## Abstract

Background/Aim: The aims of this study were to evaluate the cell survival uncertainty distribution of radiation and to assess the accuracy of predictions of tumor response by using three different in vitro experimental cell cultures with radiosensitizers (including etanidazole). Materials and Methods: Using EMT6 cells and X-rays, the cell survival fraction was obtained from 15, 34, and 21 different experiments under normoxic, hypoxic, and hypoxic-plus-radiosensitizer culture, respectively. Results: The α coefficients were 0.257±0.188, 0.078±0.080, and 0.182±0.116 Gy^{−1}, respectively. The β coefficients were 0.0159±0.0208, 0.0076±0.0113, and 0.0062±0.0077 Gy^{−2}, respectively. The α coefficient and the dose that killed half of the clonogens population (D_{50}) were significantly different between normoxic cell and hypoxic cell cultures (p<0.01), respectively. The use of radiosensitizers under hypoxic conditions improved radiosensitivity. Conclusion: Our results suggest that parameter value distributions are required for biophysical modeling of applications for radiotherapy.

In recent years, there have been rapid advances in radiotherapy technologies, such as volumetric modulated arc therapy, stereotactic body radiotherapy, and image-guided radiotherapy (1-5). Because clinical failures after radiation therapy (due to hypoxia, intrinsic radioresistance, and cellular proliferation) are known to induce genetic changes, radiobiological parameters and molecular biological data from tumor and critical organs could be used in clinical practice for better treatment (6, 7).

Applying biophysical models to treatment planning in radiotherapy could increase tumor controllability and reduce toxicity to normal tissues (8, 9). It is well-recognized that radiation sensitivity is affected by cell heterogeneity and radiosensitizing agents (10-12). Nevertheless, there is uncertainty surrounding radiosensitivity because of the factors involved are not well-accounted for in biophysical modeling (13, 14). In particular, hypoxic cells in tumors lead to increased radioresistance of clonogens, which affects clinical outcome (15, 16). Etanidazole and misonidazole are well-known hypoxic cell radiosensitizers but have had limited therapeutic impact on radiotherapy because of side-effects such as neurotoxicity (17). For biophysical evaluation of physical dose prescriptions, including dose fractions and biological equivalent dose (BED), the linear quadratic (LQ) model based on intrinsic radiosensitivity is commonly used in practical radiotherapy (18). However, to make precise predictions on outcomes after radiotherapy at the treatment planning stage, the above-mentioned uncertainties of radiation sensitivity would need to be carefully considered.

In this study, we evaluated the distribution of uncertainty of cell survival due to radiation and assessed tumor response predictions using three different *in vitro* experimental cell cultures. We then discuss the relationship between *in vitro* radiosensitizing activities and uncertainties in cell survival characteristics using radiobiological parameters.

## Materials and Methods

*Development of the experimental system.* Etanidazole was synthesized in our laboratory. EMT6/KU mouse mammary tumor cells (supplied by Dr. Shinichiro Masunaga, Kyoto University, Kyoto, Japan) were maintained in Eagle's minimal essential medium (E-MEM) (Sigma-Aldrich Japan, Tokyo, Japan) supplemented with 10% fetal bovine serum (JR Scientific, Inc., Woodland, CA, USA). For single-cell experiments, exponentially-growing cells were harvested from normoxic cell culture dishes by trypsinization, and suspended in test tubes containing 1 ml of E-MEM (2×10^{6} cells/ml). The hypoxic cultures were treated with 95% N_{2}–5% CO_{2} gas for 30 min. *In vitro* radiosensitization was also measured in single EMT6 cells by adding radiosensitizer under hypoxic conditions.

*Radiation procedure.* X-Ray irradiation was carried out using an X-ray unit (Hitachi X-ray unit, model MBR-1505R2) with 0.5 mm Al/1.0 mm Cu filter (150 kV, 4 Gy/min). In *in vitro* assays, cells on the dish were irradiated with 4-28 Gy. After irradiation, colony formation assays were performed.

*Biophysical modeling.* The LQ formalism is used for tumor cure probability curves, which reflect the various tumor parameters. The probability of cells surviving a single dose is given by:
(Eq. 1)
where *N* equals the number of surviving cells, *N*_{0} equals the number of tumor cells at the start of experiment, α and β are the estimates of radiosensitivity, and *D* is the total dose given. It follows directly from the above assumptions that the effect of *n* equally sized fractions and *d* equally dosed fractions can be shown by:
(Eq. 2)
The Poisson probability of there being zero surviving cells at the end of a fractionated treatment is then given as the tumor control probability (TCP) by:
(Eq. 3)
where the other parameters are as given in Eq. 1 and 2.

To evaluate the effects of the radiation sensitizer and the varying sensitivities due to the different cell cultures, data were obtained from 15, 34, and 21 different experiments under normoxic cell culture, hypoxic cell culture, and hypoxic cell culture-plus-radiosensitizer, respectively. For each cell culture, the averaged survival fraction (SF) after a single fraction was calculated based on three repeated experiments and entered into the model. Then summarized dose survival data by each cultured experiment were fitted by the model, and biological parameters, α, β, D_{50}, and γ_{50} were calculated. D_{50} and γ_{50} represented the dose that killed half of the clonogens population and the steepness of a dose–response level, which was defined as SF=0.5, respectively. The effects of cell proliferation and repair were not taken into consideration in this study.

*Statistical analysis.* Exponential regression analyses were used to assess α and β coefficients, respectively. Statistical comparisons of mean values were analyzed by two-sample independent *t*-test. All the data were analyzed using OriginLab (OriginLab Corporation, Northampton, MA, USA) scientific graphing and statistical analysis software. A *p*-value of less than 0.05 was considered statistically significant.

## Results

*Radiation response of the single cell.* Single-cell survival after single-dose fraction in different cell cultures is shown in Figure 1. Fitted curves using median parameter values of α and β coefficients from exponential regression analysis (solid and dotted lines, respectively), and the effect of each coefficient on the curves (α contribution: dark gray, β contribution: light gray) are presented in Figure 2. It can be seen that etanidazole enhanced the radiosensitivity of EMT6 cells in a dose-dependent manner under hypoxic conditions. The variations in predicted survival at higher single doses may be increased; however, this increase could be suppressed by radiosensitizers.

*Comparisons of radiobiological parameters.* The radiobiological parameters from these experiments are summarized in Table I. The α and *D*_{50} values were significantly different between normoxic and hypoxic cell cultures (*p*<0.01).

*Effects of cell survival and tumor control probability on variation in radiobiological parameters.* Figure 2 shows that when the α coefficient values were fixed (light gray), the variations in cell survival curves at high doses were increased; a similar trend is seen for the β coefficient values (dark gray) in all cell cultures. The effects of α and β coefficients on TCP (gray shaded area) are shown in Figure 3A-C. Under hypoxic conditions, the mean values of α and β coefficients were smaller and the D_{50} much higher than
under normoxic conditions (Table I). It is apparent that the TCP under such conditions was much lower than that at the same dose under normoxic conditions. The number of cells (proxy for tumor size) is another clinical factor of radioresistance, albeit less effective than the variations of α and β coefficients for detecting early cancer (N_{0}≤10^{8}) as shown in Figure 3D-F.

## Discussion

The LQ formalism with α and β coefficients provides quantification of radiobiological response, which describes the radiation inactivation of cell mixtures of different intrinsic radiosensitivity. However, in clinical setting, some factors such as inappropriate derivation of α/β values from single *in vitro* assays, clarification of radiation-induced late effects, and variations in individual α/β values, might cause unclear interpretation of the results obtained from early- and late-responding tissues (19).

Although the α coefficient is relatively constant throughout the interphase of the cell cycle (20), the intra-tumor heterogeneity could cause variations in intrinsic radiosensitivity at a single-fraction dose. Our data show that the variation of the α coefficient was nearly the same as that in previous studies (21). Consequently, it is suggested the one the variation in the α coefficient is of the same order as the radiosensitivity exhibited by asynchronous populations. It is thought that the β coefficient is relatively invariant and its contribution to cell death is much smaller at conventional treatment doses (22). However, since hypo-fractionation techniques are clinically implemented, it is suggested the effects of the β coefficient will not be negligible.

Wide ranges of the α/β ratios, which can lead to a cell-lethal dose, were shown in our study, including a negative value. The results were caused by a negative β coefficient through differing sensitivities of the cells in the heterogeneous populations at the high-dose region. Moreover, in the curve-fitting process, the data are often more complex than those described using the linear quadratic equation. In the case of single, very high-dose fraction experiments, the survival curve might be dependent on the experimental conditions.

Figure 1 shows the radiosensitivities in different cell cultures. The hypoxic cells appear to be twice as radioresistant as normoxic cells by survival fraction. Intratumoral hypoxic cell proportions are a major complicating factor in cancer therapy, and are an important target for anticancer drug design (23). It can be seen that the use of etanidazole under hypoxic conditions improved the radiosensitivity by enhancement ratio (ER) of 1.72 at mean survival fraction, a value almost equal to that of a previous study (24). Hypoxic cells, which represent one source of tumor heterogeneity, can lead to shallow response and survival curves with low α coefficient. The effects of the variations of α and β coefficients, if either one were fixed to the median value, are shown in Figure 2. Under hypoxic conditions, the effects of radiosensitizing by etanidazole are shown to increase the α coefficient, with a decrease of variation in the α and β coefficients. However, under such conditions, the β coefficient's contribution to radiosensitivity was relatively small. Consequently, the results suggest that etanidazole could lead to reduction of tumor heterogeneity at high doses, including the change of oxygen tension and electron affinity.

Figure 3 shows the variations of calculated TCP curves accounting for the discrepancies of α and β coefficients and cell numbers (tumor volume). Several authors have pointed-out that a precise prediction could potentially be possible by assuming distribution of intrinsic radiosensitivity under various cellular circumstances (14, 25). Another important factor for determining the TCP is the number of cells that should be killed to result in a tumor cure; studies have shown a consistent cell density of 0.5-1.0×10^{6}/g (26, 27). Consequently, the number of cells would be in the order of 10^{7}-10^{9} in a typical tumor volume of 0.01-100 ml in clinical settings. In addition, non-proliferating tumor cells are considered to be more resistant to radiation than proliferating cells (28). Proliferation is a highly important factor influencing the TCP, especially for highly fractionated treatment schedules (29). It could also be reasonable to consider that the variations of intrinsic radiosensitivities of cells *in vitro*, tumor cells extracted by biopsy, or the use of tumor-bearing chick embryo (30), will predict the radiation response of similar cells *in vivo*. The purpose of this study is not to claim that we fully-understand how to model the precise radiation response, but rather to show that important biophysical parameters are useful for predicting tumor response. In conclusion, our results suggest that the distributions of the parameter values are required for biophysical modeling of applications for radiotherapy. Further advancement would benefit from additional experiments employing different tumor models, and thus, *in vivo* studies are necessary.

## Acknowledgements

This work was supported by Grant-in-Aid for Young Scientists (B) No. 25861105 from MEXT Japan.

- Received April 4, 2014.
- Revision received June 10, 2014.
- Accepted June 11, 2014.

- Copyright© 2014 International Institute of Anticancer Research (Dr. John G. Delinassios), All rights reserved