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PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 53 (2008) 4031–4047
doi:10.1088/0031-9155/53/15/002
Experimental feasibility of multi-energy
photon-counting K-edge imaging in pre-clinical
computed tomography
J P Schlomka1, E Roessl1, R Dorscheid2, S Dill2, G Martens1, T Istel1,
C Bäumer3, C Herrmann3, R Steadman3, G Zeitler3, A Livne4
and R Proksa1
1
2
3
4
Philips Research Europe, Sector Medical Imaging Systems, Hamburg, Germany
Philips Research Europe, Engineering & Technology, Aachen, Germany
Philips Research Europe, Sector Medical Imaging Systems, Aachen, Germany
Philips Healthcare, Global Research and Advanced Development, Haifa, Israel
E-mail: [email protected]
Received 11 March 2008, in final form 10 June 2008
Published 8 July 2008
Online at stacks.iop.org/PMB/53/4031
Abstract
Theoretical considerations predicted the feasibility of K-edge x-ray computed
tomography (CT) imaging using energy discriminating detectors with more
than two energy bins. This technique enables material-specific imaging
in CT, which in combination with high-Z element based contrast agents,
opens up possibilities for new medical applications. In this paper, we
present a CT system with energy detection capabilities, which was used to
demonstrate the feasibility of quantitative K-edge CT imaging experimentally.
A phantom was imaged containing PMMA, calcium-hydroxyapatite, water and
two contrast agents based on iodine and gadolinium, respectively. Separate
images of the attenuation by photoelectric absorption and Compton scattering
were reconstructed from energy-resolved projection data using maximumlikelihood basis-component decomposition. The data analysis further enabled
the display of images of the individual contrast agents and their concentrations,
separated from the anatomical background. Measured concentrations of
iodine and gadolinium were in good agreement with the actual concentrations.
Prior to the tomographic measurements, the detector response functions for
monochromatic illumination using synchrotron radiation were determined in
the energy range 25 keV–60 keV. These data were used to calibrate the detector
and derive a phenomenological model for the detector response and the energy
bin sensitivities.
0031-9155/08/154031+17$30.00
© 2008 Institute of Physics and Engineering in Medicine
Printed in the UK
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1. Introduction
The attenuation properties of matter for x-rays are energy- and material dependent. This
allows, in return, deriving material properties by using a multitude of different x-ray energies
for imaging. A simple realization of this technique is known as ‘dual-energy imaging’ (Alvarez
and Macovski 1976, Kelcz et al 1979, Lehmann and Alvarez 1986). Using different incident
spectra (Lehmann et al 1981) or energy discrimination on the detector side (‘dual crystal
method’) (Barnes et al 1985, Carmi et al 2005), information about the average Z-number of
the material under investigation can be derived. In medical imaging this method can be used
to, e.g., suppress beam-hardening effects or to discriminate to some extent between calcium
or iodine and lighter elements (Z < 20), which form body tissues.
When heavier elements are used in contrast agents such as, e.g., gadolinium, gold or
bismuth their K-absorption edges lying at 50.2 keV, 80.7 keV and 90.5 keV, respectively,
become accessible for diagnostic x-ray imaging. By using more than two spectrally distinct
measurements (tube spectra, filtrations, energy bins, etc), these K-edge features can be
discriminated from the other contributions to the x-ray attenuation. To distinguish this
acquisition method from ‘dual energy CT’ it is referred to as ‘spectral CT’ in this paper.
Spectral CT in combination with a data analysis method, which allows extracting, from a
single scan, separate images of the contrast agent on the one hand and of the anatomy on
the other hand we refer to as ‘K-edge imaging’ (Lehmann and Alvarez 1986, Sukovic and
Clinthorne 1999).
K-edge imaging can be realized by using multi-bin energy-discriminating counting
detectors. New developments in direct-conversion semiconductor detectors based on CZT
(Cadmium–Zinc–Telluride) or CdTe (Cadmium Telluride) may enable the application of this
technique also for medical CT imaging (Takahashi et al 2005, Kowase and Ogawa 2006).
In a previous paper (Roessl and Proksa 2007) the theory of projection-based material
decomposition from energy-binned photon-counting data was presented. The processing
described there is based on an extension of the dual-energy method first introduced by Alvarez
and Macovski (1976) to a higher number of basis components. Roessl and Proksa showed
simulated images, which clearly allowed the differentiation between various basis components
including images showing only the contrast agent. In that work the contrast agent was based
on gadolinium, but also other high-Z materials seemed feasible. It was already mentioned that
it might be possible to use even more than 1 contrast agent simultaneously, provided sufficient
energy discrimination on the detectors side.
In the present paper we report on the experimental proof of this technique. For this task,
a research spectral CT scanner based on a rotating gantry was built, which enables convenient
multi-slice scanning. In the measurements presented here we used a technical phantom
containing several materials including two different conventional medical contrast agents.
Thus, a four-basis component decomposition was required. Separate images of the anatomy
and the contrast agents are presented. A prerequisite for the spectral analysis is the knowledge
of the spectral response of the detector. We measured this function using monochromatic
synchrotron radiation at several different primary energies and derived a phenomenological
description of the complete spectral response behavior of the detection system.
This paper is structured as follows: in section 2 we introduce the theoretical background
of spectral CT, i.e., the physical models of the attenuation and the detection of the x-rays as
well as the maximum-likelihood processing method performed prior to image reconstruction.
Section 3 introduces the experimental spectral CT system used in the studies and briefly
describes the synchrotron set-up used for detector characterization. In section 4 we present
experimental results focusing on first spectral CT phantom images. A discussion and outlook
Experimental feasibility of multi-energy photon-counting K-edge imaging in pre-clinical CT
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section completes this paper. The detector energy scale calibration and the response function
model are briefly explained in the appendix.
2. Theory
The theoretical formalism of K-edge imaging using energy-binned detection and maximumlikelihood processing of the projection data has been introduced in an earlier paper (Roessl
and Proksa 2007) and will therefore only briefly be reproduced here for completeness.
2.1. X-ray attenuation and detection
The energy dependence of the linear attenuation coefficient µ(E, x ) of materials in the
diagnostic energy range ∼15–150 keV can be approximated fairly well by a linear combination
of the photoelectric and the Compton cross sections fph (E) and fKN (E), see Alvarez and
Macovski (1976) and references therein. If no absorption edges are located within the
used energy range, the photoelectric cross section can be approximated by its E −3 energy
dependence, and we obtain
1
+ aCo (
x )fKN (E).
(1)
E3
The vector x describes the space dependence of the attenuation and the energy dependence
of the total Compton cross section fKN (E) was first derived by Klein and Nishina (1929) and
can be found in, e.g., Knoll (2000).
In the presence of elements with high atomic number Z, the above description of the
attenuation properties of matter has to be modified to correctly describe the attenuation of
the sample. In the experimental set-up presented below, we used the elements iodine and
gadolinium. Both elements are widely applied in medical contrast agents. For spectral CT
iodine has the disadvantage that its K-edge is at the rather low energy of 33.2 keV and can
therefore hardly be discriminated from other tissue in thicker objects such as, e.g., human
patients by means of its K-edge only. On the other hand, for pre-clinical applications iodine
is very well suited due to the much lower tube voltages and less severe photon starvation
below the iodine K-edge. Gadolinium is mainly known as an MRI contrast agent due to
its magnetic properties but is also used in some medical x-ray imaging applications (RemyJardin et al 2006). It should be emphasized that the two contrast materials were mainly taken
because of their easy accessibility. K-edge imaging in the medical case is not limited to just
these materials. Provided toxicity issues can be resolved, all materials with K-edge energies
above ∼40 keV, e.g., gold or bismuth, could potentially be used in human applications. For
the sake of clarity, however, we will use the indices ‘Gd’ and ‘I’ for the two K-edge materials,
noting that they are potential placeholders for other future K-edge materials.
To incorporate the attenuation of iodine and gadolinium, equation (1) now has to be
extended by the energy-dependent attenuation functions of the two elements gadolinium and
iodine (Lehmann and Alvarez 1986, Sukovic and Clinthorne 1999, Roessl and Proksa 2007):
1
x ) 3 + aCo (
x )fKN (E) + aGd (
x )fGd (E) + aI (
x )fI (E)
µ(E, x ) = aph (
E
4
≡
aα (
x )fα (E).
(2)
µ(E, x ) = aph (
x)
α=1
aGd (
x ), fGd (E), aI (
x ), fI (E) denote the local density and the mass attenuation coefficient of
gadolinium and iodine, respectively. In the second line of equation (2) the values α = 1, 2, 3, 4
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represent the photoelectric effect, the Compton effect and the gadolinium and iodine-based
contrast-agent components. The mass attenuation coefficients of the two K-edge elements
account for all attenuation effects including the Compton effect and the photo-effect with the
K-edge discontinuity of the photo cross section. While in dual-energy systems (at least) two
spectrally different measurements per x-ray path have to be performed in order to determine
x ) and aCo (
x ), the extended model equation (2) relies
the line integrals of the coefficients aph (
on a minimum of four measurements.
Our x-ray detector was operated in photon-counting mode applying energy discrimination
by six threshold values for each individual pixel k = 1 . . . 1024. Physically, the thresholds
are realized by voltages u(i,k)
T , i = 1, . . . , 6, which are fed into the pulse-height comparator
circuits. The pulse height obtained from the detector is nearly proportional to the energy of the
detected photon, but gain and offset vary from bin to bin and from pixel to pixel. Therefore, the
relationship between the measured photon energy UT(i,k) (in keV) and the threshold voltage u(i,k)
T
(in mV), which triggers the corresponding event, had to be determined through a calibration
process described in the appendix. Upon successful completion of this calibration process
of all individual pixels corresponding to a given value of i had to
the threshold voltages u(i,k)
T
be set to different but well-defined values to ensure the realization of homogeneous threshold
settings in the measured energy UT(i,k) despite the variations in the gain and offset of the detector
electronics. Thus the index k, representing the pixel dependence in the measured energy can
be omitted. In practice, slight variations of the measured energy remain, but were not taken
into account in the present processing scheme. A photon with energy Eph was counted in one
of the six adjacent bins Bi , if its measured energy equivalent Uph fulfilled UT(i) Uph < UT(i+1) .
The uppermost bin B6 had no upper threshold, i.e. UT(7) = ∞.
A discrepancy between the actual photon energy Ep and the measured energy Up arises
from the detection process. Physical effects such as electronic noise, incomplete charge
collection, energy loss due to K-escape, or other sources contribute to a degradation of the
energy resolution of the detector. As a consequence, two adjacent energy bins are not sharply
separated by the energy threshold at their common boundary. Their sensitivities are described
by so-called bin sensitivity functions Si (E) and the effects contributing to the degradation of
the energy resolution lead to an overlap of the bin-sensitivity functions. These functions were
determined experimentally as described in section 4 and the appendix.
Having described the attenuation and the detection process we can now introduce a
statistical description of the counting process via the expectation value λi of the number of
x ):
photons in the energy bin Bi and the line integrals Aα of the coefficients aα (
∞
4
Si (E)(E) exp −
fα (E)Aα D(E) dE, i = 1, . . . , 6, (3)
λi (A1 , A2 , A3 , A4 ) =
0
with
α=1
Aα =
aα (
x ) ds,
α = 1, . . . , 4.
(4)
In equation (3), (E) denotes the spectral x-ray photon fluence, and D(E) the detector
absorption efficiency.
2.2. Maximum-likelihood processing of projection data
For our application, the number of energy bins exceeds the dimension of the attenuation basis.
The system in equation (3) is therefore overdetermined, and, in general, no solution exists
for A1, A2, A3 and A4. To overcome this difficulty, the improved spectral sampling of the
Experimental feasibility of multi-energy photon-counting K-edge imaging in pre-clinical CT
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attenuation process can be combined with adequate methods of parameter estimation, such as
the least-squares method or the method of maximum likelihood. In our processing method we
used the maximum-likelihood approach, because the corresponding estimators turned out to
be efficient and unbiased in many practical situations (Cowan 1998, Eadie et al 1971).
Mi (Aα ), i = 1, . . . , N (with N = 6 in our case) denote the random variables describing
the number of photons detected in the energy bin Bi and λi (Aα ) denote their mean values.
The random variables and their corresponding mean values depend on the line integrals
Aα . Assuming that the Mi form a set of independent Poisson random variables, we
can calculate the likelihood function as the probability of an arbitrary measurement result
(M1 = m1 , . . . , MN = mN ), given a particular composition of the object parameterized by
Aα :
P (m1 , . . . , mN |λ1 (Aα ), . . . , λN (Aα )) =
N
λi (Aα )mi
i=1
mi !
e−λi (Aα ) .
(5)
Instead of directly maximizing the likelihood function P , it is usually more convenient
to minimize the negative log-likelihood L which, re-expressed as a function of the parameters
Aα , becomes
L(m1 , . . . , mN |Aα ) = −ln[P (m1 , . . . , mN |λ1 (Aα ), . . . , λN (Aα ))]
N
=
[λi (Aα ) + ln mi ! − mi ln λi (Aα )]
i=1
∼
=
N
[λi (Aα ) − mi ln λi (Aα )].
(6)
i=1
In the last step, we dropped terms independent of Aα and, therefore, irrelevant for the
minimization. By minimizing the above expression equation (6) given the measurement results
(m1 , . . . , mN ) with respect to the four parameters Aα , we obtain the maximum-likelihood
estimates AML
α .
The optimization problem can only be treated numerically. A large variety of powerful
numerical algorithms exist, which are specialized to the task of likelihood maximization. We
used the simplex method of Nelder and Mead for our calculations (Nelder and Mead 1965,
Press et al 1992).
For the processing of spectral projection data we determined the line integrals Aα as
described above for all measured paths through the object under study. Once the maximumlikelihood processing for all paths was complete, four conventional reconstruction steps using
standard filtered-back projection techniques generated four basis images (Kek and Slaney
2001).
3. Experimental set-up
3.1. CT set-up
The tomographic measurements were carried out using an experimental spectral CT scanner
based on a direct-drive rotating gantry (figure 1). On the drive motor a rotating disc was
mounted and the components were mounted onto this disc. As an x-ray source a microfocus tube (KEVEX PXS10-65 W) operating at voltages between 70 kVp and 130 kVp was
used. Energy spectra were measured prior to installation on the gantry using a germanium
detector with energy resolution of a few hundred eV. The focal spot size depends on the applied
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Figure 1. Schematic drawing and photograph of the pre-clinical spectral CT system used for this
study. The key components on a rotating gantry are a micro-focus x-ray tube (top) and a single-line
energy-binning photon-counting detector (bottom).
electrical power starting at 10 µm for low power increasing to 100 µm at a maximum power of
65 W. The measurements presented below were taken at a 100 kVp beam voltage and a 100 µA
beam current, which resulted in a beam spot of ∼12 µm (according to the manufacturer) and
a measured x-ray flux of about 3 × 105 cts pixel−1 s−1. The x-ray tube has a beryllium exit
window. No additional energy-spectrum filter or bow-tie filter was used. Slits at the tube exit
collimate the x-rays into a narrow fan beam.
As detector, a single-line photon-counting CdTe array manufactured by GammaMedicaIdeas (Northridge, Ca., USA) was employed (Tajima et al 2004). The x-rays enter the detector
through a 2 mm aluminum housing. Concerning the x-ray dose, it would be more appropriate
to reduce the detector window thickness and instead use pre-object filtering. This is planned
in a future system upgrade. The detector is equipped with 1024 pixels with 0.4 mm average
pixel pitch. The active area of each pixel is 0.38 mm × 1.6 mm with a crystal thickness of
3 mm. A lead slit placed in front of the detector crystals collimates the illuminated detector
width to 1.2 mm. For each pixel, six independent comparator threshold levels can be set
via software. One 16 bit counter is provided for each of the comparators. Read-out of
all counters takes 25 µs during which no data can be acquired. The system geometry is
adjustable providing the capability for high-resolution measurements with a small field of
view and medium resolution measurements with a larger field of view. For this purpose, the
tube and the detector are mounted on slides and can be repositioned easily. The geometry
parameters for two settings are given in table 1. For the measurement below, the medium
resolution set-up was applied. The maximum rotation speed of the system is limited to 0.33
revolutions s−1 to avoid excessive centrifugal forces on the mounted components. For the
measurements presented here, however, the gantry rotated much slower to enable good photon
statistics while maintaining a rather low photon flux onto the detector. Angular positions are
measured by an optical encoder, which directly triggers the PC-based data acquisition on the
Experimental feasibility of multi-energy photon-counting K-edge imaging in pre-clinical CT
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Table 1. Geometry parameters for two configurations of the spectral CT experimental scanner. To
switch from one configuration to the other, source and detector can be translated independently on
slides. Spatial resolution was estimated by measuring the full width at half maximum of a 50 µm
thick tungsten wire in reconstructed images.
High resolution set-up
Distance source–isocenter
100 mm
Distance isocenter–detector center
500 mm
Magnification
6
Field of view
60 mm
Spatial resolution
∼100 µm
Large field-of-view set-up
300 mm
300 mm
2
200 mm
∼250 µm
gantry. A master PC controls the data acquisition PC remotely via an ethernet link through a
slip ring.
3.2. Synchrotron set-up
Detector calibration measurements were carried out at the DESY/Hasylab facility (Hamburg,
Germany) at beam-line X1 (Hasylab 2007, Baumer et al 2008). The beam line is positioned at
a bending magnet of the DORIS ring, equipped with a Si (5 1 1) double crystal monochromator
and provides monochromatic x-ray photons in the energy range from 25 keV to 80 keV with
an energy bandwidth lower than 100 eV. The cross section of the beam was 6 mm × 0.25 mm
illuminating about 15 adjacent pixels at a time. Due to this small footprint of the synchrotron
beam, it was required to translate the detector perpendicular to the beam to cover the full active
area of the detector. Measurements were carried out with photon fluxes between 105 and 106
photons pixel−1 s−1.
4. Results
4.1. Detector calibration and characterization at the synchrotron
The spectral response was derived from so-called threshold scans. For such a scan, the detector
was illuminated under constant flux conditions with monochromatic photons of energy E.
The count rate c for a given pixel k = 1 . . . 1024 and comparator i = 1, . . . , 6 was recorded
while varying the comparator threshold voltages u(k,i)
T . From the derivative of this function
(k,i) (k,i) d
(k,i)
c
u
the
spectral
response
R
E,
U
was obtained after making use of the
(k,i)
T
T
duT
and UT(k,i) through the energy scale calibration (see appendix).
relationship between u(k,i)
T
The aim of the calibration procedure was to set the thresholds UT(k,i) of all detector pixels
k = 1 . . . 1024 to one common value UT(i) by using individual values u(k,i)
T for each comparator.
Since we assumed equal spectral
response
of
each
pixel,
the
index
kcould
also be omitted for
the spectral response R (i) E, UT(i) . The spectral response of a bin i, R (i) E, UT(i) , describes
the probability of a photon of energy E to be counted at a measured energy UT(i) . From the
response function the bin sensitivity functions S (i) (E) was calculated for given thresholds
UT(i) :
S (i) (E) =
UT(i+1)
UT(i)
R (i) (E, U ) dU
i = 1, . . . , 6
UT(7) = ∞.
(7)
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J P Schlomka et al
0.12
25 keV
30 keV
35 keV
40 keV
45 keV
50 keV
55 keV
60 keV
Normalized count rate
0.1
0.08
0.06
0.04
0.02
0
15
20
25
30
35
40
45
50
55
60
65
70
Measured photon energy/keV
Figure 2. Spectral response of one threshold in one detector pixel resulting from monochromatic
illumination with photon energies ranging from 25 keV to 60 keV. The count rate in the detector
was about 105 photons pixel−1 s−1. The data are normalized to an integrated count rate of
1 cts s−1 above 20 keV.
The bin sensitivity function gives the probability of a photon of energy E to be measured
in bin i.
Figure 2 shows exemplary, but representative experimental results for one detector pixel
and one energy threshold measured at a count rate of 105 photons pixel−1 s−1. We used eight
distinct incident energies ranging from 25 keV to 60 keV. The maximum response occurring at
the incident energy—the photo-peak—could be well described by a Gaussian with increasing
width at higher energies. This broadening could not be explained by the statistics of the
electron–hole pair generation within the crystal. Incomplete charge collection contributed
dominantly. In addition to the photo-peak, some spectra exhibited a K-escape peak (Sato et al
2005). This peak appeared about 25 keV below the photo peak. An incident photon contributes
to the K-escape peak if immediately after its photoelectric absorption a K-photon is emitted
from the host atom and leaves the active pixel volume. This results in a reduction of the
deposited energy by the energy of the K-escape photon. For Cd and Te, K-fluorescence
energies lie between 22.7 keV and 31.7 keV, in good agreement with the observed average of
25 keV. Emission of the fluorescence photon from the excited atom and escape of this photon
from the active detector pixel volume are prerequisites for the reduction in deposited energy
measured in the pixel. The latter process is energy dependent and therefore influences the
intensity of the escape peak. For higher energies, lower photo absorption cross sections and
the deeper average penetration of the primary photons will lower the K-escape probability and
consequently the escape peak intensity.
Finally, besides the photo- and the K-escape peak, a rather constant background in the
response function was found between the noise band and the photo-peak. We attribute this to
charge sharing events, i.e., the charge generated by a single incident photon is measured in
two neighboring pixels with reduced energy in each pixel. For energies above the incoming
photon energy hardly any intensity was measured, which showed that for a rate of 105 photons
pixel−1 s−1 pile-up did not play a significant role (Knoll 2000). This behavior changed when
the flux was increased to 106 photons pixel−1 s−1 leading to significant pile-up. To avoid the
degradation of the spectral response in this feasibility study by pile-up, we measured with
Experimental feasibility of multi-energy photon-counting K-edge imaging in pre-clinical CT
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10000
Measurement 0.22mm Sn foil @ 70 kV
9000
Measurement 0.22mm Sn foil @ 130 kV
8000
number of photons
Measurement 1.2mm Pb @ 130 kV
7000
simulations
6000
noise measured with 30mm Pb @ 130 kV
5000
4000
3000
2000
1000
0
10
30
50
70
90
110
130
Measured photon energy/keV
Figure 3. Measured and calculated transmission of 70 kVp and 130 kVp x-ray tube spectra through
0.22 mm of tin and 1.2 mm of lead, respectively. Measurements were performed through threshold
scans. For the calculations the response function described by equations (A.2) and (A.3) was used.
the low flux of 105 photons pixel−1 s−1. Count rate issues will be treated in more detail in
section 5.
The observation of the shape of the spectral response motivated the phenomenological
model described in the appendix. Since the shapes of the spectral responses of the individual
pixels and bins did not vary strongly, we used only one function for the description of all
pixels.
To verify the applicability of the modeled response, we measured the transmission of two
known polychromatic spectra (acceleration voltages of 70 kV and 130 kV) through tin and
lead. The two materials exhibit their K absorption edge within the x-ray range considered
here. Thus the transmission spectra show very distinct features. These spectra were measured
by threshold scans and obtained in parallel by calculations using the above spectral response
model. Figure 3 shows the good agreement of measurement and calculation.
4.2. Tomographic measurements
For the feasibility study of K-edge spectral CT a phantom was used that exhibited certain
features of clinical relevance. As described in section 1, one major application is the distinction
of the contrast agent from calcifications in a single CT scan. Furthermore, applications using
more than 1 type of contrast agent may also become relevant, e.g., in the simultaneous,
selective enhancement of different regions such as the vascular system on the one hand using
a blood-pool agent and soft plaque on the other hand using an agent targeting, e.g., fibrin.
We therefore designed the PMMA phantom shown in figure 4. It hosted 12 contrast agent
filled tubes surrounded by calcium-hydroxyapatite ([Ca5-(PO4)3(OH)], bone mineral) in a gel
matrix. Furthermore, a central reservoir was filled with water. The detailed layout is given in
the figure. As contrast agents two conventional medical contrast agents were tested, one based
on iodine, PeritrastTM5 , and one based on gadolinium: MagnevistTM6 . The concentrations of
the heavy metals in the inserts are given in table 2.
5
6
PeritrastTM , Köhler Chemie, Alsbach-Hähnlein, Germany.
MagnevistTM , Schering, Berlin, Germany.
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J P Schlomka et al
PMMA
Gd-3
Gd-2
I-1
water
I-2
I-3
Gd-1
Figure 4. Schematic drawing of the ‘coronary phantom’ used for the tomographic feasibility test
of K-edge imaging. The small holes were filled with two different contrast agents (gadolinium
and iodine based) in three different concentrations each, surrounded by the bone mineral calciumhydroxyapatite in a gel matrix. The diameter of the phantom was 8 cm, the calcium-hydroxyapatite
inserts had an outer diameter of 8 and 10 mm and an inner diameter of 5 mm. Concentrations are
given in table 2.
Table 2. Nominal and measured contrast agent concentrations of the inserts in the ‘coronary
phantom’ schematically drawn in figure 4. Standard deviations were measured by analyzing
regions of interest in the center of the inserts.
Inserts 1 (low concentration)
Inserts 2 (medium concentration)
Inserts 3 (high concentration)
Nominal
Measured
Nominal
Measured
Nominal
Measured
Iodine
concentration
(µmol ml−1)
Gadolinium
concentration
(µmol ml−1)
37.5
32 ± 25
75
68 ± 25
150
132 ± 30
30
32 ± 25
60
70 ± 25
120
116 ± 25
Per rotation 450 projections were acquired with frame duration of 250 ms. This resulted
in a total measurement time of 112.5 s per slice and a dose equivalent of 11.3 mAs. The
energy thresholds were set at 25 keV, 30 keV, 40 keV, 50 keV, 60 keV, and 80 keV. As a
first pre-processing step two-sided energy windows were calculated from the original data.
This was done by subtracting the number of photons measured above the upper threshold
from the number of photon counts measured above the lower threshold. This procedure can
possibly be problematic for high count rates when baseline shifts can occur in the detector
electronics, which was, however, not the case at the low rates used in this experiment. For the
uppermost bin no subtraction was needed and the bin remained single sided. As a next step,
we performed the normalization using an air-scan measured prior to the object measurement.
Furthermore, gain correction was done on each pixel and bin using prior transmission data
through a polycarbonate board of constant 4 cm thickness. The measurement was modeled
and the quotient between measurement and simulation was used as a correction factor for the
observed intensities. In the pre-processing algorithm this correction factor was weighted with
the measured attenuation. The weight was zero for no attenuation and 1 when the attenuation
matched the attenuation of the polycarbonate board. For other attenuation values data were
inter- or extrapolated linearly. As a final step, and to further improve the reconstruction quality,
Experimental feasibility of multi-energy photon-counting K-edge imaging in pre-clinical CT
4041
Figure 5. Reconstructed CT images of the six individual energy bins of the photon-counting
detector. The lower energy thresholds of the six bins were 25, 30, 40, 50, 60 and 80 keV (From left
to right, from top to bottom). A tube voltage of 100 kVp and a beam current of 100 µA were used.
The rotation speed was 112.5 s per turn. All slices were normalized to Hounsfield units measured
in the central inset. Level and window of the images are 150 HU/1700 HU.
a deringing method following the algorithm described in Niederlöhner (2006) was applied in
projection space.
4.2.1. Analysis of the energy-windowed data. In figure 5 the reconstruction results of the
projection data of the five two-sided energy bins and the upper single-sided bin are shown.
Already in these images the K-edge properties of the contrast agents—at least for the high
concentrations—are visible. The iodine inserts exhibit strong attenuation in the bin 30 keV–
40 keV, whereas gadolinium increases strongly in attenuation when the energy exceeds
50 keV. Hydroxyapatite shows strong decrease in attenuation with increasing energies. This
behavior is typical for medium-Z materials, where attenuation is dominated by photo electric
absorption at lower energies. These materials are therefore best visible in the lower energy
bins. The attenuation of the light materials water and PMMA is dominated by Compton scatter
and therefore the dependence on energy is much weaker. They show slightly different energy
dependence due to the small difference in their average Z number.
4.2.2. Spectral analysis. The results of the spectral decomposition applying the procedure
described in section 2.2 are shown in figures 6 and 7. Four basis functions describing
four attenuation processes were used for the procedure: photoelectric absorption, Compton
scattering, attenuation by iodine and attenuation by gadolinium. The basis functions
describing the attenuation by the heavy metals contain the total attenuation caused by these
elements, originating from the photo effect including the K-shell contribution and the Compton
scattering. Their photo-effect and Compton contributions therefore did not show up in the
other, unspecific basis function images. The photo- and the Compton attenuation images of
figure 6 were calculated at an x-ray energy of 60 keV from the first and the second term of
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J P Schlomka et al
Figure 6. Reconstructed images after material decomposition. From left to right: photo-electric
attenuation image (gray scale level/window (L/W): 3.75 × 10−3 mm−1/7.5 ×10−3 mm−1 at
60 keV photon energy), Compton scattering attenuation image (L/W 0.021 mm−1/0.042 mm−1
at 60 keV photon energy), iodine concentration image and gadolinium concentration image (L/W
50 µmol ml−1/150 µmol ml−1). Note the narrow line at the bottom of the iodine image. It can
be attributed to a sticky tape containing barium, which has its K-edge only 4.3 keV higher than
iodine.
Figure 7. Left/center: Calculated monochromatic images at photon energies of 34 keV and
51 keV. Gray scale images range from µ = 0, . . . , 1.0 mm−1 and µ = 0, . . . , 0.8 mm−1,
respectively. Right: color overlay image of the gadolinium concentration (green) and iodine
concentration (red) on a monochromatic 51 keV image.
(This figure is in colour only in the electronic version)
equation (2), respectively, using the energy-independent values aph (
x ) and aCo (
x ) obtained
through the spectral processing.
As can be seen in the images, the decomposition into the four basis functions separated
the individual materials. In the photo image the bone mineral is most prominent, the ‘soft
tissues’ water and PMMA are well visible in the Compton image, and the two contrast agents
are separately shown in the individual images almost without any anatomical background.
Some ring artifacts remain in the image mainly due to small pixel-to-pixel variations of
the threshold positions. Furthermore, during the processing all detector pixels were described
by one and the same response function, which can at best be an approximation. Differences in
the crystal quality, for example, resulted in different electronic properties of the material, e.g.
variation in charge carrier lifetime and mobility, and thus differences in the spectral response.
Additionally, ‘cross-talk’ between the two contrast agent images is visible. At the positions
of the high iodine concentrations a small negative shift occurs in the gadolinium image, and at
the positions of the high gadolinium concentrations a small positive contribution also occurs
in the iodine image. Furthermore, all images show small offsets. In the photo- and Compton
basis images, the offsets are negative. In the iodine and gadolinium images a positive offset
outside the object changes into a negative offset inside the object. These artifacts have to
be attributed to a combination of an inaccurate description of the spectral response by our
Experimental feasibility of multi-energy photon-counting K-edge imaging in pre-clinical CT
4043
model function, incomplete knowledge of the primary x-ray tube spectrum as well as limited
accuracy of the threshold positions.
4.2.3. Quantification. Besides the possibility to separate individual materials, K-edge
imaging also offers the capability for quantification. Using the two right-hand side images of
figure 6 the iodine and gadolinium concentrations were measured by averaging over regions
of interest within the 12 contrast agent filled inserts. Since two inserts were always filled
with the same concentration, the two values were averaged. The error bars were derived from
the image noise and the constant offset was taken into account by subtracting an averaged
concentration value measured near the center of the object. The quantification results are
summarized in table 2 showing that very good agreement is found between the measured
values and the nominal concentrations. For the given values of dose and spatial resolution, a
contrast-to-noise ratio of about 1 was reached at a concentration of 25 µmol ml−1. To obtain
more accurate concentration measurements or to measure lower concentrations, more dose
equivalent than the 11.3 mAs used here had to be delivered. Furthermore, the system had not
yet been optimized, e.g., the threshold positions could be tuned to the K-edges of the contrast
materials.
From the basis component images, monochromatic images for arbitrary photon energies
could be obtained. The four images were combined in such a fashion that the summed image
represents the attenuation at exactly the chosen energy, as if the image was recorded with
monochromatic radiation. This is presented in the two images on the left in figure 7. Using
this type of representation has the advantage that anti-correlated noise, as it can occur in the
material separation procedure, is strongly reduced. Such artificial images are free of any
beam-hardening effects and the energy can be chosen such that the contrast agent contribution
to attenuation is enhanced. The two examples in figure 7 were chosen at energies right above
the K absorption edges, such that the iodine and the gadolinium contributions were maximal
in the respective image.
Spectral CT sometimes is promoted as ‘Color CT’. In fact, the material-separated images
can be combined into a single image with color coding and thus produce a color image.
One such example is given in the right image of figure 7. The gadolinium and iodine
concentrations are color coded in green and red, respectively, and drawn as overlay on top of
the monochromatic 51 keV image.
5. Discussion and outlook
In this paper we demonstrated that K-edge spectral CT is experimentally feasible, confirming
simulations presented in a previous paper (Roessl and Proksa 2007). Images of the different
contrast mechanisms were reconstructed individually and the concentrations of contrast agents
were quantified. In the experiments it was shown that even two heavy metals could be
distinguished and quantified independently from a single scan.
The images do not have medical diagnostic quality since they suffer from some ring
artifacts and offsets. The causes for these artifacts are, however, already mostly known.
The offsets occurred because our model of the spectral response, the primary spectrum and
the threshold positions of the individual pixels did not perfectly describe the experimental
conditions. The ring artifacts mainly occurred due to the low-threshold positioning accuracy
inherent to the current system, which could only be adjusted to about 1.3 keV standard
deviation. Furthermore, variations in crystal quality slightly changed the spectral response
from pixel to pixel (Sato et al 2005). Since in the current version of our processing, all pixels
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J P Schlomka et al
are described by identical threshold positions and spectral response, pixel-to-pixel variations in
the spectral decomposition do occur, which as a consequence lead to the observed ring artifacts.
In future work, improved calibration and processing schemes will take these variations into
account and will lead to a clear suppression of the observed artifacts.
Immediate applications of K-edge imaging can be found in pre-clinical imaging,
where spectral CT can become an important imaging technique to provide material-specific
quantitative information in combination with high spatial resolution imaging. Naturally, one
major pre-clinical research field for spectral CT will be contrast agent research, aiming at
development of functional, disease-specific, targeted contrast agents.
The experiments presented here were taken under conditions of very low x-ray flux
accommodating the fact that state-of-the-art, high-rate photon-counting detectors cannot cope
with count rates as high as those present in human CT. In a conventional medical CT scanner
with a source–detector distance of about 1 m, high power x-ray tubes guarantee a fast data
acquisition with photon fluxes of above 108 s−1 mm−2 (without the use of a bow-tie filter).
For current-mode (energy-integrating) readout through a combination of a scintillator and
a photodiode, as is common practice in conventional x-ray CT, such high photon fluxes
pose no particular problem. With photon-counting detectors based on direct-conversion
semiconductors such as CZT or CdTe, counting photons at such high rates constitutes a
formidable task. Typical charge collection times in these materials are around 50 ns and
thus the possible maximum count rates will lie somewhere around 5 × 106 s−1, taking into
account pulse shaping and pulse height discrimination. In a recent paper (Iwanczyk et al
2007) a measured count rate of 6 × 106 s−1 was reported using a detector with 30 ns peaking
time. Our measurements were carried out at much lower rates, since at high rates pile-up
will occur and the spectral response will degrade. It is therefore an important task to develop
correction schemes in the form of additional hardware components in the detector itself or
software correction schemes, which will allow good spectral performance at these rates. Frey
et al (2007a, 2007b) already investigated this issue and presented a pile-up correction scheme.
Even when pile-up correction can be achieved, there still remains a discrepancy between a
rate of ∼5 × 106 s−1 achievable in a pixel and the CT rate of above 108 s−1 per mm2. The
most straightforward approach here is sub-structuring of the pixels’ anodes to reduce the count
rate per pixel. However, when the pixel size reaches the size of the charge cloud produced
by a stopped photon and the subsequent diffusion toward the anode, charge sharing will
strongly increase and spoil the spectral response. Furthermore, Compton scatter and K-escape
crosstalk will also increase. Therefore, there is a physical lower limit for admissible sub-pixel
sizes, determined by an unacceptable loss of spectral information due to the above-mentioned
effects.
Further steps have to be taken to reach CT count rate capability by photon-counting
detectors. In a recent patent application it was suggested to use layers of detectors
on top of each other to share the high count rates between more layers (Tkaczyk
et al 2007). Since attenuation caused by humans is rather pronounced, the count rate
drops quickly when going from the unattenuated beam into the patient. The ‘count rate
problem’ is therefore confined to rays passing through the peripheral parts of the body. It was
also suggested in Tkaczyk et al (2007) to design the detector such that the count rates are
distributed unevenly between the layers. The result is that for the high rate in the unattenuated
primary beam some layers remain active while other layers saturate. The idea now is to disable
overloaded detector layers and read out only the layers that are still active. The influence of
this data acquisition scheme on noise performance has still to be investigated.
Finally, the experiments presented here were acquired in a fan-beam geometry with
only one detector line and without the use of any anti-scatter grid. On the other hand, any
Experimental feasibility of multi-energy photon-counting K-edge imaging in pre-clinical CT
4045
commercial CT system nowadays uses the cone-beam geometry instead. It is well known from
conventional CT that scattered radiation can become a significant image quality issue when no
counter measures are applied (Engel et al 2008b). For spectral CT this issue could potentially
be even more problematic since energy loss through Compton scatter will introduce additional
changes in the transmitted spectra. Simulations, however, showed that even for rather thick
objects this issue can be solved by the use of 2D anti-scatter grids (Engel et al 2008a).
A combination of all steps described above may allow photon-counting to enter the
medical CT domain, which in combination with novel contrast agents will enable new K-edge
imaging applications.
Acknowledgments
We acknowledge Naor Wainer and Ami Altman (Philips Healthcare, Haifa, Israel) for fruitful
and lively discussions, Bjørn Sundal (GammaMedica-Ideas, Oslo, Norway) for ongoing
technical detector support and Adam Webb (Hasylab/DESY, Hamburg, Germany) for technical
support during the synchrotron measurements.
Appendix
A.1. Detector energy scale calibration
For the energy scale calibration we measured the detector response at two known energies
El , l = 1, 2 by threshold scans (see section 4.1). We then determined u(k,i)
T ,MAX,El as the
(k,i) d
. Then for each pixel and threshold a linear
positions of the maxima of (k,i) c uT
duT
and energy UT(k,i) was assumed. The individual gains g (k,i) and the
relationship between u(k,i)
T
(k,i)
of all thresholds described this relationship and could be determined from the two
offsets o
measurements:
(k,i)
u(k,i)
T ,MAX,E2 − uT ,MAX,E1
(k,i)
(k,i)
(k,i)
=
g
U
+
o
,
g
=
,
u(k,i)
T
(A.1)
E2 − E1
(k,i)
o(k,i) = u(k,i)
E1 .
T ,MAX,E1 − g
Equations (A.1) were used to calculate the correct voltage settings for all pixels, such that
all thresholds were set to the same photon energy level.
A.2. Response function model
The phenomenological model for the response function was motivated by the analysis of
the response function measurements (see section 4.1). The model function consists of two
Gaussian peaks, one at the incident energy and one at an energy reduced by the average energy
of K-escape photons. Furthermore, a constant background for energies below the incident
energy is present in the model. This results in the following formula:
1
1 (U − E)2
exp −
R(U, E) = c1 (E) √
2 σ1 (E)2
2π σ1 (E)
1
1 (U − Ee − E)2
+ c2 (E) √
+ B(U, E) .
(A.2)
exp −
2
σ2 (E)2
2π σ2 (E)
The background B(U, E) has a constant value on the U -scale of c3 for U < (E − 3σ1 )
and is then linearly ramped down to zero within a width of 6σ1 . Ee is the average energy of an
4046
J P Schlomka et al
Table 3. Parameters used in equation (A.3) resulting from the fit of equation (A.2) to the measured
data shown in figure 2.
Parameter
Value
a1
a2
a3
a4
a5
a6
0.5
0.015 keV−1
0.042 keV−1
0.213 × 10−3 keV−2
1.61 keV
0.025
escape photon (For CdTe this is ∼25 keV). The constant c1 (E) is taken such that the number
of photons of the incoming flux is preserved.
The constants c2 (E) and c3 (E) as well as the width of the photo- and escape peak
σ1 (E) and σ2 (E)depend on the incident energy E. We used the measured response functions
(figure 2) and included also measurements using a 57Co radioactive source with 122 keV photon
energy to derive the dependences by fitting the measured spectra to the model function. To
reduce the number of free parameters, the widths of the photo peak and the escape peak were
assumed to be equal (σ (E) = σ1 (E) = σ2 (E)). From the fit to the data one gets the following
relationships valid for the energy range 0–150 keV (energy taken in keV) (see table 3):
a1 · exp(−a2 E), for E Ee
c2 (E) =
0, for E < Ee
(A.3)
c3 (E) = a3 − a4 E
σ (E) = a5 + a6 E.
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