Dosimetric accuracy of dynamic couch rotation during volumetric modulated arc therapy (DCR-VMAT) for primary brain tumours

Radiotherapy treatment plans using dynamic couch rotation during volumetric modulated arc therapy (DCR-VMAT) reduce the dose to organs at risk (OARs) compared to coplanar VMAT, while maintaining the dose to the planning target volume (PTV). This paper seeks to validate this finding with measurements. DCR-VMAT treatment plans were produced for five patients with primary brain tumours and delivered using a commercial linear accelerator (linac). Dosimetric accuracy was assessed using point dose and radiochromic film measurements. Linac-recorded mechanical errors were assessed by extracting deviations from log files for multi-leaf collimator (MLC), couch, and gantry positions every 20 ms. Dose distributions, reconstructed from every fifth log file sample, were calculated and used to determine deviations from the treatment plans. Median (range) treatment delivery times were 125 s (123–133 s) for DCR-VMAT, compared to 78 s (64–130 s) for coplanar VMAT. Absolute point doses were 0.8% (0.6%–1.7%) higher than prediction. For coronal and sagittal films, respectively, 99.2% (96.7%–100%) and 98.1% (92.9%–99.0%) of pixels above a 20% low dose threshold reported gamma  <1 for 3% and 3 mm criteria. Log file analysis showed similar gantry rotation root-mean-square error (RMSE) for VMAT and DCR-VMAT. Couch rotation RMSE for DCR-VMAT was 0.091° (0.086–0.102°). For delivered dose reconstructions, 100% of pixels above a 5% low dose threshold reported gamma  <1 for 2% and 2 mm criteria in all cases. DCR-VMAT, for the primary brain tumour cases studied, can be delivered accurately using a commercial linac.


Introduction
Radiotherapy treatment plans that use dynamic couch rotation during volumetric modulated arc therapy (DCR-VMAT) improve organ at risk (OAR) sparing over coplanar VMAT, while maintaining planning target volume (PTV) dose coverage (Podgorsak et al 1988, Krayenbuehl et al 2006, Shaitelman et al 2011, Yang et al 2011, Fahimian et al 2013, Popescu et al 2013, Smyth et al 2013, Liang et al 2015, MacDonald and Thomas 2015, Papp et al 2015, Wild et al 2015, Smyth et al 2016, Dong et al 2018, Fix et al 2018, Langhans et al 2018, Lyu et al 2018, Smyth et al 2019. Single-arc DCR-VMAT using optimized trajectories has been shown to reduce the contralateral hippocampus, temporal lobe, and cochlea mean dose by 30%, 29% and 14%, respectively, for a cohort of fifteen primary brain tumour cases (Smyth et al 2016). However, to fully realize this modelled OAR sparing, DCR-VMAT plans must be delivered accurately. The International Commission on Radiation Units and Measurements (ICRU) recommends that 85% of measurement points should be within 5% or 5 mm of the planned dose (ICRU 2010), although stricter criteria of 3% and 3 mm are generally used in practice (Clark et al 2014). If delivered doses are significantly different from prediction, this could increase the risk of side effects or compromise tumour control. In addition, clinical adoption of DCR-VMAT would be limited if its delivery is Dosimetric accuracy of dynamic couch rotation during volumetric modulated arc therapy (DCR-VMAT) for primary brain tumours significantly slower than coplanar VMAT and requires patient treatment appointments to be extended beyond their current duration.
Dosimetric accuracy and mechanical errors have been reported for some dynamic couch rotation techniques. Fahimian et al (2013) and Liang et al (2015) investigate the dosimetric accuracy of trajectory modulated arc therapy (TMAT), a combination of dynamic couch rotation and fixed gantry rotation, for two accelerated partial breast irradiation (APBI) cases. Manser et al (2019) and Fix et al (2018) report the dosimetric accuracy of DCR-VMAT for a prostate case using a manually defined trajectory and a head and neck case using a geometrically optimized trajectory, respectively. As well as dosimetric accuracy,  quantify linacreported mechanical errors during delivery for their mathematically-defined trajectory-based VMAT (TVMAT) technique for four intracranial stereotactic plans from linac log files. Log files record the machine parameters regularly during beam delivery, with the period between log samples depending on the combination of linac manufacturer and control system version (Pasler et al 2015).
This paper focuses on investigating the dosimetric accuracy of single-arc DCR-VMAT plans for five primary brain tumour cases. The dosimetric effect of mechanical errors and the static approximation of dynamic couch rotation used during treatment plan dose calculation are investigated for the first time by reconstructing delivered dose distributions from log files. Finally, results are benchmarked against the corresponding coplanar VMAT plans for each of the five cases studied.

Beam modelling
A TrueBeam (Varian Medical Systems, Sunnyvale, CA) linac was modelled in the Pinnacle 3 (v9.10, Philips Medical, Madison, WI) and in-house AutoBeam (Bedford 2009(Bedford , 2013 treatment planning systems (TPS). TrueBeam is the only currently available machine capable of delivering dynamic couch rotation treatment plans, however in principle DCR-VMAT can be delivered on any VMAT capable C-arm linac.
Modelling was performed for a 6 MV beam within Pinnacle 3 using its auto-modelling features and the literature (Chang et al 2012, Glide-Hurst et al 2013, Philips Medical 2013 to inform modelling parameters. Validation was performed using a 30 cm × 30 cm × 30 cm water phantom with dose calculated on a 2.0 mm × 2.0 mm × 2.0 mm grid. Absolute point doses, relative output factors, percentage depth doses, and relative dose profiles were compared with validation measurements for jaw-defined field sizes. Validation of modulated deliveries was performed by measuring the dosimetric accuracy of coplanar VMAT plans for each patient case.

Treatment planning and delivery
VMAT and DCR-VMAT plans, each using a single arc, were produced for five patient cases with primary brain tumours (table 1). Treatment plans for the TrueBeam model were optimized in AutoBeam (v5.5a) to receive 54 Gy in 30 fractions using the objectives described in table 2. During treatment plan optimization, jaws under the multi-leaf collimator (MLC) banks were set as static and retracted to 10 cm in preparation for TrueBeam delivery. Plans were exported to Pinnacle 3 for final dose calculation using the local clinical standard settings of a 2.5 mm × 2.5 mm × 2.5 mm dose grid resolution and the adaptive convolve algorithm. Dose calculation for DCR-VMAT was performed using multiple static control points, each with associated gantry and couch positions, as is standard for coplanar VMAT within Pinnacle 3 .
For DCR-VMAT plans, patient-specific trajectories were determined using the geometric heuristic optimization technique described previously (Smyth et al 2013(Smyth et al , 2016. The organs at risk and their relative importance values used during treatment plan optimization were also used for trajectory optimization (table 2). Each DCR-VMAT trajectory used a single gantry arc from 179° to 181°, with maximum couch and gantry rotations between adjacent control points of 2°. No additional processing or smoothing was performed on the trajectories prior to treatment planning or delivery. Couch rotation speed between adjacent control points was not explicitly included in treatment plan optimization but was determined by the linac control system at delivery.
As dynamic couch motion during beam delivery was not supported within the clinical TrueBeam control software, plans were delivered using research and development access with motion restrictions removed ('Devel-  (Mishra et al 2014). The steps from trajectory optimization to plan delivery, comparisons performed, and systems used are summarized in figure 1.

Dosimetric accuracy
A 30 cm × 30 cm × 30 cm phantom, consisting of multiple slabs of solid water, was used for dosimetric verification. The expected dose distribution for each treatment plan when delivered to the verification phantom was calculated in Pinnacle 3 . The adaptive convolve algorithm and a 2.0 mm × 2.0 mm × 2.0 mm resolution dose grid were used for all cases.
For each plan, a position for point dose measurement was identified in a region of homogeneous dose within the PTV. A region of interest (ROI) that approximated the 0.125 cm 3 collecting volume of a Semiflex ionisation chamber (PTW, Freiburg, Germany) was contoured, centred on the measurement position, and the mean dose to the ROI for a single fraction delivery defined the predicted dose. Measurements were performed using the Semiflex chamber and a Unidos electrometer (PTW, Freiburg, Germany); three measurements were taken and averaged for each plan.
Radiochromic film measurements were performed using EBT3 (Lot number 04051602; Ashland Advanced Materials, Bridgewater, NJ). To characterize the dose to colour value conversion for the film batch, six strips were cut from a single sheet of film and irradiated to 25, 50, 100, 200, 400 and 800 cGy in a water-equivalent phantom, in line with Lewis and Chan (2015) and manufacturer recommendations 1 . A seventh film strip was left unirradiated. Films were scanned using an Epson 11000XL flatbed scanner (Epson America, Inc., Long Beach, CA) in transmission mode, with a resolution of 72 dpi. To reduce uncertainties caused by film curling, a 2 mm thick glass compression plate was placed on top of the films during scanning (Palmer et al 2015). Films were analysed using FilmQA Pro (v3.0, Ashland Advanced Materials, Bridgewater, NJ) software.
Coronal and sagittal planes through the PTV were measured for each VMAT and DCR-VMAT plan. Two film strips were cut from each film sheet, one of which was irradiated to 170 cGy, and used to scale the calibration curve for that measurement (Lewis et al 2012). Dosimetry was analysed using the triple channel method to mitigate uncertainties due to the film scanner and variations in film thickness (Micke et al 2011). Film to plan registration was performed by aligning the marked film isocentre position with the plan isocentre position, small discrepancies between marked and actual film position were removed using the optimization option in FilmQA Pro. Comparison of red colour channel measurements with predictions was performed using two-dimensional gamma analysis with criteria of 3% (global dose difference normalisation) and 3 mm (γ 3G/3 ). Analysis with a stricter distance to agreement criterion of 1 mm (γ 3G/1 ) was also performed. When reporting passing rates for gamma analysis, pixels below a low dose threshold of 20% were excluded (Clark et al 2014).

Linac log file analysis
Linac log files were acquired during delivery of each treatment plan. TrueBeam log files record the primary readout of the linac motion axes and MLC leaf positions every 20 ms during beam delivery, as well as values interpolated from the original DICOM plan (Eckhause et al 2015). These form 'delivered' and 'expected' log file values, respectively, making it possible to determine mechanical errors every 20 ms during treatment. Expected and delivered log file values for gantry rotation, couch rotation, and all MLC leaves were extracted using a MATLAB (v2010b, The Mathworks, Nantick, MA) script. For each parameter the root-mean-square error (RMSE) was calculated according to equation (1).
where N was the total number of log file samples, and D and E were the delivered and expected log file parameter values for sample n.
To determine if RMSE values of individual MLC leaves were correlated with the total motion of the MLC leaf, Spearman's rank correlation coefficients were calculated in MATLAB. This was performed for each MLC leaf bank for both VMAT and DCR-VMAT. If the p-value associated with a correlation coefficient was less than 0.05, the correlation was judged to be statistically significant.

Linac log file dose reconstruction
The dosimetric difference between the Pinnacle 3 treatment plan and dynamic plan delivery was determined by reconstructing a plan from each log file. VMAT and DCR-VMAT plans were created in Pinnacle 3 with control points specified by the delivered log file values of gantry rotation, couch rotation, aperture shape, and cumulative monitor units. To reduce the control points to a manageable number for calculation within Pinnacle 3 , every fifth log file sample was used, resulting in a beam with ten control points per second. Reconstructed plan doses were calculated on the patient CT data using the local clinical standard settings of a 2.5 mm × 2.5 mm × 2.5 mm dose grid resolution and the adaptive convolve algorithm.
Planned and delivered dose cubes were exported to CERR v5.2 (Deasy et al 2003) for comparison using threedimensional (3D) gamma analysis for all voxels above a 5% low dose threshold with 2% and 2 mm acceptance criteria (γ 2G/2 ). Dose criteria were relative to the global maximum of the planned dose cube, which was used as the reference distribution. Both dose calculations shared the same beam model, dose grid settings, and dose calculation algorithm. This left two sources of error in this comparison: (1) the number of control points used to calculate the dose, and (2) the mechanical errors recorded in the delivered log file. Therefore, stricter gamma analysis criteria were used for these comparisons than for the radiochromic film measurements. To identify the main cause of any discrepancies, an additional dose distribution was reconstructed from the expected linac log files and compared with the original treatment plan.

Beam modelling
Absolute point dose measurements and relative output factors of jaw-defined fields used for TrueBeam model validation were within ±1% of predictions. Pinnacle 3 percentage depth doses and profiles agreed with validation measurements to within 2% or 2 mm (generally 1% or 1 mm). Results for the validation of modulated delivery using coplanar VMAT plans are presented in section 3.3 to allow direct comparison against DCR-VMAT measurements.

Dosimetric accuracy
Median (range) differences in absolute dose from plan prediction were 0.8% (0.6%-1.7%) for DCR-VMAT compared with 1.3% (0.6%-1.6%) for VMAT. Complete results are presented in table 4. Linac output on the day of measurement, which remained as a potential source of uncertainty in the point dose results, was 0.4% higher than ideal.

Linac log file analysis
Linac log file analysis showed similar gantry rotation RMSE for coplanar VMAT (median 0.055°, range 0.051-0.067°) and DCR-VMAT (median 0.057°, range 0.051-0.059°). Couch rotation RMSE for DCR-VMAT was 0.091° (0.086-0.102°). Full results are presented in table 6. Maximum couch rotation error for all VMAT cases was 0.002°. RMSE for individual MLC leaves are presented in figure 7. Although all MLC errors were small, statistically significant (p < 0.001) strong correlations were found between RMSE and the total recorded leaf motion calculated from delivered log files. Spearman coefficients were 0.82 and 0.88 for coplanar VMAT (leaf banks A and B, respectively) and 0.83 for DCR-VMAT (both leaf banks). Gamma analysis maps comparing DCR-VMAT treatment plan dose and reconstructed dose from delivered log files are shown in figure 8. These evaluate the effect of errors due to the different number of control points used to calculate the dose and mechanical errors recorded in the log file. All comparisons reported 100% of voxels within the body ROI passing a γ 2G/2 , however, some case-specific differences were seen in the gamma analysis maps. The expected dose reconstructions, which excluded the effect of log file reported delivery errors, also reported 100% of voxels passing γ 2G/2 when compared to the plan dose. Absolute dose differences between delivered and expected dose reconstructions were within 0.3 Gy for all cases.

Linac log file dose reconstruction
As the version of CERR used could not perform gamma analysis with local dose difference normalisation, or with distance criteria below half the voxel size, reanalysis with stricter gamma criteria (e.g. γ 2L/2 or γ 1G/1 ) was not performed. However, analysis using γ 2G/2 criteria was sufficient to identify any significant differences resulting from the finer positional sampling of the log file dose reconstructions for the clinical standard dose calculation resolution used.

Discussion
This paper describes the dosimetric accuracy of single arc DCR-VMAT for five primary brain tumour cases. DCR-VMAT meets clinical standards of dosimetric accuracy, with point dose measurements all within 2% and gamma analysis (γ 3G/3 ) pass rates >90% (most >95%) for coronal and sagittal radiochromic film measurements. There are several possible sources of uncertainty in the point dose and film measurements, including any discrepancies between the delineated chamber volume and the effective measurement point in the phantom, any deviation of the actual solid water block densities from the water density assigned in the TPS, errors in phantom positioning and alignment, and uncertainties in the film calibration or readout. We have attempted to minimize these    (2018) have calculated the uncertainty in absolute dose measurement for triple-channel film dosimetry using Epson 10000XL flatbed scanners to be 2%-3% for the target doses measured in this study. For doses close to the low dose threshold used in our analysis, they calculate that the uncertainty increases to 10%. The scope of this study is limited to conventionally fractionated primary brain tumours to evaluate the feasibility of DCR-VMAT treatment delivery for a site where it has demonstrated potential clinical benefit (Smyth et al 2016). Although primary brain tumours may not require the extensive MLC modulation necessary for sites such as the head and neck (Fix et al 2018), more complex trajectories can be used due to the larger non-collisional space around the patient . Further investigation of the plan quality and dosimetric accuracy for other sites that may benefit from DCR-VMAT, including stereotactic indications in the brain and body, is warranted in a future study.
A full dosimetric comparison of the two techniques used in this paper has been presented in Smyth et al (2016) for a 15-patient cohort of primary brain tumours. Relevant dose volume histogram parameters for PTV and OARs, integral dose, conformity, homogeneity, and gradient indices are presented and analysed. DCR-VMAT is shown to produce statistically significant differences in PTV homogeneity that are judged to be clinically acceptable in light of significant OAR sparing over VMAT. The cases presented here are a subset of that cohort and the plans produced differ from Smyth et al (2016) only in the linac model used (TrueBeam versus Synergy (Elekta AB, Stockholm, Sweden) with Agility MLC) and the method of target dose normalisation in Pinnacle 3 (not normalised versus normalised to PTV mean dose). In this work, vertex segments of arc are permitted during trajectory optimization, which could result in an undesirable volume of very low exit dose through the patient's length. While some of this low dose can be constrained during plan optimization, an alternative approach is to explicitly exclude from trajectory optimization any beam orientations where the beam would continue through the patient beyond the limits of their CT scan (Wild et al 2015).
These results are consistent with the data presented in the literature to date for other techniques using dynamic couch rotation. Fahimian et al (2013) report a single TMAT delivery for a prone partial breast treatment plan. The deviation of point dose measurement from plan prediction is 2.4%, while the gamma analysis pass rate for γ 3G/3 is 93%. In a follow-up paper, Liang et al (2015) also report results for a single delivery. For that case, the deviation in measured point dose from plan prediction is 1.6% and the gamma analysis pass rate for γ 3G/3 is 90.2%.  report the validation of TVMAT is within 2.2%, and 96%-100% of film pixels meet gamma criteria of γ 2G/2 for the four plans under investigation. Manser et al (2019) investigate the dosimetric accuracy of a manually defined DCR-VMAT trajectory for a prostate case and find 96% of diodes meet gamma criteria of γ 2G/2 in comparison to a research Monte Carlo dose calculation. Fix et al (2018) report 99.5% of radiochromic film pixels meet gamma criteria of γ 2G/2 for a head and neck DCR-VMAT treatment plan that uses geometric trajectory optimization and a Monte Carlo dose calculation. The results in our paper use a commercial adaptive convolution superposition dose calculation algorithm and are consistent with reports of coplanar VMAT in a national audit using a diode array (Clark et al 2014). The median (range) passing rate for γ 3G/3 is 98.8% (83.8%-100%) for linac and TPS combinations that do not share a common vendor (Type 2 combinations), as is the case in this work.
Passing rates for γ 3G/3 may be insensitive to clinically significant errors introduced during treatment planning or TPS commissioning, particularly when using arrays, but these risks can be mitigated by evaluating deviations in point doses and dose profiles (Nelms et al 2013) as performed in our paper. Gamma analysis results can also vary significantly between measurement devices and calculation software (Hussein et al 2017). Future work on DCR-VMAT should include a systematic investigation of gamma analysis sensitivity to technique-specific error combinations (e.g. miscalibration of machine parameters, such as couch rotation and MLC position, or patient misalignment) for a range of clinical sites using multiple measurement devices. A limitation of the measurements in this paper is that they do not use an anthropomorphic phantom. However, other groups also report results in water equivalent plastic (Fahimian et al 2013, Liang et al 2015, Fix et al 2018. Using a cubic phantom, as in our study, may increase the chance of detecting errors that have been caused by inaccurate MLC, gantry, and couch synchronization, when compared to an anthropomorphic head phantom with more gradual changes in contour. Another limitation is that the measurements in this work only measure planar dose distributions. Although it is common to use detector arrays that may also interpolate between multiple measurement planes and evaluate the full three-dimensional dose distribution, the use of these devices generally requires a coplanar delivery. Verification of DCR-VMAT plans must also include the contrib-   ution of the dynamic couch motion, which rules out the use of gantry-mounted diode arrays. Alternative volumetric measurement techniques, such as gel dosimetry, should be explored in future work. Log file reported errors that have been determined for DCR-VMAT are small and have limited dosimetric effect.  analyse log files for TVMAT deliveries and report couch rotation RMSE of 0.041-0.051° and gantry rotation RMSE of 0.042-0.050°. The larger couch rotation error results in this paper could be due to differences in inertia between the TVMAT and DCR-VMAT techniques. TVMAT rotates the couch fully in one direction before sweeping back, while the optimized DCR-VMAT trajectories that have been investigated in this paper allow either clockwise or anti-clockwise rotations throughout (figure 2). In a previous study, a simulated systematic 2° error in couch rotation for DCR-VMAT increases OAR dose by up to 10% (Smyth et al 2013), although a misalignment of that size is unlikely based on log file analysis. This work investigates log file reported errors, however, Agnew et al (2014) and Neal et al (2016) demonstrate that there can be discrepancies between the log file reported and physical positions of linac components that are not identified by log file analysis.  recommend validating the accuracy of log file records and suggest techniques for couch rotation.
Although not performed in our study, this validation step would be crucial before using log file values for pretreatment delivery quality assurance in the absence of dosimetric measurements such as those presented here.
This paper is the first to report linac log file dose reconstruction for dynamic couch rotation techniques. The large number of samples that has been used in reconstruction gives a close approximation of dynamic dose calcul ation and demonstrates that couch and gantry control point spacing of 2° models dynamic delivery on the treatment machine to within 2% and 2 mm. The dosimetric effect of linac reported mechanical errors, determined from the difference between delivered log file and expected log file dose reconstructions, was within 0.3 Gy for all cases in this study. Similar investigations for coplanar VMAT using Monte Carlo dose calculation find differences of approximately 2%, which is consistent with the results in this paper (Teke et al 2010, Boylan et al 2013. An alternative to static approximation during dose calculation is to model dynamic linac motion directly within Monte Carlo dose calculation (Fix et   DCR-VMAT delivery is slower than VMAT, with median (range) delivery times of 125 s (123-133 s) and 78 s (64-130 s), respectively. These differences are unlikely to be clinically important, especially when considering other aspects of the patient treatment such as pre-treatment verification imaging. Comparison with published data is challenging due to the different techniques and dose prescriptions that have been evaluated (Fahimian et al 2013, Liang et al 2015, Wild et al 2015, Fix et al 2018. Wild et al (2015) estimate times based on machine constraints for three intracranial plans, with results from 3.9 min to 6.9 min depending on the complexity of the trajectory and patient geometry. Fix et al (2018) report an average increase in beam on time of 20% for DCR-VMAT when compared with VMAT for five cases across four different tumour sites. For the brain cases that have been investigated in our study, the median increase in delivery time is 60.3% but range from a 5.4% decrease to a 108% increase. However, in the worst case the absolute increase in delivery time of DCR-VMAT over the corresponding VMAT plan is 69 s.
As with other delivery techniques, rigorous quality control testing of DCR-VMAT with strict tolerances is necessary (Wilson and Gete 2017). As well as existing tests for VMAT, additional tests to confirm accurate syn- Figure 8. Gamma analysis results, comparing the treatment plan dose distribution against the dose distribution reconstructed from delivered log file parameters. Axial, coronal and sagittal views are presented for all cases. Gamma analysis used acceptance criteria of 2% and 2 mm for doses above a 5% threshold. Red colour wash indicates γ > 1. chronous motion of linac gantry, couch, and MLC are required. Proposed synchronicity tests for VMAT (Bedford et al 2015, Mans et al 2016 and TMAT (Yu et al 2014) rely on the linac's on-board imaging device and therefore may not be feasible for DCR-VMAT due to the risk of collisions during non-coplanar motion.
Although we have shown that DCR-VMAT can be delivered accurately for the five cases studied, issues such as patient safety and comfort must be investigated prior to clinical implementation. Rotating the patient during treatment could induce intrafractional motion, which may be mitigated using improved patient immobilization. Dynamic couch motion and the potential for patient-gantry collisions could also affect patient compliance. Performing a 'Day Zero' simulation of the treatment with the patient present may be a simple method of providing reassurance, assuming technological issues have been resolved. Patient stability during dynamic couch motion should be further investigated in future work.

Conclusion
Results from the five patient cases in this paper suggest that clinical implementation of dynamic couch rotation during VMAT is feasible for primary brain tumours, provided that issues around patient safety, motion, and compliance are resolved. DCR-VMAT plans have been delivered to within a clinically acceptable level of accuracy and with a maximum delivery time of around 2 min using a commercial linear accelerator. Future work should focus on investigating patient compliance and intrafractional motion, and move towards implementing DCR-VMAT for primary brain tumours within a clinical trial.