Effect of Irradiation Time on Biological Effectiveness and Tumor Control Probability in Proton Therapy

International Journal of

Radiation Oncology biology

physics

www.redjournal.org

Physics Contribution

Effect of Irradiation Time on Biological Effectiveness and Tumor Control Probability in Proton Therapy Hideyuki Takei, PhD,* and Taku Inaniwa, PhDy *Faculty of Medicine, University of Tsukuba, Ibaraki, Japan; and yDepartment of Accelerator and Medical Physics, National Institute of Radiological Sciences, National Institutes for Quantum and Radiological Science and Technology, Chiba, Japan Received Dec 13, 2018. Accepted for publication May 1, 2019.

Summary The effect of irradiation time on biological effectiveness was systematically evaluated in proton therapy for various target sizes, depths, and prescribed doses per fraction. Spread-out Bragg peak plans were created using a constant relative biological effectiveness of 1.1, and the biological doses were then calculated based on the microdosimetric kinetic model. The biological dose largely decreased with longer irradiation time or higher prescribed dose.

Purpose: The biological effectiveness of proton beams may decrease with irradiation time because of sublethal damage repair (SLDR). The purpose of this study is to systematically evaluate this effect in hypofractionated proton therapy for various target sizes, depths, and prescribed doses per fraction. Methods and Materials: Plans with a single spread-out Bragg peak beam were created using a constant relative biological effectiveness (RBE) of 1.1 to cover targets of 6 different sizes located at 3 different depths in water. Biological doses of 2, 3, 5, 10, and 20 Gy (RBE) were prescribed to the targets. First, to investigate the depth variation of the biological effectiveness, the biological dose in instantaneous irradiation was recalculated based on the microdosimetric kinetic model. SLDR was then taken into account in the microdosimetric kinetic model during treatments to obtain the irradiation timeedependent biological effectiveness for irradiation time T of 5 to 60 minutes and beam interruption time s of 0 to 60 minutes. The tumor control probabilities were calculated for single-fraction proton therapy fields of different Ts and ss, and the curative doses were evaluated at a tumor control probability of 90%. Results: The biological effectiveness decreased with longer T and s and higher prescribed dose. The maximum decrease in the biological effectiveness was 21% with a 20 Gy (RBE) prescribed dose. In single-fraction proton therapy, the curative dose increased linearly by approximately 33% to 35% with the increase of T from 0 to 60 minutes. Conclusions: The biological effectiveness varies largely with T and s because of SLDR during treatments. This effect was pronounced for high prescribed doses per fraction. Thus, the effect of SLDR needs to be considered in hypofractionated and single-fraction proton therapies in relation to size and depth of the target. Ó 2019 Elsevier Inc. All rights reserved.

Reprint requests to: Hideyuki Takei, Faculty of Medicine, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305 8575 Japan. Tel: þ81 29 853 5600; E-mail: [email protected] Int J Radiation Oncol Biol Phys, Vol. 105, No. 1, pp. 222e229, 2019 0360-3016/$ - see front matter Ó 2019 Elsevier Inc. All rights reserved. https://doi.org/10.1016/j.ijrobp.2019.05.004

Disclosures: There is no conflict of interest.

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Time effect on proton biological dose

Introduction

Methods and Materials

Proton therapy can deliver high dose to the target while sparing normal tissues. Recently, hypofractionated and single-fraction proton therapies, which are performed in many facilities, have attracted attention.1-5 In proton radiation therapy treatment planning, a constant value of relative biological effectiveness (RBE) of 1.1 has been used in most clinical cases.6 However, recent studies suggest that the RBE value of the proton beam increases with the depth in the target.7 The RBE of ionizing radiation has been studied both theoretically and experimentally. The microdosimetric kinetic model (MKM), developed by Hawkins, is a theoretical model to predict the cell-survival fraction after radiation exposure.8-10 The MKM was further developed by Kase et al11 to be applicable in charged particle therapy with wide ranges of linear energy transfer (LET). The model was experimentally validated for various ion species, including protons.12,13 Takada et al tested the MKM for proton radiation therapy combined with Monte Carlo beam transportation simulations.14 The MKM can be used to investigate the depth variation of the RBE of proton beams. In general, proton radiation therapy treatment plans are designed based on the assumption that the beams are delivered instantaneously. However, in actual treatments, the beams are delivered over a period of time. The biological effectiveness of the therapeutic proton beams decreases with irradiation time because of sublethal damage repair (SLDR).15,16 Inaniwa et al investigated the effect of irradiation time on the biological effectiveness of therapeutic carbon-ion beams based on the MKM.17,18 They revealed that the longer the irradiation time and the higher the fractionated dose, the more significant the influence of SLDR on biological effectiveness. Manganaro et al confirmed a similar effect for proton beams.19 Inaniwa et al also suggested that the effect of SLDR is significant for low-LET radiation, such as protons, compared with high-LET radiation, such as carbon ions. However, these studies reported only a limited variety of cases such as lung and prostate. The influence of SLDR on biological effectiveness varies with the dose per fraction and the LET distribution, which depend on the depth and the size of the tumor. Thus, the reduction in biological effectiveness resulting from prolonged irradiation time should depend on the depth and the size of the tumor and the fraction dose. To the best of our knowledge, however, systematic investigations on these dependencies have not been performed even for proton radiation therapy. In this study, first, we investigated the depth variation of the RBE of therapeutic proton beams. Then, we investigated the tumor depthe, tumor sizee, and fractionated doseedependent reduction of the biological effectiveness of the proton beams resulting from SLDR at various irradiation times and interruption times. The MKM was used for both studies. We refer to the product of the absorbed dose and the RBE as "biological dose" throughout this study.

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The Geant4 Monte Carlo simulation code20-22 was used to simulate mono-energetic proton beams. The standard package was used for electro-magnetic interactions, and the binary cascade model23 was used for hadronic interactions. The production of secondary particles, including neutrons, was considered. The step length was set at 0.05 mm. Because we aimed to systematically investigate biological effectiveness, no specific design of accelerator or other beam delivery systems was simulated. We generated 3  107 protons with an initial energy E0 at the entrance of a cuboid water phantom with a uniform distribution of 50  50 mm2. E0 corresponded to the water equivalent range of 1 to 330 mm with 1 mm steps. The dimensions of the phantom were 300  300  400 mm3 with the longest side parallel to the beam direction. The phantom volume was divided into 1  1  1 mm3 units (referred to as “voxels”) to record the spatial distribution of the particle species by atomic number Zp ; kinetic energy Ek, and energy deposit e: The absorbed dose distributions were derived by integrating e at each voxel.

Treatment plan Spread-out Bragg peak (SOBP) plans were made for the targets defined in the phantom with a constant RBE of 1.1. We use the term "constant-RBE-weighted dose" for the product of the absorbed dose and the constant RBE of 1.1. The mono-energetic proton beams were superimposed to create SOBP fields using formulae described by Jette and Chen.24 The cross section of the target was set to 30  30 mm2, which was sufficiently covered by the proton beam. With regard to tumor depth, mono-energetic proton beams with E0 of 230, 155, and 80 MeV (corresponding to the water equivalent range of 330, 167, and 52 mm, respectively) were selected as the highest-energy beams and formed SOBP fields. We refer to these fields (targets) as deep, middle, and shallow fields (targets), respectively. With regard to tumor size, we defined targets of different lengths in the range of 20 to 120 mm in steps of 20 mm for the deep and middle fields and 20, 40, and 50 mm for the shallow fields. With regard to fraction dose, constant-RBE-weighted doses Dpre of 2, 3, 5, 10, and 20 Gy (RBE) were prescribed to the targets.

Instantaneous irradiation The depth variation of the RBE was investigated by recalculating the planned biological dose based on the MKM. The MKM is a model used to predict the radiationinduced cell-survival fraction from the specific energy z absorbed by a subcellular structure “domain.”8-10 Kase et al

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attributed the decrease in the cell survival fraction to the overkill effect observed in high-LET radiation using the dose-mean, saturation-corrected, single-hit specific energy of the domain z1D .12 The natural logarithm of the cell survival fraction S after radiation exposure of a macroscopic dose D is given by 
ð1Þ ln S Z  a0 þ bz)1D D  bD2 where a0 is the linear coefficient of the linear-quadratic (LQ) model at the limit of LET Z 0 and b is the quadratic coefficient of the LQ model. Both a0 and b are independent of the radiation type. For mono-energetic proton beams, the z)1D distribution can be calculated from the distribution of Zp and Ek using an amorphous track structure model.25 Then, the z)1D distribution of an SOBP field can be derived as dose-weighted averages of z)1D of the constituent mono-energetic beams at each voxel. In proton SOBP fields, z)1D and LET increases toward the distal edge of the target.12-14 Thus, equation (1) implies that S must depend on the depth even if D is uniformly delivered to a target. The acute dose Dacute , defined as the product of the absorbed dose and the variable RBE in instantaneous irradiation, can be calculated as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aX þ a2X  4bD ln S Dacute Z ð2Þ 2b where aX is a linear coefficient of the LQ model for a reference radiation. A 200 kV x-ray was selected as the reference radiation in this study. We used the values of aX Z 0:3130 Gy1, a0 Z 0:172 Gy1, and bZ 0:0615 Gy2 determined for human salivary gland tumor cells throughout the study.26 We recalculated the acute dose distributions with equation (2) based on the MKM model.

Continuous and interrupted irradiation The quadratic coefficient of the LQ model deals with cell death from accumulation of sublethal damage. The effect of SLDR during irradiation can be taken into account by using 0 an irradiation-time-dependent coefficient b .17,18 S after the continuous irradiation over a period of time T is predicted by 
0 ð3Þ ln S Z  a0 þ bz)1D D  b D2 with 2b



1 þ e2ðaþcÞtr bZ 1 2 2 ða þ cÞT 1  e2ðaþcÞtr ða þ cÞ T
 eðaþcÞT 1  e2ðaþcÞðtr TÞ þ 1  e2ðaþcÞtr 0

ð4Þ

where 1 =ða þ cÞ represents the lifetime of the sublethal damage, which is occasionally repaired or transformed to lethal damage, including cell death. We used the values of a Z 3:65  104 min1, c Z 3:61  102 min1, and tr Z 1:37  102 min.18

We recalculated the equivalent acute dose distributions for continuous irradiation by substituting equations (3) and (4) for equation (2). Because the RBE is the ratio of the radiation dose of interest to reference radiation at the same biological effect under the same conditions, except for the radiation type, the LQ parameters for a reference radiation, aX and b; must vary with the irradiation time T: However, in this study, the same aX and b values as TZ 0 were used because this study is concerned with the effect of irradiation time on the biological effectiveness of therapeutic proton beams against instantaneous irradiation. The term "biological effectiveness" was used with this definition throughout this study. In this definition, RBE-weighted absorbed dose was defined as "equivalent acute dose." For interrupted irradiation, we considered the interruption time s between the first and the second irradiation with macroscopic doses D1 and D2 over periods of time T1 and T2 ; respectively. S after the interrupted irradiation is expressed as     ln S Z  a0 þ bz)1D;1 D1  a0 þ bz)1D;2 D2 ð5Þ  b1 D21  b2 D22  b3 D1 D2 where z)1D;1 and z)1D;2 are z)1D s of each irradiation.18 b1 ; b2 , and b3 are given by  2b 1 þ e2ðaþcÞtr b1 Z 1 ða þ cÞT 1 1  e2ðaþcÞtr ða þ cÞ2 T 21
 eðaþcÞT1 1  e2ðaþcÞðtr T1 Þ þ ð6Þ 1  e2ðaþcÞtr  2b 1 þ e2ðaþcÞtr b2 Z 1 2 2 ða þ cÞT2 1  e2ðaþcÞtr ða þ cÞ T 2
 eðaþcÞT2 1  e2ðaþcÞðtr T2 Þ þ ð7Þ 1  e2ðaþcÞtr and

b3 Z


2

2b

ða þ cÞ T1 T2



ð1  e2ðaþcÞtr Þ

 eðaþcÞðsþT2 Þ

þ eðaþcÞs þ eðaþcÞðT1 þsþT2 Þ  eðaþcÞðT1 þsÞ þe

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ð8Þ

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In this study, D1 ZD2 and T1 ZT2 were used. The equivalent acute dose distributions and median doses were calculated for TZ 5; 15; 30; 45; and 60 minutes with s Z 0; 1; 2; 5; 10; 15; 30, and 60 minutes.

Tumor control probability and curative dose The tumor control probability (TCP) was evaluated for the target. Only single-fraction irradiation was considered because the effect of T was highlighted in the

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Time effect on proton biological dose

Results

irradiation. The TCP for the single-fraction irradiation is expressed as "
0 2 ! a0  a0 1 TCP Z pffiffiffiffiffiffi exp  2s2a0 2psa0 # Z Z Z expð  rcell ðxÞSðxÞÞdx da00

The acute and equivalent acute doses were calculated, as shown in Figure 1 for the 80-mm deep target. The median doses are shown in Figure 2 for the 50-mm and 80-mm deep, middle, and shallow targets.

Z

ð9Þ

Instantaneous irradiation The red lines in Figure 1 show the acute dose distributions of different Dpre values for instantaneous irradiation. In each distribution, a peak was observed near the distal edge of the target. The highest peak of greater than 110% of Dpre was observed with Dpre Z 2 Gy (RBE). The acute dose decreased as Dpre increased. The median doses delivered to the target were 1.98, 2.92, 4.78, and 18.38 Gy (RBE) with Dpre of 2, 3, 5, and 20 Gy (RBE), respectively.

where sa0 is a standard deviation of a0 0 with the mean value a0 representing variation of radiosensitivity between patients.18 rcell ðxÞ and SðxÞ are the clonogenic density and the survival fraction of clonogenic cells at position x.27 sa0 and rcell are 0.15 Gy1 and 1.0107 mL1, respectively.18 The curative dose Dcur was defined as the dose with a TCP value of 90%. Variations of Dcur were investigated with different cell survival parameters, as reported by Furusawa et al (aX Z 0:313 Gy1, bZ 0:0615 Gy2),26 Kase et al (aX Z 0:164 Gy1, bZ 0:05 Gy2),11 and Okamoto et al (aX Z 0:241 Gy1, bZ 0:036 Gy2).28 2.2

Dose [Gy]/ [Gy (RBE)]

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Continuous and interrupted irradiation The equivalent acute dose distributions were calculated with various T and s: The median doses decreased to 1.81,

T = 0 min T = 5 min T = 15 min T = 30 min T = 45 min T = 60 min DRBE = 1.1 Dphys Interrupted

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Fig. 1. Dose distributions of the 80-mm deep target with different irradiation times T and interruption time s: The absorbed dose Dphys and the constant relative biological effectiveness (RBE)-weighted dose DRBE Z 1:1 are also shown. Four panels are the distributions for Dpre of 2, 3, 5, and 20 Gy (RBE).

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Fig. 2. The median doses in the (a) 80-mm deep, (b) 80-mm middle, and (c) 50-mm shallow targets with different prescribed dose Dpre s and irradiation time Ts. The bars show the statistical errors. 2.61, 4.11, and 14.47 Gy with TZ 60 minutes with Dpre of 2, 3, 5, and 20 Gy (RBE), respectively. The time-dependent variations of the median dose are shown in Figure 2. The statistical errors were  0.5% for all targets.

Tumor control probability The TCP curves for various fields were evaluated for single-fraction proton therapy, as shown in Figure 3. The TCP curves shifted to higher dose as T or s increased.

Curative dose Dcur linearly increased by approximately 33% to 35% with T increasing from 0 to 60 minutes for all targets. Furthermore, for the deep target, Dcur maximally increased by approximately 16% with the increase in target length with TZ 60 minutes (Fig. 4a). The maximum increase of Dcur was 31% from sZ 0 to 60 minutes. Variations of Dcur are shown with different cell survival parameters in Figure 4d to 4f. The statistical errors were  0.5% for all targets.

Discussion Instantaneous irradiation The acute dose had a peak at the distal edge of the target because of increasing LET toward the edge. As a result, the range of the beam was longer by a few millimeters in the acute dose distribution compared with that expected from the constant-RBE-weighted dose.29 This can result in

damage to the normal tissues behind the target. The height of the peak decreased as the prescribed dose increased because the quadratic term in the cell survival becomes dominant at higher D and suppresses the effect of the LET variation in the linear term, as expressed in equation (1). The acute dose was approximately 6% lower compared with the constant-RBE-weighted dose at the entrance of the proton beam and was mostly independent of the prescribed dose. Under realistic conditions, a small amount of contamination by low-energy protons created by beam delivery devices can increase the dose near the patient’s skin. Takada et al simulated a double-scattering beam delivery system, except for patient-specific devices such as a compensator or a patient collimator.14 Although low-energy contamination was simulated in their study, the acute dose was comparable to that in this study at the entrance of the proton beam. However, Titt et al reported that the patient collimator is a major source of low-energy protons.30 Further study is needed to investigate Dcur near the patient’s skin using the patient-specific devices.

Continuous and interrupted irradiation The decrease in the equivalent acute dose was large at higher prescribed doses. For example, the median doses of the 80-mm deep target were 1.98 Gy (RBE) (99.0% of Dpre Z 2 Gy [RBE]) and 18.38 Gy (RBE) (91.9% of Dpre Z 20 Gy [RBE]) at TZ 0: Assuming TZ 15 minutes and sZ 5 minutes in an actual treatment, the equivalent acute doses decreased to 1.92 Gy and 16.62 Gy (96.0% and 83.1% of Dpre ), respectively. Two gray (RBE) per fraction is typical in a conventional fractionated proton therapy,

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Tumor control probability

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Fig. 3. Tumor control probability curves for single-fraction proton therapy with variations of the target length (a-c) and the interruption time s (d-f). Six panels are tumor control probability curves for the 20-mm, 60-mm, and 120-mm (a, d) deep and (b, e) middle fields and (c, e) the 20-mm- and 50-mm shallow fields.

whereas Dpre of 20 Gy (RBE) is close to Dcur of the singlefraction irradiation ranging from 21.6 to 38.4 Gy, as shown in Figure 4. Thus, the biological effectiveness is more sensitive to T and s in single-fraction irradiation compared with that in fractionated treatment. Becaise 1.0% to 21.0% decreases in biological effectiveness were observed, the effect of SLDR during irradiation needs to be considered, especially for single-fraction irradiation. Moreover, the equivalent acute dose must be more sensitive to T and s in proton therapy than in carbon therapy because the contribution of the quadratic term in cell survival is larger in low-LET radiation. Kase et al reported that the values of a for human salivary gland cells were 0.18 to 0.23 Gy1 and 0.43 to 1.02 Gy1 for 160 MeV protons and 290 MeV/u carbons, respectively, both with 60-mm SOBP.12 We assumed the time structure was independent of the position in the target, which provided a good assumption for passively scattered proton therapy. However, in pencil beam scanning, the target is irradiated sequentially, layer by layer, from deep to shallow, to form a single-field uniform dose, which may result in nonnegligible irradiation time dependence on the depth in the target.

Tumor control probability and curative dose Dcur varied with the target length because of the difference in the number of clonogenic cells (Fig. 4). A larger fraction of clonogenic cells received high equivalent acute dose at the peak at the distal edge in smaller target volumes. Dcur strongly depends on the target length being shorter than 40 mm. The maximum difference in Dcur was approximately 16% between 20 and 120 mm target length. No dependence of Dcur on depth was observed. Dcur increased by approximately 12% and 39% with aX Z 0:164 Gy1, bZ 0:05 Gy2 and aX Z 0:241 Gy1, bZ 0:036 Gy2, respectively, independent of the size and the depth of the target. A uniform value of cell density rcell Z 1:0  107 mL1 was used in this study. This depends on the type of tumor and patient.31,32 Variation in rcell has a direct impact on Dcur : it increases by approximately 1 Gy with rcell Z 1:0  108 mL1. Further studies of the clonogenic density, including the homogeneous distribution, are required for a more accurate estimation. Use of multifield irradiation moderates over- and underdosing within the target, which allows us to achieve better dose coverage and homogeneity. Nevertheless, interruption time of the beam is unavoidable during

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Fig. 4. Curative doses Dcur as a function of the irradiation time T in a single-fractionated treatment. Dcur variations were plotted with different interruption times s (a-c) and sets of cell survival parameters: aX Z 0:313 Gy1 and bZ 0:0615 Gy2;26 aX Z 0:164 Gy1 and bZ 0:05 Gy2;11 and aX Z 0:241 Gy1 and bZ 0:036 Gy2;28 (df). Six panels are Dcur for 20-120-mm (a, d) deep and (b, e) middle targets and (c, f) 20-50-mm shallow targets. switching of the field, such as during rotating the gantry or repositioning the patient. Inaniwa et al reported that a curative dose of 36.6 Gy with sZ 0 shifted to 39.2 and 43.3 Gy (7.1% and 18.3% increase) with sZ 15 and 30 minutes, respectively, with T1 ZT2 Z 7:5 minutes in carbon therapy.18 With the same Ts and ss, Dcur of 28.0 Gy shifted to 30.9 and 35.9 Gy (10.8% and 28.2% increase) for 40-mm middle target in this study, indicating greater effect of SLDR in proton therapy than in carbon therapy. Inaniwa et al recalculated the biological dose of a clinical plan whereas we used the water phantom; this is considered one of the reasons for higher curative doses in their studies.

Conclusions The equivalent acute dose and the TCP were systematically evaluated for parameters of proton beams accounting for irradiation time. The median dose of the target decreased

significantly with longer T and s; or higher prescribed dose. Thus, the biological effectiveness was more sensitive to T and s in single-fraction treatment than in multifractionated treatment. Dcur was approximately 33% to 35% higher with TZ 60 minutes compared with TZ 0 in single-fraction irradiation. Dcur maximally varied by about 16% by the target length, but no dependence on the target depth was observed. Further studies are required for treatments using scanning beam. The results in this study suggest that the irradiation time needs to be considered, especially in treatments with high doses per fraction.

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Preliminary results of a phase I/II clinical study. Int J Radiat Oncol Biol Phys 2007;68:786-793. Hong TS, Wo JY, Yeap BY, et al. Multi-institutional phase II study of high-dose hypofractionated proton beam therapy in patients with localized, unresectable hepatocellular carcinoma and intrahepatic cholangiocarcinoma. J Clin Oncol 2016;34:460-468. Amichetti M, Amelio D, Minniti G. Radiosurgery with photons or protons for benign and malignant tumours of the skull base: A review. Radiat Oncol 2012;7:210. Halasz LM, Bussie`re MR, Dennis ER, et al. Proton stereotactic radiosurgery for the treatment of benign meningiomas. Int J Radiat Oncol Biol Phys 2011;81:1428-1435. 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:R419-R472. Gerweck LE, Kozin SV. Relative biological effectiveness of proton beams in clinical therapy. Radiother Oncol 1999;50:135-142. Hawkins RB. A statistical theory of cell killing by radiation of varying linear energy transfer. Radiat Res 1994;140:366-374. Hawkins RB. A microdosimetric-kinetic model of cell death from exposure to ionizing radiation of any LET, with experimental and clinical applications. Int J Radiat Biol 1996;69:739-755. Hawkins RB. A microdosimetric-kinetic model for the effect of nonPoisson distribution of lethal lesions on the variation of RBE with LET. Radiat Res 2003;160:61-69. Kase Y, Yamashita W, Matsufuji N, et al. Microdosimetric calculation of relative biological effectiveness for design of therapeutic proton beams. J Radiat Res 2013;54:485-493. Kase Y, Kanai T, Matsumoto Y, et al. Microdosimetric measurements and estimation of human cell survival for heavy-ion beams. Radiat Res 2006;166:629-638. Kase Y, Kanai T, Matsufuji N, et al. Biophysical calculation of cell survival probabilities using amorphous track structure models for heavy-ion irradiation. Phys Med Biol 2008;53:37-59. Takada K, Sato T, Kumada 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;59:91-99. Elkind MM, Sutton H. Radiation response of mammalian cells grown in culture. 1. Repair of x-ray damage in surviving Chinese hamster cells. Radiat Res 1960;13:556-593. Elkind MM. Repair processes in radiation biology. Radiat Res 1984; 100:425-449. Inaniwa T, Suzuki M, Furukawa T, et al. Effects of dose-delivery time structure on biological effectiveness for therapeutic carbon-ion beams evaluated with microdosimetric kinetic model. Radiat Res 2013;180: 44-59.

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