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Journal Articles

Liquid water radiolysis induced by secondary electrons generated from MeV-energy carbon ions

Tsuchida, Hidetsugu*; Tezuka, Tomoya*; Kai, Takeshi; Matsuya, Yusuke*; Majima, Takuya*; Saito, Manabu*

Journal of Chemical Physics, 161(10), p.104503_1 - 104503_8, 2024/09

Although fast ion beams can damage DNA by chemical products such as secondary electrons produced by their interaction with water in living cells, the process of formation of these chemical products in the Bragg peak region used in particle therapy is not fully understood. To investigate this process, we performed experiments to evaluate the yields of radiolytic products produced when a liquid water jet in vacuum is irradiated with a MeV-energy carbon beam. In addition, ionization processes in water due to incident ions and secondary electrons were simulated using a radiation transport Monte Carlo code. The results indicated that the primary source of ionization in water is secondary electrons. Finally, we show that these elementary processes contribute to the development of radiation biophysics and biochemistry to study the formation mechanism of DNA damage.

Journal Articles

Evaluation of relative biological effectiveness for diseases of the circulatory system based on microdosimetry

Sato, Tatsuhiko; Matsuya, Yusuke; Hamada, Nobuyuki*

Journal of Radiation Research (Internet), 65(4), p.500 - 506, 2024/07

We therefore evaluated the mean and uncertainty of relative biological effectiveness (RBE) for diseases of the circulatory system (DCS) by applying a microdosimetric kinetic model specialized for RBE estimation of tissue reactions. For this purpose, we analyzed several RBE data for DCS determined by past animal experiments and evaluated the radius of the subnuclear domain best fit to each experiment as a single free parameter included in the model. Our analysis suggested that RBE for DCS tends to be lower than that for skin reactions, and their difference was borderline significant due to large variances of the evaluated parameters. These findings will help determine RBE by ICRP for preventing tissue reactions.

Journal Articles

Cell-cycle dependence on the biological effects of boron neutron capture therapy and its modification by polyvinyl alcohol

Matsuya, Yusuke; Sato, Tatsuhiko; Kusumoto, Tamon*; Yachi, Yoshie*; Seino, Ryosuke*; Miwa, Misako*; Ishikawa, Masayori*; Matsuyama, Shigeo*; Fukunaga, Hisanori*

Scientific Reports (Internet), 14, p.16696_1 - 16696_14, 2024/07

Boron neutron capture therapy (BNCT) is a unique radiotherapy to selectively eradicate tumor cells using boron compounds (e.g., 4-borono-L-phenylalanine [BPA]) that are heterogeneously taken up at the cellular level. However, the impacts of tempo-spatial heterogenicity on cell killing remain unclear. With the technical combination of radiation track detector, cell cycle analysis, and biophysical simulations, we demonstrated the cell cycle-dependent heterogenicity of BPA uptake and following biological impacts of $$^{10}$$B(n, $$alpha$$)$$^{7}$$Li reactions in HeLa cells expressing Fluorescent Ubiquitination-based Cell Cycle Indicators (FUCCI), as well as its modification effects of polyvinyl alcohol (PVA). As a result, we revealed that the intracellular BPA concentration in the S/G2/M phase was higher than that in the G1/S phase and that PVA modified the cell cycle dependence. Further, these findings lead to the development of the first BPA-PVA-based model for predicting BNCT treatment effects. These outcomes may contribute to more precision of therapeutic efficacy, when BNCT is combined with PVA and/or cell cycle-specific anticancer agents.

Journal Articles

The Impact of dose rate on responses of human lens epithelial cells to ionizing irradiation

Matsuya, Yusuke; Sato, Tatsuhiko; Yachi, Yoshie*; Date, Hiroyuki*; Hamada, Nobuyuki*

Scientific Reports (Internet), 14, p.12160_1 - 12160_14, 2024/05

Understand mechanisms of radiation cataracts that are of concern in the field of radiation protection and radiation therapy. However, biological effects in HLEC following protracted exposure have not yet fully been explored. Here, we investigated the temporal kinetics of DNA double-strand breaks (DSBs) and cell survival of HLEC after exposure to photon beams at various dose rates, compared to those of human lung fibroblasts (WI-38). In parallel, we quantified the recovery for DSB and cell survival using a biophysical model. The study revealed that HLEC cells have a lower repair rate than WI-38 cells. There is no significant impact of dose rate on cell survival in both cell lines in the dose-rate range of 0.033-1.82 Gy/min. On the other hand, the experimental residual DSBs showed inverse dose rate effects (IDREs) compared to the model prediction, highlighting the importance of the IDREs in evaluating radiation effects on the ocular lens.

Journal Articles

DNA damage response in a 2D-culture model by diffusing alpha-emitters radiation therapy (Alpha-DaRT)

Nojima, Hitomi*; Kaida, Atsushi*; Matsuya, Yusuke; Uo, Motohiro*; Yoshimura, Ryoichi*; Arazi, L.*; Miura, Masahiko*

Scientific Reports (Internet), 14, p.11468_1 - 11468_13, 2024/05

Diffusing alpha-emitters radiation therapy (Alpha-DaRT) is a unique radiotherapy that uses seeds emitting alpha particles placed in solid tumors to kill cancer cells surrounding the seeds. Although the DNA damage response is an important cellular response that determines cell death after radiation; however, how DNA damage response occurs during Alpha-DaRT treatment has not yet been explored. In this study, we measured the spatiotemporal characteristics of the DNA damage response, including the number of DNA double-strand breaks and G2 arrest, during Alpha-DaRT treatment by cell experiments using HeLa cells expressing the Fucci cell cycle visualization system. As a result, we found a strong correlation between the number of alpha particles detected by solid-state track detector CR-39 and $$gamma$$-H2AX staining, a marker for detecting DNA damage, and that the area of G2-arrested cells spread over a wider area up to 24 hours. In addition, time-lapse observations revealed that cell cycle dynamics change depending on the distance from the seed. The experimental model in this study revealed for the first time the spatiotemporal information of the DNA damage response around the seed during Alpha-DaRT treatment.

Journal Articles

Generality assessment of a model considering heterogeneous cancer cells for predicting tumor control probability for stereotactic body radiotherapy against non-small cell lung cancer

Saga, Ryo*; Matsuya, Yusuke; Obara, Hideki*; Komai, Fumio*; Yoshino, Hironori*; Aoki, Masahiko*; Hosokawa, Yoichiro*

Advances in Radiation Oncology (Internet), 9(4), p.101437_1 - 101437_5, 2024/04

The curative effects after radiotherapy are evaluated by the index of tumor control probability (TCP), and the treatment regimen has been determined empirically based on clinical experiences. In recent years, in order to determine TCP for any treatment regimens based on cell experiments, it is necessary to consider the existence of radioresistant cancer stem cells, which are included in tumors at from a few to several tens of percent. Our previous study has proposed an integrated microdosimetric-kinetic (IMK) model that explicitly considers cancer stem cells, and successfully reproduced cancer cell death obtained from cell experiments and clinical TCP. However, the verification so far has been limited to comparison with the clinical data of Hirosaki University Hospital, and comparative verification with clinical data of other facilities has not been performed. In this study, we focused on the stereotactic radiotherapy against non-small cell lung cancer that prescribes a large dose at once, and compared the public data collected by meta-analysis with the IMK model. As a result, it was found that the IMK model considering cancer stem cells well reproduced the clinical TCP regardless of the observed facility type. This work would contribute to the development of technology for predicting curative effects of radiotherapy with high precision.

Journal Articles

Changes in molecular conformation and electronic structure of DNA under $$^{12}$$C ions based on first-principles calculations

Sekikawa, Takuya; Matsuya, Yusuke; Hwang, B.*; Ishizaka, Masato*; Kawai, Hiroyuki*; Ono, Yoshiaki*; Sato, Tatsuhiko; Kai, Takeshi

Nuclear Instruments and Methods in Physics Research B, 548, p.165231_1 - 165231_6, 2024/03

 Times Cited Count:0 Percentile:0.11(Instruments & Instrumentation)

One of the main causes of radiation effects on the human body is thought to be damage to DNA, which carries genetic information. However, it is not fully understood what kind of molecular structural changes DNA undergoes upon radiation damage. Since it has been reported that various types of DNA damage are formed when DNA is irradiated, our group has investigated the relationship between DNA damage and various patterns of radiation-induced ionization induced by radiation. Although we have so far analyzed DNA damage in a simple system using a rigid body model of DNA, more detailed calculations are required to analyze the molecular structural changes in DNA, which are considered to be important in considering the effects on the human body. In this study, we attempted to clarify the molecular conformational changes of DNA using OpenMX, a first-principles calculation software that can discuss electronic states based on molecular structures. Specifically, we calculated the most stable structure, band dispersion, and wave function of DNA under the assumption that one and two electrons are ionized by various radiation. In the presentation, we will discuss the relationship between the energy dependence of each incident radiation type and the molecular conformational change of DNA. In addition, the radiation-induced changes in the basic physical properties of DNA (corresponding to the initial stage of DNA damage) will be discussed from the viewpoints of both radiation physics and solid state physics.

Journal Articles

Development of a model for evaluating the luminescence intensity of phosphors based on the PHITS track-structure simulation

Hirata, Yuho; Kai, Takeshi; Ogawa, Tatsuhiko; Matsuya, Yusuke; Sato, Tatsuhiko

Nuclear Instruments and Methods in Physics Research B, 547, p.165183_1 - 165183_7, 2024/02

 Times Cited Count:0 Percentile:0.02(Instruments & Instrumentation)

The luminescence efficiency of the phosphors for swift ions is known to decrease because of the quenching effects. To obtain the precise dose distributions using phosphor detectors, understanding the mechanisms of quenching effects is mandatory. Here, we developed a new model for estimating the luminescence intensity of phosphors based on the track-structure modes for arbitrary materials implemented in PHITS. The developed model enabled the simulation of the quenching effects of the BaFBr detector and was verified by comparing the results to the corresponding measured data. The present model is expected to contribute to developing phosphor detectors worldwide.

Journal Articles

A Step-by-step simulation code for estimating yields of water radiolysis species based on electron track-structure mode in the PHITS code

Matsuya, Yusuke; Yoshii, Yuji*; Kusumoto, Tamon*; Akamatsu, Ken*; Hirata, Yuho; Sato, Tatsuhiko; Kai, Takeshi

Physics in Medicine & Biology, 69(3), p.035005_1 - 035005_12, 2024/02

 Times Cited Count:0 Percentile:0.02(Engineering, Biomedical)

Time-dependent yields of chemical products resulted in water radiolysis play a great role in evaluating DNA damage response after exposure to ionizing radiation. Particle and Heavy Ion Transport code System (PHITS) is a general-purpose Monte Carlo simulation code for radiation transport, which allows to determine several atomic interactions such as ionizations and electronic excitations as physical stage. However, a chemical code for simulating products of water radiolysis does not exist in the PHITS package. Here, we developed a chemical simulation code dedicated for the PHITS code, hereafter called PHITS-Chem code, which enables calculating G values of water radiolysis species (OH radical, e$$_{aq}$$$$^{-}$$, H$$_{2}$$, H$$_{2}$$O$$_{2}$$ etc) by electron beams. The estimated G values during 1 $$mu$$s are in agreement with the experimental ones and other simulations. This PHITS-Chem code enables simulating the dynamics in the presence of OH radical scavenger, and is useful for evaluating contributions of direct and indirect effects on DNA damage induction. This code will be included and be available in the future version of PHITS.

Journal Articles

Recent improvements of the Particle and Heavy Ion Transport code System; PHITS version 3.33

Sato, Tatsuhiko; Iwamoto, Yosuke; Hashimoto, Shintaro; Ogawa, Tatsuhiko; Furuta, Takuya; Abe, Shinichiro; Kai, Takeshi; Matsuya, Yusuke; Matsuda, Norihiro; Hirata, Yuho; et al.

Journal of Nuclear Science and Technology, 61(1), p.127 - 135, 2024/01

 Times Cited Count:8 Percentile:99.39(Nuclear Science & Technology)

The Particle and Heavy Ion Transport code System (PHITS) is a general-purpose Monte Carlo radiation transport code that can simulate the behavior of most particle species with energies up to 1 TeV (per nucleon for ions). Its new version, PHITS3.31, was recently developed and released to the public. In the new version, the compatibility with high-energy nuclear data libraries and the algorithm of the track-structure modes have been improved. In this paper, we summarize the upgraded features of PHITS3.31 with respect to the physics models, utility functions, and application software introduced since the release of PHITS3.02 in 2017.

Journal Articles

Modeling for predicting survival fraction of cells after ultra-high dose rate irradiation

Shiraishi, Yuta*; Matsuya, Yusuke; Kusumoto, Tamon*; Fukunaga, Hisanori*

Physics in Medicine & Biology, 69(1), p.015017_1 - 015017_14, 2024/01

 Times Cited Count:0 Percentile:0.02(Engineering, Biomedical)

FLASH radiotherapy (FLASH-RT) using ultra-high dose rate ($$>$$ 40 Gy/sec) is known as a new treatment which is expected to enable preserving normal tissue functions, compared to the conventional radiotherapy (CONV-RT) with high dose rate ($$leqq$$ 6 Gy/min). To date, it is believed that the modulation of chemical processes caused by interactions between radiation tracks under FLASH-RT is a key factor in the functional preservation of normal tissues; however, the relationship between changes in chemical processes and cellular responses remains uncertain. In this study, we developed a prediction model (integrated microdosimetric-kinetic (IMK) model for FLASH-RT) taking into account of the relationship between the chemical process and the DNA damage yields (which is the initial response) under ultra-high dose rate irradiation, to investigate the cellular mechanisms. As a result, the developed model considering the chemical-processes dependent change in DNA damage yields successfully reproduced the measured cell-killing effects of both CONV-RT and FLASH-RT for various cell line types. This model development would contribute on not only precisely understanding of cellular mechanisms after FLASH-RT irradiation but also enabling the prediction of therapeutic effects with high precision.

Journal Articles

${it In vitro}$ and in silico study of biological effects on cancer cells in the presence of metallic materials during radiotherapy

Nagano, Takuya*; Matsuya, Yusuke; Kaida, Atsushi*; Nojima, Hitomi*; Furuta, Takuya; Sato, Kaoru; Yoshimura, Ryoichi*; Miura, Masahiko*

Journal of Radiation Research (Internet), 12 Pages, 2024/00

In X-ray therapy, radiation regimen is planned to eliminate tumors while minimizing side effects on normal tissue. When irradiating the oral cavity, which includes dental metallic crowns, intense mucositis can occasionally be induced. However, the mechanism underlying the radiosensitization remains unclear. In this study, we investigated the radiosensitization mechanism using cell experiments and computational simulations. As a result, the enhancement ratio observed in the cell experiments was 1.2-1.4, which was found to be predominately attributed to local dose increase near metal. On the other hand, as a result of dose evaluation based on CT images as a preclinical test, it was found that the dose increase was underestimated due to the complex anatomical structure of the human body, and microscopic dose evaluation was necessary. This outcome contributes to the precise understanding of side effects on normal cells around metals.

Journal Articles

First-principles simulation of an ejected electron produced by monochromatic deposition energy to water at the femtosecond order

Kai, Takeshi; Toigawa, Tomohiro; Matsuya, Yusuke; Hirata, Yuho; Tezuka, Tomoya*; Tsuchida, Hidetsugu*; Yokoya, Akinari*

RSC Advances (Internet), 13(46), p.32371 - 32380, 2023/11

 Times Cited Count:0 Percentile:0.00(Chemistry, Multidisciplinary)

Although scientific knowledge of photolysis and radiolysis of water is widely used in the life sciences and other fields, the formation mechanism of the spatial distribution of hydrated electrons (spur) resulting from energy deposition to water is still not well understood. The chemical reaction times of hydrated electrons, OH radicals, and H$$_{3}$$O$$^{+}$$ in the spur strongly depend on the spur radius. In our previous study, we elucidated the mechanism at a specific given energy (12.4 eV) by first-principles calculations. In the present study, we performed first-principles calculations of the spur radius at the deposition energies of 11-19 eV. The calculated spur radius is 3-10 nm, which is consistent with the experimental prediction (~4 nm) for the energy range of 8-12.4 eV, and the spur radius gradually increases with increasing energy. The spur radius is a new scientific knowledge and is expected to be widely used for estimating radiation DNA damage.

Journal Articles

Development of an electron track-structure mode for arbitrary semiconductor materials in PHITS

Hirata, Yuho; Kai, Takeshi; Ogawa, Tatsuhiko; Matsuya, Yusuke*; Sato, Tatsuhiko

Japanese Journal of Applied Physics, 62(10), p.106001_1 - 106001_6, 2023/10

 Times Cited Count:2 Percentile:66.71(Physics, Applied)

Optimization of semiconductor detector design requires theoretical analysis of the process of radiation conversion to carriers (excited electrons) in semiconductor materials. We, therefore, developed an electron track-structure code that can trace an incident electron trajectory down to a few eV and simulate many excited electron productions in semiconductors, named ETSART, and implemented it into PHITS. The accuracy of ETSART was validated by comparing calculated electron ranges in semiconductor materials with the corresponding data recommended in ICRU Report 37 and obtained from another simulation code. The average energy required to produce a single excited electron (epsilon value) is an important value that describes the characteristics of semiconductor detectors. Using ETSART, we computed the epsilon values in various semiconductors and found that the calculated epsilon values cannot be fitted well with a linear model of the band-gap energy. ETSART is expected to be useful for initial and mechanistic evaluations of electron-hole generation in undiscovered materials.

Journal Articles

Biophysical simulations for estimating biological effects after exposure to ionizing radiation; Current state and future prospects

Matsuya, Yusuke; Saga, Ryo*

Radiation Environment and Medicine, 12(2), p.81 - 90, 2023/08

Monte Carlo radiation transport simulations and biophysical models are powerful tools to evaluate the biological effects after ionizing radiation in radiation protection and radiation therapy. When exposing human body to radiation, DNA lesions as an early biological response are induced by deposition energy, leading to cell death with a certain probability. To precisely evaluate such effects, it is needed to perform translational studies among radiation physics, chemistry, and biology. Here, we introduce two simulation tools for predicting biological effects, i.e., Particle and Heavy-Ion Transport code System (PHITS) and integrated microdosimetric-kinetic model (IMKM). First, PHITS track-structure calculation at DNA scale enables to estimate the DNA damage yields by electrons and protons. Meanwhile, the IMKM considering various biological factors such as DSB repair kinetics and cancer stem-liken cells can successfully reproduce in vitro cell survival and clinical outcome. This review shows the development history and future prospect of the PHITS and the IMKM, which can expect to be further applied to the research fields of radiation research and quantum life science.

Journal Articles

Improvement of the hybrid approach between Monte Carlo simulation and analytical function for calculating microdosimetric probability densities in macroscopic matter

Sato, Tatsuhiko; Matsuya, Yusuke*; Ogawa, Tatsuhiko; Kai, Takeshi; Hirata, Yuho; Tsuda, Shuichi; Parisi, A.*

Physics in Medicine & Biology, 68(15), p.155005_1 - 155005_15, 2023/07

 Times Cited Count:2 Percentile:77.68(Engineering, Biomedical)

In this study, we improved the microdosimetric function implemented in PHITS using the latest track-structure simulation codes. The improved function is capable of calculating the probability densities of not only the conventional microdosimetric quantities such as lineal energy but also the numbers of ionization events occurred in a target site, the so-called ionization cluster size distribution, for arbitrary site diameters from 3 nm to 1 um. As a new application of the improved function, we calculated the relative biological effectiveness of the single-strand break and double-strand break yields for proton irradiations using the updated PHITS coupled with the simplified DNA damage estimation model, and confirmed its equivalence in accuracy and its superiority in computational time compared to our previously proposed method based on the track-structure simulation.

Journal Articles

Modelling oxygen effects on the in- and out-of-field radiosensitivity of cells exposed to intensity-modulated radiation fields

Matsuya, Yusuke; McMahon, S. J.*; Butterworth, K. T.*; Yachi, Yoshie*; Saga, Ryo*; Sato, Tatsuhiko; Prise, K. M.*

Physics in Medicine & Biology, 68(9), p.095008_1 - 095008_12, 2023/04

 Times Cited Count:1 Percentile:55.59(Engineering, Biomedical)

Hypoxia induces radioresistance in tumors, leading to malignant progression in intensity-modulated radiation therapy. To date, it has been shown that intercellular signalling between cells positioned inside and outside radiation field impacts on cellular radiosensitivity under hypoxia and normoxia. However, the mechanistic role of intercellular communication in hypoxia remains to be fully understood. In this study, we modelled the cell-killing effects of intercellular signalling in hypoxia to better understand the underlying mechanisms of response. We used the oxygen enhancement ratio (OER) given from early DSB yields and modelled the in- and out-of-field radiosensitivity. As a result, the model analysis provides an mechanistical interpretation that the probability of hits for releasing cell-killing signals is dependent on oxygen. Our data also suggested that the field-type independent OER value, which can be given by uniform-field exposure, can be applied when predicting both in- and out-of-field radiosensitivity. These results would contribute to more precise understanding of intercellular signalling under heterogeneous exposure to intensity-modulated radiation fields.

Journal Articles

Initial yield of hydrated electron production from water radiolysis based on first-principles calculation

Kai, Takeshi; Toigawa, Tomohiro; Matsuya, Yusuke*; Hirata, Yuho; Tezuka, Tomoya*; Tsuchida, Hidetsugu*; Yokoya, Akinari*

RSC Advances (Internet), 13(11), p.7076 - 7086, 2023/03

 Times Cited Count:3 Percentile:73.63(Chemistry, Multidisciplinary)

Scientific insights of water radiolysis are widely used in the life sciences and so on, however, the formation mechanism of radicals, a product of water radiolysis, is still not well understood. We are challenging to develop a simulation code to solve this formation mechanism from the viewpoint of radiation physics. Our first-principles calculations have revealed that the behavior of secondary electrons in water is governed not only by collisional effects but also by polarization effects. Furthermore, from the predicted ratio of ionization to electronic excitation, based on the spatial distribution of secondary electrons, we successfully reproduce the initial yield of hydrated electrons predicted in terms of radiation chemistry. The code provides us a reasonable spatiotemporal connection from radiation physics to radiation chemistry. Our findings are expected to provide newly scientific insights for understanding the earliest stages of water radiolysis.

Journal Articles

An Analytical method for quantifying the yields of DNA double-strand breaks coupled with strand breaks by $$gamma$$-H2AX focus formation assay based on track-structure simulation

Yachi, Yoshie*; Matsuya, Yusuke*; Yoshii, Yuji*; Fukunaga, Hisanori*; Date, Hiroyuki*; Kai, Takeshi

International Journal of Molecular Sciences (Internet), 24(2), p.1386_1 - 1386_14, 2023/01

 Times Cited Count:2 Percentile:66.37(Biochemistry & Molecular Biology)

When living cells are irradiated with radiation and complex damage is formed within a few nanometers of DNA, it is believed to induce biological effects such as cell death. In general, complex DNA damage formed in cells can be detected experimentally by fluorescence microscopy, because the area around the damage site emits light like a focus point when a fluorophore is used. However, this detection method has not been able to analyze the degree of complexity of DNA damage. Therefore, in this study, we addressed on the measured focus size and evaluated the degree of complexity of DNA damage using a track structure analysis code. As a result, we found that as DNA damage becomes more complex, the focus size also increases. Our findings are expected to provide a new analytical method for elucidating the initial factors of radiation biological effects.

Journal Articles

Translational study for stereotactic body radiotherapy against non-small cell lung cancer, including oligometastases, considering cancer stem-like cells enable predicting clinical outcome from ${it in vitro}$ data

Saga, Ryo*; Matsuya, Yusuke; Sato, Hikari*; Hasegawa, Kazuki*; Obara, Hideki*; Komai, Fumio*; Yoshino, Hironori*; Aoki, Masahiko*; Hosokawa, Yoichiro*

Radiotherapy and Oncology, p.109444_1 - 109444_9, 2023/00

 Times Cited Count:2 Percentile:77.68(Oncology)

When treating non-small cell lung cancer (NSCLC), stereotactic body radiotherapy (SBRT) with high-dose irradiation is often utilized. The fractionation schemes and curative effects can be evaluated by mathematical models for predicting cell survival curve. Such model parameters can be determined from in vitro experiment, but they are empirically determined based on experiences in clinics. As such, there is a large gap between in vitro and clinical study. As such background, translational study between in vitro cell survival and clinical curative effects is necessary. In this study, explicitly considering existence of cancer stem-like cells (CSCs), we developed an all-in-one model for predicting both in vitro cell survival and clinical curative effects (integrated microdosimetric-kinetic (IMK) model) and performed retrospective evaluation of clinical outcomes following SBRT for NSCLC in Hirosaki University Hospital. As a result, the IMK model successfully reproduced both in vitro cell survival and the tumor control probability with various fractionation schemes (i.e., 6-10 Gy per fraction). The developed model would contribute on precisely understanding the impact of CSCs on curative effects after SBRT for NSCLC with high precision.

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