 10° in 30° to 180° range in the polar angle were used.

Experimentally, a specially designed measurement set up was used to position the in-air ionization chamber at different co-ordinates of measurement by inserting chamber in its material′s slots and the source in the water phantom. The set up had dimensions of 29 Χ 25 Χ 27 cm and comprised water equivalent material and low Z acrylic plates. This set up was fixed in the water phantom. A fine laser beam was projected over the set up to verify its saggital, transverse, and coronal cross-section planes. There were two parallel aligned scale systems which helped to determine exact horizontal and vertical positions of the in-air ionization chamber and of the applicator. However, for the calculation study of the air kerma strength, S _k, was determined in a separate simulation of 10 ⁸ histories. The source was positioned at the center of an air volume of 4 Χ 4 Χ 4 m ³ with a composition and density as recommended in TG-43 U1 of air of 40% relative humidity. It was calculated along the transverse axis of the source from 0 cm to 150 cm using water hollow 1 Χ 1 cm cylindrical voxels/cells. This configuration was chosen in order to simulate a real experimental measurement with a therapy level detector calibrated in water. These scoring voxels/cells assure volume averaging artifacts < 0.1% for distances greater than 5 mm from the source. ^[18] The scored energy in water was converted to air kerma by multiplication of the ratio of mass attenuation coefficients of air and water. Air attenuation and scattering was corrected with the factor 1.012 ^[19],[20]

Result

The measured and MC calculated dose rate constant values are 1.104 ± 0.99% cGy h ^-1 U ^-1 , and 1.106 ± 0.85% cGy h ^-1 U ^-1 with EGSnrc, which agree within ± 1% to each other, and also show similarity to the published value of 1.108 ± 0.13% cGy h ^-1 U ^-1 by Daskalov et al., ^[11] and 1.105 ± 0.85% cGy h ^-1 U ^-1 value of dose rate constant obtained in this work of the same source using MC GEANT4. In this work the calculation formalism proposed by TG-43 has been applied.

The radial dose functions for mHDR-v2 ¹⁹² Ir source are presented in [Table - 1] and [Figure - 2]. The measured and calculated radial dose functions agree within 2% for distances up to 5 cm. However, for distances greater than 5 cm, the relative difference was found within 6% up to distance 10 cm. These results compare favorably with the published data of Daskalov et al. ^[11]

The 2D anisotropy functions (r = 5 cm.) for mHDR-v2 ¹⁹² Ir source is presented in [Table - 2] and [Figure - 3]. The measured and calculated values of 2D anisotropy functions (r = 5 cm) agree within 2% for polar angles 25 ⁰ < θ < 140°. However, at angles θ < 25° and θ > 140°, the deviations were of the order of 2.3--6.28%. These results compare favorably with the published data of Daskalov et al. ^[11]

Discussion

The dose rate distribution obtained is shown in [Table - 3]. The uncertainty in the evaluation of measurement of dose distribution was performed as per the E-4/02 1999 draft for the expression of the uncertainty of measurement in calibration. ^[21] The sources for uncertainty may arise from chamber, electrometer, temperature, and pressure, measurement set up and primary calibration of the ionization chamber.

The accuracy in determining the positioning of the chamber center was ± 0.2 mm from the absolute center. The outer diameter of the source applicator was 1.35 mm, and the outer diameter of the source was 0.9 mm. This means that source could be displaced to a maximum of ± 0.215 mm from the central axis of the applicator. The uncertainty in the positioning the applicator was 0.1 mm. Thus, the maximum uncertainty in positioning chamber, source, and applicator may be taken as ± 0.515 mm. The uncertainty due to positional error was performed for a reference distance 10 cm. Thus, the overall uncertainty including temperature and pressure, stability of the chamber, leakage, and chamber calibration was measured to be ± 1.32 mm.

The calculated uncertainties of dose rate have been evaluated according to the recommendations of TG-43 U1 considering the type A or statistical uncertainty due to the MC simulation of photon histories in dose rate and air kerma strength simulation, and the type B uncertainty due to the contribution of underlying cross-section data and that arising from the geometrical model of the source. In the simulation of water, the uncertainty in dose rate along the transverse axis is approximately equal to 0.5% except along the longitudinal axis where it has reached to more or less 1%.

Simulation of air kerma strength yielded an uncertainty of roughly 0.5%. The average type A uncertainty in the calculated study may be taken as 0.667% for all points. To estimate the uncertainty by MC due to the variations of the geometry from one source to another in the manufacturing process, the uncertainty is evaluated keeping the worst possible situation for the core and capsule dimensions of the source [Figure - 1]. First, the thinnest capsule and thickest core possible and second, the thickest capsule and thinnest core possible are assumed here, which showed 0.5% variation to be considered.

The dose rate per unit air kerma strength in cGyh ^-1 U ^-1 around the mHDR-v2 ¹⁹² Ir source measured in this study is presented in [Table - 3]. Although ionization chambers are energy independent and show a linear response to the dose, the steep dose gradient inside the active volume of the ionization chamber nearer to the brachytherapy source gives large uncertainties in the measurement. The non-uniform photon fluence caused by the divergence of the incident photon is greatest for ionization chambers in the vicinity of the brachytherapy source. The MC and measured results show greater difference at smaller distance between the ionization chamber and brachytherapy source, which may be due to combination of steep dose gradient effect and positional error of the source, chamber, and applicator during measurement.

A comparison of dose distributions using EGSnrc and GEANT4 with Rayleigh scattering showed dose differences smaller than 2% for distances up to 5 cm. The measured and MC calculated radial dose functions show very good agreement for distances not more than 5 cm. For distances greater than 5 cm, the relative difference between measured and calculated data is slightly larger, which may be due to the different uncertainties and volumetric averaging effect. Approximately the same results are found when the measured data of this study are compared with the published values of Daskalov et al., ^[11] except of large distances, which may be due to the effect of size on the water phantom also.

The measured and MC calculated 2D anisotropy functions shows fair agreement for polar angles 25 ⁰ < θ < 140 ⁰ . However, at angles θ < 25 ⁰ and θ > 140 ⁰ deviations are much larger, which may be due to uncertainties and volumetric averaging effect. However, approximately same results are found when the measured data of this study are compared with the published values of Daskalov et al., ^[11] which may be due to very small voxel/cell sizes were chosen to have high resolution for 2D anisotropy function, which may have increased the statistical uncertainty.

Conclusion

In this study, the TG-43 dosimetric parameters have been determined for the ¹⁹² Ir mHDR-v2 source experimentally and theoretically using the MC EGSnrc and GEANT4. The results obtained in this study compare favorably to each other and to those reported previously. The radial dose function measured and calculated study of this source also show agreement with each other and with the published data. These dosimetric parameters can be used as input data to verify the calculations of TPS for exact dose delivery to the patient in brachytherapy.

References

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