Calculated relative biological effectiveness (RBE) for initial DNA double-strand breaks (DSB) from flattening filter and flattening filter-free 6 MV X-ray fields

Objectives: We evaluated the radiobiological effectiveness based on the yields of DNA double-strand breaks (DSBs) of field induction with flattening filter (FF) and FF-free (FFF) photon beams. Methods: We used the particle and heavy ion transport system (PHITS) and a water equivalent phantom (30 × 30 × 30 cm3) to calculate the physical qualities of the dose-mean lineal energy (yD) with 6 MV FF and FFF. The relative biological effectiveness based on the yields of DNA-DSBs (RBEDSB) was calculated for standard radiation such as 220 kVp X-rays by using the estimating yields of SSBs and DSBs. The measurement points used to calculate the in-field yD and RBEDSB were located at a depth of 3, 5, and 10 cm in the water equivalent phantom on the central axis. Measurement points at 6, 8, and 10 cm in the lateral direction of each of the three depths from the central axis were set to calculate the out-of-field yD and RBEDSB. Results: The RBEDSB of FFF in-field was 1.7% higher than FF at each measurement depth. The RBEDSB of FFF out-of-field was 1.9 to 6.4% higher than FF at each depth measurement point. As the distance to out-of-field increased, the RBEDSB of FFF rose higher than those of FF. FFF has a larger RBEDSB than FF based on the yields of DNA-DSBs as the distance to out-of-field increased. Conclusions: The out-of-field radiobiological effect of FFF could thus be greater than that of FF since the spreading of the radiation dose out-of-field with FFF could be a concern compared to the FF. Advances in knowledge: The RBEDSB of FFF of out-of-field might be larger than FF.


INTRODUCTION
Compared to the conventional flattening-filter photon beam (FF), a flattening filter-free photon beam (FFF) allows for an approximately two-to fourfold increase in the dose rate. [1][2][3] The high dose rate afforded by FFF photon beams is an advantage in that it shortens the beam-on time by approx. 10-30%. 2,3 The use of an FFF also helps minimize the intrafraction motion of tumors, 4 which is especially relevant for cases in which a large dose per fraction is used, such as in stereotactic body radiation therapy (SBRT) [5][6][7] since the dose rate of an FFF is higher than the dose rate that can be provided by an FF. Moreover, FFFs have been used for intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT). 5 Several research groups have reported a physical evaluation and dose distribution of FFF [8][9][10] ; however, these studies were conducted with a focus other than the dose rate when the differences between FF and FFF were evaluated. The in-field and out-of-field dose profiles of the FFF were differed from those of the FF when the actual measurements and a Monte-Carlo simulation were used to evaluate. 11,12 An FFF was irradiated with a high-dose rate photon beam, 2,3 but there have been few radiobiological evaluations to determine the effects of dose rate variations on tumor cells. The radiobiological effects of using a cell survival fraction and an FFF were reported 13,14 ; no significant difference was observed in the cell survival fraction after irradiation with a https:// doi. org / 10. 1259/ bjro. 20200072 Objectives: We evaluated the radiobiological effectiveness based on the yields of DNA double-strand breaks (DSBs) of field induction with flattening filter (FF) and FF-free (FFF) photon beams. Methods: We used the particle and heavy ion transport system (PHITS) and a water equivalent phantom (30 × 30 × 30 cm 3 ) to calculate the physical qualities of the dose-mean lineal energy (y D ) with 6 MV FF and FFF. The relative biological effectiveness based on the yields of DNA-DSBs (RBE DSB ) was calculated for standard radiation such as 220 kVp X-rays by using the estimating yields of SSBs and DSBs. The measurement points used to calculate the in-field y D and RBE DSB were located at a depth of 3, 5, and 10 cm in the water equivalent phantom on the central axis. Measurement points at 6, 8, and 10 cm in the lateral direction of each of the three depths from the central axis were set to calculate the out-offield y D and RBE DSB . Results: The RBE DSB of FFF in-field was 1.7% higher than FF at each measurement depth. The RBE DSB of FFF outof-field was 1.9 to 6.4% higher than FF at each depth measurement point. As the distance to out-of-field increased, the RBE DSB of FFF rose higher than those of FF. FFF has a larger RBE DSB than FF based on the yields of DNA-DSBs as the distance to out-of-field increased. Conclusions: The out-of-field radiobiological effect of FFF could thus be greater than that of FF since the spreading of the radiation dose out-of-field with FFF could be a concern compared to the FF. Advances in knowledge: The RBE DSB of FFF of out-offield might be larger than FF. photon beam at high dose rates. 13,14 Our 2018 study of the radiobiological effects of FFF beam using A549 (non-small-cell lung cancer) cells showed no significant difference in cell motility or the cell survival fraction. 15 However, these studies evaluated the radiobiological effect only on the in-field dose distribution, and the effects on tumor cells based on the difference in dose profiles with the out-of-field distribution have not been established. The dose spreading out-of-field of the FFF also differed from that of the FF since an FF and an FFF have different dose profiles. It is thus necessary to evaluate the radiobiological effects of FFF in an out-of-field condition.
DNA strand breaks such as single-and double-strand breaks (SSBs and DSBs) are induced along ionizing radiation tracks in cells composed mainly of liquid water. 16,17 Monte-Carlo simulations have been very useful to estimate the yields of DNA strand break by assessing the track structures for electrons in liquid water. Researcher have sought to conduct track structure simulations at the nanometer scale of secondary electrons and to predict the track structure of electrons for calculations of the spatial distribution of DNA hits. However, calculating both the energy deposition and the free radical reaction to DNA takes a significant amount of time to evaluate. A particle and heavy ion transport code system (PHITS) was shown to be able to simulate the track structure of electrons in liquid water in the incident energy range from 1 meV to 1 MeV, 18 and PHITS v.3.20 could estimate the evaluation of the impacts by low energy electrons on the yields of DNA strand break induction based on the physical processes of electrons exhibited. 19 Considering the DNA strand breaks, not only the physical conditions but also the radiobiological effectiveness was evaluated between an FF and an FFF.
In this study, we calculated the yields of DNA strand breaks (SSBs, DSBs, and the DSB/SSB ratio) to evaluate the radiobiological effectiveness of an FF and an FFF based on the difference between the in-field and out-of-field dose distributions.

Monte-Carlo simulations are calculated by the PHITS
The PHITS uses Monte-Carlo simulations code and can deal with photons, electrons, positrons, neutrons, and heavy ions. 18,[20][21][22] In the present study, we used the PHITS v.3.20 with the default setting, and we used the International Atomic Energy Agency (IAEA) phase-space file of the Varian TrueBeam linear accelerator (Varian Medical Systems, Palo Alto, CA).
The BEAMnrc code was based on the EGSnrc platform and is optimized for modeling the treatment head of radiotherapy linear accelerators. 23 This code includes several geometry and source subroutines, along with the variance reduction techniques to enhance simulation efficiency. 24 The below phasespace files were made using BEAMnrc, which is built on the EGSnrc platform. These phase-space files created by BEAMnrc were transferred to the PHITS for the calculation of the dose distribution. The irradiation geometry for the 6 MV FF and FFF was as follows: a 30 × 30 × 30 cm 3 water equivalent phantom was used; the source to skin distance (SSD) was 90 cm, and the field size was 10 × 10 cm 2 ( Figure 1). The 220 kVp photon beam, which was the reference for deriving the relative biological effectiveness (RBE), was calculated with the same geometry as that used for the 6 MV FF and FFF photon beams. The measurement points to calculate the dose-mean lineal energy and the in-field radiobiological effectiveness were located at a depth of 3, 5, and 10 cm in the water equivalent phantom on the central axis. In addition, 6, 8, and 10 cm in the lateral direction of each depth from the central axis were set as measurement points to calculate the outof-field radiobiological effectiveness.
Calculation of dose-mean lineal energy y D We calculated the physical qualities of the dose-mean lineal energy y D (keV/µm) of the 6 MV FF and FFF photon beams on each measurement point in-field and out-of-field (cut-off energy = 1.0 keV). The lineal energy y in keV/μm was given by Equation (1): The dose-mean lineal energy y D 25-27 was calculated as: where ε is the energy deposited in a domain, l is the mean chord length, y is the lineal energy, f(y) is the probability density of the lineal energy, and d(y) is the dose distribution of the lineal Estimation of SSB, DSB, and the DSB/SSB ratio by 6 MV FF and FFF irradiation using PHITS.
PHITS v.3.20 has been shown to effectively consider the track structure code to calculate the precise electron features on a scale from a single track to DNA. 19 The yields of strand breaks (SSBs and DSBs) using the PHITS calculation have been compared and verified with other published data including ICRU reports, the results of other simulation codes, and experimental data, 19 and good agreement of the DSB yield calculated by PHITS with experimental DSB data has been shown for both electron and photon irradiations. By analyzing the spatial coordinates of ionization and excitation, it was possible to calculate the generation rate of DNA damage induced on charged particle tracks. The number of events per track and the number of a pair composed of two events within 3.4 nm (10 base pairs, bp) were stochastically sampled for calculating the yields of SSBs, DSBs, and the DSB/ SSB ratio since the DNA strand breaks were induced by ionization and electronic excitation. 29,30 PHITS calculates the number of SSB and then calculates the fraction of them that lie within 10 bp on opposite strands to obtain the numbers of initial DSB.
The number of events per keV N event /E in and the number of linkages per keV N link /E in were calculated to obtain the induction yield of SSBs and DSBs, respectively [19]. PHITS defined k SSB and k DSB as proportion coefficients for SSB and DSB inductions (keV/Gy/Da), respectively, that is, the coefficients k SSB = 5.66 × 10 −12 (keV/Gy/Da) and k DSB = 1.61 × 10 −13 (keV/ Gy/Da). 19 The numbers of SSB Y SSB and DSB Y DSB (/Gy/Da) as a function of electron incident energy are defined as: We calculated the DSB/SSB ratio by using the yield ratio of DSBs and SSBs (Y DSB /Y SSB ). The energy spectra of electrons by FF and FFF on each measurement point were used to calculate the yields of SSBs and DSBs and the DSB/SSB ratio.

The RBE based on the yields of DNA-DSBs
The yield of DNA-DSBs is considered an endpoint for evaluations of radiobiological effectiveness. 31,32 The RBE obtained using the ratio of DNA-DSBs (RBE DSB ) has been calculated for standard radiation such as 220 kVp X-rays, since the absorbed dose is related to the number of DNA-DSBs per nucleus. 33 In the present study, the RBE DSB was calculated by the ratio of the number of DNA-DSBs per nucleus with a 1.0 Gy absorbed dose when FF and FFF photon beams were irradiated on each measurement point to the number of DNA-DSBs of 220 kVp X-rays as follows:

The dose-mean lineal energy y D of FF and FFF
Our calculations of the dose-mean lineal energy y D in the water equivalent phantom for the 6 MV FF and FFF are illustrated in We calculated the ratios of DSB/SSB with 6 MV FF and FFF. At the 3 cm depth, the ratios of DSB/SSB with the FF were 0.056, 0.057, 0.058, and 0.059, and those with the FFF were 0.056, 0.057, 0.059, and 0.060 at the three measurement points 6, 8, and 10 cm in the lateral direction from the central axis, respectively (Figure 4a). At the 5 cm depth, the ratios of DSB/SSB with the FF were 0.056, 0.057, 0.058, and 0.059, and those with the FFF were 0.056, 0.057, 0.059, and 0.060 (Figure 4b). At the 10 cm depth, the ratios of DSB/SSB with the FF were 0.056, 0.057 0.059, and 0.060, and those obtained with the FFF were 0.056, 0.058, 0.060, and 0.061 (Figure 4c). There was little effect on the yield of DSBs or the DSB/SSB ratio by changing the measured depth on the central axis in the comparison of FF and FFF (in-field), but the values were the larger with greater distance and the longer lateral distance from the central axis (out-of-field).  (Figure 5a). At the 5 cm depth, the corresponding values for FF were 0.74, 0.82, 0.90, and 0.94, and those for FFF were 0.75, 0.86, 0.95, and 1.00 (Figure 5b). At 10 cm deep, the corresponding values for FF were 0.74, 0.88, 0.98, and 1.00, and those for FFF were 0.75, 0.92, 1.04, and 1.07 (Figure 5c). The RBE DSB values were larger in FFF at all measurement points, and therefore FFF has a greater RBE than FF; the RBE of out-of-field was also greater.

DISCUSSION
After the FF was removed, the spectrum of the FFF photon beams with the Varian TrueBeam linear accelerator was softened and the proportion of low-energy components was increased compared to FF. 34 In addition, a characteristic of the beam profile of FFF was the lower out-of-field dose distribution compared to FF. 35 The physical qualities of the dose-mean lineal energy y D values on the central axis of FF and FFF were almost the same (Figure 2). Regarding the out-of-field, the y D values for FFF were larger than those for FF because FFF has more low-energy components ( Figure 2).
We used the DNA-DSB yield to calculate the RBE DSB values in the present study. To the best of our knowledge, this was the first study to calculate the yield of DNA-DSBs of FFF by a Monte-Carlo simulation. The RBE DSB values were almost the same in-field, even when the depth changed ( Figure 5). The result of in-field observation was equal to A549 cell survival comparing FF with FFF. 15 On the other hand, the RBE DSB outof-field values increased as the depth and the distance from the central axis increased ( Figure 5). We observed that compared to an FF photon beam, FFF has larger RBE DSB values. We speculate that (1) the energy of the photon beam shifts to a lower energy value as the depth becomes deeper and the distance from the central axis becomes larger; and (2) the tendency is larger in FFF.
Yachi et al calculated the relationship between the calculated y D values for various types of X-rays, measured the RBE DSB values, and derived an approximate formula. 30 Our present findings regarding RBE DSB values are valid in comparison with the approximate formula. On the central axis (in-field), the difference of RBE DSB values between FF and FFF was within 2% regardless of the depth and thus almost the same values. On the other hand, the RBE DSB values of FFF were greater than those of FF as the distance to out-of-field increased. The RBE DSB values of FFF were higher than those of FF by 1.7%, 4.6%, 5.6%, and 6.4% at each measurement points with a depth of 10 cm with 6 cm, 8 cm and 10 cm in the lateral direction from the central axis, respectively. The result that the RBE DSB values of FFF was larger than FF was increased as the depth and the distance from the central axis increased (Figure 5). It was considered because the proportion of low dose for FFF was increased than FF with deeper and out-of-field. The increasing the proportion of low dose for FFF could also be confirmed from the results of y D (Figure 2). As a result, the RBE at out-of-field of FFF might be greater than that of FF.
The advantages provided by the characteristics of FFF have enabled its use in IMRT and VMAT in clinical settings. 5 The irradiation technique of spreading the absorbed dose out-of-field has been reported in several radiotherapy studies. [36][37][38][39] There is also concern about a secondary cancer risk due to the spreading of the dose out-of-field. 40 Furthermore, although IMRT and VMAT use the multi-leaf collimator (MLC) to perform intensity modulation of the dose distribution, the irradiation field was formed by only the jaw without MLC to evaluate the RBE DSB value of FF and FFF in this study. The shape of the dose profile of MLC combined with jaw was different from the field by only the jaw. 41 Therefore, it is necessary to evaluate the RBE DSB value of out-offield using the MLC. It may thus be advisable to pay attention to the spreading of the dose out-of-field when FFF is used for IMRT and VMAT.
There is a study limitation to address; we obtained the result showing that the RBE DSB value of FFF was higher by approximately 6% compared to FF at the out-of-field. The clinical impact of the difference in RBE DSB values between FF and FFF is not yet known. Further studies are necessary to determine the precise effects of radiobiology.

CONCLUSIONS
FFF has greater RBE DSB values than FF based on the yield of DNA-DSBs. The RBE DSB values of FFF were higher than those of FF as the distance to out-of-field increased. The out-of-field radiobiological effectiveness of FFF could thus be greater than that of FF since the spreading of the radiation dose out-of-field with FFF could be a concern compared to the FF.

ACKNOWLEDGMENT
This research was supported by a Japan Society for the Promotion of Science (JSPS) KAKENHI grant, no. 19K17227.