A Rapid, Accurate Image Simulation Strategy for Megavoltage Cone-Beam Computed Tomography

Abstract

Intensive computation time is required to simulate images of electronic portal imaging device (EPID) using Monte Carlo (MC) technique, limiting the development of applications associated with EPID, such as mega-voltage cone-beam computed tomography (MV-CBCT). In this study, a fast, accurate simulation strategy for MV-CBCT utilizing the FastEPID technique has been developed and validated. During FastEPID simulation, photon detection was determined by pre-calculated photon energy deposition efficiency (η) and particle transport within the EPID was replaced with a pre-calculated optical photon spread function. This method is capable of reducing the time required for EPID image simulation by a factor of 90–140, without compromising image quality. MV-CBCT images reconstructed from the FastEPID simulated projections have been validated against measurement in terms of mean Hounsfield unit (HU), noise, and cupping artifact. These images were obtained with both a Catphan 604 phantom and an anthropomorphic pelvis phantom, under treatment beam energies of 2.5 MV, 6 MV, and 6 MV flattening filter free. The agreement between measurement and simulation was excellent in all cases. This novel strategy was capable of reducing the run time of a full scan simulation of MV-CBCT performed on a CPU cluster to a matter of hours, rather than weeks or months required by a conventional approach. Multiple applications associated with MV-CBCT (e.g. imager design optimization) are anticipated to gain from the implementation of this novel simulation strategy.

1. Introduction

Megavoltage cone-beam computed tomography (MV-CBCT) has been developed primarily for patient pre-treatment positioning and anatomical change monitoring in an image-guided radiation therapy (IGRT) workflow (Barker et al., 2004). MV-CBCT images are reconstructed from a series of two-dimensional (2D) projections acquired using an electronic portal imaging device (EPID) mounted on a linear accelerator (LINAC) as the LINAC rotates around the patient. The x-ray source is the LINAC treatment beam. MV-CBCT can also be used for treatment planning and dose reconstruction because the linear attenuation coefficients (μ) at the treatment beam’s energy are reconstructed directly (Langen et al., 2005). Other advantages of this imaging technique are reduction of metal artifacts due to similar attenuation between metal and human tissues at MV energies (Pouliot et al., 2005; Yin et al., 2005), and limited effect of scatter radiation compared to kilovoltage (kV) CBCT (Morin et al., 2006). However, MV-CBCT image quality suffers from the low detection efficiency of typical EPID designs (El-Mohri et al., 2001; Antonuk, 2002). Due to these advantages and challenges, MV-CBCT has attracted researchers’ attention and has been a major motivator for the development of new EPIDs (Wang et al., 2008; El-Mohri et al., 2011; Hu et al., 2019; Hu et al., 2018b; Myronakis et al., 2018; Myronakis et al., 2019).

Currently, the most widely used EPIDs generate images through an indirect photon detection process, utilizing a structure that consists of a metal layer, a phosphor layer, and an amorphous silicon flat panel matrix. Incident photons deposit energies in the phosphor layer and trigger scintillation events. Optical photons are generated through the scintillation events and collected by the flat panel matrix to form an image (Munro and Bouius, 1998; Antonuk, 2002; El-Mohri et al., 1999; Kausch et al., 1999). However, the detective quantum efficiency (DQE) is approximately 1%–1.5% (El-Mohri et al., 2001). Previous studies of EPID design demonstrated higher DQE using multiple stacked layers of phosphor-based detectors (Rottmann et al., 2016) or segmented crystalline scintillators (Sawant et al., 2005a; Sawant et al., 2005b; Wang et al., 2008; El-Mohri et al., 2011; Liu et al., 2012; Star-Lack et al., 2015).

In general, optimizing EPID architecture requires the development and testing of multiple detector designs. Through Monte Carlo (MC) simulation techniques, this process can be accelerated, and hardware implementation costs can be avoided. Simulation of particle transport through an accurate imager model can be used to generate images without physical realization. The major drawback of MC simulation, especially for MV images, is the long computation time necessitated by the simulation of many primary photons, secondary electrons, as well as the multitude of optical photon interactions in the detector scintillator. Thousands of optical photons are generated from every scintillation event, each of which needs to be tracked for accurate results. Blake et al. reported that roughly 3000 CPU-hours were required to simulate a single EPID image with 10⁷ primary particles (Blake et al., 2013). Wang et al. reported that approximately 700 000 CPU-hours were required to simulate several MV-CBCT scans, excluding optical photon transport (Wang et al., 2008). Shi et al. reported that a conventional MC simulation of a Las Vegas phantom EPID image at 1 MU took 1 383 000 CPU-hours necessitating the use of a CPU cluster (Shi et al., 2019). A novel method, FastEPID, has been proposed to accelerate MV EPID image simulation by a factor of 90–140 (Shi et al., 2019). FastEPID determines photon detection with pre-calculated photon energy deposition efficiency and replaces particle transport within the detector with a pre-calculated optical spread function.

In the current work, we present a MV-CBCT simulation strategy based on the FastEPID method and validate it against measurements with two phantoms and multiple beam energies. We demonstrate that, by utilizing the FastEPID technique, MV-CBCT simulation time can be significantly reduced without compromising image quality for a given detector, the optical spread functions and photon energy deposition efficiency values of which have previously been calculated.

2. Method and materials

The proposed MV-CBCT simulation strategy was validated against measurement using a Catphan 604 phantom (The Phantom Laboratory, Greenwich, NY, USA) and an anthropomorphic pelvis phantom (The Phantom Laboratory, Greenwich, NY, USA). Phantom projections were acquired with a Varian AS1200 imager (Varian Medical System, Palo Alto, USA). Full scans of each phantom were acquired at 2.5 MV, 6 MV, and 6 MV flattening filter free (FFF) beam energies on a Varian TrueBeam LINAC (Varian Medical System, Palo Alto, USA). Comparison of the reconstructed phantom images between measurement and simulation was performed, and simulation time was evaluated.

2.1. Simulation setup – FastEPID technique and MV-CBCT acquisition

2.1.1. MV imager and FastEPID technique

The AS1200 imager consists of a copper buildup layer, a phosphor screen, and an amorphous silicon (a-Si) photo-detector panel with a glass-based substrate. The copper layer converts high-energy photons into secondary electrons and shields against low-energy scatter radiation (Antonuk, 2002). The phosphor screen absorbs x-ray energy and generates optical photons through scintillation events. The photo-detector collects the optical photons and creates an image. Metal layers such as lead alloy are attached to the back of the detector for backscattered radiation shielding. The imager readout array size is 1280 × 1280 pixels with a pitch of 0.336 mm. The total active area is 430 × 430 mm². A detailed AS1200 MC model can be found in Shi et al (Shi et al., 2018). Raw EPID images are dark field (DF) and flood field (FF) corrected in order to eliminate fixed pattern noise, pixel sensitivity variance, and beam profile non-uniformities (Siebers et al., 2004; Seco and Verhaegen, 2013).

The FastEPID method was developed to speed up conventional MC simulation, which normally requires millions of CPU-hours to obtain a single EPID image. Here only a brief description of the FastEPID technique is presented. More details can be found in Shi et al (Shi et al., 2019).

The FastEPID method consisted of two major steps, pre-calculation with an AS1200 MC model and FastEPID simulation with a virtual detector. During the pre-calculation step, optical spread functions (OSF) and photon energy deposition efficiencies (η) at different photon energies were generated utilizing the validated AS1200 MC model(Shi et al., 2018). For a given energy E, MC simulation was performed with a mono-energetic photon pencil beam incident perpendicular at the center of the AS1200 model. The ratio of the total energy deposition to the total incident photon energy was calculated as η, and OSF is calculated following equation 1:

$$OSF(i,j)=\frac{\mathit{\text{Image}}(i,j)}{N\times \eta }$$ (Equation 1)

where Image refers to the output image formed at the a-Si panel detector from the mono-energetic beam, i and j are pixel indices, and N is the number of incident photons. OSF is the spread function due to an incident photon from a full energy deposition in the imager. The OSF size was optimized to 81 × 81 pixels to obtain suitable image quality and acceptable simulation time. The OSF and η values were collected for 41 energy bins from 30 keV to 6.5 MeV, matching the energy range of the TrueBeam LINAC treatment beam. The range can be modified to match different beam energies. In the present study, the pre-calculation procedure took less than one hour when running on a 2000-core CPU cluster.

During FastEPID simulation, the EPID model was replaced with a virtual detector filled with air. The beam and the phantom were simulated with the conventional MC technique. The virtual detector had the same pixel pitch as the AS1200 imager and was placed at the same source-to-imager distance (SSD). For photons incident on the virtual detector, the corresponding η value and OSF were calculated according to the photon energy E. If a newly generated random number (RN) was less than or equal to η(E), the incident photon was “detected”, and the photon OSF(E) was added to the final image with the center aligned to the incident position. If RN was greater than η(E), the incident photon was discarded, and the simulation proceeded to the next particle. External electrons were not considered in the FastEPID simulation as they were shielded by the copper layer of the imager. All the simulations in this study were conducted utilizing the FastEPID method developed by Shi et al (Shi et al., 2019). A potential strategy for decreasing computation time while increasing noise performance of the FastEPID method can be found in Appendix C.

Images simulated with the FastEPID method must be FF corrected to remove beam profile non-uniformities. The FF images were FastEPID simulated at high dose values and then smoothed with a median filter to avoid any fixed pattern noise introduced by the beam source.

2.1.2. Beam sources

Phase space sources are widely accepted as the source inputs in MC simulation as they are capable of characterizing the source accurately in terms of energy spectrum, angular distribution and spatial distribution (Townson et al., 2013). In the present study, 6 MV and 6 MV FFF source files were provided by the manufacturer (myvarian.com/s/montecarlo, login required), and 2.5 MV source files were generated utilizing Varian’s VirtuaLINAC, a web application running on Amazon Web Service (Amazon Web Service, Inc., Seattle, WA, USA) for MC modeling of TrueBeam (Parsons et al., 2014). Specifications of the phase space source files are listed in Table 1. The Azimuthal particle redistribution (APR) technique is applied to make repeated use of the phase space files (Bush et al., 2007). The beam sources were validated against measurement in terms of percent depth dose, relative beam profiles, and output factors. Detailed information of the validation can be found in Appendix A.

Table 1.

Varian TrueBeam phase space files.

Beam energy	File size	File number	Total number of primary photons
2.5 MV	~ 0.6 GB	15	3.3 × 108
6 MV	~ 1.8 GB	6	3.1 × 108
6 MV FFF	~ 1.1 GB	10	4.7 × 108

2.1.3. Phantoms

The Catphan 604 phantom (shown in Figure 1) consists of 4 scan sections, and is often used for commissioning and quality assurance of CBCT systems. Section 2 consists of 10 cylindrical target inserts made from different materials and arranged in a circular pattern. The top right graph on figure 1 schematically represents the arrangement of inserts. The body of the Catphan 604 is made from urethane, which is approximately soft tissue equivalent. An MC model of scan section 2 of the phantom was built following the target properties (listed in Table 2) and geometric information that were available in the product manual (https://www.phantomlab.com/s/CTP604-Manual-9-15.pdf). Two identical urethane slabs of thickness 5.5 cm were added to both ends of the phantom, taking the length of the simulated phantom from 4 cm to 15 cm.

Figure 1.

Top left: A side view of the Catphan 604 phantom. Top right: Schematic illustration of the target inserts in Catphan 604 scan section 2. Bottom left: A side view of the pelvis phantom. Bottom right: A cross-sectional view of the digitized pelvis phantom.

Table 2.

Properties of the Catphan 604 phantom and the pelvis phantom

Catphan 604 phantom
Material	Density (g/cm3)	Chemical composition (mass fraction in %)					Relative electron density to water
		H	C	N	O	Others
Air	0.00129	-	0.01	75.5	23.2	Ar: 1.3	0.001
PMP*	0.83	14.3	85.7	-	-	-	0.853
50% Bone	1.4	5	35	6	34	P: 6, Ca: 14	1.312
LDPE**	0.92	14.3	85.7	-	-	-	0.945
Polystyrene	1.03	7.7	92.3	-	-	-	0.998
Acrylic	1.18	8	60	-	32	-	1.147
20% Bone	1.14	5	51	5	30	P: 3, Ca: 6	1.084
Delrin	1.42	10	60	-	30	-	1.363
Teflon	2.16	-	25	-	-	F: 75	1.868
Urethane	1.1	8.8	60.3	5.8	25.1	-	1.080
*PMP: polymethylpentene
**LDPE: low density polyethylene

Anthropomorphic pelvis phantom
Material	Density (g/cm3)	Chemical composition (mass fraction in %)
		H	C	N	O	Others
Air	0.00129	-	0.01	75.5	23.2	Ar: 1.3
Bone	1.4	3.5	30.9	2.8	33.3	P: 8.8, Ca: 18.9, Sb: 1.9
Soft tissue	1.01	5.3	71.1	8.7	14.7	Sb: 0.2

The anthropomorphic pelvis phantom is shown in Figure 1 (bottom row). From a real diagnostic CT scan of the phantom, a digital version was derived by segmenting the CT numbers into 3 different material regions with a density conversion defined by the user. The digital phantom was built on a 512 × 512 × 210 voxel grid with a spacing of 1 × 1 × 2.5 mm³. Properties of the phantom materials provided by the manufacturer are listed in Table 2.

2.1.4. Simulated MV-CBCT acquisition

The phantoms were placed at the LINAC isocenter and oriented with the longitudinal axis perpendicular to the beam central axis. To match the measurement, a field size of 30 × 30 cm² at isocenter was modeled by terminating primary particles that fall beyond this area. The FastEPID virtual detector was placed at a source-to-imager distance (SID) of 153.5 cm (Rottmann et al., 2016). During the FastEPID simulation, the beam source and the detector were spatially fixed, while the phantoms rotated about their longitudinal axis over a full arc. The phantoms were simulated with the conventional MC method, and the imager was simulated with the FastEPID method. 720 projections were acquired with an angle increment of 0.5°. The projections were binned by 4 pixels along the superior-inferior direction.

The MU per projection was 0.01, 0.0167, and 0.05 at 2.5 MV, 6 MV, and 6 MV FFF, resulting in a total dose of 7 MU, 12 MU, and 36 MU, respectively. The different MUs for each energy was due to the technical constraints of the physical MV-CBCT measurements. The equivalence between the total number of primary particles and the MUs is explained in Appendix A.

2.2. Monte Carlo environment

An MC simulation platform, GATE (Geant4 application for tomographic emission), was used to execute the FastEPID simulation. GATE is a MC application that has been widely used in the medical physics field and well validated for dosimetric and imaging simulations. As a software based on Geant4 kernel (Jan et al., 2011), GATE is capable of simulating photons, optical photons, and charged particles, and it is often used as an MC simulation tool for imaging and dosimetric research (Agostinelli et al., 2003; Allison et al., 2006; Maigne et al., 2011; Grevillot et al., 2011). GATE is also excellent for 3D visualization, building structures with sophisticated geometry, and specifying motions of structures such as translation and rotation. By implementing an application layer on top of the core layer classes and the Geant4 kernels, GATE provides a user-friendly interface based on a dedicated scripting mechanism, which requires no knowledge of C++ programing and thus facilitates the use of GATE. In this study, GATE v7.2 and Geant4 v10.02 were used to run simulations on a CPU cluster of 3000 cores available for each user. More details about the CPU cluster can be found in Appendix B.

2.3. MV-CBCT reconstruction algorithm

MV-CBCT images were reconstructed by using the Feldkamp-Davis Kress (FDK) algorithm (Feldkamp et al., 1984), with a Hanning filter and a cutoff at 70% of the Nyquist frequency. No scatter or beam hardening correction was performed. The reconstructed volume size was 290 × 290 × 81 mm³ with 1 mm voxel size in all three dimensions.

The reconstructed voxel value represented the linear attenuation coefficient μ(x, y, z) at position (x, y, z). The μ values were converted to Hounsfield units (HU) following Equation 2:

$$HU(x,y,z)=\frac{\mu (x,y,z)-{\mu }_{\mathit{\text{water}}}}{{\mu }_{\mathit{\text{water}}}}\times 1000HU$$ (Equation 2)

where μ_water denotes the mean μ of a water equivalent region. For the Catphan 604 phantom, an annular area on the uniform urethane slab (Figure 2, left) that overlaps the circular pattern of the target inserts in scan section 2 was chosen as the water equivalent region. For the pelvis phantom, a circular uniform soft tissue area (Figure 2, right) was chosen as the water equivalent region. A denoised μ_water value was obtained by averaging over 5 consecutive slices.

Figure 2.

The chosen water equivalent region of the Catphan 604 phantom (annular area on the left image), and the pelvis phantom (circular area on the right image).

2.4. Validation studies

MV-CBCT measurements were performed on a TrueBeam LINAC (v2.7 mr3) at Varian’s Imaging Laboratory (Baden, CH). Projections of the Catphan 604 phantom and the pelvis phantom were experimentally acquired using the AS1200 imager with the specifications described in Section 2.1.4. The reconstruction process was performed as described in Section 2.3. Comparison of the phantom images reconstructed from the measured and simulated projections was performed using multiple image metrics.

2.4.1. Analysis of Catphan 604

As a measure of how faithfully the simulation captured scatter and beam hardening effects, cupping non-uniformity artifacts were evaluated in the Catphan 604 studies using the uniform urethane slab of the phantom. The artifact was quantified following Equation 3:

$$\mathit{\text{Cupping}}\mathit{\text{artifact}}=\frac{H{U}_{\mathit{\text{cen}}}+1000}{H{U}_{\mathit{\text{edge}}}+1000}$$ (Equation 3)

where HU_cen denotes the mean HU within a toroidal volume of interest (VOI) at the center of the phantom and HU_edge denotes the mean HU within a toroidal region at the edge. Both regions spanned 11 axial slices. Standard deviation within these two VOIs were calculated and compared.

Mean HU and contrast-to-noise ratio (CNR) were calculated for the Catphan 604 phantom inserts both in measurement and simulation. The CNR of each insert was calculated as follows:

$$CNR=\frac{|H{U}_{ROI}-H{U}_{bg}|}{\sqrt{({\sigma }_{ROI}^2+{\sigma }_{bg}^2)}}$$ (Equation 4)

where HU denotes the mean HU, and σ denotes the standard deviation. Subscript ROI and bg denote a circular region within the insert and an annular region surrounding the insert, respectively. A linear relationship was built between the mean HU of the inserts and the corresponding nominal relative electron density to water (RED) for each reconstruction.

2.4.2. Analysis of Pelvis Phantom

The reconstruction image of the pelvis phantom was compared between measurement and simulation. Images containing the same bone structure were displayed to illustrate the overall image performance. Two regions of interest (ROI), soft tissue equivalent region and bony region, on the central image of the reconstruction volume that aligned with the beam axis (illustrated on Figure 3) were compared in terms of mean HU and standard deviation, representing signal and noise performance, respectively. The difference of the bone structure on the central reconstruction image was caused by a 15 mm phantom position shift between simulation and measurement. The RED of the soft tissue and the bone was estimated from the mean HU utilizing the linear relationship between HU and RED derived from the Catphan 604 phantom.

Figure 3.

The chosen regions of interest on the central reconstruction image of the pelvis phantom.

2.5. Run time of MV-CBCT simulation with the FastEPID technique

The CPU cluster used in the present study was equipped with multiple CPU models with various computation speeds. Simulation jobs submitted to the cluster were randomly assigned to CPU models, resulting in a distribution of job run time. To offer a fair estimation, the simulation time utilizing the FastEPID technique was scaled to the dominant CPU model, AMD Opteron^™ Processor 6380 2.50 GHz, and normalized to a total dose of 1 MU. Results were calculated for both phantoms at all beam energies. A detailed discussion of the dependence of run time on CPU model can be found in Appendix B.

3. Results

3.1. Analysis of Catphan 604

The reconstructed images of the Catphan 604 urethane slabs obtained from measurement and simulation are compared in Figure 4. In general, the image performance agreed well between measurement and simulation. The quantified cupping artifact values are listed in Table 3, showing that the artifact captured by the simulation was similar to that of the measurement. The standard deviations of the VOIs are listed in Table 4, showing a similar noise performance between measurement and simulation.

Figure 4.

Reconstructed images of the uniform urethane slabs and the comparison of the diagonal profiles at beam energy 2.5 MV (row A), 6 MV (row B), and 6 MV FFF (row C).

Table 3.

Comparison of the cupping artifact at different beam energies

Beam energy	2.5 MV	6 MV	6 MV FFF
Measurement	0.842	0.739	0.816
Simulation	0.848	0.754	0.824
Percent difference	0.7%	2.0%	1.0%

Table 4.

Comparison of the standard deviation within VOIs at different beam energies

Beam energy	2.5 MV		6 MV		6 MV FFF
VOI	Center	Edge	Center	Edge	Center	Edge
Measurement	59.1	45.0	117.3	102.2	53.9	48.5
Simulation	56.5	45.1	149.1	124.6	64.6	54.6

The images of the Catphan 604 scan Section 2, reconstructed from the measured and FastEPID simulated projections, are compared in Figure 5. The simulation provided similar image quality compared to the measurement. The agreement in the mean HU and CNR was good for all beam energies. The mean HU increased linearly with RED, indicating the possible application of MV-CBCT for calculation of patient treatment dose and treatment planning. The equations describing the linear relationship between HU and RED are displayed on the corresponding plots in Figure 5.

Figure 5.

Reconstructed images of the Catphan 604 scan Section 2 (left columns) and the mean HU and CNR plotted against ROI relative electron density (right columns) at beam energy 2.5 MV (row A), 6 MV (row B), and 6 MV FFF (row C). The equations describing the linear relationship between HU and RED are displayed on the plots in Column 3.

3.2. Analysis of Pelvis Phantom

As shown in Figure 6, the reconstruction image of the pelvis phantom containing the same bone structure was compared, and similar image characteristics were observed between measurement and simulation. The mean HU and standard deviation values of the soft tissue and bony regions on the central reconstruction image are listed in Table 5, showing strong agreement between measurement and simulation in terms of image signal and noise performance. The estimated RED of the soft tissue and the bone (listed in Table 5) is similar to the RED value listed in Table 2.

Figure 6.

Reconstructed images of the pelvis phantom at beam energy 2.5 MV (row A), 6 MV (row B), and 6 MV FFF (row C).

Table 5.

Comparison of mean HU, noise, and estimated RED of the pelvis phantom at each beam energy

		Soft tissue			Bone
Beam energy	Image acquisition	Mean HU	Standard deviation	Estimated RED	Mean HU	Standard deviation	Estimated RED
2.5 MV	Measurement Simulation	5.1 −3.0	111.6 112.4	1.08 1.06	119.0 152.5	137.7 130.4	1.27 1.29
6 MV	Measurement Simulation	−3.0 −10.9	219.7 263.7	1.08 1.07	188.5 211.5	239.3 303.6	1.36 1.40
6 MV FFF	Measurement Simulation	−3.9 −3.6	99.1 113.4	1.08 1.07	172.6 174.5	117.5 136.6	1.36 1.35

3.3. Run time of MV-CBCT simulation with the FastEPID technique

Run time of the MV-CBCT simulation utilizing the FastEPID technique is listed in Table 6. The FastEPID-based strategy performed on a CPU cluster was able to complete a MV-CBCT simulation within 19 – 52 hours. Dependence of run time on the CPU model can be found in Appendix B.

Table 6.

Run time of MV-CBCT simulation

Beam energy	Total MU	Catphan 604 phantom	Pelvis phantom
2.5 MV	1	31.6 hours	52.0 hours
6 MV	1	35.8 hours	42.8 hours
6 MV FFF	1	19.0 hours	31.9 hours

4. Discussion

A novel, FastEPID-based strategy for rapid MV-CBCT simulation was developed and validated. Projections of two phantoms at 2.5 MV, 6 MV, and 6 MV FFF beam energies were simulated using the FastEPID technique. Phantom images reconstructed from the simulated projections demonstrated close agreement with those reconstructed from the measured projections. The simulation time was approximately 19 – 52 hours for a total dose of 1 MU. By contrast, a conventional MC simulation would require 90 – 140 times longer run time, resulting in weeks or months computation time. Thanks to the large reduction in simulation time, the proposed simulation strategy can accelerate the development of new imager designs and clinical applications associated with MV-CBCT (Rottmann et al., 2016; Hu et al., 2018a; Hu et al., 2019; Lozano et al., 2019; Ferguson et al., 2019).

A dependence of the run time on the beam energy was observed in the proposed strategy. When delivering the same total dose, simulation with 2.5 MV and 6 MV ran longer than that with 6 MV FFF. At 6 MV, more off-axis particles were delivered than 6 MV FFF to form a flat profile across the field, causing longer run time. At 2.5 MV, x-rays had lower energy and, consequently, more particles were needed to deliver the same dose as a 6 MV FFF beam, at the calibration depth.

No scatter or beam hardening correction was performed during the reconstruction process. The focus of this study was to evaluate the ability of FastEPID technique to rapidly and accurately simulate projections and their consequent reconstructions. Optimizing the CBCT reconstruction processing chain for image quality was not necessary for this evaluation.

Cupping artifacts are generally caused by an underestimation of reconstructed μ values and is associated with beam hardening, varying off-axis x-ray spectrum and energy-dependent EPID response (Graham et al., 2007; Glover, 1982; Cheung et al., 2009). The cupping artifact has been accurately reproduced using the simulated projections (Figure 4 Row C). Reconstructions with projections from 2.5 MV and 6 MV FFF beam energies demonstrated a reduced cupping artifact compared with 6 MV. This was attributed mainly to the slowly varying off-axis energy spectrum associated with the flattening filter free design (Parsons et al., 2014).

The run time improvement presented with the proposed strategy was achieved mainly by replacing particle transport within the detector with pre-calculated OSF data and executing simulation in parallel on the CPU cluster. Further efforts are underway to make the FastEPID algorithm suitable for highly parallelized computations on graphics processing units (GPUs). The implementation of FastEPID MV-CBCT simulation on the GPU will further accelerate the simulations by particle transport through phantom in parallel and allow the use of local computational resources (Bert et al., 2013; Jia et al., 2012).

5. Conclusion

A strategy for fast simulation of EPID projections suitable for MV-CBCT reconstruction was developed based on the FastEPID technique. Validations with two phantoms using different beam energies were performed. The run time of a full arc simulation with 720 projections, executed on a CPU cluster was reduced two orders of magnitude without compromising the reconstruction quality. The proposed strategy can potentially benefit development of novel flat panel detectors and clinical applications associated with MV-CBCT.

Appendix A. Validation of the phase space sources of TrueBeam 2.5 MV, 6 MV, and 6 MV flattening filter free (FFF).

Simulation using the phase space sources of Varian TrueBeam 2.5 MV, 6 MV, and 6 MV FFF were validated against measurement in terms of percentage depth dose (PDD), relative dose profile, and field size output factor (OF). PDD measurement was performed in a large water tank for field size of 10 × 10 cm², 20 × 20 cm², 30 × 30 cm², and 40 × 40 cm² at a SSD of 100 cm. Relative dose profile measurement was performed with the same SSD and field sizes as the PDD measurement. Relative dose profiles were recorded at 5 cm depth in water for 2.5 MV and at 1.5 cm depth for the other two beam energies and normalized to the central axis dose. The output factor was recorded at 5 cm depth in water for the field size of 30 × 30 cm², at a SSD of 95 cm. Monte Carlo simulations were performed with the same setup utilizing the phase space sources and a water tank model. The validation was quantified by the agreement between measurement and phase space based simulation.

Comparison of PDDs and relative dose profiles are illustrated in Figures A1 and A2. PDD curves plotted in the same graph are distinguished by different scale factors. Excellent agreement between measurement and simulation was observed for PDD curves, within 2% difference. Relative dose profiles matched well between measurement and simulation with a relatively large difference at the field edge, which could be caused by the modeling uncertainty of the secondary collimators. OFs at 30 × 30 cm² agreed well between measurement and simulation, as shown in Table A1. In summary, the phase space sources can be used to accurately model a Varian TrueBeam LINAC.

For a fair comparison between measurement and simulation in terms of imaging dose, the equivalence between the number of primary particles and the LINAC MU was established utilizing a calibration simulation with the same configuration as the experimental calibration. The LINAC beam used in this study was calibrated to deliver 1 MU per cGy to water at d_max with SAD = 100 cm, using a 10 × 10 cm² field size. According to the calibration simulation, 1 cGy was deposited to d_max in water by 5.34 × 10¹² particles generated from 2.5 MV phase space source. The number was 3.67 × 10¹² particles for 6 MV source and 2.29 × 10¹² for 6 MV FFF source. For dose other than 1 MU, the total number of primary particles was scaled accordingly.

Figure A1.

Measured and simulated PDD curves with 10 × 10, 20 × 20, 30 × 30, and 40 × 40 cm² field size in water for beam energy 2.5 MV (left), 6 MV (middle), and 6 MV FFF (right). For clarity, PDD curves with different field sizes have been scaled by different factors, as labeled on the graph. Subplots below each PDD graph show the PDD difference between the measured data and the simulated data.

Figure A2.

Measured and simulated relative dose profiles for beam energy 2.5 MV (left), 6 MV (middle) and 6 MV FFF (right) at 5 cm depth in water with 10 × 10, 20 × 20, 30 × 30, and 40 × 40 cm² field size. Each profile has been normalized to the central axis dose. Subplots below each profile graph show the difference between the measured data and the simulated data.

Table A1.

Output factor with 30 × 30 cm² field size

	Measurement	Phase space based simulation	Difference%
2.5 MV	1.1679	1.1412	2.3%
6 MV	1.1109	1.1053	0.5%
6 MV FFF	1.0795	1.0700	0.9%

Appendix B. Impact of CPU model on the FastEPID simulation time

The CPU cluster used in the present study was equipped with multiple CPU models that provide different computation speeds based on processor specifications, such as processor base frequency, number of cores, memory size, and memory speed. Of the six CPU models available in the cluster, the Intel® Xeon® Gold 6140 processor @ 2.3 GHz and the AMD Opteron^™ processor 6380 @ 2.5 GHz were the two dominant models. Simulation jobs submitted to the cluster were randomly assigned to CPU models, resulting in a distribution of job run times. Figure A3 shows a run time distribution for a batch of identical MC jobs. Five spikes are observed, corresponding to jobs running on five different CPU models. Spike 1 and 4 correspond to jobs running on Intel® Xeon® Gold 6140 processor and AMD Opteron^™ processor 6380, respectively. Apparently, jobs assigned to Intel® Xeon® 6140 are completed more quickly than those assigned to AMD Opteron^™ 6380.

Figure A3.

A run time distribution of identical Monte Carlo simulation jobs running on the cluster that used in the present study.

Run time of the FastEPID-based simulation strategy was evaluated with the less powerful CPU, AMD Opteron^™ processor 6380, in Section 3.4. To further understand the strength of the FastEPID technique, the run time was re-evaluated with the more powerful CPU, Intel® Xeon® Gold 6140. As shown in Table A2, the MV-CBCT simulation run on a cluster consisting of only Intel® Xeon® Gold 6140 processors takes less than a day, much faster than if run on an AMD Opteron^™ processor 6380 CPU cluster.

Table A2.

Run time of FastEPID MV-CBCT simulation with Intel® Xeon® Gold 6140 CPU @ 2.30 GHz

Beam energy	Total MU	Catphan 604 phantom	Pelvis phantom
2.5 MV	1	9.0 hours	18.8 hours
6 MV	1	10.2 hours	15.3 hours
6MV FFF	1	5.4 hours	10.8 hours

Appendix C. A potential strategy for decreasing computation time while increasing noise performance of the FastEPID method

During the pre-calculation process of the FastEPID method, a mono-energetic pencil beam consisting of 10⁷ primary photons is simulated to form an OSF. Hence, the OSF contains the noise feature representing the case of 10⁷ photons incident at a given pixel for a given energy bin. But in reality, the number of photons incident on a single pixel within a single energy bin is much fewer than 10⁷. Therefore, the original FastEPID tends to provide lower noise by using less noisy OSFs. A potential strategy is to introduce an OSF-sampling process. In the new FastEPID method, 37 OSFs are pre-calculated with various number of primary x-rays from 1 × 10³ to 1 × 10⁷ for each energy bin. During FastEPID simulation, the number of incident photons (N_inci) is recorded for each image pixel at each energy bin. The final EPID image is generated with the OSFs sampled based on the N_inci.

The new FastEPID method was validated against the conventional MC simulation and the original FastEPID simulation. A 10 × 10 cm² planar source sampled from a TrueBeam 6 MV spectrum was placed right above the imager to form a 10 × 10 cm² open field. The images were simulated with a large number of primary photons (up to 5 × 10¹⁰). The signal (mean value), noise (standard deviation), and SNR² of a central area on the open field image were plotted against the number of primary photons, as shown in Figure A4. By introducing the OSF-sampling process, the image noise increases compared to the original FastEPID result and agrees better the conventional simulation result. Meanwhile, the SNR² of the new FastEPID simulation decreases and has a good agreement with the conventional simulation as well.

Figure A4.

The signal, noise, and SNR² of a central area on the open field image

Images of a Las Vegas (LV) phantom were simulated with the new FastEPID method following the method introduced by Shi et al. (Shi et al., 2019), and validated against measurement, conventional MC simulation, and the original FastEPID simulation. Phantom images acquired at 1 MU are illustrated in Figure A5. The overall image performance is similar among measurement and simulations. The SNR, CNR, and contrast of ROI A (the hole on the top right) and B (the hole on the right in the 2^nd row) are shown in Figure A6 and A7, respectively. Compared to the original FastEPID method, the new FastEPID results have better agreement with the conventional simulation.

The original and new FastEPID methods required 7.34 hours and 4.31 hours to generate 1 MU LV phantom image on a 2000-core CPU cluster, respectively. The improvement in simulation time is due to an algorithm modification. During the original FastEPID, OSFs are added to the EPID image one after another for all detected photons. During the new FastEPID, parameters recording the number of incident photons, the number of detected photons, and the accumulated scale factors between energy bins are computed for each pixel on each energy bin. After all photons are simulated, the EPID image is generated from these parameters and the properly sampled OSFs. Therefore, the new method saves time by reducing the number of OSF addition operations.

Figure A5.

Las Vegas phantom images acquired at 1 MU

Figure A6.

SNR, CNR, and contrast of ROI A

Figure A7.

SNR, CNR, and contrast of ROI B