Which of the following grids would have a higher grid factor and therefore a high mas?

Phys Med Biol. Author manuscript; available in PMC 2020 Nov 15.

Published in final edited form as:

PMCID: PMC6937210

NIHMSID: NIHMS1064351

Abstract

To suppress scatter in cone beam computed tomography (CBCT), two-dimensional antiscatter grids (2D grid) have been recently proposed. In this work, we developed several grid prototypes with higher grid ratios and smaller grid pitches than previous designs, and quantified their primary and scatter transmission properties in the context of CBCT for radiation therapy.

Three focused 2D grid prototypes were developed with grid ratios at 12 and 16, and grid pitches at 2 and 3 mm. Their scatter transmission properties were measured between 80–140 kVp, and benchmarked against a high performance radiographic grid (1D grid) using a Varian TrueBeam CBCT system. The effect of source-grid misalignment on the primary transmission and the improvement in contrast-to-noise ratio (CNR) were also evaluated.

Changing the grid pitch from two to three mm increased the average primary transmission from 84% to 89%. Maximum scatter-to-primary ratio (SPR) with grid ratio of 12 was 0.3, and increasing the grid ratio to 16 reduced SPR by 30%. A 10 mm misalignment in 2D grid position led to a 6–8% reduction in average primary transmission, and reduction was more pronounced for the higher grid ratio. 2D grids provided up to factor of seven lower SPR and 21% better primary transmission than the 1D grid, and their scatter transmission exhibited lower energy dependence. While 2D grids provided up to factor of 2.3 higher CNR improvement, a significant variation in CNR improvement was not observed among different grid pitch and ratios.

In summary, grid ratio of 16 and grid pitch of 2 mm can keep SPRs below 0.2 even in high scatter conditions, while keeping primary transmission fractions above 80%, key benefits of the investigated 2D grids in improving image quality of CBCT. However, such grids require precise alignment in source-grid geometry during CBCT acquisitions. This study also implies that 2D grids can provide substantially better scatter suppression and primary transmission than high-performance 1D grids currently available.

1. Introduction

Scattered radiation is one of the fundamental causes of image quality degradation in CBCT. To reduce scatter intensity, conventional antiscatter grids (1D grids) inherited from radiography and fluoroscopy have been extensively investigated in the context of CBCT(Wiegert et al., 2004; Sisniega et al., 2013; Siewerdsen et al., 2004; Lazos and Williamson, 2010). Although 1D grids improve CT number accuracy, the improvement is often not sufficient, requiring additional scatter correction methods to be employed in conjunction with 1D grids. An improvement in low-contrast object visualization was observed only in moderate to high scatter intensity environments. In low-scatter intensity environments, such as imaging of head or breast CT, soft tissue visualization may even be degraded due to the noise penalty introduced by relatively low primary x-ray transmission of 1D grids.

To address the shortcomings of 1D grids, 2D grids for CBCT were recently introduced. In these studies, 2D grids exhibited superior scatter suppression and primary transmission performance over 1D grids(Altunbas et al., 2017) and substantially improved CT number accuracy and CNR(Alexeev et al., 2018). Moreover, it was suggested that septal shadows of 2D grids can be suppressed to minimize associated artifacts in CBCT images (Alexeev et al., 2019). While these studies have shown the potential benefits of a 2D grid approach, they employed a relatively low grid ratio, a key parameter in determining the scatter suppression efficiency, and the effect of grid pitch on the transmission properties were not explored.

Hence, in the present study, the effects of higher grid ratio and grid pitch on the x-ray transmission properties were evaluated. Furthermore, the dependence of scatter transmission on x-ray energy and the effect of grid misalignment (with respect to the x-ray source) on the primary transmission were studied. Another aim of our study is to benchmark the performance of 2D grid prototypes with respect to new-generation radiographic antiscatter grids with high grid ratios (Fetterly and Schueler, 2009; Stankovic et al., 2017).

2. Materials and Methods

2.1. Antiscatter grid properties and experiment setup

The rationale for fabricating different prototypes was to investigate the effect of a single grid geometry parameter, e.g. grid pitch, on the transmission properties, while keeping other geometry parameters, e.g. grid ratio, constant. To reduce fabrication costs, three grid prototypes were developed that were deemed feasible to fabricate (Table 1). In the first two prototypes, grid pitch was varied between 2 and 2.91 mm grid pitch is distance between the centers of two adjacent through-holes, measured at the bottom surface of the grid, i.e. the surface facing the detector), while keeping the grid ratio at 12. Base on the literature on radiographic grids (Fetterly and Schueler, 2007; Chan and Doi, 1982), similar scatter rejection performance was expected from these two prototypes (due to their identical grid ratios and septal thicknesses). On the other hand, these prototypes had different grid pitches, which was expected to affect primary transmission performance. In the third prototype, grid ratio was increased to 16, while keeping the grid pitch at 2 mm. Grid pitches below 2 mm were not investigated to preserve high primary transmission. Grid ratios above 16 and grid pitches more than 3 mm were not considered either, since such grids would increase the grid height, and make grid-source alignment more challenging in CBCT systems for radiation therapy.

Table 1.

Evaluated 1D and 2D Grid Configurations

As indicated in Table 1, the suffixes in the grid names indicate the grid pitch and the ratio of each prototype: 1) 2DGrid_R12P2 has a grid ratio of 12.3 and grid pitch of 2 mm; 2) 2DGrid_R12P3 has a grid ratio of 12.5 and grid pitch of 2.91 mm; and 3) 2DGrid_R16P2 has a grid ratio of 15.8 and grid pitch of 2 mm. All prototypes were fabricated from pure tungsten and have septal thickness of 0.1 mm (Fig. 1(a)). Each prototype was composed of two subunits of size 3 cm × 20 cm that were merged together on an aluminum frame to achieve 3 cm ×x 40 cm total area. All grid septa in both fan and cone directions were aligned, or focused, toward the x-ray source in half-fan geometry of the TrueBeam CBCT system (Varian Medical Systems, Palo Alto, CA). 2D grids were additively manufactured by Philips (Best, Netherlands) using the Direct Metal Laser Sintering (DMLS) process, where tungsten powder was fused layer-by-layer using a laser beam. To benchmark the performance of the 2D grids, a high-performance, commercial 1D grid was employed (Smit Rontgen, Netherlands), which has a grid ratio of 21 and fiber spacers between its lead septa(Fetterly and Schueler, 2009).

(a) Photo of the 2DGrid R16P2 prototype. (b) Assembled grid was integrated with the support frame and the support frame was mounted on the FPD in the TrueBeam CBCT system. (c) CAD rendering of the 2D grid, where outer walls are removed, and septa are visible. Due to focusing of septa towards the x-ray source, each septum has a slightly different slant. Distal grid septa (further from the piercing point, magnified section shown in red rectangle) have larger slant than the proximal grid septa (closer to the piercing point, magnified section shown in green).

Antiscatter grids were mounted on a Paxscan 4030CB detector in the TrueBeam CBCT system by using an aluminum support plate (Fig. 1(b)). Because the active area of the 2D grids was smaller than the area of the FPD (3 × 40 cm2 vs. 30 × 40 cm2), the FPD regions not covered by the grid were shielded using 1.5 mm thick lead. Likewise, the active area of the 1D grid was also reduced to 3 × 40 cm2 by covering the remaining active area of the grid with 1.5 mm thick lead sheets. While the active area on the FPD was small, the x-ray cone incident on the FPD still covered the full active area of the FPD (30 × 40 cm2) to achieve identical object scatter conditions in the clinical CBCT system.

Phantom irradiation geometry and detector-source position emulated Varian’s half-fan geometry (Fig. 2), where center of the flat panel detector (FPD) was offset by 16 cm to increase the field of view. Source to detector and source to isocenter distances were 150 and 100 cm, respectively. X-ray field of view was 30 × 40 cm2 in detector plane, and 20 × 26 cm2 at isocenter plane.

(a) Side view (transverse plane) of the experiment setup. X-ray fan angle was indicated with red dashed lines. (b), Beam-eye-view of the x-ray detector and grid geometry. The grid covers the central 3 × 40 cm2 section of the detector. Piercing point (projected location of x-ray source) is 16 cm offset from the center of the detector. X-ray field covers the full area of the detector (30 × 40 cm2), such that scatter conditions in TrueBeam’s half-fan CBCT geometry is mimicked.

Due to mechanical tolerances, initial grid alignment with respect to x-ray source was not ideal, which affects primary transmission. To achieve optimal grid-source alignment, the grids were translated in two orthogonal directions within the detector plane and flood projections were acquired. The optimal grid position was selected based on the position that provided the highest primary transmission. This process was repeated for all 2D and 1D grids before the measurements described in the following sections.

The CBCT system was operated in TrueBeam’s Developer mode, where x-ray exposure and image acquisition were controlled via XML scripts. FPD (Paxscan 4030CB, Varex, UT) was operated in dynamic gain mode(Roos et al., 2004) and the pixel size was 0.388 mm. Projections were acquired with a 0.9 mm thick Ti beam filter. Bow tie filter was not employed, since the goal of our study was to quantify the effects of 2D grid parameters on primary and scatter transmission properties, which might be biased by the bow tie filter (Altunbas et al., 2017).

2.2. Measurement of primary transmission and its dependence on grid alignment

For primary transmission measurements, 100 flood projections were acquired at 125 kVp with and without the grid in place. For any given grid configuration, all flood projections were averaged and then the pixel values were averaged in a 2 × 3 cm2 region of interest (ROI) and centered 10 cm away from the piercing point (i.e., the projected location of the isocenter on the image plane). The average primary transmission Tp was calculated as

TP=P(with grid)P(without grid),

(1)

where P is the average image signal in the ROI with and without the antiscatter grid in place.

Focusing geometry may not be ideal at each location within a grid, which may result in spatial varying degradation of TP. To assess the TP variation within a grid, TP was calculated across the long axis of each grid by shifting the ROI with 0.5 cm increments. Subsequently, standard deviation of Tp was calculated, as a metric to evaluate Tp uniformity.

Due to the relatively large grid pitch of 2D grids with respect to detector pixel pitch, primary fluence incident on each pixel varies from pixel to pixel. Pixels located in the 2D grid’s septal shadows receive lower primary fluence, whereas pixels toward the center of grid’s through-holes receive close to 100% of the primary fluence incident on the grid structure. To quantify the pixel-to-pixel variation in primary transmission, pixel-specific primary transmission (PPT) was calculated for each pixel within the ROI and was presented in cumulative primary transmission histograms.

The effect of grid misalignment on primary transmission:

When grid septa are not perfectly aligned toward the x-ray source, their projected shadows on the detector plane become larger and primary transmission is degraded. There are several sources of suboptimal grid alignment, such as positioning errors during installation of the grid and deviations in detector-source geometry due to gantry flex during CBCT acquisition.

To quantify the effects of suboptimal grid alignment on primary transmission, grids were offset by 5 and 10 mm with respect to their optimal position, and primary transmission was remeasured at each offset position. Offsets were applied in the transverse direction (in the source-detector rotation plane) and in the Z-direction (along the axis of rotation) in a sequential fashion. For 2D grids, the direction of offset (i.e., transverse versus Z-direction) had 2% or less effect on the primary transmission fraction. Therefore, for a given offset magnitude, primary transmission values in transverse and Z-directions were averaged, and are presented in Section 3. On the other hand, the 1D grid’s septa were parallel to the transverse directions and offsets in the transverse direction did not affect its primary transmission. Hence, for the 1D grid, primary transmission variations for offsets in the Z-direction are presented in Section 3.

2.3. Measurement of scatter transmission and its dependence on energy

Experiment set up was illustrated in Fig. 2. Scatter intensity was measured using a tungsten carbide disc with dimensions 3 mm in thickness and 4 mm in diameter. The beam-stop was mounted on a thin acrylic tray and placed between the x-ray source and the phantom, while its distance to the detector plane was kept at 70 cm. Hence, the projected beam-stop shadow remained at the same size in all experiments, and the shadow of beam-stop in projections was 10 cm away from the piercing point at detector plane. To generate scatter, 30 × 30 cm2 acrylic cuboid slabs were employed as phantoms, and the total thickness of the slabs was varied to be between 10 and 40 cm. An air gap between the front surface of the detector and the treatment couch was kept at 18 cm throughout all experiments. X-ray source was at 12 o’clock position and the FPD at 6 o’clock position. Acrylic slabs were placed on the carbon fiber treatment couch during experiments; therefore, the resultant x-ray attenuation and scatter were due to both acrylic slabs and the treatment couch.

In each scatter measurement experiment, 100 projections were acquired and averaged. The scatter signal intensity S was obtained by averaging the image signal in the ROI placed in the beam-stop shadow. Scatter transmission fraction Ts was calculated using the following:

TS= S(with grid)S(without grid)×100,

(2)

where S is the scatter intensity measured with and without the grid. In addition to scatter transmission, scatter-to-primary ratio (SPR) was also calculated:

SPR=S(with grid)P(without grid)

(3)

P was measured by acquiring an additional projection set without the beam-stopper. The mean ROI value without the beam-stopper yields the total signal (P + S). P was calculated by subtracting the scatter signal from the total signal. ROI location for primary measurements coincided with the ROI location for scatter measurements.

To quantify the effect of x-ray energy on scatter transmission Ts and SPR, measurements were performed at 80, 125, and 140 kVp. At 80 kVp, Ts and SPR measurements were reported for up to 30 cm thick phantom as the scatter signal intensity was not sufficient for accurate measurement of Ts and SPR even at the maximum x-ray tube mAs.

2.4. Evaluation of contrast-to-noise ratio improvement

Reduced scatter and primary transmission due to antiscatter grids have competing effects on the contrast-to-noise ratio (CNR). While reduced scatter transmission increases CNR, poorer primary transmission increases image noise and reduces CNR(Neitzel, 1992). To assess the cumulative effect of both primary and scatter transmission, CNR improvement provided by each grid was measured using a contrast phantom.

The contrast phantom was a 2.5 cm thick, 30 × 30 cm2 cuboid acrylic slab, where six circular holes were drilled with varying depths, which served as contrast objects. Holes were 6 mm in diameter and their depth varied from 2.5 to 10 mm, with 2.5 mm increments. The contrast phantom was combined with uniform, 30 × 30 cm2 acrylic slabs to achieve total phantom thickness of 20 and 40 cm. At each phantom thickness, 50 projections were acquired at 125 kVp with and without the contrast phantom. The x-ray tube technique was 0.4 and 4 mAs per frame for 20 and 40 cm thick phantoms, respectively. Projections without the phantom were used to create gain maps and subsequently used for pixel gain correction(Altunbas et al., 2014) of the contrast phantom projections. After application of the gain maps, CNR was calculated using the following:

CN R=I(contrast)−I(background)(σcontrast+σbackground)/ 2,

(4)

where I and σ are the mean signal intensity and the standard deviation within the ROI placed in contrast object and the background, respectively. The signal intensity in the contrast object was measured by placing a circular ROI (it was placed in the third contrast object from the left in Fig. 9), whereas the background signal was measured using a ring-shaped ROI surrounding the contrast object. Mean and standard deviation of CNRs were obtained from CNRs measured in 50 projection frames. Subsequently, CNR improvement factor (Kcnr) was calculated as the ratio of mean CNRs measured with and without the grid. The standard deviation of Kcnr was calculated from standard deviations of CNRs by employing error propagation methods(Knoll, 2010).

Projection images of a low contrast phantom for all grid configurations. Images in each column have the same display window width. Images in the top row were provided as reference only, to display the contrast objects clearly.

To ensure that CNR measurements were not affected by the FPD’s stochastic electronic noise(Maolinbay et al., 2000), detector entrance exposures were kept sufficiently high to minimize the contribution of electronic noise on total image noise. For the Paxscan 4030CB FPD used in this study, the effect of electronic noise on total image noise was reported to be minimal down to 5 μ/frame detector entrance exposure (Roos et al., 2004). Thus, targeted detector entrance exposures were at or above this value during the CNR measurement experiments.

The grid entrance exposures were the same for all grid configurations at any given phantom thickness, whereas the detector entrance exposures were different for each grid due to their different scatter and primary transmission properties.As the exposure meter could only be placed on the top surface of grids (instead of between the grid and the FPD), the detector entrance exposures were estimated by taking into account the primary and scatter transmission properties of the grids(Neitzel, 1992):

Expdet=ExpgridTP1+ SPRgrid1+SPRno grid,

(5)

where Expdet and Expgrid are detector and grid entrance exposures, respectively. Grid entrance exposures were measured by placing an exposure meter at the entrance surface of the grids (RaySafe X2, Glenwood, IL).

3. Results

3.1. Primary transmission properties

When 2D grids were at their optimally aligned position, their average primary transmission, Tp, was in the range of 84–89% (Table 2). R12P3 grid provided the highest primary transmission and R16P2 provided the lowest primary transmission. 1DGrid R21 provided 69.9% average primary transmission, which is in agreement with the literature(Fetterly and Schueler, 2009). Standard deviation of primary transmission across the length of 2D grid modules was 0.5%, or less, indicating that grid focusing geometry did not deviate from one grid location to another, and uniform Tp was maintained along the length of the grid module.

Table 2.

Average Primary Transmission as a Function of Grid Offset

When grids were offset from their optimal position, the average primary transmission was reduced as expected (Table 2). For 2D grids, 5 and 10 mm offsets reduced Tp by 2.2–3.6% and 5.6–8.2%, respectively. For 1DGrid R21, 5 and 10 mm offsets in Z-direction led to a 5% and 10.7% reduction in Tp, respectively. Offsets in transverse direction did not affect the primary transmission of the 1D grid as this direction was parallel to its grid septa. The grid ratio was the main factor that influenced the primary transmission degradation due to grid offset. As a result, 1DGrid R21 and 2DGrid R16P2 exhibited the largest primary transmission degradation due to grid offset. Grid height was the secondary factor that influenced primary transmission degradation due to grid offset; although both R12P2 and R12P3 grids had the same grid ratio, the reduction in primary transmission for R12P3 was larger due to its increased grid height.

Primary transmission histograms provided better insight about pixel-to-pixel variation in primary transmission (Fig. 3). Pixel-specific primary transmission (PPT) for 2D grids varied between 44.5% and 98.5%. Whereas PPT of 1D grid varied only between 67.5% and 72.2%. For each 2D grid, more than 98% of all pixels received at least 50% primary transmission. In other words, less than 2% of detector pixels receive less than 50% primary transmission, for all 2D grid configurations evaluated. Overall, the trends in PPT values for each grid were in line with their respective average primary transmission; R12P3 had the highest PPT values, whereas R16P2 had the lowest PPT values among 2D grids.

Pixel-specific primary transmission histograms (PPT) for all grid configurations. All measurements were performed at the optimal grid position, i.e., the grid position that provides the maximum primary transmission.

PPT histograms were also evaluated on both edges and center of each grid. As shown in Fig. 4, PPT histograms varied minimally across different locations in each grid, which implied that grid focusing geometry and grid septum thickness were consistent throughout each grid module.

Pixel-specific primary transmission histograms (PPT) measured at 3 different locations: at left edge, center, and right edge of the grid module. The variation in primary transmission histograms was minimal as a function of location due to focused geometry of grid septa.

PPT degradation due to grid offset, or grid misalignment, was more pronounced in the PPT range of 50–80% for all 2D grids (Fig. 5) and the largest PPT degradation was observed with the 2DGrid R16P2. On the other hand, PPT degradation in the PPT range of 80–100% was substantially lower. In contrast to 2D Grids, the change PPT histogram shape was not observed with the 1D grid, however PPT histogram shifted toward lower values as a function of grid offset.

Effect of grid offset on the pixel-specific primary transmission. Offsets were applied in the Z- direction (direction parallel to the CBCT’s axis of rotation).

3.2. Scatter transmission properties

Ts and SPR values at 125 kVp for all grids are shown in Fig. 6 and Table 3. Ts showed relatively strong dependence on phantom thickness. At 10 cm phantom thickness, Ts for 2D grids was in the range of 7–9%, which was reduced to 1.7–2.7% at 40 cm phantom thickness. The R16P2 grid provided the lowest scatter transmission and Ts for the R12P2 and R12P3 grids were comparable due to their similar grid ratios. Ts of the 1D grid was in the range of 1015%, which was 2–6 times higher than the Ts of 2D grids.

Ts (a) and SPR (b) comparisons of all antiscatter grids at 125 kVp. In (c), SPR for no grid configuration was omitted, and SPR plot was rescaled to indicate the differences among different grids clearly.

Table 3.

Ts and SPR Values for all grids measured at 125 kVp

Similar trends were observed in the SPR measurements (Fig. 6, Table 3). At 10 cm phantom thickness, the SPR values for all 2D grids were quite similar at around 0.1. At 40 cm phantom thickness, these values were in the range of 0.21–0.32, where R16P2 provided the lowest SPR. R12P3 provided slightly lower SPRs than the R12P2 grid, which was partly due to its better primary transmission. When compared with the 2D grids, the SPR of the 1D grid was much higher, reaching up to 1.41 at 40 cm phantom thickness. The variation in SPR as a function of phantom thickness was less with 2D grids. SPR of 2D and 1D grids increased by a factor of 23 and 7, respectively, when phantom thickness was increased from 10 to 40 cm.

Ts of 2D grids showed relatively small dependence on beam energy (Fig. 7). In the 80–140 kVp range, Ts of 2D and 1D grids varied by 9.4–13.2% and 35.5%, respectively, at 20 cm phantom thickness. Dependence of SPR on beam energy showed similar trends (Fig. 8). In the range of 80–140 kVp and at 20 cm phantom thickness, SPRs of 2D grids varied by 15.6–17.9%, whereas SPRs of the 1D grid varied by 39.6% in the same energy range. 2D grid parameters had little effect on the energy dependence of scatter transmission; the change in Ts showed only 4% variation among the 2D grids when x-ray energy was increased from 80 to 140 kVp.

Ts as a function of phantom thickness at three different energies.

SPR as a function of phantom thickness at three different energies.

3.3. Low contrast object visualization and CNR improvement

Before the CNR measurements, detector entrance exposures were evaluated to determine whether stochastic electronic noise had any noticeable impact on CNR measurements. For 20 cm thick phantom, grid entrance exposure was 85 μR/frame for all grids. Detector entrance exposures for 2D grids were in the range of 22–23 μR/frame and 23 μR/frame for the 1D grid. For the 40 cm thick phantom, grid entrance exposure was 50 μR/frame. Detector entrance exposures for all 2D grids were 5–6 μR/frame and 9 μR/frame for the 1D grid. Because the detector entrance exposures were at or above the threshold of 5 jR/frame (see Section 2.4), the effect of stochastic electronic noise on CNR measurements was deemed small.

Projection images of the contrast phantom at 20 and 40 cm thicknesses are shown in Fig. 9. To show the contrast objects clearly, a reference projection was displayed in the top row, where phantom thickness was only 10 cm. In each column, gray scale window was the same for all grid configurations. At 20 cm phantom thickness, all contrast objects were visible with all grids. However, the image acquired without a grid appeared noisier than the images acquired with grids, indicating that the CNR was lower than the images acquired with grids. When phantom thickness was increased to 40 cm, contrast objects were poorly visualized without a grid in place. While the 1D grid provided large improvement in contrast visualization, the improvement was even larger with 2D grids from a qualitative perspective. The effect of 2D grid type on contrast visualization appeared to be minimal.

The measured CNR improvement factors, KCNR, supported our qualitative observations (Table 4). For 20 cm thick phantom, 2D grids improved CNR by a factor 1.4–1.5, whereas the 1D grid improved CNR by a factor of 1.2. For 40 cm thick phantom, 2D grids improved CNR up to a factor 2.3, whereas 1D grid improved CNR by a factor of 1.5. KCNR values were not significantly different among 2D grids with different grid pitch and ratios.

Table 4.

CNR Improvement Factor (Kcnr) for all grid configurations

4. Discussions

In the grid ratio range of 12–16, 2D grids can achieve SPRs below 0.3 in the high scatter conditions found in pelvis CBCT imaging. Increasing the grid ratio from 12 to 16 reduces SPR by 30%, down to 0.2. It was previously reported that a 2D grid with a grid ratio of eight could reduce SPR down to 0.5 under very similar imaging conditions(Altunbas et al., 2017). Thus, it is reasonable to state that an increase in grid ratio by a factor of two leads to roughly a factor of two reduction in SPR in imaging conditions pertinent to radiation therapy. Such large reductions in SPR due to increased grid ratio can provide drastic improvements in the CT number accuracy of CBCT. Scatter transmission of 2D grids varied in the range of 10% between 80–140 kVp, a typical energy range used in spectral CT applications, and the energy dependence of scatter transmission was similar among all three 2D grids evaluated.

The radiographic 1D grid evaluated in this study has a grid ratio of 21, which has the highest grid ratio among commercially available radiographic grids that we found. Even though it has a much higher grid ratio than 2D grids, 2D grids provided a factor of up to 7 lower SPRs than the radiographic grid. The scatter suppression performance of 2D grids was more prominent for thicker objects. As reported previously, this is due to larger angular dispersion of scattered x-rays exiting thicker objects; 2D grid structure is more efficient than 1D grid structure in attenuating scatter for thicker, or larger, objects. When compared with 2D grids, energy dependence of scatter transmission is factor of two-three larger with the radiographic grid. Because 2D grids provide much lower SPRs than 1D grids, particularly at higher energies, they may play an important role in enabling spectral CBCT applications, where scatter is a major contaminant of the x-ray spectrum (Zbijewski et al., 2014; Schmidt, 2010).

Average primary transmission of 2D grids were in the range of 84–89%, whereas radiographic 1D grids with fiber spacers provided 70% primary transmission; this is primarily due to the large grid pitch of 2D grids, meaning a lower percentage of detector pixels reside underneath the grid’s tungsten footprint. For a grid with a square hole, 2.9 mm pitch, and 0.1 mm septal thickness, only 6.2% of the detector area is covered by tungsten septa; in other words, the theoretical upper limit on primary transmission is 93.8%. Because our measurements yielded 89.1% primary transmission for such a grid geometry, the difference between the theoretical and measured primary transmission of the 2D grid is about 5%. Several factors lead to this difference, such as focal spot and off-focal radiation clipping due to grid septa, small errors in grid–source alignment, and differences in ideal and fabricated grid geometries.

While increasing the grid ratio improves scatter suppression and increasing the grid pitch improves primary transmission, they also degrade primary transmission due to grid-source misalignment. For a grid ratio of 16, grid misalignment of 10 mm in the detector plane can reduce average primary transmission by more than 8%. Increasing the grid pitch to 2.9 mm results in larger grid heights, which degrades average primary transmission by 7% for 10 mm grid source misalignment. Grid–source misalignment had a much larger effect on pixel-specific transmission (Fig. 3), particularly for R12P3 and R16P2 grids where minimum pixel-specific transmission reduced from 44% down to 30% due to 10 mm grid misalignment, whereas minimum pixel-specific primary transmission of the R12P2 grid was 38%. Because both R12P3 and R16P2 grids have large grid heights (30+ mm vs. 23.3 mm for R12P2), their septal shadows become larger due to grid misalignment, and more detector pixels were obstructed by septal shadows. For example, for the R12P3 grid, about 8.5% of the detector pixels receive less than 50% primary transmission when the grid is misaligned by 10 mm. As evident from Fig. 5, detector pixels with pixel-specific primary transmission values in the range of 50–80% were affected more from grid–source misalignment. Such pixels were located either directly underneath, or adjacent to septal shadows. Hence, increased septal shadow size due to a 5–10 mm grid offset affects such detector pixels proximal to grid shadows. On the other hand, pixels located toward the center of the through-holes (i.e., pixels that receive more than 80% primary transmission) were affected minimally from grid offsets.

Although grid–source geometry can be established within a few millimeters during the system calibration phase, grid-source position may deviate from its ideal geometry due to gantry flex. Therefore, 2D grid pitch and ratio should be tailored for each CBCT system by considering the uncertainties in grid-source alignment, and its consequences on gird-source alignment.

The improvement in CNR was evaluated in two phantom thicknesses—20 and 40 cm—which are typical anterior-posterior and lateral separations in the human torso that we observe clinically. 2D grids provided about a factor of 1.5–2.2 CNR improvement with respect to projections acquired without grids. 2D grids also provided a factor of 1.2–1.5 more CNR improvement than the radiographic grid. The CNR improvement was less with 20 cm thick phantom due to relatively lower scatter fraction in projections. Although R12P3 and R12P2 grids provided slightly higher CNRs than R16P2 grid, these differences were relatively small (less than 10%). There were two reasons why we did not see significant KCNR differences among the 2D grids: 1) Because CNR has the following relationship (Neitzel, 1992) with respect to SPR and primary intensity P:

small variations in SPR have even smaller impact on CNR. With 2D grids, maximum SPR values with the thickest phantom were quite low (in the range of 0.2–0.3), irrespective of 2D grid type. As a result, the change in CNR improvement due to grid-to-grid variations in SPR was small. Likewise, the primary transmission among 2D grids varied between 84% and 89%. Such a variation in primary transmission has a small impact on CNR values. 2) Noise and signal variations introduced by other factors, such as fixed-pattern noise, detector lag, and ghosting, play an important role when measuring CNR at low detector entrance exposures. This is specifically an issue for CNR measurements with the 40 cm thick phantom, where detector pixel values were three orders of magnitude less than the ones in flood field projections. Even though, stochastic electronic noise was minimized by keeping the detector entrance exposure above 5 μ/frame; nonlinear effects in pixel gain at such low exposure introduce fixed-pattern noise(Altunbas et al., 2014), and may bias CNR measurements.

In CNR measurements with 40 cm thick contrast phantom, x-ray technique was 4mAs per projection frame, the highest tube technique available in our imaging protocol. Because 2D grids reduce detector entrance exposures due to efficient scatter suppression, such a tube output yielded only 5 μR/frame of detector entrance exposure. In a typical pelvis CBCT protocol, the tube technique is typically a factor of 2–3 less than for 4mAs per frame and detector entrance exposures may go down to 1–2 μR/frame. In such a CBCT imaging scenario, the CNR improvement benefits of 2D grids may be deteriorated by electronic noise. Thus, to utilize the full extent of CNR improvement by 2D grids, detector noise properties and detector entrance exposures should also be considered.

In our prototypes, septa heights reached 35 mm at 0.1 mm septal thickness, corresponding to aspect ratio of 350. The use of metal additive manufacturing was essential in realizing such high septal aspect ratios. Our work implicitly indicates that the proposed high grid ratio 2D grids for CBCT are feasible to fabricate from tungsten via a direct metal laser sintering process. While our project employed small area prototypes, larger grids to cover the full area of FPDs may be manufactured by tiling multiple grid modules.

Our study has several limitations. First, our prototypes were developed mainly for CBCT systems in radiation therapy. However, our study did not include image quality evaluations in CBCT images. This is because our work was about the effect of grid design parameters on the primary and scatter transmission properties. Such transmission measurements are done in projection images only. We plan to investigate the effect of grid parameters on CBCT image quality in a separate work, since it requires substantially different set of investigations. Second, our study does not address how to correct septal shadows in projections. Based on our experience, standard gain correction methods can reduce, but may not fully eliminate, septal shadows(Alexeev et al., 2019). For example, gantry flex can introduce small distortions in source-detector geometry, which, in return, reduce the efficacy of gain correction and may introduce grid shadow-induced ring artifacts (Alexeev et al., 2019). Third, FPD is shifted laterally in most CBCT systems for radiation therapy, to allow small and large field of view CBCT scans. However, 2D grid can be out of focus, when detector is shifted laterally from it optimally aligned position. This challenge may require fabrication of interchangeable grids for different geometries, or tilting the detector towards x-ray source, to realign grid septa towards focal spot. Finally, our prototypes covered a small fraction of the detector’s active area. While we demonstrated that focusing geometry was precise for smaller grids, focusing performance of large area grids, particularly in the cone direction, remains to be investigated.

5. Conclusions

This is the first study that demonstrated the effect of 2D grid pitch and ratio on its primary and scatter transmission properties. Our work indicates that that 2D grids for FPD-based CBCT can reduce scatter-to-primary ratios in the 0.2–0.3 range even in very high scatter conditions (such as in lateral projections of human pelvis) while keeping average primary transmission above 80%.

Our study evaluated grid ratios up to 16. Higher grid ratios will reduce the scatter fraction further and, in return, may better improve CT number accuracy in CBCT images. However, higher grid ratios are expected to provide diminishing returns in CNR improvement. We believe that higher grid ratio 2D grids (i.e. higher than 16) are better suited for applications that demand high CT number accuracy, such as quantitative imaging and multi-energy CBCT(Schmidt, 2010). If the primary goal of the imaging task is to improve CNR, then such a goal may be achieved at lower grid ratios.

Finally, 2D grids can provide substantially better scatter suppression and primary transmission at lower grid ratios than new-generation 1D antiscatter grids with fiber spacers. Increasing the grid ratio of 1D grids cannot achieve scatter suppression performance similar to 2D grids, particularly in high scatter intensity conditions such as in imaging of the pelvis.

Acknowledgements

This work was funded in part by grants from NIH/NCI (R21CA198462) and Cancer League of Colorado.

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