Research ArticleExperimental Studies
Open Access

Estimation of Tumor Control Probability of Carbon Ion Radiotherapy Using Cancer Type-specific Sensitivity Data

EUNHYE YU, TAKAHIRO OIKE, MAKOTO SAKAI, MUTSUMI TASHIRO and TATSUYA OHNO
Anticancer Research January 2026, 46 (1) 113-122; DOI: https://doi.org/10.21873/anticanres.17927

Abstract

Background/Aim: This study aimed to evaluate whether the predictive performance of tumor control probability (TCP) by carbon ion radiotherapy (CIRT) could be improved by incorporating cancer type-specific carbon ion sensitivity data obtained from non-small cell lung cancer (NSCLC).

Materials and Methods: A TCP model based on the linear-quadratic (LQ) formalism and fractionated irradiation was employed, with σ defined as an index of inter-tumor heterogeneity on radiosensitivity. The LQ model parameters α and β for NSCLC were obtained from 13 cell lines subjected to carbon ion irradiation under clinically relevant conditions, followed by clonogenic assays. The human salivary gland (HSG) cell line was used as a control. The α and β values were incorporated into the TCP model, and agreement with the clinical data (i.e., the local control rates for 48 NSCLCs treated with CIRT, as previously reported) was evaluated using the coefficient of determination (R2) derived from least-squares fitting.

Results: When σ was set to 0.20, the NSCLC-derived TCP curve showed better agreement with the clinical data than the HSG cell-derived TCP curve (R2: 0.72 vs. 0.53, respectively). Similarly, when σ was set to 0.15, the NSCLC-derived curve showed better agreement with the clinical data (R2: 0.56 vs. 0.38, respectively). Furthermore, when weighting factors of 1, 3, and 10 were applied to the two data points with TCP=1.0, the NSCLC-derived TCP curve showed consistently better agreement with the clinical data than the HSG cell-derived TCP curve (R2: 0.74 vs. 0.55, 0.78 vs. 0.63, and 0.79 vs. 0.65, respectively).

Conclusion: Incorporation of cancer type-specific carbon ion sensitivity data can improve the predictive performance of TCP modeling compared with the conventional HSG cell-based approach.

Keywords:

Introduction

Carbon ion radiotherapy (CIRT) is a promising radiotherapy modality that offers superior dose conformality and a greater cell-killing effect than photons (1). The cell-killing effect of carbon ions at an equivalent physical dose is influenced by variations in linear energy transfer (LET) along the beam depth (2). In Japan, the effect of LET differences on the cell-killing effect of carbon ions is addressed during dose prescription by using the clinical dose, which is defined as the physical dose weighted by the relative biological effectiveness (RBE) (3). The RBE values are derived from measurement of clonogenic survival of human salivary gland tumor (HSG) cells irradiated with carbon ions (3). In practice, the clonogenic survival data are fitted to the linear-quadratic (LQ) model, and the resulting α and β parameters, which are determined for each beam energy, are incorporated into the treatment planning systems. In that sense, clinical dose prescriptions for CIRT are performed using the HSG-derived α and β values, regardless of cancer type.

Results from basic research have demonstrated that cancer cells exhibit a wide range of sensitivities to carbon ions (4-6). This finding suggests that the use of cancer type-specific carbon ion sensitivity data may allow for more accurate prediction of antitumor effects; however, this remains to be elucidated. In fact, previous studies have evaluated the tumor control probability (TCP) of CIRT in non-small cell lung cancer (NSCLC) (7) and prostate cancer (8) using the α and β values derived from HSG cells, or even by treating these values as free parameters for fitting. To address this gap, we aimed to investigate whether the predictive performance of TCP in CIRT could be improved through incorporation of cancer type-specific carbon ion sensitivity data.

Materials and Methods

Study overview. A TCP model based on the concepts of the LQ model and fractionated irradiation was used. The LQ model parameters α and β were obtained from cell experiments and incorporated into the TCP model. Then, the agreement between the TCP model and the clinical data was evaluated. NSCLC was chosen as a model for analysis. The carbon ion sensitivity data for 13 NSCLC cell lines were obtained, and data from HSG cells were used as a reference. For the clinical data, the local control rates of 48 NSCLCs treated with CIRT, as reported by Miyamoto et al., were utilized (9).

The TCP model. It is assumed that the relative frequency of the number of surviving clonogenic cells in a given tumor after treatment follows a Poisson distribution (10). TCP is the probability that no surviving clonogenic cells remain in a tumor, which corresponds to the zero-order term of the Poisson distribution, expressed as follows: (10, 11):

Embedded Image (1)

where Ns denotes the average number of surviving clonogenic cells per tumor after treatment.

For fractionated radiotherapy, in which the LQ model and a time factor accounting for cancer cell proliferation are taken into consideration, Ns is expressed as follows (12):

Embedded Image (2)

where N0 is the number of clonogenic cells in the tumor prior to treatment; n is the number of fractions; d is the fractionated dose (Gy); Td is the average doubling time of the tumor cells (days); and T is the overall treatment time (days).

Individual tumors within a given cohort should exhibit different radiosensitivities. To account for this, and to achieve a better fit with clinically observed data, the distribution of α among individual tumors within the cohort was incorporated (13). When gi is the probability density of tumors having α=αi, the overall mean TCP for the cohort is expressed as follows (11):

Embedded Image (3)

Assuming that αi follows a Gaussian distribution, gi is expressed as follows:

Embedded Image (4)

where αm and σ are the mean and standard deviation of α, respectively. Thus, the TCP for the cohort is obtained as follows:

Embedded Image (5)

Using Equation 5, the TCP was calculated by performing numerical integration of αi over the range −5σ to 5σ, with a step size of 0.01. The following values were used: N0=109, Td=7, (7), and T=42 (9). Fitting the TCP model to the clinical data was performed using least-squares fitting (7). For several analyses, fitting was performed by assigning a weighting factor to the clinical data points, with a local control rate of 1.0, as reported by Kanai et al. (7). The extent of agreement between the TCP model and the clinical data was evaluated using the coefficient of determination (R2), derived from least-squares fitting. These calculations were performed using Python (version 3.7.3, Python Software Foundation, Beaverton, OR, USA).

Cell experiments. The 13 human NSCLC lines were cultured in RPMI-1640 (Sigma-Aldrich, St. Louis, MO, USA) supplemented with 10% fetal bovine serum (Life Technologies, Carlsbad, CA, USA; Table I). Clonogenic assays were performed as previously described (14). Briefly, cells were seeded in 6-well plates (n=4) and cultured at 37°C until they attached to the plates (6-12 h, depending on cell line). The cells were exposed to carbon ions, at 1, 2, 3, or 4 Gy, at the Gunma University Heavy Ion Medical Center. The beam specification was as follows: 290 MeV/nucleon; and an average LET at the center of a 6 cm spread-out Bragg peak (SOBP) of approximately 50 keV/μm (4). After incubation for an additional 10-14 days, the cells were fixed with methanol and stained with crystal violet. Colonies comprising at least 50 cells were counted under an inverted microscope. The surviving fractions were calculated after normalization to the corresponding un-irradiated controls. The survival data were fitted to the LQ model, and the α and β values were obtained. In cases where the β values were extremely small positive, zero, or negative, the α/β ratio becomes difficult to interpret (i.e., extremely large, undefined, or negative, respectively). As no consensus exists regarding the appropriate handling of such situations, these cases were treated as missing values in the present study.

View this table:
Table I.

Linear quadratic (LQ) model parameters for the cell lines used in this study.

In CIRT in Japan, the HSG cell line is used for standardization of clinical doses (3); however, this cell line has been reported to be cross-contaminated with HeLa cells in multiple laboratories. In addition, authentication of uncontaminated HSG cells is theoretically impossible due to the absence of genotypic data for the original line at the time of their establishment (15). From this standpoint, the present study adopted the α and β values for HSG cells (α=0.76 and β=0.076) obtained at the National Institutes for Quantum Science and Technology (formerly the National Institute of Radiological Sciences, Chiba, Japan), where the standardization of clinical carbon ion doses was first established, and under irradiation settings consistent with those used in the aforementioned experiments with NSCLC cells (7).

Clinical data. As a reference for the CIRT outcomes of NSCLC, clinical data reported by Miyamoto et al. were employed (9). Their study presents the results of a dose-escalation trial for stage I NSCLC, in which the prescribed dose ranged from 59.4 Gy (RBE) to 95.4 Gy (RBE), delivered in 18 fractions (Table II). Among the 48 tumors analyzed, 26 were adenocarcinomas and 22 were squamous cell carcinomas. In the present study, the tumor control was defined according to the local control rates reported by Miyamoto et al. The local control rate from the clinical results was plotted as a function of the physical dose (Gy) instead of the clinical dose; this was done by applying an RBE value of 2.38 at the center of a 60-mm SOBP, as previously described (7).

View this table:
Table II.

Clinical data for carbon ion radiotherapy of non-small cell lung cancer used for tumor control probability modeling (9).

Results

The α and β values of the 13 NSCLC cell lines were obtained from clonogenic assays following carbon ion irradiation (Table I). TCP curves for each individual NSCLC cell line were generated based on Equation 1 using the cell line-specific α and β values, since the distribution of α (considered in Equation 3-5) can be neglected in this context (Figure 1). As expected, the TCP curves showed substantial shifts along the dose axis, reflecting the diversity of radiosensitivity among cell lines. Nevertheless, no histology-specific trends in the curve shape were identified. Based on these findings, in the subsequent analyses the mean α and β values across all examined NSCLC cell lines were used as the representative α and β values for NSCLC cells.

Figure 1.
Figure 1.

Tumor control probability (TCP) curves generated using the α and β values derived from each of the 13 non-small cell lung cancer cell lines. The lower right-hand panel compares the TCP curves by histological subtype. Adeno: Adenocarcinoma. Cell lines with the β values <0.001 are not shown.

Next, we compared the predictive performance of the TCP model between the setting using the α and β values derived from HSG cells with that using the values derived from NSCLC cells on the clinical outcome of CIRT for 48 stage I NSCLCs (9). In Equation 5, which describes the TCP model, σ represents the extent of inter-tumor heterogeneity in radiosensitivity (7). Given that the true σ value for the population is unknown, we employed 0.20, the σ value estimated from least-squares fitting of the TCP model to clinical outcomes and in which α, β, and σ were treated as free parameters. The α and β values for HSG cells, or those for NSCLC cells, were substituted for αm and β, respectively, in Equation 5. As a result, the R2 value for the NSCLC cell-derived TCP curve outperformed that for the HSG cell-derived TCP curve (R2: 0.72 vs. 0.53, respectively; Figure 2).

Figure 2.
Figure 2.

Tumor control probability (TCP) curves generated using the α and β values for human salivary gland (HSG) cells or for non-small cell lung cancer (NSCLC) cells, with σ fixed at 0.20. The R2 values obtained from least-squares fitting of the TCP model to the clinical data are shown.

The study by Kanai et al., which analyzed the fitting of the HSG cell-derived TCP curve to CIRT outcomes using the same clinical dataset used in the present study, concluded that the σ value that best described the clinical outcomes was 0.15±0.05 (7). Therefore, we next compared the predictive performance of the TCP model using the cell type-specific α and β values but employing a σ value of 0.15. As a result, the R2 value for the NSCLC cell-derived TCP curve outperformed that for the HSG cell-derived TCP curve (R2: 0.56 vs. 0.38, respectively; Figure 3).

Figure 3.
Figure 3.

Tumor control probability (TCP) curves generated using the α and β values for human salivary gland (HSG) cells or non-small cell lung cancer cells, with σ fixed at 0.15. The R2 values obtained from least-squares fitting of the TCP model to the clinical data are shown.

The study by Kanai et al. also performed least-squares fitting of the TCP model to clinical outcomes using the HSG cell-derived α and β values, treating σ as a free parameter (7). Therefore, we next compared the predictive performance of the TCP model using cell type-specific α and β values. In that analysis, Kanai et al. performed curve fitting by assigning “large weighting factors” to the two data points showing TCP=1.0, based on the assumption that these points were reliable due to saturation of the local control rate at 100%; however, the actual values for the weighting factors used were not provided in the manuscript. Therefore, we performed curve fitting by employing three different weighting factors: 1, 3, and 10. As a result, the R2 value for the NSCLC cell-derived TCP curve outperformed that for the HSG cell-derived TCP curve for all weighting factors analyzed (R2: 0.74 vs. 0.55, 0.78 vs. 0.63, and 0.79 vs. 0.65, for the weighting factors 1, 3, and 10, respectively; Figure 4). Taken together, these data indicate that the predictive performance of the TCP during CIRT could be improved by incorporating cancer type-specific carbon ion sensitivity data.

Figure 4.
Figure 4.

Tumor control probability (TCP) curves generated using the α and β values for human salivary gland (HSG) cells or non-small cell lung cancer (NSCLC) cells by applying a weighting factor of 1, 3, or 10 to data points showing TCP=1.0. The σ value was treated as a free parameter for least-squares fitting. The R2 values obtained from least-squares fitting of the TCP model to the clinical data are shown.

Discussion

We found that incorporating in vitro carbon ion sensitivity data derived from 13 NSCLC cell lines into the TCP model improved concordance with the clinical outcomes of CIRT for NSCLC. As a reference control, we used the study by Kanai et al. (7), which examined the fit of TCP, obtained using the sensitivity data derived from HSG cells, to the same clinical dataset. In that study, the authors demonstrated that the TCP based on HSG cell data was generally consistent with clinical outcomes, and so they concluded that the parameters that best accounted for the results were as follows: α=0.75±0.5, σ=0.15±0.05 (assuming β=0.076 and Td=7). In the present study, we evaluated the fit of the TCP model to clinical outcomes under multiple assumptions regarding the parameters, including those concluded by Kanai et al. Across all settings, the TCP based on NSCLC cell line-derived data consistently demonstrated a superior fit over the TCP based on HSG cell line-derived data. These findings indicate that the predictive performance of the TCP for CIRT can be improved by incorporating cancer type-specific carbon ion sensitivity data. The results suggest that the use of cell line-derived, cancer type-specific α and β values may facilitate prediction of optimal clinical dose-fractionation schemes for cancer types with limited clinical data. Moreover, cancer type-specific α and β values could also be implemented to LET-modulated CIRT that has been attracting interest in recent years (16, 17). To further validate these findings, additional studies involving other cancer types are warranted.

For decades, attempts have been made to predict the clinical outcomes of photon therapy using a TCP model based on the LQ parameters derived from cultured cells. Yaes et al. investigated TCP by incorporating α and β values from cell lines derived from six cancer types (18). In that study, the authors demonstrated that, for head and neck squamous cell carcinoma, the TCP curve based on cell line data was considerably steeper than that derived from clinical data. This observation is consistent with our findings, as shown in Figure 1. As a potential explanation for this discrepancy, Peters et al. suggested inter-tumor heterogeneity of radiosensitivity among clinical tumors (19). In the present study, we also assumed inter-tumor heterogeneity of radiosensitivity and so introduced σ as the parameter representing this variability. Since the true value of σ in the population is unknown, we performed multiple validations, each with σ set to a different value. In all cases, incorporation of σ brought the steepness of the cell line-derived TCP curve closer to that of the clinical data-derived TCP. In this regard, it can be said that the notion proposed by Peters et al. was confirmed by the present study. In addition, when σ was treated as a free parameter when fitting the TCP model to the clinical data, the resulting σ value was comparable with the median absolute deviation of the α values obtained from the NSCLC cell lines (i.e., approximately 0.25). Although further validation is warranted, this finding indicates the possibility that σ for a given cancer type cohort may be estimable from in vitro cell experiments.

As another potential explanation for the discrepancy between cell line- and clinical data-derived TCP, Weichselbaum et al. suggested intra-tumor heterogeneity of radiosensitivity within a clinical tumor, in which the presence of a small subset of radioresistant clones is assumed (20). It has been considered that this discrepancy is resolved by assuming that, within a tumor consisting of 109 cancer cells (defined as N0 in the present study), approximately 200 cells are intrinsically radioresistant. Weichselbaum et al. further speculated that the cause of this intrinsic cancer cell radioresistance is an enhanced DNA damage repair capacity. If this is the case, incorporating variations of β into TCP modeling may improve the predictive performance of clinical outcomes, since repair capacity is considered to be represented by β in the clonogenic survival curves approximated by the LQ model. In the present study, variation in the β term was not taken into account in the TCP model, which used the settings employed in previous studies (7, 13). Supporting this approach, Kanai et al. reported that variation in the β value of HSG cells with respect to varying carbon ion LET was modest (7); however, other studies have shown that cancer cells exhibit a wide range of β values in response to carbon ions under clinically relevant experimental settings (6, 21), suggesting the need for considering incorporating the β variation into the TCP model in the future. Nevertheless, doing so would render TCP modeling more complex, warranting further investigation.

When attempting to predict clinical TCP using cancer cell-derived radiosensitivity data, attention should be paid to the potential discrepancy in radiosensitivity between cultured cell lines and clinical tumors within a given cancer type. For example, it is well established that the α/β value for prostate cancer in the clinical setting is as low as 1-2 (22), whereas that for prostate cancer cell lines is typically much higher (23). This discrepancy may be attributable to the fact that prostate cancer cell lines commonly used in radiation research are derived from metastatic lesions and lack androgen sensitivity in most cases; thus, they exhibit biological characteristics distinct from those of primary prostate cancers, which are the targets of definitive radiotherapy in clinical practice. For this reason, direct application of cell line-derived radiosensitivity data to clinical TCP prediction is unlikely to be feasible in the context of this cancer type. Indeed, Kang et al. performed TCP modeling for CIRT in prostate cancer using equations based on the LQ model; however, their analysis treated α and β as free parameters (8). From this standpoint, clinical TCP prediction based on cell line-derived data requires careful evaluation of the biological properties of the cell lines employed.

The present study has the following limitations. First, the clinical dataset did not include physical dose data; therefore, direct comparison in units of Gy were not feasible. Second, the TCP model incorporated multiple parameters for which accurate estimation of true values is inherently difficult (i.e., σ, N0, and Td). These parameters constitute sources of uncertainty regarding the predictive performance of the TCP model. Third, as described in the Methods section, negative β values were treated as missing values due to the lack of consensus regarding their interpretation, which may have influenced the TCP estimation results. Lastly, in this study, differences in the weighting of TCP across clinical data plots, arising from variations in the number of cases per plot, were not taken into account. This decision was made because such differences have not been addressed in previous studies and incorporating them would substantially increase the complexity of the model.

In summary, the present study demonstrates that incorporation of cancer type-specific carbon ion sensitivity data can improve the predictive performance of TCP modeling compared with the conventional HSG cell-based approach. These findings suggest that cell type-specific biological parameters should be considered carefully when estimating clinical TCP in CIRT. Further validation with larger datasets and across additional cancer types is warranted to establish the generalizability of this approach, and to support its translation into clinical treatment planning.

Acknowledgements

This work was supported by Takeda Science Foundation, Shimadzu Science Foundation, Nishikawa Medical Foundation, the Japanese Society for Radiation Oncology, the Headquarters of Gunma University, and GHMC.

Footnotes

  • Authors’ Contributions

    E.Y. performed experiments, analyzed data, and wrote the manuscript. T. Oike conceptualized the project, performed experiments, and finalized the manuscript. M.S. and M.T. supervised TCP analysis. T. Ohno supervised entire project and acquired funding. All Authors read and agreed with the final version.

  • Conflicts of Interest

    The Authors declare no conflicts of interest in relation to this study.

  • Artificial Intelligence (AI) Disclosure

    No artificial intelligence (AI) tools, including large language models or machine learning software, were used in the preparation, analysis, or presentation of this manuscript.

  • Received September 26, 2025.
  • Revision received October 7, 2025.
  • Accepted October 20, 2025.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

References

  1. ↵
    1. Durante M,
    2. Orecchia R,
    3. Loeffler JS
    : Charged-particle therapy in cancer: clinical uses and future perspectives. Nat Rev Clin Oncol 14(8): 483-495, 2017. DOI: 10.1038/nrclinonc.2017.30
    OpenUrlCrossRefPubMed
  2. ↵
    1. Oike T,
    2. Kakoti S,
    3. Sakai M,
    4. Matsumura A,
    5. Ohno T,
    6. Shibata A
    : Analysis of the relationship between LET, γH2AX foci volume and cell killing effect of carbon ions using high-resolution imaging technology. J Radiat Res 64(2): 335-344, 2023. DOI: 10.1093/jrr/rrac098
    OpenUrlCrossRefPubMed
  3. ↵
    1. Kanai T,
    2. Endo M,
    3. Minohara S,
    4. Miyahara N,
    5. Koyama-ito H,
    6. Tomura H,
    7. Matsufuji N,
    8. Futami Y,
    9. Fukumura A,
    10. Hiraoka T,
    11. Furusawa Y,
    12. Ando K,
    13. Suzuki M,
    14. Soga F,
    15. Kawachi K
    : Biophysical characteristics of HIMAC clinical irradiation system for heavy-ion radiation therapy. Int J Radiat Oncol Biol Phys 44(1): 201-210, 1999. DOI: 10.1016/s0360-3016(98)00544-6
    OpenUrlCrossRefPubMed
  4. ↵
    1. Amornwichet N,
    2. Oike T,
    3. Shibata A,
    4. Ogiwara H,
    5. Tsuchiya N,
    6. Yamauchi M,
    7. Saitoh Y,
    8. Sekine R,
    9. Isono M,
    10. Yoshida Y,
    11. Ohno T,
    12. Kohno T,
    13. Nakano T
    : Carbon-ion beam irradiation kills X-ray-resistant p53-null cancer cells by inducing mitotic catastrophe. PLoS One 9(12): e115121, 2014. DOI: 10.1371/journal.pone.0115121
    OpenUrlCrossRefPubMed
    1. Osu N,
    2. Kobayashi D,
    3. Shirai K,
    4. Musha A,
    5. Sato H,
    6. Hirota Y,
    7. Shibata A,
    8. Oike T,
    9. Ohno T
    : Relative biological effectiveness of carbon ions for head-and-neck squamous cell carcinomas according to human papillomavirus status. J Pers Med 10(3): 71, 2020. DOI: 10.3390/jpm10030071
    OpenUrlCrossRefPubMed
  6. ↵
    1. Nachankar A,
    2. Oike T,
    3. Hanaoka H,
    4. Kanai A,
    5. Sato H,
    6. Yoshida Y,
    7. Obinata H,
    8. Sakai M,
    9. Osu N,
    10. Hirota Y,
    11. Takahashi A,
    12. Shibata A,
    13. Ohno T
    : (64)Cu-ATSM predicts efficacy of carbon ion radiotherapy associated with cellular antioxidant capacity. Cancers (Basel) 13(24): 6159, 2021. DOI: 10.3390/cancers13246159
    OpenUrlCrossRefPubMed
  7. ↵
    1. Kanai T,
    2. Matsufuji N,
    3. Miyamoto T,
    4. Mizoe J,
    5. Kamada T,
    6. Tsuji H,
    7. Kato H,
    8. Baba M,
    9. Tsujii H
    : Examination of GyE system for HIMAC carbon therapy. Int J Radiat Oncol Biol Phys 64(2): 650-656, 2006. DOI: 10.1016/j.ijrobp.2005.09.043
    OpenUrlCrossRefPubMed
  8. ↵
    1. Kang YM,
    2. Ishikawa H,
    3. Inaniwa T,
    4. Iwai Y,
    5. Matsufuji N,
    6. Kasuya G,
    7. Okonogi N,
    8. Liu YM,
    9. Chao Y,
    10. Wakatsuki M,
    11. Tsujii H,
    12. Tsuji H
    : The clinical relative biological effectiveness and prostate-specific antigen kinetics of carbon-ion radiotherapy in low-risk prostate cancer. Cancer Med 12(2): 1540-1551, 2023. DOI: 10.1002/cam4.5045
    OpenUrlCrossRefPubMed
  9. ↵
    1. Miyamoto T,
    2. Yamamoto N,
    3. Nishimura H,
    4. Koto M,
    5. Tsujii H,
    6. Mizoe JE,
    7. Kamada T,
    8. Kato H,
    9. Yamada S,
    10. Morita S,
    11. Yoshikawa K,
    12. Kandatsu S,
    13. Fujisawa T
    : Carbon ion radiotherapy for stage I non-small cell lung cancer. Radiother Oncol 66(2): 127-140, 2003. DOI: 10.1016/s0167-8140(02)00367-5
    OpenUrlCrossRefPubMed
  10. ↵
    1. Joiner MC,
    2. van der Kogel AJ
    1. Bentzen SM
    : Dose-response relationships in radiotherapy. In: Basic Clinical Radiobiology. Joiner MC, van der Kogel AJ (eds.). 4th ed. New York, NY, USA, CRC Press, pp. 56-67, 2009.
  11. ↵
    1. Webb S,
    2. Nahum AE
    : A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density. Phys Med Biol 38(6): 653-666, 1993. DOI: 10.1088/0031-9155/38/6/001
    OpenUrlCrossRefPubMed
  12. ↵
    1. Fowler JF
    : The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol 62(740): 679-694, 1989. DOI: 10.1259/0007-1285-62-740-679
    OpenUrlAbstract/FREE Full Text
  13. ↵
    1. Breit A
    1. Nahum AE,
    2. Tait DM
    : Maximising control by customized dose prescription for pelvic tumours. In: Advanced Radiation Therapy: Tumour Response Monitoring and Treatment Planning. Breit A (ed.). Heidelberg, Germany, Springer pp. 425-431, 1992.
  14. ↵
    1. Anakura M,
    2. Nachankar A,
    3. Kobayashi D,
    4. Amornwichet N,
    5. Hirota Y,
    6. Shibata A,
    7. Oike T,
    8. Nakano T
    : Radiosensitivity differences between EGFR mutant and wild-type lung cancer cells are larger at lower doses. Int J Mol Sci 20(15): 3635, 2019. DOI: 10.3390/ijms20153635
    OpenUrlCrossRefPubMed
  15. ↵
    1. Lin LC,
    2. Elkashty O,
    3. Ramamoorthi M,
    4. Trinh N,
    5. Liu Y,
    6. Sunavala-Dossabhoy G,
    7. Pranzatelli T,
    8. Michael DG,
    9. Chivasso C,
    10. Perret J,
    11. Chiorini JA,
    12. Delporte C,
    13. Tran SD
    : Cross-contamination of the human salivary gland HSG cell line with HeLa cells: A STR analysis study. Oral Dis 24(8): 1477-1483, 2018. DOI: 10.1111/odi.12920
    OpenUrlCrossRefPubMed
  16. ↵
    1. Nakaji T,
    2. Shinoto M,
    3. Yamada S,
    4. Inaniwa T
    : In Silico study of simultaneous integrated boost carbon-ion radiotherapy for locally advanced pancreatic cancer. Anticancer Res 44(9): 3821-3828, 2024. DOI: 10.21873/anticanres.17208
    OpenUrlAbstract/FREE Full Text
  17. ↵
    1. Masuda T,
    2. Koto M,
    3. Ikawa H,
    4. Takei H,
    5. Aoki K,
    6. Nakaji T,
    7. Kasamatsu K,
    8. Inaniwa T
    : Design of multi-ion therapy for head and neck cancers using carbon-, oxygen-, and neon-ion beams: potential efficacy against tumor hypoxia. Phys Med Biol 70(8): 085003, 2025. DOI: 10.1088/1361-6560/adc5d6
    OpenUrlCrossRef
  18. ↵
    1. Yaes RJ
    : Some implications of the linear quadratic model for tumor control probability. Int J Radiat Oncol Biol Phys 14(1): 147-157, 1988. DOI: 10.1016/0360-3016(88)90062-4
    OpenUrlCrossRefPubMed
  19. ↵
    1. Peters LJ,
    2. Withers HR,
    3. Thames HD Jr.,
    4. Fletcher GH
    : Tumor radioresistance in clinical radiotherapy. Int J Radiat Oncol Biol Phys 8(1): 101-108, 1982. DOI: 10.1016/0360-3016(82)90392-3
    OpenUrlCrossRefPubMed
  20. ↵
    1. Weichselbaum RR
    : Radioresistant and repair proficient cells may determine radiocurability in human tumors. Int J Radiat Oncol Biol Phys 12(4): 637-639, 1986. DOI: 10.1016/0360-3016(86)90073-8
    OpenUrlCrossRefPubMed
  21. ↵
    1. Kobayashi D,
    2. Oike T,
    3. Shibata A,
    4. Niimi A,
    5. Kubota Y,
    6. Sakai M,
    7. Amornwhichet N,
    8. Yoshimoto Y,
    9. Hagiwara Y,
    10. Kimura Y,
    11. Hirota Y,
    12. Sato H,
    13. Isono M,
    14. Yoshida Y,
    15. Kohno T,
    16. Ohno T,
    17. Nakano T
    : Mitotic catastrophe is a putative mechanism underlying the weak correlation between sensitivity to carbon ions and cisplatin. Sci Rep 7: 40588, 2017. DOI: 10.1038/srep40588
    OpenUrlCrossRefPubMed
  22. ↵
    1. van Leeuwen CM,
    2. Oei AL,
    3. Crezee J,
    4. Bel A,
    5. Franken NAP,
    6. Stalpers LJA,
    7. Kok HP
    : The alfa and beta of tumours: a review of parameters of the linear-quadratic model, derived from clinical radiotherapy studies. Radiat Oncol 13(1): 96, 2018. DOI: 10.1186/s13014-018-1040-z
    OpenUrlCrossRefPubMed
  23. ↵
    1. Nahum AE,
    2. Movsas B,
    3. Horwitz EM,
    4. Stobbe CC,
    5. Chapman JD
    : Incorporating clinical measurements of hypoxia into tumor local control modeling of prostate cancer: Implications for the α/β ratio. Int J Radiat Oncol Biol Phys 57(2): 391-401, 2003. DOI: 10.1016/s0360-3016(03)00534-0
    OpenUrlCrossRefPubMed
Back to top

In this issue

Print
Download PDF
Article Alerts
Email Article
Citation Tools
Reprints and Permissions
Estimation of Tumor Control Probability of Carbon Ion Radiotherapy Using Cancer Type-specific Sensitivity Data
EUNHYE YU, TAKAHIRO OIKE, MAKOTO SAKAI, MUTSUMI TASHIRO, TATSUYA OHNO
Anticancer Research Jan 2026, 46 (1) 113-122; DOI: 10.21873/anticanres.17927
Twitter logo Facebook logo Mendeley logo

Jump to section

Keywords