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Fast X-Ray Luminescence Computed Tomography Imaging Xin Liu∗ , Member, IEEE, Qimei Liao, and Hongkai Wang
Abstract—X-ray luminescence computed tomography (XLCT) opens new possibilities to perform molecular imaging with X-ray. However, challenges remain in dynamic XLCT imaging, where short scan time, good spatial resolution, and whole-body field of view should be considered simultaneously. In this paper, by the use of a single-view XLCT reconstruction method based on a compressive sensing (CS) technique, incorporating a cone beam XLCT imaging system, we implement fast 3-D XLCT imaging. To evaluate the performance of the method, two types of phantom experiments were performed based on a cone beam XLCT imaging system. In Case 1, one tube filled with the X-ray-excitable nanophosphor (Gd2 O3 :Eu3 + ) was immerged in different positions in the phantom to evaluate the effect of the source position on single-view XLCT reconstruction accuracy. In Case 2, two tubes filled with Gd2 O3 :Eu3 + were immerged in different heights in the phantom to evaluate the whole-body imaging performance of single-view XLCT reconstruction. The experimental results indicated that the tubes used in previous phantom experiments can be resolved from single-view XCLT reconstruction images. The location error is less than 1.2 mm. In addition, since only one view data are needed to implement 3-D XLCT imaging, the acquisition time can be greatly reduced (∼1 frame/s) compared with previous XLCT systems. Hence, the technique is suited for imaging the fast distribution of the X-ray-excitable nanophosphors within a biological object. Index Terms—Fluorescence, hybrid imaging, image reconstruction techniques, optical tomography, X-ray imaging.
I. INTRODUCTION -RAY luminescence computed tomography (XLCT) has been recently proposed as a new molecular imaging modality [1]–[7]. In principle, when the imaged object is irradiated with X-ray, the X-ray-excitable nanophosphors in the imaged object will produce visible or near-infrared (NIR) luminescence which can be measured by sensitive photon detectors, as shown in Fig. 1. Subsequently, by solving a mathematical
X
Manuscript received September 22, 2013; revised November 22, 2013; accepted December 6, 2013. Date of publication December 11, 2013; date of current version May 15, 2014. This work was supported by the National Natural Science Foundation of China under Grant 81371604, Grant 81230035, and Grant 81071220, and by the Shaanxi Natural Science Foundation under Grant 2013JM4008. Asterisk indicates corresponding author. ∗ X. Liu is with the School of Biomedical Engineering, Fourth Military Medical University, Xi’an 710032, China (e-mail: [email protected]). Q. Liao is with the Department of Computation Application, School of Biomedical Engineering, Fourth Military Medical University, Xi’an 710032, China (e-mail: [email protected]). H. Wang is with the Crump Institute of Molecular Imaging, David Geffen School of Medicine, University of California, Los Angeles, CA 90066 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBME.2013.2294633
Fig. 1.
Schematic diagram of CB-XLCT imaging.
model, the 3-D distribution of the nanophosphors in the imaged object can be recovered. Compared with other optical molecular imaging modalities, e.g., fluorescence molecular tomography (FMT) [8]–[10] or bioluminescence tomography (BLT) [11]–[13], XLCT offers two main advantages. First, the X-ray excitation spectrum is undetectable with photon detectors. As a result, the autofluorescence can be avoided, which is helpful for imaging low concentration information. Second, XLCT is expected to have increased depth imaging performance compared with the other optical imaging because of the high penetration of X-ray photons in tissues, which offers the potential to use clinically available. With the advances in the X-ray-excitable nanophosphors [14]–[17], imaging systems, and reconstruction methods [1]–[7], dynamic XLCT imaging is now possible. By adding time as a new dimension, dynamic XLCT imparts the ability to capture the complete dynamic course of the X-rayexcitable nanophosphors (drug) within small animals in vivo. It is also helpful for better studying metabolic processes of nanophosphors-based drugs. Nevertheless, challenges still remain in imaging fast and whole-body biological activities using XLCT, where short scan time, good spatial resolution, and whole-body field of view (FOV) need to be considered simultaneously. For example, in a current widely used narrow beam XLCT imaging system [1]–[3], to collect XLCT data, an X-ray source and detector were mounted on opposite sides of the imaged object, similar to the first-generation X-ray CT scanning strategy. A disadvantage of such system was that the data acquisition generally took long time (typically, ≥624 s) [2]. To reduce the imaging time, Chen et al. designed a cone beam X-ray luminescence computed tomography (CB-XLCT) imaging system [6]. In their reports, by using a cone beam X-ray illumination and a highly sensitive charge-coupled device (CCD) camera detection, they decreased the data acquisition time. However, to collect multiple-view data (generally, ≥four views) which were used to perform XLCT reconstruction, a rotating mechanism
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was used. This meant to rotate the imaged object and to repeat the measurements several times in XLCT imaging processes, leading to the increased imaging time (typically, ≥134 s). As a result, the previous XLCT imaging techniques were not suitable for imaging fast distribution of the nanophosphors within a biological object. The goal of this paper is to improve acquisition speed without significant lose of spatial resolution; therefore, we extend the application of XLCT for fast dynamic imaging study. To achieve the goal, a simple and effective strategy is to use single-view data acquired by a CB-XLCT system. The imaging approach can directly reduce XLCT imaging time because only one view data need to be acquired to implement 3-D XLCT imaging and the imaged object need not to be rotated in imaging processes. That is, the integrating time of CCD for collecting single-view data is the imaging time of XLCT system. However, due to the high scattering of light in biological tissues, the reconstruction of XLCT is an ill-posed problem [6]. Moreover, the ill-posedness will further aggravate if underdetermined data (e.g., single-view data) are used. As a result, the ill-posedness will adversely affect the image quality of XLCT reconstruction. Note that in most biological applications, based on the biological characteristics, the X-ray-excitable nanophosphors are sparsely distributed in the tissues. This means that the nanophosphors in imaging domain are generally very sparse. As a result, the compressive sensing (CS) technique can be used in XLCT reconstruction processes to get high-quality and robust reconstruction results, even if the measurement data are very limited [18], [19]. In addition, it should also be noted that the performance of CS depends on the restricted isometry property (RIP) of the measurement matrix, i.e., the measurement matrix must be incoherence or orthogonality. To improve the RIP, i.e., to improve the recovery performance of sparse signals, recently, a preconditioning matrix method has also been widely used, as described in [20]–[22]. These methods together provide the possibility to implement the single-view XLCT reconstruction. Based on the consideration of previous problems, in this paper, by applying a CS technique to a single-view XLCT reconstruction, combined with a CB-XLCT imaging system, we implement fast 3-D XLCT imaging. To evaluate the performance of the method, two types of phantom experiments were performed based on a CB-XLCT imaging system. In Case 1, one tube filled with the X-ray-excitable nanophosphor (Gd2 O3 :Eu3+ ) was immerged in different positions in the phantom to evaluate the effect of the source position, i.e., the distribution of nanophosphor in imaged object, on single-view XLCT reconstruction accuracy. In Case 2, two tubes filled with Gd2 O3 :Eu3+ were immerged in different heights in the phantom to evaluate the wholebody imaging performance of single-view XLCT reconstruction. Here, the X-ray-excitable nanophosphor we employed was Gd2 O3 :Eu3+ , due to its NIR emission wavelength. The experimental results indicate that the tubes filled with Gd2 O3 :Eu3+ can be resolved from single-view XCLT reconstruction images. The location error is less than 1.2 mm. In addition, since only one view data need to be collected to implement 3-D XLCT imaging, the imaging time can be greatly reduced (∼1 frame/s) compared with the previous XLCT systems. Hence, the tech-
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 61, NO. 6, JUNE 2014
nique is suited for imaging the fast distribution of the X-rayexcitable nanophosphors (other similar materials or chemical elements) within a biological object. This paper is organized as follows. In Section II, the imaging model and reconstruction method are described. In Section III, the experimental materials are detailed. In Section IV, the experimental results are shown. Finally, we discuss the results and draw conclusions in Section V. II. METHODS A. Forward Problem In XLCT imaging, X-rays are emitted from the X-ray source and travel through tissues. As shown in Fig. 1, as soon as X-ray is transported to nanophosphors in tissues, the nanophosphors will emit visible or NIR light, which can be expressed according to [4], as follows: S(r) = ηA(r)ρ(r)
(1)
where S(r) is the source energy density (W/mm3 ), ρ(r) is the density (concentration) of the nanophosphor (g/mL), A(r) is the X-ray intensity (W/mm2 ), and η is the light yield which is defined as the quantum yield per unit nanophosphor concentration. According to Lambert–Beers’ law, during the course of X-rays traveling through the tissues, the X-ray intensity distribution A(r) can be expressed as follows: r μ(τ )dτ (2) A(r) = A0 exp − r0
where A0 (r) is the X-ray source intensity at the initial position r0 , and μ(τ ) is the X-ray attenuation coefficient (mm−1 ) which can be obtained from X-ray transmission data using an attenuation-based CT technique. Since biological tissue has highly scattering and weakly absorbing properties in the NIR spectral window, the NIR light S(r) (e.g., the emitted NIR light from Gd2 O3 :Eu3+ ) in the tissues can be obtained by solving the following diffusion equation [23] combined with the Robin-type boundary condition [24]: ⎧ ⎨ −∇[D(r)∇Φ(r)] + μa (r)Φ(r) = S(r) r ∈ Ω (3) ⎩ 2γD(r) ∂Φ(r) + Φ(r) = 0 r ∈ ∂Ω ∂n where Ω is the domain of the imaged object and ∂Ω is the boundary; Φ(r) is the photon flux density (W/mm2 ); μa (r) is the absorption coefficient (mm−1 ); D(r) = 1/(3(μa (r) + μs (r)) is the diffusion coefficient (mm) with μs (r) being the reduced scattering coefficient (mm−1 ); n denotes the outward normal vector to the boundary ∂Ω, and γ is a constant depending upon the optical reflective index mismatch at the boundary. Knowing the optical properties, the diffusion equation can be solved using the finite-element method [25]. Based on the finite-element theory, (3) can be discretized into the following matrix equation: KΦ = FηAρ
(4)
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with ⎧ 1 ⎪ ⎪ ⎨ Kij = Ω (D∇ψi ∇ψj + μa ψi ψj )dr+ 2γ ∂ Ω ψi ψj dr ⎪ ⎪ ⎩ Fij = ψi ψj dr Ω
(5) where Kij and Fij are the elements of matrices K and F, respectively. ψi and ψj are the volume elements that discretize the imaging domain and form a geometrical mesh defined over the entire imaging domain. Since the matrix K is positive definite, (4) can be changed to Φ = Jρ
(6)
−1
where J = K FηA. Finally, by removing the unmeasurable interior values Φi g n o in Φ and the rows of the matrix J corresponding to Φi g n o , the final matrix equation is generated as follows: Φm eas = Wρ
(7)
where W is a weight (measurement) matrix describing the forward model of the CB-XLCT imaging. B. Inverse Problem The goal of XLCT reconstruction is to recover the X-rayexcitable nanophosphor density ρ from the measured photon density Φm eas on the boundary ∂Ω. However, as mentioned in Section I, due to the high scattering of light in biological tissues and the use of underdetermined data (single-view data), the weight matrix W in (7) is poorly conditioned. As a result, it is impractical to solve ρ directly from (7). Considering that in most biological applications, the distributions of X-ray-excitable nanophosphors in tissues are very sparsely, herein, the CS technique [18], [19] is used to obtain high-resolution and robust XLCT reconstruction images. Note that the performance of CS depends on the RIP of the measurement (weight) matrix W [18], [19], i.e., the measurement matrix W must be incoherence or orthogonality. To improve the RIP, i.e., to improve the recovery performance of sparse signals, in this paper, a preconditioning matrix method [20]–[22] is used. More specifically, by multiplying both sides of (7) by a preconditioning matrix P, we obtain # Φ# m eas = W ρ
(8)
#
where W = PW denotes the preconditioned forward matrix, and Φ# m eas = PΦm eas denotes the preconditioned measurements. It is well known that the RIP can be improved by the use of the preconditioning matrix P [20]–[22]. However, optimizing to have the best RIP is a combinatorial optimization problem. In this paper, according to the description in [20] and [21], to minimize the coherence of W# , the preconditioning matrix P is given as follows: P = (ΛΛT + λI)−1/2 UT T
Fig. 2. CB-XLCT imaging system. (i) EMCCD. (ii) Lens. (iii) Lead shield. (iv) X-ray tube. (v) Rotation stage. (vi) X-ray detector panel. In XLCT imaging processes, the imaging system is enclosed in a light-tight environment to avoid the outside light effect. Note that the rotation stage (v) is unnecessary for XLCT imaging.
(9)
where UΛV is the singular value decomposition of the forward matrix W, I is an identity matrix, λ is a regularization parameter, and T represents transposition operation.
After preconditioning, the nanoparticle density distribution ρ(r) can be recovered by solving the following optimization problem: # min ρ0 subject to Φ# m eas = W ρ ρ
(10)
where ρ0 denotes the 0 -norm of ρ. In this paper, we do not intend to develop any new method for solving (10). Instead, considering the time consumption of reconstruction, we use a standard orthogonal least squares (OLS) method for the solver (10). The details of the process can be found in [26]. In addition, we also point out that there are many recent works [27]–[31] in developing efficient methods for addressing the optimization problem. All these methods can be directly used to further improve the optimization efficiency. III. EXPERIMENT MATERIALS A. CB-XLCT Imaging System To evaluate the performance of the method, we performed the physical phantom experiments on a custom-made CB-XLCT system. As shown in Fig. 2, the imaging system included a cone beam X-ray source (iv), a CMOS X-ray detector panel (vi), and a electron-multiplying CCD (EMCCD) camera (i). The X-ray source used in the system was a microfocus X-ray source with the maximal power of 80 W (Oxford Instrument, U.K.) and could irradiated 13 μm cone beam X-rays. It was placed 26.5 cm away from the surface of the imaged object. The transmitted X-rays were detected by a CMOS X-ray flatpanel detector (2923, Dexela, U.K.) with pixel size of 74.8 μm covering a 3888 × 3072 digital image matrix. A −80◦ cooled EMCCD camera (iXon DU-897, Andor, U.K.) coupled with a 50-mm f/1.8D lens (ii) (Nikon, Melville, NY) was positioned at 90◦ toward the X-ray axis, which was used to collect the luminescent photons emitted from the imaged object. To protect the EMCCD chip from X-ray irradiation, a 4 mm depth of lead shield (iii) was used.
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D. Imaging Protocol In luminescence imaging, the X-ray source voltage and current were set to 80 kV and 1 mA, respectively. The integrating time of EMCCD was set to 1 s, the EM gain was set to 260, and the EMCCD binning was set to 1 × 1. Since only single-view luminescent data need to be acquired to implement 3-D XLCT imaging, the total XLCT imaging time was 1 s. In X-ray scanning, the X-ray source voltage and current were set to 45 kV and 1 mA, respectively. Full-angle X-ray projection images were obtained with a step of 1◦ , resulting in 360 angular positions. The integrating time of each projection was 600 ms. Finally, a steel anchor point, which could be imaged in the two imaging systems, was plastered on the phantom surface to provide the height information for coregistration. E. Reconstruction of Experimental Data Fig. 3. Setup for two types of physical phantom experiments. The transparent glass tubes (outer diameter 0.4 cm) filled with the X-ray-excitable nanophosphors (Gd2 O3 :Eu3 + ) was placed inside a cylinder phantom (a glass cylinder of 3.0 cm outer diameter filled with 1% intralipid and water). (a) Case 1: One tube was immersed in different positions in the phantom to evaluate the effect of the source position on single-view XLCT reconstruction accuracy. (b) Case 2: Two tubes were immersed in different heights in the phantom to evaluate the whole-body imaging performance of single-view reconstruction.
The system can perform not only XLCT imaging, but also conventional X-ray imaging. When collecting the luminescence images, the EMCCD camera was used. When collecting the X-ray images, the X-ray flat panel detector was used. Note that the rotation stage (v) in Fig. 2 is unnecessary for XLCT imaging, which is only needed in XCT imaging. B. Experimental Sets In the experiments, a transparent glass cylinder (outer diameter 3.0 cm; see black circles in Fig. 3) was used as the phantom. The phantom was filled with 1% intralipid and water, with the absorption coefficient μa = 0.02 cm−1 and reduced scattering coefficient μs = 10 cm−1 . One (two) transparent glass tube (tubes) (outer diameter 0.4 cm; see the red circles in Fig. 3) filled with Gd2 O3 :Eu3+ was used as the X-ray luminescent sample. To evaluate the performance of the method, two types of phantom experiments were performed. In Case 1, the phantom contained one tube filled with Gd2 O3 :Eu3+ . But, the tube was immerged in three different positions (I–III) in the cylinder phantom [see Fig. 3(a)], which were used to evaluate the effect of the source position, i.e., the distribution of the nanophosphor in imaged object, on single-view XLCT reconstruction accuracy. In Case 2, two tubes were immerged in the phantom and were far away from each other with center distance 2.9 cm along Z-axis, as shown in Fig. 3(b). It was used to evaluate the whole-body imaging performance of single-view reconstruction. C. X-Ray-Excitable Nanophosphors In our experiments, the Gd2 O3 :Eu3+ was used as a luminescent activator due to its NIR emission wavelength. Here, Gd2 O3 :Eu3+ was synthesized using a co-precipitation method.
For XLCT reconstruction, the forward model W was generated by the finite-element method. In detail, the cylinder phantom in Fig. 3 was discretized into 2991 nodes and 12 425 tetrahedral elements. The detectors were located on the boundary finite-element nodes which were between 5.3 cm height range and inside 160◦ FOV. Reconstructions were performed using the OLS method [26]. In the reconstruction, ρ = 0 was used as the initial solution of (10) and Φ# m eas was used as the initial residual vector. For Experiment 1, λ = 2e−4 , λ = 2e−3 , and λ = 2e−4 were used as the regularization parameters for Cases I–III, respectively. For Experiment 2, λ = 7e−1 was used as the regularization parameter. The reconstruction was terminated after 130 iterations or when mean square error of the current residual was less than 1e−16 . The time cost of reconstruction was about 7.5 s on an Intel 2.80-GHz Quad processor and 12-GB RAM personal computer. For XCT reconstruction, the reconstruction was performed using the Feldkamp–Davis–Kress (FDK) method [32]. In this paper, the FEM was implemented in COMSOL Multiphysics 3.3 (COMSOL, Inc., Burlington, MA, USA). The OLS and FDK methods were implemented in MATLAB 7.3 (MathWorks, Inc., Natick, MA). IV. RESULTS A. Case 1: One Tube Immersed in Three Different Positions in the Phantom Fig. 4 shows the 2-D projection images of X-ray and luminescence from Case 1. In this case, one tube filled with the X-ray-excitable nanophosphor was placed in the three different positions in the phantom (I–III) to evaluate the effect of the source position on single-view XLCT reconstruction accuracy. Fig. 4(a)–(c) shows the luminescence projection images, which are acquired by the EMCCD camera (integrating time: 1 s; EM gain: 260; CCD binning: 1 × 1). Fig. 4(d)–(f) depicts the corresponding X-ray projection images, which are acquired by the X-ray detector panel. Fig. 5 shows the reconstructed tomographic images from Case 1. The bottom row of Fig. 5 shows the reconstructed XCT tomographic image. The top row of Fig. 5 shows the reconstructed XLCT tomographic image, which have been fused with
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TABLE I SINGLE-VIEW RECONSTRUCTION RESULTS OF XLCT FROM CASE 1
TABLE II IMAGING TIME FOR THE DIFFERENT XLCT IMAGING SYSTEMS AND IMAGING METHODS
Fig. 4. Projection images of the X-ray-excitable nanophosphors (Gd2 O3 : Eu3 + ) from Case 1. In this case, one tube filled with Gd2 O3 :Eu3 + was immersed in the different positions in the phantom (I–III) to evaluate the effect of the source position on single-view XLCT reconstruction accuracy. (a)–(c) depict the 2-D luminescence projection images acquired by EMCCD camera (Integrating time: 1 s; EM gain: 260; CCD binning: 1 × 1). (d)–(f) depict the corresponding 2-D X-ray projection images acquired by X-ray detector panel.
Fig. 6. Three-dimensional visualization results of the reconstructed XLCT tomographic images from Case 1. (a) I, (b) II, and (c) III. These XLCT tomographic images were obtained by using the OLS method, incorporating the single-view data [see Fig. 4(a)–(c)].
Fig. 5. XLCT reconstruction results (Case 1) for illustrating the effect of the source position (I–III) on single-view XLCT reconstruction accuracy. The top row depicts the reconstructed XLCT images obtained by single-view data [see Fig. 4(a)–(c)]. The bottom row depicts the corresponding XCT tomographic images. The green curves in top row depict the phantom boundary obtained by back-projecting the 72 white light images, which are used to validate the registration accuracy of XLCT and XCT systems.
the corresponding XCT images. These XLCT images were obtained by the OLS method, incorporating the single-view data [see Fig. 4(a)–(c)]. The time cost for XLCT reconstruction was about 7.5 s. The experimental results indicate that it is feasible to perform 3-D XLCT imaging using single-view data. The tube immersed in different positions in the phantom can be resolved from singleview XCLT reconstruction images and the location errors are less than 1.2 mm (see Table I). Here, the location error is determined by calculating the distance between the center of the tube in the reconstructed XCT images and the location of the maximum value of the reconstructed XLCT images. In addition, we also observe that the reconstruction results were not significantly affected by the position information of the tube placed
in the phantom. Finally, we should note that the imaging time can be greatly reduced (∼1 frame/s) compared with the other XLCT imaging systems (see Table II) because only one view data need to be acquired to implement 3-D XLCT imaging. Fig. 6 shows the 3-D visualization results of the reconstructed XLCT tomographic images, which reflects the 3-D location information of the tube filled with Gd2 O3 :Eu3+ in the phantom (Case 1). These XLCT tomographic images were obtained by the use of the OLS method, incorporating the single-view data [see Fig. 4(a)–(c)]. The results further validate the feasibility of single-view XLCT reconstruction. B. Case 2: Two Tubes Immersed in Different Heights in the Phantom Fig. 7 shows the 2-D X-ray projection image and 2-D luminescence projection image from Case 2, respectively. In this case, two tubes filled with Gd2 O3 :Eu3+ were immerged in different heights in the cylinder phantom, which was used to evaluate the whole-body imaging performance of single-view reconstruction. Fig. 8 demonstrates the simultaneous whole-body imaging performance of single-view XLCT reconstruction. Fig. 8(a) depicts the 3-D visualization result of the reconstructed two
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the imaging time of XLCT can be greatly reduced (see Table II). This means that we can achieve the whole-body imaging at a high time resolution (∼1 frame/s) by the use of the single-view reconstruction method combined with the CB-XLCT imaging system. V. DISCUSSION
Fig. 7. Projection images of the X-ray-excitable nanophosphors (Gd2 O3 : Eu3 + ) from Case 2. In this case, two tubes were immerged in different heights in the cylinder phantom to evaluate the whole-body imaging performance of single-view XLCT reconstruction. (a) Two-dimensional X-ray projection image. (b) Corresponding 2-D luminescence projection image acquired by EMCCD camera (Integrating time: 1 s; EM gain: 260; CCD binning: 1 × 1).
Fig. 8. Phantom experiment (Case 2) for illustrating the simultaneous wholebody imaging performance of single-view XLCT reconstruction. (a) Threedimensional visualization results of the reconstructed XLCT tomographic images, where two tubes filled with Gd2 O3 :Eu3 + were immerged in the phantom and were far away from each other with center distance 2.9 cm along Z -axis. Note that these XLCT tomographic images were reconstructed by using singleview data [see Fig. 7(b)], incorporating the OLS method. The black circles in (a) indicate the positions of investigated slices. (b) and (c) Reconstructed XLCT tomographic images corresponding to the black circles indicated in (a). The images in (b) and (c) are normalized by the maximum of the reconstructed results and then displayed on the same color scale. TABLE III SINGLE-VIEW RECONSTRUCTION RESULTS OF XLCT FROM CASE 2 (UNIT: MM)
tubes. Similar to Section IV-A, the XLCT reconstruction was performed by using single-view data [see Fig. 7(b)] and the time cost of reconstruction was about 7.5 s. Fig. 8(b) and (c) shows the reconstructed XLCT tomographic images corresponding to the black circles in Fig. 8(a). The experimental results indicate that two tubes with a relatively large distance (2.9 cm center-to-center distance along Z-axis) can be localized simultaneously and the location error is less than 1.2 mm (see Table III). In addition, similar to Case 1,
XLCT has been proposed as a new molecular imaging modality. However, challenges still remain in imaging fast and wholebody biological activities using XLCT, where short data collection time, optimal image quality, and whole-body FOV should be considered simultaneously. In this paper, by applying the CS technique to single-view data acquired by a CB-XLCT system, we implemented fast XLCT imaging and then evaluated its performance using two types of physical phantom experiments. It was shown in the phantom experiments that the tubes filled with the X-ray-excitable nanophosphor could be located from the reconstructed XLCT images (see Figs. 5, 6, and 8). The location errors were less than 1.2 mm (see Tables I and III). Moreover, we also found that the position information of the tube immersed in the phantom has slight effect on the singleview XLCT reconstruction results (see Figs. 5 and 6). It further validated the robustness of single-view XLCT reconstruction. On the other hand, it was worth noting that in this paper, the reconstructed XLCT results were obtained by using single-view data. In other words, the integrating time of CCD for collecting single-view data was the imaging time of the XLCT system. As a result, the imaging time could be greatly reduced compared with previous XLCT imaging systems (see Table II). Further, by using the single-view scanning strategy, the whole-body 3-D XLCT tomographic image could also be achieved (see Fig. 8). Based on the experimental results, we believe that the singleview reconstruction method combined with the CB-XLCT system provides an attractive method for dynamic XLCT imaging study. First, this technique allows us to achieve the whole-body 3-D XLCT imaging at a high time resolution (e.g., ∼1 frame/s implemented in this paper). Second, the imaging time resolution (i.e., the integrating time of CCD) can be further improved when a large X-ray tube current is used (e.g., 30 mA used in [2]). As a result, this technique has the potential in real-time XLCT imaging. Finally, this imaging method and system are fairly flexible to extend to other optical imaging modalities, e.g., FMT or BLT. It should be noted that in this paper, the obtained reconstruction results of XLCT are based on a basic assumption that the X-ray-excitable nanophosphors are sparsely distributed in the imaged object. The sparse/compressible property is critical for the imaging quality of the single-view XLCT reconstruction [18], [19]. In addition, due to the ill-posed problem in the reconstruction, the spatial resolution of the single-view reconstruction based on the CB-XLCT system is relatively lower than that of narrow beam XLCT [2]. For example, based on the proposed method, it may also be difficult to resolve the locations of the two tubes if the two tubes are closer to each other. So, a tradeoff between imaging time and reconstruction performance must be considered. To further improve the spatial resolution of the single-view reconstruction, the following methods could
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be considered: 1) constructing the forward model using the radiative transport equation or Monte Carlo simulation method rather than using the diffusion approximation model; 2) solving the reconstruction problem combined with a priori information provided by CT or magnetic resonance imaging; and 3) applying the permissible region strategy to decrease the ill-posedness of XLCT reconstruction. When the previous methods were used in single-view reconstruction, the reconstruction quality of XLCT could be expected to be further improved. On the other hand, in the XLCT reconstruction processes, the parameter λ in (9) is important. In the study, the parameter is selected empirically based on the reconstruction results. Moreover, in this study, the experiments are performed based on a homogeneous physical phantom, which is simpler than the in vivo animal study. Ultimately, in in vivo experiment, the specificity, sensitivity, toxicity, and the stability of the X-ray-excitable nanophosphor in biological tissues need to be thoroughly considered. Systematic studies will be investigated in our future work. In conclusion, by applying the CS technique to a single-view XLCT reconstruction, combined with a CB-XLCT imaging system, we implement fast 3-D XLCT imaging. The technique provides a relative good imaging quality (location errors
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Fast X-Ray Luminescence Computed Tomography Imaging Xin Liu∗ , Member, IEEE, Qimei Liao, and Hongkai Wang
Abstract—X-ray luminescence computed tomography (XLCT) opens new possibilities to perform molecular imaging with X-ray. However, challenges remain in dynamic XLCT imaging, where short scan time, good spatial resolution, and whole-body field of view should be considered simultaneously. In this paper, by the use of a single-view XLCT reconstruction method based on a compressive sensing (CS) technique, incorporating a cone beam XLCT imaging system, we implement fast 3-D XLCT imaging. To evaluate the performance of the method, two types of phantom experiments were performed based on a cone beam XLCT imaging system. In Case 1, one tube filled with the X-ray-excitable nanophosphor (Gd2 O3 :Eu3 + ) was immerged in different positions in the phantom to evaluate the effect of the source position on single-view XLCT reconstruction accuracy. In Case 2, two tubes filled with Gd2 O3 :Eu3 + were immerged in different heights in the phantom to evaluate the whole-body imaging performance of single-view XLCT reconstruction. The experimental results indicated that the tubes used in previous phantom experiments can be resolved from single-view XCLT reconstruction images. The location error is less than 1.2 mm. In addition, since only one view data are needed to implement 3-D XLCT imaging, the acquisition time can be greatly reduced (∼1 frame/s) compared with previous XLCT systems. Hence, the technique is suited for imaging the fast distribution of the X-ray-excitable nanophosphors within a biological object. Index Terms—Fluorescence, hybrid imaging, image reconstruction techniques, optical tomography, X-ray imaging.
I. INTRODUCTION -RAY luminescence computed tomography (XLCT) has been recently proposed as a new molecular imaging modality [1]–[7]. In principle, when the imaged object is irradiated with X-ray, the X-ray-excitable nanophosphors in the imaged object will produce visible or near-infrared (NIR) luminescence which can be measured by sensitive photon detectors, as shown in Fig. 1. Subsequently, by solving a mathematical
X
Manuscript received September 22, 2013; revised November 22, 2013; accepted December 6, 2013. Date of publication December 11, 2013; date of current version May 15, 2014. This work was supported by the National Natural Science Foundation of China under Grant 81371604, Grant 81230035, and Grant 81071220, and by the Shaanxi Natural Science Foundation under Grant 2013JM4008. Asterisk indicates corresponding author. ∗ X. Liu is with the School of Biomedical Engineering, Fourth Military Medical University, Xi’an 710032, China (e-mail: [email protected]). Q. Liao is with the Department of Computation Application, School of Biomedical Engineering, Fourth Military Medical University, Xi’an 710032, China (e-mail: [email protected]). H. Wang is with the Crump Institute of Molecular Imaging, David Geffen School of Medicine, University of California, Los Angeles, CA 90066 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBME.2013.2294633
Fig. 1.
Schematic diagram of CB-XLCT imaging.
model, the 3-D distribution of the nanophosphors in the imaged object can be recovered. Compared with other optical molecular imaging modalities, e.g., fluorescence molecular tomography (FMT) [8]–[10] or bioluminescence tomography (BLT) [11]–[13], XLCT offers two main advantages. First, the X-ray excitation spectrum is undetectable with photon detectors. As a result, the autofluorescence can be avoided, which is helpful for imaging low concentration information. Second, XLCT is expected to have increased depth imaging performance compared with the other optical imaging because of the high penetration of X-ray photons in tissues, which offers the potential to use clinically available. With the advances in the X-ray-excitable nanophosphors [14]–[17], imaging systems, and reconstruction methods [1]–[7], dynamic XLCT imaging is now possible. By adding time as a new dimension, dynamic XLCT imparts the ability to capture the complete dynamic course of the X-rayexcitable nanophosphors (drug) within small animals in vivo. It is also helpful for better studying metabolic processes of nanophosphors-based drugs. Nevertheless, challenges still remain in imaging fast and whole-body biological activities using XLCT, where short scan time, good spatial resolution, and whole-body field of view (FOV) need to be considered simultaneously. For example, in a current widely used narrow beam XLCT imaging system [1]–[3], to collect XLCT data, an X-ray source and detector were mounted on opposite sides of the imaged object, similar to the first-generation X-ray CT scanning strategy. A disadvantage of such system was that the data acquisition generally took long time (typically, ≥624 s) [2]. To reduce the imaging time, Chen et al. designed a cone beam X-ray luminescence computed tomography (CB-XLCT) imaging system [6]. In their reports, by using a cone beam X-ray illumination and a highly sensitive charge-coupled device (CCD) camera detection, they decreased the data acquisition time. However, to collect multiple-view data (generally, ≥four views) which were used to perform XLCT reconstruction, a rotating mechanism
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was used. This meant to rotate the imaged object and to repeat the measurements several times in XLCT imaging processes, leading to the increased imaging time (typically, ≥134 s). As a result, the previous XLCT imaging techniques were not suitable for imaging fast distribution of the nanophosphors within a biological object. The goal of this paper is to improve acquisition speed without significant lose of spatial resolution; therefore, we extend the application of XLCT for fast dynamic imaging study. To achieve the goal, a simple and effective strategy is to use single-view data acquired by a CB-XLCT system. The imaging approach can directly reduce XLCT imaging time because only one view data need to be acquired to implement 3-D XLCT imaging and the imaged object need not to be rotated in imaging processes. That is, the integrating time of CCD for collecting single-view data is the imaging time of XLCT system. However, due to the high scattering of light in biological tissues, the reconstruction of XLCT is an ill-posed problem [6]. Moreover, the ill-posedness will further aggravate if underdetermined data (e.g., single-view data) are used. As a result, the ill-posedness will adversely affect the image quality of XLCT reconstruction. Note that in most biological applications, based on the biological characteristics, the X-ray-excitable nanophosphors are sparsely distributed in the tissues. This means that the nanophosphors in imaging domain are generally very sparse. As a result, the compressive sensing (CS) technique can be used in XLCT reconstruction processes to get high-quality and robust reconstruction results, even if the measurement data are very limited [18], [19]. In addition, it should also be noted that the performance of CS depends on the restricted isometry property (RIP) of the measurement matrix, i.e., the measurement matrix must be incoherence or orthogonality. To improve the RIP, i.e., to improve the recovery performance of sparse signals, recently, a preconditioning matrix method has also been widely used, as described in [20]–[22]. These methods together provide the possibility to implement the single-view XLCT reconstruction. Based on the consideration of previous problems, in this paper, by applying a CS technique to a single-view XLCT reconstruction, combined with a CB-XLCT imaging system, we implement fast 3-D XLCT imaging. To evaluate the performance of the method, two types of phantom experiments were performed based on a CB-XLCT imaging system. In Case 1, one tube filled with the X-ray-excitable nanophosphor (Gd2 O3 :Eu3+ ) was immerged in different positions in the phantom to evaluate the effect of the source position, i.e., the distribution of nanophosphor in imaged object, on single-view XLCT reconstruction accuracy. In Case 2, two tubes filled with Gd2 O3 :Eu3+ were immerged in different heights in the phantom to evaluate the wholebody imaging performance of single-view XLCT reconstruction. Here, the X-ray-excitable nanophosphor we employed was Gd2 O3 :Eu3+ , due to its NIR emission wavelength. The experimental results indicate that the tubes filled with Gd2 O3 :Eu3+ can be resolved from single-view XCLT reconstruction images. The location error is less than 1.2 mm. In addition, since only one view data need to be collected to implement 3-D XLCT imaging, the imaging time can be greatly reduced (∼1 frame/s) compared with the previous XLCT systems. Hence, the tech-
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nique is suited for imaging the fast distribution of the X-rayexcitable nanophosphors (other similar materials or chemical elements) within a biological object. This paper is organized as follows. In Section II, the imaging model and reconstruction method are described. In Section III, the experimental materials are detailed. In Section IV, the experimental results are shown. Finally, we discuss the results and draw conclusions in Section V. II. METHODS A. Forward Problem In XLCT imaging, X-rays are emitted from the X-ray source and travel through tissues. As shown in Fig. 1, as soon as X-ray is transported to nanophosphors in tissues, the nanophosphors will emit visible or NIR light, which can be expressed according to [4], as follows: S(r) = ηA(r)ρ(r)
(1)
where S(r) is the source energy density (W/mm3 ), ρ(r) is the density (concentration) of the nanophosphor (g/mL), A(r) is the X-ray intensity (W/mm2 ), and η is the light yield which is defined as the quantum yield per unit nanophosphor concentration. According to Lambert–Beers’ law, during the course of X-rays traveling through the tissues, the X-ray intensity distribution A(r) can be expressed as follows: r μ(τ )dτ (2) A(r) = A0 exp − r0
where A0 (r) is the X-ray source intensity at the initial position r0 , and μ(τ ) is the X-ray attenuation coefficient (mm−1 ) which can be obtained from X-ray transmission data using an attenuation-based CT technique. Since biological tissue has highly scattering and weakly absorbing properties in the NIR spectral window, the NIR light S(r) (e.g., the emitted NIR light from Gd2 O3 :Eu3+ ) in the tissues can be obtained by solving the following diffusion equation [23] combined with the Robin-type boundary condition [24]: ⎧ ⎨ −∇[D(r)∇Φ(r)] + μa (r)Φ(r) = S(r) r ∈ Ω (3) ⎩ 2γD(r) ∂Φ(r) + Φ(r) = 0 r ∈ ∂Ω ∂n where Ω is the domain of the imaged object and ∂Ω is the boundary; Φ(r) is the photon flux density (W/mm2 ); μa (r) is the absorption coefficient (mm−1 ); D(r) = 1/(3(μa (r) + μs (r)) is the diffusion coefficient (mm) with μs (r) being the reduced scattering coefficient (mm−1 ); n denotes the outward normal vector to the boundary ∂Ω, and γ is a constant depending upon the optical reflective index mismatch at the boundary. Knowing the optical properties, the diffusion equation can be solved using the finite-element method [25]. Based on the finite-element theory, (3) can be discretized into the following matrix equation: KΦ = FηAρ
(4)
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with ⎧ 1 ⎪ ⎪ ⎨ Kij = Ω (D∇ψi ∇ψj + μa ψi ψj )dr+ 2γ ∂ Ω ψi ψj dr ⎪ ⎪ ⎩ Fij = ψi ψj dr Ω
(5) where Kij and Fij are the elements of matrices K and F, respectively. ψi and ψj are the volume elements that discretize the imaging domain and form a geometrical mesh defined over the entire imaging domain. Since the matrix K is positive definite, (4) can be changed to Φ = Jρ
(6)
−1
where J = K FηA. Finally, by removing the unmeasurable interior values Φi g n o in Φ and the rows of the matrix J corresponding to Φi g n o , the final matrix equation is generated as follows: Φm eas = Wρ
(7)
where W is a weight (measurement) matrix describing the forward model of the CB-XLCT imaging. B. Inverse Problem The goal of XLCT reconstruction is to recover the X-rayexcitable nanophosphor density ρ from the measured photon density Φm eas on the boundary ∂Ω. However, as mentioned in Section I, due to the high scattering of light in biological tissues and the use of underdetermined data (single-view data), the weight matrix W in (7) is poorly conditioned. As a result, it is impractical to solve ρ directly from (7). Considering that in most biological applications, the distributions of X-ray-excitable nanophosphors in tissues are very sparsely, herein, the CS technique [18], [19] is used to obtain high-resolution and robust XLCT reconstruction images. Note that the performance of CS depends on the RIP of the measurement (weight) matrix W [18], [19], i.e., the measurement matrix W must be incoherence or orthogonality. To improve the RIP, i.e., to improve the recovery performance of sparse signals, in this paper, a preconditioning matrix method [20]–[22] is used. More specifically, by multiplying both sides of (7) by a preconditioning matrix P, we obtain # Φ# m eas = W ρ
(8)
#
where W = PW denotes the preconditioned forward matrix, and Φ# m eas = PΦm eas denotes the preconditioned measurements. It is well known that the RIP can be improved by the use of the preconditioning matrix P [20]–[22]. However, optimizing to have the best RIP is a combinatorial optimization problem. In this paper, according to the description in [20] and [21], to minimize the coherence of W# , the preconditioning matrix P is given as follows: P = (ΛΛT + λI)−1/2 UT T
Fig. 2. CB-XLCT imaging system. (i) EMCCD. (ii) Lens. (iii) Lead shield. (iv) X-ray tube. (v) Rotation stage. (vi) X-ray detector panel. In XLCT imaging processes, the imaging system is enclosed in a light-tight environment to avoid the outside light effect. Note that the rotation stage (v) is unnecessary for XLCT imaging.
(9)
where UΛV is the singular value decomposition of the forward matrix W, I is an identity matrix, λ is a regularization parameter, and T represents transposition operation.
After preconditioning, the nanoparticle density distribution ρ(r) can be recovered by solving the following optimization problem: # min ρ0 subject to Φ# m eas = W ρ ρ
(10)
where ρ0 denotes the 0 -norm of ρ. In this paper, we do not intend to develop any new method for solving (10). Instead, considering the time consumption of reconstruction, we use a standard orthogonal least squares (OLS) method for the solver (10). The details of the process can be found in [26]. In addition, we also point out that there are many recent works [27]–[31] in developing efficient methods for addressing the optimization problem. All these methods can be directly used to further improve the optimization efficiency. III. EXPERIMENT MATERIALS A. CB-XLCT Imaging System To evaluate the performance of the method, we performed the physical phantom experiments on a custom-made CB-XLCT system. As shown in Fig. 2, the imaging system included a cone beam X-ray source (iv), a CMOS X-ray detector panel (vi), and a electron-multiplying CCD (EMCCD) camera (i). The X-ray source used in the system was a microfocus X-ray source with the maximal power of 80 W (Oxford Instrument, U.K.) and could irradiated 13 μm cone beam X-rays. It was placed 26.5 cm away from the surface of the imaged object. The transmitted X-rays were detected by a CMOS X-ray flatpanel detector (2923, Dexela, U.K.) with pixel size of 74.8 μm covering a 3888 × 3072 digital image matrix. A −80◦ cooled EMCCD camera (iXon DU-897, Andor, U.K.) coupled with a 50-mm f/1.8D lens (ii) (Nikon, Melville, NY) was positioned at 90◦ toward the X-ray axis, which was used to collect the luminescent photons emitted from the imaged object. To protect the EMCCD chip from X-ray irradiation, a 4 mm depth of lead shield (iii) was used.
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D. Imaging Protocol In luminescence imaging, the X-ray source voltage and current were set to 80 kV and 1 mA, respectively. The integrating time of EMCCD was set to 1 s, the EM gain was set to 260, and the EMCCD binning was set to 1 × 1. Since only single-view luminescent data need to be acquired to implement 3-D XLCT imaging, the total XLCT imaging time was 1 s. In X-ray scanning, the X-ray source voltage and current were set to 45 kV and 1 mA, respectively. Full-angle X-ray projection images were obtained with a step of 1◦ , resulting in 360 angular positions. The integrating time of each projection was 600 ms. Finally, a steel anchor point, which could be imaged in the two imaging systems, was plastered on the phantom surface to provide the height information for coregistration. E. Reconstruction of Experimental Data Fig. 3. Setup for two types of physical phantom experiments. The transparent glass tubes (outer diameter 0.4 cm) filled with the X-ray-excitable nanophosphors (Gd2 O3 :Eu3 + ) was placed inside a cylinder phantom (a glass cylinder of 3.0 cm outer diameter filled with 1% intralipid and water). (a) Case 1: One tube was immersed in different positions in the phantom to evaluate the effect of the source position on single-view XLCT reconstruction accuracy. (b) Case 2: Two tubes were immersed in different heights in the phantom to evaluate the whole-body imaging performance of single-view reconstruction.
The system can perform not only XLCT imaging, but also conventional X-ray imaging. When collecting the luminescence images, the EMCCD camera was used. When collecting the X-ray images, the X-ray flat panel detector was used. Note that the rotation stage (v) in Fig. 2 is unnecessary for XLCT imaging, which is only needed in XCT imaging. B. Experimental Sets In the experiments, a transparent glass cylinder (outer diameter 3.0 cm; see black circles in Fig. 3) was used as the phantom. The phantom was filled with 1% intralipid and water, with the absorption coefficient μa = 0.02 cm−1 and reduced scattering coefficient μs = 10 cm−1 . One (two) transparent glass tube (tubes) (outer diameter 0.4 cm; see the red circles in Fig. 3) filled with Gd2 O3 :Eu3+ was used as the X-ray luminescent sample. To evaluate the performance of the method, two types of phantom experiments were performed. In Case 1, the phantom contained one tube filled with Gd2 O3 :Eu3+ . But, the tube was immerged in three different positions (I–III) in the cylinder phantom [see Fig. 3(a)], which were used to evaluate the effect of the source position, i.e., the distribution of the nanophosphor in imaged object, on single-view XLCT reconstruction accuracy. In Case 2, two tubes were immerged in the phantom and were far away from each other with center distance 2.9 cm along Z-axis, as shown in Fig. 3(b). It was used to evaluate the whole-body imaging performance of single-view reconstruction. C. X-Ray-Excitable Nanophosphors In our experiments, the Gd2 O3 :Eu3+ was used as a luminescent activator due to its NIR emission wavelength. Here, Gd2 O3 :Eu3+ was synthesized using a co-precipitation method.
For XLCT reconstruction, the forward model W was generated by the finite-element method. In detail, the cylinder phantom in Fig. 3 was discretized into 2991 nodes and 12 425 tetrahedral elements. The detectors were located on the boundary finite-element nodes which were between 5.3 cm height range and inside 160◦ FOV. Reconstructions were performed using the OLS method [26]. In the reconstruction, ρ = 0 was used as the initial solution of (10) and Φ# m eas was used as the initial residual vector. For Experiment 1, λ = 2e−4 , λ = 2e−3 , and λ = 2e−4 were used as the regularization parameters for Cases I–III, respectively. For Experiment 2, λ = 7e−1 was used as the regularization parameter. The reconstruction was terminated after 130 iterations or when mean square error of the current residual was less than 1e−16 . The time cost of reconstruction was about 7.5 s on an Intel 2.80-GHz Quad processor and 12-GB RAM personal computer. For XCT reconstruction, the reconstruction was performed using the Feldkamp–Davis–Kress (FDK) method [32]. In this paper, the FEM was implemented in COMSOL Multiphysics 3.3 (COMSOL, Inc., Burlington, MA, USA). The OLS and FDK methods were implemented in MATLAB 7.3 (MathWorks, Inc., Natick, MA). IV. RESULTS A. Case 1: One Tube Immersed in Three Different Positions in the Phantom Fig. 4 shows the 2-D projection images of X-ray and luminescence from Case 1. In this case, one tube filled with the X-ray-excitable nanophosphor was placed in the three different positions in the phantom (I–III) to evaluate the effect of the source position on single-view XLCT reconstruction accuracy. Fig. 4(a)–(c) shows the luminescence projection images, which are acquired by the EMCCD camera (integrating time: 1 s; EM gain: 260; CCD binning: 1 × 1). Fig. 4(d)–(f) depicts the corresponding X-ray projection images, which are acquired by the X-ray detector panel. Fig. 5 shows the reconstructed tomographic images from Case 1. The bottom row of Fig. 5 shows the reconstructed XCT tomographic image. The top row of Fig. 5 shows the reconstructed XLCT tomographic image, which have been fused with
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TABLE I SINGLE-VIEW RECONSTRUCTION RESULTS OF XLCT FROM CASE 1
TABLE II IMAGING TIME FOR THE DIFFERENT XLCT IMAGING SYSTEMS AND IMAGING METHODS
Fig. 4. Projection images of the X-ray-excitable nanophosphors (Gd2 O3 : Eu3 + ) from Case 1. In this case, one tube filled with Gd2 O3 :Eu3 + was immersed in the different positions in the phantom (I–III) to evaluate the effect of the source position on single-view XLCT reconstruction accuracy. (a)–(c) depict the 2-D luminescence projection images acquired by EMCCD camera (Integrating time: 1 s; EM gain: 260; CCD binning: 1 × 1). (d)–(f) depict the corresponding 2-D X-ray projection images acquired by X-ray detector panel.
Fig. 6. Three-dimensional visualization results of the reconstructed XLCT tomographic images from Case 1. (a) I, (b) II, and (c) III. These XLCT tomographic images were obtained by using the OLS method, incorporating the single-view data [see Fig. 4(a)–(c)].
Fig. 5. XLCT reconstruction results (Case 1) for illustrating the effect of the source position (I–III) on single-view XLCT reconstruction accuracy. The top row depicts the reconstructed XLCT images obtained by single-view data [see Fig. 4(a)–(c)]. The bottom row depicts the corresponding XCT tomographic images. The green curves in top row depict the phantom boundary obtained by back-projecting the 72 white light images, which are used to validate the registration accuracy of XLCT and XCT systems.
the corresponding XCT images. These XLCT images were obtained by the OLS method, incorporating the single-view data [see Fig. 4(a)–(c)]. The time cost for XLCT reconstruction was about 7.5 s. The experimental results indicate that it is feasible to perform 3-D XLCT imaging using single-view data. The tube immersed in different positions in the phantom can be resolved from singleview XCLT reconstruction images and the location errors are less than 1.2 mm (see Table I). Here, the location error is determined by calculating the distance between the center of the tube in the reconstructed XCT images and the location of the maximum value of the reconstructed XLCT images. In addition, we also observe that the reconstruction results were not significantly affected by the position information of the tube placed
in the phantom. Finally, we should note that the imaging time can be greatly reduced (∼1 frame/s) compared with the other XLCT imaging systems (see Table II) because only one view data need to be acquired to implement 3-D XLCT imaging. Fig. 6 shows the 3-D visualization results of the reconstructed XLCT tomographic images, which reflects the 3-D location information of the tube filled with Gd2 O3 :Eu3+ in the phantom (Case 1). These XLCT tomographic images were obtained by the use of the OLS method, incorporating the single-view data [see Fig. 4(a)–(c)]. The results further validate the feasibility of single-view XLCT reconstruction. B. Case 2: Two Tubes Immersed in Different Heights in the Phantom Fig. 7 shows the 2-D X-ray projection image and 2-D luminescence projection image from Case 2, respectively. In this case, two tubes filled with Gd2 O3 :Eu3+ were immerged in different heights in the cylinder phantom, which was used to evaluate the whole-body imaging performance of single-view reconstruction. Fig. 8 demonstrates the simultaneous whole-body imaging performance of single-view XLCT reconstruction. Fig. 8(a) depicts the 3-D visualization result of the reconstructed two
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the imaging time of XLCT can be greatly reduced (see Table II). This means that we can achieve the whole-body imaging at a high time resolution (∼1 frame/s) by the use of the single-view reconstruction method combined with the CB-XLCT imaging system. V. DISCUSSION
Fig. 7. Projection images of the X-ray-excitable nanophosphors (Gd2 O3 : Eu3 + ) from Case 2. In this case, two tubes were immerged in different heights in the cylinder phantom to evaluate the whole-body imaging performance of single-view XLCT reconstruction. (a) Two-dimensional X-ray projection image. (b) Corresponding 2-D luminescence projection image acquired by EMCCD camera (Integrating time: 1 s; EM gain: 260; CCD binning: 1 × 1).
Fig. 8. Phantom experiment (Case 2) for illustrating the simultaneous wholebody imaging performance of single-view XLCT reconstruction. (a) Threedimensional visualization results of the reconstructed XLCT tomographic images, where two tubes filled with Gd2 O3 :Eu3 + were immerged in the phantom and were far away from each other with center distance 2.9 cm along Z -axis. Note that these XLCT tomographic images were reconstructed by using singleview data [see Fig. 7(b)], incorporating the OLS method. The black circles in (a) indicate the positions of investigated slices. (b) and (c) Reconstructed XLCT tomographic images corresponding to the black circles indicated in (a). The images in (b) and (c) are normalized by the maximum of the reconstructed results and then displayed on the same color scale. TABLE III SINGLE-VIEW RECONSTRUCTION RESULTS OF XLCT FROM CASE 2 (UNIT: MM)
tubes. Similar to Section IV-A, the XLCT reconstruction was performed by using single-view data [see Fig. 7(b)] and the time cost of reconstruction was about 7.5 s. Fig. 8(b) and (c) shows the reconstructed XLCT tomographic images corresponding to the black circles in Fig. 8(a). The experimental results indicate that two tubes with a relatively large distance (2.9 cm center-to-center distance along Z-axis) can be localized simultaneously and the location error is less than 1.2 mm (see Table III). In addition, similar to Case 1,
XLCT has been proposed as a new molecular imaging modality. However, challenges still remain in imaging fast and wholebody biological activities using XLCT, where short data collection time, optimal image quality, and whole-body FOV should be considered simultaneously. In this paper, by applying the CS technique to single-view data acquired by a CB-XLCT system, we implemented fast XLCT imaging and then evaluated its performance using two types of physical phantom experiments. It was shown in the phantom experiments that the tubes filled with the X-ray-excitable nanophosphor could be located from the reconstructed XLCT images (see Figs. 5, 6, and 8). The location errors were less than 1.2 mm (see Tables I and III). Moreover, we also found that the position information of the tube immersed in the phantom has slight effect on the singleview XLCT reconstruction results (see Figs. 5 and 6). It further validated the robustness of single-view XLCT reconstruction. On the other hand, it was worth noting that in this paper, the reconstructed XLCT results were obtained by using single-view data. In other words, the integrating time of CCD for collecting single-view data was the imaging time of the XLCT system. As a result, the imaging time could be greatly reduced compared with previous XLCT imaging systems (see Table II). Further, by using the single-view scanning strategy, the whole-body 3-D XLCT tomographic image could also be achieved (see Fig. 8). Based on the experimental results, we believe that the singleview reconstruction method combined with the CB-XLCT system provides an attractive method for dynamic XLCT imaging study. First, this technique allows us to achieve the whole-body 3-D XLCT imaging at a high time resolution (e.g., ∼1 frame/s implemented in this paper). Second, the imaging time resolution (i.e., the integrating time of CCD) can be further improved when a large X-ray tube current is used (e.g., 30 mA used in [2]). As a result, this technique has the potential in real-time XLCT imaging. Finally, this imaging method and system are fairly flexible to extend to other optical imaging modalities, e.g., FMT or BLT. It should be noted that in this paper, the obtained reconstruction results of XLCT are based on a basic assumption that the X-ray-excitable nanophosphors are sparsely distributed in the imaged object. The sparse/compressible property is critical for the imaging quality of the single-view XLCT reconstruction [18], [19]. In addition, due to the ill-posed problem in the reconstruction, the spatial resolution of the single-view reconstruction based on the CB-XLCT system is relatively lower than that of narrow beam XLCT [2]. For example, based on the proposed method, it may also be difficult to resolve the locations of the two tubes if the two tubes are closer to each other. So, a tradeoff between imaging time and reconstruction performance must be considered. To further improve the spatial resolution of the single-view reconstruction, the following methods could
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be considered: 1) constructing the forward model using the radiative transport equation or Monte Carlo simulation method rather than using the diffusion approximation model; 2) solving the reconstruction problem combined with a priori information provided by CT or magnetic resonance imaging; and 3) applying the permissible region strategy to decrease the ill-posedness of XLCT reconstruction. When the previous methods were used in single-view reconstruction, the reconstruction quality of XLCT could be expected to be further improved. On the other hand, in the XLCT reconstruction processes, the parameter λ in (9) is important. In the study, the parameter is selected empirically based on the reconstruction results. Moreover, in this study, the experiments are performed based on a homogeneous physical phantom, which is simpler than the in vivo animal study. Ultimately, in in vivo experiment, the specificity, sensitivity, toxicity, and the stability of the X-ray-excitable nanophosphor in biological tissues need to be thoroughly considered. Systematic studies will be investigated in our future work. In conclusion, by applying the CS technique to a single-view XLCT reconstruction, combined with a CB-XLCT imaging system, we implement fast 3-D XLCT imaging. The technique provides a relative good imaging quality (location errors
