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A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom
Physica Medica xxx (2016) xxx–xxx
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Original paper
A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom q Zhicheng Zhang a,b, Shaode Yu a,b, Xiaokun Liang a,c, Yanchun Zhu a,⇑, Yaoqin Xie a,⇑ a
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China Shenzhen College of Advanced Technology, University of Chinese Academy of Sciences, Shenzhen, China c School of Information Engineering, Guangdong Medical College, Dongguan, China b
a r t i c l e
i n f o
Article history: Received 1 February 2016 Received in Revised form 14 May 2016 Accepted 30 June 2016 Available online xxxx Keywords: Ultrafast micro-CT Carbon nanotube Motion artifact Temporal resolution
a b s t r a c t Artifacts induced by respiratory motion during routine diagnosis severely degrades the image quality. The increase of scanning speed plays an important role to avoid motion artifacts. Limited to the mechanical structure of conventional CT, the increase of gantry rotational speed is unsustainable and a more feasible way is to increase the number of X-ray sources and detectors like the dual-source CT. This paper focuses on high-speed scanning CT and proposes a novel ultrafast micro-CT (UMCT) system based on carbon nanotube (CNT). At each exposure position, all of the X-ray sources are fast activated by turns and the flat-panel detectors collect the corresponding projection data. Then, the gantry will be contrarotated 40° to prepare for the next exposure until the rotation covers full 360°. Because each exposure is very fast, the organ motions of in vivo human body can be greatly reduced. This paper introduces the UMCT system design, image reconstruction algorithm and experimental results. Simulation experiment was also carried out on UMCT system. The result validated the feasibility of the UMCT system. Ó 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
1. Introduction 3D microscopy which has a high spatial resolution can be revealed non-destructively for fine-scale internal structures is X-ray-based three-dimensional (3D) imaging for a limited field of view (FOV) [1,2]. It has been widely used in small animal imaging and plays an important role in the research of human organ, exploration of disease mechanisms and effectiveness of drug assessment [3]. As to currently commercial scanners, it is still a big challenge to perform in vivo micro-CT on small animals because of their much faster physiological motion than that of human. Motion artifacts severely degrade the micro-CT imaging quality and significantly affect the effectiveness of disease diagnosis [4].
q This work is supported in part by grants from Guangdong Innovative Research Team Program of China (Grant No. 2011S013), National 863 Programs of China (Grant Nos. 2012AA02A604 and 2015AA043203), National Key Research and Develop Program of China (Grant No. 2016YFC0105102), Shenzhen Key Lab for Molecular Imaging (ZDSY20130401165820357), National Natural Science Foundation of China (Grant No. 81501463), Natural Science Foundation of Guangdong Province (Grant No. 2014A030310360) and Beijing Center for Mathematics and Information Interdisciplinary Sciences. ⇑ Corresponding authors. E-mail addresses: [email protected] (Y. Zhu), [email protected] (Y. Xie).
Conventional micro-CT uses a hot cathode based X-ray source. According to the theory of thermionic electron emission, the electron source must be heated above 2000 °C in order to allow free electrons to escape from its surface [5], thus it is impossible for hot cathode based X-ray source to be switched on and off instantaneously. Using field-emission sources to replace thermionic sources was suggested over 50 years ago. However, lacking of chemically stable cathode material frustrated efforts to fabricate reliable cold cathode field emission devices [6]. Fortunately, carbon nanotube (CNT) was reported in 1991 [7] and it was suggested that this new material had great potential for use as an electron field emitter [8]. CNT has the inherent advantage of stable emission, long lifetimes, and low emission threshold potentials [9]. Lu et al. used CNT as cathode materials in X-ray source to replace conventional filament in 2002 for the first time [10]. The devices consisted of a multiple sources array within a single source [11,12]. Recently, they transferred their attention to radiation using CNT based X-ray source [13,14]. Compared with traditional X-ray source, CNT based X-ray source demonstrates vast advantages. Above all, generating little heat inside the cold cathode source is crucial for the minimization of an X-ray source and prolongs its lifetime. Moreover, the amount of electron emission is up to its surface electric field intensity, consequently CNT based X-ray source is readily
http://dx.doi.org/10.1016/j.ejmp.2016.06.016 1120-1797/Ó 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
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controllable in a pulse operation by adjusting the grid voltage when the cathode is earthed or controlling the insulated gate bipolar transistor (IGBT) open and close with a designed pulse [12,15]. In addition, due to the desired gaussian distribution, the intensity distribution of the focal spot obtained from a pinhole measurement can provide better spatial resolution than either uniform or bimodal intensity distributions, not the double-peaked distribution commonly found on thermionic X-ray sources [16]. In view of the excellent properties of CNT materials, several groups have recently disclosed the concept of multi-source X-ray imaging using CNT based X-ray source. Jonathan S. Maltz et al. proposed a stationary-gantry tomosynthesis system for on-line image guidance in radiation therapy base on a 52-source cold cathode based X-ray source [6]. Zhou et al. proposed a spatially distributed multi-beam field emission X-ray source for stationary digital breast tomosynthesis [17–21]. The systems proposed by Jonathan S. Maltz and Zhou can obtain pretty high temporal resolution on account of no any mechanical movement during imaging process. But digital tomosynthesis only acquired fewer projections as compared to conventional CT scanners, it yielded images similar to conventional tomography with a limited depth of field [22]. Li et al. designed a multi-source instant CT for superfast imaging [23], but their system still needed several rotation times during covering the range of 360°. It is always desirable to reduce the gantry motion and speed up scanning process. In this paper, a novel design of ultrafast micro-CT (UMCT) system is presented. It consists of 39 CNT based X-ray sources and 3 flat-panel detectors equally distributed in 2 concentric circles. When all the 39 sources have been activated according to a certain order, the gantry will be contrarotated 40° twice and 39 more projections are further acquired after each rotation. In the end, an iterative reconstruction algorithm is employed due to limited number of projections [24]. The remaining of this paper is organized as follows. In Section 2, the CNT based X-ray source and the design of UMCT system are introduced in detail, followed by the introduction of an iterative reconstruction algorithm. Section 3 provides the simulation results of the proposed system design. Discussions and conclusions are in Sections 4 and 5, respectively.
Fig. 1. CNT based X-ray source. (A) A schematic diagram of the CNT based X-ray source and (B) our home-made CNT based X-ray source.
trode is also used in the present design, the focal-spot size is controlled by the potential of the focus electrode. 2.1.2. System design In order to achieve in vivo high—temporal—resolution image, an UMCT system is proposed as manifested in Fig. 2, which consists of 3 subsystems equally distributed in 2 concentric circles A and B. For each subsystem, there are n (n e N+) CNT based X-ray sources equally placed in the range of certain degree h (h e (0, 2p)) in the circle A of radius R (R e R+) and a flat-panel detector with the minimum size d d (d e R+) facing the middle source of the corresponding n X-ray sources, which is placed in the circle B of radius l (l e R+). r (r e R+) is the radius of FOV. In this design, since the overall size of the gantry geometry is limited in practice, the gantry configuration need to be carefully calculated following some principles: (1) h must be a divisor of 120, like 40, for 360°—scanning after a limited number of rotation. (2) The detector must be placed in the appropriate position in order to acquire complete projection data. For example, the upper
2. Methods 2.1. Ultrafast micro-CT (UMCT) This section presents a detailed system design. The system consists of CNT based X-ray source and derivation of the relationship among various parameters.
2.1.1. CNT based X-ray source A schematic diagram of the CNT based X-ray source is illustrated in Fig. 1(A). The source consists of CNT based fieldemission cathode, focus electrode, grid electrode and anode housed in a vacuum chamber at 106 torr base pressure with a beryllium window. When the grid voltage reaches a certain value, the electron is emitted in the free state, then X-ray is generated under the interaction between high-speed electron and anode target. The grid voltage depends on the structure of CNT material and the distance between cathode and grid electrode. Our home-made CNT based X-ray source is manifested in Fig. 1 (B). The size of CNT material placed on cathode is 2 5 mm2, the distance between the grid electrode and cathode is 250 lm. The current is controlled by the voltage between grid electrode and cathode, while the X-ray photon energy is determined by the acceleration voltage between the anode and the cathode. The focus elec-
Fig. 2. 2D schematic diagram of UMCT. where h is the covered range of a set of sources with n carbon nanotube based X-ray sources, R is the radius of circle A, r is the radius of FOV, l is the distance between the center of circle A and the flat-panel detector, d is the minimum size of flat-panel detector.
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
Z. Zhang et al. / Physica Medica xxx (2016) xxx–xxx
left edge of horizontal detector in Fig. 2 must be placed at the point P(XP, YP), P is the intersection of the yellow light path and the red light path in the third quadrant. Different configuration parameters will lead to different size of FOV. In this study, we ignore the effects of the focal spot size. Under the condition of the full use of gantry space, the relationship among all parameters has been obtained as below,
d ¼ 2 jX P j
ð1Þ
and
l ¼ jY p j
ð2Þ
where
pffiffiffi Rrð 3r þ RÞ Xp ¼ 2ðR2 þ r 2 Þ cos 23 p 2h
ð3Þ
pffiffiffi Rrð 3r RÞ Yp ¼ 2ðR2 þ r 2 Þ cos 23 p 2h
ð4Þ
3
In the proposed system, there are 3 subsystems, each subsystem consists of 13 CNT based X-ray sources and a flat-panel detector. During the operation of UMCT system, the gantry will stop to wait for exposure in three positions in an interval of 40° in order to achieve a 360°—scanning as shown in Fig. 4. At each exposure position, three CNT based X-ray sources distributed in the three subsystems respectively will be fast pulse-exposed synchronously and 13 exposure is required. Iterative reconstruction algorithm is employed for the UMCT system because of only 117 projections during the scan. 2.2. Reconstruction of UMCT In conventional CT, as the source and detector are rotated along the gantry, the shape of the X-ray beam is consistent during scanning [25]. While in UMCT, the shape of the X-ray beam changes from view to view as shown in Fig. 5. In order to optimize the sparse reconstruction, iterative reconstruction methods based on total variation (TV) minimization are applied. Supposed that the reconstruction model in UMCT is a discrete linear system,
Here, parameters d and l can be calculated when h R and r are fixed. The corresponding system design is manifested in Fig. 3. 13 CNT based X-ray sources can be placed in the range of 40°.
Fig. 3. 3D design of UMCT.
Fig. 5. Three examples about the shape of X-ray beam. The yellow light path is emitted from the 13th source, the red light path is emitted from the 20th source, the green light path is emitted from the 36th source.
Fig. 4. Three exposure positions in the process of system operation.
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
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g ¼ Mf ;
ð5Þ
g is the measured projections and M is the system matrix. With this discrete model, image reconstruction can be thought as an inversion of Eq.1. And this problem can also be converted into a constrained optimization problem [24,26–28]:
minimizejjf jjTV subject tojjMf gjj2 62; 2P 0; f i P 0:
ð6Þ
The minimization of fidelity term is solved using simultaneous algebraic reconstruction technique (SART) and the reconstruction algorithm has been implemented with in-house developed software using VS2012 and CUDA 7.0 and running on a workstation with Intel(R) Xeon(R) of 3.5GHZ, 16 GB DDR RAM and NVIDIA Quadro K4000.
3. Results Before building a real UMCT system, a CNT based X-ray source has been made (Fig. 1(B)) and its volt-ampere characteristics between grid voltage and anode current was explored. After that, a phantom study was utilized to validate the feasibility of UMCT.
3.1. Performance of CNT based X-ray source The curve of volt-ampere characteristics of our home-made CNT based X-ray source was plotted in Fig. 6. In this experiment, the anode current was recorded by adjusting the grid voltage in the range of 0–1700 V. It can be seen that when the voltage is less than 900 V, the current changes slowly. That means, the surface electric field intensity of CNT is not big enough to inspire free electrons. While the voltage exceeds 900 V, the current shows an approximate exponential growth. An imaging experiment was also carried out (Fig. 7). It used our home-made CNT based X-ray source and a flat-panel detector with the pixel size of 75 lm 75 lm. The object was a 3 mm diameter screw. In the process of the whole experiment, the acceleration voltage linking to the anode of X-ray source was 30 kV, the grid voltage was 1400 V, and the focus voltage was —200 V. Fig. 7(A) shows the real object and Fig. 7(B) shows the projection image obtained by the imaging system.
Fig. 6. Volt-ampere characteristics curve of CNT based X-ray source.
Fig. 7. (A) A screw for imaging and (B) its projection image.
3.2. A phantom study With the UMCT system, a 3D Shepp-Logan phantom with 256 256 256 voxels was employed for a simulation study and the acquired voxel size is 250 250 250 lm3 and the voxel size of commercial equipment is about 10–500 lm [1]. In Fig. 8, (A1–A3) demonstrates the simulation results, (B1-B3) illustrates 3D Shepp-Logan phantom, and (C1-C3) shows 1D profiles for the comparison between the Shepp-Logan phantom and the simulation results along the central line. It can been seen that the SART method performs well for the UMCT reconstruction with 50 iterations. The maximum error is 0.366 and the RMSE (Root Mean Square Error) is only 0.000425. 4. Discussion It is crucial to capture a clear image of fast moving organs for disease diagnosis, especially for thoracic and abdominal diseases. For existing CT systems, it is quite difficult or impossible due to the slow response of commercial X-ray sources and the mechanically—limited rotation speed [29]. In this paper, a novel UMCT system built upon CNT based X-ray source is presented. Because of the excellent field emission characteristics of CNT material, the anode current and focus spot can be controlled in a fast on-off mode, while the gantry keeps static. The volt-ampere characteristics of CNT based X-ray source is firstly observed in Fig. 6 and the curve shows that the voltampere relationship can be approximated as an exponential function after the voltage reaches 900 V. It is found that the current is almost unchanged as the voltage increases, while when the grid voltage reaches a certain threshold (900 V in this study), the current increases quickly. It has been reported that the delay between the onset of the grid voltage and X-ray photon can be adjusted within a certain range (0–100 ls) due to the capacitance and the in-line resistor used for over-current protection in the control circuit, which can be essentially eliminated by reducing the resistance [10]. Therefore, electron emission can be readily controlled for the cold cathode by controlling its surface electric field strength. The amount of electron emission is proportional to its surface electric field strength. Moreover, the current can be stable by adjusting the grid voltage automatically using a high frequency power supply. Towards the practical applications of CNT based X-ray sources, the X-ray flux is a big challenge. There are 2 ways to increase the Xray flux compared with other system: Increase of the size of CNT material used in X-ray source [30] and the another is to grow CNT material on a specific silicon wafer, because different pattern on silicon wafer will lead to different current [31]. In proposed system, the second way to increase the X-ray flux is adopted in order to ensure the size of the CNT based X-ray source. In proposed sys-
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
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Fig. 8. A simulation study using a 3D Shepp-Logan phantom.(A1–A3) Simulation results in transverse, sagittal and coronal section respectively; (B1–B3) 3D Shepp-Logan phantom in transverse, sagittal and coronal section respectively; (C1–C3) 1D profiles for the comparison between the Shepp-Logan phantom and the simulation results along the central line.
tem, only 39 sets of sources can be installed in the gantry that restricts the number of projections, and consequently a sparse reconstruction method (SART plus TV) is chosen to tackle this image reconstruction problem. The reconstructed result is presented in Fig. 8. It can be seen that the simulation result is pretty good without any distortion neither in transverse, sagittal nor coronal section. The aim of this work is to propose a novel structure of micro-CT, the system has not been manufactured temporarily and exact scanning time cannot be measured. So the temporal resolution of proposed system can been estimated by theoretical analysis. There are two factors that affect the temporal resolution: the exposure time of CNT based X-ray source [32] and gantry rotation time [33]. owing to the intrinsic instantaneous response time of the field emission process, the exposure time of CNT based X-ray source is up to the X-ray flux under the same dose level. For the present study, the CNT based X-ray source was operated at 30 kV and 0.5 mA anode current, which is far from the CNT limitation. As improvement of the distribution and growth pattern of CNT, the X-ray flux will be increased, the exposure time can be reduced accordingly, which is about 0.1–5 ms (e.g. 1 ms) [23]. The best achievable gantry speed for a single source MDCT is 0.27 s covering the range of 360° [34] of commercially equipment. In proposed system, the gantry only covers the range of 80 80°, the time required for rotating gantry is only 360 ¼ 0:22 time of the fastest CT at the same level of manufacturing, accordingly the temporal resolution can be estimated as 13 3 1 ms + 0.22 270 ms = 98.4 ms. 5. Conclusion A novel UMCT system built upon the CNT based X-ray sources is described in this paper. It performs well in a quasi-static way, three
stationary scanning in an interval of 40° covers the range of 360°, and a phantom study has validated its efficiency. This system paves the way for ultrafast CT imaging and sheds light on many other task-oriented imaging system in a near future. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ejmp.2016.06. 016. References [1] Ritman E. Micro-computed tomography – current status and developments. Annu Rev Biomed Eng 2004;6:185–208. http://dx.doi.org/10.1146/annurev. bioeng.6.040803.140130. [2] Ritman E. Current status of developments and applications of micro- CT. Annu Rev Biomed Eng 2011;13:531–52. http://dx.doi.org/10.1146/annurev-bioeng071910-124717. [3] McGonigle P, Ruggeri B. Animal models of human disease: challenges in enabling translation. Biochem Pharmacol 2014;87(1):162–71. http://dx.doi. org/10.1016/j.bcp.2013.08.006. [4] Cao G, Lee Y, et al. A dynamic micro-CT scanner based on a carbon nanotube field emission X-ray source. Phys Med Biol 2009;54(8):2323. http://dx.doi.org/ 10.1088/0031-9155/54/8/005. [5] Sugie H, Tanemura M, et al. Carbon nanotubes as electron source in an X-ray tube. Appl Phys Lett 2001;78:2578–80. http://dx.doi.org/10.1063/1.1367278. [6] Maltz J, Fuerst J, et al. Fixed gantry tomosynthesis system for radiation therapy image guidance based on a multiple source X-ray tube with carbon nanotube cathodes. Med Phys 2009;36(5):1624–36. http://dx.doi.org/10.1118/ 1.3110067. [7] Lijima S. Helical microtubules of graphitic carbon. Nature 1991;354 (6348):56–8. http://dx.doi.org/10.1038/354056a0. [8] Fransen M. Field emission energy distributions from individual multi-walled carbon nanotubes. Appl Surf Sci 1999;146(1):312–27. http://dx.doi.org/ 10.1126/science.1060928. [9] Baughman R, Zakhidov A, de Heer W. Carbon nanotubes – the route toward applications. Science 2002;297(5582):787792. http://dx.doi.org/ 10.1126/science.1060928.
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
6
Z. Zhang et al. / Physica Medica xxx (2016) xxx–xxx
[10] Yue G, Qiu Q, et al. Generation of continuous and pulsed diagnostic imaging Xray radiation using a carbon-nanotube-based field-emission cathode. Appl Phys Lett 2002;81(2):355–7. http://dx.doi.org/10.1063/1.1492305. [11] Zhang J, Yang G, et al. Multiplexing radiography using a carbon nanotube based X-ray source. Appl Phys Lett 2006;89(6):1–3. http://dx.doi.org/10.1063/ 1.2234744. [12] Zhang J, Yang G, et al. Stationary scanning X-ray source based on carbon nanotube field emitters. Appl Phys Lett 2005;86(18):1–3. http://dx.doi.org/ 10.1063/1.1923750. [13] Hadsell M, Zhang J, et al. A first generation compact microbeam radiation therapy system based on carbon nanotube X-ray technology. Appl Phys Lett 2013;103(18):183505. http://dx.doi.org/10.1063/1.4826587. [14] Hadsell M, Cao G, et al. Pilot study for compact microbeam radiation therapy using a carbon nanotube field emission micro-CT scanner. Med Phys 2014;41 (6):061710. http://dx.doi.org/10.1118/1.4873683. [15] Heo S, Kim H, et al. A vacuum-sealed miniature X-ray tube based on carbon nanotube field emitters. Nanoscale Res Lett 2012;7(1):1–5. http://dx.doi.org/ 10.1186/1556-276X-7-258. [16] Cheng Y, Zhang J, et al. Dynamic radiography using a carbon-nanotube- based field-emission X-ray source. Rev Sci Instrum 2004;75(10):3264–7. http://dx. doi.org/10.1063/1.1791313. [17] Qian X, Rajaram R, et al. Design and characterization of a spatially distributed multibeam field emission X-ray source for stationary digital breast tomosynthesis. Med Phys 2009;36(10):4389–99. http://dx.doi.org/10.1118/ 1.3213520. [18] Tucker A, Qian X, et al. Optimizing configuration parameters of a stationary digital breast tomosynthesis system based on carbon nanotube X-ray sources. SPIE Med Imaging 2012. http://dx.doi.org/10.1117/12.911530. 831307831307-10. [19] Qian X, Tucker A, et al. High resolution stationary digital breast tomosynthesis using distributed carbon nanotube X-ray source array. Med Phys 2012;39(4):2090–9. http://dx.doi.org/10.1118/1.3694667. [20] Shan J, Chtcheprov P, et al. Stationary chest tomosynthesis using a CNT X-ray source array. SPIE Med Imaging 2013. http://dx.doi.org/10.1117/12.2007993. 86680E-86680E-12. [21] Tucker A, Kuzmiak C, et al. Feasibility of stationary digital breast tomosynthesis as an effective screening tool for patients with augmentation mammoplasty. SPIE Med Imaging 2013. http://dx.doi.org/10.1117/ 12.2007907. 86685N-86685N-10.
[22] Ha A, Lee A, et al. Digital tomosynthesis to evaluate fracture healing: Prospective comparison with radiography and CT. Am J Roentgenol 2015;205(1):136–41. http://dx.doi.org/10.2214/AJR.14.13833. [23] Li L, Chen Z, Jin X. The multi-source instant CT for superfast imaging: system concept, reconstruction algorithms and experiments. Nucl Sci Symp Med Imaging Conf (NSS/MIC) 2013:1–4. http://dx.doi.org/10.1109/ NSSMIC.2013.6829107. [24] Sidky E, Kao C, Pan X. Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT. J Xray Sci Technol 2009;14:119–39. http://dx.doi.org/10.1364/J0SAA.25.001772. [25] Gonzales B, Spronk D, et al. Rectangular computed tomography using a stationary array of CNT emitters: initial experimental results. SPIE Med Imaging 2013. http://dx.doi.org/10.1117/12.2008030. 86685K-8. [26] Sidky E, Duchin Y, et al. A constrained, total-variation minimization algorithm for low-intensity X-ray CT. Med Phys 2011;38(S1):S117–25. http://dx.doi.org/ 10.1118/1.3560887. [27] Bian J, Siewerdsen J, et al. Evaluation of sparse-view reconstruction from flatpanel-detector cone-beam CT. Phys Med Biol 2010;55:6575–99. http://dx.doi. org/10.1088/0031-9155/55/22/001. [28] Han X, Bian J, et al. Optimization-based reconstruction of sparse images from few-view projections. Phys Med Biol 2012;57:52455273. http://dx.doi.org/ 10.1088/0031-9155/57/16/5245. [29] Achenbach S, Ropers D, et al. Contrast-enhanced coronary artery visualization by dual-source computed tomography – initial experience. Eur J Radiol 2006;57(3):331–5. http://dx.doi.org/10.1016/j.ejrad.2005.12.017. [30] Cheng Y, Zhou O. Electron field emission from carbon nanotubes. CR Phys 2003;4(9):1021–33. http://dx.doi.org/10.1016/S1631-0705(03)00103-8. [31] Oh S, Zhang J, et al. Liquid-phase fabrication of patterned carbon nan- otube field emission cathodes. Appl Phys Lett 2004;84(19):37383740. http://dx.doi. org/10.1063/1.1737074. [32] Cao G, Burk L, Lee Y, et al. Prospective-gated cardiac micro-ct imaging of freebreathing mice using carbon nanotube field emission X-ray. Med Phys 2010;37(10):5306–53122. http://dx.doi.org/10.1118/1.3491806. [33] Petersilka M, Bruder H, et al. Technical principles of dual source ct. Eur J Radiol 2008;68(3):362–8. http://dx.doi.org/10.1016/j.ejrad.2008.08.013. [34] Russo V, Garattoni M, et al. 128-slice ct angiography of the aorta without ecggating: efficacy of faster gantry rotation time and iterative reconstruction in terms of image quality and radiation dose. Eur Radiol 2016;26(2):359–69. http://dx.doi.org/10.1007/s00330-015-3848-3.
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
Contents lists available at ScienceDirect
Physica Medica journal homepage: http://www.physicamedica.com
Original paper
A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom q Zhicheng Zhang a,b, Shaode Yu a,b, Xiaokun Liang a,c, Yanchun Zhu a,⇑, Yaoqin Xie a,⇑ a
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China Shenzhen College of Advanced Technology, University of Chinese Academy of Sciences, Shenzhen, China c School of Information Engineering, Guangdong Medical College, Dongguan, China b
a r t i c l e
i n f o
Article history: Received 1 February 2016 Received in Revised form 14 May 2016 Accepted 30 June 2016 Available online xxxx Keywords: Ultrafast micro-CT Carbon nanotube Motion artifact Temporal resolution
a b s t r a c t Artifacts induced by respiratory motion during routine diagnosis severely degrades the image quality. The increase of scanning speed plays an important role to avoid motion artifacts. Limited to the mechanical structure of conventional CT, the increase of gantry rotational speed is unsustainable and a more feasible way is to increase the number of X-ray sources and detectors like the dual-source CT. This paper focuses on high-speed scanning CT and proposes a novel ultrafast micro-CT (UMCT) system based on carbon nanotube (CNT). At each exposure position, all of the X-ray sources are fast activated by turns and the flat-panel detectors collect the corresponding projection data. Then, the gantry will be contrarotated 40° to prepare for the next exposure until the rotation covers full 360°. Because each exposure is very fast, the organ motions of in vivo human body can be greatly reduced. This paper introduces the UMCT system design, image reconstruction algorithm and experimental results. Simulation experiment was also carried out on UMCT system. The result validated the feasibility of the UMCT system. Ó 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.
1. Introduction 3D microscopy which has a high spatial resolution can be revealed non-destructively for fine-scale internal structures is X-ray-based three-dimensional (3D) imaging for a limited field of view (FOV) [1,2]. It has been widely used in small animal imaging and plays an important role in the research of human organ, exploration of disease mechanisms and effectiveness of drug assessment [3]. As to currently commercial scanners, it is still a big challenge to perform in vivo micro-CT on small animals because of their much faster physiological motion than that of human. Motion artifacts severely degrade the micro-CT imaging quality and significantly affect the effectiveness of disease diagnosis [4].
q This work is supported in part by grants from Guangdong Innovative Research Team Program of China (Grant No. 2011S013), National 863 Programs of China (Grant Nos. 2012AA02A604 and 2015AA043203), National Key Research and Develop Program of China (Grant No. 2016YFC0105102), Shenzhen Key Lab for Molecular Imaging (ZDSY20130401165820357), National Natural Science Foundation of China (Grant No. 81501463), Natural Science Foundation of Guangdong Province (Grant No. 2014A030310360) and Beijing Center for Mathematics and Information Interdisciplinary Sciences. ⇑ Corresponding authors. E-mail addresses: [email protected] (Y. Zhu), [email protected] (Y. Xie).
Conventional micro-CT uses a hot cathode based X-ray source. According to the theory of thermionic electron emission, the electron source must be heated above 2000 °C in order to allow free electrons to escape from its surface [5], thus it is impossible for hot cathode based X-ray source to be switched on and off instantaneously. Using field-emission sources to replace thermionic sources was suggested over 50 years ago. However, lacking of chemically stable cathode material frustrated efforts to fabricate reliable cold cathode field emission devices [6]. Fortunately, carbon nanotube (CNT) was reported in 1991 [7] and it was suggested that this new material had great potential for use as an electron field emitter [8]. CNT has the inherent advantage of stable emission, long lifetimes, and low emission threshold potentials [9]. Lu et al. used CNT as cathode materials in X-ray source to replace conventional filament in 2002 for the first time [10]. The devices consisted of a multiple sources array within a single source [11,12]. Recently, they transferred their attention to radiation using CNT based X-ray source [13,14]. Compared with traditional X-ray source, CNT based X-ray source demonstrates vast advantages. Above all, generating little heat inside the cold cathode source is crucial for the minimization of an X-ray source and prolongs its lifetime. Moreover, the amount of electron emission is up to its surface electric field intensity, consequently CNT based X-ray source is readily
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Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
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controllable in a pulse operation by adjusting the grid voltage when the cathode is earthed or controlling the insulated gate bipolar transistor (IGBT) open and close with a designed pulse [12,15]. In addition, due to the desired gaussian distribution, the intensity distribution of the focal spot obtained from a pinhole measurement can provide better spatial resolution than either uniform or bimodal intensity distributions, not the double-peaked distribution commonly found on thermionic X-ray sources [16]. In view of the excellent properties of CNT materials, several groups have recently disclosed the concept of multi-source X-ray imaging using CNT based X-ray source. Jonathan S. Maltz et al. proposed a stationary-gantry tomosynthesis system for on-line image guidance in radiation therapy base on a 52-source cold cathode based X-ray source [6]. Zhou et al. proposed a spatially distributed multi-beam field emission X-ray source for stationary digital breast tomosynthesis [17–21]. The systems proposed by Jonathan S. Maltz and Zhou can obtain pretty high temporal resolution on account of no any mechanical movement during imaging process. But digital tomosynthesis only acquired fewer projections as compared to conventional CT scanners, it yielded images similar to conventional tomography with a limited depth of field [22]. Li et al. designed a multi-source instant CT for superfast imaging [23], but their system still needed several rotation times during covering the range of 360°. It is always desirable to reduce the gantry motion and speed up scanning process. In this paper, a novel design of ultrafast micro-CT (UMCT) system is presented. It consists of 39 CNT based X-ray sources and 3 flat-panel detectors equally distributed in 2 concentric circles. When all the 39 sources have been activated according to a certain order, the gantry will be contrarotated 40° twice and 39 more projections are further acquired after each rotation. In the end, an iterative reconstruction algorithm is employed due to limited number of projections [24]. The remaining of this paper is organized as follows. In Section 2, the CNT based X-ray source and the design of UMCT system are introduced in detail, followed by the introduction of an iterative reconstruction algorithm. Section 3 provides the simulation results of the proposed system design. Discussions and conclusions are in Sections 4 and 5, respectively.
Fig. 1. CNT based X-ray source. (A) A schematic diagram of the CNT based X-ray source and (B) our home-made CNT based X-ray source.
trode is also used in the present design, the focal-spot size is controlled by the potential of the focus electrode. 2.1.2. System design In order to achieve in vivo high—temporal—resolution image, an UMCT system is proposed as manifested in Fig. 2, which consists of 3 subsystems equally distributed in 2 concentric circles A and B. For each subsystem, there are n (n e N+) CNT based X-ray sources equally placed in the range of certain degree h (h e (0, 2p)) in the circle A of radius R (R e R+) and a flat-panel detector with the minimum size d d (d e R+) facing the middle source of the corresponding n X-ray sources, which is placed in the circle B of radius l (l e R+). r (r e R+) is the radius of FOV. In this design, since the overall size of the gantry geometry is limited in practice, the gantry configuration need to be carefully calculated following some principles: (1) h must be a divisor of 120, like 40, for 360°—scanning after a limited number of rotation. (2) The detector must be placed in the appropriate position in order to acquire complete projection data. For example, the upper
2. Methods 2.1. Ultrafast micro-CT (UMCT) This section presents a detailed system design. The system consists of CNT based X-ray source and derivation of the relationship among various parameters.
2.1.1. CNT based X-ray source A schematic diagram of the CNT based X-ray source is illustrated in Fig. 1(A). The source consists of CNT based fieldemission cathode, focus electrode, grid electrode and anode housed in a vacuum chamber at 106 torr base pressure with a beryllium window. When the grid voltage reaches a certain value, the electron is emitted in the free state, then X-ray is generated under the interaction between high-speed electron and anode target. The grid voltage depends on the structure of CNT material and the distance between cathode and grid electrode. Our home-made CNT based X-ray source is manifested in Fig. 1 (B). The size of CNT material placed on cathode is 2 5 mm2, the distance between the grid electrode and cathode is 250 lm. The current is controlled by the voltage between grid electrode and cathode, while the X-ray photon energy is determined by the acceleration voltage between the anode and the cathode. The focus elec-
Fig. 2. 2D schematic diagram of UMCT. where h is the covered range of a set of sources with n carbon nanotube based X-ray sources, R is the radius of circle A, r is the radius of FOV, l is the distance between the center of circle A and the flat-panel detector, d is the minimum size of flat-panel detector.
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
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left edge of horizontal detector in Fig. 2 must be placed at the point P(XP, YP), P is the intersection of the yellow light path and the red light path in the third quadrant. Different configuration parameters will lead to different size of FOV. In this study, we ignore the effects of the focal spot size. Under the condition of the full use of gantry space, the relationship among all parameters has been obtained as below,
d ¼ 2 jX P j
ð1Þ
and
l ¼ jY p j
ð2Þ
where
pffiffiffi Rrð 3r þ RÞ Xp ¼ 2ðR2 þ r 2 Þ cos 23 p 2h
ð3Þ
pffiffiffi Rrð 3r RÞ Yp ¼ 2ðR2 þ r 2 Þ cos 23 p 2h
ð4Þ
3
In the proposed system, there are 3 subsystems, each subsystem consists of 13 CNT based X-ray sources and a flat-panel detector. During the operation of UMCT system, the gantry will stop to wait for exposure in three positions in an interval of 40° in order to achieve a 360°—scanning as shown in Fig. 4. At each exposure position, three CNT based X-ray sources distributed in the three subsystems respectively will be fast pulse-exposed synchronously and 13 exposure is required. Iterative reconstruction algorithm is employed for the UMCT system because of only 117 projections during the scan. 2.2. Reconstruction of UMCT In conventional CT, as the source and detector are rotated along the gantry, the shape of the X-ray beam is consistent during scanning [25]. While in UMCT, the shape of the X-ray beam changes from view to view as shown in Fig. 5. In order to optimize the sparse reconstruction, iterative reconstruction methods based on total variation (TV) minimization are applied. Supposed that the reconstruction model in UMCT is a discrete linear system,
Here, parameters d and l can be calculated when h R and r are fixed. The corresponding system design is manifested in Fig. 3. 13 CNT based X-ray sources can be placed in the range of 40°.
Fig. 3. 3D design of UMCT.
Fig. 5. Three examples about the shape of X-ray beam. The yellow light path is emitted from the 13th source, the red light path is emitted from the 20th source, the green light path is emitted from the 36th source.
Fig. 4. Three exposure positions in the process of system operation.
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
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g ¼ Mf ;
ð5Þ
g is the measured projections and M is the system matrix. With this discrete model, image reconstruction can be thought as an inversion of Eq.1. And this problem can also be converted into a constrained optimization problem [24,26–28]:
minimizejjf jjTV subject tojjMf gjj2 62; 2P 0; f i P 0:
ð6Þ
The minimization of fidelity term is solved using simultaneous algebraic reconstruction technique (SART) and the reconstruction algorithm has been implemented with in-house developed software using VS2012 and CUDA 7.0 and running on a workstation with Intel(R) Xeon(R) of 3.5GHZ, 16 GB DDR RAM and NVIDIA Quadro K4000.
3. Results Before building a real UMCT system, a CNT based X-ray source has been made (Fig. 1(B)) and its volt-ampere characteristics between grid voltage and anode current was explored. After that, a phantom study was utilized to validate the feasibility of UMCT.
3.1. Performance of CNT based X-ray source The curve of volt-ampere characteristics of our home-made CNT based X-ray source was plotted in Fig. 6. In this experiment, the anode current was recorded by adjusting the grid voltage in the range of 0–1700 V. It can be seen that when the voltage is less than 900 V, the current changes slowly. That means, the surface electric field intensity of CNT is not big enough to inspire free electrons. While the voltage exceeds 900 V, the current shows an approximate exponential growth. An imaging experiment was also carried out (Fig. 7). It used our home-made CNT based X-ray source and a flat-panel detector with the pixel size of 75 lm 75 lm. The object was a 3 mm diameter screw. In the process of the whole experiment, the acceleration voltage linking to the anode of X-ray source was 30 kV, the grid voltage was 1400 V, and the focus voltage was —200 V. Fig. 7(A) shows the real object and Fig. 7(B) shows the projection image obtained by the imaging system.
Fig. 6. Volt-ampere characteristics curve of CNT based X-ray source.
Fig. 7. (A) A screw for imaging and (B) its projection image.
3.2. A phantom study With the UMCT system, a 3D Shepp-Logan phantom with 256 256 256 voxels was employed for a simulation study and the acquired voxel size is 250 250 250 lm3 and the voxel size of commercial equipment is about 10–500 lm [1]. In Fig. 8, (A1–A3) demonstrates the simulation results, (B1-B3) illustrates 3D Shepp-Logan phantom, and (C1-C3) shows 1D profiles for the comparison between the Shepp-Logan phantom and the simulation results along the central line. It can been seen that the SART method performs well for the UMCT reconstruction with 50 iterations. The maximum error is 0.366 and the RMSE (Root Mean Square Error) is only 0.000425. 4. Discussion It is crucial to capture a clear image of fast moving organs for disease diagnosis, especially for thoracic and abdominal diseases. For existing CT systems, it is quite difficult or impossible due to the slow response of commercial X-ray sources and the mechanically—limited rotation speed [29]. In this paper, a novel UMCT system built upon CNT based X-ray source is presented. Because of the excellent field emission characteristics of CNT material, the anode current and focus spot can be controlled in a fast on-off mode, while the gantry keeps static. The volt-ampere characteristics of CNT based X-ray source is firstly observed in Fig. 6 and the curve shows that the voltampere relationship can be approximated as an exponential function after the voltage reaches 900 V. It is found that the current is almost unchanged as the voltage increases, while when the grid voltage reaches a certain threshold (900 V in this study), the current increases quickly. It has been reported that the delay between the onset of the grid voltage and X-ray photon can be adjusted within a certain range (0–100 ls) due to the capacitance and the in-line resistor used for over-current protection in the control circuit, which can be essentially eliminated by reducing the resistance [10]. Therefore, electron emission can be readily controlled for the cold cathode by controlling its surface electric field strength. The amount of electron emission is proportional to its surface electric field strength. Moreover, the current can be stable by adjusting the grid voltage automatically using a high frequency power supply. Towards the practical applications of CNT based X-ray sources, the X-ray flux is a big challenge. There are 2 ways to increase the Xray flux compared with other system: Increase of the size of CNT material used in X-ray source [30] and the another is to grow CNT material on a specific silicon wafer, because different pattern on silicon wafer will lead to different current [31]. In proposed system, the second way to increase the X-ray flux is adopted in order to ensure the size of the CNT based X-ray source. In proposed sys-
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
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Fig. 8. A simulation study using a 3D Shepp-Logan phantom.(A1–A3) Simulation results in transverse, sagittal and coronal section respectively; (B1–B3) 3D Shepp-Logan phantom in transverse, sagittal and coronal section respectively; (C1–C3) 1D profiles for the comparison between the Shepp-Logan phantom and the simulation results along the central line.
tem, only 39 sets of sources can be installed in the gantry that restricts the number of projections, and consequently a sparse reconstruction method (SART plus TV) is chosen to tackle this image reconstruction problem. The reconstructed result is presented in Fig. 8. It can be seen that the simulation result is pretty good without any distortion neither in transverse, sagittal nor coronal section. The aim of this work is to propose a novel structure of micro-CT, the system has not been manufactured temporarily and exact scanning time cannot be measured. So the temporal resolution of proposed system can been estimated by theoretical analysis. There are two factors that affect the temporal resolution: the exposure time of CNT based X-ray source [32] and gantry rotation time [33]. owing to the intrinsic instantaneous response time of the field emission process, the exposure time of CNT based X-ray source is up to the X-ray flux under the same dose level. For the present study, the CNT based X-ray source was operated at 30 kV and 0.5 mA anode current, which is far from the CNT limitation. As improvement of the distribution and growth pattern of CNT, the X-ray flux will be increased, the exposure time can be reduced accordingly, which is about 0.1–5 ms (e.g. 1 ms) [23]. The best achievable gantry speed for a single source MDCT is 0.27 s covering the range of 360° [34] of commercially equipment. In proposed system, the gantry only covers the range of 80 80°, the time required for rotating gantry is only 360 ¼ 0:22 time of the fastest CT at the same level of manufacturing, accordingly the temporal resolution can be estimated as 13 3 1 ms + 0.22 270 ms = 98.4 ms. 5. Conclusion A novel UMCT system built upon the CNT based X-ray sources is described in this paper. It performs well in a quasi-static way, three
stationary scanning in an interval of 40° covers the range of 360°, and a phantom study has validated its efficiency. This system paves the way for ultrafast CT imaging and sheds light on many other task-oriented imaging system in a near future. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ejmp.2016.06. 016. References [1] Ritman E. Micro-computed tomography – current status and developments. Annu Rev Biomed Eng 2004;6:185–208. http://dx.doi.org/10.1146/annurev. bioeng.6.040803.140130. [2] Ritman E. Current status of developments and applications of micro- CT. Annu Rev Biomed Eng 2011;13:531–52. http://dx.doi.org/10.1146/annurev-bioeng071910-124717. [3] McGonigle P, Ruggeri B. Animal models of human disease: challenges in enabling translation. Biochem Pharmacol 2014;87(1):162–71. http://dx.doi. org/10.1016/j.bcp.2013.08.006. [4] Cao G, Lee Y, et al. A dynamic micro-CT scanner based on a carbon nanotube field emission X-ray source. Phys Med Biol 2009;54(8):2323. http://dx.doi.org/ 10.1088/0031-9155/54/8/005. [5] Sugie H, Tanemura M, et al. Carbon nanotubes as electron source in an X-ray tube. Appl Phys Lett 2001;78:2578–80. http://dx.doi.org/10.1063/1.1367278. [6] Maltz J, Fuerst J, et al. Fixed gantry tomosynthesis system for radiation therapy image guidance based on a multiple source X-ray tube with carbon nanotube cathodes. Med Phys 2009;36(5):1624–36. http://dx.doi.org/10.1118/ 1.3110067. [7] Lijima S. Helical microtubules of graphitic carbon. Nature 1991;354 (6348):56–8. http://dx.doi.org/10.1038/354056a0. [8] Fransen M. Field emission energy distributions from individual multi-walled carbon nanotubes. Appl Surf Sci 1999;146(1):312–27. http://dx.doi.org/ 10.1126/science.1060928. [9] Baughman R, Zakhidov A, de Heer W. Carbon nanotubes – the route toward applications. Science 2002;297(5582):787792. http://dx.doi.org/ 10.1126/science.1060928.
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016
6
Z. Zhang et al. / Physica Medica xxx (2016) xxx–xxx
[10] Yue G, Qiu Q, et al. Generation of continuous and pulsed diagnostic imaging Xray radiation using a carbon-nanotube-based field-emission cathode. Appl Phys Lett 2002;81(2):355–7. http://dx.doi.org/10.1063/1.1492305. [11] Zhang J, Yang G, et al. Multiplexing radiography using a carbon nanotube based X-ray source. Appl Phys Lett 2006;89(6):1–3. http://dx.doi.org/10.1063/ 1.2234744. [12] Zhang J, Yang G, et al. Stationary scanning X-ray source based on carbon nanotube field emitters. Appl Phys Lett 2005;86(18):1–3. http://dx.doi.org/ 10.1063/1.1923750. [13] Hadsell M, Zhang J, et al. A first generation compact microbeam radiation therapy system based on carbon nanotube X-ray technology. Appl Phys Lett 2013;103(18):183505. http://dx.doi.org/10.1063/1.4826587. [14] Hadsell M, Cao G, et al. Pilot study for compact microbeam radiation therapy using a carbon nanotube field emission micro-CT scanner. Med Phys 2014;41 (6):061710. http://dx.doi.org/10.1118/1.4873683. [15] Heo S, Kim H, et al. A vacuum-sealed miniature X-ray tube based on carbon nanotube field emitters. Nanoscale Res Lett 2012;7(1):1–5. http://dx.doi.org/ 10.1186/1556-276X-7-258. [16] Cheng Y, Zhang J, et al. Dynamic radiography using a carbon-nanotube- based field-emission X-ray source. Rev Sci Instrum 2004;75(10):3264–7. http://dx. doi.org/10.1063/1.1791313. [17] Qian X, Rajaram R, et al. Design and characterization of a spatially distributed multibeam field emission X-ray source for stationary digital breast tomosynthesis. Med Phys 2009;36(10):4389–99. http://dx.doi.org/10.1118/ 1.3213520. [18] Tucker A, Qian X, et al. Optimizing configuration parameters of a stationary digital breast tomosynthesis system based on carbon nanotube X-ray sources. SPIE Med Imaging 2012. http://dx.doi.org/10.1117/12.911530. 831307831307-10. [19] Qian X, Tucker A, et al. High resolution stationary digital breast tomosynthesis using distributed carbon nanotube X-ray source array. Med Phys 2012;39(4):2090–9. http://dx.doi.org/10.1118/1.3694667. [20] Shan J, Chtcheprov P, et al. Stationary chest tomosynthesis using a CNT X-ray source array. SPIE Med Imaging 2013. http://dx.doi.org/10.1117/12.2007993. 86680E-86680E-12. [21] Tucker A, Kuzmiak C, et al. Feasibility of stationary digital breast tomosynthesis as an effective screening tool for patients with augmentation mammoplasty. SPIE Med Imaging 2013. http://dx.doi.org/10.1117/ 12.2007907. 86685N-86685N-10.
[22] Ha A, Lee A, et al. Digital tomosynthesis to evaluate fracture healing: Prospective comparison with radiography and CT. Am J Roentgenol 2015;205(1):136–41. http://dx.doi.org/10.2214/AJR.14.13833. [23] Li L, Chen Z, Jin X. The multi-source instant CT for superfast imaging: system concept, reconstruction algorithms and experiments. Nucl Sci Symp Med Imaging Conf (NSS/MIC) 2013:1–4. http://dx.doi.org/10.1109/ NSSMIC.2013.6829107. [24] Sidky E, Kao C, Pan X. Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT. J Xray Sci Technol 2009;14:119–39. http://dx.doi.org/10.1364/J0SAA.25.001772. [25] Gonzales B, Spronk D, et al. Rectangular computed tomography using a stationary array of CNT emitters: initial experimental results. SPIE Med Imaging 2013. http://dx.doi.org/10.1117/12.2008030. 86685K-8. [26] Sidky E, Duchin Y, et al. A constrained, total-variation minimization algorithm for low-intensity X-ray CT. Med Phys 2011;38(S1):S117–25. http://dx.doi.org/ 10.1118/1.3560887. [27] Bian J, Siewerdsen J, et al. Evaluation of sparse-view reconstruction from flatpanel-detector cone-beam CT. Phys Med Biol 2010;55:6575–99. http://dx.doi. org/10.1088/0031-9155/55/22/001. [28] Han X, Bian J, et al. Optimization-based reconstruction of sparse images from few-view projections. Phys Med Biol 2012;57:52455273. http://dx.doi.org/ 10.1088/0031-9155/57/16/5245. [29] Achenbach S, Ropers D, et al. Contrast-enhanced coronary artery visualization by dual-source computed tomography – initial experience. Eur J Radiol 2006;57(3):331–5. http://dx.doi.org/10.1016/j.ejrad.2005.12.017. [30] Cheng Y, Zhou O. Electron field emission from carbon nanotubes. CR Phys 2003;4(9):1021–33. http://dx.doi.org/10.1016/S1631-0705(03)00103-8. [31] Oh S, Zhang J, et al. Liquid-phase fabrication of patterned carbon nan- otube field emission cathodes. Appl Phys Lett 2004;84(19):37383740. http://dx.doi. org/10.1063/1.1737074. [32] Cao G, Burk L, Lee Y, et al. Prospective-gated cardiac micro-ct imaging of freebreathing mice using carbon nanotube field emission X-ray. Med Phys 2010;37(10):5306–53122. http://dx.doi.org/10.1118/1.3491806. [33] Petersilka M, Bruder H, et al. Technical principles of dual source ct. Eur J Radiol 2008;68(3):362–8. http://dx.doi.org/10.1016/j.ejrad.2008.08.013. [34] Russo V, Garattoni M, et al. 128-slice ct angiography of the aorta without ecggating: efficacy of faster gantry rotation time and iterative reconstruction in terms of image quality and radiation dose. Eur Radiol 2016;26(2):359–69. http://dx.doi.org/10.1007/s00330-015-3848-3.
Please cite this article in press as: Zhang Z et al. A novel design of ultrafast micro-CT system based on carbon nanotube: A feasibility study in phantom. Phys. Med. (2016), http://dx.doi.org/10.1016/j.ejmp.2016.06.016