Shielding disc backscatter calculations in intraoperative radiotherapy using a Monte Carlo simulation based on the method of energy spectra reconstruction

Dose measurements

A 20 × 30 × 20 cm³ water phantom was fabricated to accommodate a holder for a gafchromic film, a shielding disc, and an applicator fixation (Fig. 1a and b). The grey part of the holder allows placing the gafchromic film parallel to the beam axis and fixing the shielding disc at a precisely defined depth. The film positioning using the holder is fraught with 2 mm uncertainty. The purple part fixes the applicator, allowing the applicator and the shielding disc to be maintained mutually coaxially.

Specific information about phantom components:

1. (1)

   Phantom holder: Original Prusa i3 MK3S + 3D printer (Prusa Research; Prague, Czech Republic) was used to print the phantom holder by fused deposition modelling technology with polylactic acid filament¹¹.

2. (2)

   Shielding disc: the disc made of surgical stainless steel (316 L alloy¹²), 7 cm in diameter and 0.5 cm thick.

3. (3)

   Film: Self-developing EBT4 Gafchromic films (Ashland Inc. Bridgewater, NJ, USA). The EBT4 films are near tissue equivalent, have high spatial resolution (25 μm or less), enable non-uniformity correction using multi-channel dosimetry, and decrease UV/visible light sensitivity compared to previous generations. The film’s response is independent of temperature (up to 60⁰C), atmospheric pressure, and the direction of the irradiation beam. These films allow us to measure the doses (optimal range from 0.2 to 10 Gy) obtained by radiation beams with energies ranging from 100 keV to 18 MeV¹³.

We measured PDD for the 6 MeV, 9 MeV, and 12 MeV electron beams formed by the 6 cm diameter applicator hard docked to the AQURE mobile accelerator (NCNR, Świerk, Poland)¹⁴. The applicator was fixed perpendicular to the water in the phantom, with its tip touching the water’s surface. Two measurement geometries were used. The first one included the shielding disc placed on the R90 depth: 19, 27, and 31 mm for 6, 9, and 12 MeV electron beams, respectively⁴. The disc was positioned parallel to the water surface and aligned coaxially with the electron beam. The EBT4 films were placed along the central axis of the beam (CAX), positioned above (from the water’s surface to the top of the disc) and below (from the bottom surface of the disc to the phantom base) the shielding disc (Fig. 1d). The second setup, which does not include the shielding disc, employs a single sheet of EBT4 film placed in the CAX from the water’s surface to the phantom base (Fig. 1c). Films were irradiated with a dose of 9 Gy defined at the points of maximum dose located below the water surface at the depths of 11, 16, and 18 mm for 6, 9, and 12 MeV electron beams, respectively⁴.

The calibration procedure of the EBT4 films

For the dose calibration, the film was cut into pieces (3 × 3 cm²) and irradiated with an electron beam (20 × 20 cm², 9 MeV, TrueBeam, Varian Medical Systems, USA) in ranges from 1 to 12 Gy. The film was positioned in a water-equivalent solid phantom, where the dose was measured by the ion chamber. The film readout procedure for calibration and measurements was done 36 h after irradiation, using the flatbed scanner Epson Perfection 850 Pro scanner (Seiko Epson Corporation, Japan) with a 4 mm glass plate over the film and with the following parameters: scan resolution 300 dpi, no colour correction, transmission mode, 48-bit Red-Green-Blue (RGB), and saved in the uncompressed TIFF data format. Scans were analysed using Mephysto mc², Film Analyze 1.8 (PTW Freiburg, Freiburg, Germany; single red channel analysis from RGB). For such a calibration procedure, the reading of doses from the film used further in the experiment is subject to 2% uncertainty.

(a) Shielding disc (steel circle) and the holder elements: grey for gafchromic film and shielding disc fixation and purple for fixing the applicator, (b) The setup of the holder with the shielding disc in the phantom, (c) Measurement geometry without the shielding disc, (d) Measurement geometry with the shielding disc.

Monte Carlo simulations

The model of the MC simulation was created in the Geant4 v.11.01.p01 package¹⁵. Based on the technical documentation of the AQURE mobile accelerator, the exact geometry of the beam-forming system was used³ with previously reconstructed energy spectra for 6, 9, and 12 MeV electron beams. The energy spectra were previously reconstructed using the Dual Annealing method with Tikhonov regularization⁶, for which mono-energetic depth dose distributions for a 10 cm diameter applicator were used as input data⁹ (the description of the method is included in the appendix). The spectra that were reconstructed for the applicator with a diameter of 10 cm were validated for other sizes of the applicator, including the applicator with a diameter of 6 cm⁹.

The aim of this study is to validate the accuracy of our model for non-standard geometries. Therefore, the phantom system and both geometries used during the measurements (with and without a disc) were reproduced and included in the MC simulation model. The geometry with the shielding disc represents non-standard geometry. The detectors were placed in the water phantom in the beam axis at 1 mm intervals from the water surface to a depth of 10 cm. Each detector had a 1 mm thickness in the direction of propagation of the beam. In the case of the simulation with the shielding disc, the detectors were placed in the same way, except for the disc area. The phantom was placed so that its surface was in contact with the end of the applicator. As a result, for each of the three nominal energies (i.e. 6, 9 and 12 MeV) of the electron beam formed by the 6 cm diameter applicator, the PDD distributions were determined twice – for geometry with and without the shielding disc. The number of simulated primary electrons emitted from the source (exit window of the accelerator) for each simulation was 10¹⁰. The energy spectra of the primary electrons were determined in the previous study⁶. The cut-off for secondary produced particles was set to 0.1 mm. Simulations were carried out in parallel on five computers (dual Intel Xeon E5 2.4 GHz, 32 GB RAM each). Figure 2 shows the exact geometry of the beam-forming system and the phantom with the location of the detectors used for MC simulations and the shielding disc (the case of the non-standard geometry).

The geometry of the beam-forming system and the phantom with the location of the detectors used for MC simulations and the shielding disc.

Data analysis

In the first step, the simulated and the measured PDDs were compared by analysing the absolute point-to-point difference between the doses and the gamma analysis method¹⁶. The comparisons were performed for both scenarios – when the PPDs were obtained for geometry with and without the shielding disc.

The gamma analysis was performed in global mode with the criteria of 2% as the acceptable dose difference (DD) and 2 mm as the acceptable distance to agreement (DTA). The analyses were performed without any dose threshold to enable analysis in the contamination area of the PDD curves where the doses are lower than 1% of the maximum dose.

The measurement validation of the MC simulation allows for a direct comparison of the simulated PDDs between the scenarios with and without the shielding disc. The dose difference between the scenarios with and without shielding permits the establishment of the effect of the shield on the dose distribution.

The dose differences (DD) at depth (d) were defined as:

where PDD_{MC, disc} and PDD_MC are the values from the percentage depth doses at the same depth (d) obtained respectively from the simulations with and without the shielding disc.