Theoretical and empirical investigations of KCl:Eu²⁺ for nearly water-equivalent radiotherapy dosimetry

Abstract

Purpose: The low effective atomic number, reusability, and other computed radiography-related advantages make europium doped potassium chloride (KCl:Eu²⁺) a promising dosimetry material. The purpose of this study is to model KCl:Eu²⁺ point dosimeters with a Monte Carlo (MC) method and, using this model, to investigate the dose responses of two-dimensional (2D) KCl:Eu²⁺ storage phosphor films (SPFs).

Methods: KCl:Eu²⁺ point dosimeters were irradiated using a 6 MV beam at four depths (5–20 cm) for each of five square field sizes (5×5–25×25 cm²). The dose measured by KCl:Eu²⁺ was compared to that measured by an ionization chamber to obtain the magnitude of energy dependent dose measurement artifact. The measurements were simulated using DOSXYZnrc with phase space files generated by BEAMnrcMP. Simulations were also performed for KCl:Eu²⁺ films with thicknesses ranging from 1 μm to 1 mm. The work function of the prototype KCl:Eu²⁺ material was determined by comparing the sensitivity of a 150 μm thick KCl:Eu²⁺ film to a commercial BaFBr_0.85I_0.15:Eu²⁺-based SPF with a known work function. The work function was then used to estimate the sensitivity of a 1 μm thick KCl:Eu²⁺ film.

Results: The simulated dose responses of prototype KCl:Eu²⁺ point dosimeters agree well with measurement data acquired by irradiating the dosimeters in the 6 MV beam with varying field size and depth. Furthermore, simulations with films demonstrate that an ultrathin KCl:Eu²⁺ film with thickness of the order of 1 μm would have nearly water-equivalent dose response. The simulation results can be understood using classic cavity theories. Finally, preliminary experiments and theoretical calculations show that ultrathin KCl:Eu²⁺ film could provide excellent signal in a 1 cGy dose-to-water irradiation.

Conclusions: In conclusion, the authors demonstrate that KCl:Eu²⁺-based dosimeters can be accurately modeled by a MC method and that 2D KCl:Eu²⁺ films of the order of 1 μm thick would have minimal energy dependence. The data support the future research and development of a KCl:Eu²⁺ storage phosphor-based system for quantitative, high-resolution multidimensional radiation therapy dosimetry.

INTRODUCTION

Intensity modulated radiation therapy (IMRT) is associated with sophisticated treatment planning and dose delivery.^{1, 2} Quantitative experimental validation is required to assure that the delivered dose agrees with the planned dose.^{3, 4} Ideally, complex IMRT dose distributions would be verified in three dimensions. However, a convenient and cost effective three-dimensional (3D) dosimeter is not yet available.^{5, 6, 7, 8} Alternatively, as suggested by the American Association of Physicists in Medicine (AAPM),³ 3D dose distribution verification can be effectively accomplished by loading phantoms with an array of high-resolution two-dimensional (2D) dosimeters such as radiographic⁹ or radiochromic films^{10, 11} distributed throughout the phantoms. Because these films are fundamentally single-use detectors, they cannot be reliably calibrated. Quantitative dosimetry with single-use films requires the acquisition of a sensitometric curve each time a dosimetric measurement is made, but this practice is based on the assumption that each individual film has the same response as others in the batch, and, for radiographic film, that the processor remains stable between developed films. Therefore, an alternative, reusable planar dosimeter is highly desirable for IMRT commissioning and quality assurance.

Recently, Han et al.¹² reported the use of a novel storage phosphor material, europium doped potassium chloride (KCl:Eu²⁺), for quantitative megavoltage radiation therapy dosimetry. The mechanism of photostimulated luminescence (PSL) is, in principle, similar to the most commonly used material in computed radiography (CR), BaFBr_0.85I_0.15:Eu²⁺. However, the lower effective atomic number of KCl:Eu²⁺ compared to BaFBr_0.85I_0.15:Eu²⁺—18 versus 49—makes it more conducive to radiation therapy dosimetry. Among the many desirable dosimetric characteristics of KCl:Eu²⁺, one to note is its excellent radiation hardness. Han et al.¹² reported that the dosimeter could be reused at least 100 times at 2 Gy per use. Future development would involve the creation of a large-area KCl:Eu²⁺-based storage phosphor film (SPF) with minimized energy dependence using modern thin film techniques, for example, tape casting^{13, 14} or physical vapor deposition (PVD).^{15, 16, 17}

In this paper, we report on Monte Carlo (MC) studies of the dose response of a KCl:Eu²⁺-based planar dosimeter irradiated in a 6 MV therapeutic beam. The purpose is to determine whether decreasing the dosimeter thickness could mitigate the residual energy dependence, and, if so, to determine the thickness that yields a nearly water-equivalent dose response while providing sufficient signal. Prior to film simulation, comparisons were made between experimental data acquired by irradiating KCl:Eu²⁺ point dosimeters in the 6 MV beam and MC simulation data to determine whether dosimeter response could be accurately modeled using MC.

MATERIALS AND METHODS

KCl:Eu²⁺ point dosimeter measurements

Prototype KCl:Eu²⁺ point dosimeters, 7 mm in diameter and 1 mm thick, were fabricated in-house.¹² The dosimeters were irradiated using a 6 MV photon beam generated by a Varian 23EX linear accelerator (Varian Medical Systems, Palo Alto, CA) in a flat homogeneous water-equivalent phantom. The phantom consisted of 40×40 cm² solid water slabs (SW-457, Gammex RMI, Middleton, WI) stacked to a thickness of 30 cm. A 5 mm thick slab with holes of 7.5 mm in diameter and 2 mm in depth served to host the dosimeters during irradiation. The dosimeter plane was oriented perpendicular to the beam central axis. Prior to irradiation, the dosimeters were optically bleached (annealed) for 5 s using a 500 W tungsten-halogen lamp.

The dosimeters were irradiated individually to a dose of 200 cGy at four depths (5–20 cm) for each of the five square field sizes (5×5–25×25 cm²) and read using a laboratory PSL readout system, as described by Han et al.¹² The number of monitor units was calculated based on calculation protocols used in our clinic. The delivered doses were verified using a 0.6 cm³ Farmer-type ionization chamber (PTW N23333, Friedberg, Germany) inserted into a 40×40×3 cm³ solid water slab that is positioned at the same point. In addition to the 200 cGy irradiations, a sensitometric curve for the dose range of 170–250 cGy was obtained at a depth of 10 cm and a field size of 10×10 cm². Varying field sizes and depths alters the incident fluence spectra, i.e., the scatter-to-primary photon ratios, at the dosimeter plane.¹⁸ The ratio of the measured dose using the sensitometric curve to the dose measured by an ionization chamber, R, at field size f and depth d, was used to indicate the magnitude of energy dependent dose measurement artifact, given by

$$R=\frac{D_{w,\mathrm{K}\mathrm{Cl}}}{D_{w,\mathrm{I}\mathrm{C}}},$$ (1)

where D_w,KCl was the dose-to-water measured by a KCl:Eu²⁺ dosimeter, calibrated at 10×10 cm² field size and 10 cm depth, and D_w,IC was the dose-to-water measured by an ionization chamber. Comparisons between measurements and MC simulations indicated whether the dose response of a KCl:Eu²⁺ dosimeter could be accurately modeled by MC.

Monte Carlo simulations

BEAMnrcMP (Ref. ¹⁹) and DOSXYZnrc (Ref. ²⁰) were employed to simulate the response of KCl:Eu²⁺ dosimeters in clinically relevant applications. BEAMnrcMP is a general purpose MC simulation system based on EGSnrcMP (Ref. ²¹) and was used to model a Varian 23 EX linear accelerator operating in 6 MV mode and to generate phase-space files. The modeling included an electron source with a Gaussian distribution, a tungsten target, a primary collimator, a flattening filter, a mirror, two dose monitoring chambers, and a pair of secondary collimators. The phase-space file was used as the input source for DOSXYZnrc to simulate the 3D dose distribution in a 40×40×40 cm³ solid water phantom both with and without dosimeters. The simulated dosimeter was defined by its composition, KCl, and physical density, 1.987 g∕cm³. The amount of europium was of the order of ppm, so it was ignored in the simulations. The elemental composition of the solid water was defined according to the following weight fractions,¹⁸ H: 0.081, C: 0.672, N: 0.024, O: 0.199, Cl: 0.001, and Ca: 0.023, and the density was 1.043 g∕cm³. The KCl:Eu²⁺ point dosimeter was modeled using the same dimensions as the prototypes used in this study, 7 mm in diameter and 1 mm thick. The simulation geometry resembled the measurements as closely as possible. The simulated R was calculated by

$$R=\raisebox{1ex}{${\left(\frac{D_{\mathrm{K}\mathrm{Cl}}}{D_w}\right)}_{f,d}$}\!\left/ \!\raisebox{-1ex}{${\left(\frac{D_{\mathrm{K}\mathrm{Cl}}}{D_w}\right)}_{10\times 10,10}$}\right.,$$ (2)

where f was the field size, d was the depth, D_KCl and D_w were the MC simulated doses to KCl and to solid water per incident particle, respectively.

A series of simulations was then conducted for films with thicknesses of 1, 3, 10, 15, 20, 30, 40, 100, and 1000 μm for 10×10 and 20×20 cm² fields. The absorbed dose-to-KCl:Eu²⁺ along the central axis was scored at depths of 1.5, 5, 10, 15, 20, 25, and 30 cm. A dosimeter size of 3×3 cm² was used in order to achieve good statistics. Off-axis dose profiles generated by KCl:Eu²⁺ extending from the central axis to 20 cm off-axis were obtained using variable grid sizes, 0.5×3 cm² in the penumbra region and 1×3 or 2×3 cm² in low dose gradient regions. Simulations were repeated by filling the dosimeter cavities using solid water phantom material in order to obtain the absorbed dose-to-water. It was found that dose-to-water did not change with the cavity thickness. Thus, the dose-to-water for a 1 mm thick layer was used to represent dose-to-water for all cavity thicknesses.

As demonstrated in Sec. 3B, the thinner KCl:Eu²⁺ film exhibited a more waterlike dose response than thicker samples. Therefore, dose response characteristics for a 1 μm thick film were analyzed in more detail, including off-axis dose profiles and percentage depth dose profile along the central axis, both with and without a substrate or base. Simulations of a 1 μm thick BaFBr_0.85I_0.15:Eu²⁺ film were also performed for comparison.

The Monte Carlo parameters that affect low-energy photon modeling were included in the simulation, including bound Compton scattering, photoelectron angular sampling, Rayleigh scattering, atomic relaxations, and electron impact ionization. The default photon and electron kinetic energy cutoffs were used in BEAMnrc, 10 and 189 keV, respectively. For DOSXYZnrc simulation, 1 keV, the lowest kinetic energy cutoff allowed by the simulation system, was used for both photons and electrons in order to accurately simulate the dose deposition in the thinnest dosimeters. Up to 4×10⁸ histories were used to achieve good statistics for both BEAMnrc and DOSXYZnrc. For a 1 μm thick dosimeter, the statistical uncertainty was typically less than 1% for dose along the central axis, 5% within the field, and 15% outside the field. The statistical uncertainty decreased as dosimeter thickness increased. All simulations were run on a Linux Dual CPU computer, with a typical run time of 50 h for each simulation.

Theoretical estimation of ultrathin KCl:Eu²⁺ dosimeter sensitivity

An important question is whether an ultrathin KCl:Eu²⁺ dosimeter will be sufficiently sensitive for megavoltage beam dosimetry. The sensitivity of a 1 μm thick KCl:Eu²⁺ dosimeter was calculated as follows.

The energy absorbed in the dosimeter was

$$E_{\mathrm{K}\mathrm{Cl}}=D_{\mathrm{K}\mathrm{Cl}}\rho {\left(\Delta x\right)}^{2}d,$$ (3)

where ρ was the density of KCl, Δx was the pixel size used by a 2D scanner, and d was the dosimeter thickness.

The number of photoelectrons, N, generated per pixel at the PMT cathode was then

$$N=\frac{E_{\mathrm{K}\mathrm{Cl}}}{W_{\mathrm{K}\mathrm{Cl}}}\eta Q_E,$$ (4)

where W_KCl was the work function for KCl:Eu²⁺, the energy that must be absorbed from the beam to produce a PSL photon, η was the light collection efficiency, and Q_E was the PMT quantum efficiency.

In order to obtain W_KCl, the sensitivity of a thick KCl:Eu²⁺ film was compared against a commercial BaFBr_0.85I_0.15:Eu²⁺-based SPF (Fuji HRIII), the work function of which, W_Ba, was previously measured by Li et al.²² The thick KCl:Eu²⁺ film was produced in-house using a tape casting method. In brief, a homogeneous suspension containing KCl:Eu²⁺ storage phosphor particles, liquid vehicle, and polymer binder was formed and subsequently cast by “doctor-blade” onto a polyethylene terephthalate substrate to form a 150 μm thick KCl:Eu²⁺ film with coating weight of 28 mg∕cm². The coating weight of the BaFBr_0.85I_0.15:Eu²⁺-based film was determined to be 53 mg∕cm² by multiplying the material’s physical density of 5.1 g∕cm³, filling factor of 61%,²³ and film thickness of 170 μm. Both films were irradiated to 230 MU using a 10×10 cm² 6 MV field at a depth of 5 cm, corresponding to 200 cGy dose-to-water, and read immediately after irradiation on a laboratory scale PSL readout system similar to that described by Han et al.¹² except that the stimulation source consisted of a 5 mW 594 nm He–Ne laser, attenuated by an neutral density filter (OD=2), and that the films were fixed to a precision x-y positioning stage. A central axis scan was obtained at 1×1 mm² pixel size. The average of 20 pixel values was taken as the reading. W_KCl was then obtained by solving

$$\frac{{\mathrm{PSL}}_{\mathrm{K}\mathrm{Cl}}}{{\mathrm{PSL}}_{\mathrm{Ba}}}=\frac{M_{\mathrm{K}\mathrm{Cl}}{\left(\Delta x\right)}^2{D}_{\mathrm{K}\mathrm{Cl}}∕W_{\mathrm{K}\mathrm{Cl}}}{M_{\mathrm{Ba}}{\left(\Delta x\right)}^2{D}_{\mathrm{Ba}}∕W_{\mathrm{Ba}}},$$ (5)

where PSL_KCl and PSL_Ba were the measured PSL signals from the KCl and BaFBr_0.85I_0.15:Eu²⁺ films, respectively, M_KCl and M_Ba were the coating weights for KCl and BaFBr_0.85I_0.15:Eu²⁺, respectively, Δx was the pixel size, and D_KCl and D_Ba were the doses to KCl and BaFBr_0.85I_0.15, respectively.

RESULTS

MC modeling of KCl:Eu²⁺ point dosimeters

Figure 1 shows the measured and simulated dose responses of a 1 mm thick KCl:Eu²⁺ point dosimeter along the central axis for varying field sizes and depths, normalized to the calibration conditions, i.e., at a depth of 10 cm in a 10×10 cm² field. The data points in Fig. 1 represent the measured data and the solid lines represent the simulations. The calibration of a relative dosimeter determines response per unit dose to water at the central axis of a calibration field, which has a specific scatter-to-primary ratio. Energy dependence artifacts will occur if the scatter-to-primary ratio in the measured field is different than that under the calibration conditions. Since KCl has a larger effective Z than water, it over-responded to low-energy scattered photons due to the Z³ dependence for photoelectric interactions. The magnitude of over-response depends on the scatter-to-primary ratio, which, in our experiment, was the largest at 20 cm depth in a 25×25 cm² field. Excellent agreement between measurement and simulation, overall to within 2%, demonstrated that MC could accurately model the complex photon and electron transport in both the dosimeter and the surrounding tissue-equivalent medium.

Figure 1.

The relative sensitivity of 1 mm thick KCl:Eu²⁺ dosimeters as a function of the field size and depth. Symbols: Measured data (Ref. ¹²), lines: MC simulated data. The measurement uncertainty is 2.5%.

KCl:Eu²⁺ dose response as a function of dosimeter thickness

Figure 2 shows the simulated absorbed dose to KCl:Eu²⁺ as a function of the dosimeter thickness ranging from 1 μm to 1 mm, normalized to that of a 1 mm thick dosimeter in a 20×20 cm² field at a depth of 10 cm. The absorbed dose to KCl:Eu²⁺ increases with the dosimeter thickness. For comparison, we also simulated the dose response for cavity sizes of 10 μm, 100 μm, and 1 mm filled with the solid water phantom material. We found that the absorbed dose to water did not change with the thickness, as expected, and was approximately 3% less than that to a 1 mm thick KCl:Eu²⁺ dosimeter.

Figure 2.

Monte Carlo simulated dose to KCl:Eu²⁺ as a function of dosimeter thickness in a 6 MV, 20×20 cm² field at a depth of 10 cm, normalized to that of 1 mm thick dosimeter.

KCl:Eu²⁺-generated dose distribution profiles for dosimeters with thicknesses of 1, 10, and 100 μm at a depth of 20 cm for a 6 MV beam, 10×10 cm² field size are shown in Fig. 3. A 100 μm thick film showed a strong over-response in the peripheral region where low-energy scattered photons are dominant. The over-response to scattered photons would cause dose measurement errors in complex IMRT dose distributions with spatially varying scatter-to-primary photon ratios.^{18, 24, 25} By contrast, the 10 μm thick film over-responded significantly less as evidenced by the closer agreement to the actual dose profile. A 1 μm thick KCl:Eu²⁺ film responded accurately in the peripheral region, showing nearly water-equivalent dose response.

Figure 3.

Monte Carlo simulated dose profiles for KCl:Eu²⁺ films with thicknesses of 100, 10, and 1 μm exposed by the 6 MV beam at a depth 20 cm and a field size of 10×10 cm².

Table 1 compares the absolute over-responses in percentage of KCl:Eu²⁺ films with varying thickness at 5 cm outside the field edge for a 20×20 cm² field at 20 cm depth (i.e., 17 cm off axis). This is a severe test of energy dependence on low-energy scattered photons because so few primary photons are present. Note that the relative over-response ranged from 0.15% to 4.2% if normalized to the central axis. Also listed are the experimental data reported by Schembri and Heijmen for Al₂O₃:C, radiochromic EBT and radiographic XV films.²⁶ Radiochromic EBT film has an effective Z of 6.9, slightly lower than that of water, while Al₂O₃:C and AgBr have effective atomic numbers of 11 and 43, respectively. The simulations data suggest that a thinner KCl:Eu²⁺ film will be more water equivalent. An ultra thin-coated KCl:Eu²⁺ film 1 μm thick would have a nearly water-equivalent response in the penumbra.

Table 1.

MC simulated absolute over-responses for KCl:Eu²⁺ films as a function of thickness at 5 cm outside of a 20×20 cm² beam edge at 20 cm depth. The asterisk ( ^*) refers to experimental data of other dosimeters from Schembri and Heijmen (Ref. ²⁶) for comparison.

Material	Thickness (μm)	Over-response (%)
KCl:Eu2+	1	2.6
	3	13.4
	10	35.6
	15	48.7
	20	57.1
	30	63.1
	40	72.0
	100	71.5
Al2O3:C*	300	15.5
Radiochromic*	17	−4.2
Radiographic*	0.4	47.2

Dose response for a 1 μm thick KCl:Eu²⁺ film

Percentage depth dose and off-axis profile

Figure 4a illustrates KCl:Eu²⁺-generated off-axis dose profiles for a 1 μm thick KCl:Eu²⁺ SPF irradiated at the depths of 10, 20, and 30 cm for a 20×20 cm² field at SSD 100 cm in a 6 MV beam. The percentage depth dose is shown in Fig. 4b. The dosimeter-generated off-axis profiles matched with the solid water data at all depths. Note that the off-axis data are noisy because of the relatively poor statistics due to the small voxel size. The KCl-generated percentage depth dose along central axis matched with the solid water data to within 1.3% at all depths.

Figure 4.

Monte Carlo simulated KCl:Eu²⁺ generated off-axis dose profiles at depths of 10, 20, and 30 cm (a) and percentage depth dose profile (b) for a 1 μm thick KCl:Eu²⁺ film for a 20×20 cm² field at SSD=100 cm in the 6 MV beam.

Comparison with BaFBr_0.85I_0.15:Eu²⁺ material

If producing an ultrathin KCl:Eu²⁺ film would improve its energy response, the question arises as to whether doing the same with the commercial BaFBrI:Eu²⁺ material would also make that dosimeter more water equivalent. Figure 5 illustrates MC simulated dose profiles for a 1 μm thick BaFBr_0.85I_0.15:Eu²⁺ film compared to that of a 1 μm thick KCl:Eu²⁺ film. Because of the greater atomic number, the strong over-response was not removed for a thin BaFBr_0.85I_0.15:Eu²⁺ film.

Figure 5.

Monte Carlo simulated dose profiles for a 1 μm thick KCl:Eu²⁺ film and a 1 μm thick BaFBrI:Eu²⁺ film at depth of 20 cm for a 20×20 cm² field at SSD=100 cm.

Effect of SiO₂ substrate

It is feasible to create SPFs with thickness of the order of 1 μm using a PVD technique onto a substrate. Ideally, a nearly water-equivalent substrate material should be used, for example, a low Z plastic. Alternatively, quartz glass (SiO₂, Z=12) or alumina ceramic sheet (Al₂O₃, Z=11) could be used. To investigate the effect of a substrate, the dose responses were simulated for a thin KCl film coated on a SiO₂ substrate. As shown in Fig. 6, the KCl-generated percentage depth dose and off-axis profiles matched well to solid water data.

Figure 6.

Monte Carlo simulated off-axis dose profiles at depths of 10, 20, and 30 cm (a) and percentage depth dose profile (b) for a 1 μm thick KCl:Eu²⁺ film for a 20×20 cm² field at SSD=100 cm in the 6 MV beam coated on a 1 mm thick SiO₂ substrate.

Theoretical estimation of ultrathin KCl:Eu²⁺ sensitivity

The work function W of BaFBr_0.85I_0.15:Eu²⁺, irradiated by the 6 MV photon beam, was previously determined to be 160 eV, independent of the measured dose from 1 to 1000 cGy.²² According to simulations, in a 1 cGy∕MU dose-to-water irradiation at 10×10 cm² and 5 cm depth, D_KCl was approximately 0.9 cGy∕MU for a 150 mm thick film and D_Ba was 1.08 cGy∕MU.²² Using Eq. 5, the W for the prototype KCl:Eu²⁺ was determined to be 157 eV. The W value is almost the same as that of BaFBr_0.85I_0.15:Eu²⁺, indicating that KCl:Eu²⁺ is an excellent storage phosphor material.

Table 2 lists the parameters that were used to approximate the sensitivity for a 1 μm thick KCl:Eu²⁺ dosimeter. Several estimations were made based on the accepted data. According to this approximation, over 10 000 photoelectrons∕pixel would be generated at the PMT cathode. This magnitude of photoelectrons can be easily collected and amplified by a PMT based detection system.²⁷ Conceptually, the much greater dose produced by radiation therapy beams than diagnostic beams, cGy versus μGy, will result in an excellent signal from KCl:Eu²⁺ with micrometer dimension for radiotherapy dosimetry measurements. This is supported by the storage capability of a KCl:Eu²⁺ material that is comparable to that of the conventional BaFBr_0.85I_0.15:Eu²⁺ material.

Table 2.

Sensitivity estimation for a 1 μm thick KCl:Eu²⁺ at a dose-to-water of 1 cGy in 6 MV.

Parameter	Value
Density ρ (g∕cm3)	1.987
Thickness d (μm)	1
Dose-to-water (cGy)	1
Dose-to-KCl DKCl (cGy)	0.77
Pixel size (Δx)2 (mm2)	0.5×0.5
Work function WKCl (eV)	157
Light collection efficiency η (%)	30
PMT QE QE (%)	30
Calculation results	Value
Energy absorbed per pixel EKCl (eV)	2.39×107
No. of PSL photons per pixel	1.52×105
Photoelectrons per pixel N	1.37×104

DISCUSSION AND CONCLUSIONS

Quantitative radiation therapy dosimetry requires energy independence of dosimeter materials. KCl:Eu²⁺ storage phosphor has much lower effective Z compared to commercial available CR material but it is still larger than that of water. Due to the Z³ dependence of the photoelectric mass attenuation coefficient, shown in Fig. 7 (Ref. ²⁸), KCl:Eu²⁺ over-responds to low-energy scattered photons compared to ideal water-equivalent dosimeters. However, because of the dynamics of megavoltage photon dose deposition, the effective material atomic number alone does not determine dosimeter behavior. According to Burlin cavity theory,²⁹

$$\frac{{\overline{D}}_g}{D_w}=\xi \cdot {\left(\frac{\overline{L}}{\rho }\right)}_w^g+(1-\xi )\cdot {\left(\frac{\overline{{\mu }_{\mathrm{en}}}}{\rho }\right)}_w^g.$$ (6)

Figure 7.

Mass attenuation coefficient as a function of the incident photon energy for KCl, H₂O, and BaFBr_0.85I (Ref. ²⁸).

The energy response behavior of a dosimeter is therefore a result of matching the mass stopping power ratio ${(\overline{L}∕\rho )}_w^g$, the mass energy-absorption coefficient ratio ${(\overline{{\mu }_{\mathrm{en}}}∕\rho )}_w^g$ and a thickness dependent parameter ξ in the design of the dosimeter. However, the complicated behavior of primary and scattered photon interactions and the secondary electrons they produce in both dosimeter or cavity and surrounding tissue requires investigation by techniques such as Monte Carlo simulations. As shown in Fig. 1, excellent agreement between simulation and measurement with a point dosimeter demonstrated that MC is useful for predicting the dose response of a KCl:Eu²⁺ thin film when irradiated by a megavoltage therapeutic beam.

As shown in Fig. 2, for an ultrathin film, for example, 1 μm thick, dose deposition in the cavity can be modeled by Bragg–Gray and Spencer–Attix theories.²⁹ We calculated the ratio of mass collision stopping powers for KCl and water as a function of incident electron energy ranging from 10 keV to 10 MeV from eq. (8.13) in Attix.²⁹ The ratio was found to be between 0.7 and 0.8, consistent with the simulated absorbed dose in KCl (i.e., 0.75 cGy per 1 cGy dose-to-water). Bragg–Gray theory suggests that photon interactions in the cavity are negligible, and the absorbed dose in the cavity is deposited solely by those electrons crossing the cavity (crossers) generated by interactions in the surrounding medium. The weak dependence of the mass collision stopping power ratio for KCl and tissue (water) on the secondary electron spectrum may explain the nearly water equivalent dose response for an ultrathin coated KCl:Eu²⁺ film demonstrated by the simulation.

It is well known that the energy dependence of a dosimeter is largely the result of photoelectric interactions of low-energy scattered photons with the dosimetry material. The projected maximum range for, say, a 30 keV secondary electron generated by photoelectric interactions in water is about 20 μm.²⁹ Because the range in a medium is roughly independent of Z for electrons (and positrons),²⁹ the above range in KCl:Eu²⁺ reduces to about 10 μm when scaled by KCl’s physical density of 1.987 g∕cm³. If the dosimeter size is of the order of a few microns, it is highly probable that secondary electrons created in the active layer, so-called starters, deposit a significant fraction of their energy outside the dosimeter’s sensitive volume, reducing the energy dependent measurement artifact. With the increase in dosimeter or cavity dimension, the range of the above starters becomes smaller than the cavity size, and thus starters become insiders. As a result, increased energy dependence occurs.

Schembri and Heijmen²⁶ reported that no field size and depth dependence was observed using a 0.3 mm thick Al₂O₃:C dosimeter for field sizes ranging from 4×4 to 30×30 cm² and depths from 1.5 to 35 cm. These data are encouraging; the thin-coated KCl:Eu²⁺ is predicted to have a more waterlike response in the penumbra than Al₂O₃:C (Table 1), implying that it will also have improved in-field response characteristics. Similar to CR material, Al₂O₃:C functions using optically stimulated luminescence but using a different storage mechanism. It has a luminescent lifetime on the order of hundreds of milliseconds to seconds,^{30, 31} much larger than that of KCl:Eu²⁺, 1.6 μs,³² which would make it impractical for 2D readout systems. For example, assuming a KCl:Eu²⁺ dosimeter of 20×20 cm² with 0.5×0.5 mm² pixels and a readout dwell time of three times the luminescent lifetime, the time to read the array would be 0.77 s (=3×1.6 μs∕pixel×400×400 pixels). However, the readout time for Al₂O₃:C would be of the order of 10⁶ longer.

SPFs with thickness of the order of 1 μm may be created using a PVD technique onto a substrate. Besides water-equivalent plastic substrate, SiO₂ glass or alumina ceramic sheets may be used. They are more thermoresistant and thus can be heated to a relatively high temperature, for example, 400 °C. This may assist phosphor film formation with better crystallinity because sufficient thermal energy is required for crystal growth and densification. Our simulation data shown in Fig. 6 indicate that a KCl film coated on a SiO₂ would still have minimal energy dependence, consistent with Al₂O₃ data reported by Schembri and Heijmen.²⁶ PVD leads to the best results when phosphor crystals with high crystal symmetry are used as the evaporation source. Fortunately, potassium chloride (KCl) belongs to this group³³ and is one of a class of compounds whose vapors consist of particles having stoichiometric composition (or are at least composed primarily of such molecules). Therefore, stoichiometric europium doped potassium chloride thin films may be obtained by direct vaporization of these compounds. By contrast, classic alkaline earth fluorohalides with complicated crystal structures tend to decompose under vacuum deposition, leading to suboptimal results.

Our preliminary data and theoretical estimations show that ultrathin KCl:Eu²⁺ SPFs will provide excellent signal strength over a clinically relevant dose range. If higher sensitivity is desired, one possible solution is to create a multilayer SPF interlaced by buffer layers. Buffer layers made of low Z transparent materials, for example, a polymer, absorb secondary electrons generated by the interaction between low-energy scattered photons and the KCl:Eu²⁺ material, and prevent them from reaching other KCl:Eu²⁺ layers, thus improving the energy response. Buffer material can also be coated between the KCl:Eu²⁺ layer and, for example, SiO₂ substrate, to minimize the interference of bulky SiO₂ material.

In conclusion, Monte Carlo simulation data demonstrate that dosimeter thickness not only has a direct impact on sensitivity, but the thickness also plays an important role in determining the overall energy response of a dosimeter. The data presented above suggest that a KCl:Eu²⁺-based film with a thickness of the order of a few microns could provide a reusable, quantitative, high-resolution, high-sensitivity two-dimensional dosimeter with nearly water-equivalent dose response.