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Abstract— Contrast-enhanced digital mammography (CEDM) is an alternative to conventional X-ray mammography for imaging dense breasts. However, conventional approaches to CEDM require a double exposure of the patient, implying higher dose and risk of incorrect image registration due to motion artifacts. A novel approach is presented, based on hyperspectral imaging, where a detector combining positional and high-resolution spectral information (in this case based on Cadmium Telluride) is used. This allows simultaneous acquisition of the two images required for CEDM. The approach was tested on a custom breast-equivalent phantom containing iodinated contrast agent (Niopam 150®).Two algorithms were used to obtain images of the contrast agent distribution: K-edge subtraction (KES), providing images of the distribution of the contrast agent with the background structures removed, and a dual-energy (DE) algorithm, providing an iodine-equivalent image and a water-equivalent image. The high energy resolution of the detector allowed the selection of two close-by energies, maximising the signal in KES images and enhancing the visibility of details with low surface concentration of contrast agent. DE performed consistently better than KES in terms of contrast-to-noise ratio of the details; moreover, it allowed a correct reconstruction of the surface concentration of the contrast agent in the iodine image.Comparison with CEDM with a conventional detector proved the superior performance of hyperspectral CEDM in terms of the image quality/dose trade-off.

Index Terms—X-ray detectors, X-ray applications, Mammography, Spectroscopy, Medical diagnostic imaging.

Submitted 20th December 2016. Revised 13th May 2017; accepted 13th

May 2017.SS was sponsored by the Ministry of Health Malaysia.

The authors are grateful to John-William Brown, Steve Craig and Bob Doran for their support to the project.

* Corresponding author, e-mail s.pani@surrey.ac.uk.S. Pani and P.J Sellin are with the Department of Physics, University of

Surrey, Guildford, GU2 7XH, UKS.C. Saifuddin was with the Department of Physics, University of Surrey

and is now with the Ministry of Health Malaysia.F.I.M. Ferreira was with the Department of Physics, University of Surrey

and is now with the Centre for Health Care Management and Policy, University of Surrey.

N. Henthorn was with the Department of Physics, University of Surrey and is now with the Ion Beam Centre, University of Surrey.

P. Stratmann was with the Department of Physics, University of Surrey and RWTH Aachen, Templergraben 5552056 Aachen, Germany. He is now with Technical University of Munich, Germany.

P. Seller, M. C. Veale and M. D. Wilson are with STFC Rutherford Appleton Laboratories, Harwell Oxford,Didcot,OX11 0QX UK.

R. J. Cernik is with the School of Materials, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

© 2017 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org.

I. INTRODUCTION

X-ray mammography is, to date, the most commonly used breast screening technique.However, its limitations come to light when imaging dense breasts, for which the average attenuation coefficient is very close to that of tumours, leading to low contrast and therefore poor detection rate [1].High breast density is also linked to increased risk of developing breast cancer [2,3]; therefore, the need for limiting the dose is stronger in patients with denser breasts.Of the radiographic alternatives proposed to tackle the difficulty in imaging denser breasts, digital breast tomosynthesis (DBT) appears to be the most successful for screening, allowing different planes of the organ to be placed in focus, and partially removing the lack in visibility resulting from structure overlap [4,5]. However, DBT does not intrinsically provide lesion enhancement, and may therefore be limited in its scope for classification of a lesion as benign or malignant or for identification of small lesions in multi-focal cancers; moreover, cases have been reported where its effectiveness in the examination of the extreme density groups is not greater than that of full-field digital mammography [6,7]. Additionally, it requires dose levels comparable to those of conventional mammography [8, 9]; as it is mostly used in addition to it, rather than as a replacement, the overall dose is doubled, whilst it is desirable that any additional procedure provides only a fraction of the dose provided by conventional mammography. Finally, the increased associated costs and interpretation times suggest that widespread implementation of DBT may not be recommendable in all cases [10].Contrast agent planar imaging is a valid method to increase the visibility of a benign or malignant tumour; a contrast agent enters the blood flow and its overall amount is increased in regions with increased vascularisation, such as cancer. Kinetic imaging (uptake- and washout- patterns of contrast agent from a lesion) may also be used as an indicator of malignancy [11].The preferred contrast agent for most mammographic procedures is iodine, due to its lower toxicity compared to gadolinium and its K-edge at an energy (33.2 keV) within the range of typical mammographic spectra.However, the visibility of a contrast agent, particularly in low surface concentrations (the product x × , where x is the thickness of a region containing contrast agent, and is its concentration), may be prevented by the presence of non-uniform background. This limitation can be removed by contrast-enhanced digital mammography (CEDM), which has been proposed, and extensively modeled, by various authors to

High energy resolution hyperspectral X-ray imaging for low-dose contrast-enhanced digital

mammography

Silvia Pani*, Sarene C. Saifuddin, Filipa I.M. Ferreira, Nicholas Henthorn, Paul Seller, Paul J. Sellin, Philipp Stratmann, Matthew C. Veale, Matthew D. Wilson, Robert J. Cernik

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address cases with difficult visibility or uncertain diagnosis in conventional mammography [12-19]. Enhancement of regions with increased contrast agent uptake allows visualization of small-sized lesions in multifocal cancers, and accurate identification of lesion margins to inform surgery. Recent CEDM trials [20-22] have demonstrated increased sensitivity and specificity compared to conventional mammography, and comparable results to breast MRI, with obvious advantages in terms of accessibility and costs. Although CEDM cannot be proposed as an alternative for mammographic screening of the whole population normally recommended for screening, due to the longer overall times needed for patient preparation, injection of contrast agent and, if applicable, dynamic imaging, it appears as a promising option for screening of certain groups of the population: for instance, women with dense breasts, for whom the sensitivity of conventional mammography is decreased, or women with a family history of breast cancer. Moreover, it could be used as a second-stage examination before biopsy to identify any small lesion foci.Various approaches to CEDM have been implemented [23], broadly divided into subtraction methods and dual-energy methods.Subtraction methodologies are divided into temporal subtraction (TS) and K-edge subtraction (KES). In the former, two images are acquired before and after the injection of the contrast agent, respectively, and in the latter two images are acquired with beam energies below and above that of the K-edge of the contrast agent, respectively; in both cases, logarithmic subtraction is performed giving an enhanced image of the distribution of the contrast agent [24]. In dual-energy (DE) imaging [25], an object is projected onto a basis consisting of two arbitrary materials (in this case, a water-equivalent image and a contrast agent-equivalent image), the latter giving an image of the contrast agent only, and allowing absolute measurements of surface concentration. Correct quantification of contrast agent uptake allows increased specificity in static and dynamic imaging allowing, for instance, assessment of therapy effectiveness.However, the comparatively broad energy spectra that can be obtained with conventional beams may prevent complete background removal, thus potentially limiting the visibility of smaller lesions. Much effort has therefore been put in identifying suitable combinations of spectra to optimize the image quality/dose trade-off. Most authors proposed various combinations of filters and tube voltage [15,26-28]; alternatively, Sarnelli et al [29] proposed the use of quasi-monochromatic, tunable beams, obtained with a conventional source and a mosaic crystal monochromator, as a more accessible alternative to the “gold standard” characteristics, in terms of narrow band width and tuneability, of synchrotron beams.All the above methodologies, however, find their limitation in the need for two exposures. Besides increasing the patient dose, this may cause artifacts from incorrect image registration in case of patient movement.

A detector that joins spectroscopic and positional capability, allowing the so-called hyperspectral imaging, allows the two images needed for KES or DE imaging to be acquired simultaneously by simply integrating two different bands of the detected spectrum, thus removing the above limitations. In recent years, various semiconductor materials have been characterised with a view to combine spectroscopic capability with position sensitive capability [30-33]. Of these materials, Cadmium Telluride (CdTe) and Cadmium Zinc Telluride (CdZnTe) appear particularly promising due to their high atomic number, ensuring high efficiency, and relatively high band gap, allowing operation at room temperature or with moderate cooling [34-36].Previous work on CEDM using photon counting detectors has focused on multi-threshold devices [37], allowing images at different energy bands to be obtained by subtraction of images obtained with different amplitude threshold. However, the energy resolution of such devices is the order of several keV in the diagnostic energy range [38,39]. This may pose limitations on background removal and on the achievable contrast.The HEXITEC collaboration has developed fully spectroscopic, position sensitive detector systems for medical and non-medical applications based on CdTe sensors [40-44]. This work looks at using HEXITEC for CEDM using KES and DE by integrating different regions of the spectrum transmitted after a breast-equivalent phantom.

II.THEORY

Consider two monochromatic X-ray beams with energies Elow

and Ehigh, respectively. An object consisting of iodine and a generic “background” material (which may consist of several materials with similar attenuation properties), in surface concentrations (I and (bg, is imaged using the two beams. The X-ray mass attenuation coefficients for the two energies are (µ/I

low, (µ/Ihigh, and (µ/bg

low, (µ/bghigh for the

two materials, respectively. If I0low, I0

high are the incident X-ray intensities for the low-energy beam and the high-energy beam at a generic point in the image, respectively, then the transmitted logarithmic intensities, if scatter is negligible, are:

Llow=ln(I 0low

I low)=(μ

ρ )I

low( ρx ) I+(μ

ρ )bg

low( ρx )bg

Lhigh= ln(I 0high

I high)=(μ

ρ )I

high( ρx ) I+(μ

ρ )bg

high( ρx )bg

(1)KES works under the approximation (µ/bg

low ≈ (µ/bghigh; in

this case, it is possible to obtain an image that is only dependent upon the iodine distribution:

S=Lhigh−Llow≈(( μρ )

I

high−( μ

ρ )I

low) ( ρx )I(2)

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If the two energies are on either side of the K-edge for iodine (33.2 keV [45]), the mass attenuation coefficients of iodine differ significantly, giving rise to a high signal in the subtracted image.Although more complex approaches have been proposed for noise removal and spectral optimization [46,47], the limitation of this approach in its simplest form is that it relies on the two beam energies to be close enough for the variation in the attenuation coefficient of the background to be negligible. This is easily achieved with a synchrotron source, where the tuneability of the beam allows the selection of energies very close to each other, as well as to the K-edge of iodine, allowing on one hand optimum background removal, and on the other hand maximum signal by exploiting the maximum difference in the attenuation coefficients of iodine on the two sides of the K-edge [13]. With a conventional source the capability for tuning the average energy of the beam can only be achieved, to a limited extent, by adjusting the beam kilovoltage and using appropriate filtering. On the other hand, the advantage of this algorithm is that it doesn’t rely on knowledge of the exact attenuation coefficients of the two materials providing the aim is not to obtain absolute measurements of contrast agent concentration but simply to remove the background. Although it can potentially be used for quantitative measurements as well, it would require the two energies to be too close for the capability of a conventional source: if the approximation (µ/bg

low ≈ (µ/bg

high does not hold, equation (2) cannot be simplified and retains two unknown variables, (I and (bg.1

In the more generic DE approach [25], two base materials are chosen (in this case iodine and water), and each image point is represented as a vector. The projections of this vector onto the two base vectors are obtained by replacing (bg in Equations 1 with (w, the water-equivalent surface concentration of the phantom, and solving the equations for (I and (w. Equations 1 may then be solved for the surface concentration of each material:

( ρx )I=(μρ )

w

highLlow−(μ

ρ )w

lowLhigh

(μρ )

w

high

(μρ )

I

low−(μ

ρ )I

high

(μρ )

w

low

( ρx )w=−(μ

ρ )I

highLlow+(μ

ρ )I

lowLhigh

(μρ )

w

high

(μρ )

I

low−(μ

ρ )I

high

(μρ )

w

low

(3)This approach can be used more widely than the KES algorithm as it doesn’t rely on the presence of a K-edge, or on the separation of the two energies, as long as the attenuation

11 For instance, a separation of 1 keV symmetrically about the K-edge of iodine, with a 5 cm water-equivalent object and a 5 mg/ml surface concentration of iodine would give )I (x)I = 0.14 and )w (x)w = 0.06, where )I and are the differences in the mass attenuation coefficients of iodine and water, respectively (data from [50]), the water term no longer being negligible compared to the iodine term.

coefficients of the two materials at the two energies are distinguishable. If sample scattering is not negligible, as is the case for non-clinical systems that don’t have an anti-scatter grid, as is the case for the present work, the transmission through the object can be written as follows:

I low=I 0low (exp(−(μ

ρ )I

low( ρx ) I−(μ

ρ )w

low( ρx )w)) (1+R low)

I high=I 0high(exp (−(μ

ρ )I

high( ρx ) I−(μ

ρ )w

high( ρx )w))(1+ Rhigh )

(4)Where Rlow, Rhigh are the scatter-to-primary ratios for the low and high energy, respectively, i.e., the ratio of the number of scattered photon/unit area to the number of primary photons/unit area. To a first approximation, the scatter-to-primary ratio can be assumed to be constant across the field-of-view [48]. Solving Equations 4 for (x)I, (x)w, one obtains

( ρx )I=(μρ )

w

highΛlow−(μ

ρ )w

lowΛhigh

(μρ )

w

high

(μρ )

I

low−(μ

ρ )I

high

(μρ )

w

low

( ρx )w=−(μ

ρ )I

highΛlow+(μ

ρ )I

lowΛhigh

(μρ )

w

high

(μρ )

I

low−(μ

ρ )I

high

(μρ )

w

low

(5)where

Λalignl¿ low ¿high¿=Lalignl ¿ low ¿high ¿¿+ ln (1+Ralignl¿ low ¿high ¿¿)¿(6)

III. METHODS

A. Experimental set upThe X-ray source used is a Hamamatsu L11091 tungsten-anode source (Hamamatsu, Japan); for the present study, it was operated at 50 kVp with 3 mm Al filtration. With these parameters, the average energy (33.0 keV) and the maximum spectral intensity (31.5 keV) [49] are close to the K-edge of iodine. This limits dose delivery from spectral components not contributing to the image. The X-ray tube current was kept to 2 µA throughout the measurements in order to ensure absence of pulse pile-up. A set of custom test objects was developed for this study. Each test object consisted of a plastic box (thicknesses along the beam direction 3.5 cm, 5 cm, 7.5 cm) filled with acrylic spheres of different sizes simulating glandular tissue. Each box was further filled with olive oil to simulate adipose tissue; a 6-mm thick PMMA slab with cylindrical holes 3 mm, 2 mm and 1 mm in diameter was superimposed to it. The holes were

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filled with Niopam 150® (Bracco, UK) clinical iodine-based contrast agent diluted at different iodine concentrations (50-150 mg/ml) by distilled water using a pipette.The source-sample distance was 65 cm and the source-detector distance was 75 cm. The acquisition time ranged between 10 minutes for the 3.5 cm object and 15 minutes for the 7.5 cm object, for the acquisitions the results of which are shown in Sections IV.C. The entrance air kerma on the phantom surface was measured using a Farmer chamber NE2571A (Nuclear Enterprises/Bicron, USA) and the Mean Glandular Dose (MGD) was calculated as described in Section III.I.For the acquisition of objects larger than the field of view of the detector, images were acquired in a “step and shoot” mode, by shifting the whole object by 1.8 cm (detector width – 2 mm overlap) to acquire different regions of the object. A VT-80 stepper motor and a SMC Corvus-eco controller (PI miCos GmbH, Germany) were used. The acquisition time was kept constant at each position. Full-field images were obtained offline, by averaging the boundary pixels of adjacent images.

B. Detector characterisationThe detector used is based on a 2 × 2 cm2, 1-mm thick CdTe sensor (Acrorad Co Ltd, Japan). The sensor is bump-bonded to an 80 × 80 array of identical readout channels, giving a pixel pitch of 250 µm.The detector thickness allows 99.9% absorption efficiency up to 50 keV [50]. The detector was biased at -500 V and Peltier-cooled at 20º C. The energy resolution was measured from a variable-energy X-ray (VEX) source (AMC.2084, Radiochemical Centre Amersham) consisting of an Am-241 source emitting gamma rays at 59.5 keV. The gamma rays hit foils of different materials and cause the emission of fluorescence X-rays in a conical distribution within a solid angle of approximately 0.5 sr. No further collimation was applied to the source or detector for these measurements.Figure 1 shows spectra obtained at 20º C for the Mo foil (characteristic X-rays at 17.5 keV and 19.6 keV [45]) and for the Tb foil (characteristic X-rays at 44 keV and 50.3 keV [45]). The data demonstrate an energy resolution <1 keV across the range when summing the spectra from all pixels. For comparison, the spectrum from a single pixel is shown, demonstrating the improved discrimination of the Tb K1 and K2 lines at 50.3 keV and 51.7 keV [45], respectively.

(a)

(b)Figure 1. Spectra obtained from the Mo characteristic lines (a) and the Tb characteristic lines (b) at 20º C.

More work on the detector characterization can be found in refs [40],[51],[52]. Data were read and downloaded to a PC using a base CameraLinkTM framegrabber card and dedicated data acquisition and conversion software. Images were obtained by summing, pixel by pixel, different energy bands of the detected spectra.Each detector pixel was calibrated in energy using characteristic X-rays between 17.5 keV (Mo K line) and 44.5 keV (Tb K line) from the above-described VEX source. Automated peak search, in a user-specified ADC channel range, was carried out in the spectra produced by each pixel. A linear fit of energy (E) vs spectral channel number (ch), E = m0 + m1 × ch, was then performed pixel by pixel. With the exception of 68 noisy pixels out of 6400, the average coefficients are m0 = (1.5 ± 0.5) keV and m1 = (0.288 ± 0.011) keV/channel.Gain equalization of spectra was performed via linear interpolation so as to have each spectrum channel corresponding to the same energy for all pixels. This is crucial when choosing the integration bands to build the images above and below the K-edge, respectively. If the bands are chosen from a spectrum obtained by summing all pixels channel by channel with no gain calibration, the drop in transmitted intensity across the K-edge is less steep, its width resulting from the convolution of the ideal spectrum by the energy resolution of the detector and by the curve representing the distribution of gain across all pixels; therefore, a selection of

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the integration bands from such a spectrum is necessarily more conservative and leads to the two bands being further apart in energy. By linearly interpolating the spectra from all calibrated pixels, the dependency on the spread in gain is removed, and the two bands can be selected closer to the physical K-edge of iodine. Figure 2 shows a comparison of a section, around the iodine K-edge, of the spectra obtained by summing the spectra acquired by all pixels behind an iodine detail before and after linear interpolation. It is clear that the drop in X-ray transmission resulting from the presence of the K-edge becomes steeper in the latter case.

Figure 2. Section of the spectra obtained before and after individual pixel calibration and correction for gain spread, showing the drop in X-ray transmission across the K-edge.

C.Selection of energy bandsAfter gain equalisation, the lower and upper limits of the K-edge were identified from a spectrum obtained by summing the spectra from all pixels behind an iodine detail as qualitatively illustrated in Figure 3. The lower and upper limit of the K-edge were identified as the points where the derivative of the spectral intensity approaches zero.

Figure 3. Example of spectrum used to identify the spectral bands to form the “low energy” and “high energy” images for KES and DE imaging.

The low-energy image was obtained by integrating, pixel by pixel, an appropriate number of spectral channels to the left of the lower limit, and the high energy image was obtained by integrating pixel by pixel the same number of channels to the right of the higher limit of the K-edge. The two bands were approximately 2.5 keV apart. It was decided to keep the

extremities of the two windows fixed and change their width to allow comparison between DE and KES, the latter failing when the energies are too far away from the physical K-edge of iodine.

D.Calculation of unattenuated beam intensityIn a photon counting device the intensity on the detector from an unattenuated beam, I0, cannot be obtained by removing the object from the beam, as this would cause pulse pile-up and alteration of detector spectral and dose rate response. For this purpose, several spectra were obtained by further filtering the beam with known thicknesses of aluminum. The source and detector were left uncollimated at the same distance as in the imaging setup, and the filters were placed approximately 5 cm from the source. For each channel of the spectrum in the range 30-36 keV a fit of the form y=A0 e-A1x

was performed, where y is the measured counts for that spectral channel and x is the aluminium thickness.A0 was used as an estimate for the unattenuated beam intensity for each spectral channel. This was deemed possible due to the high energy resolution of the detector, and to the absence of sharp variations in the beam spectrum at energies above 30 keV, which removed the need for a deconvolution by the detector energy resolution.The validity of this approach was tested by comparing the A1

coefficient of the fit with the linear attenuation coefficient of aluminium as obtained from the Xmudat utility [50]. The results shown in Figure 4 confirm the correctness of the reproduction of the attenuation coefficient of aluminum.

Figure 4. Comparison of the attenuation coefficient of aluminium from Xmudat [50] with the A1 parameter from the exponential fit carried out on each spectral channel to determine the unattenuated beam intensity. Error bars for the A1 parameter have been added on a subset of the points for ease of reading.

E. Quantitative evaluation Quantitative evaluation of the images was carried out in terms of the contrast-to-noise ratio (CNR) of details:

(7)where D is the average signal in the detail region (in this case the central region of the cylinder), B is the average signal in the background and B is the standard deviation associated to the background region. Three equivalent data sets were used

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in each case. The region size was 1.25 cm (50 pixels) along the detail length. The detail region was 6 pixels wide for the 3 mm detail, 4 pixels wide for the 2 mm detail and 3 pixel wide for the 1 mm detail. In particular, CNR was used to identify the optimum width of the integration band on the two sides of the K-edge as the one maximising its value for a certain detail. For all data sets presented here, CNR was measured on the recombined images (i.e., obtained with KES or the iodine component of the DE images).

F. Scatter-to-primary ratioThe scatter-to-primary ratio is strongly dependent upon thickness and composition of the object, in the case of mammography the relative amounts of adipose and glandular tissue [53]. For the present work, it was measured for PMMA blocks with the same equivalent thickness as the test objects, PMMA representing a 50% glandular, 50% adipose breast [54].The “linear extrapolation method” [55] was used, consisting of acquiring images of PMMA blocks with the same thicknesses as the test objects, with superimposed lead discs of increasing diameter between 5 mm and 12 mm and thickness 2 mm, and extrapolating to zero diameter the plot of the ratio of the signal behind the discs to the signal outside the discs versus the disc diameter. For a 2 keV integrating band, chosen as a good compromise between high CNR and reliability of quantitative measurements, as discussed below in Section IV.C, the scatter-to-primary ratios measured for the low-energy and the low energy images are given in Table 1.

Overall phantom thickness (cm) Rlow Rhigh

4.1 0.13 ± 0.03 0.11 ± 0.03

5.6 0.50 ± 0.06 0.40 ± 0.06

8.1 0.55 ± 0.07 0.48 ± 0.06Table 1. Scatter-to-primary ratios for the low energy band (Rlow) and for the high energy band (Rhigh) for the three phantoms used.

Given the relative dimensions of sample and detector it appeared reasonable to assume the scatter-to-primary ratio to be constant across the image field.

G.Calculation of iodine surface concentrationIf the mass attenuation coefficients for X-rays are known for the two base materials, Equations 7 may be used to give an estimate of the iodine and water surface concentration; in this case, the iodine surface concentration corresponds to the tube diameter times the mass concentration of iodine in each tube.The procedure was carried out, for three different concentrations, on images obtained using a 2 keV integration band. The surface concentration of iodine was measured near the middle of the iodine-equivalent images for the three tubes.The values for the attenuation coefficients of iodine and of water at the central energies of each of the two bands were

obtained from the XMudat utility [50] and are listed in Table 2.

BeamAverage

energy (keV)

() iodine

(cm2/g)

() water

(cm2/g)

Low energy 30.3 8.15 0.370

High energy 34.9 31.3 0.308Table 2. Mass attenuation coefficients used for the DE images with the HEXITEC system [50].

H.Comparison with charge-integrating systemHyperspectral CEDM was compared, for the 5 cm thick object, with conventional CEDM carried out using a conventional charge-integrating detector (Hamamatsu C7942 flat panel with a CsI scintillator) and two spectra with average energies above and below the K-edge, respectively. The spectra were obtained by appropriately filtering beams from a high-power W-anode source (Comet MXR-225). The low-energy beam was obtained using a 250 µm Tin filter in order to remove or strongly reduce the spectral components above 29.2 keV (Sn K-edge [45]), and the high-energy beam was obtained using a 12.5 mm Al filter in order to remove the low-energy components. The source-object distance was 60.5 cm, and the source-detector distance was 66.5 cm.The DE algorithm was used; the mass attenuation coefficients to be applied to the DE equations were obtained as a weighted average of the attenuation coefficients for the spectra:

( μρ )=

∑iI i Ei ( μ

ρ )i

∑iIi Ei (8)

where ( μ/ ρ ) is the average mass attenuation coefficient, Ei

and Ii are the energy and intensity of the i-th spectral

component, respectively and ( μ/ ρ )i is the mass attenuation coefficient for the same component. Energy was included in the weighting factor because for a charge-integrating device the signal is proportional to the energy deposited. Spectral and attenuation data were obtained from IPEM Report 78 [49] and XMudat [50], respectively.

The kilovoltage for the low-energy beam was set to 45 kVp; minimum variation in signal was observed when varying the tube voltage due to the significant removal of the high-energy component of the beam by the filter. The optimum kilovoltage for the high energy beam was chosen as the one giving maximum CNR in the iodine image obtained using the dual-energy algorithm. Table 3 shows the CNR for the 3 mm tube filled with undiluted contrast agent as a function of the tube voltage. Whilst the low signal obtained with low kVp leads to a noisy image and therefore poor CNR, the broad spectrum obtained with high kVp settings makes a single value of the attenuation

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coefficients inadequate for the DE algorithm, leading to poor background removal and hence higher residual anatomical noise.2 50 kVp represents a compromise between the two opposite effects and was therefore chosen as the optimum voltage for this purpose.

Source voltage (kV)

CNR

42 26 ± 4

45 45 ± 5

50 62 ± 6

55 43 ± 5

60 47 ± 5Table 3. CNR as a function of the tube voltage for the high energy beam in the conventional DE images.

Images with the two spectra were acquired for 15 seconds each. The mass attenuation coefficients used in the DE algorithm are listed in Table 4.

Beam

Average

energy (keV) iodine

(cm2/g)

water

(cm2/g)

Low energy (45 kV, 250 µm Sn filter)

26.3 13.8 0.482

High energy (50 kV, 12.5 mm Al filter)

38.8 20.2 0.281

Table 4. Mass attenuation coefficients used for the DE images with the conventional system [50].

Comparison between images obtained with HEXITEC and with the conventional system was carried out in terms of the Image Quality Factor (IQF), obtained by replacing the signal-to-noise ratio with the CNR in [56]:

IQF=CNR 2

MGD (9)where MGD is the mean glandular dose, calculated as described in Section III.I, and the CNR was measured on the reconstructed iodine image. The IQF was calculated for the same regions of the phantom in both modalities.

I. DosimetryThe MGD was calculated by measuring the entrance surface air kerma (ESAK) for each image using a Farmer ionization

2 Here, “residual anatomical noise” is used to define the variation in signal resulting from incomplete background removal in the iodine images.

chamber model NE2571A (Nuclear Enterprises/Bicron, USA) and then applying the methodology proposed by Dance and coworkers [57,58]:MGD=Kgcs (9)where K is the ESAK, g is a coefficient depending on the Half Value Layer (HVL) of the beam and on the breast thickness, c is a coefficient depending on the glandularity and s is a coefficient depending on the anode-filter combination.A 50% adipose-50% glandular composition was assumed. Therefore, the c coefficient, accounting for the glandularity, was taken as 1. As the spectra are different from those used in Dance’s 2000 model [57], the coefficient s was left 1, as was done in the 2014 paper [58].For the coefficient g, firstly a linear interpolation between the values at 5 cm thickness and 6 cm thickness was calculated for all tabulated HVL values. The HVLs lay in all cases outside the tabulated range in both papers, the ranges being 0.3-0.6 mmAl in the 2000 paper and 2.4-3.6 mmAl in the 2014 paper. It was decided to linearly extrapolate the coefficient g data from the 2000 paper for the low-energy beam used in the conventional image (HVL = 0.75 mmAl) as the tabulated data proved linear across the range available and the measured HVL was very close to this range; for the beam used in the HEXITEC acquisitions (HVL = 1.95 mmAl) and the high-energy beam used in the conventional acquisitions (HVL = 3.67 mmAl) the coefficient g was obtained by fitting a second-order polynomial to the tabulated data in the 2014 paper and extrapolating it to the measured HVL values.

IV. RESULTS AND DISCUSSION

A. Gain equalization and energy resolutionThe advantage resulting from gain equalization is demonstrated in Figure 5, showing the profile across the KES image of a 3 mm tube with iodinated contrast agent: as the equalisation improves the effective energy resolution of the detector, the low and high energy bands can be selected closer together and the difference in the attenuation coefficient of iodine at the two energies is greater; therefore, the signal is improved by approximately 8%, and the CNR is improved from 39 ± 3 to 51 ± 3.

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Figure 5. Profiles from KES images of a 3 mm tube containing iodine obtained without and with gain equalization, showing the improvement in signal brought by the correction.

This suggests that a detector with a poorer energy resolution, requiring the two energy bands to be chosen further apart, would lead to more significant signal reduction, thus compromising the visibility of details with small size or low contrast agent concentration.

B. DE vs KESFigure 6 shows the CNR of the 3 mm detail for the 150 mg/ml concentration and three object thicknesses.

(a)

(b)

(c)Figure 6. Comparison of CNR of the 3 mm detail as a function of the spectral band width used for forming the “high energy” and “low energy” images: (a) 3.5 cm object; (b) 5 cm object; (c) 7.5 cm object.

The generic dual-energy algorithm performs consistently better than the KES algorithm. This is due to the fact that the DE algorithm is less strictly dependent upon the average energies used for the two images, whereas the KES algorithm requires the two energies to be as close as possible to each other in order to fully exploit the steep increase in the

attenuation coefficient of iodine across the K-edge. A wider integration band implies a lower average energy for the low-energy image and a higher average energy for the high-energy image, thus bringing the two average energies further apart. The optimum band width, as the one giving the maximum CNR, results from a compromise between two factors: on the one hand, a narrow band implies close-by average energies for the two images, and hence greater difference between the attenuation coefficients of iodine in the two images, ensuring greater contrast; moreover, a wide band causes the background removal (in KES) and the decoupling into two materials (in DE) to be incomplete, increasing the amount of residual anatomical noise. On the other hand, a broader band implies higher statistics, and hence lower Poisson noise on the image.The maximum CNR is achieved in DE with a broader band than in KES; this is because DE is less strongly reliant on the two energies being close to each other, and its less stringent assumption is that the mass attenuation coefficients of the base materials used have a measurable difference; therefore, it benefits more strongly from the increase in statistics resulting from a wider band. In DE, the optimum band width, as the one giving the highest CNR, appears to be between 2 keV and 5 keV.However, quantitative measurements become unreliable for wider bands due to the presence of the characteristic lines of

cadmium (23 and 26 keV for K and K respectively [45])

and of tellurium (27 and 31 keV for K and K respectively [45]), resulting from characteristic X-rays absorbed in a different pixel from the one where the photoelectric absorption took place. These lines are visible in the spectrum in Figure 3.

For the subsequent work, it was therefore decided to use 2 keV as the width of the spectral regions to be integrated for the two images.

C.Calculation of iodine concentrationFigure 7 shows the original low-energy and high-energy images of the 5 cm test object (with undiluted Niopam 150 ®), obtained with 2 keV spectral bands, and the KES and DE water-equivalent and iodine-equivalent images, obtained from them. Both the KES and the DE iodine image show good background removal, with improved visibility of the structures, such as bubbles and variations in concentration from partial crystallization of the contrast agent, compared to the original images. Quantitative measurements were carried out after cleaning the tubes to limit the risk of crystallized contrast agent on the walls and ensuring that no bubbles were present in the region of interest. Figure 8 shows a comparison of the profile across a 3 mm diameter tube filled with undiluted contrast agent (150 mg/ml iodine concentration) in iodine-equivalent images without and with the corrections for scatter (Equations 3 and 5, respectively).

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The correction for scatter, which is a constant offset, brings the average background level in the iodine image to zero as is correct to expect. Although this correction is small for comparatively large details and concentrations as the ones used here, it may significantly affect quantitative assessment for low surface concentration. For instance, typical values of surface concentrations for breast cancers may be as low as 1-2 mg/cm2 [59].

(a)

(b)

(c)

(d)

(e)Figure 7. Images of the 5 cm thick test object with a 150 mg/ml contrast agent concentration, obtained with four lateral translations of the objects and a 10 min acquisition time in each position. The details are, from left to right, the 3 mm tube, the 2 mm tube and the 1 mm tube. a) Low energy image, obtained from a 2 keV wide band centered at 30.3 keV; b) high energy image, obtained from a 2 keV wide band centered at 34.9 keV; c) KES image; d) water-equivalent image from the DE algorithm; e) iodine-equivalent image from the DE algorithm. In all cases white represents high signal intensity and dark means low signal intensity: in a) and b) white is high photon count; in c) and e) it means high iodine surface concentration; in d) it means high water-equivalent thickness. The speckles visible in the images result from noisy pixels as well as pixels with significantly different gain from average, for which automatic calibration fails.

Figure 8. Comparison of the profile across iodine-equivalent images of a 3 mm tube filled with undiluted Niopam® 150 with and without the corrections for scatter. Figure 9 shows plots of the calculated surface concentrations of iodine for the three objects. The mean glandular dose for each acquisition is specified in the caption.

(a)

(b)

(c)Figure 9. Reconstructed surface concentrations of iodine for the three objects: a) 3.5 cm object, MGD 50 µGy; b) 5 cm object, MGD 49 µGy; c) 7.5 cm object, MGD 49 µGy.

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The data were fitted with a linear function of the form y = m0

+ m1 x, where y is the reconstructed surface concentration and x is the nominal surface concentration, and the fitting parameters are shown in Table 5. In the ideal case, one should have m0 = 0, and m1 = 1. As these conditions are met, within error, in almost all cases, the reconstruction algorithm proves to work correctly.

Object thickness (cm)

m0 (mg/cm2) m1 (dimensionless)

3.5 -1.4 ± 1.6 1.16 ± 0.12

5 1.4 ± 1.1 0.96 ± 0.08

7.5 0.5 ± 0.9 0.89 ± 0.12

Table 5. Fitting parameters for the reconstructed vs nominal surface concentration of iodine.

D.Comparison with conventional imagingTable 6 shows a comparison of the IQF measured on the DE images of the three iodine details for undiluted contrast agent for the hyperspectral images at an MGD of 49 µGy and the images obtained with a conventional, charge-integrating detector, with MGD of 0.25 mGy and 0.40 mGy for the low energy image and the high energy image, respectively. The sum of these values was used for the calculation of the IQF.

Tube Ø (mm) IQF HEXITEC (mGy-1)

IQF conventional(mGy-1)

1 13000 ± 4000 350 ± 140

2 61000 ± 11000 2500 ± 700

3 92000 ± 19000 5900 ± 1300

Table 6. IQF for the images of the three tubes for HEXITEC and the conventional system.

The main reason for the difference in IQF is the significant difference in doses for the two procedures, the HEXITEC images being obtained in a single exposure, whereas two exposures, one of which with a low-energy spectrum, are required for dual energy imaging with any conventional detectors, and therefore the overall dose is higher in the conventional case.

In order to assess the relative importance of different factors contributing to noise, and hence to CNR, the standard deviation was measured, for the low and the high energy spectra, on images of uniform pieces of PMMA giving comparable counting statistics to those measured in the background regions adjacent to the details (Ilow, Ihigh). Then it was measured in the regions I0 was measured from (I0

low, I0

high). Finally, error propagation was applied to the iodine component of Equation 3 to give a (x)calc only dependent on detector and Poisson noise. Any residual noise outside the details in the iodine image results from incomplete background removal due to partial failure of the dual-energy algorithm as well as from the correlation between Poisson noise and anatomical noise [60]. This residual noise, here termed residual anatomical noise and comprising both the anatomical variations and the non-quadratic correlation term, was calculated asσ res=√σ

meas2−σcalc2

(10)where calc is the standard deviation calculated as described above and meas is the standard deviation as measured on the iodine images outside the iodine details. As can be seen from the results in Table 7, there is a greater component of residual anatomical noise for the conventional system. This shows the improvement brought by a high-resolution spectroscopic detector, for which the selection of narrow energy bands makes a monochromatic treatment realistic.

meas

(g/cm2)calc

(g/cm2)res

(g/cm2)

HEXITEC 0.50 × 10-3 0.41× 10-3 0.28× 10-3

Conventional 1.0 × 10-3 0.75× 10-3 0.66× 10-3

Table 7. Measured, calculated and residual anatomical noise in the background of the iodine-equivalent images.

More specifically, measurements on dark field images and on images of uniform PMMA slabs for both detectors, and error propagation on Equation 3, gave the results in Table 8 for the Poisson and detector contributions, Poiss and det respectively, to meas, demonstrating that the photon-counting nature of the HEXITEC system allows the noise to be essentially Poisson-like, giving greater CNR for a given signal.

Poiss

(g/cm2)det

(g/cm2)

HEXITEC 0.40 × 10-3 0.10 × 10-3

Conventional 0.25 × 10-3 0.71× 10-3

Table 8. Poisson and detector noise in the background of the iodine-equivalent images.

It should be pointed out that the conventional system used here does not use the same X-ray spectra as commercial dual-energy systems; however, it is worth noting that the GE dual-energy system [61] is based on a Rhodium anode-Rhodium

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filter combination for the low energy spectrum, with a lower average energy than the spectrum used here due to the presence of the Rh K-lines and of the Rh K-edge at a lower energy than the Sn K-edge (23.3 keV compared to 29.2 keV [45]). Therefore, the spectrum used here represents, on the dosimetric side, a better scenario than that of a commercial system.

V. CONCLUSIONS AND FURTHER WORK

This paper presented a quantitative evaluation of the capability of a fully spectroscopic, position-sensitive CdTe detector for dual-energy imaging for the visualization and quantification of iodine-based contrast agent in a breast-equivalent phantom. The spectroscopic capability of the device allows images at arbitrary energies to be obtained, thus improving the contrast-to-noise ratio with respect to a conventional dual-energy system due to the possibility of optimizing the selection of the energy. The possibility of obtaining an arbitrary number of images at different energies with a single exposure allows minimization of the dose to the patient for multi-energy procedures; moreover, the photon-counting capability of the detector allows the noise on the individual images to be purely statistical, further improving the contrast-to-noise ratio for a certain dose compared to a system based on a conventional detector.A dual-energy algorithm allows correct reconstruction of the surface concentration of the contrast agent for a range of detail thicknesses, phantom thicknesses and contrast agent concentrations. The high energy resolution of the detector plays a crucial role in image quality, allowing on one hand optimum background removal in KES and DE, and on the other hand increased CNR in KES due to the possibility of choosing energy bands with minimum separation and therefore exploiting the maximum difference in the attenuation coefficients of the contrast agent.The surface concentrations used in this study are greater than typical surface concentrations achieved in real-life scenarios [59]; however, the smallest detail (1 mm diameter) filled with a 50 mg/ml iodine concentration (overall surface concentration 5 mg/cm2) was visible with an MGD of 49 µGy; this, together with the fact that CNR increases proportionally to the square root of dose, suggests that even a 1 mg/cm2 surface concentration could be detected with an MGD of approximately 1.25 mGy, still compatible with clinical requirements.3 The main limitation of the current system is the low counting rate capability, which does not allow clinically viable acquisition times, in terms of both patient discomfort and presence of motion artifacts; the latter could potentially impact both the detail sharpness and the background removal capability. However, improvements in the ASIC and reduction in the shaping time, could bring the acquisition times to the order of

3 This can be confirmed for DE images by using the definition of CNR and applying error propagation on Eq 3, knowing that I ∝ MGD when the spectral parameters of the source are kept constant.

1 min, which is closer to clinical acquisition times but still poses a risk of motion artifacts. Further reduction in the shaping time would come at a more significant cost in terms of energy resolution, thus imposing a trade-off between speed and CNR; this would have to be assessed carefully, but could lead to future use of a photon-counting energy-sensitive detector with energy-resolving capability for quantitative imaging of contrast agent distribution.Scatter removal allows improved quantification of contrast agent surface concentration, which is particularly crucial in the presence of low surface concentrations resulting from small lesion size. Although this work focuses on the quantification of the contrast agent uptake, the potential provided by the availability of an arbitrary number of images at different energies is great: for instance, it is possible to co-register anatomical (from the water equivalent component) and functional (from the iodine component) information, or to modify the algorithm to a three-energy one, and further decouple the water-equivalent image into an adipose-equivalent and a glandular-equivalent one, the latter providing quantitative information on breast density that can be used to predict cancer risk. Any quantitative work, however, will have to take into account any limitations resulting from the presence of the characteristic lines of Cd and Te in the selection of the energy bands.Further work will include the use of sub-pixel resolution post-processing algorithms based on calculation of the centroid of the charge distribution, in order to achieve closer spatial resolution to that of clinical mammographic systems, and the evaluation of alternative contrast agents such as those based on gold nanoparticles; the possibility of functionalizing the nanoparticles to specifically target cancer cells, together with the properties of photon counting detectors with spectroscopic capability, will further increase the effectiveness of hyperspectral CEDM in early detection and staging of breast cancer.

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