Physica Medica 30 (2014) 374e379
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Physica Medica journal homepage: http://www.physicamedica.com
Original paper
Helical differential X-ray phase-contrast computed tomography Jian Fu a, Marian Willner b, Liyuan Chen a, Renbo Tan a, Klaus Achterhold b, Martin Bech b, c, *, Julia Herzen d, Danays Kunka e, Juergen Mohr e, Franz Pfeiffer b a
Beijing University of Aeronautics and Astronautics, 100191 Beijing, China Technische Universität München, 85748 Garching, Germany c Lund University, Department for Medical Radiation Physics, 22185 Lund, Sweden d Institute of Materials Research, Helmholtz-Zentrum Geesthacht, 22607 Hamburg, Germany e Karlsruhe Institute of Technology, Institute for Microstructure Technology, 76344 Eggenstein-Leopoldshafen, Germany b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 July 2013 Received in revised form 9 January 2014 Accepted 11 January 2014 Available online 8 February 2014
We report on the first experimental results of helical differential phase-contrast computed tomography (helical DPC-CT) with a laboratory X-ray tube source and a TalboteLau grating interferometer. The results experimentally verify the feasibility of helical data acquisition and reconstruction in phase-contrast imaging, in analogy to its use in clinical CT systems. This allows fast and continuous volumetric scans for long objects with lengths exceeding the dimension of the detector. Since helical CT revolutionized the field of medical CT several years ago, we anticipate that this method will bring the same significant impact on the future medical and industrial applications of X-ray DPC-CT. Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Keywords: Differential phase-contrast Computed tomography Helical scan
Introduction X-Ray computed tomography (CT) is a powerful tool for medical and industrial applications such as clinical diagnosis, nondestructive testing and material evaluation. However, the usual CT modality is not suitable for extended long objects due to the limited field of view of the detector [1e4]. Since 1990, many attempts have been made to address this problem. The most successful approach is helical or spiral CT [1e4], in which the object is continuously translated through the beam while data is acquired. This allows a large axial coverage within one single scanning process with sufficient reconstruction accuracy and has enabled a broad use of the technique in clinical and industrial applications. Over the last years several phase-contrast imaging techniques have been developed [5e25], which rely on the phase shift introduced to the incoming X-rays when passing through an object. This method provides better image quality in soft-tissue and low atomic number samples. One of the recent developments is differential phase-contrast CT (DPC-CT) based on a grating interferometer [17e 25]. DPC-CT has first been implemented at X-ray synchrotron
* Corresponding author. Technische Universität München, Physics Department E17, James-Franck-Strasse 1, 85748 Garching, Germany. Tel.: þ49 89 289 10807. E-mail addresses: [email protected] (J. Fu), [email protected] (M. Bech), [email protected] (F. Pfeiffer).
radiation sources [18e20] and recently been transferred to labbased X-ray tube sources [21e25]. Several experimental case studies reported in the literature demonstrate that DPC-CT offers improved soft-tissue contrast and more internal structure details than absorption-contrast CT [22,24,25]. A first numerical investigation of helical DPC-CT has been performed by Qi et al. [26], who adapted the reconstruction algorithm of Taguchi [2] and Hu [3] to differential phase-contrast imaging and proved its validity on simulated data. Another numerical case study on helical DPC-CT has been done by Li et al. [27]. However, a proof of principle on experimental data has yet to be shown. The new aspect of the work presented here is to supplement the theoretical considerations of helical DPC-CT by providing an alternative reconstruction algorithm and give the first experimental demonstration on a real biological specimen using a grating-based X-ray tube source imaging system. Methods and materials A three-dimensional object can be described by a complex refractive index distribution n(x,y,z) ¼ 1 d(x,y,z) þ ib(x,y,z), where x, y, and z describe the coordinate system of the sample. In conventional absorption-contrast CT, the imaginary part b is measured by the attenuation of the X-rays transmitted through the specimen. In differential phase-contrast imaging one measures the effect of variations of the real part d by evaluating the tiny refraction angles
1120-1797/$ e see front matter Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ejmp.2014.01.005
J. Fu et al. / Physica Medica 30 (2014) 374e379
of X-rays induced by the specimen with a grating TalboteLau interferometer [21]. Correspondingly, a differential phase-contrast R projection can be expressed by aðy0 ; z0 ; qÞ ¼ vð dðx; y; zÞdlÞ=vy, 0 0 l detector, q the where y and z describe the coordinate system of the rotation view angle of the object around the z-axis and l the incident ray direction. Figure 1(a) and (b) depicts the considered helical DPC-CT scanning geometry. It is similar to the standard DPC-CT, in which the source grating G0, the phase grating G1 and the absorption grating G2 form the TalboteLau interferometer and a sample holder rotates the object over 360 during data acquisition. At each view angle, a phase-stepping procedure is performed and allows attenuation and phase information to be extracted (a detailed description of the method can be found in Refs. [20,21]). The 3D volume of the object can finally be reconstructed by standard CT algorithms. The only modification for the differential phase-contrast data is the application of the imaginary Hilbert filter [22]. In helical scanning mode there is an additional vertical translation of the sample with each rotation step. In the presented helical DPC-CT scanning mode in Fig. 1(a) and (b), the X-ray source and the detector form a cone-beam geometry. In this work, we adapt the corresponding cone-beam helical CT reconstruction algorithm proposed by Noo [4]. This algorithm 0 0 conceptually converts the DPC projections a(y ,z ,q) to a stack of fan0 beam sinograms p(y ,g), each associated with one axial z-slice. Here, g represents the associated fan-beam scanning view angle ranging from 0 to 2p. Once the fan-beam sinograms are built, reconstruction is performed for each z-slice using the classical fan-beam
375
filtered back-projection in combination with the imaginary Hilbert filter [22]. 0 0 Mathematically the conversion equation between a(y ,z ,q) and 0 p(y ,g) is
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y02 þ x02 c pðy0 ; gÞzqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aðy0 ; z0 ; qÞ; y02 þ z02 þ x02 c
(1)
where
z0 z
y02 þ x02 c Dz: xc x0c
(2)
Figure 2 depicts this conversion operation. Dz is the vertical distance between the virtual fan-beam focus spot and the actual helical one (also see Fig. 1(b)). The scaling factor in Eq. (1) accounts for the difference of the length of the X-ray beam in fan-beam circular orbit and helical orbit. Eq. (2) describes a parabola on the detector for the helical data at the view angle q. The measurements on this parabola provide the estimates of all the ray-sums in the fan-beam projection at view angle g and axial position zt. So, in this algorithm, each fan-beam projection is fully estimated from a single helical projection. To obtain a full fan-beam sinogram for a given zslice, this conversion step requires only the data for the segment of the helix that is centred on the position zt. The maximum distance Dz between a helical focus spot and a virtual fan beam focus spot is then equal to 0.5h.
0
0
0
Figure 1. (a) The helical DPC-CT data acquisition scheme with an X-ray tube source and a three-grating TalboteLau interferometer. (x,y,z) and (x ,y ,z ) are two sets of coordinates 0 0 describing the inspected sample and the detector respectively. y and z are the indexes of detector channels. xc is the distance from the X-ray tube to the rotation center and x0c the distance from the X-ray tube to the detector. (b) The geometrical relationship among the imaging parameters. h is the axial sample translation per rotation and defined as the helical 0 0 pitch. a(y ,z ,q) represents the DPC data from the y0th channel of the z0th row array at the view angle q. zt is the axial position of the reconstructed target slice.
376
J. Fu et al. / Physica Medica 30 (2014) 374e379
Figure 2. The geometrical description of the conversion operation in Eq. (1) at one view angle.
When using the converted fan-beam sinogram to reconstruct the target slice, the algorithm employs the short-scan reconstruction technique of 2D absorption-contrast CT [28]. It will suppress the axial blur since the short-scan technique only needs the projections in the view angle range ½0; p þ 2arcsinðr=x0c Þ and provides a small axial slice thickness. Here, r is half the length of the detector. In pseudo code, this algorithm consists of three steps: (i) Fix the axial position of the reconstructed slice z, and determine the 0 0 angular range of q under which the helical data a(y ,z ,q) will be involved into the conversion to estimate the fan-beam sinogram 0 pz(y ,g). (ii) Calculate one complete fan-beam sinogram using Eqs. (1) and (2). (iii) Apply the short-scan fan-beam FBP algorithm with an imaginary filter to reconstruct the slice image. Results A TalboteLau interferometer, combined with an ENRAF Nonius rotating anode X-ray tube and a single photon counting detector (Pilatus II from Dectris, Switzerland), was used to verify the validity of the proposed helical DPC-CT. A mouse, approved by the local ethics committee, was chosen as the specimen. It was decalcified before the measurements to avoid streak artifacts caused by the bones. The sample was fixed in formalin and placed in a plastic cylinder with a diameter of 29 mm. The three gratings of the interferometer were fabricated at the Institute of Microstructure Technology (IMT) and by Microworks (both Karlsruhe, Germany) with periods of 5.4 mm and were arranged in a symmetric setup configuration. The distances between source and phase grating as well as phase and absorption grating were 87.5 cm. The whole interferometer was installed 60 cm away from the X-ray source operated with a Molybdenum target. The phase grating was made of nickel and had a height of about 8 mm, introducing a phase-shift of p to incoming X-rays with a mean energy of 22.8 keV. The heights of the source and absorption gold grating structures were roughly 50 mm. The photon-counting detector Pilatus II had a pixel size of 172 172 mm2 and a silicon sensor thickness of 450 mm. A helical tomography scan and a standard one for comparison have been performed. In both scans the tube voltage and the current were set to 35 kVp and 70 mA respectively. Without an object in the beam, an average count of 630 photons per second was detected on the detector. The mouse specimen was mounted 8 cm in front of the phase grating and the detector 5 cm behind the absorption grating, which results in a sample magnification of 1.72. For the helical scan, the specimen rotated and translated vertically in a step-by-step mode. The number of the sampling view
angles was 344 over 360 . Ten full rotations were completed in total. The vertical shift per projection was set to 5 mm. The resulting helical pitch h during one full rotation was 1.72 mm. Taking the sample magnification factor into account, the effective slice thickness was 100 mm and the sample was translated about 17 detector pixel rows per rotation. For the standard scan, one rotation over 360 without sample translation was performed. The number of the sampling view angles was 350 to ensure that the exposure dose for one slice is almost the same as that of the helical scan. For each sampling view, we executed 11 phase steps with 5 s exposure time per projection image. Taking the time for scanning movements into account, it took about 8 h per rotation. The air dose in our experiment was about 2.5 Gy per rotation (This value was estimated from the dose data reported in Ref. [31]. Our tube source experiment setup is the same as the one in Ref. [31], in which details about the measurement of X-ray dose can be found). However, due to the low detective quantum efficiency (DQE) of the used detector and the attenuation by the gratings, the actual dose that contributed to the projection images was about 1 Gy. Figure 3 displays the helical DPC-CT imaging results. Figure 3(a) and (b) shows the helical differential phase-contrast and absorption-contrast CT slice images by applying the classical FBP algorithm to the fan-beam sinogram converted with Eq. (1). For comparison, Fig. 3(c) and (d) illustrates the corresponding differential phase-contrast and absorption-contrast CT slice images from the standard scanning. Observing Fig. 3, we can conclude that the helical DPC-CT slice and the standard scanning DPC-CT slice have almost the same quality. They both reveal details of internal structure which are difficult to recognize in absorption-contrast CT slice images. Furthermore, one can find that the helical DPC-CT slice has some blurring by doing a careful observation on the structure edges in the enlarged regions in Fig. 3(a) and (c). The profiles along the vertical dash dot red line and the vertical solid blue line in the enlarged regions in Fig. 3(a) and (c), presented in Fig. 3(e), depict this phenomenon quantitatively. The blurring is caused by the helical scanning mode and the approximation of the conversion operation in Eq. (1). The reconstruction of one slice in helical DPCCT needs projection data of a larger sample region than in standard DPC-CT. This is the well-known volume effect in tomography and smoothes some structure details. In order to compare the spatial resolution of the helical and standard DPC-CT in a quantitative manner, we calculated the modulation transfer function (MTF) by applying an FFT to the profiles in Fig. 3(e). First, we evaluated the edge spread function (ESF) by selecting the curves from pixel 272 to 278 in Fig. 3(e). Then the corresponding point spread function (PSF) was produced by taking the derivative of the ESF curves. We padded zero to the PSF to increase the number of sampling points in frequency domain. Finally, the modulation transfer function (MTF) was calculated by taking the Fourier transform of the PSF. Figure 3(f) presents the resulting MTF curves. Obviously, both the helical DPC-CT and the standard DPC-CT have a spatial resolution of 4 lp/mm (line pair per millimeter) with a modulation of about 5%. Furthermore, the modulation at high frequencies is a little lower in helical DPC-CT than in standard DPC-CT. This implies a slightly reduced spatial resolution in helical DPC-CT compared to standard DPC-CT. Contrast-to-noise ratios (CNRs) of selected regions of interest (ROIs) were analyzed to quantitatively assess the contrast in helical and standard DPC-CT. Three ROIs were selected for each slice image: i) covering the structure with high gray value, ii) covering surrounding tissue, iii) probing image noise. A separate ROI for the determination of noise was used because internal tissue structures can increase the standard deviation within a ROI and distort the noise measurement. The third ROI was hence placed within a homogenous region, where the standard deviation only reflects actual
J. Fu et al. / Physica Medica 30 (2014) 374e379
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Figure 3. The helical DPC-CT experimental results. (a) and (b) are the reconstructed helical differential phase-contrast and absorption-contrast CT slices with a size of 335 335 pixels at the same axial position. (c) and (d) are the reconstructed standard scanning phase-contrast and absorption-contrast CT slices with a size of 335 335 pixels at the same axial position as in (a) and (b). The images were scaled from the minimum to maximum value according to a linear gray scale. (e) depicts the profiles along the vertical dash dot red line and the vertical solid blue line in the enlarged regions in (a) and (c). (f) presents the modulation transfer function (MTF) curves calculated by applying an FFT to the profiles in (e). For each slice image, the regions of interest (ROIs) marked by the three colored circles are chosen to calculate contrast-to-noise ratios (CNRs) of the images. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
image noise. The CNR, based on the mean values of regions 1 and 2 (M1 and M2) and the standard deviation of region 3 (s3), was then calculated according to
CNR ¼
jM1 M2j : s3
(3)
In Fig. 3, the chosen ROIs are displayed in each image as colored circles: red (ROI 1) covering the structure with high gray value, blue (ROI 2) covering surrounding tissue and yellow (ROI 3) covering a homogeneous region. Every ROI has a diameter of 10 pixels. Table 1 lists the individual CNRs as well as their respective ratio that reflects the relative contrast improvement of phase over attenuation contrast, i.e. the relative contrast gain. Obviously, the CNR value in helical DPC-CT is a little better than in standard DPC-CT. This is
probably due to the blurring in the helical DPC-CT images, which involves a small noise reduction. To give an impression of the entire reconstruction from the helical DPC data, a selection of the reconstructed slices and the volume rendering of the results are displayed in Fig. 4(a) and (c). For comparison, the corresponding axial DPC-CT slice images and the volume rendering from the standard scanning are presented in
Table 1 The contrast-to-noise ratio analysis for helical and standard DPC-CT. Scan mode
Attenuation contrast
Phase contrast
Relative contrast gain
Helical CT Standard CT
1.1310 1.2192
9.9326 8.7561
8.78 7.18
378
J. Fu et al. / Physica Medica 30 (2014) 374e379
Figure 4. The reconstructed volume from the helical DPC data. First and third row show the axial DPC-CT slice images and the volume rendering of the results from the helical DPCCT scanning. Second and fourth row are the corresponding results from the standard DPC-CT scanning.
Fig. 4(b) and (d). Here, the converted fan-beam sinograms are smoothed by a 5-points mean value filter to suppress the noise. Obviously, apart from the blurring, the image quality of the helical DPC-CT is comparable to that of the standard DPC-CT. Discussion and conclusion Currently, the proposed helical DPC-CT is time-consuming compared to the standard helical absorption-contrast CT. However, there is room for further scanning speed improvement and dose reduction by exploring new phase signal retrieval methods, developing detectors with high DQE and reducing the thickness of the gratings substrates [31]. For example Zanette et al. recently reported a data acquisition and processing method that optimizes dose efficiency by a factor of 4 and enables fast clinical acquisition protocols, while maintaining image quality [30,29]. State-of-the art CMOS imaging detectors can reach a DQE of 70% at small pixel sizes of 75 mm (Dexela 2923) [32]. New gratings are produced on silicon wafers with a thickness of 100 mm instead of 500 mm as used within our study [31]. Assuming a dose-optimized setup, low-dose tube source DPC-CT measurements would reach a range that is compatible with in-vivo imaging of small animals [31]. Additionally, further work should address the optimization of scan parameters, e.g. the helical pitch, with regards to dose exposure and image quality as well as an experimental comparison of the performance of different helical DPC-CT reconstruction algorithms.
In summary, we have successfully demonstrated helical differential phase-contrast CT and its first experimental verification. The results with a grating-based X-ray tube source imaging system show the validity of the adopted helical phase-contrast data acquisition scheme and the reconstruction algorithm. Similar to helical CT having revolutionized the field of clinical CT several years ago, we anticipate that this method will have a significant impact on the future applications of DPC-CT. Acknowledgments J. Fu, L. Y. Chen and R. B. Tan acknowledge support from National Natural Science Foundation of China (50875013, 11179009), China Beijing Municipal Natural Science Foundation (4102036), Program for New Century Excellent Talents in University (NCET) from Ministry of Education of P.R. China, and Beijing NOVA program (2009A09). F. Pfeiffer, K. Achterhold, M. Bech, J. Herzen and M. Willner acknowledge financial support through the DFG Cluster of Excellence Munich-Center for Advanced Photonics (MAP), the DFG Gottfried Wilhelm Leibniz Program and the European Research Council (FP7, Starting grant 240142). The prototype system was developed and the experiments were performed at the Department of Physics, Technische Universität München, Munich, Germany. This work was partly carried out with the support of the Karlsruhe Nano Micro Facility (KNMF, www.kit.edu/knmf), a Helmholtz Research Infrastructure at Karlsruhe Institute of Technology (KIT, www.kit.edu).
J. Fu et al. / Physica Medica 30 (2014) 374e379
References [1] Kalender WA. Technical foundations of spiral CT. Semin Ultrasound CT MRI 1994;15:81e9. [2] Taguchi K, Aradeate H. Algorithm for image reconstruction in multi-slice helical CT. Med Phys 1998;25:550e61. [3] Hu H. Multi-slice helical CT: scan and reconstruction. Med Phys 1999;26:5e 18. [4] Noo F, Defrise M, Clackdoyle R. Single-slice rebinning method for helical conebeam CT. Phys Med Biol 1999;44:561e70. [5] Bonse U, Hart M. An x-ray interferometer. Appl Phys Lett 1965;6:155e6. [6] Davis TJ, Gao D, Gureyev TE, Stevenson AW, Wilkins SW. Phase-contrast imaging of weakly absorbing materials using hard x-rays. Nature 1995;373:595e 8. [7] Ingal VN, Beliaevskaya EA. X-ray plane-wave topography observation of the phase contrast from a non-crystalline object. J Phys D 1995;28:2314e7. [8] Snigirev A, Snigireva I, Kohn V, Kuznetsov S, Schelokov I. On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation. Rev Sci Instrum 1995;66:5486e92. [9] Ingal VN, Beliaevskaya EA. Phase dispersion radiography of biological objects. Phys Med 1996;12:75e81. [10] Momose A, Takeda T, Hirano K. Phase-contrast x-ray computed tomography for observing biological soft tissues. Nat Med 1996;2:473e5. [11] Nugent KA, Gureyev TE, Cookson DF, Paganin D, Barnea Z. Quantitative phase imaging using hard x-rays. Phys Rev Lett 1996;77:2961e4. [12] Wilkins SW, Gureyev TE, Gao D, Pogany A, Stevenson AW. Phase-contrast imaging using polychromatic hard x-rays. Nature 1996;384:335e7. [13] Chapman D, Thomlinson W, Johnston RE, Washburn D, Pisano E, Gmür N, et al. Diffraction enhanced x-ray imaging. Phys Med Biol 1997;42:2015e25. [14] Cloetens P, Ludwig W, Baruchel J, van Dyck D, van Landuyt J, Guigay JP, et al. Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays. Appl Phys Lett 1999;75:2912e4. [15] Fitzgerald R. Phase-sensitive x-ray imaging. Phys Today 2000;7:23e7. [16] Zhou SA, Brahme A. Development of phase-contrast x-ray imaging techniques and potential medical applications. Phys Med Eur J Med Phys 2008;24:129e 48. [17] Momose A. Phase-sensitive imaging and phase tomography using x-ray interferometers. Opt Express 2003;11:2303e14.
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Contents lists available at ScienceDirect
Physica Medica journal homepage: http://www.physicamedica.com
Original paper
Helical differential X-ray phase-contrast computed tomography Jian Fu a, Marian Willner b, Liyuan Chen a, Renbo Tan a, Klaus Achterhold b, Martin Bech b, c, *, Julia Herzen d, Danays Kunka e, Juergen Mohr e, Franz Pfeiffer b a
Beijing University of Aeronautics and Astronautics, 100191 Beijing, China Technische Universität München, 85748 Garching, Germany c Lund University, Department for Medical Radiation Physics, 22185 Lund, Sweden d Institute of Materials Research, Helmholtz-Zentrum Geesthacht, 22607 Hamburg, Germany e Karlsruhe Institute of Technology, Institute for Microstructure Technology, 76344 Eggenstein-Leopoldshafen, Germany b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 July 2013 Received in revised form 9 January 2014 Accepted 11 January 2014 Available online 8 February 2014
We report on the first experimental results of helical differential phase-contrast computed tomography (helical DPC-CT) with a laboratory X-ray tube source and a TalboteLau grating interferometer. The results experimentally verify the feasibility of helical data acquisition and reconstruction in phase-contrast imaging, in analogy to its use in clinical CT systems. This allows fast and continuous volumetric scans for long objects with lengths exceeding the dimension of the detector. Since helical CT revolutionized the field of medical CT several years ago, we anticipate that this method will bring the same significant impact on the future medical and industrial applications of X-ray DPC-CT. Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Keywords: Differential phase-contrast Computed tomography Helical scan
Introduction X-Ray computed tomography (CT) is a powerful tool for medical and industrial applications such as clinical diagnosis, nondestructive testing and material evaluation. However, the usual CT modality is not suitable for extended long objects due to the limited field of view of the detector [1e4]. Since 1990, many attempts have been made to address this problem. The most successful approach is helical or spiral CT [1e4], in which the object is continuously translated through the beam while data is acquired. This allows a large axial coverage within one single scanning process with sufficient reconstruction accuracy and has enabled a broad use of the technique in clinical and industrial applications. Over the last years several phase-contrast imaging techniques have been developed [5e25], which rely on the phase shift introduced to the incoming X-rays when passing through an object. This method provides better image quality in soft-tissue and low atomic number samples. One of the recent developments is differential phase-contrast CT (DPC-CT) based on a grating interferometer [17e 25]. DPC-CT has first been implemented at X-ray synchrotron
* Corresponding author. Technische Universität München, Physics Department E17, James-Franck-Strasse 1, 85748 Garching, Germany. Tel.: þ49 89 289 10807. E-mail addresses: [email protected] (J. Fu), [email protected] (M. Bech), [email protected] (F. Pfeiffer).
radiation sources [18e20] and recently been transferred to labbased X-ray tube sources [21e25]. Several experimental case studies reported in the literature demonstrate that DPC-CT offers improved soft-tissue contrast and more internal structure details than absorption-contrast CT [22,24,25]. A first numerical investigation of helical DPC-CT has been performed by Qi et al. [26], who adapted the reconstruction algorithm of Taguchi [2] and Hu [3] to differential phase-contrast imaging and proved its validity on simulated data. Another numerical case study on helical DPC-CT has been done by Li et al. [27]. However, a proof of principle on experimental data has yet to be shown. The new aspect of the work presented here is to supplement the theoretical considerations of helical DPC-CT by providing an alternative reconstruction algorithm and give the first experimental demonstration on a real biological specimen using a grating-based X-ray tube source imaging system. Methods and materials A three-dimensional object can be described by a complex refractive index distribution n(x,y,z) ¼ 1 d(x,y,z) þ ib(x,y,z), where x, y, and z describe the coordinate system of the sample. In conventional absorption-contrast CT, the imaginary part b is measured by the attenuation of the X-rays transmitted through the specimen. In differential phase-contrast imaging one measures the effect of variations of the real part d by evaluating the tiny refraction angles
1120-1797/$ e see front matter Ó 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ejmp.2014.01.005
J. Fu et al. / Physica Medica 30 (2014) 374e379
of X-rays induced by the specimen with a grating TalboteLau interferometer [21]. Correspondingly, a differential phase-contrast R projection can be expressed by aðy0 ; z0 ; qÞ ¼ vð dðx; y; zÞdlÞ=vy, 0 0 l detector, q the where y and z describe the coordinate system of the rotation view angle of the object around the z-axis and l the incident ray direction. Figure 1(a) and (b) depicts the considered helical DPC-CT scanning geometry. It is similar to the standard DPC-CT, in which the source grating G0, the phase grating G1 and the absorption grating G2 form the TalboteLau interferometer and a sample holder rotates the object over 360 during data acquisition. At each view angle, a phase-stepping procedure is performed and allows attenuation and phase information to be extracted (a detailed description of the method can be found in Refs. [20,21]). The 3D volume of the object can finally be reconstructed by standard CT algorithms. The only modification for the differential phase-contrast data is the application of the imaginary Hilbert filter [22]. In helical scanning mode there is an additional vertical translation of the sample with each rotation step. In the presented helical DPC-CT scanning mode in Fig. 1(a) and (b), the X-ray source and the detector form a cone-beam geometry. In this work, we adapt the corresponding cone-beam helical CT reconstruction algorithm proposed by Noo [4]. This algorithm 0 0 conceptually converts the DPC projections a(y ,z ,q) to a stack of fan0 beam sinograms p(y ,g), each associated with one axial z-slice. Here, g represents the associated fan-beam scanning view angle ranging from 0 to 2p. Once the fan-beam sinograms are built, reconstruction is performed for each z-slice using the classical fan-beam
375
filtered back-projection in combination with the imaginary Hilbert filter [22]. 0 0 Mathematically the conversion equation between a(y ,z ,q) and 0 p(y ,g) is
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y02 þ x02 c pðy0 ; gÞzqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aðy0 ; z0 ; qÞ; y02 þ z02 þ x02 c
(1)
where
z0 z
y02 þ x02 c Dz: xc x0c
(2)
Figure 2 depicts this conversion operation. Dz is the vertical distance between the virtual fan-beam focus spot and the actual helical one (also see Fig. 1(b)). The scaling factor in Eq. (1) accounts for the difference of the length of the X-ray beam in fan-beam circular orbit and helical orbit. Eq. (2) describes a parabola on the detector for the helical data at the view angle q. The measurements on this parabola provide the estimates of all the ray-sums in the fan-beam projection at view angle g and axial position zt. So, in this algorithm, each fan-beam projection is fully estimated from a single helical projection. To obtain a full fan-beam sinogram for a given zslice, this conversion step requires only the data for the segment of the helix that is centred on the position zt. The maximum distance Dz between a helical focus spot and a virtual fan beam focus spot is then equal to 0.5h.
0
0
0
Figure 1. (a) The helical DPC-CT data acquisition scheme with an X-ray tube source and a three-grating TalboteLau interferometer. (x,y,z) and (x ,y ,z ) are two sets of coordinates 0 0 describing the inspected sample and the detector respectively. y and z are the indexes of detector channels. xc is the distance from the X-ray tube to the rotation center and x0c the distance from the X-ray tube to the detector. (b) The geometrical relationship among the imaging parameters. h is the axial sample translation per rotation and defined as the helical 0 0 pitch. a(y ,z ,q) represents the DPC data from the y0th channel of the z0th row array at the view angle q. zt is the axial position of the reconstructed target slice.
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Figure 2. The geometrical description of the conversion operation in Eq. (1) at one view angle.
When using the converted fan-beam sinogram to reconstruct the target slice, the algorithm employs the short-scan reconstruction technique of 2D absorption-contrast CT [28]. It will suppress the axial blur since the short-scan technique only needs the projections in the view angle range ½0; p þ 2arcsinðr=x0c Þ and provides a small axial slice thickness. Here, r is half the length of the detector. In pseudo code, this algorithm consists of three steps: (i) Fix the axial position of the reconstructed slice z, and determine the 0 0 angular range of q under which the helical data a(y ,z ,q) will be involved into the conversion to estimate the fan-beam sinogram 0 pz(y ,g). (ii) Calculate one complete fan-beam sinogram using Eqs. (1) and (2). (iii) Apply the short-scan fan-beam FBP algorithm with an imaginary filter to reconstruct the slice image. Results A TalboteLau interferometer, combined with an ENRAF Nonius rotating anode X-ray tube and a single photon counting detector (Pilatus II from Dectris, Switzerland), was used to verify the validity of the proposed helical DPC-CT. A mouse, approved by the local ethics committee, was chosen as the specimen. It was decalcified before the measurements to avoid streak artifacts caused by the bones. The sample was fixed in formalin and placed in a plastic cylinder with a diameter of 29 mm. The three gratings of the interferometer were fabricated at the Institute of Microstructure Technology (IMT) and by Microworks (both Karlsruhe, Germany) with periods of 5.4 mm and were arranged in a symmetric setup configuration. The distances between source and phase grating as well as phase and absorption grating were 87.5 cm. The whole interferometer was installed 60 cm away from the X-ray source operated with a Molybdenum target. The phase grating was made of nickel and had a height of about 8 mm, introducing a phase-shift of p to incoming X-rays with a mean energy of 22.8 keV. The heights of the source and absorption gold grating structures were roughly 50 mm. The photon-counting detector Pilatus II had a pixel size of 172 172 mm2 and a silicon sensor thickness of 450 mm. A helical tomography scan and a standard one for comparison have been performed. In both scans the tube voltage and the current were set to 35 kVp and 70 mA respectively. Without an object in the beam, an average count of 630 photons per second was detected on the detector. The mouse specimen was mounted 8 cm in front of the phase grating and the detector 5 cm behind the absorption grating, which results in a sample magnification of 1.72. For the helical scan, the specimen rotated and translated vertically in a step-by-step mode. The number of the sampling view
angles was 344 over 360 . Ten full rotations were completed in total. The vertical shift per projection was set to 5 mm. The resulting helical pitch h during one full rotation was 1.72 mm. Taking the sample magnification factor into account, the effective slice thickness was 100 mm and the sample was translated about 17 detector pixel rows per rotation. For the standard scan, one rotation over 360 without sample translation was performed. The number of the sampling view angles was 350 to ensure that the exposure dose for one slice is almost the same as that of the helical scan. For each sampling view, we executed 11 phase steps with 5 s exposure time per projection image. Taking the time for scanning movements into account, it took about 8 h per rotation. The air dose in our experiment was about 2.5 Gy per rotation (This value was estimated from the dose data reported in Ref. [31]. Our tube source experiment setup is the same as the one in Ref. [31], in which details about the measurement of X-ray dose can be found). However, due to the low detective quantum efficiency (DQE) of the used detector and the attenuation by the gratings, the actual dose that contributed to the projection images was about 1 Gy. Figure 3 displays the helical DPC-CT imaging results. Figure 3(a) and (b) shows the helical differential phase-contrast and absorption-contrast CT slice images by applying the classical FBP algorithm to the fan-beam sinogram converted with Eq. (1). For comparison, Fig. 3(c) and (d) illustrates the corresponding differential phase-contrast and absorption-contrast CT slice images from the standard scanning. Observing Fig. 3, we can conclude that the helical DPC-CT slice and the standard scanning DPC-CT slice have almost the same quality. They both reveal details of internal structure which are difficult to recognize in absorption-contrast CT slice images. Furthermore, one can find that the helical DPC-CT slice has some blurring by doing a careful observation on the structure edges in the enlarged regions in Fig. 3(a) and (c). The profiles along the vertical dash dot red line and the vertical solid blue line in the enlarged regions in Fig. 3(a) and (c), presented in Fig. 3(e), depict this phenomenon quantitatively. The blurring is caused by the helical scanning mode and the approximation of the conversion operation in Eq. (1). The reconstruction of one slice in helical DPCCT needs projection data of a larger sample region than in standard DPC-CT. This is the well-known volume effect in tomography and smoothes some structure details. In order to compare the spatial resolution of the helical and standard DPC-CT in a quantitative manner, we calculated the modulation transfer function (MTF) by applying an FFT to the profiles in Fig. 3(e). First, we evaluated the edge spread function (ESF) by selecting the curves from pixel 272 to 278 in Fig. 3(e). Then the corresponding point spread function (PSF) was produced by taking the derivative of the ESF curves. We padded zero to the PSF to increase the number of sampling points in frequency domain. Finally, the modulation transfer function (MTF) was calculated by taking the Fourier transform of the PSF. Figure 3(f) presents the resulting MTF curves. Obviously, both the helical DPC-CT and the standard DPC-CT have a spatial resolution of 4 lp/mm (line pair per millimeter) with a modulation of about 5%. Furthermore, the modulation at high frequencies is a little lower in helical DPC-CT than in standard DPC-CT. This implies a slightly reduced spatial resolution in helical DPC-CT compared to standard DPC-CT. Contrast-to-noise ratios (CNRs) of selected regions of interest (ROIs) were analyzed to quantitatively assess the contrast in helical and standard DPC-CT. Three ROIs were selected for each slice image: i) covering the structure with high gray value, ii) covering surrounding tissue, iii) probing image noise. A separate ROI for the determination of noise was used because internal tissue structures can increase the standard deviation within a ROI and distort the noise measurement. The third ROI was hence placed within a homogenous region, where the standard deviation only reflects actual
J. Fu et al. / Physica Medica 30 (2014) 374e379
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Figure 3. The helical DPC-CT experimental results. (a) and (b) are the reconstructed helical differential phase-contrast and absorption-contrast CT slices with a size of 335 335 pixels at the same axial position. (c) and (d) are the reconstructed standard scanning phase-contrast and absorption-contrast CT slices with a size of 335 335 pixels at the same axial position as in (a) and (b). The images were scaled from the minimum to maximum value according to a linear gray scale. (e) depicts the profiles along the vertical dash dot red line and the vertical solid blue line in the enlarged regions in (a) and (c). (f) presents the modulation transfer function (MTF) curves calculated by applying an FFT to the profiles in (e). For each slice image, the regions of interest (ROIs) marked by the three colored circles are chosen to calculate contrast-to-noise ratios (CNRs) of the images. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
image noise. The CNR, based on the mean values of regions 1 and 2 (M1 and M2) and the standard deviation of region 3 (s3), was then calculated according to
CNR ¼
jM1 M2j : s3
(3)
In Fig. 3, the chosen ROIs are displayed in each image as colored circles: red (ROI 1) covering the structure with high gray value, blue (ROI 2) covering surrounding tissue and yellow (ROI 3) covering a homogeneous region. Every ROI has a diameter of 10 pixels. Table 1 lists the individual CNRs as well as their respective ratio that reflects the relative contrast improvement of phase over attenuation contrast, i.e. the relative contrast gain. Obviously, the CNR value in helical DPC-CT is a little better than in standard DPC-CT. This is
probably due to the blurring in the helical DPC-CT images, which involves a small noise reduction. To give an impression of the entire reconstruction from the helical DPC data, a selection of the reconstructed slices and the volume rendering of the results are displayed in Fig. 4(a) and (c). For comparison, the corresponding axial DPC-CT slice images and the volume rendering from the standard scanning are presented in
Table 1 The contrast-to-noise ratio analysis for helical and standard DPC-CT. Scan mode
Attenuation contrast
Phase contrast
Relative contrast gain
Helical CT Standard CT
1.1310 1.2192
9.9326 8.7561
8.78 7.18
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Figure 4. The reconstructed volume from the helical DPC data. First and third row show the axial DPC-CT slice images and the volume rendering of the results from the helical DPCCT scanning. Second and fourth row are the corresponding results from the standard DPC-CT scanning.
Fig. 4(b) and (d). Here, the converted fan-beam sinograms are smoothed by a 5-points mean value filter to suppress the noise. Obviously, apart from the blurring, the image quality of the helical DPC-CT is comparable to that of the standard DPC-CT. Discussion and conclusion Currently, the proposed helical DPC-CT is time-consuming compared to the standard helical absorption-contrast CT. However, there is room for further scanning speed improvement and dose reduction by exploring new phase signal retrieval methods, developing detectors with high DQE and reducing the thickness of the gratings substrates [31]. For example Zanette et al. recently reported a data acquisition and processing method that optimizes dose efficiency by a factor of 4 and enables fast clinical acquisition protocols, while maintaining image quality [30,29]. State-of-the art CMOS imaging detectors can reach a DQE of 70% at small pixel sizes of 75 mm (Dexela 2923) [32]. New gratings are produced on silicon wafers with a thickness of 100 mm instead of 500 mm as used within our study [31]. Assuming a dose-optimized setup, low-dose tube source DPC-CT measurements would reach a range that is compatible with in-vivo imaging of small animals [31]. Additionally, further work should address the optimization of scan parameters, e.g. the helical pitch, with regards to dose exposure and image quality as well as an experimental comparison of the performance of different helical DPC-CT reconstruction algorithms.
In summary, we have successfully demonstrated helical differential phase-contrast CT and its first experimental verification. The results with a grating-based X-ray tube source imaging system show the validity of the adopted helical phase-contrast data acquisition scheme and the reconstruction algorithm. Similar to helical CT having revolutionized the field of clinical CT several years ago, we anticipate that this method will have a significant impact on the future applications of DPC-CT. Acknowledgments J. Fu, L. Y. Chen and R. B. Tan acknowledge support from National Natural Science Foundation of China (50875013, 11179009), China Beijing Municipal Natural Science Foundation (4102036), Program for New Century Excellent Talents in University (NCET) from Ministry of Education of P.R. China, and Beijing NOVA program (2009A09). F. Pfeiffer, K. Achterhold, M. Bech, J. Herzen and M. Willner acknowledge financial support through the DFG Cluster of Excellence Munich-Center for Advanced Photonics (MAP), the DFG Gottfried Wilhelm Leibniz Program and the European Research Council (FP7, Starting grant 240142). The prototype system was developed and the experiments were performed at the Department of Physics, Technische Universität München, Munich, Germany. This work was partly carried out with the support of the Karlsruhe Nano Micro Facility (KNMF, www.kit.edu/knmf), a Helmholtz Research Infrastructure at Karlsruhe Institute of Technology (KIT, www.kit.edu).
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