ISSN 1547-4771, Physics of Particles and Nuclei Letters, 2016, Vol. 13, No. 7, pp. 808–811. © Pleiades Publishing, Ltd., 2016. Original Russian Text © G.E. Gorlachev, S.M. Polozov, A.V. Dalechina, A.I. Ksenofontov, A.V. Kistenev, 2016, published in Pis’ma v Zhurnal Fizika Elementarnykh Chastits i Atomnogo Yadra, 2016.
PHYSICS AND TECHNIQUE OF ACCELERATORS
Effects of Initial Electron Beam Parameters of a Linear Accelerator on the Properties of Bremsstrahlung Radiation in a Radiotherapy Setting G. E. Gorlacheva, *, S. M. Polozovb, A. V. Dalechinab, c, A. I. Ksenofontovb, and A. V. Kisteneva aBurdenko b
Scientific Research Neurosurgery Institute, Moscow, 125047 Russia National Research Nuclear University MEPhI, Moscow, 115409 c Moscow Gamma Knife Center, Moscow, 125047 Russia *e-mail:
[email protected] Received February 29, 2016
Abstract—The dependence of the initial electron-beam parameters on absorbed dose distributions have been investigated using a CyberKnife radiotherapy accelerator (Accuray, United States). To describe the initial electron-beam characteristics, simulations of the linear electron accelerator are performed and the electron distributions in the beam of a linac output are analyzed. The radial distributions of electrons are assumed exponential, whereas the energy electron distributions are approximated by monoenergetic and rectangular spectra. There is no significant dependence of depth-dose curves in a phantom on the shape of the electron beam. Importantly, a clear dependence of the radiation field profile on the size of the electron beam is observed not just in the penumbra region, but also in the open part. DOI: 10.1134/S1547477116070244
INTRODUCTION The accuracy requirements for dose delivery in radiotherapy are very high. Total errors of an absolute dose that are inclusive of measurement errors should not exceed 5%. Such high levels of precision in arbitrary clinical situations, in which irregular fields and significant heterogeneities of the environment are observed, can only be provided by the Monte Carlo method. To implement this method, a radiation source model is required. One of the most common approaches includes direct simulations of the radiation generation and also its transport inside the radiotherapy treatment head. This approach relies on knowledge of the initial electron-beam parameters of a linear accelerator (for a comprehensive review of the current state of the field and existing problems, see [1]). Due to the apparent segregation of the fields of accelerator technologies and radiation dosimetry, radiation dosimetry specialists use simplified approximations of electron-beam parameters by Gaussian distributions of energy spectra and radial intensities. One of the most fundamental studies used in the field of dosimetry modeling describes a radiation source of a typical medical linear electron accelerator, the size of which was determined as 1.5 ± 0.1 mm at full width at half maximum (FWHM) [2]. The fact that the direct Monte Carlo modeling of dose distributions does not ensure the sufficient fidelity of experimental data
forms the basis of this multidisciplinary research. The main assumption that we make here is that the traditional description of an electron beam hitting a radiation target is inaccurate. Here, the results of electrophysical simulations of a linear accelerator were used as the initial distribution of electrons on the target. MATERIALS AND METHODS To determine the sensitivity of radiation parameters to the parameters of an accelerated electron beam, electrophysical simulations of a C-band CyberKnife accelerator (Accuray, United States) with an energy of 6 MeV were carried out. Further, the modeling of radiation transport by the Monte Carlo method and a comparison with experimental dosimetry data obtained from a real radiotherapy unit were performed. The BEAMDULAC-BL program was used for electrophysical modeling [3]. Radiation transport simulations were carried out using software developed in-house; the software was written in C++ and reproduced the physics and algorithms of the EGS4 transport package [4]. The radiophysical modeling was performed for a typical linear C-band electron accelerator with an operating frequency of 5700 MHz. The results are presented as distribution graphs (Fig. 1) and in digital format, which includes information on the energy values, position, and direction of each electron at the target level.
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A series of calculations with varying injection currents and intensities of the accelerating field were carried out. As a result, the dynamics of 15 000– 20 000 electrons was recorded for each simulation. The electron distributions were further analyzed and approximated to satisfy the requirements for radiation transport modeling. The modeling geometry, as it was defined in the numerical experiment and displayed in a graphical format by the software, is shown in Fig. 2. A tungsten wafer with a thickness of 2 mm was used as the radiation target. The primary and main radiation field collimators were described in accordance with the specification of the accelerator manufacturer. The distance between the source and the reference plane at which the field size is defined was 80 cm; the diameter of the simulated field was 6 cm. The water phantom was located at a distance of 70 cm from the source. A dose scoring matrix consisted of conical rings with a thickness of 1 mm in depth and radius. Dose distributions were calculated for 109 electrons for each set of beam parameters. To improve the statistics of dose distributions, a particle-split technique was used, according to which each particle leaving the accelerator was split into 100 particles with a lower energy before its further transport in the air and phantom. Typical calculation PHYSICS OF PARTICLES AND NUCLEI LETTERS
times on a desktop computer with 12 parallel processes were 40 min per single case. The CyberKnife dose and depth-dose distribution measurements that were performed at the Burdenko Scientific Research Neurosurgery Institute were used as a reference. The measurements were acquired using Primary collimator
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a PTW PinPoint ionization chamber with an effective detector size in the scanning direction of 1 mm. It should be noted that any geometric distortions are negligible due to such a small detector size. The noise amplitude of measurements was within 0.5%, and this value should be considered the relative error of radiation-field dose profile measurements. RESULTS AND DISCUSSION The energy spectra and radial electron distributions at the accelerator output, which were obtained upon processing of the results of electrophysical simulations, are presented in Fig. 3. The energy spectra display an obvious dependence on the accelerator operation conditions. Moreover, two energy peaks with different amplitudes are observed, the overlay of which in some cases resulted in a rectangular shape of the spectrum. In contrast to the widely accepted Gaussian approximation, the radial profile of the beam intensity was described by the exponential function. A comparison of dose distributions, calculated by the Monte Carlo method, with the experimental data are shown in Fig. 4. The depth–dose curves correlate with the electron-beam energy distributions. Importantly, broadening of the electron spectrum did not result in noticeable changes in the depth–dose distributions, whereas changes in the average energy led to significant effects. It should however be noted that the experimental data cannot be perfectly described by theoretical distributions, even when the optimal
energy is used. This is likely due to inaccuracies in radiation interaction cross sections that were used in our calculations and also imprecise information about the material and structure of the target that affects the bremsstrahlung spectrum. The shape of radiation beam profiles was dependent on the size of the electron beam not only in the penumbra but also in the field. In comparison with the Gaussian distribution, the exponential approximation of the electron beam profiles allowed us to better describe the dose distributions in both regions simultaneously. In another study with analogous research goals, where accelerators with large radiation fields were investigated, no similar dependence was identified [5]. This is due to the fact that the CyberKnife accelerator uses a primary collimator with a diameter whose size is comparable to the size of the electron beam. As a consequence, the collimator serves as a shield for bremsstrahlung photons depending on the location of their appearance in the target. CONCLUSIONS A significant impact, in terms of radiation-therapy dosimetry, of the parameters of an electron-beam accelerator on the radiation-field dose distributions were demonstrated using simulations of radiation transport in the radiotherapy unit of a CyberKnife type with narrow fields. The thickness of the electron beam and its profile were found to be particularly important. It was shown that these parameters affect
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Fig. 4. Depth–dose distributions (a) and lateral profiles of the radiation fields (b) as calculated by the Monte Carlo method and measured using a CyberKnife unit. The depth–dose distributions are presented for a series of monoenergetic electron beams (mono) and a single electron beam with a rectangular spectrum from 6 to 8 MeV (rect). The r0 parameter reflects the radius at which the electron-beam intensity is reduced e times.
not only the size of the radiation field penumbra, but also the shape of its cross-dose distributions. In addition, no significant effects of the electron-beam spectrum on the radiation parameters, including depth– dose distributions and the shapes of radiation field cross profiles, were detected. REFERENCES 1. A. V. Dalechina, A. I. Ksenofontov, and G. E. Gorlachev, “Review of modeling of radiation sources of electron accelerators for dosimetric Monte Carlo calculations in radiotherapy,” Vestn. NIYaU MIFI 3, 316–328 (2014). 2. E. Loewenthal, E. Loewinger, E. Bar-Avraham, and G. Barnea, “Measurement of the source size of a 6- and
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18-MV radiotherapy linac,” Med. Phys. 19, 687–690 (1992). 3. T. V. Bondarenko, E. S. Masunov, and S. M. Polozov, “BEAMDULAC-BL code for 3D simulation of electron beam dynamics taking into account beam loading and Coulomb field,” Probl. At. Sci. Technol., Ser.: Nucl. Phys. Invest., No. 6, 114–118 (2013). 4. W. R. Nelson, H. Hirayama, and D. W. O. Rogers, “The EGS4 code system,” Report SLAC-265 (Stanford Linear Accelerator Center, Stanford, CA, 1985). 5. D. Sheikh-Bagheri and D. W. Rogers, “Sensitivity of megavoltage photon beam Monte Carlo simulations to electron beam and other parameters,” Med. Phys. 29, 379–390 (2002).
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Translated by S. Khoronenkova
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