To explore the possibility of creating UHDR mini beams, Monte Carlo simulations were carried out reproducing different devised suitable collimator templates, which are passive spatial distribution modulators. These templates are integrated into the beam optic system to achieve mini-beam spatial distributions.

The mini-beam templates have been designed with the GEANT4 [34] version 10.7.2 Monte Carlo code. In particular, the Sordina IORT Technologies S.p.A. (SIT, Italy) ElectronFlash linear accelerator (linac) available at the Centro Pisano for Flash Radiotherapy (CPFR) was fully modelled, in terms of beam optics, geometry and input energy spectra with the Geant4 code, and a dedicated application was recently inserted within the official advanced examples of the Geant4 distribution with the name “eFLASH_radiotherapy.” For each simulation, the GEANT4 standard_opt4 physics list with 10⁸ primary particles and 0.1 mm production cuts were set. A water phantom was implemented just after the template to score the dose, using a 0.125 × 0.125 × 0.5 mm³ voxel size.

A fundamental requisite for a useful mini-beam structure, defined as having distinct peaks and valleys with high peak-to-valley dose ratio, is avoiding bleed-through of electrons through the septa, thus high Z materials are needed. In fact, by keeping the thickness equal to the practical range of the electron energy (9 MeV nominal energy), we noticed a significant reduction of PVDR for plastic materials, such as Teflon, as opposed to Tungsten due to septa bleed-through, as shown in Figure 1. Similar results have been reported also in [35] in the context of experimental IORT beam limiting devices.

Thus, we designed the collimators to have a thickness of 5 mm and be made of Tungsten. Each of the designed templates differs mainly in hole structure (grid or planar slits) and center-to-center distance (ctc), so that it is possible to study the effect of varying these parameters.

To further strengthen the reliability of dose evaluations in terms of spatial distribution, we compared the Monte Carlo simulations with experimental data acquired with radiochromic gafchromic films, which are currently considered the most suitable dosimeters with high spatial resolution (below 25 µm [36]). However, it is important to acknowledge that these dosimeters have certain limitations, mostly related to the accuracy of dose reading [37]. To address this, we conducted a comparative analysis by comparing the gafchromic data with results obtained from three independent Monte Carlo simulation codes: Electron Gamma Shower by the National Research Council Canada (EGSnrc) [38], Geant4, and FLUKA [39, 40]. The realistic input energy spectrum and spatial distribution before the Titanium window were provided by SIT Sordina company. To validate the accuracy of the simulations, we compared them with measurements obtained using the FlashDiamond [41] detector, including PDD and dose profile measurements. In order to obtain absolute dose values from the simulations, we normalized the mini-beam dose percentage with respect to an open field measurement at the buildup region. This normalization was then scaled to the desired depth using the PDD curve.

The flash linac adopted is the Triode-Gun equipped ElectronFlash manufactured by SIT, available at the CPFR in Pisa, Italy. It operates at energies of 7 and 9 MeV, delivering a dose-rate of up to 5,000 Gy/s. Field size and Normal Treatment Distance (NTD) is achieved by means of passive collimation with polymethyl methacrylate (PMMA) cylindrical tubes, called applicators. Each applicator is uniquely identified by its diameter (ex. Applicator 100 mm, 50 mm, 40 mm, etc.). With this linac it’s possible to achieve flash conditions and vary the main parameters (Dose per pulse, pulse width, pulse repletion frequency ecc.) independently from one and another, without changing experimental setup or beam collimation [42].

Measurements were performed using the ElectronFlash linac in 9 MeV mode with a 40 mm diameter applicator. For electron flash, beam monitoring is critical as conventional systems based on ionization chambers are not compatible with the high beam current [43]. As in the case of flash with protons [44], beam monitoring is a topic of great interest which requires non-conventional solution. In fact, ElectronFlash comes equipped with a IEC 60601-2-1 [45] compliant beam current transformer (ACCT) based monitoring system, which correlates the beam current to delivered dose in the form of monitor units (MU) displayed on the machine human interface (HMI) system. After an initial MU calibration check without the mini-beam template, we fixed the pulse width (t_p), pulse repetition frequency (PRF), and dose per pulse to ensure each gafchromic film received the same dose at the open field electron beam build up depth (R100). The EBTXD gafchromic films [36] were analyzed with an Epson Expression scanner 10000XL after 48 h, 254 DPI with the background subtracted from a pre-irradiation scan. From the scan, we converted the optical density (OD) to dose with previously measured dose calibration curves. Each film was irradiated accumulating a total dose of 23.5 Gy at R100, using a dose per pulse of about 0.2 Gy/p, t_p of 4 µs and a PRF of 50 Hz.

The mini-beam templates were attached to the applicator using a 3D-printed nylon holder, and the films were placed between slabs of a plastic water phantom to measure the dose profile at each depth. The total phantom dimensions are 30 × 30 × 15 cm³, with singular slab thickness ranging from 1 mm to 1 cm. For each template we evaluated the main characteristics, such as ctc, PVDR, irradiated surface, and the effect of hole type and dimensions.

As by design, the nylon holder does not extend beyond the template, ensuring that only the tungsten is in contact with the phantom. For each template, we measured the dose profile at various depths ranging from 0 up to 4 mm water depth, using 25.6 × 25.6 mm² films positioned perpendicular to the beam axis in the water equivalent phantom. In the case of GRID templates, we sampled additional points along the depth to evaluate the PDD (percentage depth dose). For the PLANAR templates, a 51.2 × 51.2 mm² film was placed parallel to the beam axis at a depth of 4 mm, with normalization to the entrance dose measured using a 25.6 × 25.6 mm² film positioned perpendicular to the beam axis during the same irradiation.

Each of the Monte Carlo codes show good agreement with the open field experimental data in the water phantom, as shown in Figure 2. Gamma index analysis [46] was performed for the Monte Carlo curves, comparing each one with the FlashDiamond data. With a Dose Difference (DD) of 3% and a Distance to Agreement (DTA) of 3 mm, we have obtained over a 90% agreement for the curves across all Monte Carlo codes. We decided on these values of DD and DTA due to the dose response and spatial resolution of the FlashDiamond detector [41]. Thus, we can reasonably use the Monte Carlo codes for a comparison with the experimental data.

The final collimators which have been constructed are shown in Figure 3, which also shows a picture of the template attachment on the PMMA applicator and a close-up of the setup, and in Table 1 the main geometric characteristics of each one is summarized. Each one is 5 × 5 × 0.5 cm³ and is made of Tungsten, to ensure minimal electron septa bleed-through and maintain a useful mini-beam structure. Since the templates are made of a high Z material, it is useful to evaluate secondary radiation and its effect on the mini-beam distribution. As shown in Figure 4, Bremsstrahlung photons, evaluated in the worst-case scenario of the grid_conf2 template (the one with least open volume), constitute less than 10% for depth up to 5 mm of the dose, which is deposited mostly at depths beyond the desired mini-beam structure. A rough approximation can be made by utilizing the radiative stopping powers listed in the National Institute of Standards and Technology (NIST) tables for Tungsten [47]. This calculation overlooks any directional or geometric aspects of the beam and yields an estimate of approximately 10% of the maximum dose attributable to radiative loss.

The templates used for measurement, referenced in Table 1, are as follows:

1. Grid_conf1

In Figures 5, 6, the transversal dose profiles obtained experimentally, at the center of the beam from 0 mm up to 4 mm in water depth are presented for the grid configurations, grid1 and grid2, along with the expected values from the Monte Carlo (MC) simulations. For all profiles, the dose is normalized to the dose at R100 of the open 40 mm field. To evaluate the agreement of the Monte Carlo simulations, we used gamma index analysis with DD of 6% and DTA of 2 mm to achieve an agreement greater than 93% with the experimental data at each depth. The choice of DD and DTA is due to the high dose uncertainty and high spatial resolution of gafchromic films, as pointed out in [36, 37, 41]. The agreement is further observed in the PVDR values reported as function of the depth depicted in Figure 7. As anticipated, a higher ctc results in a significantly greater PVDR, as the increased septa blocks adjacent hole contamination, leading to a substantial decrease in the valley dose at the expense of a lower average dose. Figure 8 illustrates the average dose PDDs (percentage depth dose) and the depth at which PVDR > 2.5 for the grid templates. As comparison, also the equivalent open field (obtained as EGSnrc simulated tungsten slab of 5 mm with an aperture of the dimensions of the hole distribution, in this case 1 cm) is shown. We can observe that a greater ctc considerably expands the “mini-beam zone” (PVDR > 2.5) while creating a steeper PDD. This mini-beam structure covers a zone up to the depth of the 50% dose deposition (R50) in water, while reducing the total penetration of the dose distribution for greater depth. This makes the grid template particularly interesting, as it is possible to obtain a large area of “mini-beam” characteristics, with the possibility of performing in vivo experiments on organs and tissues of dimensions of 5–6 mm. Figures 9, 10 present the profiles for the planar templates, showing a good agreement also above 93% of gamma index with DD 6% and DTA 2 mm. In Figure 11, the PVDR as a function of depth for the planar configuration is displayed. Apart from a slight discrepancy (15%) at the entrance, where a small increase in the valley dose can significantly impact the PVDR, the greater field size does not affect significantly the mini-beam distribution along the depth. Figure 12 shows the PDDs normalized to the entrance dose and “mini-beam zone” (PVDR > 2.5) for the templates, compared to the equivalent open beam configuration (2 × 2 cm² field). Since the positioning of the film parallel to the beam resulted in an underexposure after the R50 beyond the constructor’s tolerances, that part is omitted on the graph. As expected, with an increase in field size, we approach an open field configuration, resulting in greater penetration, as precedingly reported by [18]. Furthermore, in comparison to the grid configuration, the PDD does not significantly differ from the equivalent open field. This makes the planar template interesting from a clinical point of view, as it has a PDD practically identical to that of the conventional beam of equal energy (same depth of treatment) with the possibility of having a mini-beam effect, for example, on the skin, potentially reducing the collateral effects to this organ.

In Table 2, the main mini-beam characteristics are reported for each constructed template. We reported, for each template and each depth, the PVDR, the ratio of the dose at the peak (D_p) and the dose at the buildup depth without the template (D_open, which is to be considered a reference dose value), the ratio of the dose at the valley (D_v) and D_open, the ratio of the average dose (D_avg) and D_open, the ctc, the FWHM and finally the R50 (which is the same for each template). For the sake of legibility, uncertainties on single dose measurements are assumed to be 4%, to be appropriately propagated for each derived quantity.

Finally, we present in Table 3 the possible parameters for mini-beam-conv and mini-beam-UHDR irradiation (Average dose rate (DR), dose per pulse (DPP) and dose rate within the pulse (DR_PULSE) at the peak and average mini-beam dose), at the reference depth of 1 mm, for the peak and average dose. All values are reported as ranges in square brackets, indicating the minimum (CONV) and maximum (FLASH) values achievable. These parameters are to be considered indicative, since we can tune the ElectronFlash to obtain a wide range of characteristics in a continuous way, within the limits of proper linac function.