A simulation study to evaluate the effect of 2D antiscatter grid primary transmission on flat panel detector based CBCT image quality

Abstract

Purpose:

Two-dimensional antiscatter grids’ (2D-ASGs) septal shadows and their impact on primary transmission play a critical role in cone-beam computed tomography (CBCT) image noise and artifact characteristics. Therefore, a numerical simulation platform was developed to evaluate the effect of 2D-ASG’s primary transmission on image quality, as a function of grid geometry and CBCT system properties.

Methods:

To study the effect of 2D-ASG’s septal shadows on primary transmission and CBCT image quality, two new methods were introduced; one to simulate projection signal gradients in septal shadows, and the other to simulate septal shadow variations due to gantry flex. Signal gradients in septal shadows were simulated by generating a system point spread function that was directly extracted from projection images of 2D-ASG prototypes in experiments. Variations in septal shadows due to gantry flex were simulated by generating oversampled shadow profiles extracted from experiments. Subsequently, the effect of 2D-ASG’s septal shadows on primary transmission and image quality was evaluated.

Results:

For an apparent septal thickness of 0.15 mm, primary transmission of 2D-ASG varied between 72 – 90% for grid pitches 1 – 3 mm. In low-contrast phantoms, effect of 2D-ASG’s radiopaque footprint on information loss was subtle.. At high spatial frequencies, information loss manifested itself as undersampling artifacts, however its impact on image quality is subtle when compared to quantum noise. Effect of additive electronic noise and. gantry flex induced ring artifacts on image quality varied as a function of grid pitch and septal thickness. Such artifacts were substantially less in lower resolution images.

Conclusion:

Proposed simulation platform allowed successful evaluation of CBCT image quality variations as a function of 2D-ASG primary transmission properties and CBCT system characteristics. This platform can be potentially used for optimizing 2D-ASG design properties based on the imaging task and properties of the CBCT system.

1. INTRODUCTION

Scattered radiation is one of the major causes behind image quality degradation in CBCT. Currently, radiographic and fluoroscopic antiscatter grids (ASGs) in addition to air gap methods are the most commonly used scatter rejection techniques. However, in flat-panel detector (FPD)-based-CBCT imaging, utilization of radiographic ASGs and air gaps provides modest improvements in image quality. Improvements in the CT number accuracy is not sufficient for quantitative imaging applications, such as radiation therapy dose calculations. Moreover, radiographic ASGs may reduce contrast-to-noise ratio (CNR) when the scatter intensity is moderate in projections [1–7], which was attributed to low primary transmission through radiographic ASGs [8].

For improved suppression of scatter, we have been investigating the feasibility of using 2D-ASGs in conjunction with FPDs [9–12], particularly in the context of image-guided radiotherapy. We have shown that 2D-ASGs can substantially improve CNR and CT number accuracy, when compared to the radiographic antiscatter grids [10]. Although 2D-ASGs are efficient in reducing scatter fluence, their primary transmission properties also play a critical role in achieving high image quality. If primary transmission of 2D-ASG is suboptimal, its consequences may go beyond increased quantum noise; for example, new image artifacts might be introduced due to suboptimal suppression of septal shadows or image information might be lost partially due to obstruction of primary beam by grid septa, which may degrade image quality. Suboptimal 2D-ASG - focal spot alignment increases the apparent thickness of grid septa in projections, and primary signal loss will be higher in septal shadows, and SNR will be lower in septal shadows. Adverse effects of additive electronic noise can be more pronounced in septal shadows due to reduced primary signal. Another important issue is the gantry flex problem, which refers to change in focal spot position in relation to the detector due to mechanical flex in CBCT gantry; gantry flex may cause primary signal intensity variations in 2D-ASG’s septal shadows. If this issue is not fully addressed by flat field correction methods, it may lead to ring artifacts in CBCT images. Detector’s spatial resolution also plays an important role when assessing the effects of primary transmission properties. When spatial resolution is lower and pixel size is larger, septal shadows in primary signals are less pronounced, which may impact the effect of electronic noise, data loss, and gantry flex.

Such issues are less pronounced in conventional CT scanner simulations, where antiscatter grid is always aligned with interpixel septa in the detector, gantry flex is minimal, grid pitch is matched to pixel pitch, effect of electronic noise is not amplified in septal shadows, because large portion of the septal shadows coincide with interpixel septa.

Thus, a major challenge in implementation of 2D antiscatter grids is the artifacts and image noise associated with 2D grid’s primary transmission characteristics. To better understand and potentially address these image quality problems, primary transmission simulations are needed to parse different antiscatter grid and imaging system configurations.

To address this need, in this work, we developed a simulation platform to evaluate the effect of 2D-ASG’s septal thickness and grid pitch on the 2D-ASG’s primary transmission and CBCT image quality. In addition to 2D ASG’s physical properties, our platform simulates x-ray detector’s spatial resolution and electronic noise characteristics to evaluate how flat panel detector properties influence primary signal properties and image quality. Our work includes both new methods to study primary transmission properties, and as well as preliminary evaluations of the impact of primary transmission on CBCT image quality.

2. MATERIALS AND METHODS

Our numerical 2D-ASG simulation platform simulates the 2D-ASG projections in CBCT scans by accounting for system blurring, primary transmission through 2D-ASG via modeling of effective septal thickness and grid pitch, quantum noise, electronic noise, and effects of gantry flex. Since our work is focused on the effects of 2D-ASG’s primary transmission, scatter simulations were not performed.

2.1. Numerical Phantoms and System Geometry

To study the effect of 2D-ASG’s primary transmission properties on CBCT image quality, several numerical 3D phantoms were generated. First, a bar pattern phantom, with line pairs ranging from 1 to 21 lp/cm and CT number of 2280 HU was generated to evaluate the effect of 2D-ASG on the reconstructed images’ spatial resolution. The second phantom is a low contrast phantom with three groups of low contrast inserts of 1, 2, and 3% that mimicked the Catphan 504 - CTP515 low contrast module (Phantom Laboratory, NY). Each group has cylindrical inserts of diameters of 2, 3, 4, 5, 6, 7, 8, 9, and 15 mm, while the background was set to be 67 HU. The third phantom was designed to evaluate the effects of electronic noise, where the background was at 880 HU while the two cylindrical inserts with 4 cm diameter were at 2000 HU. The phantom attenuates the primary beam more than the other two phantoms due to its higher density, such that the electronic noise is comparable to Poisson noise in phantom projections. All phantoms have a diameter of 20 cm and thickness of 6 cm along the axial direction.

Simulated phantoms were forward projected in Varian TrueBeam’s centered detector geometry [13], with a source to image distance of 150 cm and source to axis distance of 100 cm. Total of 450 interpolation-based-forward projections were generated over 360 degrees source rotation, where the nominal detector pitch was 0.194×0.194 mm². Then, these forward projections were upsampled to 0.02×0.02 mm² to match the pixel size of the binary grid template, before binning them again at the end of simulation to reflect the pixel size used in different clinical imaging scenarios that are discussed below.

It was assumed that the x-ray beam is monoenergetic and image noise is driven by photon counting statistics and electronic noise, when present in simulated scenarios. Energy dependent detector response was excluded. This is because, the effects of 2D-ASG’s primary transmission on CBCT image quality was evaluated in relative comparisons with respect to “no grid” or a “reference” 2D-ASG configuration. Thus, energy dependent detector efficiency and other energy dependent noise factors, such as Swank noise, are assumed to be similar in all simulations and reference images.

Moreover, effects of polyenergetic beams on image quality (such as beam hardening) were excluded from our investigations. Since our goal is to investigate solely the effects of 2D-ASG’s primary transmission properties on CBCT image noise and artifacts, rather than conducting a comprehensive simulation of the imaging chain, effects of polyenergetic spectrum were omitted.

2.2. Simulation of 2D-ASG and CBCT Projections

The flow chart of the simulation platform is shown in figure 1. Briefly, simulation has the following major steps. 1) Generation of binary 2D-ASG template to simulate primary x-ray transmission through the 2D-ASG, 2) Incorporation of primary transmission of 2D-ASG in phantom projections, 3) Implementation of system blurring to emulate primary signal gradients introduced by 2D-ASG’s shadows, 4) Pixel resizing or binning, 5) Gain map correction of projections, 6) Reconstruction. In addition to these steps, electronic noise injection to projections and gantry flex were implemented in steps 4 and 5, in a subset of simulations.

Figure 1.

Flowchart shows the processes in the 2D-ASG simulation platform.

These simulation steps are elaborated in sections below. One of the critical simulation steps is the system blurring, which determines the properties of primary signal variations introduced by 2D-ASGs footprint. Therefore, particular emphasis was given to determining the system blurring function.

To model the primary x-ray transmitted through the 2D-ASG, a template of a 2D square aperture array was generated with the desired grid pitch and septal thickness. This template served as the binary attenuation map of the primary beam, where pixel values were set to 100% of primary transmission within the apertures and to zero underneath the septa to reflect that primary x-rays incident on the 2D-ASG’s septa were fully absorbed. The 2D-ASG’s septa are assumed to be perfectly aligned, or focused, towards the x-ray focal spot, matching the divergence of primary x-rays. To minimize the effects of finite pixel size on the 2D-ASG’s septum definition in the 2D binary grid template, pixel dimensions were set to 20×20 μm², significantly smaller than the septal thickness, and referred to as $\left(G_{20}\right)$. Forward projections of phantoms were also upsampled to 20×20 μm² to match the pixels of the binary grid template. Subsequently, the 2D binary grid was multiplied by each upsampled projection.

In the 2D-ASG binary template described above, the incident primary beam was assumed to be parallel to the focused septa. However, such a simplified assumption would not be highly accurate in an experiment due to several reasons. First, primary beam will not be parallel due to the divergence of the x-ray beam, that would lead to a small magnification of septal thickness in the detector plane. Second, due to finite size of the focal spot and off-focal radiation, a fraction of primary x-rays will be directly incident on the 2D-ASG septa and absorbed by the 2D-ASG. Third, in an experimental system, it is challenging to perfectly align septa towards the focal spot during the alignment process. As a result, the apparent septal thickness, $d_{app}$, of the grid structure in projections is likely to be different than 2D-ASG’s actual physical septal thickness.

Thus, a binary 2D-ASG template by itself does not depict the signal variations introduced by 2D-ASG’s footprint in the projections, as observed in experiments. Modeling of both detector and focal spot blurring are needed to model such signal variations, which are referred as septal shadows in the text. In our approach, system blurring was characterized by using one point spread function (PSF) that models blurring before integration of signal in pixels, and a subsequent pixel binning process to account for blurring due to detector pixel size.

This approach requires decoupling the effects of blurring before and after image signal detection in detector pixels. Conventional system blurring methods, such as modulation transfer function (MTF) measurement techniques [14], provide system blurring after signal integration in detector pixels. Moreover, based on our experience, detector blurring measured with such methods may not precisely emulate blurring observed in septal shadows, as observed in experiments.

Thus, in this work, an alternative approach was developed to estimate system PSF before signal integration step in pixels. This approach utilized a parametric model of PSF, where parameters of PSF was iteratively calculated to simulate septal shadows comparable to experimentally observed septal shadows. For an accurate estimation of the PSF, the following function as described by Poludniowski et al. [15] was used:

$$PSF\left(r\right)=\frac{a_1}{2\pi b_1^2}{e}^{{-r}^2/{2b}_1^2}+\frac{a_2}{2\pi b_2^2}{e}^{-r/b_2}+\frac{a_3}{2\pi b_3^2}\frac{1}{{\left(1+r^2/b_3^2\right)}^{3/2}}$$ (1)

where $a_i$ and $b_i$ are free fitting parameters, and $r$ is radial distance from the symmetry center of the PSF. The PSF term accounted for blurring in the scintillator and effects of detector backscatter. The effects of focal spot associated blurring were implicitly included in the PSF term.

To incorporate system blurring, first, a binary 2D-ASG template was generated at 5×5 μm² pixel size for a given grid pitch and apparent septal thickness. Second, binary template is convolved by the PSF in Eq (1). Finally, blurring due to integration in detector pixels was achieved by binning the template’s pixels to match the FPD’s pixel size.

Six free fitting parameters in the PSF and the apparent septal thickness ($d_{app}$) were determined from flood projections of 2D-ASG prototypes that were acquired using a linac-mounted CBCT system. Three different prototypes were used in experiments. They all had a grid ratio of 12 and nominal septal thickness of 0.1 mm. Their grid pitch was 0.8, 1.2, and 2 mm, respectively (these prototypes were referred as R12P0.8, R12P1.2, and R12P2). Each 2D-ASG was directly mounted on the FPD’s carbon-fiber faceplate and flood projections were acquired at a pixel size of 0.194×0.194 mm². The model parameters were determined by minimizing the difference between the cumulative primary transmission histograms (PTH) of the simulated 2D-ASG projection image ${PTH}_{Simulation}(a_i,b_i,d_{app})$ and the experimentally acquired 2D-ASG projection image (${PTH}_{Experiment}$):

$$\underset{a_i,b_i,d_{\mathit{app}}}{\arg \min }\frac{\sum \left|{PTH}_{Experiment}-{PTH}_{Simulation}\right|}{n}$$ (2)

where $n$ is the number of pixel value bins in PTH plots. In essence, a PTH corresponds to cumulative histogram of pixel values in a flood projection with 2D-ASG. This optimization approach was used to obtain the PSF parameters for the three different 2D-ASGs that were evaluated in experiments (figure 4(a)). In the next step, optimized PSFs were used in simulations of 2D-ASG projections. Differences among three different optimized PSFs coming from three different 2D-ASGs (figure 4) were considered small in LSF comparisons. Thus, only optimized PSF extracted from R12P1.2 ASG was selected and used in simulation studies of 2D-ASGs with different gird pitches and septal thicknesses presented in the next sections. Our approach of grid shadow simulation assumes that x-ray focal spot is a true point source, and system blurring is spatially invariant. To perform a more realistic simulation, spatially varying system blurring model can be developed by measuring PSF at different regions across the 2D-ASG. In the present work, PSF was modeled based on the measurements at the region of piercing point.

Figure 4.

Evaluation of estimated CBCT system blurring function. (a) LSFs calculated experimentally from a tilted lead plate edge using Fujita’s method and averaged line profiles of a lead plate edge (LSF_LP), and from simulation with optimization over 0.8, 1.2, and 2 mm grid pitches. [FWHM: 285, 275, 235, 255, and 255 μm; respectively]. (b) Optimized PSF derived from R12P1.2 ASG septal shadows. (c) Simulated R12P1.2 projection. (d) Experimental R12P1.2 projection. (e) Line profiles along the red dashed lines in (c) for both simulated and experimental grids.

2.3. Noise Simulation

The compounded Poisson noise model [16] is accurate to describe the detected photon numbers-based-noise. Many reports discussed using Poisson model [17–19] for quantum noise, and thus, the noise in CT transmission data can be modeled as a Poisson-distributed quantum noise plus Gaussian-distributed electronic noise [17, 20, 21]. Simulated noise model is as follows:

$$TotalNoise=Poisson\left({P(I}_o)\right)+Gaussian({\mu }_e,{\sigma }_e)$$ (3)

To generate Poisson noise level similar to that of experimentally observed noise, a CBCT scan of Catphan 504 phantom was acquired at 125 kVp and CTDIvol of 9 mGy, and by using R12P2 2D-ASG. This phantom was selected due to its similarity in size and composition to the simulated phantoms. Images of the simulated low contrast phantom, similar in size and composition to Catphan 504, were reconstructed using the same reconstruction parameters. In the simulations, primary photon fluence was iteratively adjusted, such that standard deviation of HU values in the simulated reconstructions was comparable to the HU standard deviation in the experimental CBCT images, as shown in figure 6. To simulate higher CTDI values (and associated change in noise), photon fluence in simulations was increased such that the noise variance was reduced to match the desired CTDI value.

Figure 6.

Poisson noise validation with the R12P2 grid. (a) Simulated phantom (σ=6 HU). (b) Image acquired in experiments (σ=6.5 HU).

Electronic noise was first estimated experimentally from flood projections, where x-rays were blocked using a lead plate. Mean and standard deviation of the flood projection yielded the electronic noise. The generated Gaussian noise image was added after binning template pixel to nominal pixels size in the detector.

To remove the 2D-ASG shadows in projections, a flat-field correction is essential. To create a flood field projection, i.e., projection without scanned phantom, the same processes described above were applied -except the noise simulation step- to a projection image without phantom, but with 2D-ASG in place. Noise was excluded in these simulations, because flat field calibration data is typically generated by averaging multiple flood projections, where image noise is relatively small. In the next step, a standard flat field calibration [22] was generated from flood field projections of each 2D-ASG geometry under investigation, and respective phantom projections were flat field corrected.

2.4. Gantry Flex Simulation

Due to the weight of the linac-mounted CBCT system, gantry flexes, or sags, while rotating around the imaged object. Hence, focal spot position is displaced with respect to the flat panel detector position, and positions of 2D-ASG shadows are also displaced in projections as illustrated in figure 2. Based on our experience, such septal shadow displacement is smaller than the pixel size, which is challenging to characterize accurately due to undersampling by detector pixels. While gantry-angle specific flat field correction methods [9] help to characterize gantry flex and compensate septal shadows as a function of gantry angle, their performance might be suboptimal in compensating random or unexpected fluctuations in gantry flex. Thus, fluctuations in gantry flex may challenge the suppression of 2D-ASG’s shadows in projections, and may lead to ring artifacts in the reconstructed CBCT images [23].

Figure 2.

(a) Sketch of the 2D-ASG shadow displacement due to the gantry flex. (b) Line profiles of septal shadows at different projections extracted from two CBCT scan sets. The change in locations of minimum profile values indicates septal shadow displacements during CBCT scans.

To develop a model of gantry flex and evaluate its the effect on image quality, the displacement in septal shadow positions and change septal shadow shapes due to gantry flex were first characterized in experimentally acquired CBCT scans. These scans were performed without phantoms and by using R12P2 ASG in TrueBeam CBCT system.

A new approach was developed by our group to characterize the septal shadows, which is referred as oversampled septal shadow profile (OSP). Since pixel size is relatively large (~200 μm) with respect to the septal thickness (~100 μm), septal shadow profiles are undersampled in projections, which makes characterization of septal shadows challenging. OSP method addresses this problem by rearrangement of pixels in septal shadows located in a small region of interest in a projection. Subsequently, the change in OSP properties due to gantry flex was analyzed as a function of source or scan angle in a CBCT scan. As illustrated in figure 3(a), OSP method exploits the mismatch in grid pitch and detector pixel pitch to oversample a septal shadow; each subsequent grid septum projects on to a slightly different location on the detector pixel, because the grid pitch is an integer multiple of pixel pitch, plus a distance difference of $d$. Such a difference leads to a slightly different sampling of each consecutive septal shadow. If these pixel values from consecutive septal shadows are rearranged, an oversampled profile of a septal shadow can be constructed as shown in figure 3(b). This approach allows the measurement of septal shadow width, amplitude, and position by analyzing the OSPs in the same pixel neighborhood in consecutive projections of a CBCT scan as shown in figure 7.

Figure 3.

Diagram of the proposed Oversampled Shadow Profile (OSP) method from series of line profiles to estimate the displacements due to the gantry flex. (a), Since 2D-ASG and detector pixels have different pitches, each subsequent grid wall shadow is positioned at a slightly different location with respect to the pixel array. As a result, each subsequent septal shadow is sampled at different points. (b), if the grid and pixel pitch are known, these different sampling points extracted from subsequent pixel shadows can be rearranged to obtain an OSP. (c), OSPs are generated for all projections in a CBCT scan without phantom. The change in OSP shapes, and shift -or displacement- among OSPs as a function of source angle is quantified.

Figure 7.

Estimated displacements due to gantry flex using the over-sampled septal shadow method. (a) and (b) The displacements of septal shadows with respect to the first projection in each data set in both horizontal and vertical directions; respectively. (c) and (d) The septal shadow width in both horizontal and vertical directions; respectively. (e) and (f) The septal shadow amplitude in both horizontal and vertical directions; respectively.

Since gantry flex is highly repeatable in a linac-based CBCT system, a gantry-angle specific flat field correction can reduce the adverse effects of gantry flex [23]. However, scan-to-scan, or inter-scan, variations in gantry flex may not be suppressed with this approach. To evaluate inter-scan variations experimentally and model them in our simulations, two flood field CBCT scans were performed with R12P2 ASG. The difference in displacement, width, and amplitude of septal shadows between two scans were analyzed. While the septal shadow displacement in a single scan was in the range of 160 μm, the differences in septal shadow displacements between the two scans were in the range of 2 – 10 μm in both horizontal and vertical directions (figure 7(a)–(b)). Septal shadow width and amplitude don’t change much over the CBCT scan (figure 7(c)–(f)). These observations indicate that effects of inter-scan variation in gantry flex can be approximated as linear displacements of septal shadows in vertical and horizontal directions, and septal shadow shapes, i.e., width and amplitude, were assumed to be unaffected by gantry flex. Therefore, to simulate the gantry flex effect, flood projection with 2D-ASG in place was shifted in both horizontal and vertical directions before flat-field correction of phantom projections.

2.5. Experimental Setup

The linac-mounted CBCT system (TrueBeam, Varian Medical Systems, Palo Alto, CA) was utilized to extract and validate simulation model parameters. The FPD has a pixel size of 0.194×0.194 mm² (Paxscan 4030CB, Varian Medical Systems, Palo Alto, CA), and the source to detector distance was 150 cm with a source to axis distance of 100 cm. The acquisition was carried out with XML scripts in the Developer Mode, at 125 kVp and a CTDIvol of 9 mGy for CBCT scans, without the bowtie filter. The 1×1 binning mode was used to extract PSF parameters by using ##, ##, ## prototypes. PSF parameters were extracted from flood projections acquired at a fixed gantry position. Whereas, the 2×2 binning mode (0.388×0.388 mm² pixel size) was used for CBCT scans with the ## ASG. These CBCT scans were utilized for generating model parameters in noise and gantry flex simulations. To examine the inter-scan variations of gantry flex, two flood CBCT scans with ## ASG were acquired consecutively, and inter-scan variations were analyzed.

2.6. Image Reconstruction and Analysis

The final 450 simulated projections incorporating the effects of both 2D-ASG and system characteristics were binned to different pixel sizes (0.194, 0.388, and 1.164 mm) to reflect pixels sizes used in different clinical imaging scenarios, then reconstructed by using the FDK method [13] with Hann filter. Images were reconstructed using 0.14, 0.4, 0.9 mm isotropic voxels, which were referred as high, medium, and low resolution images in the text, respectively. The simulation results have been analyzed qualitatively and quantitatively. The quantitative analysis of noise has been done by measuring the standard deviation (STD) in the reconstructed images background. In addition to simulations, 2D-ASG’s average primary transmission (PT) was theoretically calculated using a simplified model, where each 2D-ASG cell was assumed to be a square hole with a constant septal thickness. In addition, a point x-ray source was assumed to be sufficiently far from the 2D-ASG, such that primary x-rays are considered parallel to septa. The relationship between image noise and PT was also calculated theoretically [24], where it was assumed that the detector is an ideal photon counter and image noise is driven by Poisson statistics of counted x-rays.

$$PT=\frac{{\left(GridPitch-SeptalThickness\right)}^2}{{\left(GridPitch\right)}^2}\times 100\mathrm{\%}$$ (4)

$$Noise\propto \frac{1}{\sqrt{PT}}$$ (5)

where Eq. 4 represents the percentage of open section of square hole with a given grid pitch and septal thickness. The CNR and CNR loss due to the 2D-ASGs were calculated as follows:

$$CNR=\frac{\left|{\mu }_{Object}-{\mu }_{Background}\right|}{({\sigma }_{Object}+{\sigma }_{Background})/2}$$ (6)

$$CNRLoss=\frac{{CNR}_{WithoutGrid}-{CNR}_{WithGrid}}{{CNR}_{WithoutGrid}}\times 100\mathrm{\%}$$ (7)

3. RESULTS

3.1. Estimation and Validation of Simulation Parameters

An example of simulated 2D-ASG shadows in a projection is shown in figure 4. In addition, optimized PSFs extracted from 2D-ASG shadows were compared to measured line spread functions (LSFs) by using a lead plate edge placed on the detector, an established method for LSF measurements. Optimized PSFs extracted from septal shadows were converted to LSFs, and subsequently, they were compared to the measured oversampled LSF obtained using Fujita’s technique [14]. While the oversampled LSF was obtained using Fujita’s technique [14], the LSF_LP was generated from averaged line profiles from the image of a lead plate edge. While optimized LSFs agreed with the measured LSFs in general, optimized LSFs were narrower in width than the measured LSF. Also, simulated and experimental projections of the 2D-ASG with grid ratio of 12 and grid pitch of 1.2 mm (R12P1.2) are shown in figure 4(c)–(d), respectively, and corresponding line profiles are shown in figure 4(e). These comparisons qualitatively indicate that simulated and measured primary signal distributions agreed with each other. Figure 4(b) shows the estimated 3D PSF that was used for the simulations in this paper. The optimization parameters of this PSF were estimated as follows: $a_1=-0.1005$, $a_2=-0.0063$, $a_3=1.2738$, $b_1=12.6970$, $b_2=12.1627$, $b_3=15.2446$. $d_{app}$ for R12P0.8, R12P1.2, and R12P2 were 0.1563 mm, 0.1908 mm, and 0.1934 mm, respectively. These $d_{app}$ values agreed well with the analytical calculations of $d_{app}$ based on the primary transmission in the experimental data. $d_{app}$ was 0.06 – 0.09 mm thicker than the nominal septal thickness of 0.1 mm.

PTH plots acquired experimentally and calculated via simulations with optimized PSFs are shown in figure 5. PTH evaluations show that the PTH of each simulated 2D-ASG is well-matched with the PTH of the experimental measurements. Figure 6 shows that the standard deviation of HU values in simulated reconstructions is comparable to the HU standard deviation in experimental CBCT images after the iterative adjustment of the primary photon fluence.

Figure 5.

Experimental and simulated cumulative primary transmission histograms (PTH) for R12P0.8, R12P1.2, and R12P2 grids are shown in (a), (b), and (c), respectively. In simulations, three different PSFs were utilized for system blurring, which were estimated from projection images of respective 2D-ASGs. The PSF extracted from R12P1.2 ASG was also used in PTH simulations of R12P0.8 and R12P2 ASGs, which agreed well with measured PTHs.

Figure 7 shows the proposed oversampled septal shadow profile approach that allows the measurement of septal shadow width, amplitude, and position by analyzing the OSPs in the same pixel neighborhood in consecutive projections of a CBCT scan. Figure 7(a) shows that the septal shadow displacement in a single scan is in the range of 160 μm, while figure 7(b) shows that the differences in septal shadow displacements between the two scans is in the range of 2 – 10 μm in both directions. Figure 7(c)–(f) shows that the septal shadow width and amplitude don’t change much over the CBCT scan.

Figure 8(a)–(b) shows that primary transmission measured from simulated images and theoretical calculations agreed well, which validates the primary signal transmission step in simulations. For an apparent septal thickness of 0.15 mm, primary transmission is in the range of 72 – 90% for grid pitches between 1 and 3 mm. The evaluated primary transmissions of R12P0.8 are 64.17%, 64.60%, and 64.18% for theoretical, simulated, and real experimental data, respectively, at an apparent thickness of 0.156 mm, which validates the accuracy of the 2D-ASGs’ simulations. For R12P1.2, the primary transmissions are 70.76%, 70.72, and 70.78% for theoretical, simulated, and real experimental data, respectively, at an apparent thickness of 0.191 mm. For R12P2, the primary transmissions are 81.74%, 81.61%, and 81.60% for theoretical, simulated, and real experimental data, respectively, at an apparent thickness of 0.193 mm.

Figure 8.

Primary transmission measurements in simulated projections and theoretical calculations using Eq. 4 (c) are shown in (a) and (b), respectively. Noise measurements in reconstructed images and theoretical calculations of noise based on 2D-ASG primary transmission are shown in (c) and(d), respectively. Noise values were normalized with respect to grid pitch of 3 mm and septal thickness of 0.05 mm.

Noise variations in reconstructed images agreed well with the theoretically calculated noise variations in projections due to 2D-ASG’s primary transmission properties (figure 8(c)–(d)). Noise values were normalized with respect to grid pitch of 3 mm and septal thickness of 0.05 mm. For apparent septal thickness of 0.15 mm, the noise increases by a factor of 1.15 – 1.03 for the grid pitch range of 1 – 3 mm. In addition, this noise validation indicates that spatially nonuniform noise due to septal shadows in projections did not introduce additional noise penalty in reconstructed images of the low contrast phantom.

3.2. Simulation Analysis

The effect of 2D-ASG’s grid pitch and septal thickness on low contrast visualization was demonstrated in figure 9. CNR loss in 2D-ASG images with respect to images without 2D-ASG were also calculated (figure 10). For an apparent septal thickness of 0.15 mm, and a grid pitch of 1 – 3 mm, CNR loss remains less than 20%, due to relatively high primary transmission for such 2D-ASG geometries. The impact of septal thickness on CNR loss is more pronounced at lower grid pitches. For example, at a grid pitch of 2 mm, apparent septal thickness of 0.25 mm still yields less than 20% CNR loss. Whereas at a grid pitch of 0.5 mm, apparent septal thickness should be kept less than 0.1 mm to keep CNR loss less than 20%. Also, going from wall thickness of 0.2 to 0.25 mm at a grid pitch of 0.3 mm, reduces the primary transmission by a factor of 4, and therefore, the image appears substantially noisier.

Figure 9.

Low contrast phantom images demonstrate the effect of 2D-ASG grid pitch and septal thickness on low contrast visualization.

Figure 10.

A quantitative evaluation of the reconstructed simulations of the Catphan low contrast phantom (in figure 9) shows the amount of CNR loss at the 3% contrast object due to the 2D-ASGs w.r.t. the simulation without grid.

The effect of 2D-ASG’s pitch and septal thickness had minimal impact on the spatial resolution, as evaluated in high-resolution images of the bar pattern phantom (figure 11). For example, for a grid pitch 3 mm and septal thickness of 0.25 mm, 10 lp/cm bar pattern can be resolved. Likewise, for a grid pitch of 1 mm and septal thickness of 0.25 mm, 10 lp/cm is resolved.

Figure 11.

Bar pattern phantom images as a function of 2D-ASG grid pitch and septal thickness. Detector pixel size is 194 μm, and voxel size is 140 μm.

While spatial resolution -as estimated from high contrast bar pattern images- was minimally affected by primary transmission variations, an inspection of the background sections of this phantom indicated an increase in low contrast streak artifacts. To better evaluate such streak artifacts, a subset of simulations was repeated at CTDI of 9 cGy to reduce noise and without quantum noise (figure 12). Specifically, images without noise show that the streak artifacts are more pronounced when septal thickness was increased (yellow arrow). These streak artifacts are undersampling artifacts, which were attributed to information loss caused by radiopaque footprint of 2D-ASG. The visual appearance of undersampling artifacts depends on the level of quantum noise in images; even though undersampling artifacts are clearly visible in noise-free images, artifacts are masked by noise in images at CTDI of 0.9 cGy. Hence, relative contribution of undersampling artifacts to overall image quality degradation in CBCT images depends on the imaging dose. This effect was quantitatively evaluated by calculating root mean square error (RMSE) metric (figure 13(a)). For an apparent septal thickness of 0.15 mm and 2 mm grid pitch, RMSE values in noise-free images are in the range of 2 – 31 HU due undersampling artifacts. For 2D-ASGs with thicker septa, information loss and RMSE increases further. On the other hand, RMSE is substantially less in low spatial resolution images, indicating that information loss due to 2D-ASG is less important. Because high spatial frequency information loss is driven by low pass filtering effect of larger voxels. At CTDI of 0.9 cGy with septal thickness of 0.15 mm and 2 mm grid pitch, RMSE in high resolution images goes up to 131 HU due to quantum noise, an increase of 100 HU when compared to noise-free images. Relative increase in RMSE is in the range of roughly 100 – 1000%, indicating that quantum noise is a more dominant factor than information loss in overall image quality degradation at clinically relevant imaging doses (figure 13(b)).

Figure 12.

Bar pattern phantom images in high resolution mode with 2 mm grid pitch at different septal thicknesses and noise levels. The 1st, 2nd, and 3rd rows are the simulations with Poisson noise and without noise, respectively. The 1st, 2nd, and 3rd columns are the simulations with septal thicknesses of 0.05, 0.15, and 0.25 mm, respectively. When Poisson noise is absent, undersampling artifacts (yellow arrow) are more emphasized for thicker septa.

Figure 13.

A quantitative evaluation of the reconstructed simulations of the bar pattern phantom (in figure 12) shows the relatively small effect of the 2D-ASG’s information loss compared to Poisson noise at 2mm grid pitch and septal thicknesses of 0.05, 0.1, 0.15, 0.2, and 0.25 mm at low, medium, and high resolutions. (a) RMSEs due to Poisson noise and 2D-ASG information loss w.r.t. the reconstructed images without grid and noise simulations. The error corresponding to images without noise represents 2D-ASG information loss effect. (b) Percentages of RMSEs increase due to Poisson noise w.r.t. 2D-ASG information loss.

In figure 14, electronic noise was included in simulations, in addition to the quantum noise. At a fixed grid pitch of 1 mm, electronic noise induced artifacts increase significantly as septal thickness increase, indicating the importance of having higher primary transmission in electronic noise suppression. At a grid pitch of 1mm, electronic noise increased image noise by 36% on the average when compared to “no grid” CBCT imaging scenario (figure 15).

Figure 14.

Simulation of electronic noise with a high attenuation material inserts phantom and 1 mm grid pitch to demonstrate the grid properties with electronic noise.

Figure 15.

Percent increase in image noise in reconstructed images due to addition of electronic noise as a function of grid pitch and septal thickness.

The uncertainty in septal shadow displacements due to gantry flex was simulated by introducing 5 and 10 μm displacements in septal shadow positions in two simulated CBCT scans, which was based on the measured grid displacement uncertainty in CBCT scans in figure 7. For simplicity, the magnitude of simulated displacement was the same in both vertical and horizontal directions of projections. Such septal shadows displacements introduced small but noticeable ring artifacts (figure 16). Image noise due to ring artifacts increased as a function of grid pitch, septal thickness, and image spatial resolution (figure 17). In figure 16, the dashed yellow box shows the central ROI where multiple slices were averaged in the axial direction to better visualize ring artifacts. Corresponding standard deviation is also displayed. The effect of gantry flex on image artifacts was negligible in low resolution images, but artifacts are more emphasized in high resolution images.

Figure 16.

Gantry flex effect using the simulation model with a grid pitch of 2 mm and septal thickness of 0.15 mm at different sizes of detector pixels and reconstruction voxels. (Top: pixel size of 0.194 mm and voxel size of 0.140 mm. Middle: pixel size of 0.388 mm and voxel size of 0.4 mm. Bottom: pixel size of 1.164 mm and voxel size of 0.9 mm). The dashed yellow box shows the ROI of averaged slices and the corresponding standard deviation.

Figure 17.

A quantitative evaluation shows the gantry flex effect on the single reconstructed slices (in figure 16) as a function of grid pitch and septal thickness. (a) STD at septal thickness of 0.15 mm. (b) STD at grid pitch of 2 mm.

4. DISCUSSIONS

While utilization of conventional 1D-ASGs in CBCT imaging has been studied extensively [1–8], development and optimization of 2D-ASGs require a different strategy than conventional ASGs due to larger grid pitch and relatively thicker septa of the proposed 2D-ASGs. Even though 2D-ASGs enable close to 100% primary transmission in grid apertures, primary signal gradients -that is septal shadows- introduced by 2D-ASG’s footprint should be correctly accounted to further improve image quality. Thus, this work evaluated the effect of 2D-ASG’s primary transmission properties on the image quality of CBCT images.

One of the key steps in 2D-ASG simulations is the estimation of system blurring function to achieve realistic signal gradients in septal shadows. System blurring function measured with the conventional radiopaque Edge method [14] did not precisely emulate blurring observed in septal shadows. Our new method of measuring system blurring directly from 2D-ASG shadows provided better agreement between simulated and measured septal shadows. While exact reasons behind this discrepancy remain to be investigated, we speculate that conventional MTF measurement setup plays a role; in conventional methods, MTF or PSF was measured by placing a radiopaque plate on the detector, which alters detector backscatter or glare conditions. Whereas, in our method, system blurring was obtained directly from the septal shadows in experimentally acquired projections, without placing a lead plate on the detector.

Our method has several practical advantages over conventional radiopaque Edge method. First, with our method, system blurring can be measured at any location where grid is present, and spatial variations in system blurring can be quantified. With the Edge method, MTF measurements need to be repeated at different regions on the detector, by placing the edge tool to different regions. Second, our method uses the 2D-ASG itself that is already installed on the detector as PSF/MTF measurement device, and it does not require additional tools. Third, system blurring measurements can be easily repeated when imaging conditions (such as beam energy) change, by simply acquiring flood projections. Thus, it eliminates the need for additional measurements with the edge tool.

System blurring function in our method was calculated iteratively by minimizing the differences between the PTHs of simulated and measured projections. Alternatively, one may potentially calculate system blurring function by minimizing pixel-by-pixel differences between simulated and measured projections. However, this approach requires precise spatial match of grid shadows in simulated and measured data. When PTH differences are minimized (rather than pixelwise differences), this problem is mitigated. Because pixel value distributions -that is PTH- over several hundred (or thousands) pixels are affected by the system’s spatial resolution characteristics and physical properties of the grid, regardless of the spatial alignment of simulated and measured projections.

Our results showed that average primary transmission fractions of 2D-ASGs can exceed 80% at an apparent septal thickness range of 0.15 – 0.2 mm. Hence, the degradation of CNR due to reduced primary fluence incident on the detector is relatively small. While 2D-ASG’s primary transmission can be kept high, one may question how 2D-ASG’s relatively thicker septa affect image quality. Depending on the pixel size, pixels underneath 2D-ASG’s septa would be partially exposed to primary x-rays, which may cause information loss. Under the imaging conditions investigated, a noticeable effect of information loss on the appearance of phantom structures was not observed in low contrast phantoms. Increase in septal thickness and number of septa per unit area (i.e., grid pitch) caused an increase in image noise which correlated well with primary transmission fraction and associated Poisson statistics.

However, when high contrast objects were imaged at high spatial resolution, streaks, or undersampling, artifacts were observed. Such undersampling artifacts were relatively subtle, and they were mostly observed in noise-free image simulations. When quantum noise was present, undersampling artifacts were screened by noise, depending on the level of imaging dose. Moreover, undersampling artifacts were significantly less in medium to low resolution images, implying lower spatial resolution CBCT images are affected less from data loss caused by 2D-ASG’s radio-opaque footprint. In summary, data loss manifests itself as high spatial frequency undersampling artifacts, and its overall impact on image quality strongly depends on the level of quantum noise and spatial resolution of CBCT images.

The other area of investigation was the electronic noise; when compared to grid holes, primary signal is reduced in septal shadows, that makes septal shadow regions more prone to detrimental effects of electronic noise. In imaging scenarios that we evaluated, the increase in total image noise due to electronic noise was proportional to increase in septal thickness and number of septa in unit area.

Apparent septal thickness measured in experimentally acquired projections was about 50% or more higher than the nominal thickness of 0.1 mm, implying that grid’s shadows are wider than expected. While exact reasons for wider than expected grid shadows are not known, they can be potentially due to suboptimal grid-source alignment during experiments, absorption of off-focal radiation by grid septa, and physical differences between fabricated and modeled 2D-ASG.

Our new method successfully characterized the change in shape and position of septal shadows due to gantry flex in CBCT scans. We observed that gantry flex primarily caused displacement of septal shadows in detector plane, whereas change in septal shadow widths and amplitudes were minimal. Effects of gantry flex were highly repeatable; even though septal shadow displacements reach 160 μm in a CBCT scan, the difference in septal shadow positions between two subsequent CBCT scans was less than 10 μm. Yet, such small scan-to-scan variations in septal shadow positions caused small but noticeable ring artifacts in high resolution images and may reduce CNR. Gantry-angle specific gain or flat field correction cannot fully account for scan-to-scan variations in gantry flex. In principle, ring artifact correction algorithms [22, 25] can be utilized to address this issue. Long-term variations in septal shadow positions and gantry flex properties remains an area to be investigated. The time interval was about 5 minutes for inter-scan. To study inter-scan gantry flex variations, numerous scans over days or weeks need to be performed, as the gantry flex variations also depend on the number of scans, as well as the number of times of the extension and retraction of the CBCT robotic arms. Inter-scan gantry flex variations likely to increase over time.

While grid septa and pixel arrays are aligned in conventional CT scanners, grid septa are not aligned with the detector pixel array in our work that is aimed for FPD based CBCT imaging. There are several reasons behind our approach: First, keeping grid pitch independent from pixel pitch provides grid design and implementation freedom. For example, a hexagon shaped grid structure can be used with rectilinear pixel array. Second, current FPDs do not use pixelated scintillators, and thus, alignment of grid septa with inter-pixel space as in conventional CT scintillators is not applicable to current FPDs. Thirds, even if grid and pixel arrays can be perfectly aligned in simulations, grid-pixel alignment is compromised due to gantry flex during CBCT scans. As seen in our evaluations of gantry flex, grid shadow positions change as much as 160 microns during gantry rotation due to change in focal spot position in relation to the detector. Thus, if a grid shadow is perfectly aligned with a pixel column at one gantry angle, grid shadow will be shifted as much as 160 microns with respected to the pixel column at another gantry angle, degrading pixel-grid alignment.

Our simulations did not include effects of scatter, because our primary goal was to investigate the effects of primary x-rays and associated image signals on CBCT image quality. Effect of reduced dose efficiency due to reduction of primary fluence by 2D-ASGs was not evaluated either. In the future, other physics models (such as scatter estimations, energy dependent detector response and polyenergetic beams) can be included into simulations to study the impact of 2D antiscatter grids on overall CBCT image quality.

CONCOLUSION

While 2D-ASGs can substantially reduce scatter-induced image quality degradation in CBCT, their primary transmission properties may need to be carefully optimized to allay other image quality problems, such as increased image noise and image artifacts. Our primary transmission simulation methods introduced in this work can help to optimize the 2D-ASG hardware and CBCT system properties to minimize such problems. Our results indicate that primary transmission up to 90% can be achieved by optimizing grid pitch and septal thickness, and therefore increase in image noise due to 2D-ASG can be minimized. For imaging conditions and grid geometries investigated, information loss due to 2D-ASG’s radiopaque footprint has minor impact on image quality when compared to quantum noise. Effects of electronic noise and gantry flex must be also considered when using a 2D-ASG in a CBCT system. While we developed these methods to better understand the impact of 2D-ASGs on CBCT image quality, our simulations can be used for generating synthetic 2D-ASG image data, which can be useful in developing data correction strategies needed for implementation of 2D-ASGs in CBCT systems.