The commissioning that consisted in comparison between calculated and measured dose was carried out in three steps: the beam model validation, the beam output calibration verification and the commissioning tests. Through these steps, PDD, profiles, output factors and absolute dose points were extracted from the TPS and compared to measurements performed with ten different MR compatible detectors whose characteristics and use in this study are reported in Table 1.

Table 1 Characteristics of the detectors and their use in the studyReference data: TPS calculation

Plans were created on the Viewray Treatment Planning Station (Version 5.4.0.97) to generate Monte Carlo reference data under 0.35 T magnetic field with 1 mm resolution and 0.5% accuracy. The relative reference data were calculated on a numerical water phantom with a voxel size of 1 × 1 × 1 mm3 and the investigated field sizes varied from 0.42 × 0.415 cm2 to 27.2 × 24.07 cm2. PDD and profiles were extracted. The TPS profiles were fitted with a bivariate penalized spline function and the resulting curves were resampled with a 0.1 mm resolution for a better accuracy. For the output factors, output calibration verification and the commissioning tests, calculated absolute dose points were collected.

Relative dose measurements for beam model validation

All the measurements with active detectors were performed with the Beamscan MR water tank (PTW, Freiburg, Germany). The studied field sizes ranged from 0.42 × 0.415 cm2 to 27.2 × 24.07 cm2.

The PDD were measured at 78 cm SSD with seven active detectors (PTW 34045 Markus, PTW 31010, PTW 31021 and PTW 31022 ionization chambers, PTW 60019 microdiamond, PTW 60023 and SN Edge diodes).

The X/Y profiles were measured at 85 cm SSD and 5 cm depth with six active detectors (PTW 31010, PTW 31021, PTW 31022, PTW 60019, PTW 60023 and Sun Nuclear Edge). For the comparison between measured and calculated profiles, the following usual parameters were analysed: field size, penumbra [24], unflatness and symmetry [25] (“Appendix A”).

Figure 1 represents the profiles orientation in a view from the gantry at 0° when the patient is in head first supine position. The X-profiles and the Y-profiles are in the patient’s right to left and feet to head direction respectively.

Fig. 1

Profiles orientation. View of the field from the gantry at 0° with the patient in head first supine position

For a better interpretation of the profile results some complementary measurements were performed. Firstly, additional EBT3 film profiles for the 0.84 × 0.83 cm2 field size were carried out. Secondly, angular response of high resolution detectors relative to the PTW 31010 ionization chamber was assessed in the water tank (to avoid air gap effects), at SSD 78 cm, 12 cm depth with a 4.16 × 4.15 cm2 field size. The PTW 60019 microdiamond and PTW 60023 diode were oriented parallel to the beam at gantry 0° (perpendicular to the magnetic field direction) while the PTW 31010 ionization chamber and the SN Edge diode were perpendicular to the beam. Due to the limited space of the water tank in the MR-linac, angles from − 60 to + 60° with 10° steps were evaluated. To highlight the magnetic field impact, the same measurements were performed on a Truebeam Stx (Varian, Palo Alto, CA, USA) with a 6 MV FFF beam of 4 × 4 cm2 field size. Due to the water tank dimensions, the experimental set-up was at SSD 97 cm and 3 cm depth.

Output factors were measured at 85 cm SSD and 5 cm depth with six active detectors (PTW 31010, PTW 31021, PTW 31022, PTW 60019, PTW 60023 and Sun Nuclear Edge) and two passive dosemeters (LiF µcubes and EBT3 radiochromics films). Output factors with active detectors were performed from field sizes ranging from 0.42 × 0.415 cm2 to 27.4 × 24.07 cm2 whereas passive dosemeters were used for small field measurements, i.e. from 0.42 × 0.415 cm2 to 9.96 × 9.96 cm2; the reference field being 9.96 × 9.96 cm2 in both cases. OF measurements with the passive dosemeters were performed in a virtual water phantom. For EBT3 films, a calibration curve from 0.5 to 4 Gy was performed at 85 cm SSD and 5 cm depth with the 9.96 × 9.96 cm2 field size. Film preparation, lecture and analysis were performed as described in Moignier et al. [26]. Four LiF µcubes and EBT3 films were used for each field size. Two series of measurements were carried out on two different days. Additional OF measurements at 80 cm SSD and 10 cm depth were performed with PTW 60019, PTW 60023 and SN Edge detectors for field sizes ranging from 0.415 × 0.42 cm2 to 9.96 × 9.96 cm2. For output factors with active detectors, prior CAX measurements allowed the effective point of measurement to be adjusted and the detector to be centered on the maximum peak of intensity. As active detectors response in small fields is perturbated due to volume averaging and lack of electronic equilibrium, the code of practice TRS 483 provides output correction factors (k\(\frac)\) to be used to correct output factors measurements in small radiation fields. For a better interpretation of the output factor results, k\(\frac\) given by the IAEA TRS 483 and the ones from Weber et al. for the PTW 60023 [27] were applied to the values measured with the active detectors even if they are not published to correct measured OF under magnetic field. For the 1.66 × 1.66 cm2 field size, corrections factors were applied for PTW 31010, PTW, 31022, PTW 60019, PTW 60023 and SN edge detectors. For the 0.84 × 0.83 cm2 field size, only the three high resolution detectors output factors were corrected whereas for the smallest field size (0.42 × 0.415 cm2), values for the PTW 60019 only were corrected. Regarding the passive dosimeters, it has been shown that, on conventional linear accelerator, both don’t require correction factors for small fields [28, 29]. In addition, at magnetic field strength of 0.35 T, Darafsheh et al. [30] and Xhaferllari et al. [31] didn’t notice any significant difference in the response of EBT3 film irradiated in the presence or absence of an external magnetic field.

Absolute dose verification for beam output calibration

To check the beam output calibration, dose point measurements were performed at 90 cm SAD and 1.5 cm depth (zmax) for a 9.96 × 9.96 cm2 field size in a Beamscan MR water tank and in a Virtual Water phantom (Standard Imaging, WI, USA) with three ionization chambers (PTW 31010, PTW 31021 and Exradin A28 MR) suitable for reference dosimetry and positioned parallel to the magnetic field.

In addition, the consistency between calculated and measured dose with these three ionization chambers was investigated for beams of 9.96 × 9.96 cm2 field size, first in the daily phantom provided by Viewray with one beam at gantry 0°, secondly with the Delta 4 MR phantom (Scandidos, Uppsala, Sweden) with four beams at gantry 45, 110, 250 and 315° to avoid the two orthogonal detector plans. The use of different solid phantoms aimed at determining the less impacted ionization chamber by the air gap and therefore the most suitable for dose point measurement in different steps of the QA process.

The beam quality correction factors applied on the measurements for the absolute dose determination were the specific correction factors in presence of magnetic field kB,Q,Q0// published by Krauss et al.

Absolute dose verification for commissioningDose point measurements

Dose point measurements were performed using the most suitable ionization chamber determined in the previous section.

The IAEA-TECDOC-1583 recommends performing some beam specific calculation checks for a small, a medium and a large field size [32]. Dose points verifications at SSD 78 and 85 cm were performed in the water tank for points located on the central axis, off-axis and out of the field at 1.5, 5, 10 and 13 (SSD 85 cm) or 20 (SSD 78 cm) cm depth for a 3.32 × 3.32, 9.96 × 9.96, 19.92 × 19.92 cm2 and a complex field size (Fig. 2).

Fig. 2

Beam specific calculation checks. Dose point verifications on the center axis, off-axis and out of the field for 3.32 × 3.32 cm2 (a), 9.96 × 9.96 cm2 (b), 19.92 × 19.92 cm2 (c) and a complex field (d)

Points in the field were assessed with relative error whereas points out of the beam used relative normalised error [32] (“Appendix B”).

End to end clinical tests

The CIRS 002LFC thorax phantom (Sun Nuclear, FL, USA) was scanned on a Discovery RT Computed Tomography (GE, USA). On reconstructed CT images with a voxel size of 1 × 1 × 1.5 mm3, the clinical commissioning tests were done following the IAEA-TECDOC-1583 recommendations. The eight clinical cases were simulated on the TPS and the dose points reported were the mean dose in a 5 mm diameter sphere in the position 1, 2, 5, 7, 8 and 10 (Fig. 3).

Fig. 3

Dose points of the clinical test cases in the CIRS thorax phantom

Due to the specificity of the machine, no collimator rotations and no beam wedges were applied. The non-coplanar beam of case 8 was simulated with the Pseudo 4Pi function using the beam divergence. Each point was assessed with the relative reference normalised error [32].

Zeus algorithm validation

All the dose points measured during the two previous commissioning steps were used to validate Zeus, the secondary Monte Carlo calculation included in the Treatment Planning and Delivery Station (TPDS) and used for adaptive fractions as a secondary calculation check. Adaptive fractions were simulated on the MRIdian with the daily QA phantom that can provide enough MR signals. The original contours were rigidly copied and the original electronic density was applied. The 5 mm diameter sphere structures created in the original plan made it possible to have the mean Zeus calculated dose in the report.

Statistical analysis

The smoothing and comparisons between the PDD, the dose profiles in X/Y directions as well as their associated parameters (penumbra, field size, unflatness and symmetry) were performed within the generalized additive models (GAM) framework [33].

More precisely, the measured PDD can be viewed as a noisy discretization of a two-dimensional continuous process modelled as a function of depth and field size. In the same way, the measured dose profile parameters can be presented as a noisy discretization of a one dimensional continuous process modelled as a function of field size. This function was estimated from the data as a summation of a smoothing (univariate or bivariate) spline function intercept representing Monte Carlo TPS calculations (the reference) and GAM interaction terms with each MR detectors.

The comparisons between the TPS and the detector measurements was then based on the statistical inference of these interaction terms in the following way: the model provides pointwise estimation of the difference between TPS and the detector as well as the associated confidence intervals over all the continuum grid. Then, we considered in this study a significant difference when the confidence interval did not contain zero. This approach permitted to highlight the significant differences along the estimated curves and surfaces according to the field size and depth values (see Figs. 4, 5, 6, 8).

Fig. 4

PDD absolute difference between TPS (reference) and the different detectors according to the field size and the depth. In white, deviations to TPS are not statistically significant

Fig. 5

Y-profile symmetry of TPS data and detectors according to the field size with a multivariate regression approach. The blue segments in the x-axis highlight the range of values where the difference is statistically significant

Fig. 6

Y-profile left penumbra of TPS data and detectors according to the field size. The blue segments in the x-axis highlight the range of values where the difference is statistically significant

All analyses were performed using the mgcv package (https://cran.r-project.org/web/packages/mgcv/) of the R software version 4.2.1 2022.