BioMed Research International

Volume 2016, Article ID 6450124, 6 pages

http://dx.doi.org/10.1155/2016/6450124

## Cone Beam X-Ray Luminescence Tomography Imaging Based on KA-FEM Method for Small Animals

^{1}College of Life Information Science and Instrument Engineering, Hangzhou Dianzi University, Hangzhou 310018, China^{2}School of Life Sciences and Technology, Xidian University, Xi’an 710071, China^{3}School of Information Sciences and Technology, Northwest University, Xi’an, Shaanxi 710069, China

Received 21 June 2016; Revised 6 September 2016; Accepted 5 October 2016

Academic Editor: Jinchao Feng

Copyright © 2016 Dongmei Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Cone beam X-ray luminescence tomography can realize fast X-ray luminescence tomography imaging with relatively low scanning time compared with narrow beam X-ray luminescence tomography. However, cone beam X-ray luminescence tomography suffers from an ill-posed reconstruction problem. First, the feasibility of experiments with different penetration and multispectra in small animal has been tested using nanophosphor material. Then, the hybrid reconstruction algorithm with KA-FEM method has been applied in cone beam X-ray luminescence tomography for small animals to overcome the ill-posed reconstruction problem, whose advantage and property have been demonstrated in fluorescence tomography imaging. The* in vivo* mouse experiment proved the feasibility of the proposed method.

#### 1. Introduction

X-ray luminescence tomography (XLT) has been put forward as a novel imaging technology for biological imaging application based on X-ray-excitable phosphor nanoparticles [1]. These phosphor nanoparticles can produce visible luminescence light signals irradiated with X-ray which can be measured by charge coupled device (CCD) [1]. The discovery that both X-ray and visible light can propagate through tissue and that the nanophosphors agents can trace specific molecular makes XLT a proper tool for* in vivo* biomedical imaging. Nowadays, XLT technology has also been extended from narrow beam X-ray [1] to cone beam X-ray excitation [2] and is even applied in endoscopic imaging [3]. Meanwhile, with advanced specific materials for X-ray excitation, it has also been applied in small animal* in vivo* imaging [4].

The XLT modality has its unique features over other optical imaging methods such as bioluminescence and fluorescence imaging [5, 6]. It can excite the nanophosphors from different angles and avoid a significant autofluorescence in other optical imaging methods [2]. However, this technology demands long scanning time under X-ray exposure, which limits its development of fast* in vivo* biology processes [5]. Some research groups have improved the XLT imaging time resolution from different ways. Carpenter et al. proposed a limited-angle X-ray luminescence tomography method to complete reconstruction from limited-angles in narrow beam XLT system [7]. Badea et al. invented a battleship sampling paradigm to mix sampling and reconstruction in narrow beam XLT system [8]. In addition, Chen et al. designed a cone beam XLT imaging system [2] and Chen et al. put forward a reconstruction method with single view data in cone beam XLT system [3]. Even though the imaging time in the reconstruction method with single view data is reported to be less than 30 s [3], reconstructed result with planar detectors and a single view is generally insufficient for accurate 3D reconstruction [9]. The inverse problem of reconstruction is an ill-posed problem and can be improved by taking images of the experiment subject from multiple views [10] and using multispectral data [11].

It is reported that Gd_{2}O_{2}S: Tb has several peaks in the spectrum excited by X-rays and can be applied in multispectral imaging and reconstruction [12]. The multispectral property of this material has also been reported for its advantage in improving the XLT imaging quality [13]. However, the penetration property of this material under different spectral has not been discussed before. In this paper, the spectral property of the material in different tissues has been studied. The feasibility of conducting experiments in small animal has been proved through the preliminary results. The hybrid reconstruction algorithm with Kirchhoff approximation and finite element method (KA-FEM) has been studied in fluorescence tomography to overcome the ill-posedness in reconstruction [14]. Hence, we realize cone beam XLT reconstruction with KA-FEM method and perform experiments on both tissue and* in vivo* mouse. Our reconstructed results show that the KA-FEM method can be applied in reconstruction to make XLT imaging feasible for small animal imaging.

#### 2. Method

In the cone beam XLT system, X-rays are emitted from the X-ray source and travel through the tissues based on Lambert-Beers’ law. Once the nanophosphors are irradiated by X-rays, they will emit visible light. The light transport in biological tissues can be accurately modeled by diffusion approximation, owing to the highly scattering and weakly absorbing properties of the soft tissues in the spectral region. The imaging model can be expressed as follows:where is the X-ray source intensity with the initial position and is the X-ray attenuation coefficient at position that can be computed from X-ray transmission data using an attenuation-based computed tomography (CT) technique. is the light source. is the X-ray intensity, and is the nanophosphor density at position . is the light yield, while is the position vector. is the domain under consideration, and is the diffusion coefficient with as the absorption coefficient, as the anisotropy parameter, and as the scattering coefficient. is the photon flux density.

Meanwhile, it is reported that the resolution of the reconstructed results can be significantly improved using data measured at different wavelengths [15, 16]. With the surface data measured at two or more wavelengths, the significantly different system matrixes can be obtained to enhance the resolution of the problem. The ratio of the energy distribution in every spectrum can be measured and the linear relationship between the measured multispectral data and the material distribution can be obtained as follows:where, , and represent the system matrix, the measurable photon density, and the relative fraction at which the wavelength contributes in the emission spectrum, respectively. is given as follows: where and denote the lower and upper limits of the bandpass filter centered on wavelength , respectively, and is the emission spectrum.

The KA-FEM method is applied to combine the analytical method and numerical method based on finite element method to solve the imaging model and form the system equations [14]. The flow chart of the reconstruction can be divided into the KA module and the FEM module. KA method is utilized to produce the region of interest (ROI) and then FEM is used to reconstruct the final result. In the KA module, the system matrix can be expressed as as follows at the corresponding wavelength [14, 17]:where denotes the outward normal vector at surface point . denotes local planar discrete area on the surface. denotes Green’s function in infinite medium while denotes Green’s function in medium with boundary. The surface values can be obtained by the method of images [18]:where and . The coefficient takes into account the refractive index mismatch between both media [19]. Then, preliminary reconstructed results can be obtained by -norm regularization method, while in the FEM module the system matrix can be obtained by transforming the model to its weak form and discretizing the domain with the shape function and is expressed as follows at the corresponding wavelength [2]: where is the light yield and is the X-ray intensity at each vertex. is the boundary mismatch factor, which depends on the refractive indices in and in the surrounding medium. and denote the corresponding elements of the test function. Finally, the reconstructed result can be obtained with conjugate gradient least square (CGLS) method [20].

#### 3. Experiment and Result

The equipment used in our experiments consisted of a cone beam X-ray source to excite the phosphors, an electron-multiplying CCD (EMCCD) camera to sample the photon fluence, and an extra CMOS X-ray detector panel to collect the transmitted X-rays. This schematic is shown in Figure 1. In the system, the CT system contains a microfocus X-ray source (Apogee, Oxford Instruments, UK) and CMOS flat-panel detector (C7921, Hamamatsu, Japan) with pixel size of 50 *μ*m covering a 1056 × 1056 digital image matrix. The EMCCD camera (PIXIS2048, Princeton Instruments, UK) was mounted at 90° toward the X-ray axis with a Nikkor 55-mm f/2.8 D lens (Nikon, Melville, New York). To minimize the X-ray ionizing radiation to the EMCCD, a lead shield with depth of 4 mm was used.