Intensity Modulated Radiation Fields Induce Protective Effects and Reduce Importance of Dose-Rate Effects

In advanced radiotherapy, intensity modulated radiation fields and complex dose-delivery are utilized to prescribe higher doses to tumours. Here, we investigated the impact of modulated radiation fields on radio-sensitivity and cell recovery during dose delivery. We generated experimental survival data after single-dose, split-dose and fractionated irradiation in normal human skin fibroblast cells (AGO1522) and human prostate cancer cells (DU145). The dose was delivered to either 50% of the area of a T25 flask containing the cells (half-field) or 100% of the flask (uniform-field). We also modelled the impact of dose-rate effects and intercellular signalling on cell-killing. Applying the model to the survival data, it is found that (i) in-field cell survival under half-field exposure is higher than uniform-field exposure for the same delivered dose; (ii) the importance of sub-lethal damage repair (SLDR) in AGO1522 cells is reduced under half-field exposure; (iii) the yield of initial DNA lesions measured with half-field exposure is smaller than that with uniform-field exposure. These results suggest that increased cell survival under half-field exposure is predominantly attributed not to rescue effects (increased SLDR) but protective effects (reduced induction of initial DNA lesions). In support of these protective effects, the reduced DNA damage leads to modulation of cell-cycle dynamics, i.e., less G1 arrest 6 h after irradiation. These findings provide a new understanding of the impact of dose-rate effects and protective effects measured after modulated field irradiation.

Particle for Heavy Ion Transport Code System (PHITS ver. 3.02) 1 , we calculated the energy spectrum of electrons at 6 mm depth from surface for 60 Co -rays, at 10 cm depth from surface for 6 MV-linac X-rays and at 1 mm depth from surface for 200 kVp X-rays, respectively. The cut-off energy was set to be 1.0 keV through the PHITS simulation. The example of energy spectrum for 200 kVp X-rays is shown in Fig. S2A. To reduce the calculation time effectively 4 , the phase-space file for VARIAN Clinac 600C (10 x 10) was used as a source of 6 MV photons. Inputting the energy spectrum into the in-house code WLTrack for electrons 2 , the energy deposition in a domain was sampled uniformly along electron track as shown in Fig. S2B. It is noted that the cut-off energy of electrons was set to be 1.0 eV in the WLTrack calculation.
According to International Commission on Radiation Units (ICRU) Report 36 5 , the dose-mean lineal energy represented by y D is defined as follows (S1) where y is lineal energy in keV/m, f(y) is the probability density of lineal energy and d(y) is dose distribution of lineal energy. After obtaining the y-yd(y) distributions shown in Fig. S2C, we calculated the y D values for 60 Co -rays, 6MV-linac X-rays and 200 kVp X-rays. Figure S1. Illustration of geometries for calculating the y D values of 60 Co -rays, 6 MV-linac X-rays and 200 kVp X-rays. The geometries were set to be the same as the previous report. 3 Light blue area represents liquid water. The sampling points for 60 Co -rays, 6 MV-linac X-rays and 200 kVp X-rays were set at 6 mm depth, at 10 cm depth 1 mm depth from surface, respectively.   Table S1. Comparison of y D value among this work, the previous calculation by Geant4 and TEPC measurement. This work reproduced the photon-energy dependence on y D value with domain size of 1.0 m diameter.
As listed in Table S1, the y D values for three types of photons agreed well with the recommended values by Geant4 simulation and TEPC measurement 3 . As shown in Fig. S2C, the dose distribution of lineal energy (y-d(y) relation) calculated in this study coincides with the previous distribution by Gean4 simulation and the TEPC measurement 3 . These results mean that the sampling technique used in this study is precise for calculating the y D value for photon irradiations.

II. Markov chain Monte Carlo for Determining Model Parameters
The values of  0 and (a+c) were determined from the cell survival recovery curve in split-dose experiment ( Fig. 2 in the main paper). The rest of cell-specific parameters in the IMK model were determined via a Monte chain Monte Carlo (MCMC) simulation established previously. 6 Here, we summarized the detail of MCMC technique.
The Markov chain Monte Carlo (MCMC) technique provides the probability density function (PDF) of the model parameters. 7,8 This simulation technique is a hierarchical model, and we can obtain the PDF of model parameters following Markov property. 9 In the present model, the prior distribution of  = ( 0 ,  b ,  b , ) was set to be normal distribution, with maximum likelihood (ML) value as mean value and reasonable large uncertainty (such as 70% of the ML value) as standard deviation, to obtain the updated posterior distribution with efficient computing performance. Assuming that the uncertainty for -ln S follows the normal distribution, a likelihood function is given by, where N D is the number of experimental data, S expi (i = 1 ~ N D ) are the set of experimental survival for the dose d i , S cali (i = 1 ~ N D ) are those of calculated survival by the present model, and  is the standard deviation of ln S. The ratio of osterior robabi ity for the arameter's ca didate at timi g of t+1) ( candidate |d) and that for the previous condition (at timing of t) ( (t) |d) is given by This is the probability ratio to determine the set of model parameters at the next step, so called the transition probability. 9 The algorithm of MCMC used in this study is described in blue flow chart in

III. Clonogenicity of In-Field Cells under Modulated-Field Exposure
The dose-response curves on cell survival were evaluated by the clonogenic survival assay in the main paper. To be sure that the different radio-sensitivity after half-field exposure, here we show the raw image of the colony formed in this experiment. There are several types of the intercellular signals involved in the cell growth, i.e., transforming growth factor-β TGFβ . 10 The different size of colony which is linked to the dose-response curve can be explained by the reduced yield of DNA damage induction (Fig. 6B in the main paper).
However, the mechanisms to induce the modified DNA damage yield are still unclear. While keeping in mind the increase of cell growth, further investigation for cell responses under modulated fields is necessary in future study. Figure S4. Image of colonies formed after modulated-field and uniform-field exposure: A is the colonies of non-irradiated DU145 cells, B is those of the cells exposed to 10 Gy under uniform field, C is those of the cells exposed to 10 Gy under half field. Comparing the colony size formed after uniform-field exposure ( Fig S4B) with that of in-field cells after half-field exposure (Fig S4C), it is suggested that the cell viability after half-field exposure is higher than that after the conventional uniform-field exposure.

IV. Verification of the IMK model for Intercellular Communication
In this study, we incorporated the intercellular communication (IC) from in-field hit cells to out-of-field non-hit cells into the cell-killing model so-ca ed "integrated microdosimetric-kinetic (IMK) model" 11,12 . In the main paper, we show the formula of cell survival considering DNA-targeted effects (TEs) and IC as the functions of absorbed dose in Gy. Here, we show several additional results for verifying the developed model.
Using model parameters listed in Table 1 in the main paper, we also calculated the dose dependency on out-of-field cell survival based on the model for the cases of constant in-field doses 4.0 Gy or 8.0 Gy (Fig. S5). It is noted that the model formula considering DNA-TEs and IC is given as  In addition, we also compared the model prediction with the experimental data 13 for the case of the treatment with 20 M aminoguanidine (AG) which is an inhibiter of nitric oxide as one of the intercellular signals. It is noted that  value was set to be 0 under the conditions of IC inhibited case (AG+). As shown in Fig. S6, even for the case of AG treatment, the model provides the increment of surviving fraction due to the lack of IC, which suggests that the enhanced cell-killing of out-of-field cells is attributed to IC (defined as radiation-induced bystander effects).
Focusing on the model assumption that the signal effect can cover the entire region of out-of-field under the half-field exposure, the distance for signal delivery is set to be much longer than the previous reports. 14,15 According to the previous report by Koizumi et al., a calcium wave can be detected at distance below 90-100 m. 14 Meanwhile, apoptosis cells can be observed at distance below ~800 m. 15 Concerning this discrepancy, the previous studies 14, 15 used the three-dimensional tissue model while our study was conducted using cell culture dishes. For this reason, the signals might move freely in the culture medium after irradiation. Thus, it is necessary in future study to further discuss the signal diffusion distances from the viewpoints of culture dish model and three-dimensional tissue model.

V. Estimation of Impact of Low-Energy Photons on Out-of-Field Cell Survival
Applying the present model to in vitro experimental cell survival in the main paper, we evaluated the impact of modulated radiation field on dose-rate effects and radio-sensitivity (dose-response curve on cell survival). However, the lower energy scattered photons incident to out-of-field cells have a potentiality to affect lager impact on biological effects than the photons incident to in-field cells. So, we also evaluated the impact of the scattered X-rays on cell survival from the standpoint of microdosimery.
As shown in the main paper, the y D values for in-field cells and for out-of-field cells were 4.393 ± 0.007 keV/m and 4.769 ± 0.044 keV/m, respectively. To be sure the radiation quality in out-of-field area, we also calculated the dose-averaged linear energy transfer (LET) by the use of the PHITS code (ver. 3.02) 1 , and obtained the values for in-field cells and out-of-field cells were 1.346 ± 0.039 keV/m and 1.467 ± 0.285 keV/m, respectively. From the y D and dose-averaged LET values, it is suggested that the density of energy deposited along the radiation track in lead-shielding area is higher than that in in-field region.
Regarding the calculated y D , we next estimated cell survival curve based on only DNA-targeted effects (TEs) to discuss the impact of scattered photons on out-of-field cells. The formula of cell survival curve for DNA-TEs after irradiation at a constant dose-rate is given by Eq. (S5). According to the previous assumption of the conventional MK model, the parameters of  0 and  0 can be fixed independent of radiation type and the energy 16 . Adopting the assumption, we tried to estimate the dose-response curve by using Eq. (S5) and y D values for half-field exposure (Fig. 1A in the main paper).

Figure S7. Estimation of dose-response curve considering only DNA-TEs.
To discuss the impact of scattered X-rays on out-of-field cell survival, we estimated the cell survival using Eq. (S5) and model parameters for modulated exposure listed in Table 1 of the main paper. Figure S7A is the survival curves of AGO1522 cells and Fig. S7B is those of DU145 cells. As shown in these results, there is no difference to enhance cell killing by scattered X-rays for the case of half-field exposure with 225 kVp X-rays. 225 kVp X-rays (the red and blue lines). Thus, the reduction of survival of out-of-field cells is attributed to intercellular signalling from in-field cells to out-of-field cells from this model estimation.

VI. Application of Model Prediction to Clinical Dose Delivery
The reduced importance of sub-lethal damage repair (SLDR) under exposure to modulated fields was suggested in the main paper. To deepen the impact on clinical dose-rate effects, we also tried to and IMRT (5 and 9-fields) based on the present IMK model. It is noted that the parameters for modulated field (MF) case were used to estimate the cell survival under clinical regimens whilst those for uniform field (UF) case were used for uniform field at constant dose-rate. These parameters are listed in Table 1 in the main paper.

VII. Cell-Cycle Study with AG Treatment for Modulated Radiation Field
To discuss the reason why the surviving fraction of cells in-field under half-field exposure is higher than that under the uniform-field exposure, we performed flow-cytometric analysis for cell-cycle studies. Here, we show the additional in vitro experiments on cell-cycle dynamics in the presence of 100 M AG for checking whether the NO contributes to protective effects or not [16][17][18][19] because the NO-mediated bystander effect can be trigger to cause radio-resistance. 20 As the same manner as the main paper, we focused on the four timing, i.e., 0 h, 6 h, 24 h and 72 h after irradiation. Figure S9. Cell-cycle kinetics after the exposure in the presence of 100 M AG: (A) is the measured cell-cycle dynamics after full-or half-field exposure in AGO1522 cells, (B) is those in DU145 cells. * and ** mean 5% and 1% significant differences from previous cell-cycle fraction (i.e., 0 h and 6 h, 6 h and 24 h, 24 h and 72 h) as the same manner as the main paper. From these results, the inhibitor of NO does not seem to function for deleting the constant G 1 fraction until 6h after irradiation. Figure S9 show the cell-cycle dynamics (change in fractions of cells in G 1 , S and G 2 /M phases) after irradiation in the presence of 100M AG, where (A) and (B) are the AGO1522 cells and the DU145 cells, respectively. As shown in Figs. S9A and S9B, the inhibitor of NO does not seem to function for deleting the constant G 1 fraction until 6h after irradiation. Considering these, the NO might not be the dominant factor to lead to lower radio-sensitivity under half-field exposure in comparison with uniform-field (see Fig. 3 in the main paper). This interpretation is also supported by the results of cell survival shown in Fig. S6, in which the experimental data and the model prediction show the increased cell survival in the presence of the AG. To clarify the underlying mechanisms to lead to radio-resistance (the reduced DNA damage yield under half-field exposure in the main paper), further investigation is necessary.