Radiobiological effects of the interruption time in radiation therapy with photon beams based on the microdosimetric kinetic model

Background : We investigated the effect of the interruption time on the radiobiological effectiveness with photon beams based on a modified microdosimetric kinetic model. Background: The interruption time is used is that irradiation interruption occurs at sites and operations such as the gantry, collimator, couch rotation, and patient set-up in radiotherapy. However, the effect of interruption time on photon beams for tumor cells is little evaluated. Methods : The dose-mean lineal energy y D (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, or 10 min. The biological parameters 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 photon beams that were not interrupted as a reference. Results : The RBE with four-field irradiation for 8 Gy was decreased to 0.997, 0.992, 0.987, and 0.975 for τ = 1, 3, 5, and 10 min, respectively. The decrease in the RBE was within 3% compared with the non-interrupted photon beams. Conclusions : The effect of RBE was decreased by increasing the interruption time, indicating that an escalation of the prescribed dose might be necessary when the interruption time was large.


Background
When cells are irradiated with photon beams, the DNA of the cells is damaged.
This DNA damage affects the life and death of the cells. However, even when cells' is damaged, some of the cells have the ability to recover from the damage, in a recovery phenomenon known as sublethal damage repair (SLDR) [1,2]. SLDR is a rapid phenomenon that begins within several minutes and is complete within 4-6 hr after the irradiation of DNA by photon beams [1,2]. It may therefore be possible to lessen photon beams' effect of cell killing on biological effectiveness by increasing the dose-delivery time, based on SLDR [3,4]. We have evaluated the effect of the dose-delivery time on biological effectiveness with single-field photon beams based on a microdosimetric kinetic (MK) model [5,6]; we observed that at 8 Gy irradiation the surviving fraction (SF) was increased by prolonging the dose-delivery time, and the relative biological effectiveness (RBE) was decreased. When the dose-delivery time was 30 min, the decrease was approx. 2%, and in the case of 60 min, the decrease was approx. 6%.
However, there was no significant difference of the effect of an approx. 10 min dosedelivery time on the SF of RBE.
Fractionated irradiation with multiple fields has been used in radiation therapy in clinical settings for covering the radiation target with the prescribed dose and preventing toxicity to surrounding normal tissues as much as possible [7]. When multiple-field irradiation is applied, the prescribed dose is not administered consecutively; there is an interruption time, i.e., a certain interval is inserted between each radiation field. The reason why an interruption time is used is that irradiation interruption occurs at sites and operations such as the gantry, collimator, couch rotation, and patient set-up [8,9]. It is thus necessary to evaluate the effect of multiple-field irradiation to simulate clinical conditions, since the previous studies evaluated the effect of single-field irradiation on the SF and RBE. In other words, for evaluations of the SF and RBE during irradiation in a single session, it is necessary to set the dose-delivery time while taking the interruption time for each field into account.
Hawkins proposed the MK model based on dual radiation action in 1994 [10,11] in order to consider the repair-misrepair [12] and lethal and potentially lethal [13] models.
The MK model was designed to reveal the relationship between the SF and the absorbed dose (D) by calculating the energy deposition and analyzing the dose-rate effect [10,11].
Matsuya et al. proposed a modified MK model (mMK model) which considers the various irradiation methods with photon beams [14,15] and can be used to determin the change of the DNA amount per nucleus during irradiation [16]. This mMK model is able to better estimate the SF with a higher radiation dose range compared to the previous MK model, by taking the cell cycle of cells into consideration. With the mMK model it is also possible to calculate the SF of more clinically relevant conditions due to fractionated irradiation.
The effect of the interruption time on the RBE obtained with 6 MV photon beams in multiple-field irradiation has not been evaluated. Furthermore, the effect of the SLDR during the interruption time on the RBE using mMK model, which is a similar method used in previous studies, especially for particle therapy [17][18][19][20]. However, there are little studies of photon beams for the effect of interruption time on the RBE. Since photon therapy is more popular than particle therapy, this study may have great impact. We conducted the present study to determine the effects of the interruption time on RBE with the use of photon beams, using the mMK model.

The MK model
In the MK model, we used the domains in which the nucleus of the considered cell is divided into several hundred independent areas. In the model, potentially lethal lesions [keV/μm]. The parameters α0 and β0 were obtained by single instantaneous irradiation using the linear-quadratic (LQ) model. The value is a coefficient that is calculated by the dose-mean lineal energy yD, ρ, π, and rd (Eq. 2 above).

The modified MK (mMK) model
Matsuya et al. provided the mMK model, considering various irradiation schemes with photon beams [21]. The equation that determines the mMK model is: where A and B are coefficients, Gn and Gm are the amount of DNA per cell nucleus, Φn is a dimensionless parameter, ̇ is the dose rate [Gy/min], T is the dose-delivery time [min], and Dn is the absorbed dose at a regular interval [Gy] (Eq. 3). The PLL repair rate of (a + c) equated with the first-order rate λ [21,22], which was calculated using the DNA repair half-time T1/2 [26,27].
This equation (Eq. 9) takes into account the interruption of photon beams by using Eq. 3.
The interruption time of each field was defined as τn [min], and a diagram of the mMK model taking into consideration the interruption time of photon beams is given in Figure   1. The figure also shows that the deformed Eq. 6 could be considered the [min] [min]interruption time for both the linac pulse interval and each field interval. In this study, we calculated the SF when the interrupted photon beams which have two-field and four-field irradiation.

Monte Carlo simulations calculated by the particle and heavy ion transport code system (PHITS)
Monte Carlo simulations code the particle and heavy ion transport code system (PHITS) and can deal with photons, electrons, positrons, neutrons, and heavy ions [24][25][26][27][28]. In the present study, we used the PHITS version 3.02 with the default setting, and we MV photon beams (Fig. 2) was used for the PHITS calculations with the default setting; the SSD was 90 cm, the field size was 20 cm  20 cm. The measurement point was located at a depth of 10 cm, and the calculation width was 3 cm in the water-equivalent phantom material. The radius of the domain was 0.5 μm. The dose-mean lineal energy yD [26][27][28][29] was calculated as: where ε is the energy deposited in a domain, l is the mean chord length, y is the lineal energy, f(y) is the probability density of the lineal energy, and d(y) is the dose distribution of the lineal energy. The relationships between the depth of the measured position in the water equivalent phantom and the dose-mean lineal energy yD for the 6 MV photon beams (b) are illustrated in Figure 3. We noted that there was little effect on the value of yD by changing the water depth. Therefore, yD was averaged over the depth range of 10-13 cm.
The average and standard deviation values of yD for photon beams are listed in Table 1.
We used the average yD value obtained by simulating the PHITS for the calculations of the SF and biological effectiveness in the mMK model.

H460 lung cancer cells
We used the biological parameters of the human non-small-cell lung cancer cell line NCI-H460 to determine the parameters of the mMK model. The biological parameters α0 and β0 using an LQ model were first reported by King et al. [30]. Each of the DNA repairs occurred at a different rate constant, and the DNA repair rate could be calculated as λ in the mMK model (Eq. 5). The biological parameters for the mMK model simulations of the NCI-H460 cells are shown in Table 1.

The calculations of the SF and RBE for interrupted 6 MV photon beams using the mMK model
The calculation of the SF and RBE using the mMK model was performed with two-field irradiation in this study. The absorbed dose on the NCI-H460 cells was varied from 2 Gy to 8 Gy. The tumor cells were irradiated using two-field irradiation with the absorbed dose D1 at the constant dose rate ̇ (3 Gy/min). The irradiation was interrupted for a certain time (τ). Next, the absorbed dose D2 was irradiated at the constant dose rate ̇ (3 Gy/min). In the four-field irradiation, the absorbed dose for the tumor cells was D1 at a constant dose rate, ̇ (3 Gy/min). The irradiation was interrupted for a certain time (τ).
Second, the absorbed dose D2 was irradiated at the constant dose rate ̇ (3 Gy/min). The irradiation was interrupted for τ. Third, the absorbed dose D3 was irradiated at the constant dose rate ̇ (3 Gy/min). The irradiation was interrupted for τ. Finally, the absorbed dose D4 was irradiated at the constant dose rate ̇ (3 Gy/min). We divided the absorbed dose into two for the two-field irradiation and divided it into four for the fourfield irradiation. The RBE of the interrupted photon beams was defined using the instantaneous irradiation (τ = 0) that no interruption of the photon beams as a reference (Eq. 12) [17,31]:

The effect of the interruption time on the SF for 6 MV photon beams with two-field
and four-field irradiation in the mMK model Figure 4 illustrates the effect of the interruption time on the SF with the two-field and four-field irradiation. The SF was increased with the increase of the interruption time in both the two-and four-field irradiation. The difference between SFs with four-field irradiation was emphasized when the interruption time was 10 min. The effect of the interruption time was greater as the absorbed dose became higher.

The effect of the interruption time on the RBE with two-field and four-field
irradiation in the mMK model The RBE was decreased by prolonging the interruption time, and the decrease of the RBE was approx. 2.5% compared with no interrupted photon beams when the absorbed dose was 8 Gy and the photon beams were irradiated with four fields. In addition, the interruption of the photon beams for several minutes had no significant effect on RBE in this study within 3%.

Discussion
It is possible that the photon beams' cell-killing effect on the biological effectiveness was decreased with the increase of the interruption time due to SLDR. We determined the RBE of the 6 MV photon beams for various interruption times, which were calculated from the SF using the mMK model. There was no significant difference in the effect on the RBE when photon beams with two-field and four-field irradiation were interrupted for approx. 10 min compared with instantaneous irradiation (τ = 0 min).
However, an approx. 2.5% reduction of the RBE was observed when the four-field irradiation with 8 Gy was interrupted for 10 min. It may thus be necessary to make the interruption of photon beams as quick as possible, since the RBE was decreased by prolonging the interruption time.
In the clinic, the linear accelerators could be occurred the interruptions of irradiation due to mechanical troubles of linear accelerator [32]. In a linear accelerator setting, irradiation may be interrupted for a long period of time due to mechanical trouble. Additionally, Figure 7 shows that the RBE value was dependent on cell-specific values (a + c) ( = 1, 10 min). We note that the RBE was affected by the value of (a + c), and the effect of the interruption time differed by >3% when the interruption time was 10 min and the absorbed dose was 8 Gy. The cell-specific value (a + c) (which is an important factor in the mMK model) indicates the recovery from tumor sublethal damage, depending on the type of tumor cell [33,34]. It is thus necessary to more accurately

Conclusions
The approx. 10-min interruption of 6 MV photon beams had no significant effect on the biological effectiveness, since the RBE decrease was within 3%. Nevertheless, the effect of RBE for a tumor was decreased by increasing the interruption time. It is thus necessary to make the interruption time as short as possible. When the interruption time is long, it is possible that an escalation of the prescribed dose will be needed.  The radius of the domain was set to 0.5 μm in the 3-cm-wide measurement region with the water-equivalent phantom.    Fig. 7. The effect of RBE as a function of the cell-specific repair rate (a + c) with τ = 1 min (a) and τ = 10 min (b) using two-field irradiation.