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Abstract The linear energy transfer (LET) is commonly used as a parameter which describes the quality of the radiation applied in radiation therapy with fast ions. In particular in proton therapy, most models which predict the radiobiological properties of the applied beam, are fitted to the dose-averaged LET, LETd. The related parameter called the fluence- or track-averaged LET, LETt, is less frequently used. Both LETt and in particular LETd depends profoundly on the encountered secondary particle spectrum. For proton beams including all secondary particles, LETd may reach more than 3 keV/um in the entry channel of the proton field. However, typically the charged particle spectrum is only averaged over the primary and secondary protons, which is in the order of 0.5 keV/um for the same region. This is equal to assuming that the secondary particle spectrum from heavier ions is irrelevant for the resulting radiobiology, which is an assertion in the need of closer investigation. Models which rely on LETd should also be clear on what type of LETd is used, which is not always the case. Within this work, we have extended the Monte Carlo particle transport code SHIELD-HIT12A to provide dose- and track-average LET-maps for ion radiation therapy treatment plans. INTRODUCTION Linear energy transfer (LET) is commonly used as a physical parameter which relates to the relative biological effectiveness (RBE) of proton beams in radiation therapy(1). Numerous in vitro studies and some in vivo studies demonstrate an increase in the RBE towards the distal end of the spread out Bragg peak (SOBP), associated with the increased LET encountered here. Nonetheless, proton treatment protocols are routinely prescribed using a constant RBE of 1.1 over the entire SOBP(2, 3). In recent years, this practice has been challenged by reports of observed toxicities in the distal edge of the SOBPs and concerns on the safety of these protocols has been raised(4). Consequently, there is an increased interest to produce LET-maps of treatment plans in order to identify possibly high-LET areas and validate these against possible occurrences of high RBE effects. Here, we provide a tool which for a given CT-scan and irradiation plan will calculate the spatial average LET, weighted by either dose (dose-averaged, LETd) or fluence (i.e. track-averaged, LETt). Apart of choosing the weighting, one also needs to be clear on how the averaging is implemented in Monte Carlo particle transport codes, and which particles are used for calculating the average LET. The importance of choosing a proper LET-scoring method in Monte Carlo simulations was recently demonstrated in Ref.(5). However, this publication only described scoring of primary and secondary protons, which is commonly the case when working with proton beams. Heavier particles than protons are present in proton beams, induced by various nuclear reactions. In spite of their low contribution to dose, these secondary particles and fragments feature a high LET. Including or excluding particles with Z>1 was addressed(6). We will here investigate the impact of the secondary particle spectrum on the dose- and track-averaged LET scoring using the Monte Carlo particle transport tool SHIELD-HIT12A(7). This code utilizes the Multi Stage Dynamical Model (MSDM) generator in the exclusive approach, transporting secondary particles and recoil nucleus down to 25 keV/nucl. Neutron transport below 14.5 MeV is simulated using the 28 group neutron data system ABBN, see Ref.(7) and references within. SHIELD-HIT12A uses internal stopping power calculations, which optionally can be overridden by external tables. Several ion transport Monte Carlo codes are commonly used in radiation therapy research, such as Geant4(8), FLUKA(9), MCNP6/X(10), PHITS(11) and SHIELD-HIT12A. Whereas all of them give access to the full particle energy spectra at any position, only SHIELD-HIT12A provides direct ways to calculate average LETd and LETt for any part of the particle spectrum. Geant4 and FLUKA require additional routines provided by the user. PHITS and MCNP6 scores the LET spectra of the individual particles and requires the user to perform manual averaging. CALCULATION METHODS LET definitions Spatial LET distributions were obtained by extending the functionality of the SHIELD-HIT12A code. The recent version 0.7.1 is able to handle voxelized geometries in a fast and efficient manner. A common fragmentation algorithm is used to translate Hounsfield units to material compositions(12). Standard methods of scoring physical quantities (absorbed dose, particle fluence, average energy and others) are also extended to work with voxelized volumes. Dose-averaged LET is defined as the weighted average over all particles: LETd=∑iDiLETi∑iDi (1) Di denotes a dose delivered by a mono-energetic particle i with charge number zi and kinetic energy Ei, and its unrestricted electronic stopping power LETi. For Monte Carlo codes we will employ the average of the initial and final LET of a transport- or scoring step for a single particle as LETi. Track-averaged LET is defined in similar way to dose-averaged LET, but the particle fluence Φ is used as weighting factor. LETt=∑iΦiLETi∑iΦi (2) Four methods of LET-scoring were implemented, covering both dose- and track-weighted LET. In particular, we use the algorithms named ‘C’ from Ref.(5), as the reference concludes it to be superior. Upper index p denotes LET scored only for primary protons and any secondary protons encountered, excluding heavier ions, as well as deuterons and tritons. Index * denote LET scored for all charged particles. This leads to four different LET quantities: LETd☆—dose-averaged LET for all charged particles LETdp—dose-averaged LET for protons LETt☆—track-averaged LET for all charged particles LETtp—track-averaged LET for protons In either of the four cases, it must be stressed that full particle transportation is taking place, including all secondaries also heavier than protons. In other words, we simply demonstrate different ways of averaging the LET, including or excluding particles heavier than protons in Equations 1 and 2 . Simulation details A CT scan of a PBU-60 whole body phantom (Kyoto Kakagu, Japan) was used in our MC calculations. The scan was saved in DICOM format, with voxels 0.98 × 0.98 × 5 mm3. A treatment plan was prepared using the treatment planning system Eclipse 13.7 (Varian Medical Systems, Palo Alto, USA). Here, a constant dose was delivered to the planning target volume (PTV) which was located in the cerebral hemisphere. Furthermore, we assumed a pencil beam scanning facility, and kinetic energies of primary proton beam between 60 and 97 MeV were used to cover the PTV. The treatment plan was imported into SHIELD-HIT12A for recalculation. In SHIELD-HIT12A we have implemented the HU-density calibration curve from Schneider et al.(12). Furthermore, we utilized the aforementioned scoring algorithms into SHIELD-HIT12A. Here, we recalculated spatial distribution of dose, fluence, dose-averaged- and track-averaged LET, taking into consideration secondary particles created in nuclear reactions in human tissues as segmented by the Schneider algorithm(12). Scoring was done in a voxel grid synchronized with the CT voxels (512 × 512 × 211). The simulation was performed on the Prometheus supercomputer within the PLGRID infrastructure. High statistics was needed to obtain a reasonable estimate of LET including secondary particles: in total 500 parallel runs with 108 particles each were performed. RESULTS An overview of the dose distribution is shown in Figure 1. Dose and LET profiles of several LET values calculated along a cross-section of 2 × 2 cm2 are shown in Figure 2. Figure 1. View largeDownload slide CT slice of the phantom head where HU values are denoted as gray scale colors. The 95, 85 and 75% isodose lines (round contours) and the cross-section rectangle are also indicated. Beam enters from the right. Figure 1. View largeDownload slide CT slice of the phantom head where HU values are denoted as gray scale colors. The 95, 85 and 75% isodose lines (round contours) and the cross-section rectangle are also indicated. Beam enters from the right. Figure 2. View largeDownload slide Dose and dose-averaged LET profiles calculated on a 2 × 2 cm2 cross-section, as indicated in Figure 1. Figure 2. View largeDownload slide Dose and dose-averaged LET profiles calculated on a 2 × 2 cm2 cross-section, as indicated in Figure 1. Shortly before the proton beam reaches the PTV (position A in Figure 2), the dose-averaged LET excluding all particles heavier than protons was found to be ≈2 keV/um. Including the heavier secondaries increased the dose-averaged LET to ≈4 keV/um at the same position. Track-averaged LET at the same point was found to be at the level of ≈1.2 keV/um. After passing through the PTV, at a point (position B in Figure 2) where dose diminishes to 1% of the value prescribed to the PTV, the LET was also assessed. Here, dose-averaged LET reached ≈10 keV/um for protons, and ≈15 keV/um including heavier particles. Track-averaged LET was found to be ≈7 keV/um for protons and ≈9 keV/um for all charged particles. In the PTV region and in the entrance channel the contribution of secondary particles to the total dose was found to be in the range 0.1–1%. This contribution increases significantly in the distal region, where the primary beam is stopped and the residual dose is delivered by charged particles generated by mainly secondary neutrons or protons. The contribution of secondary particles to the total fluence yields a different profile than the contribution to the dose. Until the distal part of the PTV, its contribution is less than to the dose, ranging from 0.01 to 0.5%. In the distal region the fluence is dominated ( ≥99%) by secondary protons while heavier secondary particles are less likely to be generated. To investigate the influence of material composition on the LET values we simulated the proton beam presented on Figure 1 irradiating two homogeneous materials: liquid water and brain tissue. Despite different compositions, no differences larger than 1% in terms of LET were observed. All four SHIELD-HIT12A LET calculation methods were cross checked using PHITS, confirming the observations in the present study. Furthermore the calculated LETdp was found to be in agreement with values found in literature(6). DISCUSSION Values of LET scored by Monte Carlo codes are affected by the applied averaging method (track- or dose- averaging). The largest deviations in the distal part of the Bragg peak, due to nuclear reactions. This is evident when observing the large differences between LETd and LETt at position B in Table 1, highlighting the importance of calculating an accurate secondary particle spectrum as this is strongly correlated to both LET quantities. The production of secondary particles depends on the elemental composition of the material in which the proton transportation is calculated. The ability of protons to undergo non-elastic nuclear interactions depend on their kinetic energy in relation to the Coulomb barrier of the target nuclei which varies for different elements. For protons with energies up to a few MeV, the production of secondary particles could therefore vary depending on the material composition used in the calculations. This was however not observed in our study, and may be attributed to the fact that the total fraction of elements heavier than carbon which contribute mostly to the secondary particle production is similar in water and soft tissues. Table 1. Averaged LET values. Position LETd☆ LETdp LETt☆ LETtp cm keV/um keV/um keV/um keV/um 30.3 (A) 4.08 2.00 1.23 1.22 25.5 (B) 14.62 9.78 9.30 7.01 Position LETd☆ LETdp LETt☆ LETtp cm keV/um keV/um keV/um keV/um 30.3 (A) 4.08 2.00 1.23 1.22 25.5 (B) 14.62 9.78 9.30 7.01 Table 1. Averaged LET values. Position LETd☆ LETdp LETt☆ LETtp cm keV/um keV/um keV/um keV/um 30.3 (A) 4.08 2.00 1.23 1.22 25.5 (B) 14.62 9.78 9.30 7.01 Position LETd☆ LETdp LETt☆ LETtp cm keV/um keV/um keV/um keV/um 30.3 (A) 4.08 2.00 1.23 1.22 25.5 (B) 14.62 9.78 9.30 7.01 Nuclear reactions leading to production of secondary particles are rare. As a technical consequence, the variance of dose and proton-only LET Monte Carlo scorers is much lower than that of LET which includes also secondary particles. This results in much longer calculation times when assessing LET☆, contrary to LETp. In the region where protons have kinetic energies between few and few tens of MeV, secondary particles are produced with range of tens of micrometers and kinetic energy ≈1 MeV/nucleon. The most common reactions lead to production of alpha particles which yield LET values of ≈150 keV/um. Heavier secondaries reach higher values of LET which scales with the square of particle charge. These observations explain the increase in LETd☆ when compared with LETdp. For track-averaged LET, this difference is reduced in the PTV region, due to that the contribution to the fluence is <0.1 at this location. In the region behind the PTV, a similar trend is observed as for LETd. Most of the proton therapy radiobiological models assume a linear or close-to-linear relation between RBE and LET for protons. These models are based on experimental datasets, taking into account only LETdp(1, 13). As it was shown in the example treatment plan study, LET values obtained with other scoring methods may yield values which differ almost by two orders of magnitude (i.e. LETt☆ vs LETd☆ in the position B, Table 1). When applying radiobiological models on top of the quantities calculated using Monte Carlo methods, it is essential that the LET scoring method follows the same method as in the model construction. The dire need for acquiring high-quality data reporting the biological effectiveness of proton and heavier ion beams has been addressed by multiple papers, along with calls for dedicated facilities(3, 14, 15). Thus, when radiobiological experiments report RBE values for a specific endpoint and a given LET, we here wish to emphasize the importance on clearly stating how the LET was obtained, ideally with a sufficiently detailed description that the radiation field can be reproduced by independent MC calculations. Future research may even point to better radiation quality parameters than LET for characterizing the response of radiobiology in mixed radiation environments. Nonetheless, even in mono-energetic fields, the presence of secondary particles may alter the LET, as it depends on the scoring algorithm applied and whether LETd☆ or LETdp was acquired. CONCLUSION In this study we summarize some properties of dose- and track-averaged LET which tend to be overlooked. 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Radiation Protection Dosimetry – Oxford University Press
Published: Aug 1, 2018
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