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Grid and Slot Scan Scatter Reduction in Mammography: Comparison by Using Monte Carlo Techniques1

來源:放射學雜志 作者:John M. Boone PhD J. Anthony Seibert PhD Cha-M 2007-5-12
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摘要: REFERENCESScatter cleanup performance of grids, conventional and otherwise, has been studied extensively, both experimentally (1–6) and by using Monte Carlo techniques (2,7,8)。 Grids play an important role in improving image quality。ommittedPhysical Dimensions and Composition of the Grids The ......


1 From the Department of Radiology, University of California, Davis, 4701 X St, Research Imaging Laboratory, UC Davis Medical Center, Sacramento, CA 95817 (J.M.B., J.A.S.); Creatv Microtech, Inc, Potomac, Md (C.M.T.); and Lawrence Livermore National Laboratory, Livermore, Calif (S.M.L.). Received February 20, 2001; revision requested April 11; revision received June 15; accepted June 22. Supported in part by grant 1RB-0192 from the California Breast Cancer Research Program and by National Institutes of Health (NIH) grant R21 CA 82077 for support of the techniques discussed herein as they are relevant to low-kV computed tomography of a specimen; C.M.T. supported in part by grant R43-CA76752 from the NIH for the development of novel grid technology. 


     ABSTRACT

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MATERIALS AND METHODS
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APPENDIX: MATHEMATICS AND...
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PURPOSE: To evaluate a comprehensive array of scatter cleanup techniques in mammography by using a consistent methodology.

MATERIALS AND METHODS: Monte Carlo techniques were used to evaluate the Bucky factor (BF) and the contrast improvement factor (CIF) for linear and cellular grids and for slot scan and scanning multiple-slot assembly (SMSA) systems.

RESULTS: For a 28-kVp molybdenum anode–molybdenum filter spectrum with a standard detector and a 6-cm-thick 50% adipose–50% glandular breast phantom, slot scan techniques delivered an ideal BF. For slot widths greater than 4 mm, however, the CIF was lower than that achieved by the high-transmission cellular grid with a grid ratio of 3.8:1. A tungsten-septa air-interspaced cellular grid with a 4:1 grid ratio outperformed the high-transmission cellular grid in both BF and CIF. The SMSA was shown to be efficacious when 4-mm-wide slots were separated by at least 20 mm. In comparison with the literature, 3.6% agreement was achieved with other Monte Carlo studies, 3.3% with an experimental study that used a digital detector, and 13%–29% agreement was demonstrated in comparison to film-based experimental studies.

CONCLUSION: With use of consistent methods for comparison, cellular grids were shown to substantially outperform linear grids but have slightly higher BFs compared with that of slot scan geometries at the same CIF.   

 

Index terms: Breast radiography, technology, 00.112, 00.1215 • Physics, 00.99 • Radiations, 00.99


     INTRODUCTION

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INTRODUCTION
MATERIALS AND METHODS
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DISCUSSION
APPENDIX: MATHEMATICS AND...
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Scatter cleanup performance of grids, conventional and otherwise, has been studied extensively, both experimentally (16) and by using Monte Carlo techniques (2,7,8). Grids play an important role in improving image quality; however, that role is different in digital mammography in comparison to screen-film mammography (9). In screen-film mammography, scatter acts to reduce contrast in the image. In digital mammography, where contrast can be restored by image processing, scattered radiation acts to reduce the signal-to-noise ratio. In both screen-film and digital mammography, reducing the amount of scattered radiation that reaches the detector must be done in a manner that allows most or all of the primary radiation that has passed through the breast to be detected. That is where grids, air gaps, or slot scan geometries play a role.

Conventional carbon fiber–interspaced grids with grid ratios from 3.5 to 5 are used predominantly in clinical screen-film mammography today, except for magnification views. Despite the widespread use of carbon fiber linear grids, new grid designs abound, and many of these have been made possible by recent advances in material science. Fabrication techniques used for making computer chips (10,11) or fiberoptic devices (4) have been exploited for the construction of exotic antiscatter devices. As evidence of the rapid maturation of these technologies, cellular grid technology (a square pore grid with copper septa and air interspaces) has become available on one commercially available mammography system (6).

The evaluation of antiscatter techniques has historically been focused on one antiscatter approach at a time, and consequently it is difficult to quantitatively compare antiscatter technologies because of the modest degree of reproducibility that exists across evaluation methodologies. The purpose of this investigation was to evaluate a comprehensive array of scatter cleanup technologies in mammography by using the same Monte Carlo–based experimental technique.


     MATERIALS AND METHODS

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MATERIALS AND METHODS
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For this investigation, we used the simple investigational environment for radiology research applications, or SIERRA, Monte Carlo code, the performance of which has been validated in applications to diagnostic radiology (12) and mammography (13). Comprehensive information concerning the scatter-to-primary ratio (SPR) in mammography has also been reported (14); however, the focus here is not on the SPR per se, but rather how different antiscatter designs influence the SPR. Where quantitative data were available in the literature for comparisons, the Monte Carlo techniques were adopted to enable comparisons with reported data.

Monte Carlo analysis techniques allow perfect alignment of the grid with the x-ray source, and therefore primary transmission levels are expected to exceed those in real grids, where septal focusing over the surface of the grid is less than perfect. One would expect, therefore, that Monte Carlo–derived Bucky factors (BFs) would be slightly lower than physically measured BFs.

X-ray spectra used in this investigation were generated by using a computer model (15), and the computer-generated spectra were mathematically filtered with Lucite to increase the half-value layer in order to match the half-value layers at each kilovolt peak and anode-filter combination of a clinical mammography system (Mark IV; Lorad, Danbury, Conn). The addition of 3.0 mm of Lucite ( = 1.19 g/cm3) was found to match the half-value layers of the computer-generated spectra to the clinically measured half-value layers to within 0.25%, and so this thickness was used in this investigation. The spectra used for comparisons with the literature were similarly computer fit and filtered with Lucite (or aluminum for tungsten anode–aluminum filter spectra) to match the half-value layers used by other investigators, where reported.

The geometry used for the Monte Carlo simulation was typical of that for clinical mammography. The standard source-to-image distance (SID) was 65 cm, and a 1.5-cm air gap between the caudal surface of the compressed breast and the detector was used in the simulation geometry. The SID and air gap were changed to correspond to values used by other investigators for the comparison studies. The compressed breast thickness was varied from 2 to 8 cm, and in craniocaudal projection, a semicircular breast phantom with a 10-cm radius was used. A previous investigation (14) demonstrated that little correlation (r2 = 0.02) exists between the compressed breast thickness and breast area in the craniocaudal projection, and thus a constant breast area (area, 157.3 cm2, corresponding to a 10-cm breast radius) was used for all breast thicknesses. The previous study (14) also showed very little dependence on breast composition in terms of scattering properties, and thus a 50% adipose–50% glandular breast composition was used throughout this study. The SPR changes markedly across the field of view, and to represent the most severe scattering conditions, the photons emerging from a 4-cm-diameter circular region at the center of mass of the semicircular breast phantom were tallied. The center of mass corresponds to the highest SPR levels in the image.

Air gap techniques are often mentioned in the context of scatter cleanup. However, the compromises that are required to obtain meaningful scatter reduction are too great for the air gap technique to play any practical role in screening-mammography procedures. These compromises include the increased focal spot blurring due to the higher magnification, a substantial radiation dose penalty, and a reduction of the effective field of view. For these reasons, air gap techniques were not considered in this investigation.

Linear and cellular grids were studied. Conventional linear grids with physical dimensions typical of grids used clinically were modeled, with carbon fiber interspace material and lead septa. Cellular grids were also modeled by using a variety of septal materials. Whereas most mammography systems incorporate grids from a few grid manufacturers, cellular grid technology is currently available commercially from one vendor (Trex Medical/Lorad/Hologic, Bedford, Mass). Cellular grids are structurally sound without an interspace material, and thus air interspaces were modeled for these grids here. The characteristics of the grids studied are listed in the Table. The dimensions of the high-throughput cellular (HTC) grid (Lorad) were taken from Rezentes et al (6).


fig.ommitted Physical Dimensions and Composition of the Grids

 

 
The interspace channels and septa of all grids (linear and cellular) were assumed to be perfectly aligned with an x-ray point source. The maximum divergence angle in the 4-cm-diameter scatter field evaluated was ±1.8° at the 65-cm SID studied. To compute a grid transmission function that was independent of position (for simplicity), the grid computations assumed an infinite focusing distance (parallel grid septa) and scatter angles were calculated relative to normal incidence. The SID and air gap come into the calculation of the SPR because of the inverse square law affecting the primary fluence. The details of how the primary transmission of the antiscatter devices was calculated are given in the Appendix.

Slot scan geometries as proposed by Nishikawa et al (16) and representative of a commercial digital mammography system (Fischer Imaging Systems, Denver, Colo) were compared against the scatter cleanup performance of the various grid technologies. The benefit of a slot scan system is that primary photons that pass through the breast are not attenuated, and this design therefore results (in principle) in a perfect BF. The specific geometry of the slot scan system was characterized in the Monte Carlo code, and simulations were performed to assess the effect of the slot scan geometry on the SPR.

More than 2 decades ago, Barnes and colleagues (17,18) advocated the use of a scanning multiple-slot assembly (SMSA) to reduce scattered radiation in mammography. The use of multiple slots increases the geometric efficiency and reduces x-ray tube loading constraints. Although the implementation of SMSA technology proved challenging in the era of single-phase generators and screen-film mammography, the use of SMSA antiscatter techniques in the current era of high-frequency, low-ripple x-ray generators and digital mammographic detector systems may be more feasible. SMSA acquisition geometry was modeled by using both three slots and five slots for a 6-cm-thick breast.

The mathematic details of the Monte Carlo procedure and metrics used for evaluation of grid performance are described in the Appendix. The principal grid performance parameters used in this investigation were the BF and the contrast improvement factor (CIF). The BF is, for most practical purposes, equal to the increase in the average glandular dose that results from using a grid. Thus, low BFs are better. The CIF is the relative improvement in contrast due to the use of the grid, and so high CIF values are better. The relationship between CIF and BF is given by the equation CIF = Tp x BF, where Tp is the primary transmission factor of the grid. Maximum dose efficiency occurs for antiscatter devices when Tp approaches 1.

A direct comparison between grid technology targeted for screen-film mammography and that for digital mammography is confounded by the fact that different x-ray spectra are often used. Consequently, grid performance was assessed with use of spectra and detector systems appropriate for both screen-film (eg, 28-kVp molybdenum anode-molybdenum filter [Mo-Mo]) and digital (eg, 40-kVp tungsten anode–aluminum filter) mammography.

Chan et al (2) promoted the use of graphs for analysis of grid performance, which present the CIF as a function of the BF. This very useful graphical tool was adopted in our study, as it represents a simple but elegant format for evaluating the cost-benefit (ie, cost = BF, benefit = CIF) performance of an antiscatter device. As discussed by Chan et al (2), for an ambient SPR0 level in the absence of a grid, corresponding to S0/P0 (which is a function of the breast thickness, beam energy, and field of view), the CIF and the BF parameters for an ideal grid both become 1 + SPR0. Thus, the performance of a grid with 100% primary transmission is represented by a line of unity slope that extends from the origin of the graph at (BF = 1, CIF = 1) to (1 + SPR0, 1 + SPR0). The BF cannot be lower than this theoretical limit, and the CIF cannot be higher; therefore, the performance of real grids must be below and to the right of this line. Comparisons between two points on the CIF versus BF graphs involve two parameters; however, since BF and CIF are similarly scaled, a useful measure for comparison between two results (eg, result A and result B) can be derived by computing the vector distance between two points on these graphs, that is, d = [(BFA - BFB)2 + (CIFA - CIFB)2]. Normalizing d by the length of the ideal grid performance vector, which starts at BF = 0, CIF = 0, such that r = 2(1 + SPR0), the average difference (100% x d/r) in grid performance for results A and B can be quantified.


     RESULTS

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Energy versus Angle Results
An isometric plot (which shows one parameter as a function of two others in a "wire frame" surface display) of the scattered energy versus angle characteristics for a typical mammographic spectrum (25-kVp Mo/Mo and a 5-cm-thick breast) is illustrated in Figure 1. These data were determined by Monte Carlo simulation. The energy distribution at a given angle retains the general shape of the transmitted primary beam (not shown); however, there is a reduction in the relative fluence at higher angles. It was determined from the Monte Carlo analysis that below 15 keV, scattered fluence exiting the breast was about 80% Rayleigh and 20% Compton scattering, and this reversed to about 30% Rayleigh and 70% Compton at 24 keV. Figure 1 shows the scattered photon properties that are incident upon the grid for a very typical 25-kVp Mo-Mo spectrum and a 5-cm-thick breast.


fig.ommitted Figure 1. Isometric plot illustrates Monte Carlo-calculated scattered radiation that is incident on the detector or grid. Number of scattered photons (vertical axis) is shown as a function of photon energy and scatter angle. These data illustrate the scattered photon characteristics that emerge from a 5-cm-thick, 50% adipose-50% glandular breast by using a 25-kVp x-ray beam Mo-Mo entrance spectrum.

 

 
Grid transmission (energy vs angle) is shown isometrically in Figure 2 for three different grid technologies. Figure 2a shows the performance of a conventional carbon fiber–interspaced linear grid with a 5:1 grid ratio, probably the most common grid used in screen-film mammography today. Primary transmission occurs at the = 0° profile in this Figure and is appreciably lower than unity due to the attenuation of primary photons in the carbon fiber interspaces of the grid and due to the fractional area of the grid covered by lead septa. The attenuation is more severe at x-ray energies below about 10 keV; however, few primary photons exit the breast at this energy due to the filtration of the breast and in the x-ray tube (Fig 1). The angle versus energy performance of the HTC grid with a grid ratio of 3.8 is illustrated in Figure 2b. Although the cellular grid has a lower grid ratio than that of the linear grid (3.8 vs 5.0), its two-dimensional structure improves scatter rejection performance. Owing to the greater efficiency of the cellular grid design, the scatter transmission is virtually zero for scattered photons with angles greater than about 20°. At energies above about 25 keV, x-ray penetration of the copper septa starts to occur, with significant penetration at 50 keV. Primary transmission (at = 0°) of the cellular grid is noticeably better than for the 5:1 carbon fiber linear grid, owing to the air interspace material and the high fraction of open area. The primary transmission for air-interspaced grids is essentially equivalent to the open area of the grid, which for the cellular grid was 91.6%. The scatter transmission properties of an 18.5:1 grid ratio cellular air-interspaced grid with lead-glass septa (4) is shown in Figure 2c. The open area of the microchannel plate used to generate the transmission properties in Figure 2c was 78.9%, resulting in a lower primary transmission than that of the cellular grid. However, the much higher grid ratio of the microchannel plate (18.5:1) leads to better rejection of small-angle scatter.


fig.ommitted Figure 2a. Isometric plots illustrate the probability of grid scatter transmission, Ts, with the wire-framed box defining unit probability, for three grid technologies. Ts (vertical axis) is shown as a function of scatter energy and angle of incidence on the grid (relative to normal). (a) Ts for a conventional linear carbon fiber-interspaced grid with a 5:1 grid ratio. (b) Ts for a cellular grid with copper septa (Lorad HTC) and a 3.8:1 grid ratio. At higher energies, penetration occurs through the copper septa. (c) Ts for an air-interspaced (microchannel plate) grid with lead-glass septa and an 18.5:1 grid ratio. The very high grid ratio results in excellent small-angle scatter rejection.

 

 

fig.ommitted Figure 2b. Isometric plots illustrate the probability of grid scatter transmission, Ts, with the wire-framed box defining unit probability, for three grid technologies. Ts (vertical axis) is shown as a function of scatter energy and angle of incidence on the grid (relative to normal). (a) Ts for a conventional linear carbon fiber-interspaced grid with a 5:1 grid ratio. (b) Ts for a cellular grid with copper septa (Lorad HTC) and a 3.8:1 grid ratio. At higher energies, penetration occurs through the copper septa. (c) Ts for an air-interspaced (microchannel plate) grid with lead-glass septa and an 18.5:1 grid ratio. The very high grid ratio results in excellent small-angle scatter rejection.

 

 

fig.ommitted Figure 2c. Isometric plots illustrate the probability of grid scatter transmission, Ts, with the wire-framed box defining unit probability, for three grid technologies. Ts (vertical axis) is shown as a function of scatter energy and angle of incidence on the grid (relative to normal). (a) Ts for a conventional linear carbon fiber-interspaced grid with a 5:1 grid ratio. (b) Ts for a cellular grid with copper septa (Lorad HTC) and a 3.8:1 grid ratio. At higher energies, penetration occurs through the copper septa. (c) Ts for an air-interspaced (microchannel plate) grid with lead-glass septa and an 18.5:1 grid ratio. The very high grid ratio results in excellent small-angle scatter rejection.

 

 
Figure 3 illustrates the performance of the standard carbon fiber–interspaced linear grid over a range of grid ratios from 2:1 to 7:1. Figure 3a shows the results for a typical screen-film mammography system, where a 28-kVp Mo-Mo spectrum is used for a 6-cm-thick breast. Figure 3b shows the results for a higher energy spectrum (40-kVp tungsten anode–aluminum filter), which may be more appropriate for some digital mammography systems. The carbon fiber linear grid performance serves as a useful benchmark for evaluating the effectiveness of the more exotic antiscatter technologies. The performance of the cellular grid spanning grid ratios from 2:1 to 6:1 is also shown in Figure 3, as is the performance of microchannel plates, as described by Fahrig et al (4). These high-grid-ratio devices have excellent scatter rejection as evidenced by a high CIF, but the BF is also high. The performance of the nickel septa grid technology as proposed by Tang, Fischer, and colleagues (10,11) (grid ratios from 2:1 to 7:1) is illustrated for nickel septa previously fabricated grids and for a proposed grid design. The nickel septa proposed grids have performance that largely parallels that of the HTC design. A tungsten septa grid was modeled with high open area (96%). The 15-µm tungsten septa were more effective at preventing septal penetration and improving contrast because of the high atomic number (Z = 74) and high density (19.3 g/cm3) of tungsten.


fig.ommitted Figure 3a. Graphs of CIF as a function of BF for the antiscatter devices tested in the current study. (a) Results for a 28 kVp Mo/Mo spectrum and a 6-cm-thick breast of 50% glandular-50% adipose tissue. (b) Results for a 40-kVp tungsten anode-aluminum filter (W/Al) spectrum and a 6-cm-thick breast. Slot scan system results ( along 100% primary transmission line) correspond (from top to bottom) to 1-, 2-, 3-, 4- (Slot scan 4 mm), 8- (SS 8 mm), 12- (SS 12 mm and circled), 16-, 20-, and 24-mm slot widths. Linear carbon fiber-interspaced (CF) grid results are shown for grid ratios from 2:1 to 7:1 ( on line marked Linear CF Grid; 5:1 result is circled and labeled). Cellular grid results are shown for grid ratios 2:1, 3:1, 3.8:1, 4:1, 5:1, and 6:1 ( on line marked HTC; 3.8:1 grid ratio, corresponding to the Lorad commercial product, is boxed and labeled). Note that the 12-mm-wide slot has a slightly lower CIF than the 3.8:1 HTC grid or the 5:1 linear CF grid. Performance of a nickel septa (Ni-Septa) grid, by using the technology fabricated (F) by Tang, Fischer, and colleagues (10,11), is illustrated for grid ratios from 2:1 to 7:1 ( on line [solid in a, dotted in b] marked F); performance of a proposed (P) grid ( overlying line marked HTC) is shown as well. Note that the proposed grid performance parallels that of the HTC design. A theoretic tungsten septa grid with grid ratios from 2:1 to 7:1 ( on line marked W-Septa) demonstrates superior performance of this high-density septal material with a high atomic number (Z = 74). The very high grid ratio microchannel plate grids ( at MCPs), as discussed by Fahrig et al (4), are also illustrated.

 

 

fig.ommitted Figure 3b. Graphs of CIF as a function of BF for the antiscatter devices tested in the current study. (a) Results for a 28 kVp Mo/Mo spectrum and a 6-cm-thick breast of 50% glandular-50% adipose tissue. (b) Results for a 40-kVp tungsten anode-aluminum filter (W/Al) spectrum and a 6-cm-thick breast. Slot scan system results ( along 100% primary transmission line) correspond (from top to bottom) to 1-, 2-, 3-, 4- (Slot scan 4 mm), 8- (SS 8 mm), 12- (SS 12 mm and circled), 16-, 20-, and 24-mm slot widths. Linear carbon fiber-interspaced (CF) grid results are shown for grid ratios from 2:1 to 7:1 ( on line marked Linear CF Grid; 5:1 result is circled and labeled). Cellular grid results are shown for grid ratios 2:1, 3:1, 3.8:1, 4:1, 5:1, and 6:1 ( on line marked HTC; 3.8:1 grid ratio, corresponding to the Lorad commercial product, is boxed and labeled). Note that the 12-mm-wide slot has a slightly lower CIF than the 3.8:1 HTC grid or the 5:1 linear CF grid. Performance of a nickel septa (Ni-Septa) grid, by using the technology fabricated (F) by Tang, Fischer, and colleagues (10,11), is illustrated for grid ratios from 2:1 to 7:1  on line [solid in a, dotted in b] marked F); performance of a proposed (P) grid ( overlying line marked HTC) is shown as well. Note that the proposed grid performance parallels that of the HTC design. A theoretic tungsten septa grid with grid ratios from 2:1 to 7:1 ( on line marked W-Septa) demonstrates superior performance of this high-density septal material with a high atomic number (Z = 74). The very high grid ratio microchannel plate grids ( at MCPs), as discussed by Fahrig et al (4), are also illustrated.

 

 
Slot Scan
The performance of a slot scan system is also illustrated in Figure 3. Because the primary beam is not attenuated in a well-calibrated slot scan system, its performance lays along the line defined by 100% primary transmission. However, as the slot width increases, the CIF performance of the slot scan system degrades. For example, the 12-mm-wide slot has a slightly lower CIF than that of the 3.8:1 cellular grid or the 5:1 linear carbon fiber grid.

The performance of an SMSA, as proposed by Barnes and colleagues (17,18), is shown in Figure 4. The inset in Figure 4 illustrates the scatter distribution across the field, orthogonal to the slot direction. Tube loading is reduced when the slots are closer together, but if the separation between slots is too close, scattered radiation produced in one slot’s x-ray beam will contaminate the image data in the other slot. The use of multiple slots (three or five) degrades the CIF when the (center-to-center) spacing of the slots is less than 21 mm. With a minimum spacing of 20 mm between 4-mm-wide slots, as many as nine slots could be active across the imaging field of view. This suggests that tube loading (ie, exposure time) could be reduced by almost a factor of 10 by using SMSA technology, compared with that of a single-slot system. The SMSA performance using 4-mm slot width shown in Figure 4 demonstrates a CIF of 1.54 when cross-talk between slots is eliminated. This performance is equivalent to that of the 4-mm-wide slot scan illustrated in Figure 3.


fig.ommitted Figure 4. Graph shows the results of slot scan geometry by using multiple slots (SMSA technology). Illustrated are a three-slot  and a five-slot  configuration. A 4-mm-wide slot with an air gap of 15 mm was modeled. Scatter distribution orthogonal to the long axis of one slot is illustrated in the inset. AU = arbitrary units, Mo/Mo = molybdenum anode-molybdenum filter.

 

 

     DISCUSSION

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Comparison of Results with that of Other Published Studies
Figure 5 illustrates the CIF versus BF performance of linear grids (aluminum and carbon fiber interspaced) and of the HTC grid. The values reported by several different authors were compared with the results derived in this study. Figure 5a is for a 4-cm-thick breast at 24-kVp Mo-Mo, and Figure 5b is for an 8-cm-thick breast at 30 kVp Mo-Mo; therefore, these results span the range of realistic mammography techniques. The difference between the data reported by Dance and Day (7) and the results of this study was 3.3% for the 3.5:1 aluminum-interspaced grid, and the average difference for the 5:1 carbon fiber–interspace grid was 5.4%.


fig.ommitted Figure 5a. Graphs show CIF as a function of BF for the antiscatter devices investigated in the current study () compared with the results of other investigations: Dance and Day (7), Wagner (19) (25-kVp Mo-Mo, BR12 phantom, for a 4:1 grid), and Rezentes et al (6) (25-kVp Mo-Mo, 12.4 x 12.4-cm field of view, and a 50% adipose-50% gladular phantom for their method 1 [M1] and method 2 [M2]). (a) Results for a 24-kVp Mo-Mo and a 4-cm-thick breast. (b) Results for a 30-kVp Mo-Mo and an 8-cm-thick breast. Al = aluminum-interspaced linear grid, CF = carbon fiber-interspaced linear grid, HTC = cellular grid.

 

 

fig.ommitted Figure 5b. Graphs show CIF as a function of BF for the antiscatter devices investigated in the current study () compared with the results of other investigations: Dance and Day (7), Wagner (19) (25-kVp Mo-Mo, BR12 phantom, for a 4:1 grid), and Rezentes et al (6) (25-kVp Mo-Mo, 12.4 x 12.4-cm field of view, and a 50% adipose-50% gladular phantom for their method 1 [M1] and method 2 [M2]). (a) Results for a 24-kVp Mo-Mo and a 4-cm-thick breast. (b) Results for a 30-kVp Mo-Mo and an 8-cm-thick breast. Al = aluminum-interspaced linear grid, CF = carbon fiber-interspaced linear grid, HTC = cellular grid.

 

 
Wagner (19) and Rezentes et al (6) studied grid performance experimentally. Rezentes et al reported two different measurement techniques; the results of both are shown in Figure 5. For the method 1 comparison, the differences between their results and the results of this study averaged 33.4% (range, 29.5%–37.7%) for the 3.8:1 cellular grid, 21.4% (range, 20.1%–24.1%) for the 3.7:1 carbon fiber linear grid, and 31.6% (range, 26.9%–36.7%) for the 5:1 carbon fiber linear grid. For the 5:1 carbon fiber linear grid using method 2 of Rezentes et al (6) (their General Electric 600T mammography system data), the average difference compared with the results of this study was 13.2%. The average difference between the results of this study and those of the Wagner study for a 4:1 carbon fiber grid was 16.1%.

Chan and colleagues (2) were early pioneers in both the Monte Carlo and physical evaluations of grid performance in mammography. Using Monte Carlo techniques as a guide and using the grid technology of the day, Chan and colleagues manufactured 17 aluminum-interspaced lead septa grids and experimentally determined their BF and CIF by using a 6-cm-thick slab of Lucite and a 35-kVp molybdenum anode–molybdenum plus aluminum filter spectrum. Although aluminum-interspaced grids are not used in modern mammography systems, comparison with the results of the study by Chan et al serves as validation of this technique and also lends perspective to why aluminum should not be used. Like Rezentes et al (6), Chan et al (2) reported two different measurement techniques for determining CIF and BF, and the results of both are illustrated in Figure 6. Compared with Chan et al’s "transmission" measurement technique, the average difference with our results was 26.9%, and the "phantom" measurement technique differed by an average of 33.2%.


fig.ommitted Figure 6. Graph shows CIF as a function of BF for 17 grids physically evaluated by Chan et al (2) compared with the results of this study. Chan et al used two measurement techniques: transmission and phantom. The geometry of each grid (15 x 15-cm field of view, 6-cm-thick Lucite phantom, and 35-kVp molybdenum anode-molybdenum plus aluminum filter spectrum [Mo/(Al+MO)]) was emulated in Monte Carlo simulations in the current study, and results are illustrated (). Computed performance of mammography grids with aluminum interspaces (25-µm septa, 100-µm interspace) for grid ratios from 1:1 to 10:1 is shown (solid line) for comparison.

 

 
In the same comprehensive article in which Chan et al reported their experimental studies (2), the performance of these grids as calculated by using Monte Carlo techniques was reported. Figure 7 compares the Monte Carlo results of Chan et al with those of our study. Data for two carbon fiber–interspaced grids and two aluminum-interspaced grids are shown. For the four grid designs compared, the average differences (each averaged over four grid ratios) were 3.3% for air-interspaced thin septa (21 µm), 3.9% for air-interspaced thick septa (42 µm), 2.6% for aluminum-interspaced thin septa, and 3.1% for aluminum-interspaced thick septa. The agreement for these four comparisons is excellent; however, our results demonstrate a slightly higher primary transmission (BF/CIF) than those of Chan et al for the aluminum-interspaced grids.


fig.ommitted Figure 7. Graph shows the Monte Carlo (MC) results obtained by Chan et al (2) compared with data computed in the current study for the same spectrum and four grid designs. The four grid designs (left to right) and the average differences (each averaged over four grid ratios) between the Chan et al results and our results are as follows: 21-µm lead/104-µm air, 3.3%; 42-µm lead/83-µm air, 3.9%; 21-µm lead/104-µm aluminum, 2.6%; and 42-µm lead/83-µm aluminum, 3.1%.

 

 
Microchannel plate grids are made from fiberoptic technology (20) and are used in proximity-focus image intensifier systems (eg, night vision goggles) and in detector systems for high-energy nuclear physics experiments. Fahrig et al (4) studied the use of microchannel plates for antiscatter grids in mammography. The four grids evaluated by Fahrig et al were cellular structures made of lead-glass septa with air interspaces. The dimensions of each grid are given in the Table. The conditions used in the experimental setup of Fahrig et al were emulated in our comparison to the extent possible. Figure 8 illustrates the excellent agreement (3.3% average difference) between the two sets of results. Fahrig et al also measured the grid transmission as a function of x-ray angle (fig 6 in their article), and these data were determined here by using Monte Carlo techniques for the same grid dimensions. The scatter transmission versus angle data are seen to compare very well in the inset of Figure 8.


fig.ommitted Figure 8. Graph shows CIF as a function of BF for the four microchannel plate grids studied by Fahrig et al (4), with grid ratios from 11.2 to 18.5, compared with results of the current study. The average difference between the Fahrig et al results and our results is 3.3%. Also, grid transmission versus angle for their grid 1 is compared with our Monte Carlo results (inset).

 

 
Study Discrepancies and Analysis
Performance of antiscatter grids, cellular grids, and slot scan systems was assessed by using a consistent measurement approach that allows a direct comparison of the costs (BF) and benefits (CIF) of these different antiscatter technologies. The comparisons between the results of this study and published data indicate wide discrepancies in some cases. Compared with Monte Carlo studies performed a generation ago, relatively minor disagreements averaging 3.6% ( = 0.98%) were observed. Compared with experimental measurements using a digital detector system (the Fahrig et al study [4]), the agreement was found to be 3.3%. When film was used to measure BF and CIF experimentally, differences ranging from 13% to 38% were found. The simulations here assumed no scattering interactions in the grid, and this may be a source of bias in comparing our Monte Carlo results with those of experimental studies. Furthermore, in experimental settings, small-angle scattering is difficult to exclude from the primary component of the beam. Alignment of microscopic grid structures with a distant x-ray source is also a difficult experimental accomplishment. Measuring contrast (required for determining the CIF) by using the beam stop method (6) requires extrapolation to zero beam stop diameter. As discussed elsewhere (13), the choice of extrapolation function will affect the results.

Slot scan techniques are capable of very efficient scatter suppression; however, tube loading becomes a problem and compromises become necessary. The 1-mm-wide slot approaches near-ideal scatter cleanup (Fig 3), but for practical issues (tube loading), an approximately 12-mm slot width is used on a commercial slot scan digital mammography system. Whereas the BF of the slot is far superior to that of a linear or cellular grid, the contrast improvement of the 12-mm slot is equivalent to that of a linear carbon fiber grid with grid ratio in the 4:1 (28-kVp Mo-Mo) to 5:1 (40-kVp tungsten anode–aluminum filter) range. Scanning multiple slots may be practical for digital mammography systems that use a large-field-of-view integrating detector system. (General Electric, Fuji, and Hologic currently manufacture such systems.) The performance of the 4-mm-wide scanning slots with a 6-cm-thick breast at 28 kVp reaches a maximum CIF of 1.54 as long as there is sufficient separation between slots (Fig 4), and this is equivalent in performance of a single slot width of 4 mm, for a 6-cm-thick breast and 28-kVp beam as shown in Figure 3a.

The comparisons of the various grid technologies as illustrated in Figure 3 suggest the important parameters for achieving efficient scatter rejection with use of cellular grid technology: The septa need to be all attenuating, the interspace material needs to be completely transparent, and the open area needs to be very high. This suggests that very thin septa are needed, but to maintain high attenuation in thin septa, a high-density material such as tungsten is needed.


     APPENDIX: MATHEMATICS AND TECHNIQUE DETAILS

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ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX: MATHEMATICS AND...
REFERENCES
 
Incident Scatter and Primary Fields
Monte Carlo studies (12,13) were used to simulate the x-ray energy reaching a 4-cm-diameter circle at the center of mass of a semicircular breast phantom, and the data were tallied. The tally represented the energy (E) and angle () distribution of scattered and primary x-ray photons exiting the center of the caudal surface of the breast. For each breast thickness and x-ray spectrum, the scattered photon distribution exiting the breast, S(E,), was computed by using 108 incident photons. The primary photon distribution exiting the breast, P(E,), where P = 0 for > 0, was also tallied.

Grid Transmission
The algorithm used to calculate grid transmission essentially used a large image of the grid combined with vector-based graphical routines to calculate the thickness of septa and interspace materials intersected by each photon impinging on the grid. All grids simulated had thicknesses that were spatially invariant. Thus, the three-dimensional properties of the grid could be accurately modeled by using a two-dimensional "picture" of the grid, in addition to the known grid thickness. Conceptually, a 2 by 2-million pixel "image" of the grid, with 1 x 1-µm pixel dimensions, was used. For the linear and cellular grids modeled in this study, two orthogonal projections of the image completely describe the grid geometry and were used instead of a full matrix (thus requiring 4 Mbyte instead of 4 Tbyte of memory). This technique was necessary to ensure that x-ray pathlengths through orthogonal septal intersections were determined accurately. The simulation parameters were sufficient to accurately calculate the septal and interspace pathlengths of scatter incident on grids at angles from 0° to 89°, for grids up to 17 mm thick. Since grid designs are periodic, the evaluation of grid properties need only be performed on one period of the grid (which we call the structural unit), the pattern of which repeats itself over the grid surface. Once each grid design was characterized, primary and scattered photons were simulated to be incident on the grid. Photons with energies from 1 to 50 keV (in 1-keV intervals) were incident on the grid at angles ranging from 0° to 89°, in 1° intervals. The probability of grid transmission for an incident photon with energy E and incident angle was computed by averaging the transmission probability over the grid’s structural unit and over all azimuthal scatter angles (0–2). The sampling used for numerical integration was sufficiently small (spatial sampling 10–150 µm, angular sampling 10°–20°) to obtain relatively artifact-free grid transmission functions. This technique described herein is numerical integration, and therefore no stochastic noise is induced by this procedure. For each photon incident on the grid, the pathlengths through both the septa and interspace were computed to within 1 µm, and the Lambert-Beers law was used to compute the probability of grid transmission, G(E,).

Scattered or characteristic photons produced within the grid were not modeled in this investigation. Given the relatively low x-ray energies studied and the high atomic number of the grid septa, the scattering cross section is low. For example, at 10 keV the scattering cross section (Rayleigh and Compton) relative to the total cross section is 0.7%, 0.6%, and 2.6% for nickel, copper, and lead, respectively. These values increase only to 4.8%, 4.6%, and 5.0%, respectively, at 30 keV. The K edges of the nickel (Z = 28) and copper (Z = 29) septa modeled are at 8.30 and 9.84 keV, respectively, and the L edge of lead is at 14.71 keV. For nickel and copper, the K-shell fluorescent yield is about 40%, and the L-shell fluorescent yield of lead is about 20%. Furthermore, the mean free path (1/µ) of the characteristic x-ray photons produced in the septa are 24, 28, and 6 µm, respectively, for nickel, copper, and lead. While primary transmission through the interspace material was modeled accurately, scattering in the interspace material was not computed. For modern grids using carbon fiber, very little scattering occurs; however, for the comparisons with early aluminum-interspaced grids, some discrepancies may occur.

Detector Absorption
A 34 mg/cm2 Gd2O2S intensifying screen (Min-R; Kodak, Rochester, NY) was used as the principal detector for this study. The energy and angular dependence of photon energy absorption were computed by using the mass energy absorption coefficients for this phosphor (21), and this function was represented as D(E,). For comparison with the work of Farhig et al (4), in which a bismuth germanate detector was used, ideal detector absorption was assumed, D(E,) = 1.

Slot Scan Transmission
The performance of the slot scan systems was simulated without the use of a grid transmission function G(E,), just discussed. Instead, the field of view was narrowed to the slot width under study (ie, the slot ran lengthwise from the chest wall to the nipple in a craniocaudal mammographic projection), and the total scatter reaching the detector plane was integrated (even outside the slot dimensions). The primary radiation was calculated by using Monte Carlo techniques as well—primary photons were separated from scatter photons because the past history of each photon was known. An SID of 65 cm and an air gap of 1.5 cm were used, as with the grid simulations.

For the SMSA, the scatter spread function for a single slot was computed (Fig 4 inset), and this profile was essentially convolved with a comb function (evenly spaced -functions), where the spacing between combs is given by the separation between the centers of the slots (abscissa in Fig 4). Penumbra effects (which reduce the efficiency of slots) were not simulated.

The BF of a grid is related to how much the milliampere seconds of the examination needs to be increased (at the same kilovolt peak) to account for the presence of the grid. The BF calculated for a slot scan system or an SMSA is, however, not indicative of the increase in milliampere seconds that would be necessary. The milliampere seconds required for slot scan geometries is far higher, and this affects the practicality of such procedures due to x-ray tube loading constraints.

Calculation of Grid Performance Metrics
The scatter energy deposited in the detector was calculated as:

The scattered signal in the absence of a grid, S0, was calculated by using Equation A1, where G(E,) = 1. The signal produced by the primary x-ray beam deposited in the detector was computed as:

The primary signal in the absence of a grid, P0, was calculated by using Equation A2 where the grid transmission at all energy and angles was unity.

Various other parameters related to grid performance can be calculated from the values of S, S0, P, and P0. The primary transmission, Tp, is given by P/P0, and the scatter transmission (Ts) is given by S/S0. The BF is related to the CIF by the following relationship: Tp = BF/CIF. The selectivity, , is given by the ratio Tp/Ts. The BF is an important parameter used in grid analysis and is given by the following equation:

The BF is (essentially) the increase in x-ray technique (milliampere seconds) required to compensate for the reduced amount of radiation striking the detector due to the presence of the grid, compared to when a grid is not present. Since scattered radiation contributes to the radiation levels at the detector, even perfect antiscatter devices will have BFs greater than unity. For electronic (digital) detectors with large dynamic range and adjustable sensitivity, the BF is more conceptual, since the increase in exposure required to replace the signal lost due to the scatter reduction can be implemented by increasing the electronic gain of the detector instead of increasing the x-ray exposure.

The contrast degradation factor, CDF, attributable to scattered radiation in the absence of a grid is given by the following equation:

In the presence of a grid, the CDF becomes

and for any useful grid, CDF < CDF0. The CIF of an antiscatter technique is given by the ratio

 

     REFERENCES

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ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX: MATHEMATICS AND...
REFERENCES
 

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