Accumulated dose implications from systematic dose-rate transients in gated treatments with Viewray MRIdian accelerators

The combination of magnetic resonance (MR) imaging and linear accelerators (linacs) into MR-Linacs enables continuous MR imaging and advanced gated treatments of patients. Previously, a dose-rate transient (∼8% reduced dose rate during the initial 0.5 s of each beam) was identified for a Viewray MRIdian MR-Linac (Klavsen et al 2022 Radiation Measurement 106759). Here, the dose-rate transient is studied in more detail at four linacs of the same type at different hospitals. The implications of dose-rate transients were examined for gated treatments. The dose-rate transients were investigated using dose-per pulse measurements with organic plastic scintillators in three experiments: (i) A gated treatment with the scintillator placed in a moving target in a dynamic phantom, (ii) a gated treatment with the same dynamic conditions but with the scintillator placed in a stationary target, and (iii) measurements in a water-equivalent material to examine beam quality deviations at a dose-per-pulse basis. Gated treatments (i) compared with non-gated treatments with a static target in the same setup showed a broadening of accumulated dose profiles due to motion (dose smearing). The linac with the largest dose-rate transient had a reduced accumulated dose of up to (3.1 ± 0.65) % in the center of the PTV due to the combined dose smearing and dose-rate transient effect. Dose-rate transients were found to vary between different machines. Two MR-Linacs showed initial dose-rate transients that could not be identified from conventional linearity tests. The source of the transients includes an initial change in photon fluence rate and an initial change in x-ray beam quality. For gated treatments, this caused a reduction of more than 1% dose delivered at the central part of the beam for the studied, cyclic-motion treatment plan. Quality assurance of this effect should be considered when gated treatment with the Viewray MRIdian is implemented clinically.


Introduction
The combination of magnetic resonance imaging (MR) and linear accelerators in MR-Linacs has been clinically available since 2017 (Raaymakers et al 2017). These machines offer real-time high soft-tissue contrast imaging during treatment, thus enabling improved motion management. Currently two commercially available MR-Linac systems have the ability to process MR image data and to switch the beam on and off in real time during gated treatments. The beam-on is guided by the position of the tumor, surrogate structures or organs at risk, thereby limiting unnecessary irradiation of healthy tissue. As a consequence, MR-Linacs have the potential to reduce planning margins compared to treatments without real-time imaging or treatments with surrogatebased gating, for example, in lung treatments (Corradini et al 2019). The Viewray MRIdian 0.35 T MR-Linac can perform gating based on real time 2d cine images acquired at 4 or 8 frames per second.
In a previous study, a dose-rate transient was found on the Viewray MRIdian MR-Linac located at Rigshospitalet in Copenhagen, Denmark (Klavsen et al 2022). This dose-rate transient occurred each time the beam turned on, even after gating induced beam holds. Typically, the dose rate would be reduced by 15% at beam start, followed by a 0.5 s ramp-up period to stable dose rate (Klavsen et al 2022). The origin and clinical implications of the dose-rate transient was not discussed in the study, nor did it show whether the feature was accelerator specific or general to the ViewRay system. A new study was therefore designed.
Of particular interest for this work was the question of how the internal monitor chamber in the linac would compensate for dose-rate transients, and to what extend the transients could be linked to: (i) a reduced fluence rate during the initial part of the beam-on period.
(ii) changes in the x-ray beam quality during the initial part of the beam-on period.
We have no technical information about features in the linac design that potentially could lead to, for example, transients in beam orientation, field size or monitor chamber response, and such aspects were not directly studied in this work. However, dose-rate changes may be related to other aspects than (i) and (ii).
Plastic scintillation dosimeters (PSDs) were chosen for the study due their excellent water equivalence, high time resolution, and ability to perform measurements without causing artifacts on the MR-images (Klavsen et al 2022, Ferrer et al 2023, Uijtewaal et al 2023. Previous studies have found that PSDs provide accurate time-resolved dose measurements in moving phantoms in conventional linacs (Lambert et al 2006, Beierholm et al 2008, Beierholm et al 2015, Sibolt et al 2017, Santurio and Andersen 2019. A challenge with PSDs, however, is the separation of the signal, generated in the scintillator, from the unwanted light produced when the optical fibers are irradiated (Beddar et al 1992a, Archambault et al 2005, Therriault-Proulx et al 2013. This unwanted stem signal is mostly Cerenkov light, and although the Cerenkov yield is not directly affected by the magnetic field, its angular distribution is. The amount of Cerenkov light seen by the instrument can therefore be affected by the magnetic field as the fiber cable will only guide light within the critical angle of the fiber. It has been found that the chromatic removal technique (Frelin et al 2005, Therriault-Proulx et al 2011, Therriault-Proulx et al 2013, Simiele et al 2018 efficiently reduces the influence of the stem signal on PSD-measurements, even in magnetic fields (Klavsen et al 2022). The ME40 scintillator system developed at the Technical University of Denmark (DTU) (Beierholm et al 2011 was selected as read-out instrumentation for the study as it can perform dose-per-pulse measurements synchronously for two scintillators. This system is capable of absolute dosimetry traceable through calibrations via alanine pellets (Ankjaergaard et al 2021, Klavsen et al 2022 providing accurate dose measurements in magnetic fields (Billas et al 2021).
Previous studies have examined dose delivery during gated measurements on MR-Linacs using detectors without time resolution (i.e. integrating detectors), or dose reconstruction (Crijns et al 2011, Lamb et al 2017, Green et al 2018, Stark et al 2020, Boyeet al 2022, Ehrbaret al 2022, Wahlstedt et al 2022. These studies also found a reduction in dose at the center of the beam.
The aim of this study was three-fold: First, to investigate whether the initial dose-rate transient is a unique feature to the specific accelerator or if it is a general characteristic associated with the Viewray MRIdian model type. Secondly, to evaluate the components contributing to the dose-rate transient. Thirdly, to determine the effect of initial dose-rate transients on dose delivery, for example, during gated treatments. The key question being if dose-rate transients affect the dose coverage of the target in a systematic way.

Methods
In this study three experimental setups were used: section 2.4 describes One setup in Solid Water (Gammex technology Sun Nuclear, Norfolk, USA) with two scintillators. Two setups used a CIRS 008 V phantom (Viewray Dynamic Phantom model 008 V, CIRS Sun Nuclear, Norfolk USA), which is an MRI compatible phantom containing a movable piston with detector inserts. These setups were: (i) Gated treatment with a static target (section 2.5) and (ii) gated treatment with a moving target (section 2.6).

Accelerators
Four MRIdian (Viewray Inc., Denver, USA) MR-Linac's were studied. These were located at (i) Copenhagen University Hospital, Rigshospitalet, Denmark (linac A), (ii) University Hospital Zürich, Zürich Switzerland (linac B), (iii) Heidelberg University Hospital, Heidelberg Germany (linac C), and (iv) Copenhagen University Hospital Herlev and Gentofte (linac D). The three main linacs investigated were A, B, and C. Linac D was only investigated for a dose-rate transient, but no further measurements were done. All MRIdians have a 0.35 T magnetic field and a 6 MV Flattening Filter Free (FFF) beam with a beam quality of TPR 20,10 = 0.65 (IAEA 2001).

Scintillator system
Four plastic scintillators based on BCF-60 green scintillator material were used. All scintillators had a diameter of 1 mm, and the lengths were 1 mm, 2 mm (two probes), and 5 mm. Each scintillator was coupled to a 9 m long PMMA optical fiber. Scintillator signals were measured using ME40-systems developed by DTU (Beierholm et al 2011. The ME40-system allows for simultaneous dose-per-pulse measurements with two scintillators using the MR-Linac synchronization signal as the trigger. Two ME40-systems provided simultaneous dose-per-pulse measurements with four scintillators. The stem signal and scintillation signal were separated into two channels, one predominantly for scintillation signal the other for stem signal, where it was collected by photomultiplier tubes in preparation for a twochannel chromatic stem removal. (Beierholm et al 2011 Each linac synchronization signal started an 80 μs integration period, followed by background measurement of identical length but delayed by 200 μs. The Viewray MRIdian MR-Linac has a pulse frequency of 100-120 Hz which means that a pulse is fired every 8.3 ms to 10 ms. The length of the pulse is in the order of 5 μs. As a new 80 μs integration period is triggered for every linac pulse (every 8.3 ms to 10 ms), the pulse is completely covered by the integration period. The 200 μs delay guaranties that no pulse is present during the subsequent background measurement.
Each scintillator was calibrated for relative dosimetry with the two-channel chromatic removal method described in (Frelin et al 2005). The scintillators were placed in solid water and irradiated twice in the MR-Linac, each time with a different amount of optical fiber in the beam.

Dose-rate transients
The time-resolved nature of the ME40 system made it possible to measure the dose-rate transients by reporting the dose-per-pulse during the initial seconds after a beam-on event. This data can be taken from any of the following static measurement setups.

Beam quality dependence
Proxy TPR 20,10 measurements, as described below, on a dose-per-pulse basis were performed in order to test if the beam quality remains constant during the entire beam delivery, including the initial seconds. Measurements were carried out using a Solid Water phantom at a source-to-surface distance (SSD) of 90 cm, a 9.96 × 9.96 cm 2 field size, and two scintillators positioned 10 cm apart on the central axis of the phantom. Four depth pairs were used for all three linacs (A, B, and C) with the top scintillator placed at depth 2 cm, 4 cm, 6 cm or 8 cm, and the bottom scintillator at depth 12 cm, 14 cm, 16 cm, or 18 cm, respectively. At linac B and C, measurements were also carried out with the top scintillator at depth 0 cm or 1 cm, and the bottom scintillator at depth 10 cm or 11 cm, respectively. For each configuration, five measurements were performed with a 60 s pause between each irradiation to ensure consistent cool down of the machine between measurements. A single set of five measurements were done with a 20 s pause (shortest pause possible) to minimize the warm-up between measurements. The dose ratio between the top and the bottom scintillators, with the top scintillator as the denominator, was evaluated with a local polynomial regression through the LOESS regression function (Cleveland et al 1992) in two ways; (i) a LOESS regression on the total data set with the ratio of each measurement normalized to the mean ratio after 5 s (stable beam), and (ii) a LOESS regression on dose measured by each scintillator normalized to the stable beam. A ratio between the top and bottom detectors was calculated as the ratio between the model fits. This ratio was separated into three groups: Group 1 if the initial ratio was below 0.99, group 2 if the initial ratio was between 0.99 and 1.01, and group 3 if it was above 1.01. Having an initial normalized depth dose ratio below 0.99 essentially means that there is a 1% change in beam quality (proxy TPR 20,10 ) from start to end.

Gated treatment with a static target
The dose delivery stability was tested by placing the scintillators in a stationary cavity away from the movable piston in the CIRS V008 phantom, see figure 1, position 2, 3 and 4. This configuration made it possible to decouple the effect of the dose-ratetransient on the dose delivery of a gated treatment from the dose smearing caused by residual motion of the target during gating.
For linac A, 617 monitor units (MU) were delivered through a single circular shaped field with a diameter of 3 cm at gantry angle 0°. The scintillator was located at the center of this beam. Gating was performed on a cubic structure of the phantom piston (visible on MR-images) illustrated by gating structure 6 in figure 1. The piston was moved in a sinusoidal motion with either a 5 s or 10 s period, and amplitude of 12.75 mm. Two combinations of motion patterns and gating windows were investigated: (i) 3 mm gating window and 5 s period, and (ii) 5 mm gating window and 10 s period. For all measurements, on all MR-Linacs, the region-of-interest (%ROI) was set to 0, meaning no area of the gated structure was allowed outside the gating window. The dose delivered should be the same in gated and static treatments with this setup.
For linac B and C, 200 MU were delivered for a 9.96 cm × 9.96 cm square field from gantry 0°. The scintillator was located at the center of this beam. Furthermore, the motion patterns chosen here were (i) 3 mm gating window and 5 s period and (ii) 3 mm gating widow and a 10 s period. As for linac A, gating was performed on the gating structure 6 in figure 1.
For linac A, B, and C, the gated treatments were compared with a non-gated treatment. Figure 1 shows the placement of the detectors in the phantom. For linac A, the cavity to the left of the piston was chosen (position 3) while for linac B and C, the cavity above the piston was chosen (position 2). For all three linacs, the scintillators were placed in a 3D printed rod (black ASA plastic), custom designed for the cavities.

Gated treatment with a moving target
To investigate the effect of motion and gating, the scintillators were placed in the moving piston (position 1, figure 1). Two different motion patterns were investigated: A sinusoidal movement with periods of (i) 5 s and (ii) 10 s respectively, both with an amplitude of 12.75 mm. These were compared to a static measurement with no piston movement. Two gating windows was investigated a 3 mm and a 5 mm both with a 0% ROI.
The treatment plan for linac A consisted of nine static MLC collimated fields from different angles aimed at a spherical target (GTV) diameter 2 cm with an isotropic PTV margin of 5 mm. A total of 617.4 MU were used. The dose to 99% of the GTV (D99%) was 93.5 Gy whereas the dose to 1% of the volume (D1%) was 96.7 Gy. The corresponding numbers for the PTV were D99% = 82.1 Gy and D1% = 96.6 Gy. The beam was a 6 MV FFF beam. The dose matrix was calculated by the Monte Carlo algorithm of the ViewRay TPS, with an accuracy of 0.2% and spatial resolution of 1 mm. The same treatment plan was used for all measurements and gating was used for all measurements except the static case.
The scintillators were placed inside the piston cavity (position 1, figure 1) in grooves on the surface of a 3D printed rod in black ASA plastic. The groove width was set to exactly match the thickness of the optical fiber cables, so that the scintillators were mechanically fixed by the rod. Blank fiber cables were used as distance pieces to ensure the correct position off-set of the scintillators. Submillimeter air gaps might have formed between the rod and the phantom. As the gaps were equal for all measurements we estimate the air to have negligible influence on the relative dosimetry. The scintillators were placed to cover the center and the penumbra, as shown in figure 2, and the dose profile was extracted from the dose matrix by a Matlab script. The positions were found based on distances measured on MR-images which were translated to positions on the rod. The setup on linac B and C was different from that on linac A, since only one ME40 system was available during these measurements. The measurements were carried out with only one scintillator at the center position. The scintillator was placed in the same 3D printed rod used at linac A. The plans used at each linac were created individually at each hospital to be as similar as possible, using the same parameters: same target, beam angles, and total dose. For linac B the treatment plan consisted of nine static MLC collimated fields from the same angles as linac A aimed at a spherical target (GTV) of diameter 2 cm with an isotropic PTV margin of 5 mm. A total of 589.3 MU was used. The dose to 99% of the GTV (D99%) was 91.84 Gy whereas the dose to 1% of the volume (D1%) was 96.95 Gy. The corresponding numbers for the PTV were D99% = 88.63 Gy and D1% = 96.6 Gy. For linac C the treatment plan used 589.3 MU and the numbers for the GTV were D99% = 93.11 Gy and D1% = 95.6 Gy and for the PTV D99% = 88.69 Gy and D1% = 95.6 Gy.

Accumulated dose simulations
To further investigate the effect of the dose-rate transients, a mathematical dose-accumulation model was made in R (R Core Team 2022).
The model had three inputs: (i) A dose profile extracted from the inline direction (superior-inferior) of the final dose distribution of the nine-field plan from linac A. It was calculated by the Monte Carlo algorithm of the ViewRay treatment planning system and extracted through a Matlab script with a 1 mm resolution.
(ii) Position of the scintillator at each time step of the irradiation. Two photodiodes in the phantom motor drive provided a real time signal for the most superior and most inferior piston positions, and hence the piston position could be calculated for all time points by interpolation. Combining the piston positions with the data from the time resolved scintillator system, the exact position of the scintillator for each pulse could be determined.
(iii) An option to conduct the computation with or without a dose-rate transient. This was simulated for linac A using a multiplicative factor increasing linearly from 0.85 to 1 over a transient period of 0.5 s. The magnitude and duration of the doserate-transient was based on our experimental findings, an example can be seen in the left most panel of figure 3.
The model computes the accumulated dose to any point in the movable phantom by adding the static dose profile from the treatment planning system translated vertically in accordance with the one dimensional motion pattern of the phantom.
The model was used in three ways in this study: (i) For producing comparison data for the scintillator measurements in section 3.5. (ii) To determine the influence of movement (dose smearing) on the dose received by each detector by comparing simulations with and without motion, but still beam gated by the input data from the scintillator. (iii) To determine the dose shift caused by the dose-rate transient in section 3.6. Two treatments were chosen for investigation: the 5 s period and 3 mm gating window, and 10 s period and 5 mm gating window treatment carried out at linac A. In both cases, normalized dose profiles were simulated with and without the dose-rate transient turned on.
The model does not account for difference in beam intensity from field to field in the nine-field plan as only the final dose distribution was available and not a dose distribution for each field. Thus, only the change in dose-rate was modelled and only the relative dose distribution was used for comparison and not the absolute dose.

Uncertainties for the scintillator measurements
The uncertainty on the integrated scintillator dose measurements is shown in table 1. The measurement uncertainties of the scintillator originate mainly from three sources: reproducibility, temperature, and limitations in removal of the stem signal. The reproducibility refers to the uncertainty for measurement within one site as these measurements were compared to each other. The stem signal was found to have a 0.1% influence per cm of fiber cable in the primary beam (Klavsen et al 2022). The scintillator signal is sensitive to temperature changes with a temperature coefficient of (−0.547 ± 0.010) %/°C, (Buranurak et al 2013, Wootton and Beddar 2013, Klavsen et al 2022. We estimate the temperature was stable within 0.5°C during measurements. The total uncertainty on one measurement is 0.46% while comparing two measurements from the same linac the uncertainty is 0.65%. Furthermore, when comparing to the gated treatments from section 2.5, a 2 mm uncertainty was estimated on the scintillator positioning compared to the static dose profile.

QA based on monitor unit linearity test
In order to evaluate whether the dose-rate transient could be seen in standard linac QA procedures, a monitor unit linearity measurement (dose versus monitor units) was acquired from linac A, B, and C. The length of the dose-rate transient is around 0.5 s for linac A and up to 2 s for linac B. The Viewray MRidian system has a dose rate between 600 and 650 MU/min. If the dose-rate transients can be seen in a standard monitor unit linearity measurement, we would expect it to be visible for low amounts of MU (below 10 MU). For linac A both the set and delivered monitor units were acquired, while for linac B and C only the set amount was acquired.

Dose-rate transients
Dose-rate transients were identified at the initial part of the beam for three out of the four investigated linacs. Examples of characteristic dose-rate transients, which were present every time the beam turned on, are shown in figure 3. All the machines presented a unique and highly reproducible starting behavior.
Linac A had an initial dose rate of approximately 85% of the stable output which was reached after a 0.5 s ramp-up period. Linac B had a V-shaped time trace, starting with a dose-rate reduction from 95% to 90% followed by a ramp-up to stable output (100%) of about 3 s. Linac C had a slight dose-rate transient starting initially at 98% but had slowly increasing dose rate during beam on. The only machine without any initial dose-rate transient was linac D. The dose-rate transient from linac A was used in the simulations in sections 3.5 and 3.6.
A notable larger spread for the dose per pulse is seen for linac C and D than for A and B; the source of this spread was not identified.
The dose-rate transient for linac A was not constant throughout the treatments. A larger reduction in dose-per-pulse was observed in the beginning of a treatment than towards the end as shown in figure 4. This figure compares three setups at linac A: one continuous beam (non-gated) and two gated. For the measurement in panel (b), the detector was held in place as described in section 2.5, and for panel (c) moved as described in 2.6. Panel (b) and (c) in figure 4 consists of many beam-on/off cycles, though due to the scale of the x-axis, the individual beam cycles can be hard to distinguish, thus panel (d) highlights a section of panel (c) to visualize the presence of the  dose-rate transient. The large beam-off gaps in panel c are due to gantry rotations for which the beam was turned off.

Beam quality dependence
The dose-rate transient for linac A was present at all depths measured, as shown in figure 5. Simultaneous measurements are depicted with the same color. Besides the initial dose-rate transient, no systematic change in dose rate was found for any depth. Figure 6 shows the ratio between the bottom and the top detector, where the top detector is the denominator. The signal was normalized to the mean value of this ratio during steady beam, which was defined to be after 5 s of beam on. For all linacs, the dose ratio per pulse fluctuates ±2%. For linac A, the dose received by the lower detector increases during the first 0.5 s which is reflected by the increasing ratio, with an average initial difference to the stable beam of 1%. For linac B, the ratio starts out stable, but then drops by 0.5% before increasing to the stable ratio again. For linac C, no significant changes in the ratio are found. The red lines in figure 6 indicate a LOESS regression with a prediction interval in the marked area. Figure 7 shows the ratio between LOESS regressions for the bottom scintillator and the top  scintillator for linac A. Thirteen measurements show a significant initial increase in the ratio while no measurements show an initial decrease. In eight measurements no change in ratio is observed. Table 2 shows the comparison of accumulated dose between the gated and static measurements with a static target described in section 2.5. The dose was Figure 6. Changes in depth-dose ratios on a dose-per-pulse basis with 10 cm distance between detectors as a function of time. All measurements, regardless of depth, were included and normalized to the mean of the stable beam for the corresponding measurement. The red line is a LOESS fit to individual dose-per-pulse depth ratios with a prediction interval of one standard deviation between the two dashed lines. reduced by 0.2% to 1% compared to the static nongated setups, for all the gated treatments. The difference was largest at linac A for the plan with the shortest beam-on times, which was the 5 s period with the 3 mm gating window. For this plan the beam-on time was between 0.25-0.5 s every time the beam turned on. For the measurements at linac A, the MUs measured by both the primary and secondary dose chamber were noted, while for linac B and C, only the prescribed MUs were recorded. For these measurements the detector was unaffected by dose smearing as it didn't move. In the following sections, the plans will be denoted with the period time of the sinusoidal movement and the gating window, e.g., a plan using a 5 s period and a 3 mm gating window will be denoted 5 s 3 mm. Table 3 shows a comparison of the point dose measured at the central scintillator (placement shown in figure 2) for the nine-field-gated measurements described in section 2.6. The linacs used were A, B, and C. The dose measured for the moving detectors is shown relative to the dose measured for a non-gated static detector, receiving the same treatment plan for the same linac. The doses measured for the dynamic cases are generally lower than that for the static with a relative dose difference ranging from −1.3% to −3.1% for linac A, from −1.3% to −2.3% for linac B, and from −0.3% to −1.1% for linac C.

Dose distribution
The doses measured by the scintillators at linac A (figure 2, left panel) for gated measurements with a dynamic target are shown as symbols in figure 8. For comparison, dose profiles simulated by our model (section 2.7) are shown in dotted and dashed lines along with the static dose profile predicted by the treatment system (solid black). The uncertainty on the scintillators' position relative to the target was estimated to be 2 mm in each direction. A comparison of the predicted profile and actual scintillator output measured for the static treatments allowed us to estimate the offset of the scintillator group to −1.5 mm. The positions in figure 8 are corrected by this offset. The result for the PSD is normalized to the center detector for the static measurement while the simulated data is normalized to the center of the static dose profile. Dose in the outer penumbra region (20 mm) increased from 0.7% for the static measurement to 25% for the gated measurements, while the dose for the inner penumbra decreased from 54% to 46%.
The effect of longitudinal target motion in a static dose distribution was simulated by our model (section 2.7) for the treatment plan used at linac A. Table 4 shows the results for the modelled gated treatments with and without a moving target. For all simulations shown in table 4 the same dose-rate-transient was implemented. The largest effect of movement is found in the penumbra region 20 mm from the center of the GTV where the estimated dose (relative to the point 0 mm for the static case) went Table 2. Comparison of dose received with a static detector, with and without gating. For the measurements the gantry was placed at 0 degree and 1 field was used, see section 2.5 for details. For measurements at linac A, the count at both monitor chambers was noted while for linac B and C only the planned MU for the treatment was recorded. For linac A the detector was placed in position 2 shown in figure 1 and for linac B and C the detector was placed in position 3 (figure 1).

Effect of dose-rate transients on accumulated dose distributions
The simulated influence of the dose-rate transient on dose distribution was minimal as shown in figure 9, where two combinations of movement patterns and gating windows were simulated, (i) 5 s period 3 mm gating window and (ii) 10 s period 5 mm gating window. Each simulation was made twice, once with the approximate dose-rate-transient enabled and once without. The bottom panels show the difference between the curves. The maximum shift in dose received to a point was found to be 0.5% for the 5 s period. Figure 10 shows the ionization chamber linearity measurements from linac A, B, and C versus the set amount of MU as requested from the linac console. For linac A, the data are also shown as function of the delivered amount of MU as reported by the monitor chamber. These measurements indicate that the output is linear from 5 MU and above. Using the set MU, a slight overshoot is observed below 5 MU. For linac A, an undershoot is seen only at 1 MU when using the monitor chamber reading as reference. Significant uncertainty is associated with the measurements.

Discussion
In this study, we conducted scintillator based doseper-pulse measurements at four MRIdian sites and found unique dose-rate transients for three of the machines and one machine without any dose-rate transient. For each machine, the transients were highly reproducible and occurred at each beam on for the studied gated treatments under cyclic-motion conditions.
We hypothesize that the dose-rate transients may originate from (i) an initial change in fluence rate or (ii) an initial change in x-ray beam quality.

Change in fluence rate (i)
A change in photon fluence rate (i.e. rate of photons emitted by the linac) will be compensated by a well working linac monitor chamber system by a prolonged beam time to deliver a given number of monitor units. For linac A and B, an increase in total delivery time was indeed seen for the gated treatments compared to the static treatment (tables 2 and 3). This indicates that a part of the dose-rate transient is simply due to initial changes in the photon fluence rate.

Change in x-ray beam quality (ii)
The linac monitor chamber system is calibrated to give a specified dose under reference conditions per monitor unit for a given beam quality. Dynamic changes in x-ray beam quality during beam delivery will therefore affect the actual dose delivered in a treatment. Under such conditions, the monitor chamber will not be able to ensure that the requested dose is delivered. Linac A and B showed a decrease in the dose-per-pulse ratio between the two detectors positioned 10 cm apart of about 1% and 0.5%, respectively, during the dose-rate transient (figures 6 and 7). This indicates that the beam energy is not stable at beam onset. Moreover, the duration of the instability (about 0.5 s in figure 7) corresponds to that of the dose-rate transient ( figure 3). Beierholm et al (2011) also found unique initial dose-rate transients in several linacs, though the transients there were resolved within the first 30 linac pulses. In comparison for linac A it took around 60 pulses to stabilize (figure 3).

Other changes
We do not have access to information or direct measurements that can reveal what happens inside the Viewray MRIdian during beam start up. However, we speculate that there could potentially be transients in beam orientation or other parameters that primarily Table 4. Output at different scintillator positions (0, 15, 20 and 25 mm) predicted by our dose-accumulation model (section 2.7). The positions are relative to the center of the GTV described in section 2.6. Columns labelled 'a' show computations based on the actual motion pattern and beam-on timing from our experiments whereas the 'b'-columns show computations where the target was considered static and only the beam on and off timing from the experiment was used. A linear dose-rate transient approximation for linac A was applied in all cases. The dose outputs are normalized against the dose at position 0 mm for the static case. The two measurements with a 5 s period were repeated. The computations reflect the motion patterns of the measurements in chronological order. would influence the internal monitor chambers. In that context, it is interesting to note that the two monitor chambers of linac A agreed within 0.03% for static treatments, but significantly deviated from each other for gated treatments, as seen for example for the 5 s period 3 mm gating window plan where the difference adds up to 1.04% (table 2). This supports the hypothesis that the source of the transients may go beyond simple changes in fluence rate at a constant x-ray beam quality.

Effect on gated treatments
The dose delivery in gated treatments were investigated for linac A, B, and C in setups varying slightly from site to site (section 2.6). For gated measurements with a moving target, the detector placed centrally in the target measured less dose compared to the corresponding measurements with a static target (table 3). For linac A, a maximum reduction in total dose of 3.1% was registered while linac B had a maximum reduction of 2.3%. Linac C showed the lowest difference between the static and gated treatments with a maximum dose reduction of 1.1%. This is in accordance with the finding that linac C had a negligible dose-rate transient ( figure 3) and thus would not be affected by it. We suspect that the reductions are partly due to: (i) the reduction caused the dose-rate transient. (ii) Target motion within a non-perfectly homogeneous FFF field (dose smearing). Based on the MC calculated dose profile from linac A (figure 2) the dose at ±5 mm of central axis was 99.7% and at ±10 mm it was 97% . Also, due to the limited frame rate (4 frames per s ) and a system latency of 120 ms , part of a gated treatment is delivered with the detector outside the gating window. A difference of 1% was found between the 5 s 3 mm gated measurements with a static target, compared with the corresponding nongated measurement (table 2). Here the second cause (ii) is ruled out. The 10 s and 5 mm movement for linac A resulted a reduction of 0.2% (table 2), if the same effect is found on the corresponding gated measurements with a moving target, most of the 1.3% reduction (table 3) would be due to dose smearing. This is in agreement with the measurements at linac C. The simulations in table 4 show a max difference between results with and without movement of 0.5% for the detector at 0 mm. We therefore expect that about 0.5%−1% of the reduction on the central axis is due to dose smearing, and the dose-rate transient is the main factor for the rest.

Effect on dose profiles
Gated treatments with a moving target caused a broadening of the longitudinal dose profile through the target as shown in figure 8. This is consistent with simulations and previous measurements with Gafchromic film . The relative dose measured by the scintillator at a longitudinal offset of 20 mm was 0.7% of the max dose for the static measurement but increased to a maximum of 25% for the gated measurements. For the scintillator placed at 15 mm, the normalized dose went from 54% to 46%. The observed difference in the penumbra region is primarily due to dose smearing as the detector moves over a steep dose gradient. The dose-rate transient on the other hand only accounts for a dose shift of around 0.5% as seen in figure 9.

Study limitations
The gated measurements with a moving target were performed using a broad beam (3 cm diameter) with static MLC fields (non-IMRT) and a simple sinusoidal target motion. This is a simplification of the clinical situation, in which treatment plans usually consist of several IMRT fields and breath-hold techniques are used. This can be seen as a limitation as the effect of transients could be larger for small beams or more complex fields more closely resembling real treatment plans. However, without the simplification in our setup, it will be hard to pinpoint the effect of dose-rate transients on delivered dose, and the phenomena studied are also present at the clinic. As the cine images and tracking information is available in the MRIdian, it is possible to simulate the effect of dose smearing and the dose-rate transient, if the dose-rate transient is known for the particular machine. The maximum difference in dose of 3.1% between the gated measurement with a moving target and the corresponding measurement with a static target found in this study (table 3) will likely be smaller in a clinical setup as moving tumors are often treated in guided breath-holds with a typical gating time of more than 20 s. Ehrbar et al (2022) found that residual motion in gated breath-hold treatments of liver and lung caused a 1.7% reduction in dose compared to the planned dose without taking a dose-rate transient into account. The dose smearing effect created by the movement has a greater impact. In terms of clinical impact, hypofractionated treatments are more sensitive to dose uncertainties as demonstrated by Brunt et al (2020) which found that a 4% increase in dose led to a significant increase in normal tissue toxicity.

QA based on monitor-unit linearity test
The monitor unit linearity test in figure 10 demonstrates well working monitor chambers within uncertainties but showed no deviations which could reveal the doserate transients in figure 3. The offsets between 1 and 5 monitor units were similar for all three linacs regardless of differences in dose-rate transients. This supports that most of the dose-rate transients were due to changes in fluence rate which will not affect a well-working monitor chamber rather than changes in beam quality which would affect the monitor chamber reading.

Conclusion
The study shows that the existence of dose-rate transients is not unique to the Viewray MRIdian in Copenhagen previously identified (Klavsen et al 2022). The source of the transients could not be identified conclusively, but it is likely to consist of multiple components including an initial change in photon fluence rate and an initial change in x-ray beam quality. For gated treatments, this caused a reduction of more than 1% dose delivered at the central part of the beam (i.e. in the primary treatment volume) for the studied cyclic-motion treatment plan. Quality assurance of this effect should therefore be considered when gated treatment with the Viewray MRIdian is implemented clinically.