A novel multilayer MV imager computational model for component optimization

Abstract

Purpose

A novel Megavoltage (MV) multilayer imager (MLI) design featuring higher detective quantum efficiency and lower noise than current conventional MV imagers in clinical use has been recently reported. Optimization of the MLI design for multiple applications including tumor tracking, MV‐CBCT and portal dosimetry requires a computational model that will provide insight into the physics processes that affect the overall and individual components’ performance. The purpose of the current work was to develop and validate a comprehensive computational model that can be used for MLI optimization.

Methods

The MLI model was built using the Geant4 Application for Tomographic Emission (GATE) application. The model includes x‐ray and charged‐particle interactions as well as the optical transfer within the phosphor. A first prototype MLI device featuring a stack of four detection layers was used for model validation. Each layer of the prototype contains a copper buildup plate, a phosphor screen and photodiode array. The model was validated against measured data of Modulation Transfer Function (MTF), Noise‐Power Spectrum (NPS), and Detective Quantum Efficiency (DQE). MTF was computed using a slanted slit with 2.3^° angle and 0.1 mm width. NPS was obtained using the autocorrelation function technique. DQE was calculated from MTF and NPS data. The comparison metrics between simulated and measured data were the Pearson's correlation coefficient (r) and the normalized root‐mean‐square error (NRMSE).

Results

Good agreement between measured and simulated MTF and NPS values was observed. Pearson's correlation coefficient for the combined signal from all layers of the MLI was equal to 0.9991 for MTF and 0.9992 for NPS; NRMSE was 0.0121 for MTF and 0.0194 for NPS. Similarly, the DQE correlation coefficient for the combined signal was 0.9888 and the NRMSE was 0.0686.

Conclusions

A comprehensive model of the novel MLI design was developed using the GATE toolkit and validated against measured MTF, NPS, and DQE data acquired with a prototype device featuring four layers. This model will be used for further optimization of the imager components and configuration for clinical radiotherapy applications.

1. Introduction

Electronic portal imaging devices (EPIDs) provide an efficient image acquisition workflow for radiotherapy treatment localization and verification.¹ Their inherent image digitization and processing capability surpassed the use of film‐based portal imaging and the associated time‐consuming process of film development and digitization.^{1, 2} Despite the workflow advantages of EPIDs, the imaging performance is diminished by low contrast and low detective quantum efficiency (DQE) as a result of the therapeutic range of x‐ray energies used to form the image.²

Current conventional EPID designs generally include (a) a copper (Cu) build‐up plate to convert the incoming Megavoltage (MV) energy x‐rays to electrons; (b) a thin phosphor screen, typically on the order of few hundred micrometers made of terbium doped gadolinium oxysulfide grains (Gd₂O₂S:Tb or “GOS”), to convert electrons to optical photons; and (c) an integrating amorphous silicon (a‐Si) flat panel detector to capture the optical photons exiting the phosphor screen. Previous efforts to improve EPID imaging performance characteristics have mainly focused on replacing the phosphor material with segmented crystalline scintillators,^{3, 4, 5, 6} exploiting Cerenkov radiation⁷ or employing direct detection methods.⁸ Such studies often demonstrate very high DQE; for example, Star‐Lack et al.⁵ reported a DQE approximately 25 times higher than that of a conventional EPID. The main drawbacks are the cost and complexity of manufacturing and implementation, which can be challenging obstacles to clinical translation.

An alternative, cost‐effective and readily implementable approach to improve DQE performance is to use a stacked multilayer design of Gd₂O₂S:Tb‐based EPID.⁹ Four separate layers of build‐up plate, phosphor, and a‐Si detector were stacked within the housing used for one conventional EPID (Fig. 1). The MultiLayer Imager (MLI) design utilizes currently available Gd₂O₂S:Tb phosphor panels and copper build‐up plates and has improved readout electronics modules. The readout combines images obtained by different layers during acquisition time, based on user requirement. The MLI demonstrated approximately five times higher zero frequency DQE and five times lower zero frequency noise, described by the noise‐power spectrum (NPS), compared to conventional EPID performance.⁹

Figure 1.

Schematic representation of the multilayer imager. The main components shown are, the build‐up plate made of copper, the Gd₂O₂S:Tb phosphor, and the a‐Si detector. The bottom plate is a lead‐based alloy for electron backscatter.

Further optimization of the MLI components requires knowledge of the underlying physics and the effect on imaging performance. Such information is difficult to obtain experimentally and can have high implementation cost or it may not be possible to measure. In addition, investigation of specific applications, e.g., MV cone beam computed tomography (MVCBCT), can be quickly “prototyped” and optimized computationally. In general, quantitative insight on physics and novel acquisition techniques can be readily obtained at very low cost through computational experiments (i.e., Monte Carlo simulations). Conversely, accurate and realistic computations require a model that has been previously validated against measured data. The purpose of this work is to develop a comprehensive computational model of the MLI that will incorporate x‐ray, electron and optical photon transport, and validate it against measured imaging metrics such as the modulation transfer function (MTF), NPS, and DQE. The broader future goal is to use the model as a tool for MLI optimization.

2. Methods

2.A. Multilayer imager model

The main MLI components are shown in the schematic in Fig. 1 (not to scale). There are four layers; each layer contains a combination of a Cu conversion plate, a Gd₂O₂S:Tb phosphor, and an a‐Si flat panel array detector. A metal alloy based on lead (Pb) is placed at the bottom of the imager for backscatter shielding.

The Cu plate thickness was equal to 1 mm. The modeled phosphor is the PI‐200 x‐ray scintillator screen manufactured by Mitsubishi Chemical Corporation (Tokyo, Japan). The coating weight was 200 mg/cm² and the thickness was equal to 0.436 mm. The density was calculated as 4.578 g/cm³ which corresponds to a packing density of 62.5%. A protective sheet of polyethylene terephthalate (PET) and a supportive plastic sheet were also modeled. The a‐Si detector array was modeled as a silica (SiO₂)‐based material. The density of the bottom plate Pb alloy was set equal to 10.95 g/cm³; the alloy thickness was 3 mm. An extensive presentation of the hardware components and experimental measurements can be found in Rottmann et al.⁹

2.B. Monte Carlo software

The Geant4 Application for Tomographic Emission (GATE)^{10, 11} was used to implement the computational model of the MLI. GATE is a medical physics Monte Carlo simulations application that has been extensively validated for imaging and dosimetric studies.^{11, 12, 13} It is based on the Geant4 toolkit^{14, 15} and can simulate photon, charged particle and optical photon transport in the same model. Implementation of the MLI model was carried out through descriptive scripts. The scripts contained information on geometric parameters of the simulated environment, e.g., detectors and phantoms, material composition, optical properties, x‐ray beam, and the physics model that governed the computational experiment. In this work, GATE version 7.2 with Geant4 version 10.02.p01 was used. All computational experiments were executed on our institute‐wide computation cluster. The number of x‐ray photons used to form the slit image at each computational experiment was 10⁷. Output information on detected optical photons and associated x‐ray events was obtained in list mode from which it was possible to retrieve information on the number of detected optical photons, the x‐ray interaction event, the detector pixel that detected the photons and the corresponding MLI layer. The average statistical error (0.38%) was calculated using counting statistics in the slit image.

2.C. Beam model

The Varian Truebeam™ linear accelerator head model, used in the current work, was constructed by Constantin et al.¹⁶ and obtained through the International Atomic Energy Agency (IAEA) website.¹⁷ Their model was implemented in Geant4 and demonstrated agreement with experimental dosimetric data within 2%. The phase space files were generated directly above the secondary collimators, independent of field size. The x‐ray energy spectrum of the beam is shown in Fig. 2. We used GATE to generate a narrow slit beam and sampled x‐ray energies from the beam spectrum shown in Fig. 2.

Figure 2.

Energy spectrum extracted from the phase space file of the Varian Truebeam 6 MV model constructed by Constantin et al.¹⁵ The horizontal axis is in logarithmic scale.

2.D. X‐ray and charged‐particle physics models

Geant4 developers suggest the use of specific lists of physics models for medical physics applications.¹⁸ These physics lists provide higher accuracy for electron and hadron tracking than standard physics lists used in high energy physics. The robustness of the MLI model was tested by using three of the suggested physics lists. The selected physics lists were (a) Penelope, (b) Livermore, and (c) Standard option 4. Production cuts for photons, electrons, and positrons were set to 0.01 mm. Auger electrons, characteristic x‐rays, and particle‐induced x‐ray emissions were enabled by default. Computations were re‐executed for each physics list and the results were compared with measurements. The comparison between physics lists is summarized in Fig. 7 and Table 3. The remaining figures and tables presented in the results section were obtained using Penelope as the reference physics list.

Figure 7.

MTF (a), NNPS (b), and DQE (c) curves obtained using different physics lists.

Table 3.

Correlation coefficient and NRMSE values between measured and simulated NPS and DQE data for the combined signal from all layers. Simulated values were obtained from three different physics lists. (α = 5%)

Physics list	Correlation coefficient (r)		NRMSE
	NPS	DQE	NPS	DQE
Penelope	0.9992 [0.9986–0.9996]	0.9797 [0.9546–0.9910]	0.0194	0.0686
Livermore	0.9991 [0.9985–0.9995]	0.9891 [0.9538–0.9908]	0.0256	0.0742
Standard opt 4	0.9991 [0.9986–0.9995]	0.9795 [0.9542–0.9909]	0.0226	0.0692

2.E. Optical physics model

Optical photon interaction physics were recently implemented in GATE¹⁹ and are based on the Geant4 optical photon tracking algorithms.²⁰ In summary, optical interactions include refraction and reflection at medium boundaries, bulk absorption, Mie scattering and Rayleigh scattering. Rough and smooth surfaces can be modeled as well. Mie scattering is an important mode of optical interaction in Gd₂O₂S:Tb phosphors. Mie scattering is the dominant optical scattering mode due to the large average phosphor grain size compared to the scintillation optical photon wavelength. This scattering process produces an anisotropic optical photon emission, usually forward biased for Gd₂O₂S:Tb phosphors. The Mie scattering algorithm implemented in Geant4 is based on the computational model of the Milagro gamma‐ray observatory.²¹ The model exploits the computationally less intensive Henyey‐Greenstein (HG) approximation, which is an approximate analytical solution of the Maxwell equations for optical photons scattered by spherical particles.²²

The standard procedure to model a specific Mie scattering angle probability distribution in Geant4 is to fit the distribution data to the HG curve. HG fitting can be implemented in the model either using one parameter corresponding to forward only (or backward only) scattering anisotropy or three parameters corresponding to forward and backward scattering anisotropy and their ratio. The fitting approach however may result in deviations between the data and the HG fit, which will affect the figures of merit calculated from the simulation results. To overcome this Geant4 limitation, we modified the Geant4 and GATE code to employ random sampling on the Mie scattering distribution data directly rather than using HG fitting. A condensed table look‐up method²³ was utilized for direct sampling of the discrete cumulative distribution function (CDF) of the Mie scattering angle. The Mie scattering angle probability ($P\left(\mathit{\theta }\right)$) provided by an online software described in Section 2.F was normalized over 4π. In the Monte Carlo model, the CDF of the cosine of the angle is sampled. The angle distribution was modified to obtain the distribution probability of the cosine angle from which the CDF was constructed. The number of bins used for the CDF was 360 over a cosine range from −1 to 1. The resulting CDF probabilities differ in the fourth decimal and were distributed in a large vector with 10⁴ elements. A random integer is generated during simulation runtime and used as index of a corresponding cosine value. In Fig. 3, example CDFs obtained from various values of phosphor and binder refractive indices are demonstrated.

Figure 3.

Example CDF curves constructed using Mie scattering angle probabilities obtained from different phosphor/binder refractive index combination. Solid line: GOS RI = 2.3 and binder RI = 1.0; dashed line: GOS RI = 2.8 and binder RI = 1.0; dot‐dashed line: GOS RI = 2.3 and binder RI = 1.5 and dotted line: GOS RI = 2.6 and binder RI = 1.5.

2.F. Optical parameters

Phosphor grains were modeled as spheres with a diameter of 9 μm — the average grain size according to the manufacturer. The phosphor refractive index (RI) value and absorption length were derived from previous publications^{24, 25, 26, 27, 28, 29, 30, 31}; a value of 2.3 for the refractive index and 4 cm absorption length were used in this work. The binder refractive index was provided by the manufacturer as 1.5, although a value of 1.0 was suggested for the simulations as the dominant material between phosphor grains is air and only a small amount of binder is used.¹ The optical emission of the phosphor was assumed monoenergetic at 2.25 eV (545 nm). The reflectivity of the top PET layer above the GOS phosphor was specified by the manufacturer to be 96% at 545 nm. The average number of optical photons generated after each energy deposition in the phosphor (scintillation yield) was set equal to 600 optical photons per MeV (opt/MeV). The real value of scintillation yield for Gd₂O₂S:Tb phosphors is around 60000 opt/MeV; Star‐Lack et al.³⁰ have shown that a value close to 500 opt/MeV would produce the same MTF, DQE, and NPS curves as with a scintillation yield equal to 60000 opt/MeV, with a major reduction in the computation time.

The Mie scattering coefficient (μ _s ) and anisotropy factor for phosphor/binder mixture were derived analytically from basic properties such as phosphor and binder refractive index, grain size and packing fraction using an open‐source third party software.³² The software implements the Mie scattering calculation algorithm described in Bohren and Huffman,³³ using Bessel functions, and generates values for optical anisotropy and Mie scattering coefficient at angles selected by the user. The optical parameters used in this work are summarized in Table 1.

Table 1.

Optical properties used in the current work

Property	Value
Phosphor scintillation yield (optical photons/MeV)	600
Phosphor grain size (μm)	9
Phosphor refractive index	2.3
Binder refractive index	1.0
Photon emission wavelength (nm)	545
Calculated anisotropy factor g	0.7734
Calculated Mie scattering length (μm)	3.68
PET reflectivity	96%

2.G. Validation

MTF, normalized noise‐power spectrum (NNPS) multiplied by input fluence (q) and DQE were used as figures of merit for the validation of imaging performance of our model compared with measured data. The slit image method was used to calculate MTF.³⁴ The slit angle was set at 2.3^° and 0.1 mm wide. qNNPS was calculated using the autocorrelation function technique³⁵ and is equal to the NPS divided by the mean signal and multiplied by incident photon fluence.³⁶ The application of this technique in random sampling computational experiments was discussed extensively in Star‐Lack et al.³⁰ and a similar approach was employed in our study. In summary, qNNPS can be calculated through the Fourier transform of the squared optical point spread function produced by individual energy depositions.³⁶ DQE is then calculated as

$$DQE=\frac{MT{F}^2}{qNNPS}$$ (1)

Comparison with experimental data was quantified using the root‐mean‐square‐error normalized to the range of measured values

$$NRMSE=\sqrt{\frac{{\sum }_{i=1}^N{\left(x_i^s-x_i^m\right)}^2}{N}}\times \frac{1}{\left(x_{max}^m-x_{min}^m\right)}$$ (2)

where $x_i^s$ is the simulated value, $x_i^m$ the corresponding measured value, $x_{max}^m$ and $x_{min}^m$ the maximum and minimum measured value for the used metric (i.e., MTF, qNNPS or DQE) and N the number of frequency bins. Values of NRMSE close to zero indicate better agreement with measured data.

The Pearson's correlation coefficient (r) between measured and simulated data was also calculated using the following formula

$$r=\frac{{\sum }_{i=1}^N\left(x_i^s-{\overline{x}}_i^s\right)\left(x_i^m-{\overline{x}}_i^m\right)}{\sqrt{{\sum }_{i=1}^N{\left(x_i^s-{\overline{x}}_i^s\right)}^2{\sum }_{i=1}^N{\left(x_i^m-{\overline{x}}_i^m\right)}^2}}$$ (3)

${\overline{x}}_i^s$ is the average simulated value and ${\overline{x}}_i^m$ the average measured value of the corresponding figure of merit across all spatial frequency bins. In this study, a value of r equal to 1 would indicate a perfect match between measured and simulated data. Correlation coefficient was calculated with significance level (α) equal to 5%. Confidence intervals were also calculated.

2.H. Effect of electron transport and optical photons on MTF

The effect of electron and optical transport on the MTF was separately evaluated. Three simulation experiments were carried out: (a) electron transport was completely removed from the model; (b) optical photon generation and transport were removed and electron transport included; and (c) optical photon generation and transport and electron transport were included but the optical photon yield was set equal to 1 optical photon per MeV. MTF curves were calculated for each of the three cases and compared.

3. Results

The measured and simulated normalized NPS data are displayed in Fig. 4, for (a) layer one, (b) layer two, (c) layer three, and (d) layer four of the MLI detector. There was very good agreement between measured and simulated values. The noise increase observed in the measured NPS at lower layers is accurately predicted by the Monte Carlo model. The NRMSE and correlation coefficient (r) between measured and simulated NPS data were calculated using Eqs. (2) and (3) for each layer and shown in Table 2.

Figure 4.

Normalized NPS plots for (a) layer 1, (b) layer 2, (c) layer 3, and (d) layer 4 of the MLI. Dotted lines correspond to measured values; solid lines correspond to simulated data.

Table 2.

Correlation coefficient and NRMSE values between measured and simulated NPS and DQE data for each MLI layer. Confidence intervals for r are also reported in brackets and smaller font size. Significance level α = 5%

Layer	MTFa		NPS		DQE
	r	NRMSE	r	NRMSE	r	NRMSE
1	0.9992 [0.9989–0.9994]	0.0116	0.9992 [0.9986–0.9995]	0.0205	0.9928 [0.9838–0.9968]	0.0983
2	0.9990 [0.9986–0.9992]	0.0136	0.9998 [0.9997–0.9999]	0.0112	0.9940 [0.9865–0.9974]	0.0892
3	0.9989 [0.9986–0.9992]	0.0129	0.9993 [0.9987–0.9996]	0.0209	0.9926 [0.9832–0.9967]	0.0977
4	0.9991 [0.9986–0.9992]	0.0121	0.9989 [0.9980–0.9994]	0.0372	0.9978 [0.9951–0.9990]	0.0878
All	0.9991 [0.9986–0.9992]	0.0121	0.9992 [0.9986–0.9996]	0.0194	0.9920 [0.9821–0.9965]	0.0686

^aMTF values were reported for layer 1 and then for the combined signal from layers 1 and 2, layers 1, 2 and 3 and layers 1, 2, 3 and 4. Hence, for MTF the last table value, marked “All” is equal to the value at layer 4.

In Fig. 5, the measured MTF values were plotted with the simulated MTF curves for (a) layer one, (b) layers one and two combined, (c) layers one, two and three combined, and (d) all layers combined. There is a slight depression in measured MTF when more layers are combined, which is accurately reproduced by the simulated model. The corresponding NRMSE and r values are shown in Table 2.

Figure 5.

Measured and simulated MTF for (a) layer one, (b) layers one and two combined, (c) layers one, two, and three combined, and (d) all layers combined. Dotted lines correspond to measured values; solid lines correspond to simulated data.

MTF, NPS, and DQE calculated with simulated data using the combined signal from all four layers were compared with the corresponding measured data. MTF results are shown in Fig. 6(a), NNPS in Fig. 6(b) and DQE in Fig. 6(c). NRMSE and r values for MTF, NPS, and DQE are shown in the last row of Table 2.

Figure 6.

Measured (dotted line) against simulated (solid line) curves for (a) MTF, (b) NNPS, and (c) DQE from the signal obtained after combination of all four MLI layers.

The comparison between the three physics lists suggested by the Geant4 developers for medical physics computational experiments is shown in Fig. 7. MTF was generally unaffected by the choice of physics; small differences can be seen for NNPS and DQE. The data curves correspond to the combined signal from all layers. The spatial frequency axis limits were reduced to enhance the differences. In terms of quantification, the correlation coefficient and NRMSE values between NNPS and DQE measured and simulated data corresponding to Figs. 7(b) and 7(c) are shown in Table 3.

The effect of electron and optical photon transport in the model is shown in Fig. 8 for the calculation of MTF. The MTF curve without electron transport (dashed line) showed the same trend as the MTF calculated using both electron and optical transport (solid line) and slightly higher values at almost all frequencies. The model without optical transport (dash‐dotted line) demonstrated much higher MTF after approximately 0.2 mm⁻¹ spatial frequency. Finally, the model with scintillation yield equal to 1 optical photon per MeV (dotted line), appears to have exactly the same trend as the one with a scintillation yield of 600 optical photons per MeV (solid line).

Figure 8.

MTF calculation from Monte Carlo simulation model with electron and optical transport (solid), without electron transport (dashed), without optical generation and transport (dash‐dotted) and with optical transport having a scintillation yield of 1 optical photon per MeV (dotted line).

4. Discussion

The multilayer imager (MLI) simulated in this paper is a novel megavoltage imager with a stacked configuration of four individual layers, each one similar to conventionally designed EPIDs. A difference between each MLI layer and the commercial Varian AS1200 single layer imager is the thickness of the scintillator layer. The scintillator layer of the AS1200 is 290 μm while the thickness of the same layer in each of the MLI layers is 436 μm. A result of this is that each MLI layer has an increased efficiency of 25% compared to the AS1200. Therefore, when all of the MLI layers are combined, the total efficiency is five times that of the AS1200. A more complete presentation of the imaging performance characteristics of the MLI and comparison with the AS1200 can be found in Rottmann et al.⁸

The signal and noise performance of an indirect imaging system (such as the MLI) can be fully characterized in terms of MTF, NPS, and DQE.³⁷ The Swank factor was implied in the measurement and calculation of NPS and DQE. Direct measurement of Swank factor was not feasible with our current set‐up. Scintillation pulse‐height distributions have been previously measured using keV emitting gamma‐sources to derive Swank factor.³⁸ However, this approach in the context of the current study would have required (a) MeV pencil beam pulses and (b) dismantling the MLI to remove the copper build‐up layer. Both these tasks were beyond the scope of this work.

The accuracy of the computational results is dependent on the proper selection and modeling of optical parameters. There can be differences in the calculated qNNPS when the Mie scattering angle distribution is approximated using the HG fit rather than the direct CDF method used in this study. These differences can be propagated to the calculation of DQE, potentially compromising the overall accuracy of the results. The use of CDF for Mie scattering data sampling, effectively removes uncertainties inherent in the HG approximation. An increase of a factor of two in the computational time was observed when the CDF was used in comparison with one‐parameter HG approximation fitting. In comparison with three‐parameter HG fitting, there was not a noticeable difference in computational time.

The results for MTF and qNNPS (Figs. 4 and 5) in individual layers of the MLI demonstrated very good agreement with measured data, quantified in Table 2. DQE results (Fig. 6) were sensitive to small MTF discrepancies, attributed to the square power of MTF in Eq. (1). Small deviations between measured and simulated MTF resulted in larger deviations between measured and simulated DQE. As seen in Fig. 6 for DQE, larger deviations start above 0.2 cycles/mm, which is consistent with MTF data, whereas the trend of the DQE curve follows that of qNNPS [Fig. 6(b)]. Quantification of correlation and NRMSE between simulated and measured DQE displayed in Table 2, show good agreement. In general, computationally obtained DQE is greater than measured DQE at higher frequencies, although they both show similar decreasing trends. At low frequencies, the combined signal MTF curve [Fig. 6(a)] obtained from simulation shows a very small deviation from the measured one, which is reflected in the low frequencies of the DQE curve.

Moreover, measured MTF is prone to variations depending on the experimental technique used (i.e., slit, edge, or wire), geometrical specifications, (e.g., slit angle, width and positioning) and the processing algorithm utilized to construct the MTF (e.g., flood field correction, line spread function tail fitting etc.). NPS measurements are more straightforward than MTF, and the use of the autocorrelation method described in Star‐Lack et al.³⁰ enables fast qNNPS simulations. qNNPS as the first reference for validation of model parameters and optical transport is suggested in computational studies where MTF, NPS, and DQE are involved.

Use of different physics lists provided by Geant4 developers did not reveal great differences in the MTF, qNNPS, and DQE curves (Fig. 7). Quantification data displayed in Table 3, show that Penelope physics perform slightly better than Livermore and Standard Option 4 physics lists. In this work, all computational experiments were performed using Penelope as the reference physics list.

Electron and optical transport strongly affect MTF, as shown in Fig. 8. Suspension of electron transport resulted in increased MTF at almost all spatial frequencies. The observed increase in MTF was mainly attributed to the electron range that was effectively reduced to zero. Electron transport suspension compels all energy depositions to be local to the x‐ray interaction position. At MeV energies, electrons are mostly forward scattered, hence, the difference between the MTF curves with and without electron transport was relatively small. Our results indicate that scintillation yield does not have an impact on MTF, in accordance with previous studies.³⁰ The MTF increase that was observed when optical photons were completely suspended can be attributed to (a) the absence of optical transport that contributes to optical spread and MTF degradation; (b) image formation procedure which relied on electron absorption position rather than integration of optical photons reaching the detector. Each time an electron deposited energy, its position was recorded and converted to a virtual detector pixel index. In contrast, optical photons generated by one electron deposition would have dispersed to various neighboring detector pixels.

The current study is unique in terms of the modeled imager, hence, direct comparison with previously published EPID modeling studies is not feasible. However, a review of the major optical parameters and optical transport methods used in the past can be discussed. Radcliffe et al.²⁴ and Kausch et al.²⁵ have used an isotropic optical photon emission and a scattering length of 25 μm justified as the typical spacing between phosphor grains. They developed an in‐house optical transport code that tracked optical photons through random sampling of the scattering length limited by the thickness of the phosphor. Kirkby and Sloboda,²⁷ have used a scattering length of 17 μm but they did not specify how this value was produced; they employed the DETECT2000 optical tracking code.³⁹ Star‐Lack et al.³⁰ developed a Geant4‐based application. They employed three‐parameter HG fitting for optical Mie scattering and isotropic emission with scattering length equal to 17 μm with a relative phosphor/binder refractive index of 1.7. Poludniowski and Evans²⁹ developed different optical photon transport codes based on geometrical optics‐based models and the Boltzmann transport equation. They used a phosphor refractive index of 2.3 and provided a range of results on calculated anisotropy and scattering length against grain size that match the optical parameters used in our work. Blake et al.²⁸ employed Geant4 to simulate x‐ray interactions and optical transport in the phosphor. They performed a series of computational experiments using refractive index values equal to 2.2 and 2.6 and scattering length from 10 to 25 μm; they did not validate their optical parameters in terms of MTF and NPS. Liaparinos et al.³¹ developed a Monte Carlo code to simulate x‐ray and optical photon transport in granular phosphor screens. They used the same RI value as in this study for Gd₂O₂S:Tb (i.e., 2.3) and demonstrated very good agreement with experimental MTF at diagnostic x‐ray energies up to 30 kV. They did not specify whether their code can be used for studies other than phosphor screen performance. Badal and Badano⁴⁰ demonstrated that Monte Carlo computations for imaging studies can be accelerated by a factor of 27 when using a graphics processing unit (GPU) to perform the particle transport. However, they modeled a generic type of ideal detector and their computations did not involve optical photon transport; as such, their computation times cannot be directly compared with the use of cluster computing as in the current work. Nevertheless, the use of GPU for optical transport can have a substantial impact on reduction of computation time for imaging simulations with the Monte Carlo method.

It is evident that there are a variety of computational algorithms and optical parameters previously used. This hinders direct comparison of model parameters and results between simulation studies. In terms of the underlying physics and computational model design, the approach employed in the current study was to, (a) utilize a single tool to model x‐ray photons, charged particles, and optical photons and (b) use a rigorous theoretical background specifically for the optical transport parameters. As discussed earlier, the HG approximation may not be the ideal method to determine the scattered optical photon angle. Our approach allows for standardization of the computational model and straightforward comparison with similar studies.

Validation of the MLI model enables further optimization through computational evaluation of various parameters related to the design of the imager. For instance, there is increased Compton scatter from the four layers of the MLI. Monte Carlo experiments can assist in identifying sources of scatter and selectively modify them to minimize the effect. Moreover, the impact of addition or removal of layers on imaging performance can be further investigated with Monte Carlo methods. The impact of phosphor and build‐up thickness can also be further evaluated as well as the aSi detector pixel‐pitch size. Moreover, the effect on imaging performance of other scintillation materials in layer combinations with the current MLI GOS phosphor can be readily evaluated.

5. Conclusion

A comprehensive model for a novel prototype multilayer imager (MLI) was developed with the GATE/Geant4 toolkit. The model incorporates x‐ray interactions, charged‐particle transport, and optical photon transport. Comparison of simulated and measured MTF, NPS, and DQE values for a prototype device with four detection layers shows good agreement. The validated Monte Carlo model will be used for optimization of novel multilayer imager design configurations.

Conflicts of interest

No conflicts of interest to report.