Scintillating Micro-Probe Detectors for Conventional and FLASH Proton Dosimetry: Optical Transport and Geometry Modeling

1. Introduction

Proton beam therapy (PBT) achieves superior spatial dose distribution compared to conventional photon therapy by taking advantage of the physical properties of the Bragg peak, thereby sparing adjacent healthy tissues [1,2,3,4,5]. Accurately resolving these steep dose gradients requires real-time beam monitoring systems equipped with sensitive volume detectors exhibiting high spatial resolution [6,7,8]. Furthermore, the clinical transition toward high-flux delivery systems and ultra-high dose rate (UHDR) paradigms, such as FLASH radiotherapy [9,10,11], introduces stringent operational constraints that real-time dosimeters must maintain a linear response under extreme photon generation rates before reaching signal saturation [12].

In proton dosimetry, both plastic scintillators and inorganic scintillator detectors (ISDs) are actively investigated, each offering distinct operational trade-offs. Plastic scintillators benefit from water-equivalent density and rapid temporal response, enabling direct dose rate measurements across scanned proton fields [13]. However, plastic scintillators exhibit pronounced non-linear ionization quenching near the Bragg peak due to high linear energy transfer (LET), alongside lower volumetric light yields that necessitate larger sensitive volumes to maintain adequate signal-to-noise ratios [13,14]. Moreover, a common issue for plastic scintillators is Cerenkov contamination due to the larger plastic volume that creates extra light under irradiation and requires significant corrections [7,15,16,17,18,19,20]. Conversely, fiber-coupled ISDs have been systematically evaluated for proton beam verification for over two decades [21,22]. Early investigations comparing various inorganic candidates established that silver-activated zinc cadmium sulfide—$\left(\mathrm{Zn},\mathrm{Cd}\right)\mathrm{S}\text{:}\mathrm{Ag}$—embedded in polymer matrices provides exceptional volumetric light output and favorable response characteristics in proton energy ranges [8,21,23]. This heightened sensitivity allows for significant volume miniaturization down to sub-millimeter scales, making $\left(\mathrm{Zn},\mathrm{Cd}\right)\mathrm{S}\text{:}\mathrm{Ag}$-based ISDs ideal for steep-gradient fields and accurate beam characterizations, provided internal light collection efficiency and count-rate saturation ceilings are accurately modeled.

Existing theoretical models, however, rely on simplified ray-tracing assumptions that neglect bulk optical scattering and utilize a simple optical fiber insertion depth modeling with respect to the scintillator head [8]. In this work, we addressed these limitations by establishing an framework based on practical optical fiber depth modeling within the scintillating volume and implementing full Monte Carlo optical transport simulations incorporating bulk scattering. By combining detector boundary definitions with full optical transport simulations, this work provides accurate dose-rate characterizaton to guide the design and optimization of micro-volume inorganic scintillators for clinical and preclinical proton dosimetry.

2. Materials and Methods

2.1. Proton Beam Characteristics and Irradiation Setup

Proton irradiations were modeled based on the experimental beamline configuration at the Institut Pluridisciplinaire Hubert Curien (IPHC, CNRS, Strasbourg University). The facility utilizes a TR24 cyclotron (ACSI, Canada) delivering proton beams up to 25 MeV for passive radiobiology experiments [24]. The beam is scattered by an aluminum foil and collimated to establish a uniform lateral dose profile before extraction into air through a 5-mm-radius circular collimator defining the target field.

The irradiation environment was modeled as a broad, laterally uniform field encompassing the dosimeter volume. The primary proton fluence rate ($\varphi$) across the target cross-section is expressed as a function of the average beam current ($I_{\mathrm{beam}}$), elementary charge (e), and beam cross-sectional area ($A_{\mathrm{beam}}$):

$$\varphi ={\displaystyle \frac{I_{\mathrm{beam}}}{e·A_{\mathrm{beam}}}}$$

(1)

where $A_{\mathrm{beam}}=\pi r_{\mathrm{col}}^2$, with $r_{\mathrm{col}}$ representing the radius of the circular collimator.

2.2. Inorganic Scintillating Detector Architecture

The single-photon scintillation detectors analyzed in this study are constructed according to established fabrication protocols [25,26,27]. Each sensor head consists of a composite matrix of inorganic scintillator grains—silver-activated zinc cadmium sulfide, (Zn,Cd)S:Ag (Phosphor Technology Ltd.). The scintillating mixture is dispersed within a polymethyl methacrylate (PMMA) binder at a $70:30$ volume proportion. The scintillator exhibits a material density of $4.7{\mathrm{g}/\mathrm{cm}}^3$ and a median particle diameter of $6.0\mu \mathrm{m}$. This scintillating mixture forms an approximately ellipsoidal head attached directly to the cleaved end of optical fiber ($105\mu \mathrm{m}$ core diameter, Thorlabs Inc., FG105LVA).

The physical dimensions of the detector’s active volume (ellipsoidal head geometry) are characterized by full-axes lengths a, b, and c, where the fiber insertion depth into the scintillating head is specified by h, as shown in Figure 1(b). However, in the case where $a=b=c$, the ellipsoidal head of the scintillator reduces to a spherical shape. Primary proton energy deposition within the scintillator bulb generates isotropic scintillation light centered near $\lambda =660\mathrm{nm}$ (red emission).

A fraction of these emitted photons falls within the numerical aperture of the fiber core—defined by a critical acceptance angle (${\theta }_c)=0.1\mathrm{rad}$—establishing the effective optical collection domain within the scintillator head. Throughout this manuscript, this region is designated as the “effective volume” ($V_{\mathrm{eff}}$). For the ellipsoidal geometry, $V_{\mathrm{eff}}$ comprises two distinct geometric regions: a top truncated ellipsoidal cap (highlighted in yellow in Figure 1(b)) that transitions into a downward-tapering conical structure (highlighted in white in Figure 1(b)) extending toward the top of optical fiber interface.

2.3. Detection System Hardware and Readout Characteristics

Optical signal acquisition was performed using a single-photon counting module (SPD_1_VIS_M1, AUREA Technologies) characterized by a 71% spectral quantum efficiency (${ϵ}_{\mathrm{quant}}$) and a maximum count-rate ceiling of $2\times {10}^7\mathrm{photons}/\mathrm{s}$. The photon counter follows a non-paralyzable response model with a dead time (${\tau }_c$) of 20–40 ns. Measurements were recorded in continuous mode for 30 s at 1 s integration intervals.

2.4. Baseline Detection Framework and System Parameters

The single-photon counting channel response and dose-rate response model follow the dead-time characterization established by Simonin et al. [8].

For an incident proton beam characterized by fluence rate $\varphi$, the total rate of energy deposited (i.e. the incident energy flux) (${\varphi }_E$) within the efficient volume of the detector is determined by:

$${\varphi }_E=\varphi ·S_{\det }·E_{dep}$$

(2)

where $S_{\det }$ is the beam-projected cross-sectional surface area of the detector’s efficient volume and ${\mathrm{E}}_{dep}$ is the mean energy deposited per incident proton within the efficient volume.

The effective cross-sectional detection area ($S_{\det }$) is evaluated via numerical integration over the uninserted length of the scintillator head ($c-h$):

$$S_{det}=2{\int }_0^{c-h}{R}_{eff}\left(x\right)dx$$

(3)

where $x=0$ corresponds to the fiber interface, ‘c’ is the total bulb length, and ‘h’ is the optical fiber insertion length within the scintillator head. As shown in Figure 2, when ‘h’ is measured from the bottom shoulder of the ellipsoid, $h\to h_{\mathrm{shoulder}}$. The local collection radius, $R_{\mathrm{eff}}\left(x\right)=min\left[R_{\mathrm{core}}+xtan{\theta }_c,R_{\mathrm{scint}}\left(x\right)\right]$, models the expanding optical acceptance cone bounded by the fiber numerical aperture (${\theta }_c=0.1\mathrm{rad}$) and the physical scintillator casing ($R_{\mathrm{scint}}$).

The photon arrival rate (i.e., the photon flux) incident on the readout module (${\varphi }_{\gamma ,\mathrm{counter}}$)—prior to electronic dead-time processing—is evaluated by accounting for the intrinsic light yield (Y), system optical efficiencies, and primary scintillator decay losses (${\tau }_s$):

$${\varphi }_{\gamma ,\mathrm{counter}}={\varphi }_E·Y·{ϵ}_{\mathrm{geom}}·{ϵ}_{\mathrm{fiber}}·{ϵ}_{\mathrm{quant}}·e^{-Y{\varphi }_E{\tau }_s}$$

(4)

where ${ϵ}_{\mathrm{geom}}$ is the optical light collection efficiency, ${ϵ}_{\mathrm{fiber}}$ is the optical fiber transport efficiency, ${ϵ}_{\mathrm{quant}}$ is the quantum efficiency of the photodetector, and ${\tau }_s$ is the primary luminescence decay time of the scintillator.

Accounting for the electronic processing dead time (${\tau }_c$) of the acquisition system, the net output count rate recorded by the single-photon counter (${\varphi }_{\gamma }$) is expressed via the non-paralyzable dead-time model , as follows:

$${\varphi }_{\gamma }={\displaystyle \frac{{\varphi }_{\gamma ,\mathrm{counter}}}{1+{\varphi }_{\gamma ,\mathrm{counter}}·{\tau }_c}}$$

(5)

By considering the maximum saturation throughput limit of the detection channel (${\varphi }_{\gamma ,\max }=2\times {10}^7\mathrm{photons}/\mathrm{s}$), the maximum detectable primary proton fluence rate (${\phi }_{\max }$) is determined. The corresponding maximum water-equivalent dose rate (${\dot{D}}_{\max }$) is evaluated directly using the linear energy transfer (LET) obtained from the NIST PSTAR database [28]:

$${\dot{D}}_{\max }={\phi }_{\max }·\left({\displaystyle \frac{\mathrm{LET}}{{\rho }_{\mathrm{water}}}}\right)$$

(6)

where ${\rho }_{\mathrm{water}}$ is the mass density of water.

2.5. Methodological Refinements to Geometric and Optical Parameters

Recent studies evaluating the operational boundaries of inorganic scintillation dosimeters (ISDs) have developed generic framework models to calculate system dead times (${\tau }_c$, ${\tau }_s$), macroscopic light yield (Y), and maximum detectable dose rates (${\dot{D}}_{\max }$) [8,23]. Despite providing valuable insights into non-paralyzable dead-time behavior, such formalisms exhibit two crucial structural and optical limitations.

First, conventional geometric modeling references the optical fiber insertion depth from the bottom vertex of the ellipsoidal bulb ($h_{\mathrm{bottom}}$) [8], whereas the core only becomes fully embedded at the shoulder interface ($h_{\mathrm{shoulder}}$), as shown by the offset parameter $\mathsf{\Delta }h$ in Figure 2. For micro-probe dosimeters with dimensions comparable to the fiber scale, this conventional representation potentially affects the calculated detector cross-sectional area ($S_{\det }$), which can subsequently influence the accuracy of estimated mean energy deposited per incident particle ($E_{\mathrm{dep}}$). Second, previous estimates of light collection efficiency (${ϵ}_{\mathrm{geom}}$) relied solely on ray-tracing geometric acceptance, ignoring bulk optical scattering within the dense composite scintillator matrix—such as a 70% $\left(\mathrm{Zn},\mathrm{Cd}\right)\mathrm{S}\text{:}\mathrm{Ag}$ powder to 30% PMMA volume proportion—where multiple scattering may significantly alter photon path lengths and angular distributions prior to reaching the fiber core acceptance cone (${\theta }_c$).

This study introduces a refined computational and analytical framework to resolve both limitations, as well as to guide correct geometrical model for maximum dose rate response. By redefining the fiber insertion reference plane at the shoulder interface and implementing full Monte Carlo optical transport simulations incorporating bulk scattering dynamics, parameters ${\mathrm{S}}_{det}$, ${\mathrm{E}}_{dep}$ and ${ϵ}_{\mathrm{geom}}$ are evaluated. Consequently, the maximum detectable dose rate (${\dot{D}}_{\max }$) achieved by accurately modeled scintillating sensitive volume is reported.

2.6. GATE Monte Carlo Framework for Radiation and Optical Transport

Over the past several decades, the application of Monte Carlo (MC) methods in radiotherapy dosimetry has expanded significantly, establishing this simulation technique as a standard reference tool for complex radiation transport and detector modeling [29,30]. In this study, simulations were performed using GATE version 9.4.1 (built on the Geant4 toolkit, version 11.3.0), a simulation platform extensively validated and benchmarked for tracking radiation transport and optical photons in scintillation detectors across medical physics applications [31,32,33,34,35,36,37].

To accurately capture generated photons propagation and photon collection dynamics, GATE enables us to model bulk scattering, surface interactions, and fiber coupling dynamics. In this work, GATE Monte Carlo Simulations were primarily used to evaluate two key parameters: mean energy deposited per incident proton (${\mathrm{E}}_{dep}$) within the effective scintillating volume ($V_{\mathrm{eff}}$) and geometric efficiency of the optical fiber (${ϵ}_{geom}$).

2.6.1. Evaluating ${\mathrm{E}}_{dep}$

To evaluate $E_{\mathrm{dep}}$, monoenergetic proton beams were modeled under broad-beam uniform lateral illumination using the standard $\mathtt{QGSP}\_\mathtt{BIC}\_\mathtt{HP}\_\mathtt{EMY}$ physics constructor at the maximum deliverable cyclotron energy of 25 MeV and a clinically relevant FLASH energy of 230 MeV. Hits and energy deposition events occurring within the scintillator volume were accumulated across all primary proton trajectories $N_p$:

$$E_{dep}={\displaystyle \frac{1}{N_p}}{\displaystyle \sum _{i=1}^{N_p}}{E}_{\mathrm{dep},i}$$

(7)

where $E_{\mathrm{dep},i}$ is the total energy deposited by the i-th primary proton in the effective volume (${\mathrm{V}}_{eff}$) and its associated secondary particles, as recorded in the ROOT output tree.

2.6.2. Optical Simulations and Evaluating ${ϵ}_{geom}$

Unlike previous calculations [8], which evaluated geometric efficiency using a simplified ray-tracing approximation restricted strictly to optical photons within an idealized effective volume, the present work implements a fully volumetric optical transport framework. In this approach, optical photons were generated stochastically across the entire three-dimensional volume of the scintillator in GATE following the interaction of 25 MeV incident protons, accurately reproducing realistic energy deposition patterns rather than assuming localized or idealized emission (Figure 3).

The Monte Carlo model tracked individual photon trajectories through multiple internal scattering events within the powder–binder matrix, bulk volume attenuation, refraction at dielectric boundaries, and complex interactions at both the outer crystal surfaces and the optical fiber interface. Scintillation photons (${\lambda }_{\mathrm{peak}}\approx 660\mathrm{nm}$, $\tau =10\mu \mathrm{s}$ [38]) were generated isotropically using a reduced yield of $10\mathrm{photons}/\mathrm{MeV}$ to optimize computational efficiency. Intra-dosimeter scattering was modeled using the Henyey-Greenstein Mie phase function [39,40] with a mean free path (${\lambda }_{\mathrm{Mie}}=6.0\mu \mathrm{m}$) matched to the median phosphor grain size ($D_{50}=6.0\mu \mathrm{m}$) used in the scintillator detector.

At the outer boundary region of the top of optical fiber, photons were registered as accepted if their incident angle satisfied the fiber acceptance limit (${\theta }_c=0.1\mathrm{rad}$). The baseline simulated geometric collection efficiency (${ϵ}_{\mathrm{geom},\mathrm{MC}}$) was evaluated as:

$${ϵ}_{\mathrm{geom},\mathrm{MC}}={\displaystyle \frac{N_{\mathrm{accepted}}}{N_{\mathrm{generated}}}}$$

(8)

where $N_{\mathrm{generated}}$ is the total number of distinct optical photons generated throughout the scintillator volume and $N_{\mathrm{accepted}}$ is the number of photons meeting the acceptance criteria at the fiber interface.

While volumetric Monte Carlo transport captures internal light scattering far more accurately than basic ray tracing, idealized Monte Carlo geometries assume uniform physical boundaries, uniform boundary layers, and strict Numerical Aperture cutoffs. They cannot fully account for physical micro-scale variations—such as boundary scattering from surface roughness, adhesive meniscus refraction, fiber alignment tolerances, trapped micro-air voids, and localized deviations from the nominal 70:30 scintillator-to-PMMA binder volume proportion. To bridge these simulation constraints and reflect physical probe construction, an optical coupling factor (k) was introduced to scale the baseline Monte Carlo geometric efficiency (${ϵ}_{\mathrm{geom},\mathrm{MC}}$) into the true geometric collection efficiency (${ϵ}_{\mathrm{geom}}=k·{ϵ}_{\mathrm{geom},\mathrm{MC}}$).

2.7. ISD Detector Geometries and Physical Specifications

The general simulation and analytical framework described above was applied to five distinct inorganic scintillation detector geometries (designated as Detectors 1–5) as shown in Figure 4. These configurations span a broad range of sensitive volumes ($V_{\mathrm{eff}}$), optical fiber insertion length (h), and overall scintillation bulb dimensions (a, b, c), as presented in Table 1.

The physical detector configurations (Detectors 1–5) analyzed in this work were maintained identical to those characterized by Simonin et al. [8], to compare our results with respect to the real-detector’s geometric configuration achieved by using micrographic techniques. However, compared to the model in [8], the fiber insertion parameter ‘h’ is re-indexed relative to the detector’s ellipsoidal shoulder ($h_{\mathrm{shoulder}}$) rather than the bottom vertex ($h_{\mathrm{bottom}}$) to establish a physically practical insertion boundary.

In the experimental setup, the detectors are oriented for broad-beam lateral illumination and positioned centrally within the radiation field, a few millimeters downstream of the exit collimator.

3. Results

3.1. Detector Physical Parameters and Geometric Efficiency

The optical fiber insertion length discrepancy parameter ($\mathsf{\Delta }$h), detector surface areas ($S_{\det }$ of the effective volume), mean energy depositions ($E_{\mathrm{dep}}$ within the effective volume), and simulated geometric light collection efficiencies (${ϵ}_{\mathrm{geom},\mathrm{MC}}$ from Monte Carlo simulations) across all five detector configurations are summarized in Table 2. $E_{\mathrm{dep}}$ was evaluated for two proton beam energies of 25 MeV and 230 MeV, denoted as $E_{\mathrm{dep},25}$ and $E_{\mathrm{dep},230}$, respectively.

Defining the fiber insertion boundary depth (h) from the detector shoulder significantly altered the structural and energy parameters. The resulting depth shift ($\mathsf{\Delta }h$) contracts both the contact surface area ($S_{det}$) and the effective physical volume ($V_{eff}$), which ultimately suppresses the deposited energy ($E_{dep}$)—an effect that is most significant in the smallest configuration (Det 1). As the active volume increases from Det 1 to Det 5, $S_{\det }$ expands from 2,956 $\mu$${\mathrm{m}}^2$ to 300,466 $\mu$${\mathrm{m}}^2$, driving a corresponding increase in mean energy deposition per proton pass ($E_{\mathrm{dep},25}$ ranging from 0.413 to 1.132 MeV, and $E_{\mathrm{dep},230}$ ranging from 0.070 to 0.182 MeV). In contrast, the optical simulation results show a continual decrease in geometric efficiency, falling from 0.281% for Det 1 down to 0.008% for Det 5.

3.2. Global System Calibration and Non-Linear Detector Response

To determine the global system parameters governing detection channel saturation, the geometric parameters ($S_{\det }$, $E_{\mathrm{dep}}$, and ${ϵ}_{\mathrm{geom}}$) were integrated directly into the non-linear response model (Eqs. 1–4). The rate of energy deposited per unit time (${\varphi }_E$) was calculated via Eq. 2 using the calculated cross-sectional areas ($S_{\det }$) derived from the revised shoulder boundary condition ($h_{\mathrm{shoulder}}$).

Figure 5(a) displays the measured count rate (${\varphi }_{\gamma }$) across all five detectors (Det 1–5) as a function of primary proton fluence rate ($\varphi$). Figure 5(b) shows ${\varphi }_{\gamma }$ against incident energy deposition flux (${\varphi }_E$), along with the non-linear model fits (Eq. 5). In the fitting procedure, optical fiber transmission was fixed at ${ϵ}_{\mathrm{fiber}}=0.98$, evaluated from the manufacturer’s transmission spectrum weighted over the scintillator emission wavelengths. The quantum efficiency of the single photon counter was fixed at ${ϵ}_{\mathrm{quant}}=0.71$. To ensure a consistent comparison across detector geometries and isolate geometry-dependent effects, the intrinsic material properties, including the scintillation light yield ($Y=16,072\mathrm{photons}/\mathrm{MeV}$) and luminescence decay time (${\tau }_s=1.6\mathrm{ps}$), were held constant at their established values [8].

A shared global fit across Det 2–5 established a common electronic dead time of ${\tau }_c=30.79\pm 0.35\mathrm{ns}$, which was subsequently applied to cross-calibrate Det 1. Across all five detectors (Det 1–5), the extracted optical coupling factors spanned $1.34\le k\le 6.20$, resulting in true geometric efficiencies (${ϵ}_{\mathrm{geom}}$) ranging from $0.0496\%$ to $0.3767\%$. All fits demonstrated excellent agreement with experimental counts across the full fluence rate dynamic range ($R^2\ge 0.9980$).

3.3. Maximum Dose Rate Evaluation

Using the parameters evaluated from the fitting procedure, the maximum detectable primary proton fluence rate (${\phi }_{\max }$) was determined at the saturation throughput limit of the detection channel (${\varphi }_{\gamma ,\max }=2\times {10}^7\mathrm{photons}/\mathrm{s}$). The corresponding maximum water-equivalent dose rate (${\dot{D}}_{\max }$) was then evaluated using Eq. 6 for both 25 MeV and 230 MeV proton energies. Table 3 summarizes the maximum dose rates alongside the maximum fluence rates for detectors Det 1–5 for two proton energies of 25 MeV and 230 MeV.

4. Discussion

During proton interactions with the sensitive scintillating volume, evaluating the physical boundary conditions and optical dynamics provides a more accurate basis for dose rate calculations than earlier estimates [8]. Measuring the insertion depth ($h_{\mathrm{shoulder}}$) from the detector shoulder corrects the geometric baseline compared to previous work that measured from the ellipsoid base. This correction changes the effective cross-sectional area ($S_{\det }$) and average energy deposited per proton (${\mathrm{E}}_{dep}$), with the largest relative impact occurring in the smallest detector (Det 1). In addition, replacing basic ray-tracing with optical Monte Carlo simulations accounts for internal photon scattering, yielding a more realistic geometric collection efficiency (${ϵ}_{\mathrm{geom}}$). To bridge simplified Monte Carlo transport models (${ϵ}_{\mathrm{geom},\mathrm{MC}}$) and practical light scattering dynamics inside the detector, introducing the optical coupling factor (k) accounts for real-world interface dynamics, such as boundary scattering from surface roughness, optical adhesive meniscus index matching, trapped micro-air voids, and manufacturing alignment tolerances. These structural and optical updates resolve earlier underestimations and establish a more reliable input baseline for overall detector throughput.

From a clinical perspective, these revised values define clear operational limits for fiber-integrated scintillation dosimeters in ultra-high dose rate (FLASH) radiotherapy. The results confirm a direct link between the detector’s geometrical configuration and saturation, i.e., the smallest volume (Det 1) achieves the highest maximum dose rate (${\dot{D}}_{\max ,25}=364.5\pm 7.6\mathrm{Gy}/\mathrm{s}$ at 25 MeV and ${\dot{D}}_{\max ,230}=392.6\pm 8.1\mathrm{Gy}/\mathrm{s}$ at 230 MeV), while larger detectors (Det 2–5) saturate at lower flux levels because they generate more photons per proton. For Det 1, these thresholds represent a notable improvement over the previously reported ${\dot{D}}_{\max }$ values of $295\pm 2.6\mathrm{Gy}/\mathrm{s}$ at 25 MeV and $337\pm 3.0\mathrm{Gy}/\mathrm{s}$ at 230 MeV [8]. These results suggest that smaller scintillator geometries provide a higher effective sensitive-volume fraction for photon interactions, resulting in enhanced response under high-dose-rate conditions. For FLASH beam monitoring above $40\mathrm{Gy}/\mathrm{s}$ [41], reducing active volume is therefore essential to delay count-rate saturation in non-paralyzable readout channels.

This study has a few modeling limitations. First, the optical Monte Carlo simulations modeled light collection assuming direct coupling into the fiber core at the tip interface, omitting the full cladding profile and outer housing geometry at the fiber entry. Accounting for cladding dynamics at the fiber tip could further refine the geometric collection efficiency (${ϵ}_{\mathrm{geom}}$). Second, while the optical coupling factor (k) captures physical interface losses and volumetric variations (e.g., slight deviations from the nominal 70:30 scintillator-to-binder ratio across probe sizes), directly modeling micro-scale voids and surface roughness in future simulations could reduce reliance on empirical scaling factors. Third, dose rate calculations assumed continuous beam delivery, whereas clinical FLASH beams often use pulsed time structures that may alter instantaneous photon rates and dead-time behavior during peak pulses. Future work will investigate variations in optical fiber geometry relative to the scintillator volume, alongside evaluating alternative scintillating materials, to identify optimal compact detector configurations, enabling miniaturization of the detector volume while enhancing dose-rate sensitivity under FLASH proton beam conditions.

5. Conclusions

This study evaluated the maximum dose rate (${\dot{D}}_{\max }$) capabilities for fiber-integrated inorganic scintillation detectors by considering key geometrical and optical parameters. Referencing optical fiber insertion depth from the physical fiber-scintillator interface provided a more accurate geometric baseline for the active volume and cross-sectional surface area. In addition, optical Monte Carlo simulations accounted for internal photon scattering, yielding a more realistic geometric collection efficiency, which is important for measuring accurate dose rate and dose rate capabilities.

Applying these parameters to a non-paralyzable dead-time model confirmed that dose rate saturation is strongly governed by detector’s volume, as larger sensitive volumes generate higher optical photon fluxes that saturate the readout channel at lower dose rates. These findings highlight clear design trade-offs: reducing active volume delays dose rate saturation, making smaller detectors suitable for ultra-high dose rate (FLASH) dosimetry, whereas larger volumes may remain useful for conventional, high-sensitivity applications at lower fluxes. However, shrinking the detector must be balanced against maintaining sufficient energy deposition per proton to preserve an acceptable signal-to-noise ratio. Overall, accurate modeling of these parameters enables optimization of detector geometry , signal-collection efficiency, thereby supporting reliable quantitative dosimetry across conventional and high-dose-rate proton beam conditions.