@misc{oai:repo.qst.go.jp:00063213,
 author = {Matsumoto, Yoshitaka and 松本 孔貴},
 month = {Aug},
 note = {Introduction
Heavy-ion beams with high linear energy transfer (LET) have the advantage of good dose distribution for tumor and increasing relative biological effectiveness (RBE) with depth. The Heavy Ion Medical Accelerator in Chiba (HIMAC) was constructed at the National Institute of Radiological Sciences (NIRS). Clinical trials have been demonstrated using carbon-ion beams for different cancers, lung cancer, bone & soft tissue sarcomas, hepatomas, prostate cancer, choroidal cancer, rectal cancer and head and neck cancer since July 1994. Up to March 2009, over 4500 patients have been treated including over 2000 patients subject to Highly Advanced Medical Technology program.
Recently, carbon-ion beam is a candidate for use in hypofractionated radiotherapy, having small fraction number and large fraction size to some kind of tumors, malignant melanoma of choroid, non-small cell lung cancer or hepatocellular carcinoma. Hypofractionation has a benefit for patients as the abbreviation of the treatment period. In this case, RBE values at high dose region (low survival level) must be considered, however the RBE is calculated physically and is not verified biologically. To estimate the lower survival, the extrapolation of the survival data, HSG cells on HIMAC has been used for the treatment planning. However, general colony formation assay can get only first third decades' data, and it may be far-fetched that the very low survival data will be presumed from the data in 1.0 - 0.001 of surviving fraction. It is important that to obtain the survival data as possible as lower region using various methods. We tried to get the survival data and estimate the RBE values at lower survival region using a multicellular spheroid technique and the multi-process formula fitting analysis in this study.
Methods and Materials
Culture of monolayer cells
One human malignant melanoma cell line, HMV-I was used in this study. Cells were cultured in Eagle's MEM with 10% FBS and antibiotics. Exponentially growing cells were seeded in flasks in CO2 incubator, and cultured for about 2-2.5 days prior to exposure. After irradiation, cells were harvested, counted and seeded in three dishes, and then incubated for 13 - 14 days. Colonies containing more than 50 cells were counted as survivors.
Culture of muliticellular spheroids
Spheroid plates were used to make multicellular spheroids. Briefly, exponentially growing cells were seeded in the wells at concentration of 800 cells per a well 2 or 2.5 days before irradiation. Each 10-15 spheroids were then transferred to petri dishes and incubated for hours to attach the spheroids on the bottom of the dishes. Immediately before the irradiation, medium was removed from dishes, and then the samples were irradiated with X-rays or heavy-ion beams. After the irradiation, the spheroids' position was marked and cultured CO2 incubator for 13 - 14 days, and then spheroids colonies were counted. Pictures of spheroids were obtained using microscope with CCD camera, and the diameter of spheroids was measured. The average diameter of a spheroid was 209 micro-meter. Additionally, the spheroids were collected in a tube and trypsinized, and the cell number in a spheroid was counted. The average cell number in a spheroid was 1109 cells.
Irradiation
X-rays were produced by a generator operated at 200 kVp, and filtered with 0.5 mm Al and Cu. X-rays data was used for the reference survival curves for RBE calculation. Carbon or Argon ions having dose-averaged LET of 13, 35, and 100, or 300 keV/micro-meter were provided by 290 or 500 MeV/nucleon beams at NIRS-HIMAC.
Curve fitting analysis
Three dose-survival formulas were used for the fitting analysis of the data. In addition to the linear-quadratic (LQ) equation, the multi-target single-hit (MT) and the multi-process (MP) equations were used. 
SF = exp(-aD-bD2)                        (LQ)
SF = 1-(1-exp(-D/D0))n                   (MT)
SF = exp(-aD)(1-(1-exp(-D/D0))n)         (MP)
Where, SF is the surviving fraction, D is the dose (Gy), a is, b is, Do is , and n is .
The three formulas were set in a curve sitting analysis software. The experimental data was fitted with formulas and various survival parameters (a, b, D0) were calculated. At first, the survival data of only monolayer cells (SF = 10^-3 - 100) was fitted with three equations, respectively. Secondary, these fitting curves were extrapolated to low survival region (SF = 10^-3 -10^-5), and then the differences of the survival data between the experimental values and the calculation values were compared among these three equations.
Results
Survival curves of monolayer cells and spheroids
Dose-response of HMV-I cells exposed to X-rays or heavy-ion beams as a monolayer cells were fitted by the LQ equation. The curves of high LET, 100 and 300 keV/micro-meter showed linear without shoulder. The survival curves of HMV-I spheroids exposed to X-rays or heavy-ion beams could fits with the MT equation. The surviving fraction of spheroids showed 1.0 until definite dose, for example 9.0 Gy for X-rays, and then the fraction was drastically decreased depend on the dose.
Combination of survival curves of monolayer cells and spheroids
To obtain the clonogenic survival data in wide survival range, we tried to combine them that obtained from monolayer cells and multicellular spheroids. To get the lower survival data, the surviving fraction of spheroids was converted to the fraction of single cell in a spheroid. At the results, the low survival data from 10^-3 to 10^-5 of surviving fraction was obtained and plotted in addition to monolayer survival data. The fit with LQ, MT, or MP equations with experimental plots were investigated in wide survival region. For shortness' sake, X-rays data having big shoulder and 100 keV/micro-meter carbon beams data showed linear curve were used to this analysis. In this analysis, the three fitting equations were fitted to the survival data of only first three decades (monolayer cells' data), and extrapolated to 10^-5 of SF range (Fig. 1). The fitting survival curves of three equations were differed in lower survival region, and the MP equation showed best fit to experimental plots in wide region. Therefore, we used MP equation to fit the survival curves, calculate the survival parameters and estimate the RBE values in wide survival region.
Estimation of relative biological effectiveness
To estimate the RBE values in wide survival range, all the survival plots were fitted with MP equation (Fig. 2). In this analysis, these curves were fitted to all data (100 - 10^-5). The survival parameters were calculated by MP equation fitting to survival data merged monolayer cells with spheroids data. The RBE values in wide survival range (100 - 10^-9) were estimated using the parameters, and the SF-RBE curves were obtained. RBE values were decreased with decrease of the SF, and converged to about 1.1 - 1.4 values at the very low survival level, 10-^9.
Discussion
Our goal is to estimate the RBE values for heavy-ion beams at high dose (low survival) range. We tried to get the data using the spheroids' technique in this study. 
In this study, the MP equation showed bet fitting to the experimental plots in wide dose range compared with LQ and MT equation (Fig. 1) and plots for other LET beams (not shown). Whereas, LQ equation showed a good fit at higher survival range, but fitting curves kept bending in the lower survival range (Fig. 1). The LQ model is currently the most reliable method to fit, but it is known that this model showed good fit in only first three decades of a survival curve but not less than 1% survival region. Additionally, the LQ model predicts a constant increasing slope at high dose region in contrast the constant slope observed in experimental survival curves. On the other hand, MT equation showed good fitting to raw data in middle dose range, whereas especially in low dose range the equation did not fit the data (Fig. 1). The MP model showed good fit to survival data of mammalian cells exposed to X-rays more than MT model. The MP model has a demerit in the analysis because there are three parameters, however as described above, the MP model has a considerable merit as getting the better fit with experimental data. We suggest that it may be necessary we investigate the availability of the MP model in addition to the LQ model analysis to guess the cell survival and RBE values in the high dose (low survival) region as a future plan in HIMAC.
The RBE values were estimated using the survival data in wide range obtained from monolayer cells and spheroids. The values were converged to 1.1 -1.3 in low survival region (10^-9). In HIMAC, the clinical RBE, ~3.0 and biological RBE, ~1.7 is used to calculate the start clinical dose for all dose range, and then the dose-escalation study has been performed. This method to estimate the RBE too high can be said that it is consequentially safe. However, the estimate dose might be insufficient to control the tumor completely. We suggest that it becomes possible to estimate the dose necessary for treatment more strictly using the multi-process model and the RBE values obtained from the survival data as low as possible.
Conclusion
In this study, we could get the lower survival data to 10^-6 region after X-rays or heavy-ion irradiation having various LET values using multicellular spheroids technique in addition to monolayer cell survival, and we estimated RBE at wide dose region down to cell survival level, 10^-9. The RBE values were converged to around 1.3 in low survival region, so when we use hypofractionated heavy-ion therapy it must be consider that the change of RBE values depending on the fraction size., NIRS-IMP Joint Symposium on Carbon Ion Therapy},
 title = {Effect of Hypofractionation on RBE and Estimation of Therapeutic Dose},
 year = {2009}
}