Electron beam response corrections for an ultra-high-dose-rate capable diode dosimeter

Abstract

Background:

Ultra-high-dose-rate (UHDR) electron beams have been commonly utilized in FLASH studies and the translation of FLASH Radiotherapy (RT) to the clinic. The EDGE diode detector has potential use for UHDR dosimetry albeit with a beam energy dependency observed.

Purpose:

The purpose is to present the electron beam response for an EDGE detector in dependence on beam energy, to characterize the EDGE detector’s response under UHDR conditions, and to validate correction factors derived from the first detailed Monte Carlo model of the EDGE diode against measurements, particularly under UHDR conditions.

Methods:

Percentage depth doses (PDDs) for the UHDR Mobetron were measured with both EDGE detectors and films. A detailed Monte Carlo (MC) model of the EDGE detector has been configured according to the blueprint provided by the manufacturer under an NDA agreement. Water/silicon dose ratios of EDGE detector for a series of mono-energetic electron beams have been calculated. The dependence of the water/silicon dose ratio on depth for a FLASH relevant electron beam was also studied. An analytical approach for the correction of PDD measured with EDGE detectors was established.

Results:

Water/silicon dose ratio decreased with decreasing electron beam energy. For the Mobetron 9 MeV UHDR electron beam, the ratio decreased from 1.09 to 1.03 in the build-up region, maintained in range of 0.98–1.02 at the fall-off region and raised to a plateau in value of 1.08 at the tail.By applying the corrections, good agreement between the PDDs measured by the EDGE detector and those measured with film was achieved.

Conclusions:

Electron beam response of an UHDR capable EDGE detector was derived from first principles utilizing a sophisticated MC model.An analytical approach was validated for the PDDs of UHDR electron beams. The results demonstrated the capability of EDGE detector in measuring PDDs of UHDR electron beams.

1 |. INTRODUCTION

The FLASH effect, sparing normal tissue by using ultra-high-dose rate (UHDR) while maintaining tumor control is being extensively studied by the radiation oncology community world-wide.^1–4 Although the first human treatment has been conducted with the aim to test the safety and efficacy of UHDR radiation delivery, large scale of translational preclinical research is still needed to bring the FLASH effect into the clinic.⁵ Currently, the mainstay for these pre-clinical FLASH studies is UHDR electron beam,^6–12 which presents challenges related to dosimetry of the UHDR electron beams.^13,14

To deliver accurate radiation doses using UHDR electron beams for FLASH preclinical research, accurate percentage depth dose (PDD) measurements hold immense importance. Accurate PDD measurements, especially at the build-up region, during commissioning allow researchers to assess the depth of radiation penetration and tailor treatment parameters to ensure adequate dose coverage while sparing normal tissues for small animal irradiation. Therefore, tools to perform PDD measurements for UHDR electron beam in urgently needed in practice. Dosimeters including ion chamber (IC),^15,16 alanine, film, chemical-based detectors, thermos-luminescent dosimeters (TLD), optically stimulated luminescence dosimeters (OSLD), scintillator,and Cherenkov emission-based detectors have been investigated for potential application in UHDR electron beams.¹³ However, all these tools, including the time-consuming film measurements, showed limitations for PDD measurements. With the advantages of real-time response, in vivo dosimetry, high spatial resolution, reliability and robustness, the semiconductor diode detector is a versatile candidate for UHDR beam measurements. Recently, a diode detector, EDGE Detector (Sun Nuclear Corp, a Mirion Medical company, Melbourne, FL), with a newly designed electrometer, has been characterized in an UHDR electron beam demonstrating appropriateness for its FLASH application.¹⁷ However, detailed investigation of the energy response of this detector is needed for full utilization of the EDGE Detector in UHDR electron beam commissioning.

Monte Carlo (MC) simulation is a powerful computational technique widely used in the study of radiation detectors. It is employed to model the interactions between radiation and detector materials. By simulating these processes, insights can be gained into how different types of radiation behave within the detector, contributing to the overall signal. MC simulations are in favor of the determinations of some correction factors for various detectors used in the current dosimetry protocols.^18–20 Therefore, MC simulations are valuable in the field of radiation detectors, offering a versatile and quantitative approach to study the intricate processes inside the radiation detectors.

In this work, we adopted the GAMOS MC toolkit,²¹ which is GEANT4.²² kernel based, to model the EDGE Detector and investigated its electron beam response as a function of incident electron energy. A novel approach to the determination of PDDs of a UHDR electron beam with EDGE detector measurements was designed. Validations of the EDGE detector MC model and the proposed PDD determination method were performed by comparing to film measurements. To our best knowledge, this is the first study presenting the EDGE detector MC beam model and the correction method for determination of UHDR electron beam PDDs. The results presented in this work will enable use of the EDGE detector for UHDR electron beam characterization.

2 |. MATERIALS AND METHODS

2.1 |. EDGE detector and UHDR PDD measurements

The EDGE detector is a commercial N-type diffused junction silicon diode detector. The sensitive volume inside the diode is used to produce signals during beam delivery with the nominal sensitivity of 30 nC/Gy. The diode is encased in a brass housing with dimensions of 3.81 × 5.49 × 38.1 mm³ with a thin mylar entrance window centered above the sensitive volume. To facilitate the UHDR measurements, an updated 2-channel electrometer was produced with a 16-bit bi-polar Analog to Digital Converter (A2D) sampling the output signal every 400 ms and a larger amplifier feedback capacitor to make the EDGE detector work in UHDR beams was implemented. Detailed characterization of the EDGE detector and the updated electrometer has been performed and validated in UHDR beams.¹⁷

In this work, the PDD measurements for a 9 MeV UHDR electron beam produced by a Mobetron (IntraOp, Sunnyvale, CA, USA) has been conducted. As shown in Figure 1a.1,a2, the EDGE detector was mounted in an IBA blue phantom and was controlled in step-by-step mode to acquire the readings at each depth. A second EDGE detector was placed between the treatment head and the water phantom surface without disturbing the beam and was used for collection of a reference signal. In-house MATLAB (2022b) based software was adopted to extract the readings/signals at each depth. PDD curves for the UHDR beams were derive by normalizing the doses at all depths to that at $D_{\text{max}}$ (the depth of maximum dose for PDD curves). As a gold standard (Figure 1 b.1,b2), the Gafchromic EBT-XD film which was vertically held in a 3D-printed water tank was used to acquire the PDD for the same UHDR beam and setup without the presence of EDGE detector. The calibration curve for the film characterizing the dependence of optical density to dose was obtained with a clinically calibrated Trilogy (Varian Medical Systems, Palo Alto, CA) 9 MeV beam by delivering known doses ranging from 0.5 to 40 Gy to eight pieces of films.Fitting functions and calibration procedure proposed by Lewis et al. were adopted.²³

FIGURE 1.

Schematic diagrams (not to scale) and photos for EDGE PDD measurements (a1,a2) and vertical film PDD measurements (b1,b2). PDD, percentage depth dose.

2.2 |. EDGE detector MC simulation for mono-energetic electron beam

To further investigate the energy response of EDGE detector in electron beams, a MC model for the EDGE detector was configured according to the blueprint provided by the manufacturer based on the GAMOS MC toolkit. To simplify, as shown in Figure 2, the EDGE detector was divided in to three parts (Part 1–3). Part 1 refers to the sensitive volume that is filled with silicon. Part 2 refers to the whole piece of diode except for the sensitive volume. Part 3 refers to all the other parts of the EDGE detector except for the whole piece of diode. Validation of the Monte Carlo model (setup A), such as the geometry of the EDGE detector sensitive volume has been done together with the manufacturer internally.

FIGURE 2.

Schematic diagram for the EDGE detector and the three kinds of setups in the MC simulation. The symbol *** symbolizes that the corresponding parts were precisely implemented according to the geometries and materials in the blueprint provided by the manufacturer. G4_water indicates that the corresponding parts were considered as solely water regardless their detailed geometries and materials. MC, Monte Carlo

In the MC simulation, three kinds of the setups for EDGE detector were implemented as shown in Figure 2. Setup A was the full configuration of the EDGE detector in MC. Setup B was like Setup A but treating the region outside the diode as water. Setup C is the situation in which only the sensitive volume was configured, other parts of the EDGE detector were considered as water. The EDGE detector was centered at the origin of the world in MC simulation. The world was filled with water to provide electron equilibrium condition. Monoenergetic beams with energies ranging from 0.5 to 22 MeV were delivered to the EDGE detector for the three setup conditions, respectively. All mono-energetic electron beams in this work were defined as a surface beam source placing on the top surface of the detector. Absorbed dose deposited in the sensitive volume ($D_{\text{silicon}}$) was scored. The dose deposition ($D_{\text{water}}$) in water without the presence of the EDGE detector was also scored. For each simulation, a total number of 10⁹ electrons were simulated to realize dose uncertainty below 0.1%. Then, according to the Spencer-Attix formalism, the dose deposition in water $D_{\text{water}}$ is related to the dose in the silicon sensitive volume $D_{\text{silicon}}$ at the same situation by:

$${\mathrm{D}}_{\text{water}}={\mathrm{D}}_{\text{silicon}}{\left(\frac{\bar{L}}{\rho }\right)}_{\text{silicon}}^{\text{water}}\mathrm{P}$$

where $(\bar{L}/\rho {)}_{\text{silicon}}^{\text{water}}$ is the mass collision stopping-power ratio of water to silicon and $P$ is the product of all possible corrections, which is unity for an ideal cavity. For ion chambers, the cavity medium is gas and $p=P_{\text{wall}}{P}_{\text{repl}}{P}_{\text{cel}}$ is generally not unity, where $P_{\text{wall}}$ is the wall correction factor, and $P_{\mathit{repl}}$ and $P_{\mathit{cel}}$ are the replacement and central electrode correction factors, respectively. Therefore, in this work, the mass collision stopping-power ratio of water to silicon $(\bar{L}/\rho {)}_{\text{silicon}}^{\text{water}}$ for EDGE detector can be well correlated with the water/silicon dose ratios $D_{\text{water}}/D_{\text{silicon}}$ calculated based on the MC simulation results for all situations.

2.3 |. EDGE detector in UHDR electron beams

Besides the EDGE detector response in monoenergetic electron beam, a more practical scenario for the EDGE detector application is the UHDR beam. To investigate the EDGE detector response in UHDR electron beams, a validated MC beam model for the Mobetron 9 MeV UHDR electron beam was adopted. The precision of the proposed MC beam model for 9 MeV UHDR beam has been tested to well reproduce the realistic electron beams based on the commissioning data. Then, the MC model for EDGE detector in Setup A was integrated with the Mobetron UHDR electron beam model. With the same method as used for the mono-energetic electron beam simulations, the water/silicon dose ratios $D_{\text{water}}∕D_{\text{silicon}}$ were calculated.

2.4 |. Methods for the correction of EDGE PDD

As shown by the results from film and EDGE detector PDD measurements in Figure 6, the dose is always underestimated at shallow depths. For the application of EDGE detector for UHDR electron beam PDD measurements, the precise beam model is usually unknown. Therefore, a method for the correction of the raw EDGE detector PDD is needed. As shown in Figure 3, an analytical method to the correction of EDGE detector PDD for the UHDR electron beam was established based on the EDGE response in mono-energy electron beam data presented in this work. With the proposed approach, the raw PDD data (PDD(D)*) was firstly measured with EDGE detectors according to the methods illustrated in Section 2.1. Then, ${\mathrm{R}}_{50}$ was determined as the depth at which the absorbed dose falls to 50% of the maximum dose. The mean energy $\left({\bar{E}}_0\right)$ at the phantom surface can be calculated with the formula²⁴:

$${\stackrel{-}{\mathrm{E}}}_0=2.33(\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{c}\mathrm{m})\times {\mathrm{R}}_{50}(\mathrm{c}\mathrm{m})$$

FIGURE 6.

Upper panel shows the PDDs measured with vertical film (black line), EDGE detector (red line) and the corrected curve (green line), which was corrected with the approach established in this work based on raw EDGE detector data (red line); Lower panel shows the discrepancy for raw EDGE PDD (red line) and corrected PDD (green line) with film PDD as the reference. PDD, percentage depth dose.

FIGURE 3.

Workflow chart for the correction of PDDs measured with EDGE detectors: Firstly, raw PDD data (PDD(D)*) was firstly measured with two EDGE detectors (one as the reference detector and the other as the field detector) using a water phantom tank in step-by-step mode. Next, with PDD(D)*, $R_{50}$ was determined. Then mean energy $\left(E_0\right)$ at the phantom surface can be calculated with the empirical formula. In the following, the mean energy $E\left(D\right)$ at corresponding depths can be estimated. And the correction factors $f\left(D\right)$ can be determined by looking up the table containing both electron energy and the water/silicon dose ratios $D_{\text{water}}/D_{\text{silicon}}$. At last, the corrected PDD(D) is calculated as the product of $f\left(D\right)$ and PDD(D)*. PDD, percentage depth dose.

Then, the mean energy $E\left(D\right)$ at each depth can be estimated with the formula²⁴:

$$\mathrm{E}\left(\mathrm{D}\right)={\stackrel{\mathrm{‾}}{\mathrm{E}}}_0\times \left(1-\mathrm{D}/{\mathrm{R}}_{\mathrm{p}}\right)$$

where $R_p$ is the practical range which can be determined as the depth of the point where the tangent at the inflection point of the fall-off portion of the PDD(D)* curve intersects the bremsstrahlung background. With the calculated water/silicon dose ratios $D_{\text{water}}/D_{\text{silicon}}$ for $E\left(D\right)$, the correction factors $f\left(D\right)$ at the corresponding depths can be determined. Lastly, the corrected PDD(D) is the product of $f\left(D\right)$ and PDD(D)*. It should be noted that, the corrections were only performed before $D_{\mathrm{m}\mathrm{a}\mathrm{x}}$ taking advantage of the good agreement between the EDGE and film at the fall-off region behind $D_{\mathrm{m}\mathrm{a}\mathrm{x}}$.

3 |. RESULTS

3.1 |. EDGE response in mono-energetic electron beam

With the proposed three kinds of setups, water/silicon dose ratios for electron beams (0.5—22 MeV) which might be relevant for the corrections of PDD curves of common LINAC were calculated with the MC method. The dependence of the water/silicon dose ratio on energy is shown in Figure 4. For Setup A, which corresponds to the full configuration of the EDGE detector, the ratio decreased with decreasing electron beam energy. After replacing the region outside the diode with water, for Setup B, the ratio kept the value of ~1.15 for the electron beams with energy ranging from 22 down to 3 MeV. For beams with energy lower than 3 MeV, the ratio decreased with decreasing energy. For setup C, the water/silicon dose ratio was 1.16 at 22 MeV. It slightly increased with decreasing energy and peaks at ~1.25 MeV with the maximum of 1.19, and then started to decrease. More discussion about the different value and trend for the water/silicon dose ratio for various setups will be included in the discussion section.

FIGURE 4.

Dependence of water/silicon dose ratio on electron-beam energy for various levels of detail of the EDGE model as defined in Figure 2.

3.2 |. EDGE response in FLASH-relevant UHDR electron beam

With the Mobetron MC beam model and EDGE detector model (setup A), the water/silicon dose ratios for Mobetron 9 MeV UHDR beam at various depths were calculated. As shown in Figure 5, the ratio decreased from 1.09 (0 mm) to 1.03 (20 mm, $~D_{\mathrm{m}\mathrm{a}\mathrm{x}}$). This can be explained with the decreasing trend with decreasing energy for mono-energetic electron beams. Behind $D_{\mathrm{m}\mathrm{a}\mathrm{x}}$, the water/silicon dose ratio was in range of 0.98–1.02, which indicated that the dose deposition in the EDGE detector is within 2% of that in the water phantom without the presence of EDGE detector. At the tail region (38 mm and deeper), the ratio increased with depth to a plateau in value of 1.08. Possible reasons for this phenomenon maybe the significant spread of electron energy spectrum together with the complex interactions between low energy electrons and structure materials of EDGE detector, which prevent the application of water/silicon ratio of monoenergetic electron beams from explaining this trend. For the PDD correction in this work, the absolute magnitude is much lower beyond 38 mm so that PDD is acceptable at this part although no correction was performed.

FIGURE 5.

Water/silicon dose ratios for Mobetron 9 MeV UHDR beam at various depths. (Error bar in the figure represent the Type A uncertainty associated with one standard deviation). UHDR, ultra-high-dose-rate.

3.3 |. PDD corrections for the EDGE measurements

As shown in the above sections, good agreement between the film and EDGE PDDs can be achieved at the fall-off region due to the < 1.02 water/silicon dose ratios. However, for the build-up region where the water/silicon dose ratios are in range of 1.03–1.09, a method for the PDD correction was established and applied on the Mobetron UHDR beam. As shown in Figure 6, after the correction, good agreement between the corrected PDD and the film PDD was achieved. It should be noted that, corrections applied only on buildup region, and this will be reviewed in detail in the discussion section.

4 |. DISCUSSIONS

Film measurements act as the golden standard for UHDR PDD measurements in this work. As shown in Figure 6,the film PDD suffers from a little bit of noise due to the well-known film dose uncertainty although calibration was well conducted. However, the vertical placement of the film in the 3D-printed water tank fully takes the advantage of the resolution of film measurements. Therefore, although the film PDD suffers from noise, PDD of UHDR electron beam can be well described by film. Besides, to make a precise alignment of the water tank and vertical film, an in-house 3D-printed front pointer was adopted for film PDD measurements. Our results showed that vertical film in the 3D-printed water tank is better than the parallel film¹⁷ placed at various depths in the solid water phantom for PDD measurements. By using parallel film, only several points were adopted to describe the whole PDD curve and only 1–2 points were located at the build-up region. What is more, the large film uncertainty always results in a less precise description of the PDD curve with limited points. That is why the dose underestimation of EDGE detector at build-up region was not observed at its first application on the UHDR electron beam PDD measurements.¹⁷

In this work, the UHDR capable EDGE detector has been applied to perform PDD measurements for FLASH electron beams. Compared with the film measurements, dose was underestimated in the build-up region. This phenomenon promoted the further configuration of the MC model for the EDGE detector. As shown in Figure 2, for setup A, which correspond to the full configuration of the EDGE detector, all physical interactions between electrons and the components of the EDGE detector were considered. The results showed an obvious dependence of the water/silicon dose ratio on the electron beam energy. It seems that the structure materials start to affect the energy deposition inside the sensitive volume with decreasing electron energy. Then, an in-depth study (setup B) by replacing all the components in the EDGE detector except for the diode with water was conducted. For this setup, attentions were mainly paid to the effect from the Brass shell and structure material of the EDGE detector. The results showed that the water/silicon dose ratio maintained ~1.15 for the electron beams with energy ranging from 22 to 3 MeV. This indicated that the decreasing trend of the water/silicon dose ratio with decreasing energy (black line in Figure 4) above 3 MeV of EDGE detector mainly resulted from the structure materials and Brass shell of EDGE detector. In the simulation of setup C, all components except the sensitive volume inside the diode were considered as water. For this setup, the contribution from the diode outside the sensitive volume was further examined. The calculation results showed that the water/silicon dose ratio had little dependence on the electron beam energy which is well agreed with the theoretical principle of diode detector.²⁵ The decreasing trend for setup C, at energy less than 1 MeV suggested that the sensitive volume is no longer the ideal Spencer-Attix cavity for low energy electrons with limited ranges.

It was shown that the proposed method in this work for the corrections of PDD measured with EDGE detector worked well for UHDR electron beams. Although the convolution of energy spectrum for Mobetron electron beam and water/silicon dose ratio for monochromatic beams will result in a more precise result, the mean energy of Mobetron electron beam was adopted in the presented method to calculate the correction factors for the Mobetron beam. This is done based on the considerations that the energy spectrum is usually unknown while performing PDD measurements. The electron beam spectrum is usually described as a narrow-spread Gaussian shape. The mean energy is similar to the most probable energy.²⁶ Therefore, the application of mean energy instead of precise energy spectrum resulted in an acceptable corrected PDD in this work. However, it should be noticed that with the increase of penetration depth, the broadening of electron spectrum will affect the calculation of PDD correction factor at deep depth. This does not affect the method in the presented work as the corrections were applied only at the build-up region based on the considerations below. On the one hand, the estimation of the mean energy at the corresponding depth $E\left(D\right)$ will not reproduce the correct beam characteristics and then will fail to properly correct the PDD. On the other hand, good agreement has already been achieved at the falloff region within 2% (discrepancy between the measurements with EDGE and film). The proposed method would not produce a better result considering the energy straggling of electron beams at deep depth. Therefore, although only corrections at the build-up region have been performed, acceptable PDD measurements can still be achieved with the proposed method.

In this work, reproducibility of EDGE and Mobetron beam is good enough, so that the noise of measurements nearly has no effect on $D_{\mathrm{m}\mathrm{a}\mathrm{x}}$ determination. To achieve a more precise $D_{\mathrm{m}\mathrm{a}\mathrm{x}}$ location and thus an accurate PDD correction, more measurements were performed around $D_{\mathrm{m}\mathrm{a}\mathrm{x}}$ with the minimal step size of 1 mm. Therefore, it is recommended that the measurement should be repeated several times when beam or EDGE reading suffers from significant noise The step size should be decreased around $D_{\mathrm{m}\mathrm{a}\mathrm{x}}$ to achieve a precise PDD measurement and correction.

Very high-energy electron (VHEE) beams now are considered as one of the modalities to bring FLASH-RT to the clinics. Although no validation of the application of EDGE detector on such VHEE beams, we simulated the water/silicon ratio for some of the VHEE relevant electron beams. The results showed that water/silicon ratios for monoenergetic 50, 100, and 200 MeV electron beams are 1.124 ± 0.01, 1.125 ± 0.01, and 1.125 ± 0.01, respectively. These results demonstrated that the water/silicon ratio for VHEE relevant electron beams are quite stable, so that no energy-dependence-induced underestimation might occur at buildup region for these beams. What is more, it is worth noting that while this study focused on the UHDR electron beam conditions, the methodology and correction factors are readily applicable for electron beams at conventional dose rates. This is because the beam model that was utilized for the MC simulation, while validated for the FLASH beamline, does not concern the dose rate as an explicit parameter. Therefore, the correction factors are essentially applicable for electron beams at conventional dose rates. However, there are many well established methods to measure conventional electron beam PDDs, which is why the current study focused on the UHDR scenarios, considering the lack and urgent need of dosimeters which support a comprehensive characterization of UHDR electron beams.

5 |. CONCLUSIONS

This work investigated the electron beam response of an UHDR capable EDGE detector. A detailed description of EDGE detector response for various mono-energy electron beams has been quantified utilizing a sophisticated MC model. The depth dependence of the water/silicon dose ratio of EDGE detector in the UHDR Mobetron beam has been calculated. An analytical approach for the correction of PDD measured with EDGE detector has been established and verified. This work facilities the application of EDGE detector in measuring PDDs of UHDR electron beams.