DNA‐damage RBE assessment for combined boron and gadolinium neutron capture therapy

Abstract Purpose Neutron capture therapy (NCT) by 10B and 157Gd agents is a unique irradiation‐based method which can be used to treat brain tumors. Current study aims to quantitatively evaluate the relative biological effectiveness (RBE) and dose distributions during the combined BNCT and GdNCT modalities through a hybrid Monte Carlo (MC) simulation approach. Methods Snyder head phantom as well as a cubic hypothetical tumor was at first modeled by Geant4 MC Code. Then, the energy spectra and dose distribution relevant to the released secondary particles during the combined Gd/BNCT were scored for different concentrations of 157Gd and 10B inside tumor volume. Finally, the scored energy spectra were imported to the MCDS code to estimate both RBESSB and RBEDSB values for different 157Gd concentrations. Results The results showed that combined Gd/BNCT increases the fluence‐averaged RBESSB values by about 1.7 times when 157Gd concentration increments from 0 to 2000 µg/g for both considered cell oxygen levels (pO2 = 10% and 100%). Besides, a reduction of about 26% was found for fluence‐averaged RBEDSB values with an increment of 157Gd concentration in tumor volume. Conclusion From the results, it can be concluded that combined Gd/BNCT technique can improve tumor coverage with higher dose levels but in the expense of RBEDSB reduction which can affect the clinical efficacy of the NCT technique.

][7] NCT by the 10 B agents has a large thermal neutron capture cross-section of 3840 barns. 8,9In this technique 10 B can be selectively concentrated within the tumor cells and tumor boundary would be precisely determined. 10Neutron capture process by 10 B results in nuclear reaction of 10 B (n th , α) 7 Li which is shown in following equation 11 : 7 Li + 4 He + 2.79MeV 94% → 7 Li + 4 He + (0.478MeV)+ 2.31MeV During the neutron capture process by Boron agents, released high-LET (linear energy transfer) particles have a short range in tissues (about 9 µm for 4 He particles and 5 µm for the 7 Li) compared with the cellular dimensions.Therefore, selective distribution of the Boron agents inside the tumor region (known as the unique aspect of BNCT) causes a high deposited dose in tumor cells. 12,13Accordingly, high tumor cells killing efficiency can be expected for brain tumor treatment through NCT with 10 B agent. 8,14To deliver the therapeutic dose during the BNCT technique, a uniform concentration of boron agents per gram tumor should be approximately about 10 to 30 µg. 15 Due to the high LET values of the released secondary particles during the BNCT ( 4 He and 7 Li), only nearby cells to the reaction point are damaged without affecting the adjacent healthy tissues. 16lthough secondary particles with lower LET values (electrons and photons) are released during the GdNCT, 157 Gd has a higher neutron capture cross-section with respect to 10 B which can lead to lower neutron flux required for NCT technique.Besides, these released secondary particles after neutron capture by 157 Gd have long ranges inside the target volume.Hence, this issue may result in improving the dose uniformity inside the treatment target when NCT technique is used for tumor irradiation.
Totally,GdNCT releases low-LET prompt gamma rays, internal conversion (IC) electrons, x-rays, and Auger electrons which are shown in following equitation 17,18 : In each neutron capture reaction by 157 Gd, the mean energy of released gamma rays is about 2.4 MeV which can penetrate to much larger depths than the Boron reaction products.Produced Auger electrons with the average LET of 300 keV/µm can result in a large probability of producing lethal damage especially when directly bound to the DNA molecule. 19To obtain proper results during the tumor treatment via GdNCT technique, the 157 Gd concentration of about 50 to 200 µg/g tumor has been reported.Nevertheless, for deep tumors more 157 Gd concentrations may be required because the incident neutron can be remarkably attenuated by overlying tissues.Therefore, higher 157 Gd concentrations are used to ensure that required neutron capture interactions are occurred inside the tumor volume. 19,20onsidering the energy of released gamma rays and electrons during the neutron capture by 157 Gd, the released gamma rays and Auger electrons have the range of some centimeter (cm) and a few micrometers (µm) in tissue, respectively. 21,22wing to the different released secondary particles during the NCT by boron and gadolinium, the therapeutic effects of GdNCT and BNCT can be quite different.The biological effectiveness of BNCT depends on the short range 4 He and 7 Li particles, while GdNCT techniques rely on emitted Auger electrons. 23Furthermore, as mentioned previously, BCNT and GdNCT have their own merits and limitations.Higher levels of DNA damage by released secondary high LET particles during the BNCT, while improved dose uniformity would be expected for GdNCT technique with high range secondary particles.Therefore, it may be expected that a combination of a 10 B and 157 Gd may influence the treatment outcomes in terms of dose uniformity and DNA-damage RBE.Despite the 157 Gd advantages, only a few studies have been assessed the combinations of BNCT and GdNCT which relevant in vivo studies of such combination are still rare. 10To the best of our knowledge, the radiobiological characteristics of combined 10 B/ 157 Gd NCT have not been assessed.The present study aims to evaluate the potential clinical improvement of a combined 10 B/ 157 Gd NCT technique viewpoint the dose distribution and DNA-damage relative biological effectiveness (RBE) values through a hybrid Monte Carlo (MC) simulation approach.

MC simulation
To calculate the dose distribution and DNA-damage RBE values relevant to the combined BNCT and GdNCT techniques, at first the proposed head phantom by Snyder et al., 24 was simulated with Geant4.11.0 MC Code.
To do so, different parts of the employed head phantom including skin, skull, and brain were simulated using the following ellipsoidal equations: 3 ( 3 It should be mentioned that numbers and parameters in these equations are in terms of cm.
The elemental compositions of the simulated regions relevant to the Snyder phantom were taken from ICRU-46 report and have been listed in Table 1. 25 Furthermore, a hypothetical cubic brain tumor with the dimensions of 5 × 5 × 5 cm 3 was considered at the center of brain volume to score the released secondary particles energy spectra as well as dose distribution calculation.The Geant4-based simulated MC model of the Snyder head phantom along with the considered phantom inside the brain are illustrated in Figure 1.
For the tumor irradiation, the neutron source was similar to the proposed one for BNCT of brain tumors. 26n this regard, a disk shape source with 10 cm diame-ter was considered which had been placed 15 cm away from the brain center along the z-axis.Totally,the neutron source was included 89% of epithermal neutron beams (in the range of 0.5 eV to 10 keV to increase the neutron beam penetration depth) along with 1% fast neutrons contamination (from 10 keV to 2 MeV to increment the neutron beam penetrations through the skull) and 10% thermal neutrons (form 0.001 to 0.5 eV). 26mployed neutron cross-sections of 10 B and 157 Gd have been depicted in Figure 2.
It should be mentioned that simulations of the secondary particles were performed by considering 30 µg/g 10 B concentration and different 157 Gd concentrations of 0, 125, 250, 500, 1000, and 2000 µg/g within the simulated tumor,as suggested by Culbertson and Jevremovic study. 15Since Boron compounds may be also accumulated in the healthy brain cells, a 10 µg/g tumor of 10 B concentration was also simulated inside the surrounding normal brain region.It is worth to note that for energy Comparison of the total neutron cross-section relevant to 157 Gd and 10 B. 27 spectrum and dose calculations,a uniform distribution of boron and gadolinium was considered inside the tumor volume.
The G4HadronPhysicsQGSP_BERT_HP,G4Radioact iveDecayPhysics, and G4EmStandardPhysics-option4 physics were employed to model the neutron capture and electromagnetic process during the tumor irradiation with neutron source.To reduce the statistical errors below 1%, one billion primary particles were tracked by an Intel Core i7/8 GB RAM personal computer.Besides, the range cut-off value in all simulations was set to 0.1 µm to score all released electrons, particles, and ions.

Dose calculations
To evaluate the variations of dose distribution within the tumor volume with changing the 157 Gd concentrations during the combined Gd/BNCT technique, the tumor volume was divided into cubic voxels with the dimensions of 1 × 1 × 1 mm 3 and absorbed dose were scored in each voxel.Then, the dose distributions relevant to each considered 157 Gd concentration within the tumor volume were reported.

RBE estimations
To  6) 30,31 : D i indicates the received dose (in Gy) by the brain tumor from i th particle type which has been simulated by Geant4 MC code and RBE i represents the relevant fluence-averaged RBE value of the i th -type charged particle resulted from MCDS MC code.
Validity of MCDS for DNA damage calculations has been confirmed by Semenenko and Stewart. 32The MCDS algorithm for DNA damage classification differs from Monte Carlo track structure (MCTS) codes.4][35] On other words, MCDS parameters for DNA damage calculation including minimum length of undamaged base pairs between neighboring elementary damages (n min ), the ratio of base damage to strand break (f), the number of individual strand breaks (σ Sb ), and DNA segment length in terms of base pairs (n seg ) have been properly tuned to have the minimum difference compared with MCTS codes. 36This algorithm allows to simulate the DNA damage in irradiated cells with photons, monoenergetic electrons, protons, and particles up to 56 Fe with the maximum energy of 1 GeV. 36If the induced lesions over one or two strands of the DNA molecule do not face with the 10 bp (base pair) it would be marked as the SSB breaks.Besides, two single strand breaks found on the opposite DNA strand within 10 bp are marked as the DSB.The remaining ones are classified as base damaged (BD) damage. 32,37CDS code can predict the type of DNA lesions which formed by ionizing radiation in typical mammalian cells under different cell oxygenation levels through considering the free radicals which are produced during the interaction of ionizing radiation with cell cytoplasm.It is worth mentioning that the strand breaks yield calculations (both SSB and DSB yields) in present study were performed in fully aerobic (pO 2 = 100%) and hypoxia (pO 2 = 10%) conditions to evaluate the impact of cell oxygenation level on the RBE values as well.Furthermore, all MCDS simulations have been performed with a mean standard error of less than 0.1%.

Secondary charged particles energy spectra
The scored 4 He energy spectra relevant to the 30 µg/g of 10 B inside the tumor volume in combination with different 157 Gd concentrations (i.e., 0, 125, 250, 500, 1000, and 2000 µg/g tumor) have been illustrated in Figure 3.
As depicted in Figure 3, the intensities of scored 4 He energy spectra during the neutron capture process by 10 B decrement by increasing the 157 Gd concentrations from 0 to 2000 µg/g tumor.With increasing the gadolinium concentration, boron neutron capture reactions decrement due to the high thermal neutron cross-section of gadolinium agents.Hence, the released secondary particles through the 10 B neutron capture process decrease.This reduction in intensity of helium energy spectra during the combined Gd/BNCT technique may influence the RBE value.
The obtained 7 Li energy spectra relevant to 30 µg/g 10 B and different 157 Gd concentrations (i.e., 0, 125, 250, 500, 1000, and 2000 µg/g tumor) inside the tumor volume have been shown in Figure 4.A similar trend as found for 4 He can also be observed for variations of 7 Li intensity,so that increasing the 157 Gd concentration within the tumor volume decrements the intensity of the scored 7 Li secondary particles.The main reason for continuous energy spectrum of 7 Li is the multi-energy nature of incident neutrons.As the neutron energy increments,lithium ions with higher energies would be released.However, neutron absorption cross-section of 10 B reduces with increasing the neutron energy (as illustrated in Figure 2).Therefore, it can be expected that the intensity of released 7 Li particles continuously decreases when the lithium energy increments.The observed sharp peaks in Figure 3 and Figure 4 (around 1.5 and 1.7 MeV for 4 He and 0.8 and 1.09 MeV for 7 Li) are relevant to the Boron neutron capture process, as shown in Equation ( 1).In this process, two nuclei with total energy above 2 MeV are generated which are recoiled in a back-to-back manner with equal momentums.Considering the energy and energy conservation laws, the obtained energies during the neutron capture process by Boron agents (2.31 and 2.79 MeV) are finally shared between 4 He and 7 Li based on their mass ratio. 13he scored secondary electron spectra inside the tumor volume during the combined Gd/BNCT technique at different 157 Gd concentrations have been shown in Figure 5.
As indicated in Figure 5, increasing the 157 Gd concentrations inside the tumor region can increment the intensity of the secondary electron energy spectra due to the increment of neutron capture interactions at higher 157 Gd concentrations.
The contribution of Auger electrons in total electron spectra (as shown in Figure 5) has been illustrated in Figure 6.It should be noted that these Auger electrons have the most important role in determining the RBE value for 157 Gd-based neutron therapy technique.
As it can be seen in Figure 6, when the 157 Gd concentration increments from 125 to 2000 µg/g inside the tumor region, the contributions of the low energy Auger electrons increment as well.This finding can be linked to the higher interaction rate of thermal neutrons with 157 Gd when gadolinium concentration increments within the tumor region.Owing to the fact that these released Auger electrons cause a high LET value and cell killing probability, the radiation efficacy may be improved especially when the 157 Gd accumulation would be nearby the DNA molecule. 16,17,38Since most of released energy during the neutron capture by 157 Gd reaches to the gamma rays, if the Gadolinium is positioned outside the tumor cell, only gamma rays can contribute to the tumor cell killing. 38

Dose calculations
Figure 7 shows the simulated two dimensional (2D) dose distribution inside the tumor region for combined Gd/BNCT technique at different concentrations of 157 Gd.
It is worth to note that all reactions which can affect the absorbed dose inside the tumor region were considered in the present study.When thermal neutrons penetrate to the tissues, due to the reactions of biological tissue compositions ( 14 N(n,p) 14 C and 1 H(n,ɣ) 2 H),the absorbed dose inside the target can be affected.Nevertheless, secondary particles released by neutron capture reaction are the main contributors to the received dose by the target. 23he illustrated results in Figure 7 showed a nonuniform dose distribution is observed inside the tumor volume during both BNCT and combined Gd/BNCT techniques.This finding is expected because the neutron flux continuously reduces with penetrating to greater depths inside the tumor region.Ultimately, the absorbed dose decrements with increasing the depth inside the tumor volume.Nevertheless, when 157 Gd is combined with 10 B,more parts of the tumor region would be covered by the desirable dose values (red regions in Figure 7).These results can be attributed to the higher range of gamma rays and secondary electrons (products of 157 Gd neutron capture) with respect to the heavy charged particles (as the products of 10 B neutron capture) which can extend the depth of tumor coverage with higher dose levels.This issue would be more dominant when the 157 Gd concentrations inside the tumor region increments.

RBE assessments
The calculated fluence-averaged RBE values (both RBE SSB and RBE DSB ) relevant to the various 157 Gd concentrations inside the tumor volume and different cell oxygen levels have been illustrated in Figure 8.As indicated in Figure 8, fluence-averaged RBE SSB values increment with an increase in 157 Gd concentration.In this regard, fluence-averaged RBE SSB value increases by about 1.7 times when 157 Gd concentration increments from 0 to 2000 µg/g for both considered cell oxygen levels (pO 2 = 10% and 100%) in this study.RBE SSB has a direct relationship with the high energy electrons which may induce single-strand breaks with higher probability. 39On the other hand, the intensity of high energy secondary electrons which are released following the Gd-based neutron capture increases at higher 157 Gd concentrations, as shown in Figure 5. Therefore, it can be expected that the fluence-averaged RBE SSB values increase when Gadolinium uptake inside the tumor increments.
As shown in Figure 8, fluence-averaged RBE DSB values decrement when the 157 Gd concentration increases from 0 to 2000 µg/g.Accordingly, a reduction of about 26% can be observed when 157 Gd concentrations increment inside the tumor for both studied cell oxygen levels (pO 2 = 10% and 100%).When the Gadolinium concentration increases inside the tumor region, the neutron flux is further reduced due to the increased number of neutron capture reactions by the 157 Gd.This issue can consequently reduce the number of Boron neutron capture reactions and ultimately lead to the decrement of heavy charged particles ( 4 He and 7 Li) which are released following the Boron neutron capture reaction.On the other hand, these heavy charged particles are high-LET ones which can induce the double strand breaks with a much higher probability than the products of Gadolinium neutron capture reaction.Regarding to the fact that the intensity of these heavy charged particles decrements with increasing the 157 Gd concentration inside the tumor volume (as can be explicitly observed in Figure 3 and Figure 4), it can be expected that the RBE DSB value reduces at higher 157 Gd concentrations.
As illustrated in Figure 8, the obtained fluenceaveraged RBE DSB values during the combined Gd/BNCT are lower than those reported for the sole BNCT which can be attributed to the reduction of heavy charged particle intensities, as discussed earlier.Furthermore, from the results of Figure 8, when the cell oxygen level varies from 10% to 100%, the fluence- High LET particles such as alpha and lithium ions are produced during the BNCT which can lead to local energy deposition and improved RBE value.Nevertheless, very short range of these secondary ions (alpha, and lithium) and their local energy deposition nature may cause dose non-uniformity inside the target vol-ume.Although the released secondary particles during GdNCT have lower LET values with respect to BNCT, their long ranges inside the tissue can improve the dose distribution inside the target volume.However, due to the lower LET values, decreased RBE values are expected using GdNCT.Hence, combined GdNCT and BNCT for tumor irradiation can be beneficiary viewpoint to the dose distribution inside the target volume and can be harmful regarding the biological effectiveness of the delivered treatment to the patient.Finally, appropriateness or inappropriateness of the combined Gd/BNCT technique would be dependent on the followed priorities by the treatment team.In other words, if dose uniformity has priority, Gd/BNCT would be appropriate for treatment and if the clinical RBE is preferable, this combined technique can be considered as inappropriate method for radiotherapy.
Although the dose-weighted RBE is a more appropriate metric for biological evaluation, the fluenceaveraged RBE (especially when different particle types contribute to the received dose by the target volume) can be also valuable for evaluating the effect of Gadolinium concentration during the tumor irradiation with combined Gd/BNCT technique on the absorbed dose distribution and RBE values.Nevertheless, the doseweighted RBE values may be different from fluenceweighted RBE one, especially in the case of high LET particles such as alpha and helium ions.Accordingly, further considerations are needed to obtain the doseweighted RBE values which can be considered in our future studies.
The RBE DSB values corresponding to the produced secondary particles ( 7 Li and 4 He) in BNCT have been estimated by Qi et al. 40 In this study, the obtained RBE DSB of alpha particles and 7 Li nucleus were 3.27 and 3.44, respectively.Besides, for 157 Gd the RBE DSB values of about 1.5 outside of a considered cylindrical DNA molecule with 3 nm radius have been quantified by Cerullo et al. 41

CONCLUSION
The DNA-damage fluence-averaged RBE values and the dose distribution during the NCT of brain tumor with 10 B and 157 Gd combination were assessed through a hybrid MC simulation approach in the current study.From the obtained results, it can be concluded that the depth dose distribution inside the tumor volume improves when the 157 Gd agent is added to 10

F I G U R E 3
Scored energy spectra of released4 He particles during the neutron capture process by 10 B at different 157 Gd concentrations during the combined Gd/BNCT technique.

F I G U R E 4
Scored energy spectra of released7 Li particles during the neutron capture process by10 B at different 157 Gd concentrations during Gd/BNCT combination.

F I G U R E 5
Scored energy spectra of total released secondary electrons during the neutron capture process by different concentrations of 157 Gd during the combined Gd/BNCT technique.

F I G U R E 6
Scored energy spectra of released Auger electrons during the neutron capture process by different concentrations 157 Gd during combined Gd/BNCT technique.

F
I G U R E 7 2D dose distribution inside the tumor volume as the function of 157 Gd concentration; (A) 0 µg/g, (B) 125 µg/g, (C) 250 µg/g, (D) 500 µg/g, (E) 1000 µg/g, and (F) 2000 µg/g within the tumor region.averaged RBE SSB and RBE DSB values increment with the maximum values of about 1.27% and 1% when the Gadolinium concentration is about 2000 µg/g inside the tumor region.Increasing the fluence-averaged RBE SSB and RBE DSB values with the increment of 157 Gd can be linked to the fact that the indirect induced damages to the DNA molecule by chemical products (hydroxyl radicals) may increase at higher levels of cell oxygen levels.

F I G U R E 8
Calculated fluence-averaged RBE values (RBE SSB and RBE DSB ) relevant to the combination of BNCT and GdNCT techniques for various 157 Gd concentrations from 0 to 2000 µg/g inside the tumor volume as well as different cell oxygen levels.
B for brain tumor irradiation, but in the expense of decreased fluence-averaged RBE DSB value which has an important role in clinical efficacy of this treatment modality.Nevertheless, to further improve the clinical efficacy of brain tumor treatment and reduce the relevant side-effects towards normal tissues through the combined Gd/BNCT technique, the concentration ratio of 10 B to 157 Gd should be optimized through future investigations.AU T H O R C O N T R I B U T I O N S Reza Shamsabadi: Methodology, validation, formal analysis, investigation, data curation, investigation, writingoriginal draft, writing-review & editing.Hamid Reza Baghani: Conceptualization, methodology, formal analysis, writing-review & editing, visualization, project administration, supervision.

TA B L E 1
The elemental compositions relevant to the different simulated parts of employed head phantom by weight fraction.

F I G U R E 1 Simulated Snyder head phantom and a cubic brain tumor through Geant4 MC Code.
28,29CDS MC code to estimate the relevant fluence-averaged DNA damage yields for each type of released secondary particle.The MCDS output file is the strand break yields (single strand and double strand breaks) per Gray per Giga base pair (in terms of Gy −1 Gbp −1 ).Corresponding RBE values of released secondary particles (secondary electrons, alpha, and lithium) during the combined B/GdNCT technique for different concentrations of the 10 B and 157 Gd were separately estimated by dividing the calculated break yields to the obtained break yields for60Co gamma rays as a reference radiation.It is worth mentioning that the double strand break (DSB) and single strand break (SSB) yields for60Co reference radiation were considered as 8.32 and 188.84 Gy −1 Gbp −1 , respectively.28,29Finally, to evaluate the average levels of DNA damage at a multicellular scale during the combined B/GdNCT technique, the fluence-averaged RBE was determined by considering the effects of absorbed dose to the target volume through Equation ( calculate the RBE values related to the combined of Gd/BNCT technique, the last released version of Monte Carlo damage simulation (MCDS 3.10A) code was utilized.In this regard, at first secondary particles energy spectra during the combined Gd/BNCT with different 157 Gd concentrations were calculated inside the tumor volume.Then, the obtained data were separately imported to