# Characterization of a Modified Clinical Linear Accelerator for Ultra-High Dose Rate Beam Delivery
## 2 Materials and Methods
### Dosimetry Measurements  
The beam energy verification after the upgrade was performed by measuring the percentage depth dose (PDD) curves in both conventional and UHDR modes. In the first case, a complete PDD curve was obtained using the Advanced Markus (AM) chamber (Type 34045, PTW, Freiburg, Germany) and a 1D scanner water tank (Sun Nuclear Corporation, Melbourne, FL, USA) (Figure 3a), following the TRS-398 guidelines of the International Atomic Energy Agency (IAEA) [18]. In the case of UHDR irradiations, PDD curves were collected by placing EBT XD GaFChromic films (Ashland, Bridgewater, MA, USA) between PMMA slabs to avoid distortions due to the large charge recombination observed in ICs at large dose rates [19; 20]. PDD curves were measured with the water phantom and the PMMA slabs at the isocenter position both with and without the applicator (irradiation settings _ii_ and \(i\), respectively). A holder secured the applicator at the crosshair foil position, with its exit side aligned with the surface of the water tank or the PMMA (Figure 3b). The detector was always placed transversely at the center of the field. From these curves, it was possible to calculate dosimetry parameters such as the practical range (R\({}_{\text{P}}\)) and the depths where the absorbed dose was 50% (R\({}_{50}\)) and 80%  
Figure 3: (**a**) One-dimensional water phantom positioned at the isocenter (i); (**b**) setup with the applicator (ii) and the PMMA phantom. (R\({}_{80}\)) of the maximum. Based on R\({}_{50}\), the reference depth (z\({}_{\text{ref}}\)), the position at which the evaluation of the absorbed dose should be performed, was calculated as recommended in [18] as follows:  
\[z_{ref}=0.6R_{50}-0.1 \tag{1}\]  
EBT XD GafChromic films were used to quantify the beam output in terms of total dose, average dose per pulse (DPP), instantaneous dose rate in the pulse and the average dose rate. The instantaneous dose rate in the pulse was obtained from the average DPP divided by the pulse duration \(\tau\) (2 \(\upmu\)s), while the average dose rate was calculated from the number of delivered pulses (N) at a fixed PRF of 100 Hz, as reported by [PERSON] et al. [13]. \[Average\ Dose\ Rate=\frac{total\ dose}{\frac{N-1}{PRF}+\tau} \tag{2}\]  
For these measurements, EBT XD films were placed in the PMMA phantom with a buildup thickness of 18 mm. This thickness was selected based on the z\({}_{\text{ref}}\) values determined from the PDD analysis and considering the correction factors for transforming the water thickness into the equivalent PMMA thickness. In the wedge tray position, due to space restrictions, the films were irradiated without buildup. Furthermore, GafChromic films were also used to evaluate the beam spatial profiles in both irradiation modalities. When using the films, the total number of pulses N was changed according to the setting to avoid film saturation. The absolute dose of the irradiated films was evaluated in terms of net optical density (OD), as established in the manufacturer's guidelines and protocols [21; 22]. For this purpose, the films were scanned with a flatbed color scanner (Model: Epson Expression 12000 XL) used in transmission mode, acquiring 48-bit RGB images with a resolution of 100 dpi. The films were scanned twice: before the irradiation to save the background image and 24 h after irradiation to determine the absorbed dose. The analysis of the images was executed with a program developed in Matlab, where the net OD was calculated from the pixel-by-pixel difference between the OD of the irradiated and the background images. The net ODs were calculated over a Region of Interest (ROI) of the same size to the active area of the AM chamber (0.20 cm\({}^{2}\)). The conversion from the net OD to dose was executed with two different calibration curves: the first one relying on the 10 MeV conventional electron beam in the 0.5-10 Gy range, and the second one on the 9 MeV UHDR electron beam delivered at the CPFR (Pisa, Italy) for the range of 0.5-40 Gy.