A novel method for fast image simulation of flat panel detectors

Abstract

We have developed a novel method for fast image simulation of flat panel detectors, based on the photon energy deposition efficiency and the optical spread function (OSF). The proposed method, FastEPID, determines the photon detection using photon energy deposition and replaces particle transport within the detector with precalculated OSFs. The FastEPID results are validated against experimental measurement and conventional Monte Carlo simulation in terms of modulation transfer function (MTF), signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), contrast, and relative difference of pixel value, obtained with a slanted slit image, Las Vegas phantom, and anthropomorphic pelvis phantom. Excellent agreement is observed between simulation and measurement in all cases. Without degrading image quality, the FastEPID method is capable of reducing simulation time up to a factor of 150. Multiple applications, such as imager design optimization for planar and volumetric imaging, are expected to benefit from the implementation of the FastEPID method.

1. Introduction

Electronic portal imaging devices (EPIDs), an indirect photon detection modality utilizing flat-panel detector, are widely used for various clinical applications including megavoltage (MV) cone-beam computed tomography (CBCT), high-Z material artifact suppression, pre-treatment patient positioning, treatment plan quality assurance, and real-time tumor localization (Berbeco et al 2007, Grzadziel 2007, Mijnheer et al 2013, Rottmann et al 2013, Celi et al 2016). Current clinical EPIDs are composed of a metal layer, phosphor layer e.g. gadolinium oxysulfide (GOS), and an amorphous silicon flat panel matrix for indirect photon detection. Image formation is primarily the result of the collection of optical photons generated by x-ray energy deposition in the phosphor layer (Munro and Bouius 1998, El-Mohri et al 1999, Kausch et al 1999, Antonuk 2002). Currently, the detection efficiency of MV x-ray photons with a commercial EPID is approximately 1%–1.5% (El-Mohri et al 2001). Much work has been performed to increase EPID efficiency to deliver greater contrast-to-noise ratio (CNR) at lower exposures (Sawant et al 2005a, 2005b, Wang et al 2008, El-Mohri et al 2011, Liu et al 2012, Star-Lack et al 2015, Rottmann et al 2016). Monte Carlo (MC) simulation techniques are commonly utilized for detector design optimization due to the ability to simulate imager performance without the need for expensive and time-consuming physical prototyping.

The major drawback of MC simulation is the long computation time required to generate images. Generally, MV EPID images are acquired with a relatively high dose due to the low detector efficiency. For MC simulations, ‘high dose’ means more primary particles to track, causing much longer run times. Further, thousands of optical photons are produced by each event in the phosphor layer, further increasing simulation time. Blake et al reported that it took approximately 3000 CPU-hours to simulate an EPID image with 10⁷ primary x-rays (Blake et al 2013). In general, more than 10¹¹ x-ray photons are required to generate one single EPID image at 0.01 MU with $10\times 10{\text{cm}}^2$ field size (Star-Lack et al 2014, Rottmann et al 2016), necessitating about $3\times {10}^7$ CPU-hours, a requirement that is impractical for research and development.

Several published studies have attempted to reduce the simulation time without degrading EPID image quality. A detailed MC model of the Varian AS1000 EPID, introduced by Star-Lack et al, decreased the scintillation yield of GOS phosphor from the true physical yield of 60 000 photons MeV⁻¹ to 400 photons MeV⁻¹, saving significant simulation time (Star-Lack et al 2014). Similarly, the AS1200 EPID was modeled by Shi et al with a scintillation yield of 600 photons MeV⁻¹, showing no significant difference from measurement in terms of modulation transfer function (MTF), noise power spectrum (NPS), and detective quantum efficiency (DQE) (Shi et al 2018). Others have proposed pre-calculating the optical blurring kernel and convolving it with the energy deposition of each absorbed x-ray to obtain a final EPID image (Kausch et al 1999, Kirkby and Sloboda 2005). Both methods described above shorten the optical photon simulation time, but still suffer from time consuming simulation of radiation transport.

In this paper, a novel technique for fast simulation of EPID images (FastEPID) is introduced and validated against measurement and conventional MC simulation. Our method utilizes photon energy deposition efficiency and optical spread function (OSF) to form an EPID image without simulating particle transport in the imager model. Validation of the FastEPID method is performed using slit measurements, a contrast phantom and an anthropomorphic pelvis phantom. We demonstrate a decrease in the simulation time of almost two orders of magnitude without compromising image quality.

2. Method and materials

2.1. Monte Carlo simulation environment

Both the conventional EPID simulation and FastEPID were performed with GATE (Geant4 application for tomographic emission), a MC simulation platform. GATE version 7.2 and 8.0, and Geant4 version 10 were used in this study. Briefly, GATE is based on the Geant4 kernel (Jan et al 2011) and is capable of simulating photons, charged particles, and optical photon transport (Agostinelli et al 2003, Allison et al 2006). It has been widely employed as a MC simulation tool for imaging and dosimetric studies (Grevillot et al 2011, Maigne et al 2011). In GATE, descriptive scripts are used to implement the detector model and provide information about the geometric configuration, radiative and optical properties, etc. Simulations were performed on either a single workstation of 12 CPUs (3.8 GHz, 16 GB RAM, Linux system) or on a cluster of 2000 CPU cores (CPU clock speed and RAM vary with the assigned core, Linux operating system).

2.2. Conventional simulation of the AS1200 EPID

The Varian AS1200 EPID consists of three major components: a copper layer shields low energy scattered radiation and converts high energy x-rays into secondary electrons (Antonuk 2002), a phosphor screen converts x-ray energy into optical photons, and an amorphous silicon (a-Si) panel detector with glass-based substrate for optical photon detection. The phosphor screen is a Lanex Fast-Back screen (Carestream Health, Rochester, NY), consisting of a reflective support layer, a phosphor layer, and a protective foil layer. An aluminum alloy and a lead alloy layer are attached to the back of the panel to shield backscattered radiation. A cross-sectional view of the imager is shown in figure 1 (not to scale). The imager has a pitch of 0.336 mm and the readout array size is $1280\times 1280$ pixels.

Figure 1.

Cross-sectional view of the Varian AS1200 EPID model geometry.

A MC model of the AS1200 imager was built and validated against measurement in terms of MTF, NPS, and DQE (Shi et al 2018). The model consists of a series of uniform slabs representing the individual imager components listed in figure 1. Thickness, volume density, and material composition of each layer were set in the model. The EPID model has the same pitch (0.336 mm) as in the design but a smaller detection area $(22.5\times 22.5{\text{cm}}^2)$, and a readout array size of $669\times 669$ pixels.

In conventional EPID simulation, both radiative and optical photon transport were simulated, and the range cut values for x-rays, electrons and positrons were set equal to $5\mu \text{m}$. The scintillation yield in the GOS phosphor was set to 600 optical photons per MeV deposited in the GOS phosphor. The EPID image was formed at the flat panel detector layer by collecting the optical photons entering each pixel. The conventional simulation is described in greater detail in our previously published work (Shi et al 2018).

2.3. FastEPID simulation of the Varian AS1200 EPID

The FastEPID method requires the pre-calculation of OSFs and x-ray energy deposition efficiency $\left(\eta \right)$, generated utilizing the validated AS1200 model introduced previously. Later during simulation, the OSFs and $\eta$ values are employed by a ‘FastEPID’ actor to form the final image. Actor is a GATE tool attached to a given volume for a specific purpose. Both OSFs and $\eta$ values are unique to the specific EPID design. To extend the FastEPID methodology to other detector models, OSFs and $\eta$ values would be calculated for each new model.

2.3.1. Pre-calculation of OSFs and $\mathit{\eta }$

For a given incident x-ray energy $\left(E\right)$, a mono-energetic photon pencil beam perpendicularly incident on the AS1200 model at the central pixel is simulated. Energy deposition of each primary photon in the GOS phosphor is recorded, and the summation over all the primary photons gives the total energy deposition. Energy deposition efficiency, $\eta$, is then calculated as the ratio of the total energy deposition over the total incident x-ray photon energy. The output image from the mono-energetic beam is acquired at the flat panel detector layer and OSF calculated using:

$$\text{OSF}(i,j)=\frac{\mathit{\text{Output}}(i,j)}{N_{\mathit{\text{incident}}}\times \eta }$$ (1)

where $i$ and $j$ are pixel indices, Output refers to the image formed at the a-Si panel detector, and $N_{\mathit{\text{incident}}}$ is the number of x-ray photons incident on the EPID model. Normalizing in this way, OSF represents the spread function due to an incident photon when its energy is fully deposited in the phosphor layer. OSFs can be cropped to a square shape with varying size up to the total detector area. The size of the OSFs can be optimized by balancing the improvement in simulation time with the agreement with conventional simulation. OSF size optimization will be explained further in section 2.4 with results shown in section 3.1.

The OSF and $\eta$ values are collected for a range of incident energies that matches a 6 MV clinical linear accelerator (Linac) beam spectrum (0.03, 0.04, 0.05–0.1 in steps of 0.005, 0.11, 0.125–0.2 in steps of 0.025, 0.25–1 in steps of 0.05, 1.25–2 in steps of 0.25, 2, 2.5, 4, 6.5; units of MeV). For each energy level, 10⁷ primary x-rays are used, resulting in a statistical uncertainty of less than 0.3%, calculated from the number of absorbed optical photons. The workflow of the pre-calculation process is shown in figure 2. Figure 3 shows the calculated $\eta$ values as a function of incident photon energy.

Figure 2.

Diagram of the pre-calculation of OSFs (in log scale) and $\eta$ for x-ray photon energy from 30 keV to 6.5 MeV.

Figure 3.

Photon energy deposition efficiency $\eta$ as a function of photon energy.

2.3.2. FastEPID simulation

During FastEPID simulation a dummy air slab replaces the AS1200 model for photon detection. Other components in the model, such as beam source and phantom, are kept the same as the conventional simulation. The air slab has the same pixel pitch (0.336 mm) as the AS1200 imager. The slab size can be reduced for simulation convenience. In the present study, the size of the air slab was set to $225\times 225\times 1{\text{mm}}^3$, unless stated otherwise. Since the image is formed at the a-Si panel detector in conventional simulation, the air slab is placed with its surface aligned with the panel detector surface, avoiding any inverse square law correction. The source-to-image distance (SID) was 153.5 cm for both conventional and fast simulations (Rottmann et al 2016), unless otherwise stated.

The FastEPID image simulation proceeds as follows. For each x-ray photon incident on the air slab the corresponding pre-calculated $\eta$ and OSF were assigned according to its energy. For energy values that fall between energy bins, OSF and $\eta$ are calculated through linear interpolation. Detection is determined based on the comparison of a generated random number (RN) and $\eta$. If the RN was less than or equal to $\eta$, the incident photon was ‘detected’, and the corresponding OSF was added to the EPID image with the center aligned to the incident photon position. If RN was larger than $\eta$, the incident x-ray was discarded. If the photon energy falls outside of the range of 0.03–6.5 MeV, it is discarded. The workflow of the FastEPID simulation is shown in figure 4.

Figure 4.

Flow chart of FastEPID simulation.

During FastEPID simulation both primary and scattered photons are assumed to fall perpendicularly on the air slab, and to fall at the center of a single pixel. Electrons are not considered in this simulation because the copper layer of AS1200 imager shields external electrons from depositing energy in the GOS phosphor.

2.4. Impact of the OSF size and FastEPID optimization

The OSF size can vary from a small area to the size of the EPID. Because pixels outside the OSF are excluded from the simulation, selecting too small OSF size may cause the final image to suffer under-estimated pixel values. With a large OSF size, more time will be spent on OSF interpolation, potentially negating any reductions in the computation time.

The OSF size can be optimized by balancing the improvement in simulation time with a comparison between the images generated by the conventional simulation and the FastEPID method. A $4\times 4{\text{cm}}^2$ open field image was simulated by the conventional method and by the FastEPID method with OSF sizes varying from $11\times 11$ pixels to $401\times 401$ pixels. A multi-point source, modeled from Varian Truebeam $6\times$ phase space files was employed as the beam source. The description and validation of the source model can be found in appendix. 10⁸ primary x-rays were delivered in each simulation.

Images produced by FastEPID were compared to the conventional simulation image for each OSF size. The relative difference $\left(Diff\%\right)$ for $\text{pixel}(x,y)$ is calculated as follows:

$$Diff\%(x,y)=\frac{\left|I_{\mathit{\text{test}}}(x,y)-I_{\mathit{\text{ref}}}(x,y)\right|}{max\left(I_{\mathit{\text{ref}}}\right)}\times 100\%$$ (2)

where $I(x,y)$ represents the pixel value at position $(x,y)$, and $Diff\%(x,y)$ represents the relative difference at $(x,y)$. Subscript test and ref indicate the test image (FastEPID) and the reference image (conventional simulation), respectively. $Max\left(I_{\mathit{\text{ref}}}\right)$ represents the maximum pixel value in the reference image. Images were normalized to the mean value before comparison. The agreement between FastEPID and the conventional method was quantified with passing rate (PR), the ratio of the number of pixels having $Diff\%<3\%$ to the total number of pixels. The simulation time ratio of FastEPID to the conventional method was also calculated. The optimal OSF size was determined by finding the lowest time ratio with at least 95% PR.

2.5. Validation of the FastEPID simulation

FastEPID simulation with the optimal OSF size ($81\times 81$ pixels, explained in section 3.1) was validated against measurements and the conventional simulation in terms of MTF, signal-to-noise ratio (SNR), CNR, contrast, and the pixel relative difference. MTF was obtained from a slanted slit image, and the other metrics were measured for Las Vegas (LV) phantom images. Moreover, images of an anthropomorphic pelvis phantom were compared and validated.

2.5.1. Validation with MTF

MTF is normally used for the evaluation of imager spatial resolution. The measured MTF of the AS1200 imager was acquired by using the slit image method (Fujita et al 1992). The experiment has been described in greater detail previously (Rottmann et al 2016). Briefly, a slit image was obtained by illuminating the EPID with a narrow slit tilted by 1.5°. The slit was created by a pair of tungsten alloy blocks placed on top of the detector with a separation of $100\mu \text{m}$. The image was acquired with $10\times 10{\text{cm}}^2$ field size, at a 153 cm source-to-imager distance (SID), and with a 400 MU min⁻¹ dose rate. Following the procedure introduced by Fujita et al (1992), an oversampled line spread function (LSF) was obtained from the slit image, the Fourier transform of which yields the phase-averaged MTF.

For the conventional simulation of MTF, a $0.1\times 70{\text{mm}}^2$ rectangular plane x-ray photon source tilted by 1.5° was modeled directly above the EPID top surface. 10⁷ x-ray photons were uniformly launched onto the EPID and the optical photons were scored in each pixel of the panel detector to form the slit image. X-ray photon energies were sampled from the 6 MV spectrum. Following the Fujita method (Fujita et al 1992), an oversampled LSF was formed from the slit image then converted into MTF. The same geometry and procedure were used for the FastEPID simulation, with the imager model replaced by the air slab.

Agreement between the measured, the conventionally simulated and the FastEPID simulated MTF was evaluated by MTF difference at low (0.1 mm⁻¹), middle (0.75 mm⁻¹), and high (1.5 mm⁻¹) spatial frequency.

2.5.2. Validation with Las Vegas phantom

Imaging metrics for the FastEPID method were validated with a Las Vegas (LV) phantom (Herman et al 2001). The LV phantom was placed at source to surface distance (SSD) 100 cm, while the AS1200 model and the FastEPID air slab were placed at SID = 153.5 cm with a field size of $15\times 15{\text{cm}}^2$, and the central $15\times 15{\text{cm}}^2$ EPID image was obtained for analysis. The multi-point source model was used as the beam source (appendix). Since no couch was simulated in this study, the LV phantom image was acquired experimentally with the phantom standing vertically on the couch and gantry/detector rotated by 90°.

The measured EPID images were dark field (DF) and flood field (FF) corrected to eliminate fixed pattern noise, pixel sensitivity variance and non-uniformities in the beam profile (Siebers et al 2004, Seco and Verhaegen 2013). Simulated images were FF corrected to remove the effect of the beam profile. A series of high MU FFs were simulated utilizing the FastEPID method, to correct images from both simulations. As shown in section 3.1, the open field FF images simulated with the FastEPID method agreed well with the conventional method.

Normalization of the measured and simulated EPID images is necessary to account for the different interpretation of pixel value. The simulated pixel value equal to the number of optical photons that enter the pixel, where the measured pixel value is an electric signal proportional to the number of optical photons detected. In general, the former can be hundreds of times larger than the latter. EPID images can be normalized with a cross calibration (Seco and Verhaegen 2013):

$$I_{\mathit{\text{simu\_nor}}}(x,y)=I_{\mathit{\text{simu}}}(x,y)\times \frac{I_{\mathit{\text{meas}}}^{100\times 100}}{I_{\mathit{\text{simu}}}^{100\times 100}}$$ (3)

where $I(x,y)$ represents a pixel value at position $(x,y)$, and $I^{100\times 100}$ is the mean value in a central region of $100\times 100$ pixels of the image at 1 MU. The subscripts meas, simu, and simu_nor indicate the measurement, the raw simulation, and the normalized simulation, respectively.

Electronic noise cannot be removed from the measured image due to its random feature, however it is not commonly modeled with MC simulations. One way to compensate for this difference is to add reconstructed electronic noise to the simulated EPID images. To model electronic noise, a single frame DF and a 200 frame-average DF were acquired with an AS1200 imager. The averaged DF assumed to represent only the fixed pattern noise and negligible electronic noise. Subtraction of the single frame and the averaged frame results in the electronic noise alone. The electronic noise is a Gaussian distribution with zero mean and a standard deviation (STD) of 3.30. With the same mean and STD value, a Gaussian distributed noise image was randomly generated and then added to the simulated EPID images. In general, electronic noise has a dependence on the detector. The noise feature obtained from one imager cannot be used for reconstruction of another imager. In the present study, we kept all measurement on one TrueBeam machine, and the electronic noise was reconstructed consistently. Introducing electronic noise into the simulation will not affect the previous normalization due to the zero-mean value.

After the complete correction and normalization, the simulated EPID images were validated against the measured images. SNR, CNR (Bian et al 2013), and contrast were calculated for the region-of-interest (ROI) as follows:

$$\text{SNR}=\frac{S_{\text{ROI}}}{{\sigma }_{\text{ROI}}}$$ (4)

$$\text{CNR}=\frac{S_{\text{ROI}}-S_{bg}}{\sqrt{\left({\sigma }_{\text{ROI}}^2+{\sigma }_{bg}^2\right)}}$$ (5)

$$\mathit{\text{Contrast}}=\frac{S_{\text{ROI}}-S_{bg}}{S_{bg}}$$ (6)

where $S$ and $\sigma$ denote the mean pixel value and standard deviation, respectively, and subscript ROI and $bg$ denote ROI (a circular region within the holes, as shown in figure 5) and background (a donut shaped region surrounding the ROI), respectively. SNR, CNR, and contrast were calculated for two ROIs (ROI A and ROI B in figure 5) with 0.1–1 MU.

Figure 5.

Regions of interest ((A) and (B)) on the Las Vegas phantom used for FastEPID validation.

The relative difference in pixel value between measurement, the conventional simulation and FastEPID images was calculated following equation (2). For comparison between simulation and measurement, the measured image was the reference image. For comparison between FastEPID and conventional simulation, the conventionally simulated image was the reference image. The PR at $Diff\%<1\%,2\%$, and 3% was calculated, respectively. The higher the PR, the better the agreement between test and the reference images.

2.5.3. Validation with an anthropomorphic pelvis phantom

EPID images of an anthropomorphic pelvis phantom (The Phantom Laboratory, Greenwich, NY) in anterior–posterior (AP) direction and left–right (LR) direction were experimentally acquired and FastEPID simulated at 1 MU with field size $20\times 20{\text{cm}}^2$. The measured image was DF and FF corrected, while the simulated image was FF corrected, normalized, and electronic noise corrected as described above. The Gamma analysis with criteria 3%/3 mm (Low et al 1998) was employed for the quantitative evaluation of the agreement between measurement and FastEPID simulation.

2.6. FastEPID impact on simulation time

Improvement of the simulation time utilizing the FastEPID method was quantified by the time ratio of the conventional simulation to the FastEPID simulation. Results were calculated for simulations with a $4\times 4{\text{cm}}^2$ open field (section 2.4), 1 MU LV phantom (section 2.5.2), and 1 MU pelvis phantom (section 2.5.3) images.

3. Results

3.1. Impact of the OSF size and FastEPID optimization

Sample open field $(4\times 4{\text{cm}}^2)$ simulation images are shown in figure 6. The randomness of the subtraction between two images (figure 6, right) indicates that there is a minor pixel value difference between the FastEPID and the conventional method. The PR at $Diff\%<3\%$ and the simulation time ratio are shown in figure 7. For OSF size larger than $81\times 81$ pixels, the PR was greater than 95% and the FastEPID simulation time was less than 1% of the conventional method, indicating a substantial improvement in the simulation time without compromising the image quality. As expected, simulation with larger OSF sizes requires longer simulation time, while smaller OSF sizes result in relatively low PRs due to the underestimation of the pixel values. In the following validation studies, an OSF size of $81\times 81$ pixels was used.

Figure 6.

Conventional simulation (left) and FastEPID (middle) with OSF size of $81\times 81$ pixels. Subtraction between two images is shown on the right.

Figure 7.

The PR (solid line, plotted against the left $y$-axis) and time ratio of FastEPID simulation to the conventional simulation (dashed line, plotted against the right $y$-axis).

3.2. Validation with MTF

MTF curves obtained by measurement and simulations are shown in figure 8. The difference between measurement and simulations at low (0.1 mm⁻¹), middle (0.75 mm⁻¹), and high (1.5 mm⁻¹) spatial frequencies are shown in table 1. In general, the agreement of the FastEPID simulation to measurement was similar to the conventional method. MTF differences between the two simulation methods were negligible.

Figure 8.

MTF curves obtained by measurement (solid), conventional simulation (dash line), and fast simulation (dot line).

Table 1.

MTF difference at low, median, and high spatial frequencies.

Spatial frequency (${\text{mm}}^{-1}$)	0.1	0.75	1.5
$\Delta$ (measurement, conventional)	0.03	0.07	0.01
$\Delta$ (measurement, FastEPID)	0.03	0.04	0.03
$\Delta$ (conventional, FastEPID)	0.01	0.02	0.02

3.3. Validation with LV phantom

LV phantom images obtained from measurement and simulations are shown in figure 9. The SNR, CNR, and contrast of ROI A and B are shown in figure 10. While the SNR and CNR are consistent, a relatively large deviation in contrast between simulation and measurement was observed in both ROIs. Although an overestimation of contrast was found with both simulation methods, all methods (simulation and measurement) found a similar difference in contrast between ROI A and ROI B, suggesting a systematic shift.

Figure 9.

Las Vegas phantom images (1 MU under the same window/level).

Figure 10.

Signal to noise ratio (SNR), contrast to noise ratio (CNR), and contrast in ROI A (left column), and ROI B (middle column). The right column presents the difference between ROI A and B in terms of SNR, CNR, and contrast.

The PR between measurement and simulations are shown in figure 11. For each comparison, 1%, 2% and 3% $Diff\%$ were considered. In general, the FastEPID simulation provided similar agreement with measurement as the conventional method. The PR between the two simulations was slightly higher than measurement because of less noise in the simulations. A lower PR was observed at low MU value in all cases, due to the increasing impact of stochastic noise on image quality at lower doses.

Figure 11.

The PR between measurement and simulations for $\mathit{\text{Diff}}\%<1$ (left), $\mathit{\text{Diff}}\%<2$ (middle), $\mathit{\text{Diff}}\%<3$ (right).

3.4. Validation with anthropomorphic pelvis phantom

As shown in figure 12, the pelvis phantom images simulated with the FastEPID method provide similar image quality compared to the measured images, in both AP and LR directions. Normalized image profiles at different locations match well between measurement and FastEPID simulation. Gamma analysis (3%/3 mm) showed 85% agreement between measurement and FastEPID simulation in AP direction, and 90% in LR direction.

Figure 12.

Measured (left column) and FastEPID simulated (middle column) pelvis phantom images in anterior–posterior direction (top row) and in left–right direction (bottom row) at 1 MU. Image profiles (right column) of measured and FastEPID simulated images at different lines.

3.5. Improvement in simulation time

Due to the intensive radiative and optical photon transport computations, performing a conventional simulation requires weeks to obtain a single EPID image (e.g. $1.383\times {10}^6$ CPU hours for 1 MU LV phantom image). With the FastEPID method, we found an improvement in simulation run time by a factor of 90–140, depending on the phantom (as shown in table 2). The transport in the phantom is not accelerated in the present study, therefore run time improvement is lower in thicker phantoms. Pelvis phantom images were not acquired with conventional simulation due to impractical run time.

Table 2.

Simulation time and time improvement with FastEPID.

	Conventional simulation	FastEPID simulation	FastEPID simulation on CPU cluster
Open field (${10}^8$ primary photons)	1412 CPU hours	10 CPU hours	No test
Las Vegas phantom (1 MU)	$1.383\times {10}^6$ CPU hours	$1.540\times {10}^4$ CPU hours	8 h
Pelvis phantom (1 MU)	No test	$5.095\times {10}^4$ CPU hours	30 h

4. Discussion

We have presented a novel technique for fast EPID image simulation and demonstrated a large reduction in simulation time without compromising image quality. The technique, FastEPID, utilizes precalculated OSFs and energy deposition efficiencies of incident photons to form the final image without simulating particle transport in the imager model. This method has a strong dependence on the imager design, but no dependence on either the beam source or the phantom, enabling multiple applications, such as MV CBCT and imager optimization.

FastEPID simulation with an optimal OSF size $(81\times 81\text{pixels})$ has been validated against measurement and conventional simulation utilizing MTF, LV phantom and pelvis phantom. It provides an accurate prediction of MTF at low/middle/high spatial frequencies, indicating satisfactory simulation of resolution. For LV phantom simulation, FastEPID provided SNR, CNR, and contrast similar to conventionally simulated images. FastEPID simulations of an anthropomorphic pelvis phantom accurately reproduced the experimentally acquired image.

Almost 150 × savings in detector simulation time is realized with the FastEPID method. The overall simulation time, however, depends on the phantom thickness and this factor becomes more important for human sizes. We are currently investigating methods for reducing this time as well.

Electronic noise was measured and added to the simulated phantom image to better replicate the measured image. The introduction of electronic noise has a dependence on the imager and is only a factor for low dose acquisitions. For low dose EPID images, electronic noise plays an important role, particularly on SNR and CNR. One application of the present study is to apply a fast simulation method to generate MV CBCT, which is reconstructed from hundreds of low dose EPID projections. Therefore, it is necessary to have electronic noise included in the model. Other applications, like beam’s-eye-view imaging during radiation therapy procedures, will be less impacted by noise.

In the present study, approximately 25 CPU hours were used to build and validate the AS1200 MC model, and 1000 CPU hours for the collection of OSF and $\eta$ values at 41 energy bins. Utilizing a 2000 CPU cluster, the pre-calculation procedure took 30 min.

5. Conclusion

FastEPID, a novel technique for fast MV EPID image simulation was introduced and validated in multiple phantoms. Almost 150 × gain in run time was observed with the FastEPID method, without compromising image quality in terms of CNR, SNR, contrast and anatomy visualization. It is anticipated that the FastEPID technique will accelerate the development of novel MV imagers for multiple clinical applications.

Appendix. Beam model of Varian TrueBeam 6 MV: multi-point source

Phase-space files are generated by recording the properties (e.g. energy, particle type, position, and direction) of particles emerging from the treatment source. Several intrinsic shortcomings of phase-space files have hindered their use in the present study. Approximately $3\times {10}^8$ particles are saved in Varian TrueBeam 6 MV phase-space files, but more than 10¹¹ primary photons are required to obtain a $10\times 10{\text{cm}}^2$ EPID image with 0.01 MU at SID = 100 cm. Random rotation of phase space files may solve this problem, but it will introduce an insufficient photon influence at the corner of a large field size (>30 cm). Additionally, for simulations with a small field size, most particles will be blocked by the secondary collimators, causing a tremendous waste of simulation time.

In the present study, we have modeled the Varian TrueBeam 6 MV phase-space source with a multi-point source, which is formed by several point sources located at the same position. Each point source emits x-ray photons within a given solid angle that projects in a 0.5 cm width ring at the iso-center plane (SSD = 100 cm). An example showing four point-sources combined to form a multi-point source is shown in figure A1. Relative photon intensity of each point source is pre-determined from the phase space file. Photon energy is sampled from the spectrum that is pre-determined by the phase space files. The number of point sources is determined by the field size, so that the accumulated solid angle is sufficient to cover the required field size.

To determine the energy spectrum and relative intensity of each point source, the simulation was run with the phase-space source, along with the secondary collimators. To generate a multi-point source for $10\times 10{\text{cm}}^2$ field size, simulation with the TrueBeam phase-space source and $10\times 10{\text{cm}}^2$ secondary collimator was run, and particles were gathered at SSD = 100 cm plane. The number of x-ray photons that fall in each ring area (0.5 cm width) was counted, and the energy of each photon was recorded. Then, the energy spectrum and relative photon intensity were calculated accordingly. Some of the ring areas are cut by the edge of the square field size, thus the relative intensity is modified according to the area loss. For a $10\times 10{\text{cm}}^2$ field size, seventeen point sources were generated. For other sizes, the quantity is listed in table 3.

Table 3.

Number of point sources required in the multi-point source for different field size.

Field size $\left({\mathbf{c}\mathbf{m}}^2\right)$	$10\times 10$	$20\times 20$	$30\times 30$	$40\times 40$
Number of point sources	17	31	45	59

To model the source beam, seventeen point sources, generated with $10\times 10{\text{cm}}^2$ field size, were placed at the origin, and each of them emitted x-ray photons within a pre-defined solid angle, following the corresponding energy spectrum and relative intensity. The secondary collimators were attached to form the square shape open field. The same process was performed for the field sizes, with different numbers of point sources. Several energy spectrum plots for each field size are shown in figure A2.

Figure A1.

Four point sources placing together to form a multi-point source. Each point source emits x-ray photons within a given solid angle that projecting a ring shape area (width = 0.5 cm) at SSD = 100 cm plane.

Figure A2.

Energy spectrum extracted from different numbers of point sources for various field size values.

The multi-point source for each field size has been validated against experimental measurement and simulation with phase space source in terms of percentage depth dose (PDD), relative dose profile at maximum dose depth $(d_{\text{max}}=1.5\text{cm})$, and field size output factor (OF). PDD measurement was performed in a water tank with SSD of 98.5 cm (our clinical Linac was calibrated to 1 MU cGy⁻¹ at $d_{\text{max}}$, at the center of a $10\times 10{\text{cm}}^2$ field with SSD = 98.5 cm). Relative dose profile measurement was performed with water tank SSD = 100 cm, and output factors were measured a 10 cm depth in water with SSD = 95 cm. Simulations were configured with the same setup. For the output factor comparison, field sizes of $4\times 4$ and $15\times 15{\text{cm}}^2$ were also included. The validation was quantified by the difference between measurement and multi-point source simulation.

Excellent agreement was found for PDD, relative dose profile, and OF, as shown in figures A3–A5, respectively. PDD curves have been scaled by different factors to distinguish them in the same figure. In general, PDD curves agree well between measurement and multi-point source simulation, within 2% difference. A 3%–5% difference was observed at depths close to the water surface, mainly because electrons were not modeled in the multi-point source. For EPID implementation, electrons are shielded by the top copper layer, so this omission should not impact the FastEPID method. Relative dose profiles match well between measurement and the multi-point source for $10\times 10$ to $40\times 40{\text{cm}}^2$ field size. A difference was observed at the open field edge, which might be due to the uncertainty in secondary collimator modeling. Overall agreement of the OF is good with negligible difference between the measurement and multi-point source simulation.

In summary, the proposed multi-point source can be used to model a Varian TrueBeam Linac. This method saves all the beam information in a data file that is only a few kilobytes (KB). It can be sampled repeatedly without any concerns on running out of particles.

Figure A3.

Measured and simulated PDD curves with $10\times 10,20\times 20,30\times 30$, and $40\times 40{\text{cm}}^2$ field size in water. For clarity, $10\times 10,20\times 20,30\times 30$, and $40\times 40{\text{cm}}^2$ PDDs have been scaled by different factors, as labeled on the graph. A subplot representing the difference between measured data and multi-point source simulation data is shown.

Figure A4.

Measured and simulated relative dose profiles at $d_{\text{max}}$ in water with $10\times 10,20\times 20,30\times 30$, and $40\times 40{\text{cm}}^2$ field size. Each profile has been normalized to the central axis dose. Subplots below each profile graph show the difference between measurement and multi-point source simulation.

Figure A5.

Measured and simulated output factors at depth = 10 cm in water (SSD = 90 cm). A subplot indicating the OF difference between measurement and multi-point source simulation (red line), and difference between simulations with phase space files and multi-point source (black line) is shown.