Magnetic field influence on the light yield from fiber-coupled BCF-60 plastic scintillators of relevance for output factor dosimetry in MR-linacs

Organic plastic scintillators are of interest for ionizing radiation dosimetry in megavoltage photon beams because plastic scintillators have a mass density very similar to that of water. This leads to insignificant perturbation of the electron fluence at the point of measurement in a water phantom. This feature is a benefit for dosimetry in strong magnetic fields (e.g., 1.5 T) as found in linacs with magnetic resonance imaging. The objective of this work was to quantify if the light yield per dose for the scintillating fiber BCF-60 material from Saint-Gobain Ceramics and Plastics Inc. is constant regardless of the magnetic flux density. This question is of importance for establishing traceable measurement in MR linacs using this detector type. Experiments were carried out using an accelerator combined with an electromagnet (max 0.7 T). Scintillator probes were read out using chromatic stem-removal techniques based on two optical channels or full spectral information. Reference dosimetry was carried out with PTW31010 and PTW31021 ionization chambers. TOPAS/GEANT4 was used for modelling. The light yield per dose for the BCF-60 was found to be strongly influenced by the magnitude of the magnetic field from about 1 mT to 0.7 T. The light yield per dose increased (1.3 ± 0.2)% (k = 1) from 1 mT to 10 mT and it increased (4.5 ± 0.9)% (k = 1) from 0 T to 0.7 T. Previous studies of the influence of magnetic fields on medical scintillator dosimetry have been unable to clearly identify if observed changes in scintillator response with magnetic field strength were related to changes in dose, stem signal removal, or scintillator light yield. In the current study of BCF-60, we see a clear change in light yield with magnetic field, and none of the other effects.


Introduction
Fiber-coupled plastic scintillators are of interest for ionizing radiation dosimetry in megavoltage photon beams used for radiotherapy [1].This is primarily because the small scintillators (e.g. 1 mm diameter and 2 mm length) have a mass density very similar to that of water leading to insignificant perturbation of the electron fluence at the point of measurement in a water phantom relative to when the detector is absent.In contrast, perturbation can be a significant issue for air-filled ionization chambers [2,3], especially under non-reference conditions as found during field output factor measurements in small photon beams lacking partial charge-particle equilibrium [4,5].The ability for plastic scintillators to provide near perturbationfree measurements becomes even more relevant for measurements in the strong magnetic fields (currently up to 1.5 T [6]) of linacs with magnetic resonance (MR) imaging [7][8][9][10].This is because the Lorentz force leads to additional perturbation of electron trajectories in situations when the mass density of the detector material and water are not the same [3,11].
Additional advantages for dosimetry in MR-linacs are that plastic scintillators have a fast response (< 1ns) and that the read out is purely optical.Using an all-plastic detector probe based on a PMMA optical fiber cable such measurements can therefore be made without disturbing the MR imaging [12].This enables time-resolved dose-per-pulse measurements during dynamic phantom tests simulating motion management solutions where the linac beam is gated on the basis of MR scanner images analyzed in real time during the treatment [13].
A significant imperfection of scintillators is that the production of light per dose depends on the beam quality.Most importantly, it is known that the light yield per dose decreases for electrons with an energy below about 100 keV relative to electrons with higher energies [14].This so-called quenching issue is not just a problem in proton [15] and kV photon beams [16], also MV photon beams are affected [17].The quenching issue can, however, be expected to be minimal for relative dosimetry as long as the fraction of low-energy electrons remains the same for the beams under consideration.
Studies aimed for high-energy particle physics have demonstrated that the scintillator light yield tends to increase with magnetic field strength [18,19].A typical value seems to be 5−10% increase when changing the magnetic flux density (called B-field in most of the following) from 0 T to 2 T.However, little discussion has been devoted to the question of how the scintillator light yield is affected by the magnetic field during fiber-coupled dosimetry related to radiotherapy, and previous studies of this question [20][21][22] have not lead to conclusive results as recently pointed out by Looe et al [23].
Stefanowicz et al [20] saw a clear effect for both BCF-12 and BCF-60 scintillating fibers from Saint-Gobain Ceramics and Plastics Inc. (USA), but the authors suggested that the effect observed was due to changes in the energy deposition pattern of the radiation field rather than to scintillator effects.Simiele et al [21] performed a very detailed study of the BCF-12 scintillator but found significant uncertainty associated with the investigated stem removal techniques and refrained from reporting a clear conclusion on the specific influence of magnetic field on the scintillator light yield.Therriault-Proulx et al [22] studied the BCF-60 scintillator and suggested that the observed effect could possibly be explained by factors other than the changes in scintillator light yield.
The influence of magnetic fields on scintillators for radiotherapy dosimetry could directly compromise the traceability of such detectors in MR linacs, for example, if a scintillator dosimetry system is calibrated without magnetic field for measurements in an MRlinac, if scintillator dosimetry is used for measurements in the same MR-linac before and after the superconducting magnets are ramped up, or if scintillators are used both for measurements at the MR-linac iso-center and for out-of-field positions outside the main B-field [24].It could also be highly relevant if scintillators are used as reference for characterization of other detectors in an electromagnet set-up with variable B-field similar to what was used in this study.
The current study was specifically motivated by the results later presented in this manuscript as figure 8.During measurements of field output factors, we saw a significant, but unexplained, increase in light output of the order of 5% when changing the B-field from 0 T to 0.7 T. Was this increase caused by true changes of the dose at the point of measurement or imperfections in the scintillator dosimetry related to the B-field?The primary objective of this study therefore was to investigate the hypothesis that the light yield from plastic scintillators are strongly sensitive to the presence of a magnetic field.
We chose to study the green BCF-60 scintillating fiber as this material was used in the motivating experiment and because this material is in common use for scintillator dosimetry in the medical field [1,25,26].A key challenge was to separate the scintillator light from the stem signal, primarily Cerenkov light induced in the fiber cable by the ionizing radiation.Since this stem signal is known to change significantly with B-field, the stem-removal procedure would need to be effective and associated with an uncertainty much lower than the actual changes in light yield.A second key challenge was to estimate the dose in the scintillator by independent means during changing B-fields [6].

Sources of radiation
All irradiations were conducted using a Truebeam linear accelerator (Varian, USA) at the Technical University of Denmark providing 6 MV FFF or 10 MV FFF beams, where FFF is short for flattening-filter free.For most of the measurements, an external transmission monitor chamber (PTW7862, Germany) was placed in the head of the gantry to document the stability of the linac, including the lack of output variations in response to B-field changes by the electromagnet.As the output from the linac was stable at the 0.1%-level, no corrections were applied.

Electromagnet set-up
The magnetic field was provided by a water-cooled GMW 3473-70 electromagnet (USA) and a Danfysik System 8000 (Denmark) power supply (max 70 A at 65 V DC).The distance between the pole shoes of the magnet was 10 cm.The magnetic field strength was established using a transverse hall probe (Hirst Magnetic Instruments GM08, UK).To set the magnetic field to a desired value, the magnet was first run through a special sequence of alternating zero and maximum magnetic field values with the same polarity as the desired field.The relationship between current and measured magnetic field was highly linear below 0.4 T. The field uniformity was better than 1% from the point of the main measurements and 15 mm away in any direction.At a vertical distance of 30 mm and 50 mm from the center, the field dropped by 4% and 12%, respectively.An Optosigma xyz-scanner (Japan) was used for precise positioning of the detectors in a small water phantom (width, height, depth: 10 cm×19 cm×21 cm).The TRUfix adapter system from PTW (Germany) was for used for positioning of detectors.Figure 1 shows the basic geometry of the experimental set-up.Irradiations were carried out with detectors at the center of the electromagnet at the central axis of the horizontal beam at a distance of 81.6 cm from the linac iso-center (i.e.181.6 cm from the virtual source of the linac).This extended distance was chosen to avoid any influence of the electromagnet on the performance of the linac The detectors were positioned at 7 cm depth of water in either horizontal orientation (i.e.detector axis parallel with the beam) or vertical orientation (i.e.detector axis perpendicular with the beam as shown in figure 1).Irradiations were conducted at 5 cm×5 cm, 3 cm×3 cm or 1 cm×1 cm field sizes.These are the nominal field sizes at the iso-center.Scanning was used to position detectors at the central axis of the beam for B = 0 T.

Scintillator dosimetry
The main study was based on measurements using two scintillator probes previously manufactured as reported by Beierholm et al [27]: One with 2 mm of BCF-60 (id F134) attached to 9 m of fiber cable and the other (id F122) with 10 mm of BCF-60 attached to 10 m of fiber cable.For both probes, GH-4001-P PMMA fiber cable from Mitsubishi (Japan) was used (2.2 mm outer jacket diameter).The scintillator probes comprised a tight-fitting cover of light protection plastic material (i.e.without any room for air gaps).To reach the read-out instrumentation placed outside the linac bunker, one additional 12 m patch cord of quartz (FP1000URT, id F212) from Thorlabs (Germany) was used.The insert shows a scintillator in perpendicular orientation (vertical).The blue arrow is the direction of the transversal B-field if B is positive.With the magnetic field in this direction, an electron set in motion in the water in the same direction as the photon beam will feel a force in the downward direction.Likewise, a reversed B-field (negative B) will produce an upward force.
Scintillator signals were acquired using dose-perpulse ME40 reader instruments from the Technical University of Denmark [25,28].For the main measurements, we integrated all light produced from the start of the linear synchronization pulse and 100 μs onwards (i.e.we integrated much longer than the 5 μs duration of the actual gun pulse from the linac).Background correction was performed using a second reading of identical duration, but delayed 10 μs relative to the initial integration period.This technique provided a high signal-to-noise ratio.The ME40 provided measurements of light from a scintillator using two channels representing a blue part of the spectrum (from 400 nm to 475 nm) and a green part (from 520 nm to 530 nm).
Full scintillator spectra were recorded using an Oriel model 77 250 (USA) monochromator attached to a Hamamatsu 5784 (Japan) photomultiplier tube, decoupled from the blue channel of a ME40 system.The spectral data were not corrected for filtration through the fiber cable or the spectral response of the photomultiplier tube.
Supplementary measurements were carried out in a solid-water phantom (Gammex, USA) outside the electromagnet using a 20 cm long BCF-60 scintillating fiber attached to a PMMA fiber cable identical to that used for the main scintillator probes described above.The scintillator was horizontal, and the linac beam was vertical.These measurements were mainly used for identification of individual sources of light relevant for the decomposition of spectral measurements into meaningful components.

Two-channel stem removal
For each irradiation, we obtained background-corrected instrument readings in two channels: M 1 and M 2 representing the intensity of light in a blue and a green part of the optical spectrum, respectively [29].We estimated the dose to the scintillator, D using the model: where a 1 and a 2 are calibration coefficients that can be found from multiple irradiations where the same dose is given to the scintillator while changing the position of the fiber cable in the beam (i.e. with different amounts of stem signal).The technique relies on the critical assumption that the spectral shapes of the stem signal and the scintillator remain constant for the conditions at which the system is calibrated and used.
Further details about the technique can be found elsewhere [25,30].

Full spectral stem removal
For each configuration, we measured the total optical spectrum in N channels (e.g.325 channels covering the range from 305 nm to 630 nm) as represented by the vector M [26].We assumed that this spectrum can be decomposed into three components: The goodness of the model can be assessed from the magnitude and structure of the residuals  M .In this work, we use reference spectra individually normalized to unity at the maximum intensity point.These fixed reference spectra were found by first measuring the pure stem signal from a fiber cable irradiated with the scntillator outside the primary beam.The green component was obtained by irradiating a long BCF-60 scintillating fiber.The blue component was obtained by analyzing the spectrum from a short BCF-60 scintillator.

Normalized response
All results reported in this work are of a relative nature.We set the accelerator to give a fixed number of monitor units per irradiation (50 MU or more) or per time unit (400 MU/min) while, for example, changing the B-field under otherwise fixed conditions.Typically, we will signify the scintillator signal by the normalized response where the response at B = 0 T at the maximum dose point or at the central axis of the beam is used as reference.

Ionization chamber dosimetry
Although the accelerator gives a fixed number of monitor units in a sequence of irradiations, the dose to water (at the position of the detector) or the dose to the detector volume may change with B-field.To quantify any potential changes in light yield per dose to the scintillator, we therefore used ionization chamber dosimetry as reference in order to map relative changes in dose to water with magnetic field at the position of the scintillators.Measurements were carried out using PTW31010 and PTW31021 ionization chambers connected to a PTW unidos Webline electrometer (Germany).We used the chambers in horizontal orientation, parallel with the beam as to minimize the effect of the magnetic field.We used the following model for relative measurements: where D w is the absorbed dose to water in the absence of the ionization chamber and M IC is the corrected ionization-chamber reading at a given B-field.The k B -factor accounts for the change in ratio between D w and the dose to the air cavity of the ionization chamber for the given beam quality and B-field.We use Monte-Carlo computed values of k B published by Cervantes et al [5] for PTW31010 and by Delfs et al [31] for PTW31021.

Light-yield estimation
To correct the measured (relative) dose to water for a given B-field to the absorbed dose to the scintillator, we performed simple computations with TOPAS version 3.9 [32] running Geant4-10-07-patch-03 with the g4em-standard_opt4 physics list.We modelled a Varian 6 MV beam using published photon spectra [33] in a geometry resembling the key features of the set-up in figure 1.For detector materials we used G4_WATER and G4_POLYSTYRENE for water and BCF-60 scintillator, respectively.The computations gave values for the k d -correction factor defined as: where D d is the dose to the scintillator and where D w is the absorbed dose to water in the absence of the luminescence detector at a given B-field.We define the light yield Y per dose as: where M d is the photomultiplier reading (i.e. the light intensity in a single optical spectrometer channel or the total intensity over a range of channels) and D d is the absorbed dose to the material of the luminescence detector.Again, we only do relative measurements, and applying the ionization chamber results we can quantify the light yield changes with magnetic field as:

Monte-Carlo simulations of small-field profile
The Monte-Carlo model was also used for simulations of the vertical profile of a 1 cm×1 cm (nominal) 6 FFF field in the same geometry as given above.In this case, the TOPAS beam parameters (BeamAngularCutoffX=0.30°and BeamAngularSpreadX=0.286476°) were slightly modified to match the profile measured with the 2 mm scintillator for B = 0 T. The aim of the modelling was to estimate the expected change in dose to water and doseprofiles in water for the investigated geometry when the magnetic field was changed from 0 T to ± 0.7 T for this small-field scenario.

Reference spectra
Figure 2 shows stem spectra obtained by irradiating the fiber cable in perpendicular orientation with the 2 mm scintillator outside the primary beam while changing the magnetic field (horizontal 10FFF beam with nominal 5 cm×5 cm nominal field size).The data supports that the shape of the stem spectra can be taken to be independent of the B-field in the range from 0 T to±0.7 T.
Figure 3 shows the spectral response when irradiating different parts of a 20 cm long BCF-60 scintillating fiber attached to a clear GH-4001 fiber cable (vertical 10FFF beam with 3 cm×3 cm nominal field size).The attachment between fiber and scintillator was made using a 1 mm diameter hollow guide tube without any use of glue or chemicals.The probe was placed horizontally at 2 cm depth in a solid water phantom having its top surface at the iso-center (100 cm from the virtual linac source).In panel A of the figure, the irradiation was centered 46 mm from the interface between the BCF-60 and the fiber cable (coordinate 0 mm).We note that the spectrum is dominated by the stem signal.In panel B, the beam center was 9 mm into the BCF-60 and both fiber cable and scintillator was therefore in the primary beam.In addition to the stem signal, the spectrum is here seen to be dominated by two clear peaks: one in the green region and one in the blue region.In the subsequent panels, the center of the beam was moved further into the BCF-60 and away from the fiber cable.We note that the green peak of the BCF-60 is completely dominating the spectrum in panel D where the beam was centered at 116 mm from the beginning of the BCF-60 (i.e.no stem signal or blue component could be identified here).As BCF-60 is a green scintillator, we investigated the source of the blue component in a supplementary experiment where a quartz fiber cable was attached to the BCF-60 scintillating fiber rather than GH-4001.Using the quartz cable did, however, not significantly diminish the blue component, suggesting that the blue component originates from the BCF-60.
The data in figure 2 was used for estimaing the reference stem signal spectrum of equation (2).The data in panel D of figure 3 was used as a first estimate of the green reference spectrum.Subtracting these two components from a total spectrum, one can estimate the blue component.This process was repeated iteratively until convergence was reached.The fixed reference spectra were then used for analysis of all spectra without further change.

Full spectral analysis
Measurements with a large scintillator in perpendicular orientation provides the best signal-to-noise ratio for a study of the effect of magnetic fields on the scintillator light production (see figure A1 in the Supplementary Material).
Figure 4 therefore shows results of irradiating the 10 mm BCF-60 dosimeter probe in perpendicular orientation in the electromagnet set-up of figure 1 with B-fields equal to 0 T, ±0.28 T, and ±0.7 T (horizontal 10FFF beam with 5 cm×5 cm nominal field size).Similar results (not shown) were obtained at ±0.04 T and ±0.14 T. Motivated by the results of  Each panel is marked with the position of the 3 cm×3 cm beam center relative to that end of the BCF-60 that was attached to the fiber cable.A positive coordinate (e.g. 9 mm for panel B) means that the beam center was inside the BCF-60.The data within each panel have been normalized to unity at the maximum.The numerical peak value given within each panel allow for a comparison in signal size from panel to panel.For example, the meaning of scale=0.34 in panel B is that the maximum within panel B is 34% of the maximum in panel D.
the previous experiment, the data were decomposed into three components representing the stem signal, the green component, and the blue component.The residuals shown in the figure give the difference between the total signal and the sum of those three components.The magnetic field is seen to have a strong effect on the stem signal: the stem signal increases when the Lorentz force on electrons are upwards into the fiber cable (i.e. when B is negative) and the stem signal decreases relative to B = 0 T when the electrons are forced downwards (i.e. when B is positive).The low residual values support the use of the decomposition model.We note that in spite of large variations in stem signals, the estimated contributions to the green and blue components, respectively, are essentially indistinguishable when comparing positive and negative field directions for the same field strength.We further note that the data indicate a significant increase of about 4.5% of maximum signal strength of green and blue components when going from 0 T to ±0.7 T.
Figure 5 shows the coefficients for the green and blue components (i.e.α green and α blue ) resulting from the spectral analysis in equation (2).The response from the 10 mm scintillator is seen to increase gradually by about 4.5% from B = 0 T to ± 0.7 T. The curves for the green and blue components are similar.The blue component curve is, however, not as symmetrical around B = 0 T as the curve for the green component.

Two-channel analysis
Figure 6 shows the scintillator dose estimates using the two-channel chromatic stem removal technique for both scintillators (2 mm and 10 mm) and orientations (parallel and perpendicular) for B-fields in the range from below 1 mT to 0.7 T (horizontal 6FFF beam in the electromagnet set-up with 5 cm×5 cm nominal field size).We see that the response of the scintillators for all four combinations increases by 4-5 % when approaching ±0.7 T. We further note a monotonic increase of about 1% from 1 mT to 10 mT.The data  For example, we see that the green component at ± 0.7 T is about 4.5% larger than green component at B = 0 T. As will be discussed later, the data is an estimate of changes in light yield assuming that the absorbed dose to the scintillator volume was the same for all irradiations regardless of B-field. Figure 6.Response of the scintillators as function of the log 10 -transformed value of the absolute B-field in tesla using the two-channel stem removal procedure (individually normalized at B=0 T) for two sizes (2 mm and 10 mm) and orientations (parallel or perpendicular) with the 6FFF beam.Simple loess models have been fitted to the data within each panel.Significant increase in response is noted over the full range of tested B-fields from below 1 mT to 0.7 T. A plateau seems to exist between 10 mT and 100 mT. may suggest a plateau from 10 mT to 100 mT.A lack of symmetry (i.e.differences between results for positive and negative values of the B-field) for the 10 mm scintillator in perpendicular orientation may suggest that the stem removal procedure was not optimal for this configuration.
The sensitivity to low B-fields is further illustrated in figure 7 where the response for the two separate ME40 channels are plotted.The blue channel (known to be dominated by the stem signal) is a smooth function of B at B = 0 T whereas the green channel (known to be dominated by the scintillator signal and the stem signal in combination) has an almost step-wise response around B = 0 T.

Effect during output factor measurements
An important effect of the Lorentz force is that the electrons will systematically be moved by the B-field.In the experimental configuration of this work, electrons will tend to be moved upwards for negative B-fields, and downwards for positive B-fields.This effectively means that the dose maximum moves.The  effect is most clearly seen with a small field.Figure 8 shows vertical profiles recorded with the xyz-scanner mounted on the electromagnet and the 2 mm scintillator probe in perpendicular orientation.The probe was calibrated for B = 0 T conditions (i.e. for the B = 0 T light yield and signal spectra), and the doses in the figure are relative to the maximum dose point at B = 0 T using the two-channel stem removal procedure.The vertical coordinate axis has been adjusted to 0 for this position.Figure 8 shows how the maximum dose point within each measured profile indeed was moved up or down depending on the magnetic field.For 0.7 T, the movement was about 1 mm.For 0.35 T (data not shown), the movement was about 0.5 mm.More interesting, however, we see that the dose estimated by the scintillator was about 4.5% higher when the magnetic field was set to ±0.7 T compared to 0 T. Monte-Carlo computations are also shown in figure 8.Here the predicted movement of the dose maximum was about 0.9 mm at ±0.7 T compared to 0 T (i.e. in good agreement with the experimental data).The model predicted the maximum dose to decrease by about (0.7 ± 0.2)% at ±0.7 T compared to 0 T in significant disagreement with the 4.5% increase estimated from the experimental scintillator results.

Field size influence
To minimize the influence of moving the maximum dose point, the investigations were focussed on broad fields with partial charge-charged particle equilibrium (see figure A2 in the Supplementary Material).We note that the fields are relatively uniform for a nominal 5 cm×5 cm field size.

Ionization chamber dosimetry
The results of the PTW31010 and PTW31021 ionization chamber measurements in parallel orientation as shown in figure 9 with and without k B corrections published by Cervantes et al [5] and Delfs et al [31].

Uncertainty
A simple uncertainty budget for the estimated light yield per dose change when changing the B field from 0 T has been established (table 2).The correction factors (k d and k B ) assume uniform B-fields, and a 0.3% uncertainty component has been added to account for the potential impact of the non-uniformity of the B-field in the electromagnet set-up.

Discussion
4.1.BCF-60 light yield versus B Figures 5 and 6 could be taken as direct measurement of changes in scintillator light yield versus B under the assumption that the dose to the scintillator was the same for each irradiation (i.e.independent of B field).This assumption is reasonable since figure 9 with the results of the small ionization chambers demonstrated that the dose to water at the position of the scintillator light yield measurements changed by less than about 0.5% over the full span of tested B-fields.This was as expected since, for example, O'Brian et al [36] have stated that the magnetic field only slightly changes the absorbed dose to water (∼0.5%) in regions where partial charged-particle equilibrium exists.In addition, the Monte-Carlo computations of the k d -factor for the scintillators were very close to unity (see table 1), suggesting that ratio between the dose to the scintillator and water was essentially independent of the B-fields tested.Based on the uncertainty budget in table 2, we therefore assess that the relative change in light-yield-per-dose for BCF-60 is about (1.3 ± 0.2)% from 1 mT to 10 mT and about (4.5 ± 0.9)% from 0 T to 0.7 T. The indicated uncertainties are standard uncertainties (k = 1).

Low magnetic fields
The results for the low magnetic fields found in this work (figure 6), are similar to what was found by Bertoldi et al [19] for polystyrene based scintillators (i.e.scintillators like BCF-60).They saw a relative light yield increase up to 1-1.8% for a magnitude of the magnetic field up to 10 mT in good agreement with the (1.3 ± 0.2)% from 1 mT to 10 mT found in the current study.

Field size influence
Figure 8 demonstrated how the maximum dose point for a small field can change position with the B-field (cf [23]).The signal from an ideal scintillator detector without sensitivity to the magnetic field positioned at the maximum dose point for B = 0 T (and remaining there) should therefore decrease if the B-field is changed to, say, ±0.7 T. We, however, consistently saw the scintillator signal go up for stronger B-fields relative to 0 T (e.g.figure 5). Figure 8 has spatial resolution, and we see that the ∼5 % change from 0 T to±0.7 T is indeed related to the maximum dose point.For the main experiments, we used two sizes of scintillators (2mm or 10 mm length) to guard against such issues.The max dose point may move about 1 mm from 0 T to ±0.7 T, which should be well covered by the 10 mm long scintillator when used in perpendicular orientation.As an additional guard, we primarily worked with large fields, producing relatively uniform dose distributions at the point of measurements (see figure A2 in the Supplementary Material).

Isolating the scintillator signal
As pointed out by Simiele et al [21] and Therriault-Proulx et al [22], the stem removal procedure is critical for estimating the scintillator light yield.The key issue is to isolate and quantify the signal from the scintillator itself without interference from other sources of light.It was therefore important to measure the scintillator light-yield changes under different stem-signal conditions to demonstrate that the results were robust with respect to this issue.A minimum stem signal was for the 10mm scintillator in perpendicular orientation (figure 4) and the maximum configuration was for the 2 mm scintillator in parallel orientation (see figure A1 the in Supplementary Material).
The two-channel chromatic stem removal technique has been optimized for dosimetry and it does not directly isolate the individual sources of light.After the stem correction, we assume that the response is proportional to the scintillator light.However, it is difficult to judge to what extent the stem removal has been successful for a given measurement.The full spectral analysis of the data was therefore important Table 2. Uncertainty budget (relative standard uncertainty representing 68% of confidence at k = 1) for the estimated change in light-yield per dose (green part of the BCF-60 spectrum) from 0 T to ± 0.7 T using different stem removal techniques, two-channel or full spectral information for the scintillator.The uncertainty components for stem reduction, k B and k d are assumed to scale with the B-field, such that, for example, the measurement of a yield difference between 0 T and 0.35 T would be half of the numbers given in the table.

Component
Type for this study as it explicitly identified and quantified the relative importance of the main three sources of light (stem, green component and blue component).
The decomposition model was based on reference spectra with fixed shapes, independent of B-field.The small residuals in figure 4 support the validity of this model and it supports the key assumption underpinning the use of chromatic stem removal techniques with two channels or full spectral information for measurements in strong magnetic fields.
The influence of B-field on signals in the blue and green channels of the two-channel stem removal procedure (figure 7) clearly showed how the blue channel (dominated by the stem signal) was changing monotonously with B field whereas the green channel (consisting of the green scintillator component superposed by the stem contribution) made a jump at B = 0 T.This is strong 'model-free' evidence showing that the green component from the scintillator is directly affected by the magnetic field near B = 0 T whereas the dose at the position of the scintillator (here represented by the stem signal in the blue channel) is not.

The blue component
The presence of the blue component in the BCF-60 spectra was not unexpected given, for example the spectra published by Wootton and Beddar [34].As was evident from the results of the experiment in figure 3, we assume that the blue component originates from the BCF-60 scintillator itself.However, it will not be present for very long scintillators as the BCF-60 is highly transparent only in the green domain.The blue signal will be strongly attenuated before detection for a long scintillator as shown in panel D of figure 3 where the blue component has vanished after transmission through ∼10 cm of BCF-60.In the spectral decomposition we therefore treated the green and blue components independently although we expect that for a small scintillator, the two components should be strongly correlated.

Temperature influence
Temperature effects could potentially introduce an artificial connection between detector response and B-field.This is because a strong magnetic field in the electromagnet is associated with a significant power consumption by the magnet (approx.4 kW for B = 0.7 T).The magnet is therefore water cooled.However, the magnet can get hot and or cold during transients or long duration of use.This can impact on the temperature of the small water phantom positioned between the magnet pole shoes (see figure 1).The water temperature at the position of the detector was therefore monitored for all experiments.In the main experiments in figure 5, the temperature close to the scintillator ranged from 20.40 °C to 20.73 °C.With a BCF-60 temperarure coefficients of (0.55 ± 0.04) %/K [34,35], we assess that the influence of temperature variations cannot have been a significant source of uncertainty for the light-yield estimates given above.

Conclusions
• The light yield per dose for the BCF-60 scintillator (green component) was found to be strongly influenced by the magnitude of the magnetic field from about 1 mT to 0.7 T (i.e. over the entire range of tested B-fields).For example, the light yield per dose increased about (1.3 ± 0.2)% (k = 1) from 1 mT to 10 mT and it increased about (4.5 ± 0.9)% (k = 1) from 0 T to 0.7 T. The direction of the magnetic field was not found to have any effect on the scintillator light yield.
• The experimental design and analysis minimized, if not eliminated, the influence of B-field driven variations due to changes in dose, max dose point, temperature, and stem signal.The key results were robust against changes in scintillator size (2 mm versus 10 mm), orientation (parallel versus perpendicular), beam field size (small non-equilibrium field versus large field), and stem removal procedure (two-channel technique versus full spectral analysis).
• The study supports that the shape of the spectral components (stem, and green or blue light from the BCF-60 scintillator) remain independent of B-field within the tested conditions.This in turn supports the basic assumption of scintillator dosimetry in MR-linacs based on chromatic removal techniques using the two-channel method or full spectral information.The results are specific for the tested type of fiber cable (GH-4001-P PMMA) and scintillator material (BCF-60) [37,38].
• The findings have implications for calibrations and use of scintillator dosimetry systems: (i) systems need calibration in the same magnetic field as for which they are used, and (ii) it will be difficult to compare scintillator measurement in an MR-linac before and after the magnetic field is ramped up.
• The effect of magnetic field on scintillator light yield is not new for medical dosimetry, and scintillators and magnetic fields have been studied extensively for high-energy particle physics applications [18,19].What is new in this work is that the previous studies related to the influence of magnetic fields on fiber-coupled medical scintillator dosimetry [20,21,26] have been unable to clearly identify if observed changes in scintillator response with magnetic field strength were related to changes in dose, stem signal removal, or scintillator light yield.
In the current study of BCF-60, we see a clear change in light yield with magnetic field, and none of the other effects.

Figure 1 .
Figure 1.Experimental set-up with electromagnet and linear accelerator.The yellow arrow shows the direction of the photon beam.The insert shows a scintillator in perpendicular orientation (vertical).The blue arrow is the direction of the transversal B-field if B is positive.With the magnetic field in this direction, an electron set in motion in the water in the same direction as the photon beam will feel a force in the downward direction.Likewise, a reversed B-field (negative B) will produce an upward force.
α stem , α green and α blue are regression coefficients and where M stem,ref , M green,ref and M blue,ref are reference spectra for the pure stem signal and the pure scintillator signals in the green and blue domain, respectively.The α-coefficients account for production, transmission and detection of each light source.

Figure 2 .
Figure 2. Stem spectra for different B-fields (−0.7, 0 T and 0.7 T) for the 2 mm scintillator probe in perpendicular position relative to the 10FFF beam.The curves have individually been normalized to the maximum intensity point at 440 nm to allow for a direct comparison of the spectral shapes.

Figure 3 .
Figure 3. Spectra for the irradiation of different parts of a 20 cm long BCF-60 scintillator coupled with a blank fiber cable without glue.Each panel is marked with the position of the 3 cm×3 cm beam center relative to that end of the BCF-60 that was attached to the fiber cable.A positive coordinate (e.g. 9 mm for panel B) means that the beam center was inside the BCF-60.The data within each panel have been normalized to unity at the maximum.The numerical peak value given within each panel allow for a comparison in signal size from panel to panel.For example, the meaning of scale=0.34 in panel B is that the maximum within panel B is 34% of the maximum in panel D.

Figure 4 .
Figure 4. Spectra for the irradiation of the 10 mm BCF-60 scintillator at different B-fields (0 T, ±28 T, and ±0.7 T).The scintillator was in perpendicular orientation relative to the 10FFF beam.All data are normalized to the maximum of the green component for B = 0 T. The spectra have been decomposed into three components representing stem signal and green and blue scintillator components, respectively.

Figure 5 .
Figure 5. Model coefficients from the full spectral analysis of the experiment with the 10 mm scintillator in perpendicular orientation shown in figure 4 plus additional data at other B-fields.The coefficients represent the strength of BCF-60 green and blue scintillator components, respectively versus B-field.All values are relative to the signal strength at B = 0 T for the given component.For example, we see that the green component at ± 0.7 T is about 4.5% larger than green component at B = 0 T. As will be discussed later, the data is an estimate of changes in light yield assuming that the absorbed dose to the scintillator volume was the same for all irradiations regardless of B-field.

Figure 7 .
Figure 7. Simultaneous blue and green channel measurements with the ME40 instrument from the 2 mm scintillator in perpendicular orientation versus B-field.These results were used in the two-channel stem removal procedure resulting in the data shown in figure 6.Note the strong relation between the green channel and the B field around B = 0 T. No similar relation was seen for the blue channel.

Figure 8 .
Figure 8. Vertical beam profiles (6FFF) measured with the 2 mm scintillator probe in perpendicular orientation for a 1 cm×1 cm nominal field size.The measurement data (red points) have been normalized to unity for the maximum dose point at B = 0 T. The black circles are Monte Carlo computations of the dose to water normalized in the same way as the measurements.Note that the model predicts the dose at maximum dose point to decrease about 0.7% at ± 0.7 T relatively to 0 T whereas the apparent dose measured with the scintillator increases by about 4.5%.Also note that the maximum dose points for both measurement and model move about 1 mm when the±0.7 T fields are imposed.

Figure 9 .
Figure 9. Ionization chambers (individually normalized at B = 0 T) versus B-field with and without k B -correction applied.The relative standard uncertainty associated with the correction is about 0.6% and 0.3% for chamber PTW31010[5] and PTW31021[31], respectively.

Table 1 .
k d -correction factor as defined in equation (4) computed with TOPAS for detector probes used in the experimental investigation perpendicular with the 6 MV beam direction.All computations were based on the ratio of the dose to the given detector and to a water voxel of an identical size.The uncertainties given in the table are standard uncertainties (k = 1) only representing the statistical nature of the Monte Carlo technique.