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Spectral K-edge subtraction imaging

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2014 Phys. Med. Biol. 59 2485

(http://iopscience.iop.org/0031-9155/59/10/2485)

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Institute of Physics and Engineering in Medicine Physics in Medicine and Biology

Phys. Med. Biol. 59 (2014) 2485–2503 doi:10.1088/0031-9155/59/10/2485

Spectral K-edge subtraction imaging

Y Zhu1, N Samadi2, M Martinson3, B Bassey3, Z Wei4,G Belev5 and D Chapman4

1 McCaig Institute for Bone and Joint Health, University of Calgary, Calgary, AB,Canada2 Biomedical Engineering, University of Saskatchewan, Saskatoon, SK, Canada3 Physics and Engineering Physics, University of Saskatchewan, Saskatoon, SK,Canada4 Anatomy and Cell Biology, University of Saskatchewan, Saskatoon, SK, Canada5 Canadian Light Source Inc, 44 Innovation Boulevard, Saskatoon, SK, Canada

E-mail: yingzhu@ucalgary.ca

Received 4 November 2013, revised 7 March 2014Accepted for publication 27 March 2014Published 28 April 2014

AbstractWe describe a spectral x-ray transmission method to provide images ofindependent material components of an object using a synchrotron x-ray source.The imaging system and process is similar to K-edge subtraction (KES) imagingwhere two imaging energies are prepared above and below the K-absorptionedge of a contrast element and a quantifiable image of the contrast elementand a water equivalent image are obtained. The spectral method, termed‘spectral-KES’ employs a continuous spectrum encompassing an absorptionedge of an element within the object. The spectrum is prepared by a bentLaue monochromator with good focal and energy dispersive properties. Themonochromator focuses the spectral beam at the object location, which thendiverges onto an area detector such that one dimension in the detector isan energy axis. A least-squares method is used to interpret the transmittedspectral data with fits to either measured and/or calculated absorption of thecontrast and matrix material-water. The spectral-KES system is very simpleto implement and is comprised of a bent Laue monochromator, a stage forsample manipulation for projection and computed tomography imaging, and apixelated area detector. The imaging system and examples of its applicationsto biological imaging are presented. The system is particularly well suited fora synchrotron bend magnet beamline with white beam access.

Keywords: x-ray imaging, synchrotron radiation, K-edge subtraction

(Some figures may appear in colour only in the online journal)

0031-9155/14/102485+19$33.00 © 2014 Institute of Physics and Engineering in Medicine Printed in the UK & the USA 2485

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1. Introduction

X-ray imaging with induced or endogenous contrast materials has been a well-establishedmethod of imaging function of biological systems. These x-ray imaging methods includeclinical angiography utilizing the enhanced absorption of the contrast material, temporalsubtraction imaging (Suhonen et al 2008) through images taken before and after the contrastmedium injection, and the K-edge subtraction (KES) imaging (Rubenstein et al 1986) whichlogarithmically subtracts two images taken above and below the K-edge of the contrastelement. The KES method improved sensitivity to the contrast element, provided quantifiablecontrast and tissue images, and the application in line scan mode allowed imaging of livingsystems subject to motion. Since the first proposal by Jacobson (1953), the synchrotronapplication of KES has been widely used in coronary angiography (Thompson et al 1984),cerebral angiography (Kelly et al 2007), neurovascular intravenous angiography (Schultkeet al 2005), bronchography (Rubenstein et al 1995), lung imaging (Suhonen et al 2008),mammography (Bornefalk et al 2006), lymphatic imaging (Kolesnikov et al 1995) and braintumor imaging (Adam et al 2005). Many KES implementations emerged taking two imageseither sequentially (Zhang et al 2008) or simultaneously (Thompson et al 1989) using an x-raytube (Baldazzi et al 2001) or a synchrotron source (Sarnelli et al 2007). For living systemsusing a synchrotron source, a bent Laue monochromator (BLM) is typically employed toprepare imaging beams above and below the contrast element K-edge which focus at theobject location and subsequently diverge onto a line detector (Suortti and Thomlinson 1988).Conventional KES prepares the two beams by utilizing a splitter that blocks approximately1/3 of the vertical beam size to prevent ‘edge crossing’ energies beyond the monochromator(Suortti et al 1993). The use of a splitter forces the above and below K-edge imaging beamsto cross at an angle which can cause a ‘crossover’ artifact due to the different paths of the twobeams. The crossover effect is most noticeable at the edges of highly absorbing objects, suchas ribs in human coronary angiography.

Multiple-energy x-ray absorptiometry (MXA) is a composition analysis technique derivedfrom the well-established dual-energy x-ray absorptiometry—that is routinely used in theclinical determination of bone mineral density and osteoporosis diagnosis. It shares similartheory with KES without specific designated energies bracketing an absorption edge of anelement. Reported MXA measurements were taken at a few energies (Jonson et al 1988,Kozul et al 1999, Schena et al 2003).

Since the 1990s, x-ray spectromicroscopy became a popular chemical imaging techniqueessentially in the soft x-ray regime (Kirz and Jacobsen 2009). It is a combined techniqueto perform the x-ray absorption near edge structure (XANES) or the extended x-rayabsorption fine structure using a scanning transmission x-ray microscope. Over the last decade,tomographic spectromicroscopy emerged for three-dimensional (3D) chemical imaging(Johansson et al 2007). It has high spatial and spectral resolution at a cost of time-consumingraster scan and energy traversal. A small volume was imaged at two or a few energies, whichsubstantially limited the performance of XANES analysis. It is desirable that the chemicalimaging or tomography could be quickly and easily performed on larger samples, for examplesmall animals.

Similar to the KES taking dual-energy images, a new spectrum-based imaging method isconceived to take an image of an object using typically hundreds of energies (E). Sincethis spectral imaging method is optimally applied with the spectrum encompassing anabsorption edge of an element within the object, it is named Spectral KES imaging (spectral-KES). The spectral-KES algorithm shows that spectral-KES is a generalized version ofKES and KES is a special case of spectral-KES. The spectral-KES proposed in this paper

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provides a new method for performing chemical imaging of small animals in the hardx-ray regime that is fast and easy through the use of a BLM. The spectral-KES systemextends the conventional KES system to include a small focus BLM and an area detectorbeyond the focus instead of a line detector. Instead of raster scan and energy traversal,spectral-KES only requires one line-scan motion to get a raw data cube of (x, y, E) withhundreds of energies simultaneously acquired in one shot (figure 1). The enabling technologyrelies on the spatial and spectral focusing of the BLM (Schulze et al 1998) when the single rayand geometric foci are matched. It has an important consequence that each ray has a uniqueenergy and thus the BLM prepares a convergent beam whose energy changed linearly acrossthe beam.

The spectral-KES system has several advantages compared to the conventional KESsystem. The simultaneously prepared energies eliminate motion artifacts in the image andallows for the imaging of living systems. It does not block the x-rays that are near or at theK-edge of the element thereby allowing much higher imaging flux since the x-rays in theorbital plane of the synchrotron source would be fully used. The small line focus of the BLMincreases the flux and dose onto the sample due to the focused beam. The crossover artifactscould be minimized by narrowing down the vertical beam size and allowing a smaller crossoverangle than a splitter-based system. Both the projection setup and computed tomography (CT)implementation of the spectral-KES system could be performed fast enough for imaging largersamples such as a small animal. Since the spectral-KES system instantly provides a full nearedge spectrum of the contrast material at every pixel width, it is a promising technique forperforming chemical imaging such as XANES analysis for spatially resolved contrast speciesgiven enough energy resolution, and multiple components analysis given sufficient attenuationvariations.

2. Rationales

If the imaging system assumes an object as a two-component system, a contrast materialand a matrix material, the projected contrast and matrix density images are calculatedfrom the spectral-KES raw data based on equation (A.3) with their signal-to-noise ratio(SNR) performance simulated using equation (A.5). Detailed derivations of the spectral KESalgorithms are described in the appendix.

The SNR for 1 mg cm−2 of projected iodine content and 1 g cm−2 of projected watercontent are simulated using equation (A.5) over an energy band of 450 eV while changingthe energy of the center beam (figure 2(a)). The calculation assumes a total incident fluxof 1 × 106 photon/pixel width and a vertical flux distribution which is simulated for thebeam after the BLM and from the biomedical imaging and therapy (BMIT) beamline bendmagnet (BM) source at the Canadian Light Source (CLS). Figure 2(a) clearly indicates thatimaging near the iodine K-edge, i.e. 33.17 keV or 33.06 keV, achieves an optimal SNR for theiodine image or water image, respectively. This simulation indicates that optimal SNR in thecomponent image is obtained when the spectral-KES algorithm is applied near an absorptionedge of the contrast material.

These calculations are based on the root-mean-square (RMS) averaging of the attenuationcoefficients over a 450 eV energy band. To investigate the optimal energy band that couldachieve the best SNR, the same calculation is repeated for a series of energy band, rangingfrom 27 to 900 eV (figure 2(b)). The solid curves of SNRC-sKES and SNRM-sKES indicate thatthere is an optimal energy band of 252 eV or 270 eV that reaches the maximal SNR for theprojected iodine or water, respectively. Interestingly, the center imaging energies that reachthe optimal SNR are deviating away from the iodine K-edge energy with increasing imaging

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Figure 1. Schematic diagram of the spectral-KES system.

(a) (b) (c)

Figure 2. (a) The SNRs of the iodine (bold curve with reference to the bold y-axis) andwater (thin curve with reference to the thin y-axis) images using spectral-KES (sKES)are simulated with changing center imaging energy. (b) The iodine (bold curves withreference to the bold y-axis) and water (thin curves with reference to the thin y-axis)SNRs using spectral-KES (solid curves) and KES (dashed curves) are simulated withchanging energy band. (c) The center imaging energy that achieves the maximal SNR(such as in (a)) are simulated with changing energy band. The spectral-KES simulationassumes 1 mg cm−2 iodine material, 1 g cm−2 water material and a total incident flux of1 × 106 photon/pixel width. The KES simulation assumes the same amount of iodineand water and the same incident flux distribution, but with the center third of the verticalbeam blocked.

energy band (figure 2(c)). For comparison, the KES SNRs are simulated as well for the sameamount of iodine and water, and the same incident flux distribution but with the center third ofthe vertical beam blocked. The simulation indicates that the spectral-KES performs better thanKES only for certain energy bands (around 100–500 eV), this matches well with the narrowbeam requirement to minimize the cross over artifact.

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(a)

(b)

(c)

(d)

(e)

(f)

Figure 3. The spectral-KES experimental setup includes a BLM (a) on a four-bar bender,direct beam stop (b), lead shielding (c) with an aperture, two bottles of 30 mg ml−1

sodium iodide and organic iodine solution (d) stacked on top of an ion chamber, tubesof iodine solution (e) on a sample stage and the Photonic Science detector (f) at the farend.

3. Methods

3.1. Experiment

For a BLM diffracting the iodine K-edge energy for the BMIT BM beamline at the CLS, the(3 1 1) diffraction from a Si (5 1 1) wafer provides an asymmetry angle which meets with the‘magic’ condition that the single ray and geometric foci are matched (Zhang 2009). Such aBLM was built by cylindrical bending of a 600 μm thick Si (5 1 1) wafer along (3 1 1) directionin a four-bar bender. This BLM was used with a pixelated area detector without blocking thex-ray energies at and near the iodine K-edge. Besides the advantages of higher imaging fluxand shorter imaging time, this is especially an advantage on beamlines with low critical energydevices such as BMs where the high energy component, for example the iodine K-edge energy,is more compressed to the orbital plane. The spectral-KES system was setup at the BMIT BMbeamline at the CLS (figure 3). While the BLM was placed in a filtered white x-ray beamfrom the BMIT BM beamline, the (3 1 1) diffraction near the iodine K-edge of 33.17 keVwas selected by an aperture in a leaded wall which was set between the BLM and the object.This leaded wall prevented other x-ray diffractions from the crystal and the scatter from thedirect beam stop from giving background and unnecessary dose to the object, beam monitoringionization chamber and the detection systems. The photon rate was monitored by an air-filled

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ionization chamber and was found to be 2.31 × 109 photons/sec/horizontal mr/mA ringcurrent with 0.11 mm of copper filter and 0.88 mm of aluminum filter in the beamline. Thisflux rate corresponds to a minimal energy bandwidth of 1.67%. The vertical beam size atthe BLM position was about 5 mm. At the focus, the vertical beam size was measured asapproximately 0.1 mm which corresponds to a maximum dose rate of 14.4 mGy s−1 at a ringcurrent of 250 mA. The sample was placed at or near the focus. The maximal dimension ofthe sample was typically less than 50 mm which allowed for minimal beam enlargement alongthe beam path due to convergence and divergence over the size of the object. The PhotonicScience detector (FDI VHR 90 mm, 18.7 μm pixel size, Photonic Science Ltd, UK) was placedabout 2.53 m downstream of the crystal and 1.03 m downstream of the object. Two bottles of63 mg cm−2 iodine filters, sodium iodide and organic iodine (Optiray R©240 Ioversol) solution,were used to analyze the beam.

3.2. Beam profile

Images of the beam with no object (figure 4(a)) and after organic iodine filter of 63 mg cm−2

(figure 4(b)) were obtained to analyze the beam profile. A normalized attenuation image(figure 4(c)) is calculated by taking negative logarithm of figure 4(b) after a dark imagesubtraction and normalization by figure 4(a). Thus, the figure 4(c) is proportional to the linearattenuation coefficient of the filter since its thickness is constant all over the image area. Theattenuation jump line near the vertical middle of the image was identified as the K-edge ofiodine, which was defined by the maximal slope vertically across the image (figure 4(c)). AK-edge line was fitted on the measured data and plotted as a black solid line in figure 4(d).

As more noises appeared on both sides of the beam (figure 4(c)) where the incident beamintensity was low, the beam edges were defined according to an arbitrary threshold of 1%of the maximal intensity along each vertical line of the data. The top or bottom beam edgewas fitted from the measured data and plotted as a white dotted or black long-dashed line(figure 4(c)), respectively. The beam between the top and bottom beam edge lines had anaverage vertical size of 4.69 mm and an average energy range of 557 eV. Within the 557 eVenergy range, only 275 eV energy band was used in the spectral-KES calculations for betterSNR performance. The top or bottom edge of 137.5 eV below or above the K-edge energywas fitted from the measurements and plotted as a white dash-dotted or black dashed line(figure 4(d)), respectively.

The variations of the top and bottom beam edge lines implied non-uniform bending acrossthe BLM width, which resulted in an energy resolution change across the beam width witha standard deviation of 0.05 eV (figure 4(e)). The detector’s effective pixel size of 18.7 μmcorresponds to an average energy resolution of 2.2 eV energy change per vertical pixel widthand 2.4 eV/pixel after consideration of the Darwin width of a perfect crystal.

The measured mass attenuation coefficient of iodine was calculated and averaged fromthe K-edge transition image (figure 4(c)) and plotted as black solid lines in figure 5. Sincethe tabulated mass attenuation coefficients of iodine (blue dash lines) matched best with themeasured transitions after a 20 eV blurring through a convolution with a Gaussian function,that of the matrix material, which is assumed to be water, was also blurred with a 20 eVGaussian function. For comparison, the XANES data of sodium iodide measured by Feiterset al (2005) with a 2 eV energy resolution was plotted as red dotted lines (figure 5). Thefact that our measured data showed less near edge features than the Feiters’ data indicatedthat our energy resolution is worse or possibly reflected that the organic iodine has relativelyfeatureless near edge spectrum. The slopes of the three iodine K-edge transitions were plottedin figure 5(b). The Feiters’ data had the steeper slope with a FWHM of 14.2 eV centered at

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(a)

(b)

(c)

(d)

(e)

Figure 4. Images of the beam were acquired using the Photonic Science detector.Intensity-based images of the beam were obtained with no object (a) and after an organiciodine filter of 63 mg cm−2 (b). A normalized attenuation image (c) was obtained bytaking a negative logarithm of the ratio of (b) to (a). The beam energy distribution (d)within the selected beam region of 275 eV energy band was plotted relative to the iodineK-edge energy. The outside of the selected energy region was arbitrarily set to 0 justfor easy viewing. The fitted ‘K-edge’ line, top and bottom beam edge lines based on1% peak intensity (‘beam top’ and ‘beam bottom’), top and bottom energy edge linesbased on 275 eV energy band (‘energy top’ and ‘energy bottom’) were plotted from themeasured data with notations. Figure (e) is the change of energy resolution per verticalpixel width across the beam width.

33.168 keV energy, while our measured data had a milder slope with a FWHM of 32.6 eVcentered at 33.169 keV which matched well with the tabulated data after convolution. Besides,the spectral-KES covered a much wider energy range than the standard XANES analysis. Itwould be promising to obtain more sensitive data when better energy resolution is achieved.

4. Results

4.1. Spectral-KES of a ‘physics rat’ head

The test object was a ‘physics rat’ head which was printed by a rapid prototyper based on aCT scan data of a rat (Zhu et al 2007). The rat head restraint was filled with water and sealedat neck position with a cuvette and a step wedge inserted (figure 6). The 30 mg ml−1 iodine

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(a) (b)

Figure 5. Iodine mass attenuation coefficients (a) and their slopes (b) of the measureddata (black solid lines) from figure 4(c), the tabulated data after blurring (blue dashlines) and an XANES data (red dotted lines). (Reproduced from Feiters et al 2005, withpermission from the International Union of Crystallography).

(a) (b)

Figure 6. The ‘physics rat’ head sample (a) was filled with water and a cuvette of30 mg ml−1 iodine solution, inside which a step wedge (b) was inserted.

solution filled the cuvette and occupied the space left by the step wedge. While this ‘physicsrat’ head sample was vertically line-scanned 800 steps with a step size of 50 μm/step, thePhotonic Science detector took an image of the beam transmitted through the sample at eachstep. With each projection image of 2300 (x) × 301 (E) pixels, a raw data cube of 2300 (x)× 800 (y) × 301 (E) pixels covered a physical cube of 43 mm (x) × 40 mm (y) × 555 eV (E),while only half of the energies, 275 eV of the beam, was used in the data analysis. Besides ten‘dark’ images without the beam and ten ‘flat’ images without the sample, ten ‘edge’ imagesof a 63 mg cm−2 organic iodide filter were taken before and after the 800 projection imagesto analyze the beam parameters, such as the K-edge line, beam region and energy mapping asdescribed in section 3.2.

With the known energy mapping within the beam region (figure 4(d)), the maps of themass attenuation coefficients of iodine and water within the beam region were obtained, as wellas their mean square maps. Based on the spectral-KES algorithm (appendix), the projecteddensity images of the iodine (figure 7(a)) and water (figure 7(b)) were obtained using equation(A.3). The iodine image clearly showed ten steps of the projected iodine variations in the

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(a)

(b)

(c)

(d)

Figure 7. Projected density images of a ‘physics rat’ head in unit of g cm−2. (a) Spectral-KES projected iodine image. (b) Spectral-KES projected water image. (c) KES projectediodine image. (d) KES projected water image.

step wedge region and the iodine sandwiched between the cuvette and its insert. The waterimage showed no density variations in the step wedge region. A big air bubble appeared inboth images. The SNR of the projected density images were calculated using the spectral-KESSNR equation (A.5).

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(c) (d)

(a) (b)

Figure 8. The step wedge region (figure 7) was plotted versus horizontal distance, withimproved statistics by vertical averaging. It includes the projected densities of iodine (a)and equivalent water (b), the SNR of iodine (c) and water (d) images by spectral-KES(red solid lines) and KES (black dash lines), with expected values (blue dotted lines)noted.

For comparison, KES images (figures 7(c) and (d)) were obtained from the same datacube. The high and low beams were set within the selected beam region after the one thirdof the region around the K-edge line was blocked away. The energy lines of the high and lowbeams were set by averaging the energy mapping vertically while considering the beam fluxcontributions. The average beam energies for the high and low beams were 33.26 keV and33.09 keV respectively. Each projection image was then averaged into two lines of high andlow data and the projected density images were obtained using the KES algorithm. The SNRof the KES images were calculated similarly.

The step wedge regions in spectral-KES and KES (figure 7) were compared in figure 8 afterhorizontal shifting and vertical averaging for improved statistics. Figure 8(a) clearly showedthe ten steps of the projected iodine density with about 2.8 mg/cm2/step for the spectral-KESand 2.7 mg/cm2/step for the KES, both of which were expected to be 3 mg/cm2/step. Thisindicated that the spectral-KES is slightly more sensitive in iodine detection than KES, partially

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(a) (b)

Figure 9. The photo (a) and cross-section view (b) of the tubing with organic iodineconcentration noted in mg ml−1.

because the spectral-KES utilized the beam energy more accurately while the KES applicationused here simply averaged the energy bands for the high and low beams. The projected densityof equivalent water from spectral-KES exactly matched with the KES plots (figure 8(b)),both of which showed no signs of iodine and were pretty close to the expected values. Thespectral-KES showed slightly higher SNR performance on both iodine (figure 8(c)) and water(figure 8(d)) images. And the SNR plot of iodine image (figure 8(c)) directly showed that theSNR is proportional to the detected iodine content.

4.2. Spectral-KES CT of tubing with dilute iodine

A bundle of tubing segments (Intramedic R© polyethylene tubing PE330, 2.92 mm ID and3.73 mm OD, Becton Dickinson, USA) were sealed with organic iodine solution (Optiray R©240Ioversol) at concentrations of 0∼2 mg ml−1 and packed into a centrifuge tube (figure 9) as thetest object for the spectral-KES CT imaging. While the tubing was continuously rotating, thePhotonic Science detector took 2500 projections at a step angle of 0.072◦ and exposure timeof 120 ms for each projection image of 2084 (x) × 341 (E) pixels. The collected raw datacube of 2084 (x) × 2500 (θ ) × 341 (E) represented a physical cube of 39 mm (x) × 180◦

(θ ) × 557 eV (E). Only 275 eV energy band of the beam was used in the data analysis.After the beam profile analysis, sinograms of the iodine and water projected density

were obtained from the spectral-KES and KES algorithm. After the filtered back projection,the sinograms were reconstructed into iodine and water slice images (figure 10). An imageprocessing (Wei et al 2013) was performed on the iodine images to reduce the ring artifactwhich was due to the nonlinear change of synchrotron ring current decay and was moreobvious in the dilute iodine images. The variations of the iodine content in the 35 tubes(figures 10(a) and (c)) are obviously observed and well matched with the tube packingpatterns (figure 9(b)). No such variation was observed in the water images (figures 10(b)and (d)). These observations were confirmed by the measurements in figures 11(a) and (b).The background-subtracted iodine densities displayed a linear change among the tubes.The measured iodine and water densities matched close to their expected values. The fact

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(a) (c)

(b) (d)

Figure 10. CT slices of tubing by spectral-KES iodine (a) and water (b) images, KESiodine (c) and water (d) images.

that a little more iodine was detected in spectral-KES than KES, since most measurementsunderestimated the dilute iodine concentrations, indicated a slightly better sensitivity ofspectral-KES to detect dilute iodine. Due to the image artifacts, the SNR measurementsof iodine and water within the tubes were quite noisy (figures 11(c) and (d)), but the overalltrend of proportionality to the iodine content was still noticeable, and slightly better SNR inspectral-KES over KES was observed in many measurements (figure 11(c)). According to theRose criterion which requires an SNR of at least 5 to distinguish image features at 100%certainty (Bushberg et al 2012), the detection limit of our imaging system was achieved by the1.3 mg ml−1 iodine tube (SNRsKES = 5.09) which corresponds to 2.43 μg cm−2 for spectral-KES, or the 1.45 mg ml−1 iodine tube (SNRKES = 5.07) which corresponds to 2.71 μg cm−2 forKES imaging.

4.3. Spectral-KES of a mouse with injected iodine

The spectral-KES was successfully performed on a euthanized mouse injected with iodinesolution in the lung region. The mouse was placed in a centrifuge tube and vertically scanned2100 steps at 50 μm/step, the Photonic Science detector took an image at each step andcollected a raw data cube of 2300 (x) × 2100 (y) × 301 (E) pixels which covered a physical

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(c) (d)

(a) (b)

Figure 11. Measured iodine (a) and water (b) densities were averaged in each tube. SNRsof the iodine (c) and water (d) within each tube were measured in both spectral-KESand KES images.

Table 1. Spectral-KES versus KES with respect to the total amount of material detectedand the whole-image SNRs.

DV view Lateral view

Iodine image Water image Iodine image Water image

Iodine Average Water Average Iodine Average Water Average(mg) SNR (g) SNR (mg) SNR (g) SNR

KES 47.2 12.1 29.8 74.9 52.2 13.5 29.4 73.9Spectral-KES 49.6 13.4 29.9 83.4 54.6 14.8 29.6 82.8

Improvement 5.1% 10.7% 0.4% 11.3% 4.6% 9.6% 0.7% 12%

cube of 43 mm (x) × 105 mm (y) × 555 eV (E). Only 275 eV energy band of the beam wasused in the data analysis.

After the beam profile analysis, the spectral-KES and KES projected density images ofthe mouse were obtained in both dorsal-ventral (DV) and lateral views (figure 12). The iodineimages indicated that the most amount of iodine was located within the lung region while thewater images did not show signs of iodine in the same region. The total amount of iodineand water content along with the SNRs of the whole images were calculated from figure 12and listed in table 1. Table 1 showed that the spectral-KES detected a slightly more iodine(∼5%) than KES while the total amount of water was almost the same (∼0.5%) between

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(a) (c) (e)

(f)

(k)

(l)

(b)

(g) (i)

(h) (j)

(d)

Figure 12. Images of a mouse with injected iodine in the lung region in unit of g cm−2.Spectral-KES projected iodine (a) and water (b) images in DV view, iodine (g) and water(h) images in lateral view; KES projected iodine (c) and water (d) images in DV view,iodine (i) and water (j) images in lateral view. The differences between the spectral-KESand KES images are shown as (e) = (a) − (c), (f) = (b) − (d), (k) = (g) − (i) and (l) =(h) − (j).

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the two techniques. These 5% more iodine in spectral-KES were mostly distributed withinthe lung region (figures 12(e) and (k)), while the distributions of 0.5% differences in watercontent were not that obvious and not consistent between the two views (figures 12(f) and(l)). The spectral-KES images had a slightly better SNR (∼11%) than KES in both iodine andwater images at both views. It was also noted that the total amount of materials in the twoviews were pretty close but not the same. The reason may come from the different averagedflat image (without sample), ring current decay and variations, different beam height at thedetector (4.685 mm for DV view and 4.635 mm for lateral view) and thus the energy resolution(2.224 eV for DV view and 2.236 eV for lateral view) based on the different beam edges of1% peak intensity.

5. Discussions and future works

This paper proposed a novel idea of spectral-KES, derived the spectral-KES algorithms andbuild up a spectral-KES system at the BMIT BM beamline at the CLS. The major benefit of thespectral-KES is that its setup is very simple. The beam splitter and the expensive hard-to-finddual-line detector are no longer needed for simultaneous KES. Instead, it only needs a flatpanel detector which is easily available. These saved a lot of hassle in the beam alignment withthe splitter and the dual-line detector. Preliminary experiments were successfully performed onboth spectral-KES projection and CT imaging. The imaging results showed its slightly moresensitivity to detect dilute iodine (1.3 mg ml−1 iodine at SNR of 5) and slightly better SNRperformance compared with the conventional KES imaging. Elleaume et al (2002) reportedthe monochromatic (25 eV bandwidth) KES iodine detection limit of 185 μg ml−1 andtemporal subtraction iodine detection limit of 90 μg ml−1, both were measured at SNR of 3,pixel resolution of 350 μm, beam height of 1000 μm and 60 cGy dose to a ring-enclosedphantom (0.5 cm thick aluminum). Our spectral-KES detection limit of 0.65 mg ml−1 atSNR of 3 (figure 11(c)), 18.7 μm pixel resolution, 100 μm beam height and 432 cGy dose(120 ms/proj and 2500 projections at maximum 14.4 mGy s−1) corresponds to an equivalentdetection limit of 22 μg ml−1, considering SNR is proportional to iodine concentration, beamheight,

√2 times of pixel size, square root of dose and incident flux after their aluminum

ring. Even though this estimation could not be accurate since the phantom geometries are notthe same, it still provides a very good estimation which is coincident with our conclusion thatspectral-KES performs slightly better than conventional KES in terms of both quantizationand sensitivity.

The simulation analysis indicated that the spectral-KES has better SNR performancewithin a certain energy band, such as 275 eV instead of 557 eV, which nearly corresponded tothe full beam. Besides its contribution to the slightly better SNR performance, narrow energyband minimizes the image artifact due to the presence of bone in the two-component analysiswhere the impact of bone to the contrast image decreases with smaller energy band. Also,narrow energy band corresponds to small vertical beam size and small crossover angle to thebeams which will minimize the crossover artifact that plagues the BLM-based KES imaging.All of these benefits promote the spectral-KES for imaging applications of dilute contrastmaterials.

While the two-component spectral-KES analysis was successfully performed, the threeor more components analysis of spectral-KES requires the matrix of absorption coefficients tobe full rank to successfully distinguish each component. The sensitivity of spectral-KES forresolving components of more than two still needs further investigation.

Currently, the energy resolution of spectral-KES is theoretically calculated as 2.4 eV perpixel width which could be improved by increasing the sample-to-detector distance and/or

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switching to a high resolution imaging detector. The improvement of energy resolution wouldbe limited by the BLM’s intrinsic energy resolution of 0.95 or 1.29 eV considering the Darwinwidth of a perfect crystal at the BMIT BM beamline. Improvement on the intrinsic energyresolution of a BLM while maintaining the sub-micron focus condition still needs furtherinvestigation. The vertical spatial resolution is 100 μm and is set by the beam size at focus;this could be reduced to a few microns in the near future. Combined with 50–100 mm widthof the beam which is set by the BLM, this spatial resolution is great for imaging of smallanimals.

The spectral-KES can be used to interrogate the absorption properties of materials asdone with x-ray absorption spectroscopy (XAS) where a detailed spectral measurement of theabsorption of an element in the vicinity of the absorption edge can elucidate the oxidation stateand local environment of that element. The powerful XAS method has resulted in structuraland chemical state information of many systems. In the case of the structural information, thematerial need not be crystallized to determine the local environment, which is very powerfulfor biological systems. The overwhelming impact of spectral-KES is that it will bring togethercontrast imaging and elemental speciation imaging through XAS analysis which have beentotally different realms. It will be interesting to see what the merging of these two fields bringand what promising applications will be revealed in the near future.

Acknowledgments

The authors would like to thank H Zhang and B Bewer for instrumentation, S Boire, J Boireand R Sammynaiken for crystal preparation. The experiment was performed at the BMIT BMbeamlines at the CLS, which is funded by the Canada Foundation for Innovation, the NaturalSciences and Engineering Research Council of Canada (NSERC), the National ResearchCouncil Canada, the Canadian Institutes of Health Research (CIHR), the Government ofSaskatchewan, Western Economic Diversification Canada, and the University of Saskatchewan(U of S). The research project was funded by a NSERC Discovery grant (DC), a U of S GraduateScholarship (YZ), a CIHR THRUST Training Grant (YZ)—Training in Health Research UsingSynchrotron Techniques, Saskatchewan Health Research Foundation Team Grant (DC) andthe CIHR Heart and Stroke Foundation of Canada Synchrotron Medical Imaging Team Grantno. CIF 99472 (ZW).

Appendix

If the spectral-KES system assumes an object as a two-component system, a contrast material(C) and a matrix material (M), each vertical line in the pixelated detector is a measurement ofthe number of photons (N) transmitted through the object as a function of energy

Ni = N0i e− μ

ρ MiρMtM− μ

ρ CiρCtC

(1 � i � n) (A.1)

where the index i corresponds to the energy of photon detected across the vertical extent of thebeam on the detector, n is the number of energy points, ρ is the density and t is the thickness ofthe material. The mass attenuation coefficients of the two materials

(μ

ρ Mi,

μ

ρ Ci

)can be easily

measured, tabulated or modeled. Equation (A.1) can be recast as,

ri = − ln

(Ni

N 0i

)= μ

ρ MiρMtM + μ

ρ CiρCtC (1 � i � n). (A.2)

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Phys. Med. Biol. 59 (2014) 2485 Y Zhu et al

A least-squares fit derivation is performed to find the projected densities (ρMtM, ρCtC) thatbest fit the measured values, resulting in the following projected density equations

ρMtM = 1

n

μ

ρ CC

∑i

(μ

ρ Miri

)− μ

ρ CM

∑i

(μ

ρ Ciri

)μ

ρ CC

μ

ρ MM− μ

ρ

2

CM (1 � i � n)

ρCtC = 1

n

μ

ρ MM

∑i

(μ

ρ Ciri

)− μ

ρ CM

∑i

(μ

ρ Miri

)μ

ρ CC

μ

ρ MM− μ

ρ

2

CM

(A.3)

where the average of the μ

ρproducts are defined as

μ

ρ CC≡ 1

n

∑i

μ

ρ

2

Ci

μ

ρ MM≡ 1

n

∑i

μ

ρ

2

Mi

μ

ρ CM≡ 1

n

∑i

(μ

ρ Ci

μ

ρ Mi

). (A.4)

Equation (A.3) is used in data analysis to extract projected contrast and matrix density imagesfrom the spectral-KES raw data. It can be easily deduced that the KES is a special caseof the two-component spectral-KES when two energies are chosen, that is setting n = 2 inequation (A.3).

Under the assumptions of Poisson counting statistics to represent the noise from thedetected signals, the SNR of the projected density images are calculated as

SNRC =n(

μ

ρ CC

μ

ρ MM− μ

ρ

2

CM

)√∑

i

[(μ

ρ MM

μ

ρ Ci− μ

ρ CM

μ

ρ Mi

)2 (1Ni

+ 1N0i

)]ρCtC

SNRM =n(

μ

ρ CC

μ

ρ MM− μ

ρ

2

CM

)√∑

i

[(μ

ρ CC

μ

ρ Mi− μ

ρ CM

μ

ρ Ci

)2 (1Ni

+ 1N0i

)]ρMtM. (A.5)

Three assumptions: (1) equal incident flux N0i for all the energies, (2) equal transmitted fluxNi for all the energies and (3) dilute contrast material in the object, are made to simplify theSNR expressions for the projected density images as

SNRC ≈√

nN0

1 + eμt�2

μ

ρ CRMSρCtC

SNRM ≈√

nN0

1 + eμt�2

μ

ρ MRMSρMtM (A.6)

where the RMS average of μ

ρ C,μ

ρ Mand �2 term are defined as

μ

ρ CRMS≡

√μ

ρ CC

μ

ρ MRMS≡

√μ

ρ MM�2 ≡

√√√√1 −μ

ρ

2

CMμ

ρ MM

μ

ρ CC

. (A.7)

As expected, the SNR is dimensionless, and is proportional to: the amount of material present(ρCtC, ρMtM), the square root of the incident photon count (

√nN0), RMS values of the

absorption coefficient(

μ

ρ CRMS,

μ

ρ MRMS

)and the �2 term. It is the �2 term that significantly

drives the SNR curves (figure 2(a)) and peaks it near the contrast absorption edge. It is theμ

ρ CRMSterm that drives the uneven ‘shoulders’ of the contrast SNR curve (figure 2(a)) while the

even ‘shoulders’ of the water SNR curve (figure 2(a)) is due to the nearly flat μ

ρ MRMSterm. The

simplified SNR equation (A.6) was only used for better understanding of SNR relationshipwith various terms while the SNR equation (A.5) was used in all the simulation calculations.

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Phys. Med. Biol. 59 (2014) 2485 Y Zhu et al

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