# Study of a gel dosimeter based on Ag nanoparticles for applications in radiation therapy with synchrotron X-rays at ultrahigh dose rate compared to 60Co γ-rays

Yasser S. Soliman, Marie Capron, Diego Pontoni, Michael Krisch, Paolo Pellicioli

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Yasser S. Soliman, Marie Capron, Diego Pontoni, Michael Krisch, Paolo Pellicioli. Study of a gel dosimeter based on Ag nanoparticles for applications in radiation therapy with synchrotron X-rays at ultrahigh dose rate compared to 60Co γ-rays. Radiation Physics and Chemistry, 2025, 227, pp.112351. 10.1016/j.radphyschem.2024.112351. hal-05122155

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# Study of a gel dosimeter based on Ag nanoparticles for applications in radiation therapy with synchrotron X-rays at ultrahigh dose rate compared to $^{60}$Co γ-rays

<figure><img src="image_3.png" /></figure>

Yasser S. Soliman<sup>a</sup>, Marie Capron<sup>c</sup>, Diego Pontoni<sup>c</sup>, Michael Krisch<sup>b</sup>, Paolo Pellicioli<sup>b,d,*</sup>

## ARTICLE INFO

Handling Editor: Dr. Chris Chantler

**Keywords:**

Gel dosimeter

Ag nanoparticles

Dosimetry

X-ray synchrotron radiation

Radiotherapy

## ABSTRACT

A silver nitrate ($AgNO_3$) gel was developed and evaluated as a dosimeter for synchrotron X-ray-based studies in microbeam radiation therapy (MRT) and FLASH radiation therapy. The gel was irradiated at the European Synchrotron Radiation Facility (ID17 Biomedical beamline) with a continuous X-ray spectrum in the 50–600 keV range and a dose rate of 11.6 kGy/s. The spectrophotometric response after irradiation at this beamline was compared with the response at a conventional $^{60}$Co γ-ray source providing a dose rate of 0.27 Gy/s. Ag<sup>+</sup> ions in the gel dosimeter undergo reduction to Ag<sup>0</sup> nanoparticles, as detected at 450 nm, which is a surface plasmon resonance band. The intensity of this band increased linearly with increasing absorbed dose up to 100 Gy, and improved with the addition of glycerol. The gel dosimeter exhibited the lowest detectable dose (LDD) of 75.9% lower and a dose deposition of 76% higher for ID17 beamline irradiation than for $^{60}$Co irradiation. The theoretical relative response $H_{Q,Q_0}$ for the gel irradiated at the synchrotron was 1.70, which is in close agreement with the experimental relative response $F_{Q,Q_0} = 1.76$. These results confirm the dose enhancement in the gel irradiated with orthovoltage X-rays. The good properties of the silver nitrate gel, together with its increased sensitivity to orthovoltage X-ray irradiation and modest overall uncertainty of 5.8% (2σ), confirm that the gel is a valid dosimeter for measurements at ultrahigh dose rates for synchrotron radiotherapy. The dosimeter is also a promising candidate for dose enhancement factor measurements in nanoparticle-based radiotherapy techniques.

## 1. Introduction

Synchrotron X-ray facilities are highly versatile research centers capable of advancing numerous diverse scientific discoveries that could soon have a major impact on our daily lives, including the development of innovative radiation therapy techniques.

The main goal of radiation therapy is to stop or control the proliferation of tumor cells by delivering ionizing radiation to patients. Conventional radiation therapy treats tumors with low throughput and low dose rate (a few Gy/min at most) using $^{60}$Co γ-rays or electrons and X-ray beams from linear accelerators (National Cancer Institute, 2016), while synchrotron radiation sources can produce extremely high X-ray photon fluxes of up to thousands of Gy/s (Bräuer-Krisch et al., 2015; Fardone, 2013), which opens new prospects in radiation oncology

approaches.

In recent decades, synchrotron sources have enabled the development of microbeam radiation therapy (MRT), which is the most extreme configuration of spatially fractionated radiotherapy (SFRT). The MRT approach is based on irradiation fields defined by an array of beams as small as 50–100 µm wide and spaced 200–800 µm apart, delivered with ortho-voltage X-rays at ultrahigh dose rates (Adam et al., 2022; Bräuer-Krisch et al., 2015; Djonov et al., 2023; Fardone, 2013; Fernandez-Palomo et al., 2020; Sabatasso et al., 2021; Trappetti et al., 2022). At the European Synchrotron Radiation Facility (ESRF), ID17 Biomedical beamline, MRT studies are effectively performed with an array of 50 µm wide microbeams and 400 µm spacing between beamlet centers (Bartzsch et al., 2020; Bräuer-Krisch et al., 2015; Trappetti et al., 2021). The homogenous irradiation beam produced by the synchrotron source

<footnote><sup>a</sup> National Center for Radiation Research and Technology (NCRRT), Egyptian Atomic Energy Authority (AEA), P.O. Box 8029, Nasr City, Cairo, 11787, Egypt</footnote>

<footnote><sup>b</sup> ESRF - the European Synchrotron, ID17 Biomedical beamline, 71 Avenue des Martyrs, 38000, Grenoble, France</footnote>

<footnote><sup>c</sup> ESRF - the European Synchrotron, Partnership for Soft Condensed Matter (PSCM), 71 Avenue des Martyrs, 38000, Grenoble, France</footnote>

<footnote><sup>d</sup> Institute of Anatomy, University of Bern, Baltzerstrasse 2, 3012, Bern, Switzerland</footnote>

<footnote>* Corresponding author. ESRF - The European Synchrotron, ID17 Biomedical beamline, 71 Avenue des Martyrs, 38000 Grenoble, France. E-mail address: paolo.pellicioli@unibe.ch (P. Pellicioli).</footnote>
was spatially modulated using dedicated multi-slit collimators (Bräuer-Krisch et al., 2009a; Pellicioli et al., 2021). The polychromatic X-ray spectra used have an average photon energy of 100–150 keV (depending on the beam filtration used) and dose rates to water of up to 16000 Gy/s (Di Manici et al., 2024). Within these irradiation configurations, MRT is based on the delivery of radiation doses of up to several hundred gray along the beamlet path (peak dose), while the contribution of scattered radiation within the target volume between microbeams (valley dose) is minimal, with delivered radiation doses below healthy tissue toxicity.

MRT has shown significant improvements in preclinical studies, with an excellent therapeutic index in the treatment of cancer compared to more conventional approaches (Bartzsch et al., 2020; Bräuer-Krisch et al., 2003, 2009b; Grotzer et al., 2015; Lemasson et al., 2010; Schültke et al., 2017; Sierra et al., 2015). MRT has also been used in studies of neurodegenerative diseases (Bräuer-Krisch et al., 2015; Fardone, 2013; Pouyatos et al., 2016; Schültke et al., 2017; Zippo et al., 2019). Even if no dose spatial fractionation is applied to the irradiation field, such a high dose rate can be used for studies related to FLASH radiotherapy (Bourhis et al., 2019a, 2019b; Favaudon et al., 2014; Montay-Gruel et al., 2018; Spitz et al., 2019; Vozenin et al., 2019; Wardman, 2016), because the beam can deliver the prescribed dose in a few hundred milliseconds or less.

Radiation dosimetry is critical in all phases of radiotherapy, and plays a crucial role in the transition from preclinical studies to potential clinical applications (Bartzsch et al., 2020). Finding a reliable dosimeter that meets the dosimetry requirements of MRT is one of the greatest challenges, as the detector must resolve the microbeam dose distribution, not saturate at radiation doses of up to several hundred gray at ultrahigh dose rates, and be tissue equivalent for orthovoltage X-rays. A unique detector that can meet all dosimetry requirements for MRT applications has not yet been developed. Therefore, several approaches have been tested and are still under development. Among the tested detector types for MRT-specific dosimetry are ionization chambers (Bräuer-Krisch et al., 2015; Di Manici et al., 2024; Fournier et al., 2016; Livingstone et al., 2017; Prezado et al., 2011), solid-state dosimeters (Bräuer-Krisch et al., 2010; Butler et al., 2016; Doran et al., 2017; McErlean et al., 2015; Soliman et al., 2020), radiochromic films (Day et al., 2020; Ocadiz et al., 2019; Pellicioli et al., 2019), silicon-based (Davis et al., 2018; Duncan et al., 2020) and diamond-based electronic detectors (Butler et al., 2018; Livingstone et al., 2016, 2018), and gel dosimeters (Boudou et al., 2006; Bräuer-Krisch et al., 2010; Peleg Walg et al., 2021; Rahman et al., 2010, 2012; Wong et al., 2007).

This study focuses on a new formulation of gel dosimeters based on silver nanoparticles (Ag-NPs). Gel dosimeters have already been used in conventional radiotherapy to validate treatment planning systems for tumor treatment (Abdelgawad et al., 2017; De Deene, 2002; Kwiatos et al., 2018; Moftah et al., 2020; Soliman et al., 2017; Vandecasteele and De Deene, 2013). For MRT, a technique currently based on the use of orthovoltage X-rays, further studies with gel dosimeters may be particularly useful for measuring dose enhancement factors in tumors loaded with metal nanoparticles.

Ag-NPs are exciting nanomaterials due to their biomedical properties and potential applications (Dolez, 2019; Du et al., 2008; Mattea et al., 2017; Sivera et al., 2014). Ag-NPs can be envisioned as dose enhancers for Frick gel dosimetry in radiotherapy (Mattea et al., 2017; Vedelago et al., 2018). The optical absorption spectra of Ag-NPs showed a surface plasmon resonance (SPR) band in the UV-visible range of 390–450 nm (Creighton and Eadon, 1991; Tadros et al., 2021). Moreover, the SPR band depended mainly on the size of the Ag-NPs (Ramnani et al., 2007) and the surrounding medium (Xu and Zhou, 2008). The radiation-induced synthesis of nanoparticle clusters was efficient and reproducible (Soliman, 2014; Soliman et al., 2022; Temgire and Joshi, 2004). In the irradiation method, hydrogen atom radicals ($H^*$) and hydrated electrons ($e_{aq}$) formed during the radiolysis of water are very active and have effective reduction potentials that can enhance the

reduction of $Ag^+$ ions to Ag-NPs (Kapoor and Gopinathan, 1998; Marignier et al., 1985; Marin, 2014; Ramnani et al., 2007; Temgire and Joshi, 2004). Therefore, silver nitrate in aqueous media can be used effectively for radiation dosimetry (Funaro et al., 2011; Soliman, 2014; Tadros et al., 2021).

A liquid dosimeter, based on AgNO₃ and 1% sodium citrate, was prepared. Irradiation of this dosimeter produces spherical Ag-NPs, identified by the development of a sharp absorption band at ~410 nm in the colloidal liquid dosimeter (Puišo et al., 2010). Previous studies have shown that a 0.1% sodium citrate concentration results in a dosimeter with a linear response covering doses from 2 to 120 Gy (Funaro et al., 2011). A radiochromic gel dosimeter was developed from AgNO₃ in aqueous gelatin (8%) for ¹³⁷Cs γ-ray irradiation, covering a dose range of 5–100 Gy for radiotherapy and blood irradiation (Soliman, 2014). Its dose response is linear up to 100 Gy, with an overall uncertainty of ~4.56% (2σ). This gel is a nearly water-equivalent dosimeter with a photon energy range of 0.3–20 MeV (Tadros et al., 2021). The radiation sensitivity of the gel increased with increasing $Ag^+$ concentration and isopropanol content in the gel matrix. However, it decreased with an increase in $H^+$ ions and gelatin content (Tadros et al., 2021). Recently, a polyacrylamide hydrogel containing $Ag^+$ was investigated at an SPR band of 453 nm for dosimetry applications ranging from 5 Gy to 100 Gy (Soliman et al., 2022). The intensity of this band increases linearly with an increase in the absorbed dose up to 100 Gy. The addition of 15% glycerol to this hydrogel increased its radiation sensitivity by approximately 30%, confirming that glycerol played an essential role in reducing $Ag^+$ ions to Ag-NPs upon irradiation (Soliman et al., 2022).

The current work aims to further characterize the silver nitrate gel dosimeter based on a nanoparticle material previously developed by Soliman et al. (Soliman, 2014) and to evaluate its application for dosimetry in radiation therapy based on X-ray irradiation at ultrahigh dose rates. The gel dosimeter was irradiated at the ESRF - ID17 Biomedical Beamline with orthovoltage X-rays, and its response was compared with the dosimeter response after irradiation with a⁶⁰Co beam reference at the National Center for Radiation Research and Technology (NCRRT). Although the samples were irradiated with homogeneous fields only, a 0–200 Gy dose range was considered to cover the behavior of the gel when receiving both peak and valley doses in typical MRT configurations.

The radiation-induced formation of Ag-NPs in the gel dosimeter was analyzed using a spectrophotometer. The size and morphology of the Ag-NPs were recorded by atomic force microscopy (AFM) and transmission electron microscopy (TEM). The effects of glycerol on the gel reaction, water equivalence, theoretical energy dependence, and uncertainty factors were studied.

To our knowledge, this is the first time that this specific silver nitrate-based gel has been studied after irradiation with an orthovoltage X-ray synchrotron source at an ultrahigh dose rate and compared to a more conventional ⁶⁰Co beam quality. The study highlights the overall good properties of silver nitrate gel dosimeters in radiotherapy applications at high dose rates. The characterized dose increase delivered to the Ag-NP gel when irradiated with synchrotron orthovoltage X-rays shows the potential of the dosimeter for dose enhancement studies.

## 2. Materials and methods

### 2.1. Gel dosimeters preparation

Silver nitrate (99.8%), porcine skin gelatin (G2500), glycerol (99.5%) from Sigma-Aldrich, and double-distilled water were used to prepare silver nitrate gels. All the chemicals were used without additional processing. An aqueous gelatin solution (6% w/v) was prepared using double-distilled water at 40 °C with continuous magnetic stirring until a clear gelatin solution was obtained. The solution was cooled to 31–34 °C and 200 mM AgNO₃ was added while stirring. In addition, two gel compositions containing 200 mM AgNO₃ were prepared using the
same procedure but with different glycerol contents (10 and 20% v/v). All the prepared solutions were stirred at 31–34 °C for 1 h. The solutions were placed in polystyrene cuvettes ($1 \times 3 \times 1 \text{ cm}^3$) and gelled in a refrigerator at 6 °C. Gelatin was used as a capping agent to surround and stabilize Ag NPs created by exposure to ionizing radiation (Mahmoud and Abbo, 2013; Soliman, 2014). Gelatin forms a hydrogen bond with Ag-NPs via electrostatic interactions (Mahmoud and Abbo, 2013), which reduces the Ag-NP clustering formed during preparation and irradiation. Silver ions can interact with gelatin via electrostatic forces (ion dipoles) generated by oxygen- and nitrogen-rich structures in the carboxyl and amine groups of gelatin, respectively (Darroudi et al., 2013; Kapoor et al., 1994). This interaction minimizes the agglomeration of Ag NPs in the gelatin (Xu and Zhou, 2008). Glycerol ($CH_2OH-CHOH-CH_2OH$) is a nontoxic and nonvolatile solvent that can dissolve several poorly soluble compounds in water (Díaz-Alvarez and Cadierno, 2013; Liu et al., 2020). Glycerol can also be used as a reducing agent for metal ions to generate metal nanoparticles (Kou and Varma, 2013; Liu et al., 2020).

For the study, three samples were irradiated under the same conditions and each data point presented in the results is obtained as average of the response of the three samples.

## 2.2. Irradiation with synchrotron radiation

The gel dosimeter was exposed to a polychromatic X-ray beam. A detailed characterization of the beam quality, including the spectrum profile, is available from the previous work of Di Manici et al. (Di Manici et al., 2024). The main features of the spectrum were calculated in the range of 0.1–600 keV, giving a mean energy of 102 keV, an intensity peak at 86 keV, about 3.6% of photons with energy higher than 200 keV and less than 3.0% of photons with energy lower than 50 keV. The TH beam quality series is used for detector calibration, with the TH200 beam quality best matching the beam characteristics. A broad beam configuration, that is, a homogeneous field, at the ID17 Biomedical beamline of the European Synchrotron Radiation Facility was used for sample irradiation. The experimental setup, irradiation protocols, and settings were the same as those described in a previous study by Soliman et al. (2020), and only some essential information is reported here. Reference dosimetry was performed using a PTW PinPoint ionization chamber (model N31014) with an active volume of 0.015 cm³. A field of $2 \times 2 \text{ cm}^2$ was delivered to the PMMA phantom ($15 \times 15 \times 12 \text{ cm}^3$), and the reference depth was set to 2 cm from the phantom surface. The calibration of the dose rate to water and other corrections applied to the measurements of the PTW chamber have been discussed previously (Di Manici et al., 2024). The overall uncertainty of the doses determined using the PTW PinPoint ionization chamber was estimated to be 3.88% at $2\sigma$ (Di Manici et al., 2024).

The cuvettes filled with the gel dosimeter were irradiated under the same conditions established for the reference dosimetry. A hole in the dimensions of the plastic cuvettes was milled in a PMMA plate to accommodate the sample for irradiation (Fig. 1). The sample in the designated plate was then joined to the other plates to mimic the PMMA phantom used in the beam calibration. The center of the cuvette was 2 cm from the phantom surface. Both beam calibration and sample irradiation were performed in the PMMA material to avoid the use of an additional correction factor, as PMMA is not a perfect water-equivalent material for ID17 beam quality (Cameron et al., 2017). The gel dosimeter was irradiated at a dose rate of 11.6 kGy/s with absorbed doses between 10 and 200 Gy.

To accurately compare the average dose measured by the PTW ionization chamber and the cuvette filled with gel, different sizes of the active volumes of the two detectors were considered. The dose at the center of the field was averaged over $2 \times 4 \times 2 \text{ mm}^3$ for the PTW PinPoint chamber and over $2 \times 2 \times 10 \text{ mm}^3$ for the gel dosimeter. The horizontal dose intensity profile of the homogeneous field inside the phantom was checked using radiochromic film dosimetry (Pellicioli et al., 2019), whereas the dose intensity profile along the beam

<figure><img src="image_4.png" /><figcaption>Fig. 1. Picture of the PMMA slab machined to host the gel cuvette during the irradiation. The phantom used for sample irradiation is made of several PMMA plates defining a volume of $15 \times 15 \times 12 \text{ cm}^3$ (Soliman et al., 2020). The sample is located with its center at 2 cm depth from the entrance surface of the phantom.</figcaption></figure>

propagation direction was calculated using Monte Carlo simulations. The vertical dimension of 2 mm for gel analysis was fixed by the slit used in the spectrophotometer (see Section 2.4). The difference between the average dose deposited in the two different detector volumes considered should be approximately 0.07% greater for the gel dosimeter than for the ionization chamber. This difference was considered negligible.

## 2.3. Irradiation with the $^{60}$Co source

The gel dosimeters were irradiated with γ-rays in the range of 5–200 Gy using a Gamma Cell-220 Excel $^{60}$Co source manufactured by MDS Nordion (Canada) and installed at the National Center for Radiation Research and Technology (NCRRT). A customized sample holder made of PMMA was used to hold the gel samples during irradiation and to achieve electronic equilibrium with an appropriate deep dose build-up. The dose rate to water was 0.27 Gy/s, measured with the alanine dosimetry system traceable to the National Physical Laboratory (NPL), UK. The significant differences in the spectrum energy and dose rates of the irradiation beam at the two experimental facilities, the ESRF - ID17 beamline and the NCRRT - Gamma Cell facility, were carefully considered to deliver the same doses (within the irradiation uncertainties) in both laboratories.

## 2.4. Spectrophotometric measurements of the gel response

Samples irradiated at the ID17 beamline were analyzed at the ESRF using a PerkinElmer Lambda 40 UV/VIS spectrophotometer with a slit width of 2 mm over the spectral range of 350–750 nm. Samples irradiated with the $^{60}$Co source were analyzed at the NCRRT using a Thermo Fisher Scientific Evolution 500 UV-VIS spectrophotometer with a slit width of 2 mm over the same spectral range. The maximum absorption band for the irradiated samples was centered at approximately 450 nm ($\lambda_{max}$); therefore, this wavelength was chosen to calculate the dose-response curves. Despite the dose gradients present in the irradiated gel sample as described in Section 2.2, the spectrophotometer measurements reflect the signal transmitted by the entire sample and can be considered representative of the average dose delivered to the sample. The response curves were calculated based on the change in the net
absorbance ΔA as a function of the absorbed doses, where ΔA is the absorbance after irradiation (Aᵢ) – absorbance before irradiation (A₀). The absorbance spectra are presented in Section 3.1.

Furthermore, the lowest detectable dose (LDD) was obtained by estimating the dose corresponding to the three standard deviations (3SD) of the absorbance of the unirradiated gel samples I₀ (Bartolotta et al., 1993; Brai et al., 2007; Gallo et al., 2017; Lima et al., 2021) as follows:

$$LDD = \left( \frac{I_0 + 3SD - a}{b} \right) \qquad (1)$$

where a and b are the intercept and slope of the dose-response curves, respectively, obtained by linear fitting (y = a + bx) the absorbance (y-values) against the delivered doses (x-values).

## 2.5. Particle size analysis of Ag NPS

The size of the Ag-NPs formed in the gel dosimeter irradiated at the ESRF was analyzed using atomic force microscopy (AFM). Imaging was performed at room temperature (22 °C) in tapping mode at a scan rate of 2.44 Hz using an Asylum Research Cypher-S instrument provided by ESRF through the Partnership for Soft Condensed Matter (PSCM). The AFM was equipped with Bruker's Sharp Microlever MSNL probes (lever F) with a spring constant of 0.6 Nm and a typical resonance frequency of 101.8 kHz, as determined by the thermal noise method. Approximately 50 µm thick uniform layers of gel samples were spread and made to adhere to flat mica surfaces to allow AFM investigations of the gel surface. The AFM height (topography) and phase images were preprocessed using the Gwyddion software to apply polynomial background removal techniques to flatten the images. Only the nanosized regions that showed increased contrast in the phase images were attributed to the possible presence of near-surface, hard, solid nanoparticles having sharply different mechanical properties with respect to the surrounding soft gel. The corresponding regions in the topographic images were highlighted by threshold filtering, and their calculated area was used to estimate the particle size as the diameter of a circle with the corresponding area.

It should be noted that this method can detect only the nanoparticles residing at the gel surface or within a nano-thick layer below it, but it is insensitive to the presence of nanoparticles in the bulk of the gel. In addition, this method is expected to provide underestimated particle size values because the latter depends on the random and non-controllable nanoscale depth of the nanoparticle center with respect to the gel film surface. An indirect qualitative estimation of the bulk nanoparticle concentration can be inferred from the surface number density of AFM-detected nanoparticles, but such density values should be interpreted with caution because they depend both on the random effects of sample preparation and on the AFM operator's choice of specific observation areas.

The size of the Ag-NPs formed in the gel dosimeter irradiated at the NCRRT was analyzed using a Jeol JEM-100CXII transmission electron microscope (TEM) (JEOL Ltd., Japan) at the NCRRT because AFM was not available. The electron source for the microscope was tungsten (80 kV). The TEM has a resolution of 0.2 nm (crystal lattice test) and 0.45 nm (point-to-point) at 80 kV. The gel samples were diluted and sonicated. A drop of gel was then placed on a copper grid. The grid was then dried at room temperature and analyzed using TEM. The average size of the Ag-NPs was recorded using the ImageJ software.

## 2.6. Relative response and energy dependence

To measure the experimental relative responses F<sub>Q,Q₀</sub> due to the energy dependence of the gel dosimeter irradiated at the ESRF - ID17 beamline, the formalism proposed by Waldeland et al. (2010) was used, as follows (Eq. (2)):

$$F_{Q,Q_0} = \frac{(r/D_w)_{Co}}{(r/D_w)_{ESRF}} \qquad (2)$$

where r is the response of the dosimeter, and D<sub>w</sub> is the delivered dose as the absorbed dose to water. For a dosimeter with a linear response, r/D<sub>w</sub> represents the slope of the dose-response curve. In the case of the silver nitrate gel dosimeter, F<sub>Q,Q₀</sub> for the ID17 beam quality (Q) relative to the reference <sup>60</sup>Co beam quality (Q₀) is the ratio between the slope of the two dose-response curves. The energy dependence F<sub>Q,Q₀</sub> given by Waldeland et al. (2010) is comparable to the relative response r given by Anton et al. (Anton and Büermann, 2015) which is defined starting from the mass energy absorption coefficient of the dosimeter used, as described in the next section.

According to the fundamentals of theoretical dosimetry (Eisenlohr, 1987), the theoretical energy dependence factor of a dosimeter can be estimated by comparing the ratio (μ<sub>en</sub>/ρ)<sub>dosimeter,w</sub> = (μ<sub>en</sub>/ρ)<sub>dosimeter</sub>/(μ<sub>en</sub>/ρ)<sub>w</sub> at a given photon energy, with the same ratio estimated for a <sup>60</sup>Co γ-ray source, which is considered the reference beam quality (Anton and Büermann, 2015; Nasreddine et al., 2021). Waldeland et al. (2010) define this ratio H<sub>Q,Q₀</sub> as follows (Eq. (3)):

$$H_{Q,Q_0} = r^{\mu_{en}/\rho} = \frac{\left[ \frac{(\mu_{en}/\rho)_{Gel,w}}{H_{ESRF}} \right]}{\left[ \frac{(\mu_{en}/\rho)_{Gel,w}}{H_{Co}} \right]} \qquad (3)$$

where (μ<sub>en</sub>/ρ)<sub>Gel,w</sub> = (μ<sub>en</sub>/ρ)<sub>gel</sub>/(μ<sub>en</sub>/ρ)<sub>w</sub>. The mass energy absorption coefficients (μ<sub>en</sub>/ρ) of the silver nitrate gel dosimeter (μ<sub>en</sub>/ρ)<sub>gel</sub> and water (μ<sub>en</sub>/ρ)<sub>w</sub> for photon energies in the 1–20 MeV range were obtained from NIST physical reference data (Phillips et al., 1976; Seltzer, 1993). The [(μ<sub>en</sub>/ρ)<sub>Gel,w</sub>]<sub>ESRF</sub> value of the ESRF - ID17 beamline beam quality was calculated by weighting the response with the ID17 photon spectrum. To compare the theoretical and experimental values, the relative radiation chemical yield G<sub>Q,Q₀</sub> was defined as F<sub>Q,Q₀</sub>/H<sub>Q,Q₀</sub> (Waldeland et al., 2010).

## 2.7. Uncertainty budget

Uncertainties of types A and B were considered (ISO/ASTM 51707-15, 2015; Peter and Miller, 2009). Type A, u<sub>A</sub>, is evaluated using statistical methods from a series of repeated measurements, and type B, u<sub>B</sub>, is evaluated using non-statistical methods, that is, taken from the manufacturer through a supplied certificate or from the literature. Several parameters may contribute to the uncertainty in radiation dose measurements, including the calibration of the <sup>60</sup>Co-NCRRT or ID17 beamline, batch uniformity of the silver nitrate gel dosimeter, stability of the dosimeter response, spectrophotometric analysis (sensitivity and reproducibility of measurements), and calibration curve fit. These values were calculated based on extensive discussion in the literature (Abdel-Fattah et al., 2012; Mehta, 2006; Nagy et al., 2002; Tadros et al., 2021), guidelines (Mehta and Girzikowsky, 1999; Sharpe and Miller, 2009), and ISO standards (ISO/ASTM 51707-15, 2015). The uncertainty parameters of the dose measurements on the <sup>60</sup>Co-NCRRT beam using the silver nitrate gel dosimeter are listed in Table 1. The same methods were used to evaluate the uncertainty of the silver nitrate gel exposed to ESRF ID17 beam quality. The uncertainty associated with the calibration of the ID17 beam using the PTW PinPoint ionization chamber was set to 3.88% at 2σ (Di Manici et al., 2024). The overall 2σ uncertainties associated with the assessment of the absorbed doses for the <sup>60</sup>Co-NCRRT and ESRF ID17 beams were set to 5.83% and 5.14%, respectively.
<caption>**Table 1**</caption>

Uncertainty budget for doses measured with silver nitrate gel dosimeters at the ⁶⁰Co-NCRRT facility and the ESRF – ID17 beamline.

<table><thead><tr><th>Uncertainty parameter</th><th>Type of uncertainty</th><th>Standard uncertainty %</th></tr></thead><tbody><tr><td colspan="3"><strong>At the NCRRT facility:</strong></td></tr><tr><td>Dose rate calibration</td><td>B</td><td>1.10 <sup>1)</sup></td></tr><tr><td>Irradiation facility (Mehta, 2006)</td><td>B</td><td>0.32</td></tr><tr><td>Sensitivity variation of the spectrophotometer <sup>2)</sup></td><td>A</td><td>0.08</td></tr><tr><td>Reproducibility of the spectrophotometer <sup>3)</sup></td><td>A</td><td>0.30</td></tr><tr><td>Batch uniformity of the gel dosimeter</td><td>A</td><td>2.0</td></tr><tr><td>Calibration curve fitting (from residual analysis) <sup>4)</sup></td><td>A</td><td>1.67</td></tr><tr><td>Response stability (Soliman, 2014)</td><td>B</td><td>0.385</td></tr><tr><td>Irradiation temperature effect (Soliman, 2014)</td><td>B</td><td>0.391</td></tr><tr><td>Combined NCRRT standard uncertainty (u<sub>c</sub>), 1σ</td><td></td><td>2.915</td></tr><tr><td>Expanded NCRRT uncertainty (2σ), %</td><td></td><td>5.83</td></tr><tr><td colspan="3"><strong>At the ESRF – ID17 beamline:</strong></td></tr><tr><td>Dose rate calibration (Di Manici et al., 2024)</td><td>B</td><td>1.94</td></tr><tr><td>Sensitivity variation of the spectrophotometer</td><td>A</td><td>0.09</td></tr><tr><td>Reproducibility of the spectrophotometer</td><td>A</td><td>0.4</td></tr><tr><td>Batch uniformity of the gel dosimeter</td><td>A</td><td>0.65</td></tr><tr><td>Calibration curve fitting (from residual analysis)</td><td>A</td><td>1.40</td></tr><tr><td>Response stability (Soliman, 2014)</td><td>B</td><td>0.385</td></tr><tr><td>Irradiation temperature effect (Soliman, 2014)</td><td>B</td><td>0.391</td></tr><tr><td>Combined ESRF – ID17 beamline standard uncertainty (u<sub>c</sub>), 1σ</td><td></td><td>2.57</td></tr><tr><td>Expanded ESRF – ID17 beamline uncertainty (2σ), %</td><td></td><td>5.14</td></tr></tbody></table>

# 3. Results and discussion

## 3.1. Absorption spectra

The background color of the prepared gel was faint yellow, indicating the formation of Ag-NPs due to heating during preparation (Darroudi et al., 2011a; Soliman, 2014). This effect was confirmed by Soliman et al. by comparing the absorbance spectrum of an unirradiated silver nitrate gel dosimeter with a gel sample without silver nitrate (Soliman, 2014). After irradiation, the gel turned initially yellow and then yellowish-brown with increasing absorbed dose, indicating the formation of γ-ray-induced Ag-NPs identified by a surface plasmon resonance (SPR) band at 450 nm. The gel absorption spectra for different delivered doses are shown in Fig. 2. The absorption of this band increased significantly with increasing absorbed dose, with a minimal shift in the SPR band position. The consistency of the SPR band position with increasing doses up to 200 Gy suggests that the size of the Ag metallic clusters formed remained relatively stable (Ramnani et al., 2007; Soliman, 2014). The plasmon band position is mainly dependent on nanoparticle size (Darroudi et al., 2011b; Ramnani et al., 2007; Soliman, 2014). This finding is also supported by the AFM analysis reported in Section 3.2.

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Absorption spectra of silver nitrate gel dosimeters (200 mM AgNO₃, 20% glycerol) irradiated with different absorbed doses (0–200 Gy) using the X-ray beam quality of the ESRF – ID17 Biomedical beamline.</figcaption></figure>

## 3.2. Particle size analysis

Fig. 3 shows typical AFM topography images of the unirradiated (0 Gy, Fig. 3a) and irradiated gels (50 and 200 Gy, Fig. 3b and c, respectively). Using the procedure described in Section 2.5 to analyze the AFM data resulted in interpreting as nanoparticles only a subset of the bright spots visible in Fig. 3a–c. Specifically, all points with an equivalent disk radius of less than 2 nm were excluded from the counting statistics to reduce the impact of potentially misidentifying nanoparticles. For the unirradiated gel (Fig. 3a), N = 78 eligible particles were selected from four 1 × 1 mm<fnref n="2" /> AFM images acquired at different locations on the gel surface. The resulting average particle size (equivalent diameter) is d = 13.2 ± 5.0 (σ) nm with an average nanoparticle surface density of φ = 19.5 ± 7.9 (σ) nanoparticles/µm<fnref n="2" />. The corresponding values for the gel irradiated with 50 Gy (Fig. 3b) are N = 231, d = 13.0 ± 4.2 (σ) nm, and φ = 31.5 ± 18 (σ) nanoparticles/µm<fnref n="2" />. These results were obtained from seven AFM images with sizes ranging from 2 × 2 to 0.5 × 0.5 µm<fnref n="2" />. Finally, in the case of the gel irradiated with 200 Gy (Fig. 3c), three AFM images with sizes ranging from 2 × 2 to 1 × 1 mm<fnref n="2" /> yielded N = 60, d = 13.2 ± 6.4 (σ) nm, and φ = 13.0 ± 6.2 (σ) nanoparticle/µm<fnref n="2" />. The most striking and robust AFM result is the constancy of the size of the nanoparticles under different irradiation conditions, which is consistent with the absence of a red or blue shift in the surface plasmon resonance caused by irradiation (Fig. 2). The increase in the number of surface nanoparticles in the gel irradiated with 50 Gy compared to the unirradiated gel is consistent with the increasing absorption peak (Fig. 2). However, the lower value found in the 200 Gy case suggests that φ it is too susceptible to variations in sample preparation and dilution for AFM data acquisition to be a reliable index of actual nanoparticle concentration.

TEM studies of the silver nitrate gel dosimeter provided definitive evidence for the presence of nanoparticles in the gel samples. The TEM images of the unirradiated and irradiated (200 Gy) samples are shown in Fig. 4. According to ImageJ analysis of the TEM images, the diameter of Ag-NPs is 29.1 ± 14.8 (σ) nm and 25.0 ± 6.4 (σ) nm for unirradiated and irradiated sample, respectively. The range of Ag-NP size distribution is 14.0–78.9 nm for the unirradiated samples and 13.9–48.4 nm for the irradiated samples, indicating good homogeneity of Ag-NPs dispersed in the irradiated gel sample and smaller particle size formed upon radiation. These results are supported by the smaller broadening of the SPR band at higher absorbed doses (Fig. 2), which is consistent with previously observed results (Eid, 2011; Soliman, 2014). Both AFM and TEM analyses showed that the Ag-NPs produced after irradiation were spherical.

<footnote n="1">¹ As quoted from the NPL calibration certificate for the ⁶⁰Co-NCRRT facility.</footnote>

<footnote n="2">² It is a coefficient of variation for a set of twenty spectrophotometric analyses on the same irradiated cuvette sample. During the analyses, the cuvette was fixed into the sample holder.</footnote>

<footnote n="3">³ It is determined as in footnote 2), except that the irradiated cuvette was removed from the holder and then returned to the holder between measurements.</footnote>

<footnote n="4">⁴ Presented in previously published works (Abdel-Fattah et al., 2012; Peter and Miller, 2009).</footnote>
<figure><img src="image_6.png" /><figcaption>Fig. 3. AFM images for Ag-NPs study: (a) unirradiated gel sample, (b) irradiated gel sample at 50 Gy and (c) irradiated gel sample at 200 Gy on ID17 Biomedical beamline - ESRF.</figcaption></figure>

### 3.3. Influences of glycerol on the gel response

The effect of the glycerol content on the gel response at $\lambda_{max} = 450$ nm is shown in Fig. 5a. The responses of the gels in this band grew linearly with increasing absorbed doses up to 100 Gy. For gels containing 0%, 10%, and 20% v/v glycerol, the $r^2$ values obtained from the linear fitting were 0.998, 0.999, and 0.999, respectively. The intensity of this band increased with increasing glycerol content in the gel matrix, indicating a greater reduction of Ag⁺ ions in Ag-NPs when 20% v/v glycerol was used. Therefore, the radiation sensitivity, calculated as the slope of the gel response, increased with increasing glycerol content of the gel, as shown in Fig. 5b. The sensitivity of the gel dosimeter with 20% v/v glycerol was approximately 24.0% higher than that of the gel without glycerol. Therefore, a composition of 20% v/v glycerol was chosen for the present study to maximize radiation sensitivity.

Upon irradiation, water decomposes into hydrogen radicals ($H^*$) and hydroxyl radicals (OH•) (Eq. (4)). The $H^*$ radical reduces the $Ag^+$ ion to $Ag^0$ metal; however, $OH^*$ can oxidize the $Ag^0$ metal to $Ag^+$ or oxidize $Ag^+$ to an ion with a higher oxidation state (Saion et al., 2013; Schwarz et al., 1972). In addition, the solvated electrons ($e_s$) generated in a glycerol-containing medium (Temgire and Joshi, 2004) can act as strong

reducing agents for the $Ag^+$ ions (Eq. (5)). The chemical yield of solvated electrons formed in glycerol after radiolysis was greater than that of any other alcohol (Kajiwara and Thomas, 1972), which explains why glycerol plays an important role in enhancing the radiation sensitivity of this gel.

$$H_2O \xrightarrow{\text{ionizing radiation}} e_s^-, H_3O^+, H^*, OH^*, H_2, H_2O_2, H_3O^+ \quad (4)$$

$$Ag^+ + e_s^- \xrightarrow{\text{ionizing radiation}} Ag^0 \quad (5)$$

Glycerol scavenges $OH^*$ radicals by forming radicals, as shown in equations (6) and (7) (Baugh et al., 1982; Moore and Norris, 1976). This reaction inhibits the $OH^*$ radicals that cause the oxidation of $Ag^0$ metals or $Ag^+$ ions to a higher oxidation state. At the same time, it enhances the reduction of $Ag^+$ ions to $Ag^0$ NP (Belloni, 2006; Krstić et al., 2014; Temgire and Joshi, 2004) (equations (8) and (9)).

$$CH_2OH - CHOH - CH_2OH + OH^* \rightarrow *C HOH - CHOH - CH_2OH + H_2O \quad (6)$$
<figure><img src="image_7.png" /><figcaption>Fig. 4. TEM images of Ag-NPs in (a) unirradiated gel sample and (b) irradiated gel sample (200 Gy) at ⁶⁰Co source - NCRRT.</figcaption></figure>

$$CH_2OH - CHOH - CH_2OH + OH^* \rightarrow CH_2OH - C^*OH - CH_2OH + H_2O \quad (7)$$

$$^{\bullet}C HOH - CHOH - CH_2OH + Ag^+ \rightarrow Ag^o + CHO - CHOH - CH_2OH + H^+ \quad (8)$$

$$CH_2OH - C^*OH - CH_2OH + Ag^+ \rightarrow Ag^o + CH_2OH - CHO - CH_2OH + H^+ \quad (9)$$

Although an increase in gel response to orthovoltage radiation (see sections 3.4 and 3.5 below) would be observed even without the addition of glycerol, the use of the solvent resulted in an even more sensitive detector capable of discriminating small dose variations even better. In addition, the use of glycerol improves the signal-to-noise ratio of the gel at lower doses within the applied range. Depending on the dosimeter application, the improved gel response when loaded with glycerol can

be an added value to the detector.

### 3.4. Comparison of the responses of the gel dosimeter at the ID17 beamline with ⁶⁰Co γ-rays

The response of the net absorption of the irradiated gel using the ⁶⁰Co-NCRRT and orthovoltage X-rays at ID17-ESRF as a function of the absorbed dose in water is shown in Fig. 6. The dosimeter response at ⁶⁰Co was linear up to 200 Gy (correlation coefficient r² = 0.9999), but only up to 100 Gy at the ID17 beamline (r² = 0.9984). The overall response of the gel irradiated with synchrotron radiation was better fitted by a quadratic curve (r² = 0.9999). The gel dosimeter irradiated at the ID17 beamline exhibited a stronger response than the ⁶⁰Co γ-beam. The LDD of the gel dosimeters was found to be 0.63 Gy and 2.60 Gy for the gel irradiated using the ID17 beamline and the ⁶⁰Co beam quality, respectively. The radiation sensitivities up to 100 Gy for the gel samples irradiated with the ID17 beamline and ⁶⁰Co beams were 0.0153 and 0.0087 Gy⁻¹ cm⁻¹, respectively. Accordingly, the relative response, F<sub>Q, Qo</sub>, was equal to 0.0153/0.0087 = 1.7586. The sensitivity of the gel irradiated with the ID17 beam was 76% higher than that of the ⁶⁰Co beam, indicating a significantly higher dose deposition in the ID17 beam due to silver nanoparticles. The higher dose deposition and relative response (F<sub>Q, Qo</sub>) values, as well as the smaller LDD value, obtained with synchrotron radiation exposure, are related to the enhanced photoelectric interaction contribution of the orthovoltage X-rays with silver (Z = 47) in the gel matrix with respect to irradiation at the ⁶⁰Co source (NIST, 2021).

The decrease in the gel response rate when irradiated with the synchrotron spectrum at 200 Gy can be related to a saturation effect that the detector undergoes under these irradiation conditions. Below 200 keV, the photoelectric interaction increases significantly for photons interacting with silver. Therefore, a strong increase in the production of Ag-NPs is expected compared to irradiations with 60Co sources, leading to the onset of saturation effects.

### 3.5. Water equivalency and theoretical energy dependence

The ratio (μ<sub>en</sub>/ρ)<sub>Media, W</sub> between the mass energy-absorption coefficient of different media (μ<sub>en</sub>/ρ)<sub>Media</sub> and the mass energy-absorption coefficient of water (μ<sub>en</sub>/ρ)<sub>W</sub> for photon energies in the range of 0.01–10 MeV are shown in Fig. 7. The media considered were the silver nitrate gel dosimeter, alanine material, and soft tissue. The gel can be considered to be equivalent to water for photon energies above 300 keV. The weight average between the (μ<sub>en</sub>/ρ)<sub>Gel, W</sub> at different energies and the corresponding photon intensity of the ID17 beam spectrum used resulted in a (μ<sub>en</sub>/ρ)<sub>Gel, W (ESRF)</sub> of 1.67, while the corresponding (μ<sub>en</sub>/ρ)<sub>Gel, W (Co-60)</sub> value for the ⁶⁰Co beam quality was 0.983. The theoretical energy dependence H<sub>Q, Qo</sub> is 1.67/0.98 = 1.70. The relative radiochemical yields were G<sub>Q, Qo</sub> = F<sub>Q, Qo</sub>/H<sub>Q, Qo</sub> = 1.76/1.70 = 1.04 (see sections 2.6 and 3.4). The value of G<sub>Q, Qo</sub> shows that the theoretical energy dependence, H<sub>Q, Qo</sub>, is comparable to the experimentally measured value, F<sub>Q, Qo</sub>.

The plot of the mass energy absorption coefficient (Fig. 7) clearly shows that the silver nitrate gel has attenuation properties that vary greatly for beam energies below 200 keV. This factor must be carefully considered when comparing detectors irradiated at different beam energies. Further characterisation of the gel energy dependence in the orthovoltage energy range is recommended for the possible definition of correction factors. In the meantime, dose evaluation and comparison between samples can only be considered valid if performed under the same spectrum conditions.

## 4. Conclusion

A gel dosimeter based on silver nitrate (AgNO<sub>3</sub>) and glycerol has been investigated as a possible new dosimeter for studies on innovative
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** (a) The upper part of the figure shows the dose-response curve at 450 nm of the silver nitrate gel dosimeter with different glycerol content. Irradiation was performed at the ⁶⁰Co source – NCRRT with absorbed doses up to 100 Gy. A linear fit was applied to each dataset. The lower part of the figure shows the residuals of the three data set with respect to the fitted linear curve. (b) Influence of the glycerol content on the radiation sensitivity of the silver nitrate gel dosimeter. A quadratic curve was used for fitting.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** The upper part of the figure shows the dose-response functions of silver nitrate gel dosimeters exposed to orthovoltage X-rays at ID17 beamline – ESRF and to γ-rays of ⁶⁰Co – NCRRT. The net absorption for samples irradiated at the synchrotron source are best fitted with a 2nd order polynomial function (r² = 0.9999), black dashed line, but a good linear fit is found up to around 100 Gy (r² = 0.9984), black dotted line. The response at the ⁶⁰Co is well fitted using a linear function (r² = 0.9999), red dashed line. The lower part of the figure shows the residuals of the experimental data with respect to the fitted curves. For the ID17 beamline data set, the residuals are calculated with respect to the 2nd order polynomial function fit.</figcaption></figure>

MRT and FLASH radiotherapy techniques developed with synchrotron X-rays in the orthovoltage range and at ultra-high dose rates on the order of tens of kGy/s.

The response of the AgNO₃-based gel dosimeter to irradiation at the European Synchrotron Radiation Facility (ESRF) - ID17 Biomedical beamline was compared to irradiation at the ⁶⁰Co-NCRRT facility. The

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Plot of the (μen/ρ)Media,W ratio between the mass energy-absorption coefficient of different media (μen/ρ)Media and the water one (μen/ρ)W. Media considered are: silver nitrate gel dosimeter, alanine dosimeter and soft tissue. The (μen/ρ)Gel,W value of the gel is equal to 1.75 at 100 kV (the average energy of the ID17 beamline - ESRF X-ray beam spectrum) while the corresponding value for Alanine and soft tissue is almost equal to 1. Lines between graph points are intended to guide the eyes.</figcaption></figure>

AFM and TEM images of the irradiated gel confirmed that the Ag-NPs had a spherical shape. Sample analysis by spectrophotometry showed that the irradiated gel had an SPR band at 450 nm, which was associated with the presence of Ag-NPs. The intensity of the SPR peak increased linearly as the absorbed dose increased to 100 Gy. The addition of 20% v/v glycerol to the gel matrix increased the radiation sensitivity by 24.0% compared with the gel without glycerol. This was attributed to the high chemical yield of solvated electrons generated in glycerol after irradiation, which promotes the reduction of Ag⁺ to Ag-NPs. In addition, glycerol acts as a radical scavenger for OH⁺ radicals, which can oxidize Ag⁺ ions or Ag NPs to higher oxidation states. This shifts the post-
irradiation reaction towards reduction instead of oxidation, leading to
an increase in radiation sensitivity.

The relative response of the AgNO₃-based gel dosimeter irradiated at the synchrotron source with respect to ⁶⁰Co source, F<sub>Q,Qo</sub>, was 1.76, that is, the measured dose enhancement factor was 76%. The theoretical energy dependence, H<sub>Q,Qo</sub>, was calculated as 1.70. The relative radiochemical yield, G<sub>Q,Qo</sub> = F<sub>Q,Qo</sub>/H<sub>Q,Qo</sub>, was 1.04, indicating close agreement between the experimental and theoretical values of the energy dependence. The total uncertainties (2σ) of the dose measured with the silver nitrate gel at the ID17-ESRF beam and ⁶⁰Co-NCRRT facility were calculated to be 5.14% and 5.83%, respectively.

In summary, the gel based on Ag-NPs has attractive properties as a dosimeter for synchrotron radiotherapy studies because it has higher sensitivity than water-equivalent gels and can therefore better resolve small dose variations. The gel dosimeter loaded with NPs can be considered a promising tool for measuring the dose enhancement factor in nanoparticle-based radioenhancement for radiotherapy techniques as well.

CRediT authorship contribution statement

Yasser S. Soliman: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Marie Capron: Writing – review & editing, Visualization, Formal analysis. Diego Pontoni: Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Formal analysis, Data curation. Michael Krisch: Writing – review & editing, Supervision, Resources, Project administration, Formal analysis. Paolo Pellicoli: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this study.

Data availability statement

The data that support the findings of this study are available within
the article.

Declaration of competing interest

The authors declare the following financial interests/personal re-
lationships which may be considered as potential competing interests:
Yasser S. Soliman reports financial support was provided by Science and
Technology Development Fund. Yasser S. Soliman reports financial
support was provided by French Institute in Egypt. If there are other
authors, the authors declare that they have no known competing financial in-
terests or personal relationships that could have appeared to influence
the work reported in this paper.

Acknowledgement

This work was supported by the French and Egyptian governments through the Science and Technology Development Fund (STDF), project ID: 30586, granted by the French embassy in Egypt (Institut Français d'Egypte).

Data availability

Data will be made available on request.

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