

ORIGINAL ARTICLE 



Year : 2019  Volume
: 44
 Issue : 4  Page : 270275 

Establishment of a new threedimensional dose evaluation method considering variable relative biological effectiveness and dose fractionation in proton therapy combined with highdoserate brachytherapy
Daisuke Kobayashi^{1}, Tomonori Isobe^{2}, Kenta Takada^{3}, Yutaro Mori^{2}, Hideyuki Takei^{2}, Hiroaki Kumada^{2}, Satoshi Kamizawa^{4}, Tetsuya Tomita^{1}, Eisuke Sato^{5}, Hiroshi Yokota^{6}, Takeji Sakae^{2}
^{1} Graduate School of Comprehensive Human Sciences, University of Tsukuba; Department of Radiology, University of Tsukuba Hospital, Ibaraki, Japan ^{2} Graduate School of Comprehensive Human Sciences; Faculty of Medicine, University of Tsukuba; Proton Medical Research Center, University of Tsukuba Hospital, Ibaraki, Japan ^{3} Graduate School of Radiological Technology, Gunma Prefectural College of Health Sciences, Gunma, Japan ^{4} Proton Medical Research Center, University of Tsukuba Hospital, Ibaraki, Japan ^{5} Faculty of Health Science, Juntendo University, Tokyo, Japan ^{6} Department of Radiology, University of Tsukuba Hospital, Ibaraki, Japan
Date of Submission  20Nov2018 
Date of Decision  18Sep2019 
Date of Acceptance  01Nov2019 
Date of Web Publication  11Dec2019 
Correspondence Address: Prof. Tomonori Isobe 111 Tennodai, Tsukuba, Ibaraki Japan
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jmp.JMP_117_18
Abstract   
Purpose: The purpose of this study is to evaluate the influence of variable relative biological effectiveness (RBE) of proton beam and dose fractionation has on dose distribution and to establish a new threedimensional dose evaluation method for proton therapy combined with highdoserate (HDR) brachytherapy. Materials and Methods: To evaluate the influence of variable RBE and dose fractionation on dose distribution in proton beam therapy, the depthdose distribution of proton therapy was compared with clinical dose, RBEweighted dose, and equivalent dose in 2 Gy fractions using a linearquadraticlinear model (EQD2_{LQL}). The clinical dose was calculated by multiplying the physical dose by RBE of 1.1. The RBEweighted dose is a biological dose that takes into account RBE variation calculated by microdosimetric kinetic model implemented in Monte Carlo code. The EQD2_{LQL}is a biological dose that makes the RBEweighted dose equivalent to 2 Gy using a linearquadraticlinear (LQL) model. Finally, we evaluated the threedimensional dose by taking into account RBE variation and LQL model for proton therapy combined with HDR brachytherapy. Results: The RBEweighted dose increased at the distal of the spreadout Bragg peak (SOBP). With the difference in the dose fractionation taken into account, the EQD2_{LQL}at the distal of the SOBP increased more than the RBEweighted dose. In proton therapy combined with HDR brachytherapy, a divergence of 103% or more was observed between the conventional dose estimation method and the dose estimation method we propose. Conclusions: Our dose evaluation method can evaluate the EQD2_{LQL}considering RBE changes in the dose distribution.
Keywords: Dose fractionation, highdoserate brachytherapy, linearquadraticlinear model, proton therapy, relative biological effectiveness
How to cite this article: Kobayashi D, Isobe T, Takada K, Mori Y, Takei H, Kumada H, Kamizawa S, Tomita T, Sato E, Yokota H, Sakae T. Establishment of a new threedimensional dose evaluation method considering variable relative biological effectiveness and dose fractionation in proton therapy combined with highdoserate brachytherapy. J Med Phys 2019;44:2705 
How to cite this URL: Kobayashi D, Isobe T, Takada K, Mori Y, Takei H, Kumada H, Kamizawa S, Tomita T, Sato E, Yokota H, Sakae T. Establishment of a new threedimensional dose evaluation method considering variable relative biological effectiveness and dose fractionation in proton therapy combined with highdoserate brachytherapy. J Med Phys [serial online] 2019 [cited 2021 May 15];44:2705. Available from: https://www.jmp.org.in/text.asp?2019/44/4/270/272667 
Introduction   
Modern radiotherapy uses photon beams (Xrays and gamma rays) and particle beams (proton beams and carbon ion beams). In radiotherapy, combination of different kinds of radiation is often performed.^{[1],[2],[3]} This is because a higher therapeutic effect can be obtained by taking advantage of the different characteristics of each radiation.^{[4]} Combination that commingles these radiations has been implemented in recent years. There is proton therapy combined with highdoserate (HDR) brachytherapy, which uses proton beams and gamma rays.^{[5],[6],[7]} To safely conduct such combination using different kinds of radiation, accurate dose evaluation is necessary. This is because the biological effects of each radiation are completely different, and radiation damage may occur. In combination of different types of radiation, the biological dose is commonly used for dose evaluation. The biological dose relies primarily on relative biological effectiveness (RBE) and dose fractionation.
There are two major problems with the conventional dose evaluation method for proton therapy combined with HDR brachytherapy. The first problem is RBE. At many facilities, RBE of 1.1 is widely used for the proton therapy.^{[8]} However, recent studies reported that the RBE of proton therapy changes as they proceed deeper into the medium.^{[9],[10]} In the report of Takada et al.,^{[11]} it was assumed that a difference in dose of 10% or more occurs between the dose calculated by the conventional method and the dose that takes into account RBE variation at the distal of the spreadout Bragg peak (SOBP) with 155 MeV proton beam. This is because the beam quality of the proton beam is different for each depth. However, conventional treatment planning systems (TPS) do not take into account the change in beam quality for each depth of proton beam, so dose evaluation taking into account RBE variation cannot be realized.
The second problem is dose fractionation. In general, the dose fractionation for proton beam therapy is 50–70 Gy/20–35 fractions,^{[12]} and the dose fractionation for HDR brachytherapy is 28–30 Gy/4–6 fractions.^{[13],[14]} When considering biological effects, dose fractionation is as important as RBE. Dose fractionation depends on the total dose and the dose per fraction.^{[15]} An equivalent dose in 2 Gy fractions (EQD2) is used for biological dose, taking into account dose fractionation. A linearquadratic (LQ) model is generally used for the calculation of the EQD2.^{[16]} However, the dose range in which the EQD2 can be accurately calculated using the LQ model is reported to be <3.25 Gy/fraction ^{[17]} or <2.57 Gy/fraction.^{[18]} In the case of proton therapy combined with HDR brachytherapy, the dose administered ranges over a wide range, such as 2–7 Gy/fraction. Therefore, the EQD2 using a conventional LQ model is not suitable for dose evaluation in proton therapy combined with HDR brachytherapy.
To summarize the above, the conventional method uses a constant RBE or LQ model; therefore, accurate dose evaluation in proton therapy combined with HDR brachytherapy is not possible. We focused on the RBE variation in the depth direction and a dose evaluation using a linearquadraticlinear (LQL) model in proton therapy combined with HDR brachytherapy, which has not been done in previous studies. There are some biophysical models that can compute the RBE variation in the depth direction in the medium: the local effect model (LEM)^{[19]} and microdosimetrickineticmodel (MKM).^{[20]} Takada et al. used an MKM implemented in a Monte Carlo code and showed with a depthdose distribution in proton beam that an RBEweighted dose taking into account the RBE variation increases at the distal of the SOBP.^{[11]} On the other hand, the LQL model is a computational model that takes into account cell repair.^{[21]} It enables accurate evaluation up to the dose range used in HDR brachytherapy.^{[21]} With this method, it is possible to accurately evaluate biological dose in proton therapy combined with HDR brachytherapy.
The purpose of this study is to evaluate the influence of variable RBE of proton beam and dose per fraction on dose distribution and to establish a new threedimensional dose evaluation method for proton therapy combined with HDR brachytherapy.
Materials and Methods   
The biological dose used in this study is clinical dose, RBEweighted dose, and EQD2_{LQL}. The clinical dose was calculated by multiplying the physical dose by RBE of 1.1. The RBEweighted dose was defined as the biological dose calculated by the microdosimetric function ^{[22]} of the Particle and HeavyIon Transport Code System (PHITS),^{[23]} which is a Monte Carlo simulation code coupled with MKM. The RBEweighted dose is a biological dose that takes into account RBE variation in the depth direction in the medium. The EQD2_{LQL} was defined as a biological dose that makes the RBEweighted dose equivalent to 2 Gy using an LQL model.
Influence of relative biological effectiveness and dose fractionation on dose distribution in proton beam
The calculation geometry of doublescattering system of the Proton Medical Research Center at the University of Tsukuba was reproduced by PHITS.^{[11]} The RBEweighted dose was calculated by PHITS coupled with MKM. The RBEweighted dose was converted to the EQD2_{LQL} using the LQL model. The survival fraction of the LQL model is expressed by equations (1) and (2).^{[21],[24]}
where, α and β characterize the intrinsic radiosensitivity of the cells, and D and d are the total and fractional dose, respectively. G (x) is the reduction in survival owing to interaction between the lesions. δ is the additional LQL parameter. λ = ln2/Tr is the repair rate. Tr and T are the repair halftime and the treatment delivery time, respectively. Here, the treatment delivery time is sufficiently shorter than the repair halftime, and λT → 0. Therefore, the time term can be ignored. The handling of treatment delivery time in this study is discussed in the discussion section. In this case, the EQD2_{LQL} is represented by equation (3).
The absolute dose in the depth direction for a proton beam at 2 Gy/fraction and 3 Gy/fraction was compared with the clinical dose, the RBEweighted dose, and the EQD2_{LQL}. The proton beam energy was 155 MeV, and the width of SOBP was set as 30 mm. From the report of Guerrero et al.,^{[25]} the target α/β ratio was set at 9.9, and target δ was set at 0.04.
Threedimensional dose evaluation taking into account relative biological effectiveness and dose fractionation in proton therapy combined with highdoserate brachytherapy
For threedimensional dose evaluation of proton therapy combined with ^{192} Ir HDR brachytherapy using cylinders, we used the PHITS coupled with MKM and the Tsukuba plan. The Tsukuba plan is a TPS developed by Kumada et al. that employs PHITS.^{[26]} A plan simulating a gynecological disorder was prepared for a pelvic phantom (The Phantom Laboratory, USA), and the clinical dose and the RBEweighted dose were calculated. Next, the RBEweighted dose was converted to the EQD2_{LQL} using equation (3), and the threedimensional dose distributions of the clinical dose, the RBEweighted dose, and the EQD2_{LQL} were compared for the pelvic phantom in proton therapy combined with HDR brachytherapy. The dose fractionation for proton therapy was set at 69.0 Gy/23 fractions.^{[27]} The dose fractionation of HDR brachytherapy was set at 28.0 Gy/4 fractions against a reference point (Point A).^{[13],[14]} Point A is the major critical point for the dose specification of HDR brachytherapy in the treatment of gynecological cancer. From the report of Guerrero et al.,^{[25]} the target α/β ratio was 9.90, the target δ was 0.04, the normal organ α/β ratio was 3.25, and the normal organ δ was 0.09 for both proton therapy and HDR brachytherapy. Here, the RBE of ^{192} Ir used in HDR brachytherapy was set to 1.0.
Results   
Influence of relative biological effectiveness and dose fractionation on dose distribution in proton beam
[Figure 1] shows the clinical dose, the RBEweighted dose, and the EQD2_{LQL} in proton therapy. The units of the clinical dose and the RBEweighted dose are GyRBE. The unit of the EQD2_{LQL} is GyEQD2_{LQL}. As shown in [Figure 1], the depth of the proximal, the center, and the distal of the SOBP are 95 mm, 110 mm, and 125 mm, respectively. In the SOBP, the clinical dose is almost flat. At the distal of the SOBP at 2 Gy/fraction, the RBEweighted dose is 2.42 GyRBE, and the EQD2_{LQL} is 2.52 GyEQD2_{LQL}[Figure 1]a. At the distal of the SOBP at 3 Gy/fraction, the RBEweighted dose is 3.63 GyRBE, and the EQD2_{LQL} is 4.11 GyEQD2_{LQL}[Figure 1]b. On the other hand, at the proximal of the SOBP at both 2 Gy/fraction and 3 Gy/fraction, the RBEweighted dose was lower than the clinical dose.  Figure 1: Comparison of the clinical dose, the relative biological effectivenessweighted dose, and the equivalent dose in 2 Gy fractions using a linearquadraticlinear model at the central axis in water phantom on irradiation by 155 MeV proton beam with 30 mm spreadout Bragg peak width: (a) 2 Gy/fraction and (b) 3 Gy/fraction. Linearquadraticlinear model parameters of target α/β ratio and δ are 9.9 and 0.04, respectively
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Threedimensional dose evaluation taking into account relative biological effectiveness and dose fractionation in proton therapy combined with highdoserate brachytherapy
[Figure 2] shows the threedimensional dose distribution of proton therapy combined with HDR brachytherapy in the pelvic phantom. Target P is a primary lesion, and Target N is a lymph node lesion [Figure 2]a. Target N was irradiated by the proton beam from the dorsal direction. At the distal of the SOBP of the proton beam (ventral side of Target N), the clinical dose is 70–80 GyRBE [Figure 2]b, the RBEweighted dose is 90–100 GyRBE [Figure 2]c, and the EQD2_{LQL} is 100–110 GyEQD2_{LQL}[Figure 2]d. HDR brachytherapy was performed on Target P. The clinical dose at the center of TargetP is 100–110 GyRBE, and the dose decreases with distance from the center [Figure 2]b. The irradiation area of 100–110 GyEQD2_{LQL} of the EQD2_{LQL} is wider than that of the 100–110 GyRBE of the clinical dose [Figure 2]d.  Figure 2: Comparison of the clinical dose, the relative biological effectivenessweighted dose and the equivalent dose in 2 Gy fractions using a linearquadraticlinear model for threedimensional dose distributions in the pelvic phantom on irradiation proton therapy combined with highdoserate brachytherapy: (a) computed tomography image of the pelvic phantom, (b) clinical dose, (c) relative biological effectivenessweighted dose, and (d) equivalent dose in 2 Gy fractions using a linearquadraticlinear model. In threedimensional dose distributions, the units of the clinical dose and the relative biological effectivenessweighted dose are GyRBE, and the unit of the equivalent dose in 2 Gy fractions using a linearquadraticlinear model is GyEQD2_{LQL}
Click here to view 
For a quantitative evaluation, [Figure 3] shows the dose distribution of the crosssection in which the clinical dose, the RBEweighted dose, and the EQD2_{LQL} greatly changed at the distal of the SOBP of the proton beam and the irradiation range of HDR brachytherapy [red line in upper left of [Figure 3]. Position 0 mm is the center of the pelvic phantom. Position 25–45 mm corresponds to the distal of the SOBP of the proton beam, and position10 mm corresponds to the position irradiated with the same dose (28.0 Gy/4 fractions) as the reference point for HDR brachytherapy. The clinical dose, the RBEweighted dose, and the EQD2_{LQL} at position 40 mm are 77.3 GyRBE, 83.6 GyRBE, and 106.0 GyEQD2_{LQL}, respectively. The EQD2_{LQL} at position10 mm is 52.6 GyEQD2_{LQL}.  Figure 3: Comparison of the clinical dose, the relative biological effectivenessweighted dose, and the equivalent dose in 2 Gy fractions using a linearquadraticlinear model for dose profile in the pelvic phantom on irradiation proton therapy combined with highdoserate brachytherapy
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Discussion   
Validity of the results obtained in this study
From [Figure 1], the RBEweighted dose (2.42 GyRBE) at the distal of the SOBP (position 125 mm) was shown to increase by 21% compared to the clinical dose (2.0 GyRBE). In general, the lower the proton beam energy, the higher the beam quality.^{[9]} Since the energy of the proton beam becomes lower as the depth increases,^{[8]} the RBEweighted dose of the distal of the SOBP becomes higher. On the other hand, the proton beam energy of the proximal of the SOBP (position 95 mm) is high. Therefore, RBE of the proximal of the SOBP is approximately 1.0. Since the clinical dose uses RBE of 1.1, the RBEweighted dose is lower than the clinical dose at the proximal of the SOBP. The high reproducibility of the RBEweighted dose calculated and experimental data in this system was reported.^{[11]} The variable RBE of the proton beam in this study is considered reasonable and proper. On the other hand, we have to be careful about the potential differences between scanning and passively scattered beam, as noted by Paganetti ^{[9]} who refers to other papers.
The EQD2_{LQL}(4.11 GyEQD2_{LQL}) at the distal of the SOBP (position 125 mm) increases the dose by 13% compared to the RBEweighted dose (3.63 GyRBE). The report of Voyant et al.^{[28]} shows by the point dose that the EQD2_{LQL} increased by 16% compared to the clinical dose (4 Gy), which is the same as in our study.
From [Figure 3], the difference between the clinical dose (77.3 GyRBE) and the EQD2_{LQL}(106.0 GyEQD2_{LQL}) was 37% at the distal of the SOBP (position 40 mm). The difference between the clinical dose (28.0 GyRBE) and the EQD2_{LQL}(52.6 GyEQD2_{LQL}) in HDR brachytherapy (position  10 mm) was 88%. The clinical dose of ^{192} Ir used in the HDR brachytherapy sharply changes with the inverse square of the distance [Figure 2]b. That is, dose per fraction becomes higher than 7.0 Gy/fraction near the ^{192} Ir source. For example, at position  5 mm in [Figure 3], there is irradiation of 8.0 Gy/fraction (32.0 Gy/4 fractions) for HDR brachytherapy. The difference between the clinical dose (32.0 GyRBE) and the EQD2_{LQL}(65.0 GyEQD2_{LQL}) in HDR brachytherapy (position  5 mm) was 103%.
Voyant et al.^{[28]} showed by the point dose that the difference between the clinical dose (8 Gy) and the EQD2_{LQL} is 100%, in other words, more than twice, which is equivalent to our results. The more the dose per fraction exceeds 2 Gy/fraction, the greater the divergence between the clinical dose and the EQD2_{LQL}. Therefore, it is essential to take into account the RBE and dose fractionation since they have great impact on the EQD2_{LQL}.
Advantage of using the equivalent dose in 2 Gy fractions using a linearquadraticlinear model
From [Figure 1]a, it was shown that the EQD2_{LQL}(2.52 GyEQD2_{LQL}) at the distal of the SOBP (position 125 mm) at 2 Gy/fraction increases by 26% compared to the clinical dose (2.0 GyRBE). In the case of 2 Gy/fraction [Figure 1]a, the clinical dose is almost uniformly irradiated with 2 GyRBE in the SOBP (position 95–125 mm). If EQD2_{LQL} was calculated using the clinical dose, there is no difference between the clinical dose and EQD2_{LQL} in the SOBP at 2 Gy/fraction. That is, when constant RBE of 1.1 is used, there is little necessity to evaluate by using EQD2_{LQL}. However, the RBEweighted dose at the distal of the SOBP is >2 GyRBE. Therefore, even with 2 Gy/fraction, it is necessary to use the EQD2_{LQL}. Furthermore, the biological effects owing to the difference in dose fractionation increase with a higher dose per fraction, such as in HDR brachytherapy.
Therefore, in proton therapy combined with HDR brachytherapy, it is recommended to evaluate using the EQD2_{LQL}. Several reports concerning HDR brachytherapy combined with external beam therapy exist.^{[29],[30]} However, in most of these reports, evaluation is by the EQD2 using the LQ model, which is not suitable for dose evaluation in HDR brachytherapy combination. Jaikuna et al. reported that it is useful to use the LQL model for the dose evaluation of radiotherapy in which the dose per fraction is high, such as in HDR brachytherapy and stereotactic radiation therapy, that the LQ model cannot be used.^{[24]} Their report supports the propriety of our dose evaluation method.
Advantage of a Monte Carlo simulation in highdoserate brachytherapy
Dose calculation for HDR brachytherapy treats the human body as homogeneous water and does not take into account heterogeneous medium such as bone and air.^{[31]} A Monte Carlo simulation, which is the dose calculation algorithm used in this study, is capable of calculating heterogeneous medium accurately.^{[32],[33]} Therefore, even when air exists in the rectum [Figure 2]a, the physical dose can be obtained with high accuracy. Our method uses PHITS coupled with MKM, which is a dose evaluation method that can obtain both a biological dose and a physical dose. We evaluated that the uncertainty of the dose calculation in brachytherapy was <2.3%. Moreover, Takada et al. evaluated that the uncertainty of dose calculation in proton therapy was <3.1%.^{[11]} Therefore, the calculation accuracy is guaranteed for both HDR brachytherapy and proton therapy.
Limitations
Marshall et al. reported that the RBE of proton beam changes owing to differences in dose fractionation.^{[34]} Marshall et al. defined an RBE that changes with dose fractionation as RBE_{frac}. RBE_{frac} is important when RBE varies greatly depending on the endpoint setting, as the shape of the cell survival curve varies greatly, such as with carbonion beam and photon beam.^{[35]} RBE_{frac} is not taken into account in our proposed method. This is because RBE does not change significantly depending on where the endpoint is set because the shapes of the cell survival curves of proton beam and photon beam are similar. In fact, Marshall et al. showed that RBE_{frac} of the proton beam and photon beam is nearly constant above 2 Gy/fraction. Therefore, in the case where the dose is 2 Gy/fraction or higher, we consider that it is not necessary to use RBE_{frac} in proton therapy combined with HDR brachytherapy (photon beam). However, when considering carbonion beam and other forms of combination, which have significantly different shapes of photon beam and cell survival curves, it is essential to take into account RBE_{frac}.
In addition, we do not consider the time, such as treatment delivery time, but further improvement of biological dose calculation accuracy can be expected by using a model with improved MKM that takes into account time.^{[36]}
Future prospects
There are many reports of proton therapy combined with HDR brachytherapy applied to gynecological disorders such as cervical cancer.^{[5],[6],[7]} Proton beam is an excellent external irradiation method for gynecological disorders,^{[7],[37]} and the possibility of replacing the Xrays commonly used in HDR brachytherapy combination has been reported.^{[7]} Therefore, it is essential to take into account the RBE and dose fractionation.
In addition, the MKM is a biophysical model used for various kinds of radiation including photon beams and particle beams.^{[11],[38],[39]} The Tsukuba plan is a system that can calculate dose of various types of radiation, such as Xrays and neutron beams,^{[26]} in addition to proton beams and gamma rays. That is, our threedimensional dose evaluation using the Tsukuba plan and MKM can cope with new various combination therapies, which are highly versatile evaluation methods.
Conclusions   
We evaluated the influence of RBE and dose fractionation for a proton therapy combined with HDR brachytherapy on dose distribution. Taking into account the RBE variation of the proton beam in the depth direction, it became clear that the RBEweighted dose increases at the distal of the SOBP. Considering the difference in dose fractionation, it became clear that the EQD2_{LQL} at the distal of the SOBP increases more than the RBEweighted dose. In particular, the dose per fraction of proton therapy and HDR brachytherapy differ greatly. Since the conventional method uses a constant RBE or LQ model, it cannot accurately evaluate the dose of such a combination. Our dose evaluation method can evaluate the EQD2_{LQL} considering RBE changes in the dose distribution.
Acknowledgement
The numerical calculations were performed using the Cluster of Manycore Architecture processor (COMA) at the Center for Computational Sciences, University of Tsukuba.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Levin WP, Kooy H, Loeffler JS, DeLaney TF. Proton beam therapy. Br J Cancer 2005;93:84954. 
2.  SchulzErtner D, Nikoghosyan A, Thilmann C, Haberer T, Jäkel O, Karger C, et al. Results of carbon ion radiotherapy in 152 patients. Int J Radiat Oncol Biol Phys 2004;58:63140. 
3.  Kawabata S, Miyatake S, Kuroiwa T, Yokoyama K, Doi A, Iida K, et al. Boron neutron capture therapy for newly diagnosed glioblastoma. J Radiat Res 2009;50:5160. 
4.  Brahme A. Development of radiation therapy optimization. Acta Oncol 2000;39:57995. 
5.  Li YR, Kirk M, Lin L. Proton therapy for vaginal reirradiation. Int J Part Ther 2016;3:3206. 
6.  Lin LL, Kirk M, Scholey J, Taku N, Kiely JB, White B, et al. Initial report of pencil beam scanning proton therapy for posthysterectomy patients with gynecologic cancer. Int J Radiat Oncol Biol Phys 2016;95:1819. 
7.  Smit BM. Prospects for proton therapy in carcinoma of the cervix. Int J Radiat Oncol Biol Phys 1992;22:34953. 
8.  Gerweck LE, Kozin SV. Relative biological effectiveness of proton beams in clinical therapy. Radiother Oncol 1999;50:13542. 
9.  Paganetti H. Relative biological effectiveness (RBE) values for proton beam therapy. Variations as a function of biological endpoint, dose, and linear energy transfer. Phys Med Biol 2014;59:R41972. 
10.  Carabe A, España S, Grassberger C, Paganetti H. Clinical consequences of relative biological effectiveness variations in proton radiotherapy of the prostate, brain and liver. Phys Med Biol 2013;58:210317. 
11.  Takada K, Sato T, Kumada H, Koketsu J, Takei H, Sakurai H, et al. Validation of the physical and RBEweighted dose estimator based on PHITS coupled with a microdosimetric kinetic model for proton therapy. J Radiat Res 2018;59:919. 
12.  Tsujii H, Tsuji H, Inada T, Maruhashi A, Hayakawa Y, Takada Y, et al. Clinical results of fractionated proton therapy. Int J Radiat Oncol Biol Phys 1993;25:4960. 
13.  Viswanathan AN, Beriwal S, De Los Santos JF, Demanes DJ, Gaffney D, Hansen J, et al. American brachytherapy society consensus guidelines for locally advanced carcinoma of the cervix. Part II: Highdoserate brachytherapy. Brachytherapy 2012;11:4752. 
14.  MacLeod C, Cheuk R, Dally M, Fowler A, Gauden S, Leung S, et al. Australian highdoserate brachytherapy protocols for gynaecological malignancy. Australas Radiol 2001;45:438. 
15.  Barendsen GW. Dose fractionation, dose rate and isoeffect relationships for normal tissue responses. Int J Radiat Oncol Biol Phys 1982;8:198197. 
16.  Brenner DJ. The linearquadratic model is an appropriate methodology for determining isoeffective doses at large doses per fraction. Semin Radiat Oncol 2008;18:2349. 
17.  Wang JZ, Huang Z, Lo SS, Yuh WT, Mayr NA. A generalized linearquadratic model for radiosurgery, stereotactic body radiation therapy, and highdose rate brachytherapy. Sci Transl Med 2010;2:3948. 
18.  Miyakawa A, Shibamoto Y, Otsuka S, Iwata H. Applicability of the linearquadratic model to single and fractionated radiotherapy schedules: An experimental study. J Radiat Res 2014;55:4514. 
19.  Elsässer T, Scholz M. Cluster effects within the local effect model. Radiat Res 2007;167:31929. 
20.  Hawkins RB. A microdosimetrickinetic theory of the dependence of the RBE for cell death on LET. Med Phys 1998;25:115770. 
21.  Guerrero M, Carlone M. Mechanistic formulation of a linealquadraticlinear (LQL) model: Splitdose experiments and exponentially decaying sources. Med Phys 2010;37:417381. 
22.  Sato T, Watanabe R, Niita K. Development of a calculation method for estimating specific energy distribution in complex radiation fields. Radiat Prot Dosimetry 2006;122:415. 
23.  Sato T, Iwamoto Y, Hashimoto S, Ogawa T, Furuta T, Abe SI, et al. Features of Particle and Heavy Ion Transport code System (PHITS) version 3.02. J Nucl Sci Technol 2018;55:68490. 
24.  Jaikuna T, Khadsiri P, Chawapun N, Saekho S, Tharavichitkul E. Isobio software: Biological dose distribution and biological dose volume histogram from physical dose conversion using linearquadraticlinear model. J Contemp Brachytherapy 2017;9:4451. 
25.  Guerrero M, Li XA. Extending the linearquadratic model for large fraction doses pertinent to stereotactic radiotherapy. Phys Med Biol 2004;49:482535. 
26.  Kumada H, Takada K, Sakurai Y, Suzuki M, Takata T, Sakurai H, et al. Development of a multimodal monte carlo based treatment planning system. Radiat Prot Dosimetry 2017;180:28690. 
27.  Arimoto T, Kitagawa T, Tsujii H, Ohhara K. Highenergy proton beam radiation therapy for gynecologic malignancies. Potential of proton beam as an alternative to brachytherapy. Cancer 1991;68:7983. 
28.  Voyant C, Julian D, Roustit R, Biffi K, Lantieri C. Biological effects and equivalent doses in radiotherapy: A software solution. Rep Pract Oncol Radiother 2014;19:4755. 
29.  Tanderup K, Ménard C, Polgar C, Lindegaard JC, Kirisits C, Pötter R. Advancements in brachytherapy. Adv Drug Deliv Rev 2017;109:1525. 
30.  Abe T, Tamaki T, Makino S, Ebara T, Hirai R, Miyaura K, et al. Assessing cumulative dose distributions in combined radiotherapy for cervical cancer using deformable image registration with preimaging preparations. Radiat Oncol 2014;9:293. 
31.  Ma Y, Lacroix F, Lavallée MC, Beaulieu L. Validation of the oncentra brachy advanced collapsed cone engine for a commercial (192) Ir source using heterogeneous geometries. Brachytherapy 2015;14:93952. 
32.  Patel NP, Majumdar B, Vijayan V. Comparative dosimetry of gammaMed plus highdose rate ir brachytherapy source. J Med Phys 2010;35:13743. [ PUBMED] [Full text] 
33.  Sahoo S, Selvam TP, Sharma SD, Das T, Dey AC, Patil BN, et al. Dosimetry of indigenously developed (192) Ir highdose rate brachytherapy source: An EGSnrc monte carlo study. J Med Phys 2016;41:11522. [ PUBMED] [Full text] 
34.  Marshall TI, Chaudhary P, Michaelidesová A, Vachelová J, Davídková M, Vondráček V, et al. Investigating the implications of a variable RBE on proton dose fractionation across a clinical pencil beam scanned spreadout bragg peak. Int J Radiat Oncol Biol Phys 2016;95:707. 
35.  Schardt D, Elsässer T, SchulzErtner D. Heavyion tumor therapy: Physical and radiobiological benefits. Rev Mod Phys 2010;82:383425. 
36.  Sato T, Furusawa Y. Cell survival fraction estimation based on the probability densities of domain and cell nucleus specific energies using improved microdosimetric kinetic models. Radiat Res 2012;178:34156. 
37.  Song WY, Huh SN, Liang Y, White G, Nichols RC, Watkins WT, et al. Dosimetric comparison study between intensity modulated radiation therapy and threedimensional conformal proton therapy for pelvic bone marrow sparing in the treatment of cervical cancer. J Appl Clin Med Phys 2010;11:8392. 
38.  Okamoto H, Kanai T, Kase Y, Matsumoto Y, Furusawa Y, Fujita Y, et al. Relation between lineal energy distribution and relative biological effectiveness for photon beams according to the microdosimetric kinetic model. J Radiat Res 2011;52:7581. 
39.  Horiguchi H, Sato T, Kumada H, Yamamoto T, Sakae T. Estimation of relative biological effectiveness for boron neutron capture therapy using the PHITS code coupled with a microdosimetric kinetic model. J Radiat Res 2015;56:38290. 
[Figure 1], [Figure 2], [Figure 3]
