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IOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 54 (2009) 2747–2753 doi:10.1088/0031-9155/54/9/010
Soft-tissue phase-contrast tomography with an x-ray
tube source
Martin Bech1, Torben H Jensen1, Robert Feidenhans1, Oliver Bunk2,
Christian David2and Franz Pfeiffer2,3,4
1Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
2Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
3´
Ecole Polytechnique F´
ed´
erale de Lausanne, CH-1015 Lausanne, Switzerland
E-mail: bech@fys.ku.dk and franz.pfeiffer@ph.tum.de
Received 14 January 2009, in final form 9 March 2009
Published 15 April 2009
Online at stacks.iop.org/PMB/54/2747
Abstract
We report the first experimental soft-tissue phase-contrast tomography results
using a conventional x-ray tube source, with a millimeter-sized focal spot.
The setup is based on a Talbot–Lau grating interferometer operated at a
mean energy of 28 keV. We present three-dimensional ex vivo images of a
chicken heart sample, fixated in formalin. The results clearly demonstrate
the advantageous contrast attainable through phase-contrast imaging over
conventional attenuation-based approaches.
1. Introduction
X-ray radiography has been used for medical imaging since the discovery of x-rays more than
a hundred years ago. By the development of computed tomography (CT), x-ray imaging could
be further improved and non-destructive three-dimensional (3D) views of internal structures
became possible (Cormack 1963, Hounsfield 1973). In particular, for medical diagnostics
applications, x-ray CT became an invaluable tool during the last 30 years.
Today the contrast in x-ray CT images is essentially limited by the maximum tolerable
dose, and the resulting statistical constraints when measuring the x-ray attenuation precisely
along the ray trajectories. Since the absorption coefficients of soft tissue are very close to that
of water, it is very difficult to distinguish internal features in the soft material.
One way to improve the contrast is through the use of x-ray phase-contrast imaging
techniques (Snigirev et al 1995, Wilkins et al 1996). Over the last few years, essentially three
different techniques have been developed: propagation-based phase-contrast imaging (Mayo
et al 2003, Cloetens et al 2006), crystal or grating analyzer-based phase-contrast imaging
(Zhong et al 2000,Keyril
¨
ainen et al 2002,Bravin2003, Clauser 1998,Davidet al 2002,
4Present address: Department of Physics, Technical University of Munich, 85747 Garching, Germany.
0031-9155/09/092747+07$30.00 © 2009 IOP Publishing Ltd Printed in the UK 2747
2748 M Bech et al
Figure 1. Schematic view of the experimental setup. Not to scale. The G0 grating acts as
a slit array, producing parallel line sources. The sample is placed immediately in front of the
interferometer, and the detector is placed immediately after. The distance Lbetween gratings G0
and G1, and the distance dbetween gratings G1 and G2 are indicated in the figure.
Momose et al 2003), and crystal interferometer-based phase-contrast imaging (Bonse and
Hart 1965, Momose et al 1995, Beckmann et al 1999). In particular, the recent studies of
x-ray phase-contrast imaging using a grating interferometer at a synchrotron demonstrate that
it is possible to distinguish subtle details in soft materials that are indistinguishable in standard
absorption-based x-ray tomography (Weitkamp et al 2005, Momose et al 2006,Pfeifferet al
2007a,Davidet al 2007b).
Despite these good results at synchrotron radiation sources, the data recorded at ordinary
x-ray tubes have not yet demonstrated clear advantages in soft-tissue phase-contrast CT.
Here, we now present the first tomographic phase-contrast images obtained with a grating
interferometer, which demonstrate that high soft-tissue contrast can also be obtained with
standard x-ray tube sources and centimeter-sized samples.
2. Experimental setup
In the experiments presented here, a grating interferometer and a PILATUS 100K detector
module were used. The setup was installed at a Seifert ID 3000 x-ray generator operated at
40 kV/30 mA, with an effective source size of 0.8 mm (hor) ×0.4 mm (ver). The detector
had 487 ×195 pixels, with a pixel size of 172 ×172 μm2, yielding a total field of view of
83 ×33 mm2.
2.1. Interferometer
For phase-contrast x-ray imaging, we used a grating-based interferometer with three gratings in
Talbot–Lau geometry (Pfeiffer et al 2006); see figure 1. The setup comprises an x-ray source,
one grating after the source, the sample (on a tomographic rotation stage), two gratings after
the sample and the image detector. The gratings are source grating G0, phase grating G1 and
analyzer grating G2. Grating G1 is a pure Si grating, whereas gratings G0 and G2 are Si/Au
absorption gratings made by etching into a Si wafer and subsequent electro-plating of Au as
described elsewhere (David et al 2007a).
The grating G0 is mounted close to the source, and ensures a suitable horizontal transverse
coherence length of the x-ray beam for each line source created by G0. The interferometer
consisting of gratings G1 and G2 is located at a distance of L=1.4 m from the source. G1 has
Soft-tissue phase-contrast tomography 2749
a period of 3.5 μm, and a depth of 36 μm corresponding to a phase shift of πat 28 keV. Due
to the Talbot self-imaging effect (Talbot 1836), interference fringes are formed at fractional
Talbot distances corresponding to
a=jg2
1
8λ
(in plane-wave geometry), where jis an odd integer, g1is the period of the phase grating G1
and λis the wavelength. To account for magnification due to the divergent beam geometry of
our experiment, the actual fractional Talbot distances dare rescaled by
d=jg2
1
8λ
L+d
L
=La
L−a.
In the current experiment, the setup was operated at the fifth fractional Talbot distance (j =5)
corresponding to d=20 cm. The period g2of grating G2 was 2 μm, which is equal to
the interference fringe period caused by grating G1. The source grating G0 has a period of
g0=g2×L/d =14 μm, ensuring that the interference patterns from neighboring source
lines will overlap at G2 (David et al 2007a). The sample should be located immediately in
front of G1, and the detector should be immediately behind G2. In the current experiment,
these distances were approximately 50 mm and 30 mm, respectively.
2.2. Data acquisition and processing
Differential phase-contrast images are extracted from the raw image data recorded during a
phase stepping scan in the following way: a number of exposures are made while stepping the
analyzer grating G2 transversely over one period of the grating. The recorded intensity is thus
a function of pixel position (px,p
y)and grating position xg. As the analyzer grating G2 has
the same period as the interference pattern caused by G1, the exact position of the interference
pattern can be extracted from the measured intensity I(p
x,p
y,x
g), transmitted through G2.
The shift of the interference pattern from a refracted beam relative to that of the undisturbed
beam is a direct measure of the refraction angle. Knowing the angle of refraction, it is trivial
to calculate the gradient of the total phase shift ∇=2πα/λ, and the total phase shift by
integration. By using computed tomography techniques, it is then possible to quantitatively
reconstruct a three-dimensional map of the refractive index: n=1−δ+iβ. The real part δ
is related to the total electron density ρand the wavelength λby
δ=ρr0λ2
2π,
where r0=2.82 ×10−15 m is the Thomson scattering length (Als-Nielsen and McMorrow
2001). The imaginary part βof the refractive index nis related to the absorption coefficient
μ=4πβ/λ. The tomographic reconstruction of the attenuation data was carried out using
standard filtered back-projection using a Ram-Lak filter, as described, e.g., in Kak and Slaney
(2001). The differential phase-contrast signal was reconstructed using an imaginary filter
(Hilbert transform) and back-projection, as previously described in Pfeiffer et al (2007b,
2007c).
3. Results
To test the applicability of x-ray tubes for phase-contrast CT on soft tissue, we have measured
phase-contrast images of a chicken heart in a tomography setup. The heart was fixated in 4%
2750 M Bech et al
(a) (b)
Figure 2. X-ray images of a chicken heart. (a) Conventional x-ray image, attenuation contrast.
(b) Phase-contrast image. The images show a single projection, which is part of a 375 image
projection dataset. The images are displayed using a linear gray scale. The transmission values
(a) are given relative to water. The phase-contrast values (b) are given as the transverse shift of the
interference pattern in the plane of G2. The white scale bar corresponds to 5 mm.
formalin solution and kept in a cylindrical plastic container. The container was submerged in
a water bath as illustrated in figure 1.
The tomography data were recorded with 16 phase steps per projection and a total of
375 projections, covering a 360◦sample rotation. In this proof-of-principle experiment the
exposure time was 10 s per frame, yielding a total exposure time of 13 h. Please note that the
current measurement has not been optimized for low radiation dose or short exposure time.
In an improved setup, one could reduce the number of phase steps from 16 to 4, and with a
high power x-ray source, gratings for higher energy, and a detector with a higher quantum
efficiency, the exposure time and radiation dose would be lowered considerably. Figure 2
shows the conventional x-ray transmission image and the phase-contrast image from a single
projection. The fact that muscle tissue and water have almost the same attenuation coefficient
makes it difficult to see the heart in the standard x-ray image. But the less-dense adipose tissue
in the top part of the image is visible. In the differential phase-contrast image, the contour of
the heart can be faintly distinguished from the surrounding water.
Though the image contrast in a single projection (figure 2) is relatively poor, images with
much higher contrast can be obtained from virtually slicing the tomographically reconstructed
3D volume, owing to the increased statistics obtained through the many projections. As
illustrated in figures 3(a) and (e), the adipose tissue visible in figure 2is clear and distinct in
the reconstructed absorption contrast image. But the signal from the heart muscle itself is still
comparable to the background noise level. In the phase tomography dataset, figures 3(b)–(d)
and (f)–(h), both the adipose tissue and the heart muscle itself are clearly visible.
In the processing of the data, a flat-field correction of the beam transmitted through the
water tank (40 mm thickness) without the sample in place is used to correct for inhomogeneities
in the illumination and the sensitivity response of the detector. As a result the attenuation
is normalized to that of water during reconstruction, and hence the data are subsequently
calibrated to the table values for the index of refraction for water. The table values are
μ=0.36 cm−1and δ=2.94 ×10−7(Henke et al 1993), respectively.
To provide a quantitative comparison of absorption contrast to phase contrast, figure 4,
left panel, displays the pixel values along the red bold-dashed line in figures 3(a), (b), (e) and
(f). We observe that the differences in the attenuation values (μ) between the heart tissue
and water are buried in the noise level, whereas they are well resolved in the corresponding
phase-contrast signals (δ). The improved contrast is further exposed in figure 4, right panel,
which shows a histogram representation of all pixels in the axial slices in figures 3(a) and
(b). In the phase-contrast histogram two distinct peaks are seen at δ=2.94 ×10−7and
Soft-tissue phase-contrast tomography 2751
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 3. Slices through the reconstructed 3D tomography volume. (a) Axial slice, absorption
contrast. (b)–(d) Axial slices, phase contrast. (e) Frontal slice, absorption contrast. (f)–(h) Frontal
slices, phase contrast. The images are displayed on a linear gray scale. The absorption-contrast
gray scale ranges from μ=0.31 cm−1to μ=0.41 cm−1(symmetrically around the water peak),
and the phase-contrast gray scale ranges from δ=2.8×10−7to δ=3.2×10−7(covers water
and muscle tissue). Frontal and axial slices are vertically ordered pairwise such that they intersect
in the red dashed line. Voxel values along the red dashed lines of panels (a), (b), (e) and (f) are
plotted in figure 4(left panel). The black scale bar corresponds to 5 mm.
0.2
0.25
0.3
0.35
0.4
0.45
Attenuation coefficient (μ) [cm ]
Attenuation coefficient
Index of refraction
00.5 11.5 22.5 33.52.6
2.7
2.8
2.9
3
3.1
3.2
x 10
Index of refraction (δ)
Position in sample [cm]
0.2
0.25
0.3
0.35
0.4
0.45
Attenuation coefficient (μ) [cm ]
Attenuation coefficient
Index of refraction
0500 1000 1500 2000
2.6
2.7
2.8
2.9
3
3.1
3.2
x 10
Index of refraction (δ)
Voxel count
Figure 4. Left panel: plot of absorption coefficient μand the real part of refractive index δalong
the red dashed line in figures 3(a), (b), (e) and (f). Right panel: histogram of the voxels in the
entire axial slice in figures 3(a) and (b).
δ=3.07 ×10−7, corresponding to water and heart tissue, respectively. It is also noteworthy
that the cylindrical sample container and adipose tissue are distinguishable in the phase-
contrast signal at δ=2.71 ×10−7and δ=2.75 ×10−7, respectively. The absorption
histogram has only two peaks, one at μ=0.36 cm−1corresponding to water/heart, and the
other at μ=0.24 cm−1, corresponding to adipose tissue/plastic. This clearly illustrates far
better contrast using the phase signal.
Note that the y-axis scales on left and right panels of figure 4are identical.
2752 M Bech et al
4. Conclusions
In summary, we have presented the first, grating-based experimental soft-tissue phase-contrast
computed tomography results using a conventional x-ray tube source with millimeter-sized
focal spot. The results clearly demonstrate the advantageous contrast attainable through
phase-contrast imaging over conventional attenuation-based approaches.
We have particularly shown that a quantitative analysis of the sample composition is
feasible on the basis of the phase-contrast data, even though the absorption data hardly
provide any contrast at all. More precisely, we have demonstrated that quantitative electron
densities can be obtained from the measured δvalues. For a chicken heart test sample fixated
in formalin, we deduced electron densities of ρ=3.49 ×1023 cm−3for the muscle tissue,
ρ=3.13×1023 cm−3for the adipose tissue and ρ=3.08 ×1023 cm−3for the plastic cylinder,
when calibrating against an electron density for water of ρ=3.34 ×1023 cm−3.
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