Radiobiological effects of the interruption time with Monte Carlo Simulation on multiple fields in photon beams

Abstract Purpose The interruption time is the irradiation interruption that occurs at sites and operations such as the gantry, collimator, couch rotation, and patient setup within the field in radiotherapy. However, the radiobiological effect of prolonging the treatment time by the interruption time for tumor cells is little evaluated. We investigated the effect of the interruption time on the radiobiological effectiveness with photon beams based on a modified microdosimetric kinetic (mMK) model. Methods The dose‐mean lineal energy yD (keV/µm) of 6‐MV photon beams was calculated by the particle and heavy ion transport system (PHITS). We set the absorbed dose to 2 or 8 Gy, and the interruption time (τ) was set to 1, 3, 5, 10, 30, and 60 min. The biological parameters such as α0, β0, and DNA repair constant rate (a + c) values were acquired from a human non‐small‐cell lung cancer cell line (NCI‐H460) for the mMK model. We used two‐field and four‐field irradiation with a constant dose rate (3 Gy/min); the photon beams were paused for interruption time τ. We calculated the relative biological effectiveness (RBE) to evaluate the interruption time's effect compared with no interrupted as a reference. Results The yD of 6‐MV photon beams was 2.32 (keV/µm), and there was little effect by changing the water depth (standard deviation was 0.01). The RBE with four‐field irradiation for 8 Gy was decreased to 0.997, 0.975, 0.900, and 0.836 τ = 1, 10, 30, 60 min, respectively. In addition, the RBE was affected by the repair constant rate (a + c) value, the greater the decrease in RBE with the longer the interruption time when the (a + c) value was large. Conclusion The ~10‐min interruption of 6‐MV photon beams did not significantly impact the radiobiological effectiveness, since the RBE decrease was <3%. Nevertheless, the RBE's effect on tumor cells was decreased about 30% by increasing the 60 min interruption time at 8 Gy with four‐field irradiation. It is thus necessary to make the interruption time as short as possible.


| INTRODUCTION
When photon beams irradiate cells, the cells' DNA is damaged, affecting the cells' life and death. Some damaged cells can recover from the damage, via sublethal damage repair (SLDR). 1,2 SLDR begins within minutes after photon-beam irradiation and completes within 4-6 hrs. 1,2 With SLDR, lessening photon beams' cell-killing effect on relative biological effectiveness (RBE) may be possible by increasing the irradiation dose-delivery time. 3,4 The dose-delivery time's effects on radiobiological effectiveness were evaluated with single-field photon beams and a microdosimetric kinetic (MK) model; [5][6][7][8][9] the surviving fraction (SF) was increased by prolonging the dose-delivery time, and the relative biological effectiveness was decreased. 10 Fractionated irradiation with multiple-field is used clinically to cover radiation targets with the prescribed dose but prevent toxicity to surrounding normal tissues. 11 When multiplefield irradiation is applied, the prescribed dose is not administered consecutively; there is an interruption time (an interval between radiation fields) used so that irradiation interruption occurs at several sites/operations, for example, the gantry, collimator, couch rotation, and patient repositioning within each field. [12][13][14] Unlike single-field photon beam irradiation, treatment times are prolonged by interruption times.
The modified MK (mMK) model considers various irradiation methods with photon beams [15][16][17] and better estimates the SF at higher radiation dose range compared to the MK model. With the mMK model, the SF of more clinically relevant conditions can be better estimated due to the fractionated irradiation. SLDR's effects during interruption times on the RBE have been studied using the mMK model, as a method similar to those used previously, especially for particle therapy. [18][19][20][21] Few studies have examined the effects of multiple-field photon beam irradiation with interruption times on the RBE. Since photon therapy is more commonly used than particle therapy, such data may have a great impact. We evaluated the interruption time's effect on radiobiological effectiveness by setting several interruption times between multiple-field photon beams, using the mMK model. beams. The below phase-space files were made using BEAMnrc, which is built on the EGSnrc platform. 26 We transferred these phase-space files created by BEAMnrc to the PHITS system to calculate the dose distribution. The irradiation geometry default settings were used for the PHITS calculations with 90-cm SSD, 20 cm × 20 cm field size ( Fig. 1), with a 10-cm-deep measurement point, 3-cm calculation width in the water-equivalent phantom, and 0.5-μm domain radius. The dose-mean lineal energy y D 23-25 was calculated as: where ϵ = the energy deposited in a domain, l = mean chord length, y = lineal energy, f(y) = the lineal energy' probability density, and d (y) = the lineal energy' dose distribution.
The dose-mean lineal energy y D of 6-MV photon beams was calculated as a function of y-yd(y): Eq. (2). We used the average y D value obtained by simulating the calculations of the SF and biological effectiveness in the mMK model.

6-MV photon beams using the mMK model
The mMK model considered various irradiation schemes with photon beams. 17 The equation that determines the mMK model is:

3.A | The interruption time's effects on the SF with two-and four-field irradiation in the mMK model
The relationships between the measured position's depth in the water-equivalent phantom and the y D are illustrated in Fig. 3. Changing the water depth hardly affected the y D value; we thus averaged the y D over a 10-13-cm depth range. Table 1 lists the y D average and standard deviation values for photon beams. Figure 4 illustrates the various interruption times' effects on the SF with two-and fourfield irradiation. The SF was higher with the interruption time's increase in both irradiation types. The difference between SFs with four-field irradiation was emphasized with interruption times at 10, 30, or 60 min. The interruption time's effect was greater as the absorbed dose rose.

3.B | The interruption time's effect on the RBE
with two-and four-field irradiation 3.C | Relationship between the DNA repair constant rate (a + c) and the RBE with various interruption times

| DISCUSSION
We evaluated the RBE of 6-MV photon beam irradiation with interruption times calculated from the SF using the dose-mean lineal energy y D and the mMK model. The dose-mean lineal energy y D was calculated by the PHITS, and the y D was scarcely affected by changing the water depth. We thus conclude that the irradiation field's depth with various interruption times has no effect on the RBE.
The irradiation applied in radiotherapy can be interrupted due to a linear accelerator's mechanical problems, sometimes for a long term. 34 Moreover, irradiation techniques such as a respiratory gating system used to attain tumor control for lung cancer require a large absorbed dose per fraction, a protracted dose-delivery time, and a long interruption time. 10,14 Figure 5 provides the results of our calculation of the interruption times' effects on the RBE. A several-minutes-long interruption had no significant effect on the RBE within 3%, but a ≥10% reduction of the RBE occurred when the 8-Gy fourfield irradiation was interrupted for 30 or 60 min. With a >30-min longer interruption time resulted in a large RBE difference or cell SF difference caused mainly by SLDR. It may thus be necessary to shorten the photon beams' interruption as much as possible, since the RBE was decreased by prolonging the interruption time. Based on these results, we speculate that a prescribed dose taking the interruption time into account is required when a long irradiation interruption (>30 min) occurs.
We used NCI-H460 cells to calculate the interruption time's effect. The RBE value was dependent on cell-specific values (a + c) of the DNA repair constant rate τ = 10 and 60 min; Fig. 6), and the RBE was affected by the cell-specific value (a + c); the larger that this value was, the greater the decrease in RBE was ( Table 2). The

| CONCLUSIONS
The~10-min interruption of 6-MV photon beams did not significantly impact the radiobiological effectiveness, since the RBE decrease was <3%. Nevertheless, the RBE's effect on tumor cells was decreased about 30% by increasing the 60 min interruption time at 8 Gy with four-field irradiation. It is thus necessary to make the interruption time as short as possible. With a long interruption time, an escalation of the prescribed dose may be necessary.
T A B L E 2 The effect of RBE as a function of the cell-specific repair rate (a + c) for 2 and 8 Gy with various interruption time using twoand four-field irradiation.