Radiobiological evaluation considering the treatment time with stereotactic radiosurgery for brain metastases

Objective: We evaluated the radiobiological effect of the irradiation time with the interruption time of stereotactic radiosurgery (SRS) using CyberKnife® (CK) systemfor brain metastases. Methods: We used the DICOM data and irradiation log file of the 10 patients with brain metastases from non–small-cell lung cancer (NSCLC) who underwent brain SRS. We defined the treatment time as the sum of the dose–delivery time and the interruption time during irradiations, and we used a microdosimetric kinetic model (MKM) to evaluate the radiobiological effects of the treatment time. The biological parameters, i.e. α0, β0, and the DNA repair constant rate (a + c), were acquired from NCI-H460 cell for the MKM. We calculated the radiobiological dose for the gross tumor volume (GTVbio) to evaluate the treatment time’s effect compared with no treatment time as a reference. The D95 (%) and the Radiation Therapy Oncology Group conformity index (RCI) and Paddick conformity index (PCI) were calculated as dosimetric indices. We used several DNA repair constant rates (a + c) (0.46, 1.0, and 2.0) to assess the radiobiological effect by varying the DNA repair date (a + c) values. Results: The mean values of D95 (%), RCI, and PCI for GTVbio were 98.8%, 0.90, and 0.80, respectively, and decreased with increasing treatment time. The mean values of D95 (%), RCI, and PCI of GTVbio at 2.0 (a+c) value were 94.9%, 0.71, and 0.49, respectively. Conclusion: The radiobiological effect of the treatment time on tumors was accurately evaluated with brain SRS using CK. Advances in knowledge: There has been no published investigation of the radiobiological impact of the longer treatment time with multiple interruptions of SRS using a CK on the target dose distribution in a comparison with the use of a linac. Radiobiological dose assessment that takes into account treatment time in the physical dose in this study may allow more accurate dose assessment in SRS for metastatic brain tumors using CK.


INTRODUCTION
Brain metastases are common intracranial malignancies.2][3] Non-small-cell lung cancer (NSCLC) is the most common type of brain metastasis, occurring in roughly 40% of cancer patients. 4Stereotactic radiosurgery (SRS) has become increasingly important in the management of brain metastases because its use has improved the systemic disease control and reduced the effect on normal tissue. 5,6SRS with whole-brain radiotherapy (WBRT) improved local control rates compared to WBRT alone. 7,8RS is an effective treatment for patients with brain metastases from NSCLC. 9,10e CyberKnife ® (CK) system (Accuray, Sunnyvale, CA) consists of 6 MV flattening filter-free (6 MV-FFF) photon beams produced by a compact linear accelerator (linac) to a multijointed robotic manipulator with six degrees of freedom (6 DoF). 11A CK system uses the real-time X-ray exposure to locate the patient's head between the irradiation, and the linac is controlled by the 6 DoF robotic arm for precise patient positioning based on the results of the tracking algorithm. 12,13As a result, changes in the target position are relayed to the robotic arm, which adjusts the pointing of the treatment beam.SRS applied with a CK for brain metastases has shown treatment accuracy and reduces the damage to healthy tissues. 14,15It was also reported that compared to conventional (two-dimensional) radiation, the use of a CK in cases such as V12Gy of normal brain in SRS irradiation improved the target dosimetric index (e.g. the conformity index [CI]) and reduced the dose to the normal brain compared to a linac. 16Therefore, SRS with a CK for brain metastases is an effective radiation protocol in terms of the dose distribution for the target and normal tissue and the patient position accuracy.
The treatment time that is necessary when using a CK system is several times longer than that associated with a linac, since with a CK the prescription dose is irradiated using a large number of non-coplanar beams because the irradiation is performed while correcting the patient positioning during irradiation. 17In addition, multiple irradiation interruptions are required for irradiation of the prescribed dose since the CK has a large number of non-coplanar beams and corrects the position of the patient during irradiation to provide precise patient positioning.Thus, the treatment time per fraction is increased in the administration of SRS using a CK.
2][23] With the use of photon beams, as in the case of particle beams, it is possible to reduce the tumor damage by prolonging the treatment time.However, there has been no published investigation of the radiobiological impact of the longer treatment time with multiple interruptions of SRS using a CK on the target dose distribution in a comparison with the use of a linac.It is important to determine the radiobiological effect of the treatment time for tumors when using a CK, since the treatment time is longer than that of a linac.There have also been no studies that used clinical patient data and irradiation schedules to evaluate the radiobiological effects of the treatment time.We thus propose a dose evaluation method that takes into account the radiobiological effects by considering the treatment time of SRS with a CK for brain metastases.

Patients
We analyzed the cases of 10 patients with 10 brain metastases from NSCLC who underwent brain SRS using a CK during the period from July 2019 to November 2020.Table 2 summarizes the clinical characteristics of the ten patients (all males, median age 70 years, range 63-83 years).The median gross tumor volume (GTV) was 0.72 cm 3 (range 0.08-2.95cm 3 ).This study was approved by our institutional review board (IRB), and all patients provided their informed consent under our IRB concerning the use of their data for this study.

Treatment planning
Treatment plans were generated using the Accuray Precision Treatment Planning System (TPS) v. 2.0.0.1.The beam size was controlled with a circular collimator corresponding to the GTV diameter with an M6 ™ series CK (Accuray), and a 6 MV-FFF was used.The selected tracking method was 6D skull tracking, and the beam paths were full head path.Table 2 provides the treatment planning information for each patient.The isocentric and non-isocentric beam arrangement technique was used to irradiate at GTV.The dose calculation algorithm was a ray-tracing algorithm with the 1.0 mm high-resolution condition.22 Gy was prescribed to 95% of the GTV. 24lculation of the dose-mean lineal energy y D by Monte Carlo simulations with PHITS The percentage depth dose (PDD) of a fixed collimator with a 6 cm beam was modelled using Monte Carlo (MC) simulations.][27] The number of histories was 1,000,000, and material of collimator was tungsten (W).The photon and electron cut-off energies were set to 0.01 MeV and the MC calculation was performed with a statistical error <1.0%.We transferred the phase-space file created by the BEAMnrc to the particle and heavy ion transport code system (PHITS) v. 3.20 to calculate the dose distribution.The calculated PDD was compared with the measurement value by an edge detector (Sun Nuclear, Melbourne, FL) in a water phantom during the commissioning of the device (Figure 1a).The lineal energy y was calculated by PHITS v. 3.20.We obtained the dose-mean lineal energy y D value for 6 MV-FFF with 0.5 µm domain radius in the water-equivalent phantom was calculated as a function of y-yd(y): Eqs.9][30] : where ε represents the energy deposited in a domain, l is the mean chord length, y is the lineal energy, f(y) is the lineal energy' probability density, and d(y) is the lineal energy's dose distribution.Figure 1b illustrates the geometry for calculating the y D value.The irradiation geometry was 80 cm source-to-skin distance (SSD), 6 × 6 cm field size, and a 10-cm-deep measurement point in the water-equivalent phantom (Figure 1b).The

Relative radiobiological effect with treatment time with a microdosimetric kinetic model (MK model) using irradiation log files
2][33][34] In the present study, the treatment time (T) was defined as the sum of the photon beam delivery time plus the beam-to-beam interruption time.The MK model can calculate the interruption time for both the beam pulse interval and each field interval.The equation of the MK model is: We defined the interruption time of each n th field as τ n [minutes (min)], and the D n (D m ) was defined as the absorbed dose in the n th (m th ) field at a regular interval [Gy].Table 1 showed the calculation parameters for the MK model.[37] The parameter ρ is the domain's density, and r d is the domain' radius (0.5 µm).The variable y D is the dose-mean lineal energy [keV/μm], Ḋ is the dose rate [Gy/min], and T treat is the treatment time [min].In addition, the (a + c) value was the semicontinuous low-dose-rate teletherapy (SLDR) rate, and deduced by Eq. ( 6). 38,39We used another two cell-specific values (a + c) (1.0 and 2.0) to assess the radiobiological effect by varying the DNA repair date (a + c) values. 21e clinical irradiation schedule of photon beams was derived from the irradiation log file output after the end of irradiation by the CK.The log file stored time information such as the number of photon beams, the monitor unit, the time of irradiation, and the time when the photon beams were interrupted (Table 2).
In this study, we defined the treatment time as the time from the first photon beam to the last photon beam based on the time information extracted from the irradiation log files for our evaluation of the radiobiological effects of the treatment time.The   Figure 2 illustrates the photon beams' schedules considering the photon beams' interruption time in Patient 1.There were 61 photon beams, and there were 60 interruptions (τ 60 ) between the beams (Figure 2).The median treatment time, irradiation time, and interruption time in this study were 10.68 min 5.15 min, and 5.85 min (Table 2).
Calculation of the time-dependent biological dose effect with the treatment time using the MK model We defined the time-dependent biological dose effect (TBDE) considering the treatment time by using the physical dose calculated by TPS (treatment time = 0) with the photon beams as a reference (Eq.7). 40,41DE = The TBDE was derived for the dose in the target in each case, and we calculated the relationship between the physical dose of the GTV calculated using the TPS and the TBDE.

DOSIMETRIC INDICES WITH THE RADIOBIOLOGICAL DOSE (D BIO ) CONSIDERING THE TREATMENT TIME FOR GTVS
The radiobiological dose (D bio ) was calculated taking into account the effects of the treatment time during irradiation by multiplying the physical dose (D phys ) from the TPS by the TBDE (Eq.8). 18We calculated the D bio (x,y,z) by using the TBDE and D phys in all voxels (Eq.9).
The i is the voxel number, N x,y are the number of voxels on the x-y plane, and N z is the number of slices for a CT image.We defined the GTV bio as the volume of the overlapping dose of D bio and the GTV.The dosimetric indices were derived in order to evaluate the effect of the treatment time using the target  We used the calculated dose distribution to evaluate the conformity of the treatment plans for each GTV.The Radiation Therapy Oncology Group conformity index (RCI) and Paddick conformity index (PCI) were calculated for each GTV with each plan (Eqs.10, 11). 42,43I = V RX TV (10)   where V Rx is the volume of the prescription dose and TV is the volume of the GTV.The RCI could be evaluated for each target regardless of whether the target volume was over-or undercovered by the prescription volume.

PCI =
TV 2 PIV TV×PIV (11)   where TV PIV is the target volume within the prescribed isodose, TV is the volume of the GTV, and PIV is the prescription isodose volume.

Treatment time's effect on the D bio and dosimetric indices for each patient
We calculated the TBDE for each GTV considering the treatment time from the irradiation log file for the D bio .Figure 3 depicts the dose distribution >50% of the prescribed dose for three patients in the axial plane at the center of the GTV with the physical dose from the TPS and D bio considering the treatment time.The physical dose inside the GTV was revealed to be reduced by considering the treatment time.
We evaluated the dosimetric indices by using the GTV bio (radiobiological dose).The D95 (%), RCI, and PCI considering the treatment time for all patients were shown in Figure 4.
We compared the physical dose for the GTV with 100% D95 (%), 0.95 RCI, and 0.92 PCI, and we observed that the values were decreased to 98.2%, 0.83, and 0.81, respectively when the treatment time was 16.32 min in Patient 1.In Patient 2 (15.92 min) and Patient 3 (10.52min), the D95 (%) values were 98.4 and 98.9%, respectively (Table 3).The mean values of D95 (%), RCI, and PCI for GTV bio were 98.8%, 0.90, and 0.80, respectively, and decreased with increasing treatment time.The D95 (%) and RCI were decreased with a longer treatment time, with a maximum decrease of 1.8% for the D95 (%) and 0.12 for RCI on the GTV bio (Table 3).The PCI also decreased with prolonged treatment time, showing the largest decrease of 0.16 in patient 9 (Table 3).Figure 6 shows the D95 (%) varying the SLDR rate (a + c) values for all patients.

Radiobiological effect of varying the SLDR rate (a+c) values for the GTV bio
Table 4 summarizes the relationship between the SLDR rate and the D95 (%), RCI and PCI for the GTV bio .When the (a + c) value was 1.0, the D95 (%), RCI, and PCI for the Patient 1 were 96.3%, 0.81, and 0.67, respectively.The mean values of D95 (%), RCI, and PCI for GTV bio were 97.4%, 0.84, and 0.69, respectively, and decreased with increasing treatment time when (a + c) value was 1.0.
In addition, the D95 (%), RCI, and PCI for the Patient 1 were 92.9%, 0.66, and 0.44 with 2.0 (a + c) value, respectively.The mean values of D95 (%), RCI, and PCI for GTV bio were 94.9%, 0.71, and 0.49, respectively.The (a + c) value with a parameter related to the repair time had a significant effect on the D95 (%), RCI and PCI of the GTV bio .

DISCUSSION
We evaluated the radiobiological effect of the treatment time in the application of SRS for brain metastases using a CK.In this study, the maximum treatment time for brain SRS was 16.32 min, and the dosimetric indices D95 (%) and RCI of the GTV bio showed a maximum decrease.The treatment time was shorter than that in the other cases, resulting in a smaller decrease in the dosimetric indices in patient 5 (Treatment time was 6.73 min).
In addition, PCI decreases with increasing treatment time in this study, the greatest decrease was seen in Patient 9 with a treatment time of 10 min.The cause is that PCI is as low as 0.76 due to the small size of GTV of 0.08 cm 3 at the stage of treatment planning.It is considered that the effect of treatment time had a large effect compared to other 9 cases.The longer the treatment time, the greater was the reduction in the GTV bio .Other in vitro studies have reported very small dose reductions when the treatment time was within 30 min. 44,45The treatment time used in the present study was also within 30 min and the results with a small effect on the dose for the GTV were similar; our present findings can thus be considered to be valid.On the other hand, Aiyama et al concluded that the lower the CI was, the lower the local progression rates for brain SRS with 0.65 CI as the threshold. 46he PCI considering the treatment time in this study was 0.65 or more in most of the results.However, it was less than 0.65 in Patient 9.In the case of GTVs with small volume, the impact of treatment time on PCI may be significant and may require attention.
Treatment times are expected to be longer than those used herein, depending on patient treatment parameters such as prescription dose, target geometry, irradiation technique, and treatment plan to be developed.Han et al investigated treatment times >30 min in SRS for brain tumors using a CK. 16Zhang et al reported that irradiation of metastatic brain tumors using the CK requires an average treatment time of 40 min. 46Clinical case with treatment times up to 40 min with CK irradiation have been reported, and in such a case, a further decrease in the GTV bio is expected to occur.In the present study, we calculated the GTV bio using Patient 1's treatment plan information and the average deliverytime per field to assess the effects of a prolonged treatment time.
Figure 7 shows the D bio with the treatment times of 16.32 min and 40 min in Patient 1.
The D bio was decreased with the prolonging of the treatment time.The increase in the treatment time affected the dosimetric indices: the D95% decreased from 98.2 to 95.9%, the RCI decreased from 0.83 to 0.79, and the PCI decreased from 0.81 to 0.62.A longer treatment time also resulted in a large GTV bio difference caused mainly by the SLDR.A prescription dose that   takes the treatment time into account is thus considered necessary in order to consider more accurate dosimetry to the GTV with a large reduction in the GTV bio .If the rate of decrease in GTV bio is large, a way to compensate for the decreased GTV bio may be needed.The GTV bio was decreased in the prescription dose according to the TBDE of each voxel when the treatment time was prolonged.We therefore calculated the compensated dose of the GTV (GTV comp ) by multiplying (1-TBDE) for each voxel in the GTV by the physical dose in all voxels in the GTV [D GTV (x,y,z)].We calculated the optimal dose (GTV opt ) that compensates for the dose reduction due to the treatment time by adding the compensation dose GTV comp to the biological dose GTV bio reduced by the treatment time (Eq.12).
Murphy et al suggested that the treatment delivery staring node in CK treatments when creating the treatment planning should be optimized to minimize the radiobiological effect considering the treatment time. 47Therefore, it is necessary to create a treatment plan that completes the treatment as fast as possible when creating the treatment plan.In addition, treatment time should also be as fast as possible during irradiation.There are studies evaluating the impact of total treatment duration extension on tumor overall survival. 48,49wever, there are no studies evaluating a single treatment time vs clinical results, and further data evaluating tumor volume per treatment time is considered necessary.When there is a difference in clinical outcome due to prolonged treatment time, it might be possible to calculate the optimal dose GTV opt (x,y,z) considering the treatment time using the relationship between the biological dose D bio and the TBDE of the GTV by optimization in each case when the GTV bio decreases significantly, and irradiated to GTV.
We used NCI-H460 cells to calculate the treatment time's effect.The D bio was dependent on cell-specific values (a + c) of the DNA repair constant rate (Figure 5), and the TBDE was affected by the cell-specific value (a + c); the larger that this value was, the greater was the decrease in the GTV bio (Table 4).The GTV bio of the D95 (%) and the PCI were maximally decreased to 92.9% and 0.44 with the treatment time of 16.32 min when the (a + c) value was 2.0. the case of (a + c) = 2.0, it was lower than 0.65 CI reported by Aiyama et al under many conditions. 50The cell-specific value of the DNA repair indicates the recovery from tumor sublethal damage, depending on the tumor-cell type.Similar to our present results, it has been concluded that the refinement of cell-specific parameters and repair functions are important for building models that take into account biological effects in the current physical models of proton therapy. 18urther studies are necessary to evaluate how the treatment time affects specific types of tumor cells in photon therapy.
Several study limitations should be addressed.We simulated the treatment time's effects by using an MK model and tumor-cell parameters to calculate the biological dose with clinical patient data.It is necessary to compare clinical results assessing how much the reduction in GTV bio due to prolonged treatment time affects tumor volume in order to assess the validity of our present findings.We evaluated the treatment time's radiobiological effect considering only the tumor SLDR; other repair phenomena such as potentially lethal damage repair and repopulation were not considered.Moreover, the effects of tumor hypoxia and tumor reoxygenation occurring during the treatment time on the GTV bio were not evaluated.Third, the results of this study evaluated only the effect of treatment time on tumor dose in CK and did not compare the results with those of linear accelerators.

CONCLUSIONS
We proposed a dose calculation method that considers the radiobiological effect of the treatment time on tumors when brain SRS for brain metastases is applied using a CK.Cell-specific parameters such as DNA repair constant rate associated with treatment time have a significant impact on radiobiological dose reduction and should be carefully evaluated at the same time.

Figure 1 .
Figure 1.(a) Validation of MC-calculated PDD curves compared with the measurement values by the edge detector for 6 MV-FFF in liquid water.(b) Irradiation geometry for the MC calculations with 6 MV-FFF photon beams.The domain radius was 0.5 µm in the 10-cm-deep measurement point in the water-equivalent phantom.FFF, flattening filter-free; MC, Monte carlo; PDD, percentage depth dose.

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of 10 birpublications.org/bjroBJR Open;0:20220013 BJR|Open Nakano et al surviving fraction was calculated considering the interruption time for both the beam pulse interval and each field interval.

Figure 2 .
Figure 2. The photon beams' schedules using the MK model considering the photon beams' treatment time using the irradiation log file from CK in Patient 1. CK, CyberKnife ® ; MK, microdosimetric kinetic.

Figure 5
reveals that the dose distribution >50% of the prescribed dose values in the axial plane at the center of D bio calculated with (a + c) were 1.0 and 2.0 in Patient 1.

Figure 3 .
Figure 3.The dose distribution in the axial plane at the isocenter with the physical dose and radiobiological dose (D bio ) considering treatment time in Patients 1-3 ((a)-(c)).

Figure 5 .
Figure 5.The effect of (a + c) on the radiobiological dose D bio .(a) The physical dose from the TPS as the reference for Patient 1 was (b) 1.0 (a + c) and (c) 2.0 (a + c).TPS, treatment planning system.

Figure 7 .
Figure 7. D bio with the treatment times of 16.32 min and the prolonging of the treatment time 40 min in Patient 1.

Table 2 .
Characteristics, treatment planning, and treatment time in SRS for 10 patients GTV, gross tumor volume; SRS, stereotactic radiosurgery.

Table 3 .
The dosimetric indices considering the effect of treatment time for the GTV for patients GTV, gross tumor volume; PCI, Paddick conformity index; RCI, RTOG conformity index; SD, standard deviation.