Dosimetry with a clinical linac adapted to FLASH electron beams

Abstract Purpose To assess dosimetric properties and identify required updates to commonly used protocols (including use of film and ionization chamber) pertaining to a clinical linac configured into FLASH (ultra‐high dose rate) electron mode. Methods An 18MV photon beam of a Varian iX linac was converted to FLASH electron beam by replacing the target and the flattening filter with an electron scattering foil. The dose was prescribed by entering the MUs through the console. Fundamental beam properties, including energy, dose rate, dose reproducibility, field size, and dose rate dependence on the SAD, were examined in preparation for radiobiological experiments. Gafchromic EBT‐XD film was evaluated for usability in measurements at ultra‐high dose rates by comparing the measured dose to the inverse square model. Selected previously reported models of chamber efficiencies were fitted to measurements in a broad range of dose rates. Results The performance of the modified linac was found adequate for FLASH radiobiological experiments. With exception of the increase in the dose per MU on increase in the repetition rate, all fundamental beam properties proved to be in line with expectations developed with conventional linacs. The field size followed the theorem of similar triangles. The highest average dose rate (2 × 104 Gy/s) was found next to the internal monitor chamber, with the field size of FWHM = 1.5 cm. Independence of the dose readings on the dose rate (up to 2 × 104 Gy/s) was demonstrated for the EBT‐XD film. A model of recombination in an ionization chamber was identified that provided good agreement with the measured chamber efficiencies for the average dose rates up to at least 2 × 103 Gy/s. Conclusion Dosimetric measurements were performed to characterize a linac converted to FLASH dose rates. Gafchromic EBT‐XD film and dose rate‐corrected cc13 ionization chamber were demonstrated usable at FLASH dose rates.


| INTRODUCTION
The FLASH effect is defined as improved normal tissue sparing in radiation therapy when the dose rates are considerably higher (over 40 Gy/s) than those currently employed in clinical practice (about 0.2 Gy/s). 1 Improved normal tissue sparing in cell lines and in small animals were reported for FLASH radiation therapy. [2][3][4] Efforts to understand the radiobiological mechanism, including the role of oxygen immediately after a microsecond pulse, are ongoing. 3,5 Recently, a report on the first patient treated with FLASH radiotherapy was published. 6 Experimental linear accelerators are available for delivering FLASH dose rates, including Oriatron (PMB-Alcen, France). Linacs designed for intraoperative radiation therapy, which operate at high dose per pulse sequence, can be also used, for example, Novac 7 (New Radiant Technology, Italy). Recently, clinical linear accelerators were modified to deliver electron beams at FLASH dose rates by tuning nonclinical electron beams (including the pulse forming network voltage and the gun filament current), and by using pulsecounting circuits to control beam delivery. 7,8 Dosimetric characterization methodology of FLASH beams was described for modified clinical linacs and experimental linacs. 7,9 Gafchromic film (EBT2 or EBT3, Ashland, Bridgewater, NJ, USA) was predominantly used in measurements of dose. The independence of Gafchromic EBT and OSL on the dose rate (much higher in FLASH beams than in conventional linacs) was demonstrated through comparing to measurements with a Faraday cup and an integrating current transformer. 10 Beam current monitoring was used to show similar independence for EBT3 film. 11 Ionization chambers typically used in conventional linac dosimetry suffer from dose rate dependence at ultra-high dose rates. This was addressed for parallel-plate ionization chambers, [12][13][14][15] through modeling ion recombination using the work of Boag et al. 16,17 In this paper, we propose a simplified method of controlling a modified clinical Varian linac (Varian Medical Systems, Inc., Palo Alto, CA, USA) in ultra-high dose rate regime by entering the MUs through the console instead of counting pulses with a microcontroller. We evaluate the dosimetric characteristics of the FLASH electron beam that are important in radiobiological applications. In particular, we investigate dose rate and field size trade-off at various practically achievable distances from the scattering foil. We demonstrate usefulness of film dosimetry at FLASH rates for EBT-XD Gafchromic film (less sensitive than other types of Gafchromic film, hence preferred for our highdose measurements) by comparing to a model, not to other detectors.
We characterize response of a cylindrical chamber at ultra-high dose rates, and establish a dose rate-dependent correction by fitting the measured data to previously reported theoretical models.

2.A | Linac conversion to FLASH
A clinically decommissioned Varian iX linac was used in the experiments. The diagram of the system is shown in Fig. 1, together with the locations (not in scale) where the dose was measured. A FLASH 18MeV electron beam was created from an 18MV photon beam (600 MU/min unless noted otherwise) through retracting the target, and replacing the flattening filter with an electron scattering foil.
The scattering foil was mounted on the carousel as in a conventional electron beam. While it is always an electron beam travelling through the waveguide for both photon and electron clinical beams, a clinical nominally photon beam was chosen to be modified instead of modifying a clinical electron beam. This allowed taking advantage of significantly higher beam current in the waveguide for a photon beam with a flattening filter (where the target efficiency combined with attenuation in the flattening filter result in fluence reduction) compared to a typical electron beam. The 18MV photon board was used. Most of the measurements reported herein were performed with the 9 MeV scattering foil, but a few measurements were done with the 16-MeV foil. Unless stated otherwise, the subsequent paragraphs pertain to measurements with the 9-MeV foil. The carousel with the scattering foils and the flattening filter, and the target were prevented from moving to the default locations by rerouting the pneumatic system that controls the movement of the carousel and of the target. Servo control of the dose and of the steering was disabled as the internal monitor chamber was expected to provide signal incompatible with the linac electronic circuits. The beam was tuned using a standard linac maintenance protocol (Varian, C-Series Clinac ® High Energy Technical Maintenance 2 Lab Guide, Rev. E).
The dose to be delivered was programmed by entering the number of MUs at the operator console in the service mode. This method is different from the method employed by Schüler et al., where a microcontroller connected to the linac gating system was used to terminate the beam. 7

2.B | Dosimetry
Three dosimeters were used: Gafchromic EBT-XD film, OSL and cc13 ion chamber (IBA Dosimetry, Schwarzenbruck, Germany). EBT-XD film was employed instead of more commonly used EBT3. Much lower sensitivity compared to EBT3 allowed achieving higher accuracy in measurements of high doses encountered in our FLASH beam measurements, where the optical density approaches saturation (for EBT3), and the ratio of the optical density to its uncertainty becomes unfavorable. In our experiments, the film was used follow- not on the location along the axis. The film was always scanned 1 hr after the irradiation to eliminate the error associated with timedependent changes of the optical density of the irradiated film following the irradiation. Film optical density was converted to dose using in-house written software.
The OSL detectors were also calibrated in a conventional electrons beam and using solid water. During the subsequent experiments, both the film and the OSL were sandwiched between layers of superflab bolus (1.2 g/cc density, 2 cm thick upstream, 1 cm thick downstream) to keep the measurements in the flat portion of the PDD. Non-water like bolus was used as there was not enough room to place slabs of solid water inside the linac head, but the small difference in the density from the density of water has little impact on our data: only about −3% dose difference, which is small compared to other uncertainties.
Out of the three detectors employed herein, only an ion chamber can be used in vivo during irradiations of radiobiological samples, as both film and OSL require post-processing. The chamber was placed across the beam central axis (CAX) in a wax phantom (0.9 g/cc density, 6.6 cm diameter across the beam). Non-water like medium was also chosen for practical reasons, and the errors caused by such choice are small, about 1%, compared to other uncertainties in this work. Even though the chamber was calibrated using a standard protocol (in a conventional electron beam at the reference conditions), the charge collection efficiency is known to decrease with an increase of the dose rate, 16 and this effect will be investigated in the As a surrogate for in vivo animal radiobiology studies, a twopiece phantom of a mouse was 3D-printed (using PLA filament, 1.3 g/cc density) based on a CT scan of a mouse. EBT-XD film was sandwiched in the coronal plane between the two halves of the phantom, and placed such that the film was orthogonal to the CAX.

2.C | Efficiency of an ionization chamber
The efficiency f of charge collection by an ion chamber is defined as the ratio of the dose reported by the chamber to the actual dose.
The former is the ionization charge converted to the dose using a calibration in a conventional beam, while the dose concurrently measured with film was used as the latter. b) Boag classical model of recombination 16 derived for parallel-plate chambers: where u = k DPP, and k depends on the gas in the chamber, the bias, and the distance between the electrodes. We are not aware of a similar model developed specifically for cylindrical chambers like cc13. A regression algorithm was used here with the factor k being the fitted parameter, while DPP was the independent variable. c) and d) Ion recombination in the presence of free electrons (electrons liberated by an ionizing particle of the measured beam, which remain free prior to reaching the collecting electrode), also for parallel-plate chambers: where the free-electron fraction p is independent on the DPP. 17 In addition to k, we used p as the fitted parameter. Equations (2) and (3) were originally derived assuming different charge distributions in the chamber.
The fitting weights were set as the inverse of the squared ordinate in order to assign equal percent uncertainty to all data points, in spite of the ordinate varying by almost two orders of magnitude.
Neither the temperature and the pressure variations, nor the bias polarity, were corrected for, but these are second-order corrections compared to the corrections required for FLASH dose rates.

3.A | Beam energy
The beam energy was measured to confirm the energy of the electrons in the waveguide was set correctly, that is, 18 MV beam was This is dramatically different than a conventional electron beam, where the measured charge is independent of the repetition rate.
We hypothesize the relationship observed in the FLASH beam is due to the signal of the internal monitor chamber not being fully reset prior to the arrival of the next pulse. This is conceptually illus- Dependence of the field size on the SAD is plotted in Fig. 8. We

3.E | Two-dimensional dose distribution in a mouse phantom
The two-dimensional (2D) maps of the relative dose distribution in the mouse phantom are presented in Fig. 9 for both the conven-

3.G | The dose rate vs. SAD
Dose-rate dependence on the distance from the nominal beam center is plotted in Fig. 11 for various dosimeters: film, OSL, and cc13 chamber. Both the average and the during-the-pulse instantaneous dose rate are shown. Also plotted is the theoretical model, which is the inverse square law (IVSL) with the effective beam center set to 13.0 cm downstream from the nominal beam center. This value was taken from the x axis intercept in the plot of the field size divergence vs. the distance from the nominal beam center, as reported in Fig. 8

3.H | Chamber efficiency
The measured chamber efficiencies for various dose rates are plotted in Fig  Similarly to the film data, the OSL measurements presented in Figure 11 agree with the inverse-square model.
where the time of irradiation τ can be established by multiplying the MU by MU-to-time conversion factor established for the beam e.g.
from analysis of video of Cherenkov glow. Incidentally, this conversion factor is independent of the SAD. Inserting Equation 4 into the relationship between the chamber efficiency and the dose rate (as seen in Fig. 12) leads to an analytically unsolvable equation where both sides depend on f, but such an equation can be solved numerically in real time. It should be noted that any discrepancies in modeling of the chamber efficiency will affect accuracy of deciphering the value of the chamber efficiency using this procedure, and for example, a logistic model 12 or even simple spline interpolation might provide adequate results.

| CONCLUSION
It was demonstrated the dose in a FLASH electron beam (obtained by replacing the target in a nominally photon beam with an electron scattering foil) can be prescribed by entering the MUs through the console, similarly to the way a conventional linac is controlled. A set of basic dosimetric tests was performed, and, with exception of the dependence on the repetition rate, the results exhibited similar trends as in the conventional beams. Applicability of the EBT-XD film to dosimetry in FLASH mode was shown. A model of ion recombination in cc13 ionization chamber was identified to eliminate doserate dependence from dose measurements.

ACKNOWLEDGMENTS
We thank Don Ta, Dave Moreau, Gustavo Fernandez, Ayaz Rahim for technical assistance with the linac conversion, and Brennen Dobberthien for assistance during measurements.

AUTHOR CONTRIBU TI ONS
Stanislaw Szpala wrote the manuscript, designed and performed most of the measurements. Vicky Huang designed and 3D printed the mouse phantom, and performed the subsequent measurements.
Yingli Zhao participated is selected measurements. Alastair Kyle and Andrew Minchinton assisted with measurements utilizing Cherenkov radiation. Tania Karan participated in the initial setup of the experiment. Kirpal Kohli initiated and supervised the project.

CONF LICT OF I NTEREST
No conflict of interest.

D A T A A V A I L A B I L I T Y S T A T E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.