Contrast-enhanced dual-energy subtraction imaging using electronic spectrum-splitting and multi-prism x-ray lenses
Erik Fredenberg, Bjorn Cederstrom, Mats Lundqvist, Carolina Ribbing, Magnus Aslund, Felix Diekmann, Robert Nishikawa, Mats Danielsson
This is the submitted manuscript of:
Fredenberg, E., Cederström, B., Lundqvist, M., Ribbing, C., Åslund, M., Diekmann, F., Nishikawa, R. and Danielsson, M., “Contrast -enhanced dual-energy subtraction imaging using electronic spectrum-splitting and multi-prism x- ray lenses,” Proc. SPIE 6913, Medical Imaging 2008: Physics of
Medical Imaging, 691310 (2008).
The published version of the manuscript is available at: https://doi.org/10.1117/12.770501 All publications by Erik Fredenberg: https://scholar.google.com/citations?hl=en&user=5tUe2P0AAAAJ ontrast-enhanced dual-energy subtraction imaging usingelectronic spectrum-splitting and multi-prism x-ray lenses
Erik Fredenberg, a Bj¨orn Cederstr¨om, a Mats Lundqvist, b Carolina Ribbing, c Magnus ˚Aslund, b Felix Diekmann, d Robert Nishikawa, e and Mats Danielsson aa Department of Physics, Royal Institute of Technology (KTH), AlbaNova University Center,106 91 Stockholm, Sweden; b Sectra Mamea AB, Smidesv¨agen 5, 171 41 Solna, Sweden; c The ˚Angstr¨om Laboratory, Uppsala University, 751 21 Uppsala, Sweden; d Department of Radiology, Charit´e - University hospital, Charit´eplatz 1, 101 17 Berlin,Germany; e Deptartment of Radiology, University of Chicago, Chicago, IL, 60510, USA;
ABSTRACT
Dual-energy subtraction imaging (DES) is a method to improve the detectability of contrast agents over a lumpybackground. Two images, acquired at x-ray energies above and below an absorption edge of the agent material,are logarithmically subtracted, resulting in suppression of the signal from the tissue background and a relativeenhancement of the signal from the agent. Although promising, DES is still not widely used in clinical practice.One reason may be the need for two distinctly separated x-ray spectra that are still close to the absorption edge,realized through dual exposures which may introduce motion unsharpness.In this study, electronic spectrum-splitting with a silicon-strip detector is theoretically and experimentallyinvestigated for a mammography model with iodinated contrast agent. Comparisons are made to absorptionimaging and a near-ideal detector using a signal-to-noise ratio that includes both statistical and structural noise.Similar to previous studies, heavy absorption filtration was needed to narrow the spectra at the expense of alarge reduction in x-ray flux. Therefore, potential improvements using a chromatic multi-prism x-ray lens (MPL)for filtering were evaluated theoretically. The MPL offers a narrow tunable spectrum, and we show that theimage quality can be improved compared to conventional filtering methods.
Keywords: mammography; contrast-enhanced; dual-energy subtraction; x-ray optics; multi-prism lens; energyfiltering;
1. INTRODUCTION
Contrast agents are used within many fields of medical x-ray imaging to improve the contrast between structuresof similar density and atomic number. In particular, tumors are enhanced since the angiogenesis associatedwith the growth of lesions leads to an increased permeability and retention of the agent. The visibility ofbreast tumors can for instance be improved in computed tomography by intravenous administration of iodinatedcontrast agent. For standard screen-film or even digital mammography, however, the relatively low contrastresolution limits the detectability even of contrast-enhanced lesions. To emphasize the agent above what is possible with plain absorption imaging, contrast-enhanced dual-energysubtraction imaging, here referred to as dual-energy subtraction (DES) imaging, has been proposed and inves-tigated for mammography and other x-ray imaging modalities.
It relies on the fact that, at a materialspecific energy, the absorption coefficient of the contrast agent changes rapidly. A so called absorption edge iscaused by the radically increased cross section for photoelectric interaction between an incident photon and an
Electronic mail: [email protected] tom in the material as the photon energy reaches the binding energy of an atomic shell. Iodine, for instance,has a K absorption edge at 33.2 keV. To perform DES imaging, two images are acquired simultaneously orconsecutively with two different energy spectra; one with a mean energy below and one with a mean energyabove an absorption edge of the contrast agent. By combining the two images in the logarithmic domain, thesignal from any pair of materials in the object can be made to cancel, for instance glandular and adipose tissuein mammography. Constituents with a different attenuation shift between the high and low energy images arestill visible, and the signal from the contrast agent can hence be enhanced over a cluttered background.To efficiently perform DES imaging it is important to use two narrow spectra straddling the edge. One wayof providing the two spectra is to use two different anode materials with appropriate absorption filtering.
2, 4
Drawbacks of this dual spectra (DS) approach include the need for two separate exposures, and a limitedeffectiveness due to the large spread of the spectra and low flexibility in the choice of anode materials. Theseare two reasons to why DES, although an old idea, has not yet evolved into routine clinical practise.Another option to provide the two spectra is to center a single absorption filtered spectrum on the absorptionedge and use an energy sensitive detector, for instance a sandwich detector or two different detector materials, to split the spectrum electronically at the edge. One recently developed detector that has been briefly investigatedfor DES imaging is a photon-counting silicon-strip detector with two energy thresholds. It is similar to thedetector in an existing full-field digital mammography system. The performance of electronic spectrum splitting(ES) depends on how much the spectrum can be narrowed down around the edge. When absorption filteringis used there is thus a trade-off between image quality and efficiency since heavy absorption filtering and a lowacceleration voltage result in poor photon economy.The multi-prism lens (MPL) is a refractive x-ray lens with chromatic properties, which has been shown towork well at x-ray energies relevant to mammography. It can be employed as an energy filter, discriminatingagainst high as well as low energy photons, thus providing a narrow spectrum with better photon economy thanis achievable with absorption filtering. MPL filters can potentially improve on both the DS and ES approachesfor DES imaging. Narrow spectra can be produced at arbitrary energies from a wide tungsten spectrum, thusreducing the energy spread and eliminating the need for two anode materials in the DS method. Alternatively,ES of a single MPL-filtered spectrum tuned to center around the energy of the absorption edge provides moreoptimal conditions for subtraction imaging than is practically achievable with absorption filtering. In addition,the tunability of the MPL filter opens up the possibility to use contrast agents with absorption edges closer to theideal imaging energies of the imaged object, thus providing a regular absorption image of high quality in additionto the DES image. Zirconium with a K-edge at 18.0 keV has for instance been suggested for mammography. In this study, ES will be further investigated for the aforementioned silicon-strip detector in a mammographymodel with iodinated contrast agent. The improvement over absorption imaging, and the efficiency comparedto a near-perfect detector is evaluated experimentally. A theoretical model including detector imperfections isdeveloped and verified by measurements. By using this model, the potential improvement of ES by MPL filtersis evaluated. Investigations of MPL filters for the DS approach and the possibility to use novel contrast agentsare left for future studies.
2. MATERIAL AND METHODS2.1. Dual energy subtraction
Two different methods for calculating DES signals appear frequently in the literature; the weighted logarithmicsubtraction method,
2, 5, 10 and the material basis plane decomposition method.
3, 4, 6
In this study, the formerapproach will be used.The number of counts in a detector, assumed ideal, from an energy interval Ω of an impinging spectrum I ( E ) = N Φ( E ) after passing a breast of thickness d and linear attenuation coefficient µ ( E ) is n = N (cid:90) Ω Φ( E ) · exp( − µ ( E ) d ) · d E, (1)here N is the number of impinging photons and Φ( E ) is the spectral distribution with sum unity. Then, usingindices hi and lo to denote high and low energy bins, respectively, the subtracted intensity of the DES image iscalculated with the weighted logarithmic subtraction method according to I S = ln n hi − w ln n lo (2)= ln N , hi − w ln N , lo + ln (cid:90) Ω Φ hi ( E ) · exp( − µ ( E ) d ) · d E − w ln (cid:90) Ω Φ lo ( E ) · exp( − µ ( E ) d ) · d E, where w is a weight factor. Since the first two terms are constant, they will cancel when forming the DES signaldifference between two areas in the breast with different attenuation,∆ S S = (cid:175)(cid:175) I − I (cid:175)(cid:175) , (3)and hence the signal difference is independent of exposure.In this study, w was chosen so as to minimize the noise from the anatomical background, in accordance withprevious studies. Although disregarding the statistical noise and the iodine signal, this procedure will generallyresult in the optimal image quality, as is further discussed in Section 2.4. The anatomical noise was calculatedas the standard deviation of I S measured over a range of glandular fractions, g i ; σ w ( w ) = (cid:195) m − m (cid:88) i (cid:104) I S ( g i , w ) − I S ( w ) (cid:105) (cid:33) / . (4)Note that this quantity is also exposure-independent. For the optimization, w was chosen so that σ w is minimizedwhen using a linear function g i from 0.1 to 0.9. DES measurements with ES were performed in a set-up similar to a scanned-slit mammography geometry (Fig. 1).The source is a 0 . ×
12 mm tungsten target x-ray tube ∗ with variable acceleration voltage 10-60 kVp. It isviewed at a 2 . ◦ anode angle, which yields an effective source size of approximately 400 × µ m. The x-raybeam was filtered with aluminum absorption filters and collimated with a slit before passing the object andreaching the detector.Two different detector assemblies were used for the measurements; a cadmium-zinc-telluride (CZT) compoundsolid-state detector † with approximately 1 keV energy resolution to simulate nearly perfect spectrum splitting,and a silicon-strip detector with two energy thresholds to simulate more realistic conditions for medical imaging.The one pixel CZT detector was coupled to a 500 channel multi-channel analyzer, which was read out by acomputer. In that way, the energy threshold for splitting the spectrum can be set with good resolution andadjusted after the experiment.The silicon strip detector is 128 pixels wide with a 50 µ m strip-pitch in an edge-on arrangement. It iswire-bonded to a 128-channel pulse-counting application specific integrated circuit (ASIC) equipped with twoadjustable energy thresholds for each channel. To reject noise, the low-energy threshold was set to discriminateagainst pulses below approximately 5 keV. The high-energy threshold was set to approximately 33 keV, corre-sponding to the K-edge of iodine. The detector assembly is thus photon-counting with virtually no electronicnoise present, and all detected photons are divided into two bins according to their energy.Between the collimator slit and the detector, a motorized stage was placed to scan an object across thebeam and thus acquire an image. The phantom that was used for the measurements is made up of three parts(Fig. 1). A 10 mm thick polymethyl methacrylate (PMMA) slab has containers 1-9 mm deep which were filledwith iodinated contrast agent. ‡ The iodine concentration was approximately 3 mg/ml, which has been foundto be a realistic concentration for tumor uptake. In front of the PMMA slab is placed a 35 mm thick PMMA ∗ Philips PW2274/20 with high tension generator PW1830 † Amptek XR-100T-CZT ‡ Ultravist 370, BayerSchering, Germany etectorcollimator objectsource
SID filter PMMA box PMMA slabiodine containersPMMA - oil wedge
Figure 1. Top:
The set-up used for the DES experi-ments, where the detector is either a CZT or a silicon-strip detector.
Bottom:
The phantoms; a 35 mmthick PMMA box filled with PMMA and olive oil tosimulate breast tissue, a 1 cm PMMA slab with 9 io-dine containers ranging from 9 to 1 mm (only 4 areshown for clarity), and a PMMA-to-oil wedge phan-tom to simulate a range of glandularities. source slit polychromatic radiation y y d t d s s o s i transmitted peak energy image partially blocked non-peak energy image object detector d g d t L transmitted peak energy image object quasi-monochromatic radiation d i s d Figure 2.
The theoretical MPL set-up with s o =759 mm and s i = 310 mm. A d s = 10 µ m slit inthe image plane of the lens blocks radiation that is outof focus before passing the object. The lens has toothheight d t = 100 µ m and focal length 220 mm. box which can be filled with PMMA and olive oil in different compositions to simulate breast tissue. PMMAcylinders with diameters 5-10 mm immersed in oil were used to simulate anatomical clutter, and a 1.75 cm thickPMMA slab in oil was used to simulate a homogenous breast with 50% glandularity. PMMA and olive oil werechosen because the difference in linear attenuation is close to the difference for fibroglandular and adipose breasttissue. There is also a wedge phantom composed of PMMA and oil with PMMA fractions ranging from 10% to90% to simulate a variety of glandularities. The average glandular dose (AGD) to the phantom was calculatedby applying normalized glandular dose coefficients to a measured spectrum. To verify the experimental results and to make further predictions, the experiment was modeled using theMATLAB software package § with published linear absorption coefficients as input.Several detector effects have to be taken into account. As for the CZT detector, it suffers from hole-tailingdue to trapped charges in crystal imperfections, and from a limited energy resolution due to the small amount ofelectron-hole pairs that are released at each photon interaction event. Although hole-tailing extends only in thenegative energy direction (charges are lost) and both of the effects might vary with energy, for simplicity theywere joined into a gaussian that was convolved with the high and low energy spectra. The quantum efficiency ofthe 2 mm thick CZT crystal with the 0.3 mm beryllium window in front was also taken into account.The silicon strip detector does not suffer from hole-tailing to any large extent, but the limited energy resolutiondue to a low number of released charge pairs is present and was again modeled by a gaussian. Additionally,all thresholds are set separately for individual channels and therefore vary somewhat. This effect degrades theenergy resolution further and was modeled by convolving the spectrum with another gaussian. The 500 µ mthick silicon wafer was arranged at an angle of 4 ◦ , which yields an effective detector thickness of 7.2 mm, and § The MathWorks Inc., Natick, Massachusetts he quantum efficiency could be calculated accordingly. No secondary interactions of scattered photons wereconsidered. Charge sharing is a fourth effect that has to be taken into account for the position sensitive silicon-strip detector. If a photon interacts close to the midpoint between two strips, some charge might spill over to theadjacent strip and two photons of lower energy are detected instead of one high-energy photon. The ASIC thatwas used for the experiment is equipped with anti-coincidence logic which rejects the lowest pulse and puts thehighest pulse in the high-energy bin regardless of pulse height. These effects have been investigated previouslyfor a similar detector, and the same calculations were applied here to model the effect.Several of the model parameters mentioned above are unknown and the model was bench-marked to theexperiments. The iodine concentration, first of all, may not be very exact, and was therefore measured in theabsorption images. Secondly, the width of the energy resolution gaussian for both detectors was set so thatthe theoretical subtraction signal from the iodine containers matched the measurements with the CZT detector.The threshold resolution of the silicon detector, finally, was set so that the iodine signal in the acquired imagesmatched the model. There is no standard method to quantify the image quality in DES, and we introduce a figure-of-merit basedon the signal-difference-to-noise ratio (SDNR). This SDNR must take into account both the structural noisefrom the anatomical clutter as well as the statistical noise. It is important to realize that these have completelydifferent frequency distributions. Also note that we are here interested in large targets (tumors with iodineuptake), i.e. low spatial frequencies. Observer models based on integration of the signal template and NEQ(f)were not used, partly due to that the experimental data was too limited for reliable NPS caluclations. Insteadwe choose a crude method in the spatial domain, where the noise is quantified by the standard deviation of thebackground. This, however, is not just done on a pixel basis. Instead the image is subsampled (binning withoutchanging the image average) into ROIs of variable size. This ROI size ( M × M pixels) corresponds to the sizeof the details in the image that we are interested in. The method is obviously related to the NEQ-integration,since the image binning corresponds to a sampling of the NPS, in which high spatial frequencies are suppressed.We define our figure-of-merit throughSDNR tot,M = | S target − S bg | σ tot,M = | S target − S bg | (cid:113) σ quant,M + σ clutter,M (5)We will assume that the system is quantum limited. After the logarithmic subtraction the quantum noise isgiven by (since the noise is small compared to the signal and ln(1 + x ) ≈ (1 + x ) for x (cid:191) σ quant, = 1 /N hi + w /N lo . (6)For a system with white noise only we have σ quant,M = σ quant, /M, (7)whereas we expect a much smaller reduction of σ clutter,M with increasing M due to the lumpiness of the structure.The wedge-based definition of anatomical clutter noise, σ w , used for optimization of w is not a realistic onehere, since it would overestimate the relative importance of anatomical noise. To obtain a more realistic estimate,60 mammograms in CC projection were analyzed and σ clutter,M was calculated in a 60 ×
60 mm region for eachimage and a few values of M . At a ROI size of 1 mm ( M = 20 since the pixel size is 50 µ m) it was found thatthe variation expressed in glandular fraction g was σ g,M =20 = 0 .
06. The standard deviation showed a linearrelation in the range of M -values between 20 and 100, and extrapolation to M=1 gave σ g, = 0 .
08. To calculate σ clutter,M , Eq. 4 is integrated over a gaussian distribution of g with mean 0.5 and standard deviation σ g,M .Due to the different characteristics of quantum noise and anatomical noise, and that the two types of noiseare affected very differently in DES, we expect to see a large dependence of our figure-of-merit on the ROI size. .55 0.6 0.65 0.7 0.75 0.8 0.85024681012141618 w S D N R Clutter−SDNRQuantum−SDNRTotal SDNR Peak = 1300at w = 0.70
Figure 3.
Calculated SDNR tot as a function of theweighting factor. In this case M = 20, i.e. S D N R Clutter−SDNRQuantum−SDNRTotal SDNR
Peak = 1050at w=0.70
Figure 4.
Calculated SDNR tot as a function of theweighting factor. In this case M = 4, i.e. A multi-prism lens (MPL) consists of two rows of prisms facing each other at an angle and symmetrically arrangedaround the optical axis (Fig. 2). The lens halves touch at the entrance side and are separated by a distance atthe exit side of the lens. Rays entering the lens at the periphery will encounter more prisms than will centralones, and will therefore experience a larger refraction. Imaging with an MPL is one dimensional, and since therefractive index varies as E − at energies ( E ) and lens materials considered here, the lens is chromatic, thushaving different focal lengths for different x-ray energies. By placing a slit at the image plane of a particularx-ray energy ( E peak ) this energy can be picked out, whereas other energies are out of focus and preferentiallyblocked by the slit. The focal length, and thereby E peak , can be tuned by varying the angle between the lenshalves in an otherwise fixed geometry.Due to practical and time constraints a DES image acquired using the MPL could not be prepared for thisinvestigation. Nevertheless, Fig. 2 shows a schematic of an MPL set-up which is theoretically investigated inthis study. A 61 mm long epoxy lens with teeth of height 100 µ m is placed 759 mm from a 24.5 µ m source,thus providing a 10 µ m image 310 mm from the lens at a focal length of 220 mm according to the Gaussian lensformula. A slit of the same width as the image is placed in the image plane, and E peak is tuned by changing theangle between the lens halves. The spectrum of the filtering set-up is calculated using a geometrical model, andis adjusted so as to center on the K-edge of iodine. Published linear absorption coefficients and semi-empiricaldata on atomic scattering factors served as input to calculate absorption and refraction. All MPL filteredspectra are additionally filtered with aluminum in order to reduce the low energy tails.
3. RESULTS3.1. Theoretical results
Our dual-energy figure-of-merit, SDNR tot , was calculated for a number of different detector conditions and x-rayspectra. The same quantity was also calculated for the case of plain absorption imaging, and an SDNR-gaincould be calculated. The results are summarized in Table 1 for an AGD of 1 mGy in all cases. The SDNR-gainis given for M -values 1 and 20, corresponding to the pixel size 50 µ m and a ROI size of 1 mm, respectively. Notethe vastly different SDNR-gains associated with these two scales. The dependence on scale is further illustratedin Figs. 3 and 4, where SDNR tot is plotted as a function of w for ROI sizes of 1 mm and 0.2 mm, respectively.Also included is the SDNR taking only statistical noise into account as well as the clutter-only SDNR. In both able 1. Calculated SDNR at an AGD of 0.5 mGy for different spectra and detector parameters.. w opt SDNR tot gain SDNR tot rel. idealpixel 1 mm ROI 1 mm ROI
45 kV, 2 mm Al, Ideal detector 0.60 0.91 12.8 1.0045 kV, 2 mm Al, Spectroscopic detector used for exp. † ‡ ‡ † Non-pixelated CZT-detector with multi-channel analyzer ‡ Perfect energy resolution, no threshold variation, but charge-sharing includedcases the quantum noise is completely dominant. Since clutter is removed so effectively, the dependence on w is not so large. In fact, for the 0.2 mm ROI, clutter noise is so relatively insignificant that the optimum w isshifted from the value that minimizes the clutter residual.For conventional absorption imaging the opposite holds; anatomical clutter noise clearly dominates exceptfor M close to one. This means that in terms of noise our SDNR gain essentially boils down to σ absclutter /σ DESquant ,and that maximizing the iodine signal is more important than minimizing the clutter.
The iodine signal was measured with a homogenous 50% distribution of PMMA in the box in front of the iodinecontainers. Fig. 5 shows the absorption contrast as a function of depth of the iodine containers for both detectors,along with the model predictions for an iodine concentration of 3 mg/ml. If the model concentrations are matchedto the measured signals, concentrations of 3.45 and 3.75 mg/ml are obtained for the CZT and silicon detectorsrespectively. These concentrations are reasonable considering the measurement uncertainty when preparing theiodine solution. The DES signals are shown in Fig. 6. A gaussian energy resolution with a full-width-at-half-maximum (FWHM) of 1 keV for both detectors, and a threshold resolution of 0.8 keV FWHM matched themodel to the least square fit of the experimental results when assuming the above iodine concentrations. Sincethe silicon detector does not suffer from hole tailing, a somewhat better energy resolution can be expected thanfor the CZT detector. The threshold resolution is on the other hand most likely worse than 0.8 keV.Variations in the detected signals are likely due to two different effects; variation in the x-ray tube output and,for the silicon detector, drifting energy thresholds. Due to a limited detector area and count rate, in particularfor the CZT detector, the measurements required several hours each, and the tube output cannot be assumedconstant during this time. A drifting low-energy threshold of the silicon detector would affect the total numberof detected photons, thus altering absorption and subtraction signals. A drifting high-energy threshold affectsthe balance between the high- and low-energy bins, and thus the subtraction signal.
Measurements on the PMMA-to-oil wedge phantom isolated σ w so that w opt could be determined and the effectof anatomical noise subtraction visualized. Fig. 7 shows the standard deviation of the wedge signal for PMMA c o n t r a s t [ % ] CZT (M)Si (M)CZT (T)Si (T)
Figure 5.
The absorption contrast as a function ofdepth of the iodine containers for both detectors, alongwith model predictions for an iodine concentration of3 mg/ml. Outliers were removed from the data set.Statistical errors are too small to be visualized witherror bars. s S CZT (M)Si (M)CZT (T)Si (T)
Figure 6.
The DES signal difference (∆ S S ) as a func-tion of depth of the iodine containers. The model hasbeen matched to fitted experimental results. Error barscorrespond to one standard deviation statistical uncer-tainty. The DES signals of the two detectors refer toslightly different iodine concentrations and are there-fore not directly comparable. fractions 0.1-0.9 as a function of w. Optimal weight factors are found at the minima and are w opt = 0 .
63 and0.72 from experiment for the CZT and silicon detectors respectively. The effect of the weight factor is illustratedin Fig. 8, showing ∆ S s between the wedge and a PMMA fraction of 0.5 for weight factors differing from theoptimal one. To simulate anatomical clutter, the PMMA box was filled with 5 and 10 mm PMMA cylinders which wereimmersed in olive oil. The resulting absorption image at an AGD of 0.5 mGy is shown in Fig. 9, and Fig. 10shows the DES image calculated with w = 0 .
72 as determined from the wedge phantom. The 5 deepest iodinecontainers (down to 5 mm) are clearly visible. Containers 4 mm and below might also be visible, but in thatcase several false positives with the same contrast are present in the image. These false positives are again dueto drifting energy thresholds and a changed tube output. In fact, the scan stripes of the detector are clearlyvisible in the image. Although severe in this study, these problems would have less impact in a full-scale systemwhere the signals from many detectors are added and acquisition times are in the order of 10 s.To compare the phantom structure to the theoretical clutter noise based on real mammograms, a 400 by 400pixel region without iodine containers were used to calculate the PMMA-fraction standard deviation σ g,M =20 .The result was 0.08, which is close to the value of 0.06 from real mammograms. Although a crude phantom, thisshows that the resemblance to a real anatomical background is good enough for the present study. From the clutter image, a 20 ×
20 mm region without iodine containers was selected for calculation of σ tot,M fora number of M -values in the range 1 to 40. Fig. 11 shows σ tot, as a function of the weight factor (note that thismeasurement is different from the one in Fig. 7 although the plots look similar). The quantum noise seems to beabout twice as high as expected from theory, which was corroborated by a similar measurement in a DES imagewithout clutter. This is due to correlated detector noise which was not included in the theory. The detectornoise can be incorporated into σ clutter,M by substituting M for an effective M eff in Eq. 7. For M =[2, 4, 10,20] we measured M eff , DES =[1.9, 3.5, 6.2, 7.8] in a DES image without clutter. For the conventional absorption .4 0.5 0.6 0.7 0.8 0.90510152025303540 w R M S x CZT (M)Si (M)CZT (T)Si (T)
Figure 7.
The standard deviation of the DES signalfrom the PMMA-to-oil wedge phantom as a function ofthe weight factor ( w ) for both detectors as determinedby experiment and modeling. s i g n a l CZT (M)Si (M)CZT (T)Si (T) w opt − 0.15 w opt w opt + 0.15 Figure 8.
The signal difference between a range ofPMMA fractions and a fraction of 0.5 for the optimalweight factor and factors differing from the optimum. [mm] [ mm ] Figure 9.
An absorption image of the anatomical clut-ter phantom with 1-9 mm iodine containers at 45 kVand 2 mm aluminum filtration. [mm] [ mm ] Figure 10.
The corresponding DES image calculatedwith w = 0 . . The five deepest holes are visible. image of the same phantom we got M eff , abs =[2.0, 4.0, 9.5, 17], which shows that this effect is mainly in the DESimage.The measured total noise and the iodine DES signal difference gives the SDNR tot . The same measurementin the plain absorption image enables a calculation of the SDNR gain, which is plotted as a function of M inFig. 12. Also included are the teoretical SDNR gain curves, with and without correction for the measured M eff .As can be sen in the image, M eff , DES overcorrects the quantum noise. We believe this is due to a particularyhigh upper threshold variation in the image used for the measurement of M eff , DES . .5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9024681012 w ClutterQuantumTotalMeasured R M S x Figure 11.
Total noise measured in the clutter DESimage as a function of the weighting parameter, com-pared to the theoretical noise components and sum.ROI size is 1 mm ( M = 20). S DNR t o t ga i n TheoryTheory, M eff,sum
Theory, M eff,DES
Measured
Figure 12.
Measured SDNR gain of the DES imagecompared to the absorption image as a function of ROIsize. Also included are theoretical values, with andwithout compensation for the measured M eff . An MPL filtered 45 kV tungsten spectrum with 1 mm Al additional filtration is shown in Fig. 13 together withspectra filtered with 2 and 4 mm of aluminum. All spectra in Fig. 13 are normalized to unity total intensity,to visualize the spectral shape. The relative efficiency of the filtering methods can be appreciated from Fig. 14,which indicates that the lens increases the flux approximately an order of magnitude at the gain peak due toits focusing properties. This, however, is not necessarily the case since the lens spectrum was measured using asmaller focal spot, which is essential to obtain a narrow gain peak.The theoretical efficiency of the MPL filter for DES imaging is summarized in Table 1. If the lens is coupledto the silicon-strip detector it increases the SDNR by 40% compared to the 45 kV spectrum filtered with 2 mmaluminum. The limited energy resolution reduces the SDNR by 15% compared to 10% for the conventionalspectrum. This is to be expected since a limited energy resolution is more important for a spectrum concentratedaround the K-edge.
4. DISCUSSION
Two detectors were used in this study; a non-pixelated CZT detector to simulate perfect conditions for ES, and asilicon detector for simulating realistic conditions for medical imaging. For the latter, a lower quantum efficiency,a somewhat worse energy resolution, and charge sharing combined degrade the SDNR by 45%. Charge-sharingalone is responsible for 30% SDNR loss, but the effect is mitigated by the anti-coincidence logic of the ASIC.Without this feature each shared event would be registered as either two lower-energy photons or one in eachenergy bin, and the SDNR loss due to charge sharing would be 45%. An improvement of the logic with respectto DES imaging would be to discard all shared photons, to put them in a separate bin, or, ideally, to add theenergy of the two photons. In the present implemention, the merit of the anti-coincidence logic is primarily toimprove spatial resolution and provide the correct statistical weight to each photon.Since the difference in linear attenuation coefficients between adipose and fibroglandular tissue is similar tothe difference between PMMA and olive oil, in the ideal case tissue subtraction as well as iodine DES signalwould be similar to a real breast. This is not totally correct since the iodine solution contains water and whenusing a weight factor optimized to reduce the contrast between PMMA and olive oil, the water DES signal willbe negative relative the iodine signal The iodine signal is thus reduced by approximately a factor of two in the S p e c t r a l d e n s i t y ( n o r m a l i z e d ) K−edge
Figure 13.
An MPL + 1 mm aluminum filtered 45 kVtungsten spectrum together with absorption filteredspectra. The integrated density of all spectra is nor-malized to unity.
10 20 30 40 5000.51.01.52.02.53.03.54.04.5 E [keV] T r a n s m i ss i o n Figure 14.
The transmission of the MPL compared toabsorption filtering. present study. In the real case, this will be of less importance since the linear attenuation of both water andcancerous tissue is similar to the attenuation of glandular tissue and will thus yield a DES signal much smallerthan the one from iodine.Generally speaking, a narrower spectrum that is centered on the absorption edge is more efficient for DESimaging than a broader one. The MPL filter therefore improves the SDNR compared to realistic absorptionfiltered spectra (Table 1). One should note, however, that a real detector with imperfect energy resolutioncannot make much use of the energy region near the K-edge. Thus, there is a tradeoff since this region willconstitute a larger fraction of the spectrum if the spectrum is narrowed down. This may indicate that the lenswould fair better if we use two spectra peaking some distance away from the K-edge on opposite sides in a DSapproach.It is not the objective of this work to compare the electronic spectrum splitting method to the dual spectramethod. Nevertheless, it can be argued that a drawback of the ES method is that the dose cannot be distributedfreely between the low and high energy regions in order to optimize the SNR, such as is the case for the DSmethod. This, however is not a serious drawback. If one scales the part of the spectrum above the K-edge bya constant factor, while keeping the total AGD fixed, one will find that it is optimal to double the dose in thehigh energy region. This, however, will only lead to a SDNR gain of 8%.
5. CONCLUSIONS
Contrast-enhanced dual-energy subtraction imaging using electronic spectrum splitting has been investigated ina mammography model with an iodinated contrast agent. A clinically feasible silicon detector was compared toa near-ideal one, and the improvement over absorption imaging was estimated using a signal-difference-to-noiseratio that takes into account statistical as well as anatomical noise. A theoretical model of the detectors wasbenchmarked to the measurements, and the model was used to investigate the influence of different detectoreffects and the potential improvement if introducing an energy filter based on a multi-prism x-ray lens insteadof plain absorption imaging.The silicon detector provides about 50% SDNR compared to the ideal case. Although far from ideal, itwas seen in the study that the detector still improves the detectability of iodine on a lumpy background. AnMPL filter coupled to the silicon detector would improve the SDNR 40% compared to the spectrum used inhe experiment. Although a much larger improvement is possible with perfect energy resolution, this is stillsignificant considering the fact that the experimental spectrum already has substantial absorption filtering witha correspondingly low dose rate. A thorough investigation that includes the different geometrical constraintson the MPL setup is, however, necessary before any final conclusions can be drawn on this topic. The limitedenergy resolution of the detector reduces the possible improvement by the MPL filter, and it might be moreadvantageous to employ the filter in a DS approach. This is, however, left for future studies.
ACKNOWLEDGMENTS
The authors wish to thank Alexander Chuntonov for setting up the silicon-strip detector.
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