CHARACTERISTICS OF DEGRADED ELECTRON BEAMS PRODUCED BY NOVAC7 IORT ACCELERATOR

ANALELE STIINTIFICE ALE UNIVERSITATII AL. I. CUZA IASI Tomul II, s. Biofizică, Fizică medicală şi Fizica mediului 2006 CHARACTERISTICS OF DEGRADED ELECTRON BEAMS PRODUCED BY NOVAC7 IORT ACCELERATOR Dan Mihailescu 1 KEYWORDS: IORT, Monte Carlo, BEAMnrc, dosimetry, electron beams. The electron beams produced by NOVAC7 IORT accelerator have been modelled with BEAMnrc, a general purpose Monte Carlo code for simulating radiotherapy beams from linear accelerators or 60 Co units. The realistic electron beams were stored in phase-space files which have been used as input in BEAMDP code to calculate energy, angular, fluence and mean energy distributions at the phantom surface. Due to the technical limitations, such beam characteristics are difficult or even impossible to be experimentally determined. In these conditions, the use of Monte Carlo method is the only way in which we can enhance our knowledge on many aspects of the clinical beams. 1. INTRODUCTION Knowledge of clinical beams is essential for dosimetry, treatment planning, quality assurance, and design of an accelerator. In the radiotherapy of cancer, the treatment plan can only be made correctly if the characteristics of the beam are known. The physical, chemical and radiobiological effects as well as the response of various radiation detectors also depend by the beam characteristics. Experimentally it is difficult to obtain full information about beam quality because of various limitations in the clinical environments and detectors. Moreover, it is not possible, using experimental methods, to distinguish between electrons which are scattered by different beam defining system (primary collimator, jaws, applicators, etc.). The beam quality is strongly influenced by these scattered electrons that may have a large contribution to the dose distributions in a patient (or phantom) [1]. The Monte Carlo method has been shown to be suitable for modelling realistic electron beams from medical linear accelerators, including those used in the Intraoperative Radiation Therapy (IORT) [2]. IORT refers to the delivery of a single high dose of radiation (usually more then 10 Gy) at the time of surgery when the tumour bed can be precisely defined and adjacent normal tissue maximally protected. An example could include a tumour, which is unresectable from critical normal tissue or surrounding tissue that may contain microscopic cancer cells. IORT machines require dedicated collimation systems that increase the number of scattered electrons in the clinical beams. The IORT electron beams will therefore have different characteristics compared to beams obtained from standard accelerators. This paper presents detailed information and characteristics of some electron beams produced by NOVAC7 IORT accelerator. The accuracy of the simulated clinical beams was previously demonstrated [3] by comparing the calculated and measured dose distributions in water phantoms. 1 The Al. I. Cuza University of Iasi, Faculty of Physics, Depart. of Medical Physics and Biophysics

D. MIHAILESCU 104 2. MATERIALS AND METHODS Using the BEAMnrc [4] Monte Carlo code, we have simulated various beams produced by the NOVAC7 IORT accelerator. The NOVAC7 System (Hitesys SpA, Italy) [5] is a mobile electron linac for IORT that produces pulsed electron beams (2 9 cgy/pulse) with four different nominal energies: 3, 5, 7 and 9 MeV. It is equipped with an adjustable robot arm that can be focused on the operating field. The basic system includes four types of PMMA cylindrical applicators with inner diameters 4, 6, 8 and 10 cm, wall thickness 0.5 cm and lengths 69, 67, 67 and, respective, 87 cm. These applicators are available in two different forms: right (0 ) and bevelled (15, 22.5 and 45 ). The sourceto-surface distance is SSD = 80 cm, excepting the 10 cm diameter case in which SSD = 100 cm. Our simulation covers only electron beams obtained with right applicators. All nominal energies have been examined for the biggest applicator (10 cm diameter), while the 4, 6 and 8 cm diameter applicators have been investigated only for the higher nominal energies (7 and, especially, 9 MeV). BEAMnrc [4] is an EGSnrc [6] based general purpose Monte Carlo code originally developed for simulating radiotherapy beams from accelerators or 60 Co units. BEAMnrc models the therapy source with the z-axis taken as the beam-axis. The model consists of a series of component modules (CMs), each of them being contained between two planes which are perpendicular to the z-axis. There can be an arbitrary number of scoring planes which are at the back plane of a CM and thus perpendicular to the z-axis. The main output of BEAMnrc is a phase-space data file for every scoring plane. The phase-space files contain all the information about every particle that cross the appropriate scoring plane, i.e. charge (electron, photon or positron), energy, moving direction, and the entire history of that particle. The particle history is scored trough a special 28 bit variable named LATCH [4, 6]. The LATCH technique allows one, for instance, to separate the effects of primary and secondary electrons, or to identify those particles that have passed or interacted in certain components of the simulated system (accelerator, 60 Co machine or phantom). We have modelled the NOVAC7 accelerator as a series of simple BEAMnrc component modules with cylindrical symmetry centred on Z-axis (fig. 1). The accelerator head includes the exit window and a PVC structure that acts like a primary collimator. Inside of this structure there is a transmission monitor ion chamber. The PMMA cylindrical applicators are connected to the primary applicator by PMMA connectors. In BEAMnrc simulations we have used default values for EGSnrc particle s transport parameters, PRESTA-I for boundary crossing algorithm and PRESTA II as electron transport algorithm. Both photons and electrons are transported down to 10 kev kinetic energies (ECUT = 0.521 MeV, PCUT = 0.01 MeV). The cross section data were created using PEGS4 [6] with AE = 0.521 MeV and AP = 0.01 MeV including Sternheimer density effect corrections from ICRU 37 [7]. The number of histories was 10 x 10 6 for all the energies. The CPU time/history was in the interval 1.59 x 10-3 2.69 x 10-3 s, depending on the nominal energy (smaller for lower energies) and applicator size. The scoring planes have been placed before and after IORT applicator (at the phantom surface). The phase space data files obtained at these scoring planes were used as input in BEAMDP code to calculate energy, angular, fluence and mean energy distributions.

105 CHARACTERISTICS OF DEGRADED ELECTRON BEAMS Fig. 1- BEAM model used to simulate electron beams from NOVAC7 accelerator and the water phantom (not to scale). BEAMDP (BEAM Data Processor) [8] was developed to help the BEAMnrc [4] users to analyze the electron beam data obtained by the Monte Carlo simulation of the coupled transport of photons and electrons in different simulated systems. In order to calculate the energy spectra of simulated beams, the particles fluence (planar or actual) [8] is scored in a user-specified field vs. particles energy with energy bins of equal bin width within a specified spatial region. Fluence is normalized to the bin width and the number of incident particles. The angular distributions are calculated like the total number of particles scored in an angular bin of equal bin width within a specified spatial region. Fluence distribution means the total number of particles scored in spatial bins of equal area. Finally, the mean energy distribution is calculated as the ratio of the total particle energy to the total number of particles scored in a spatial bin of equal area. Full documentation (manuals and papers) can be found at the internet address http://www.irs.inms.nrc.ca, the web site of The National Research Council of Canada.

D. MIHAILESCU 106 3. RESULTS AND DISCUSSION Figure 1 shows the electron energy spectra after IORT applicator (at the phantom surface) calculated for 3, 5, 7 and 9 MeV nominal energies when a d = 10 cm diameter applicator (SSD = 100 cm) is used. All these spectra are planar fluence scored in a circular field with 10 cm diameter as a function of electron energy. For comparison, all four spectra contain the same number of electrons (i. e. the spectra are normalized to the same area). Similar calculations have been done for the 4, 6 and 8 cm applicators (9 MeV nominal energy), the parameters of all of the obtained spectra being shown in Table 1. Fig.1- Electron energy spectra at the phantom surface obtained for 10 cm IORT beams and 3, 5, 7, and 9 MeV nominal energies. The spectra are normalized to the same area. The energy bin size is 0.045 MeV. Table 1: The parameter of the electron spectra obtained at the phantom surface for IORT beams under investigation; E max,0, E p,0 and E 0 are the maximum, the most probable and, respective, the mean energy of the electrons; Γ 0 is the full width at half maximum (FWHM). Nominal energy/ Type of applicator SSD (cm) E max,0 (MeV) E p,0 (MeV) E 0 Γ 0 (MeV) (MeV) 9MeV_d10 100 8.28 7.98 6.34 0.16 9 MeV_d8 80 8.31 8.02 6.39 0.15 9MeV_d6 80 8.31 8.02 6.44 0.17 9MeV_d4 80 8.31 8.02 6.55 0.20 7MeV_d10 100 7.28 6.98 5.54 0.18 5MeV_d10 100 6.29 5.99 4.75 0.18 3 MeV_d10 100 5.10 4.80 3.79 0.18

107 CHARACTERISTICS OF DEGRADED ELECTRON BEAMS The mean energy of the IORT electrons at the phantom surface increases with the decreasing of the field size. This result can be explained analysing the figure 2. The smaller diameter applicators will give rise to more degraded electron beams, but the electron spectra have different shapes: for smaller fields, the region of high energies is increased and that of low energies is decreased. It is interesting to note that spectral distributions of scattered electrons in the case of 10 and 8 cm applicators are very similar, but this is only an effect of their different length: the 8 cm applicator is 20 cm shorter, so the effect of smaller diameter is balanced by those of smaller length. For this reason, the comparison of the effects due to the applicators of different thickness could be irrelevant. Fig. 2- Electron energy spectra at the phantom surface obtained for 9 MeV nominal energy and 4, 6, 8 and 10 cm diameter applicator. The spectra are normalized to the same area. The energy bin size is 0.045 MeV. Fig. 3- The electron energy distributions for the 9MeV_d4 IORT electron beam.

D. MIHAILESCU 108 More information about electron spectra can be obtained investigating the direct and scattered components contributions (see, for example, figure 3). The spectral distribution of the direct electrons has a prominent peak that practically gives the maximum and the most probable energy of the IORT electron energy spectra. Compared with the direct electrons, the scattered electrons are much more degraded, due to the interactions with the long IORT applicator. As a consequence, the scattered electrons energy distributions contain more electrons with low energies than those of the direct electrons. 3.2 Mean energy and fluence distributions Figures 4a and 4b show the electron mean energy distribution and the fluence distribution respectively, together with the contributions of direct and scattered electrons, calculated for the same nominal energy (9 MeV) and the same applicator (d = 10 cm, SSD = 100 cm). The direct electrons have a practically constant mean energy everywhere in the field, but its fluence decreases toward applicator wall. The mean energy of the electrons that have been scattered on IORT applicator increases slowly from the central zone to the edge of the field, but its fluence increases toward the wall (more scattered electrons are situated in the vicinity of the IORT applicator). (a) (b) Fig. 4 A comparison of the mean energy distributions (a) and fluence distributions (b) calculated for the IORT electron beam (labelled as total ) and his direct and scattered components at phantom surface (z = 0) in the case of 9 MeV nominal energy when an IORT 10 cm diameter applicator (SSD = 100 cm) is used. The mean energy distributions calculated for all IORT fields under investigation reveal an excellent uniformity: every IORT field have a circular central zone in which the medium energy remains constant in the limit of 1%. The diameters of these zones are situated in the interval 2.6 6 cm. The smaller value is obtained for d = 4 cm applicator and the biggest one for d = 10 cm applicator.

109 CHARACTERISTICS OF DEGRADED ELECTRON BEAMS In table 2 are shown the mean energies at the phantom surface (z = 0), for all electron IORT beams under investigation. To evaluate the dosimetric differences between the NOVAC7 IORT electron beams and the mono-energetic electron beams with the same R 50, we have compared the calculated mean energies with those obtained using the IAEA International Code of Practice TRS-381 [9]. According to this dosimetry protocol, the quality of a an electron beam is specified in terms of the mean electron energy at the phantom surface ( E 0 ) which is required to evaluate other quantities and parameters used in the dosimetric calculation formalism, mainly affecting the choice of water to air stopping power ratios, s w,air (see, for instance, the reference [10]). TRS-381 recommends the following empirical relationship to calculate E 0 : E ( ) 2 0 = 0.656 + 2.059 R 50 + 0.022 R 50 (1) where R 50 (the depth at which the dose falls to 50% of its maximum) is determined from the experimental depth dose curve [3]. Table 2: Comparison of the electron mean energies (in MeV) at phantom surface. The Monte Carlo values (MC) have been obtained from mean energies distributions like those illustrated in figure 4a, being calculated in small circular fields with diameter d f = 1.0 cm, centred on the z axis. The MC values are compared with those estimated using the IAEA International Code of Practice TRS-381 [9]. Δ = 100 x (MC- TRS)/TRS MC TRS-381 Δ (%) 9MeV_d10 6.44 6.86-6.1 9MeV_d8 6.49 6.90-6.1 9MeV_d6 6.47 6.94-6.9 9MeV_d4 6.61 6.86-3.5 7MeV_d10 5.60 6.03-7.1 5MeV_d10 4.79 5.16-7.2 3MeV_d10 3.82 4.11-7.1 All Monte Carlo values are lower (up to ~ 7.2 %) than those obtained using the TRS-381 protocol, due to the influence of the long PMMA IORT applicators. However, as we shown elsewhere [10], these large differences between monoenergetic (TRS-381) and clinical (realistic) beams have only a relative small influence (< 1.5 %) on the stopping-power ratios (s w,air ) values. 3. 3 Angular distributions Figure 5 shows the angular distributions of the NOVAC7 IORT electrons at the phantom surface for three particular cases: (a) the highest nominal energy - the biggest applicator (9MeV_d10), (b) the highest nominal energy the smallest applicator (9MeV_d4) and (c) the lowest nominal energy the biggest applicator

D. MIHAILESCU 110 (3MeV_d10). The angular distributions of the direct and scattered electrons are also represented in the same graphs. A comparison of the scattering angle parameters for all eight beams studied in this work is given in table 3. Fig. 5- Comparison of angular distributions of the IORT electrons for: (a) 9 MeV_d10, (b) 9 MeV_d4, (c) 3 MeV_d10. The angular bin size is 0.2.

111 CHARACTERISTICS OF DEGRADED ELECTRON BEAMS Table 3: Scattering angles (mean and most probable) at the phantom surface for different groups of electrons (all the electrons from IORT beams, direct electrons and those scattered on IORT applicator). Γ is the full width at half of maximum (FWHM). All values are expressed in degrees. IORT ( total ) Direct Scattered θ m θ p Γ θ m θ p Γ θ m θ p Γ 9MeV_d10 8.35 3.1 5.2 4.04 2.7 4.4 14.26 6.9 10.8 9MeV_d8 8.00 2.7 4.8 3.75 2.5 4.2 14.00 6.5 10.4 9MeV_d6 7.46 2.5 4.7 3.37 2.3 3.6 11.73 5.5 8.3 9MeV_d4 6.66 2.3 4.4 2.96 1.9 3.4 9.43 4.1 6.4 7MeV_d10 8.83 3.3 6.0 4.35 2.9 4.8 14.34 7.2 11.3 5MeV_d10 9.41 3.5 6.7 4.76 3.3 5.4 14.49 7.5 11.5 3MeV_d10 10.25 4.3 7.9 5.44 3.9 6.2 14.88 7.9 12.2 The angular distributions of the IORT electrons have well defined peaks at small angles, the most probable values, θ p, being between 2.3 and 4.3, and long tails that arrives until a maximum scattering angle θ max with values situated in the interval [61 79 ] (not seen in figure 5). This shape is a result of the different contributions of the principal two groups of electrons: (a) the direct electrons, with θ p [1.9 3.9 ], θ max [10 19 ] and (b) the scattered electrons with bigger scattering angles: θ p [3.5 7.9 ], θ max [61 79 ]. The scattered electrons have always larger Γ > Γ. The minimum distribution than those of direct electrons: ( ) ( ) p scattered p direct above values have been obtained for 9MeV_d4 IORT beam, while the maximum values characterises the 3 MeV_d10 beam, showing a dependence on the initial electrons energy spectra and applicator s size. Analysing the data from table 3, more information about this dependence can be obtained. For lower nominal energies, θ p, θ m and Γ have bigger values for all three IORT, direct and scattered electrons distributions, since the mass-scattering powers increases with decreasing energy [7]. In other words, at lower energies, the scattering angles have bigger values and the distributions become larger. The angular distributions are also strongly influenced by the applicator s diameter. For smaller diameters, θ p, θ m and Γ have smaller values, i. e. the scattering angles have smaller values and the distributions becomes sharper (the electrons become more forward directed). These results are similar with those obtained by Bjork et al for a treatment machine Philips/Elekta SL25 adapted for IORT [2]. The influence of the IORT applicators on electron scattering angles can be analysed comparing the angular distributions before and after long PMMA applicator (figure 6). The direct electrons after IORT applicator (figure 5) have sharper distributions. It means that only the electrons from the central part of the beam (that leave the accelerator head with small scattering angles) have the chance to reach the phantom surface without any interaction with the IORT applicator. The rest of them are absorbed or scattered on the applicator wall. As a consequence, the angular distributions of the IORT electrons at the phantom surface (figure 6) become sharper compared with those before applicator, but in the meantime they contain a greater amount of electrons with larger scattering angles, due to the scattered component.

D. MIHAILESCU 112 Fig. 6- The angular distributions before and after IORT applicators (at the phantom surface) for: (a) 9 MeV_d10, (b) 9 MeV_d4 and (c) 3 MeV_d10. For comparison, every pair of angular distributions contains the same number of electrons.

113 CHARACTERISTICS OF DEGRADED ELECTRON BEAMS Fig. 7- The angular distribution at the phantom surface of the NOVAC7 IORT electron beam 5MeV_d10 compared with that calculated by Bjork et al for an IORT beam produced by Philips/Elekta SL25 machine equipped with a 9 cm IORT cone for 6 MeV nominal energy (see Figure 6 a, from [2]). In the figure 7 is shown a comparison between the angular distributions at the phantom surface obtained for the NOVAC7 IORT electron beam 5MeV_d10 (5 MeV nominal energy, 10 cm diameter, SSD = 100 cm) and the angular distribution of an electron beam produced by a Philips/Elekta SL25 machine equipped with a 9 cm IORT cone for 6 MeV nominal energy [2]. The NOVAC7 beam has a sharper angular distribution, due to the absence of the scattering foils and to the longer IORT applicator. 4. CONCLUSIONS The realistic electron beams produced by NOVAC7 IORT accelerator have been modeled using the EGSnrc based general purpose Monte Carlo code, BEAMnrc [4] developed by Rogers et al from the National Research Council of Canada. The accuracy of the simulated clinical beams was previously demonstrated [3] by comparing the calculated and measured dose distributions in water phantoms. Important beam characteristics, such as the energy, angular, fluence and mean energy distributions of electrons at the phantom surface, have been than calculated with BEAMDP (BEAM Data Processor) code. Our investigation demonstrates the utility of the Monte Carlo simulation method to obtain detailed information of clinical electron beams. This information is important for further improving of electron beam dosimetry and treatment planning in radiotherapy.

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