Journal of X-Ray Science and Technology 22 (2014) 285–297 DOI 10.3233/XST-140425 IOS Press
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A method of extracting structural priors from images of micro-CT for fluorescence molecular tomography reconstruction Yuanzheng Menga,b , Xiaoquan Yanga,b,∗ , Yong Denga,b , Xuanxuan Zhanga,b and Hui Gonga,b a Britton
Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, Hubei, China b MoE Key Laboratory of Biomedical Photonics, Department of Biomedical Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China Received 16 January 2013 Revised 8 February 2014 Accepted 16 February 2014 Abstract. The dual-modality systems combined fluorescence molecular tomography (FMT) and micro-computed tomography (micro-CT) can provide molecular and anatomical information of small animals simultaneously. Except for anatomic localization, micro-CT should also offer boundary of different organs as reconstruction priors for FMT, which is more challenging than acquisition of structural information. In this paper, we propose a framework to extract structural priors of a living mouse with micro-CT. The iodinated lipid emulsion contrast agent was adopted to enhance the contrast of the soft tissues of the mouse. Then organs in thorax and abdomen were segmented with different approaches depending on the characteristics of the organs. Bone, lung, heart, liver, spleen, and muscles were separately segmented. And the results were compared with that manually segmented. The Tanimoto coefficient and the relative volume difference of segmented slices were measured to be 91.28 ± 5.78 and 0.27 ± 3.15, respectively. In our simulation study of FMT reconstruction, the errors of measured position and concentration of the fluorophore with priors declined by 89.7% and 79.6% in thorax, as well as 80.8% and 78.3% in abdomen, respectively, compared with the results without priors. The proposed scheme will make FMT reconstruction much more reliable and practical in small animal study. Keywords: Image segmentation, micro-computed tomography, fluorescence molecular tomography
1. Introduction Fluorescence molecular tomography (FMT), one of the noninvasive molecular imaging modalities, potentially played an important role in fundamental scientific researches and preclinical trials [1–3]. It could quantitatively acquire the bio-distribution of the fluorophore in the living small animals. Compared to the traditional molecular imaging techniques, positron emission tomography (PET), single photon emission computed tomography (SPECT), and magnetic resonance imaging (MRI), it could perform ∗
Corresponding author: Xiaoquan Yang, Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics-Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, Hubei, China. Tel.: +86 27 87792033; Fax: +86 27 87792034; E-mail: [email protected]. c 2014 – IOS Press and the authors. All rights reserved 0895-3996/14/$27.50
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multichannel imaging with non-ionizing radiation at a relatively low cost [2]. However, imaging quality of FMT is limited due to the fact that the inverse problem is ill-posed and sometimes underdetermined [4]. This makes the results of the FMT unreliable, and consequently degrades the utility of this emerging technique. Structural priors have shown substantial effect in the improvement of the performance of diffuse optical tomography [5–11]. Recently, it was also introduced to elevate resolution and quantitative accuracy of FMT [11–14]. Therefore, other imaging modalities, including micro-computed tomography (micro-CT) [15–17], MRI [18,19], photoacoustic tomography (PAT) [20], and integrated SPECT-CT system [21], have been employed to provide priors for FMT reconstruction. Compared to other complementary imaging modalities, micro-CT can provide high resolution anatomical images of small animals in-vivo with fast scanning, and directly integrate with full capable FMT system [22]. For combining with FMT, micro-CT is amenable to provide high resolution images of anatomy, boundaries of different organs and deliver low radiation dose to small animals. Unfortunately, the image quality of micro-CT is limited by the delivered radiation dose to small animals [23–26]. Therefore, it is quite a challenge to get the clear boundaries of the soft tissues in micro-CT images in small animal study in-vivo. Manual segmentation by experts can provide accurate results. However, the workload would be tremendous, especially in a longitudinal study. Several automatic segmentation methods have been proposed in the past years for clinical CT images [27–30]. Nevertheless, these approaches are not appropriate for the mouse imaging with micro-CT, due to the noise levels and soft-tissue contrasts of the images from micro-CT are quite different with these from clinical CT. Recently, several automatic segmentation methods have been developed for mouse images from rotating gantry micro-CT. X. Artaechevarria et al. proposed an effective, fast segmentation and reconstruction algorithm, which is just aimed at the murine airway [31]. Marcus Freyer et al. suggested a framework that segmented bones, lungs and heart [32]. It worked fast and achieved fine segmentation of bones using thresholds. Regarding lung and heart, the seed growing algorithm and a static undeformable model were used respectively. However, the proposed scheme only worked in the thorax. Due to the low contrast of abdominal tissue, these methods didn’t involve the segmentation of liver, spleen and so on. Martin Baiker et al. introduced an automatic segmentation approach using MRI atlas-based registration for whole-body mice images without contrast agents [33]. This method can be used to segment most of the soft tissues even for larger variations in posture compared to the previous studies. However, the segmentation accuracy of some soft tissues is still low, as the posture and shape vary significantly between each animal and the atlas. And the image registration is rather complex. Given the fact that the deformation of the animal in a rotating object micro-CT is obviously larger than that in a rotating gantry micro-CT [34,35], the aforementioned approaches (mainly for atlas-based registration which can segment most of the tissues) may yield remarkable errors for the soft tissues segmentation of the animal in a rotating object micro-CT system. In our previous work, we have constructed a combined FMT/micro-CT system [36] in which the object was rotated and the performance of the micro-CT system was evaluated [37]. However, the coupling of the two modalities only performed in space, i.e. the structural information did not be extracted and used in reconstruction of the FMT. It made the FMT unqualified in quantitative imaging. To address this issue, we proposed an image segmentation scheme to get the boundaries of the tissues enhanced by a blood pool contrast agent. The use of a blood pool contrast agent is to enhance the contrast between different tissues, especial abdominal tissues, so that we can segment them more accurately and simply. The scheme was developed as follows: threshold method for automatic segmentation of bone structures and lung, standard snake deforming algorithm for full heart segmentation, as well as watershed algorithm used to segment liver and spleen automatically. The quality of segmented dataset was further evaluated using Tanimoto coefficient and the relative volume difference. Finally, the segmented dataset was used as priors for FMT simulation to demonstrate the utility.
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2. Methods The micro-CT scanner consists of a micro-focus x-ray tube (UltraBright, Oxford Instruments, U.S.), a flat-panel detector based on amorphous silicon (PaxScan2520V, Varian Medical Systems, U.S.), and a rotation stage, controlled by a workstation (HW8200, Hewlett-Packard, U.S.). Source-to-detector distance and source-to-object distance were measured to be about 636.0 mm and 161.0 mm, respectively, and given a magnification factor of 3.95 consequentially. The system possesses a field of view of 62.5 mm in diameter and 50.0 mm in length. The spatial resolution of the system was measured to be 13.0 lp/mm (10% modulation transfer function value). Feldkamp’s filtered back-projection algorithm accelerated by GPU [38,39] has been used to reconstruct the acquired dataset. All the measurements were performed with the x-ray source operating with tube voltage of 55 kVp and a 2.5 mm-thick aluminum filter. The radiation dose was measured in the air at the axis-of-rotation with the ion chamber dosimeter (Farmer 2570, NE, U.K.). It was about 0.34 mGy per frame calculated with exposure-to-air kerma conversion factor of 8.767 mGy/R. 2.1. Small animal imaging An adult male Kunming mouse weighting about 44.5 g was used for demonstrating the proposed scheme. A dose of 1 g/kg urethane and 0.2 g/kg a-chloralose was administered intraperitoneally to anesthetize the mouse. Then a single tail-vein injection was performed to introduce an iodinated lipid emulsion blood-pool contrast agent (50 mg I/ml, ART, Quebec, Canada) with a dose of 0.1 ml/10 g. Nine hours after injection, the mouse was then fixed in a homemade PMMA chamber for scanning. The time point was chosen considering the compromised enhancement of different soft tissues [40]. All of the experiments were carried out in accordance with the Huazhong University of Science and Technology guidelines regarding the use and care of animals. 2.2. Image segmentation and validation The reconstructed data set was pretreated to remove the air, animal holder and the tail of the mouse. The holder could be subtracted, because its position is predetermined. Then, the canny edge detection was applied to each slice to obtain edge contours. An eight-connected neighborhood was used to identify the body contour in each slice, which was the largest area. Inside regions of the body contours were filled and stored as template to acquire the volume only including the body of the mouse. 2.2.1. Segmentation of bone and lung Obviously, bone structures and lung still perform higher contrast compared with other soft tissues in the CT slices (transaxial slices without specifications), even the contrast agent was used. Accordingly, thresholds were automatically chosen by analyzing the histograms in the slices of the whole data set. Take one slice in the thorax for example, its histogram was shown in Fig. 1(a) where A, B and C indicated three intensity values. The first peak on the left, between A and B, represented lung. The second peak between B and C stood for other soft tissues. The left were bone structures whose intensity were all larger than C. C could be obtained by Otsu method [41]. And another application of Otsu method to the image without bone would get the B. However, the image in abdomen would only exhibit one peak as shown in Fig. 1(b). Therefore, the B obtained from the image in abdomen would be higher than that in thorax, which could not represent lung. We defined the minimum value of B got from all the slices as
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Fig. 1. Histogram of the intensity of interested area in the slices (tail, air and holder not included) from the mouse data for the thorax (a) and abdomen (b), respectively. In (a), two distinct peaks represent lung and other soft tissue, respectively while the left for the bone structures. In (b), the single peak represents the soft tissues. A, B and C indicated the value of threshold for lung and bone structures segmentation.
the global threshold of lung to avoid missegmentation in abdomen. The gray levels were all set to 256 when Otsu was adopted. In segmentation of bone structures, a rough result was achieved by applying thresholding method. However, some local small regions, in the stomach, intestine or other contrast-enhanced organs, whose intensities were located in the range of the bone structures, might result in over-segmentation. A sixconnected neighborhood was used to identify the bone structures, which was the largest volume in the rough result. As for lung segmentation, the initial processes were similar with bone segmentation. Then, a sixconnected neighborhood was used to identify the lung volume so as to remove some independent small areas mainly lying in the digestive system and the boundary of the skin. Holes in each slice of the lung, resulting from bronchus and vascular whose intensities were lower or higher than its lobes, were filled. 2.2.2. Segmentation of heart Heart was the most challenging to identify as its intensity is very close to the tissues around the sternum and ribs. The boundary of the heart in each slice was mainly convex rather than concave, and the area of the heart was connected which leaded to only one target contour in each slice. According to the listed features and the small changes of the heart location in the slice sequence, the normalized standard snake deforming algorithm [42,43] was employed here. The snake curve x(s) = [x1 (s), x2 (s)] defined on the interval [0, 1] moves through the image to minimize the energy function shown as 1 2 1 2 (α x (s) + β x (s) ) + κEext (x(s)) ds Esnake = (1) 2 0 The minimization of Esnake for a snake is done by solving the Eq. (2), αx (s) − βx (s) − ∇Eext (x(s)) = 0
(2)
where x (s) and x (s) denote the first and second derivatives of x(s) with respect to s; Eext (x(s)) is the external energy function derived from the characteristics of the image. x (s) and x (s) denote the second and fourth derivatives of x(s) with respect to s, separately; ∇ is the gradient operator. The solution to Eq. (2) can be obtained in an iterative way. The left parameters were summarized as follows:
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α (elasticity) → weighting parameter which controls the snake’s tension; β (rigidity) → weighting parameter that control the snake’s rigidity; κ (external force) → a weight that determines the strength of the external force; γ (viscosity)→ the step size of each iteration, controls the deformation speed of the curve; n → the number of iterations.
Firstly, one initial contour f needs to be set for the whole heart segmentation. The choice of the f was important and was manually defined here. The slice where the f located should own a large area of the heart, which was normally the middle slice of the heart. It would promise the f large enough to contain all the heart in every slice, due to the normalized standard snake deforming algorithm could only shrink from the initial contour. In addition, the f should avoid including any sternums and ribs around heart, which would deteriorate the segmentation results. Full heart segmentation was accomplished as follow. As the heart is located in the thorax, the slices which included lung would contain the heart. Therefore, the slices which would be processed were chosen in advance automatically. Then the initial contour f was manually depicted in the middle slice of the heart. The f was used as the initial contour for every slice of the heart sequence above the middle slice; for the rest slices, the previous contour was taken as initial contour for the current slice. The parameters used in the algorithm were set as: α = 3; β = 0; κ = 0.6; γ = 1; n = 20, which were determined experimentally. 2.2.3. Segmentation of liver and spleen Be different with the bone structures, lung and heart, the liver and spleen have their own characteristics, thus they need other proper segmentation methods. First of all, the slices which contained spleen and liver were automatically acquired with physiological knowledge that they located in the abdomen. Then, an appropriate intensity transformation was made to enhance the contrast as the preprocessing of the slices in which the bone structures, lung and heart were removed. A marker-controlled watershed algorithm with boundary curvature ratio based merging criterion [44] was adopted to the preprocessed slices. The number of regions used in the algorithm was set to be 20 and morphological filter size was 3 × 3. These parameters were defined by repeated experiments to maintain detailed information of liver and spleen with faster merging procedure. A threshold method was then used to identify the spleen from these segmented regions. Considering spleen had the best contrast in every preprocessed slice at this time point, the maximum intensity of each slice was chosen. Then the minimum of them was defined as the threshold S for spleen segmentation. At last, a six-connected neighborhood was used to identify the spleen volume that is the largest to delete the class of the liver lobes and some noise point of which intensities were similar to spleen. As for the liver, S was its upper limit of threshold and the lower limit was estimated based on the CT number of mouse liver. Similar to the processing of spleen, a six-connected neighborhood was also used to identify the liver volume that is the largest to eliminate the interference around the sternum and ribs caused by beam hardening. 2.2.4. Validation of the image segmentation The segmented results were compared to the reference datasets acquired by a senior mouse anatomy expert to evaluate the segmentation results. Tanimoto coefficient (or Jaccard coefficient), one of the most popular criterion to evaluate the accuracy of image segmentation, was adopted here. It was defined as 100 ×
|X ∩ Y | |X ∪ Y |
(3)
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Wherein, X and Y are the segmented dataset and the reference dataset, respectively. The coefficient measured the similarity of X and Y is given in percentage between 0 and 100. The value of 100 represents the perfect segmentation while the value of 0 indicates X and Y do not overlap at all. In combination with Tanimoto coefficient, the relative volume difference (RVD) is also measured for distinguishing over- or under-segmentation. RVD is also given in percentage and is defined as follows: |X| − |Y | 100 × (4) |Y | The positive value of RVD indicates over-segmentation while the negative for under-segmentation. 2.3. FMT guided by segmentation results of micro-CT Segmentation of micro-CT data to identify different organs and structures could be used for FMT reconstruction in two ways as follows: in the forward problem, it can allow assigning more accurate absorption and reduced scattering coefficients in the initial guess based on the segmented regions; in the inverse problem, it provides constraints to ease the ill-posedness [22]. In FMT, the diffusion equation couple, which is approximation of radiation transfer equation, is employed to describe the excitation light and fluorescence propagating in the tissues [45] ∇ · [Dx (r)∇Φx (r)] − μax (r)Φx (r) = −S(r)
(5)
∇ · [Dm (r)∇Φm (r)] − μam (r)Φm (r) = −Φx (r)ημaf (r)
(6)
where, subscripts x and m represent the excitation and emission field, respectively. D(r) = 1/3(μs (r)+ μa (r)) is the diffusion coefficient. μs (r) and μa (r) are the reduced scattering coefficient and absorption coefficient, respectively; Φ(r) denotes the photon density; and ημaf (r) is the fluorescence yield. S(r) represents the isotropic source. Besides, the Robin boundary conditions are applied to solve the diffusion equation. In order to introduce the structural priors, finite element method (FEM) was used to model the Eqs (5) and (6) [46] with MATLAB (Mathwork, U.S.) routine. In the inverse problem, we used Newton-Raphson method to minimize the least-squares function [5]: 2
χ (ημaf ) =
Ns Nd
F 2 (φm ij − φij )
(7)
i=1 j=1
Where Ns and Nd denote the number of the sources and the detectors, respectively. φm ij is the measured F density, while φij is the calculated density with FEM. The fluorescence yield vector is updated with the equation:
−1 T Δημaf = J T J + λI J Δφ (8) F where J is the Jacobian matrix derived with adjoint method [4]. Δφij = φm ij − φij is the error vector between the calculated and measured density. λ is the regularization factor. In our research, Laplace regularization was used to introduce the priors in the inversion [6]. Therefore, the λ could be expressed as: ⎧ node i and node j are in the same region ⎨ −1/N node i and node j are in the different regions λ= 0 (9) ⎩ 1 i=j
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Fig. 2. Contrast-enhanced images from transaxial (a) and (b), coronal (c) and sagittal (d) slices of the same mice at 9 hours post-injection. The heart, lung, liver, spleen and abdominal aorta are well visualized. Reconstruction voxel size was 130 × 130 × 130 µm3 .
where N is the node number in one segmented region of micro-CT images. We used two transaxial segmented images of the mouse, which could be seen in Figs 4(a) and 5(a), to demonstrate the utility of the segmentation. Also two tumors with biomarkers were supposed to be in the lung and spleen with diameter of 1.6 mm, respectively. And the fluorescence yield of the biomarker was appointed to be 0.01 mm−1 . Then 12 sources and 36 detectors were used in the simulation, and the simulated fluorescence measured was added with the 2% Gauss noise. According to the segmented results, the image of Figs 4 (a) and 5(a) were meshed with 3187 nodes and 6203 elements into four regions, respectively. The meshed results and the setting of the sources (circles) and detectors (rectangular) could be seen in Figs 4(b) and 5(b). The segmented tissues, including bone, heart, lung, liver, spleen and the other tissues which were all treated as muscle could be assigned the optical parameters with the results in the previous researches [47]. Due to the excitation and emission wavelength of the biomarker we used is about 750 and 780 nm [35], respectively, the μam and μax both adopted the absorption coefficient parameters listed in the Table 1. Image reconstruction was applied with the approach described before. The reconstruction without priors was also carried out for comparison. In the comparison study, the tissues were regarded as homogeneous with the optical parameters of muscle. 3. Results 3.1. Small animal imaging Transaxial (a) and (b), coronal (c) and sagittal (d) contrast-enhanced images of an anesthetized mouse were shown in Fig. 2. The effective radiation dose was estimated to be about 150 mGy, about 2% of the
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µa (mm−1 ) 0.0267 0.0388 0.0840 0.1598 0.1598 0.0275
µs (mm−1 ) 1.9956 0.2795 2.0056 0.5780 0.5780 0.7756
Fig. 3. 3D visualization of the heart, lung, liver, spleen segmentation in place with the representation of bone structures including ribs, spine, cartilage, sternums and scapula. (Colours are visible in the online version of the article; http://dx.doi.org/ 10.3233/XST-140425)
LD50/30 for small rodent [48]. Usage of blood-pool contrast agent improved the contrast performance of soft tissues significantly. As can be seen in Fig. 2, the heart and abdominal aorta were well visualized and the liver and spleen were also defined. 3.2. Image segmentation and validation The lung, bone structures, liver and spleen were segmented automatically while heart was defined semi-automatically. Take the slices shown in Fig. 2(a) and (b) for example, the contours of liver, spleen and bone structures were depicted in the original slice as indicated in Figs 4(a) and 5(a). Figure 3 gives a 3D visualization of the heart, lung, liver, spleen segmentation in place with the representation of bone structures. Thirty segmented slices were chosen randomly and analyzed compared with the reference images, each of which was repeated five times. The Tanimoto coefficient was measured to be 91.28 ± 5.78 and RVD was 0.27 ± 3.15 which suggested our method results in slight over-segmentation. This is partially due to the blood vessels, including inferior vena cava and abdominal aorta in the liver, were contained in the region of liver, for its intensity is very similar to the liver parenchyma. Similar to the vascular in liver, the bronchus and vascular in the lung were also treated as lung tissue which could be seen in Figs 4(a)
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Table 2 Results of FMT simulation guided by priors segmented from micro-CT Thorax Abdomen
Error Position Concentration Position Concentration
Without priors 1.36 mm 198.0% 0.52 mm 49.8%
With priors 0.14 mm 40.3% 0.10 mm 10.8%
Improvement 89.7% 79.6% 80.8% 78.3%
Fig. 4. Thesegmented and reconstructed results of one thoraxslice. (a) Transaxial image of thorax with the segmented contour. (b) Sources and detectors in FMT and meshed result according to the segmented contour in (a),the red rectangles and the green circles present the sources and the detectors, respectively. (c) Reconstructed fluorophore concentration maps without the guidance of priors in a transaxial image of thorax. (d) Reconstructed fluorophore concentration maps when the priors were utilized in a transaxial image of thorax. White circles in (c) and (d) indicate the actual shape and position of the fluorophore. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/XST-140425)
and 5(a), respectively. We have not removed the blood vessels or bronchus for the consideration that the segmented data are used for guiding and constraining the FMT whose resolution is far lower than micro-CT. 3.3. FMT guided by segmentation results of micro-CT The reconstructed images of the fluorophore without and with priors could be found in (c) and (d) of Figs 4 and 5, respectively. The position and the concentration of the reconstructed fluorophore were calculated to investigate the improvement quantitatively. The position of the fluorophore was calculated with the mass center of the image. And the maximum of the reconstruction image was regarded as the concentration. In the image of thorax shown in Fig. 4(c) and (d), the errors of the position and concentration were 1.36 mm and 198.0% without priors while they reduced to 0.14 mm and 40.3% after the priors were introduced, thus gave declines by 89.7% and 79.6%, separately. Whereas in the image of
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Fig. 5. The segmented and reconstructed results of one abdomen slice. (a) Transaxial image of abdomen with the segmented contour. (b) Source and detectors in FMT and meshed result according to the segmented contour in (a), the red rectangles and the green circles present the sources and the detectors, respectively. (c) Reconstructed fluorophore concentration maps without the guidance of priors in a transaxial image of abdomen. (d) Reconstructed fluorophore concentration maps when the priors were utilized in a transaxial image of abdomen. White circles in (c) and (d) indicate the actual shape and position of the fluorophore. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/XST-140425)
abdomen in Fig. 5(c) and (d), the error of the position and concentration respectively reduced from 0.52 mm and 49.8% to 0.10 mm and 10.8%, which could also be expressed as the improvement of 80.8% and 78.3%. Results of the two cases, which also could be seen in Table 2, indicated that the segmented structural priors from micro-CT have made FMT reconstruction more accurate both in localization and quantification. 4. Discussion In this paper, we propose a framework to extract structural priors from the rotating object micro-CT for improving FMT reconstruction. With the assistance of blood-pool contrast agent, micro-CT could provide relatively clear boundaries of mouse organs. Some image segmentation approaches were employed to get the tissues separately. The FMT simulation results exhibited the improvement of reconstruction image quality after the application of segmented priors. The parameters used in the segmentation algorithm are critical for the quality of segmentation, therefore they need be chosen for optimization. In heart segmentation, the initial contour f of the heart should be depicted carefully, because the normalized standard snake deforming algorithm is normally sensitive to the initial conditions. In addition, due to a little different contrast enhancement results of heart, liver and spleen in different mice under the same experimental conditions, the parameters described in the segmentation maybe need slight adjustment.
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The Tanimoto coefficient was measured to be 91.28 ± 5.78 which indicated the segmented dataset overlap well with the reference dataset. And the RVD of 0.27 ± 3.15 showed there exited a little oversegmentation as expected, because some great vessels were not eliminated, for example inferior vena cava was treated as liver parenchyma. We have not segmented the vessels for the reasons as follows. The spatial resolution of FMT is usually no better than 1 mm, much lower than the spatial resolution of micro-CT which is tens of microns. Therefore, finer segmentation may leads to subtle improvement of the reconstruction results. Furthermore, the segmented areas of vessels are so small, which could make the meshing with FEM more complicated and reconstruction much time-consuming. Although micro-CT could not provide the optical properties of organs directly, the optical parameters could be estimated by adopting the previous results. And the mismatch of the optical parameters in forward problem still could improve the performance of the FMT [12]. In our simulation study, the disturbance of the optical properties of the tissue induced by the contrast agent was not involved. However, it should be taken into account when small animal imaging is performed. We measured the optical properties of the contrast agent with a spectrophotomete (Lambda 950, PerkinElmer, U.S.). The absorption coefficient is 0.36 mm−1 , and the reduced scattering coefficient is 8.43 mm−1 , at the wavelength of 780 nm. Consequently, the optical properties of the organs which are enhanced with the contrast agent may be changed. Nevertheless, because the micro-CT could measure the distribution of the contrast agent in the mice quantitatively, it would be easy to evaluate the changes of the optical properties of the organs. Taking the spleen for example, the iodine concentration reaches up to5.77 mg/ml and the corresponding absorption coefficient and reduced scattering coefficient is 0.0438 mm−1 and 0.973 mm−1 , respectively. The results have demonstrated the utility of our scheme of extracting structural priors from micro-CT. However, the scheme needs the blood-pool contrast agent and this makes the experiments inconvenient. As a matter of fact, in a longitudinal study, we only need to scan the mouse with the contrast agent once and obtain the segmented anatomic dataset using our proposed scheme. Then the follow-up experiments without contrast agent may be well segmented with relatively simple image registration method based on the acquired dataset rather than the general atlas. The reasons are as follows: there are no individual differences in image registration for it is the same mouse in all scans; the posture is similar, so the variations of organs are small both in shape and position. The segmentation of the tissues of the mouse in a longitudinal study will be achieved in our future studies. Acknowledgment This work was supported by the National Key Technology R&D Program of China (Grant No. 2012BAI23B02) and Specific International Scientific Cooperation (Grant No. 2010DFR30820). References [1] [2] [3] [4] [5]
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A method of extracting structural priors from images of micro-CT for fluorescence molecular tomography reconstruction Yuanzheng Menga,b , Xiaoquan Yanga,b,∗ , Yong Denga,b , Xuanxuan Zhanga,b and Hui Gonga,b a Britton
Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, Hubei, China b MoE Key Laboratory of Biomedical Photonics, Department of Biomedical Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, China Received 16 January 2013 Revised 8 February 2014 Accepted 16 February 2014 Abstract. The dual-modality systems combined fluorescence molecular tomography (FMT) and micro-computed tomography (micro-CT) can provide molecular and anatomical information of small animals simultaneously. Except for anatomic localization, micro-CT should also offer boundary of different organs as reconstruction priors for FMT, which is more challenging than acquisition of structural information. In this paper, we propose a framework to extract structural priors of a living mouse with micro-CT. The iodinated lipid emulsion contrast agent was adopted to enhance the contrast of the soft tissues of the mouse. Then organs in thorax and abdomen were segmented with different approaches depending on the characteristics of the organs. Bone, lung, heart, liver, spleen, and muscles were separately segmented. And the results were compared with that manually segmented. The Tanimoto coefficient and the relative volume difference of segmented slices were measured to be 91.28 ± 5.78 and 0.27 ± 3.15, respectively. In our simulation study of FMT reconstruction, the errors of measured position and concentration of the fluorophore with priors declined by 89.7% and 79.6% in thorax, as well as 80.8% and 78.3% in abdomen, respectively, compared with the results without priors. The proposed scheme will make FMT reconstruction much more reliable and practical in small animal study. Keywords: Image segmentation, micro-computed tomography, fluorescence molecular tomography
1. Introduction Fluorescence molecular tomography (FMT), one of the noninvasive molecular imaging modalities, potentially played an important role in fundamental scientific researches and preclinical trials [1–3]. It could quantitatively acquire the bio-distribution of the fluorophore in the living small animals. Compared to the traditional molecular imaging techniques, positron emission tomography (PET), single photon emission computed tomography (SPECT), and magnetic resonance imaging (MRI), it could perform ∗
Corresponding author: Xiaoquan Yang, Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics-Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, Hubei, China. Tel.: +86 27 87792033; Fax: +86 27 87792034; E-mail: [email protected]. c 2014 – IOS Press and the authors. All rights reserved 0895-3996/14/$27.50
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multichannel imaging with non-ionizing radiation at a relatively low cost [2]. However, imaging quality of FMT is limited due to the fact that the inverse problem is ill-posed and sometimes underdetermined [4]. This makes the results of the FMT unreliable, and consequently degrades the utility of this emerging technique. Structural priors have shown substantial effect in the improvement of the performance of diffuse optical tomography [5–11]. Recently, it was also introduced to elevate resolution and quantitative accuracy of FMT [11–14]. Therefore, other imaging modalities, including micro-computed tomography (micro-CT) [15–17], MRI [18,19], photoacoustic tomography (PAT) [20], and integrated SPECT-CT system [21], have been employed to provide priors for FMT reconstruction. Compared to other complementary imaging modalities, micro-CT can provide high resolution anatomical images of small animals in-vivo with fast scanning, and directly integrate with full capable FMT system [22]. For combining with FMT, micro-CT is amenable to provide high resolution images of anatomy, boundaries of different organs and deliver low radiation dose to small animals. Unfortunately, the image quality of micro-CT is limited by the delivered radiation dose to small animals [23–26]. Therefore, it is quite a challenge to get the clear boundaries of the soft tissues in micro-CT images in small animal study in-vivo. Manual segmentation by experts can provide accurate results. However, the workload would be tremendous, especially in a longitudinal study. Several automatic segmentation methods have been proposed in the past years for clinical CT images [27–30]. Nevertheless, these approaches are not appropriate for the mouse imaging with micro-CT, due to the noise levels and soft-tissue contrasts of the images from micro-CT are quite different with these from clinical CT. Recently, several automatic segmentation methods have been developed for mouse images from rotating gantry micro-CT. X. Artaechevarria et al. proposed an effective, fast segmentation and reconstruction algorithm, which is just aimed at the murine airway [31]. Marcus Freyer et al. suggested a framework that segmented bones, lungs and heart [32]. It worked fast and achieved fine segmentation of bones using thresholds. Regarding lung and heart, the seed growing algorithm and a static undeformable model were used respectively. However, the proposed scheme only worked in the thorax. Due to the low contrast of abdominal tissue, these methods didn’t involve the segmentation of liver, spleen and so on. Martin Baiker et al. introduced an automatic segmentation approach using MRI atlas-based registration for whole-body mice images without contrast agents [33]. This method can be used to segment most of the soft tissues even for larger variations in posture compared to the previous studies. However, the segmentation accuracy of some soft tissues is still low, as the posture and shape vary significantly between each animal and the atlas. And the image registration is rather complex. Given the fact that the deformation of the animal in a rotating object micro-CT is obviously larger than that in a rotating gantry micro-CT [34,35], the aforementioned approaches (mainly for atlas-based registration which can segment most of the tissues) may yield remarkable errors for the soft tissues segmentation of the animal in a rotating object micro-CT system. In our previous work, we have constructed a combined FMT/micro-CT system [36] in which the object was rotated and the performance of the micro-CT system was evaluated [37]. However, the coupling of the two modalities only performed in space, i.e. the structural information did not be extracted and used in reconstruction of the FMT. It made the FMT unqualified in quantitative imaging. To address this issue, we proposed an image segmentation scheme to get the boundaries of the tissues enhanced by a blood pool contrast agent. The use of a blood pool contrast agent is to enhance the contrast between different tissues, especial abdominal tissues, so that we can segment them more accurately and simply. The scheme was developed as follows: threshold method for automatic segmentation of bone structures and lung, standard snake deforming algorithm for full heart segmentation, as well as watershed algorithm used to segment liver and spleen automatically. The quality of segmented dataset was further evaluated using Tanimoto coefficient and the relative volume difference. Finally, the segmented dataset was used as priors for FMT simulation to demonstrate the utility.
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2. Methods The micro-CT scanner consists of a micro-focus x-ray tube (UltraBright, Oxford Instruments, U.S.), a flat-panel detector based on amorphous silicon (PaxScan2520V, Varian Medical Systems, U.S.), and a rotation stage, controlled by a workstation (HW8200, Hewlett-Packard, U.S.). Source-to-detector distance and source-to-object distance were measured to be about 636.0 mm and 161.0 mm, respectively, and given a magnification factor of 3.95 consequentially. The system possesses a field of view of 62.5 mm in diameter and 50.0 mm in length. The spatial resolution of the system was measured to be 13.0 lp/mm (10% modulation transfer function value). Feldkamp’s filtered back-projection algorithm accelerated by GPU [38,39] has been used to reconstruct the acquired dataset. All the measurements were performed with the x-ray source operating with tube voltage of 55 kVp and a 2.5 mm-thick aluminum filter. The radiation dose was measured in the air at the axis-of-rotation with the ion chamber dosimeter (Farmer 2570, NE, U.K.). It was about 0.34 mGy per frame calculated with exposure-to-air kerma conversion factor of 8.767 mGy/R. 2.1. Small animal imaging An adult male Kunming mouse weighting about 44.5 g was used for demonstrating the proposed scheme. A dose of 1 g/kg urethane and 0.2 g/kg a-chloralose was administered intraperitoneally to anesthetize the mouse. Then a single tail-vein injection was performed to introduce an iodinated lipid emulsion blood-pool contrast agent (50 mg I/ml, ART, Quebec, Canada) with a dose of 0.1 ml/10 g. Nine hours after injection, the mouse was then fixed in a homemade PMMA chamber for scanning. The time point was chosen considering the compromised enhancement of different soft tissues [40]. All of the experiments were carried out in accordance with the Huazhong University of Science and Technology guidelines regarding the use and care of animals. 2.2. Image segmentation and validation The reconstructed data set was pretreated to remove the air, animal holder and the tail of the mouse. The holder could be subtracted, because its position is predetermined. Then, the canny edge detection was applied to each slice to obtain edge contours. An eight-connected neighborhood was used to identify the body contour in each slice, which was the largest area. Inside regions of the body contours were filled and stored as template to acquire the volume only including the body of the mouse. 2.2.1. Segmentation of bone and lung Obviously, bone structures and lung still perform higher contrast compared with other soft tissues in the CT slices (transaxial slices without specifications), even the contrast agent was used. Accordingly, thresholds were automatically chosen by analyzing the histograms in the slices of the whole data set. Take one slice in the thorax for example, its histogram was shown in Fig. 1(a) where A, B and C indicated three intensity values. The first peak on the left, between A and B, represented lung. The second peak between B and C stood for other soft tissues. The left were bone structures whose intensity were all larger than C. C could be obtained by Otsu method [41]. And another application of Otsu method to the image without bone would get the B. However, the image in abdomen would only exhibit one peak as shown in Fig. 1(b). Therefore, the B obtained from the image in abdomen would be higher than that in thorax, which could not represent lung. We defined the minimum value of B got from all the slices as
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Fig. 1. Histogram of the intensity of interested area in the slices (tail, air and holder not included) from the mouse data for the thorax (a) and abdomen (b), respectively. In (a), two distinct peaks represent lung and other soft tissue, respectively while the left for the bone structures. In (b), the single peak represents the soft tissues. A, B and C indicated the value of threshold for lung and bone structures segmentation.
the global threshold of lung to avoid missegmentation in abdomen. The gray levels were all set to 256 when Otsu was adopted. In segmentation of bone structures, a rough result was achieved by applying thresholding method. However, some local small regions, in the stomach, intestine or other contrast-enhanced organs, whose intensities were located in the range of the bone structures, might result in over-segmentation. A sixconnected neighborhood was used to identify the bone structures, which was the largest volume in the rough result. As for lung segmentation, the initial processes were similar with bone segmentation. Then, a sixconnected neighborhood was used to identify the lung volume so as to remove some independent small areas mainly lying in the digestive system and the boundary of the skin. Holes in each slice of the lung, resulting from bronchus and vascular whose intensities were lower or higher than its lobes, were filled. 2.2.2. Segmentation of heart Heart was the most challenging to identify as its intensity is very close to the tissues around the sternum and ribs. The boundary of the heart in each slice was mainly convex rather than concave, and the area of the heart was connected which leaded to only one target contour in each slice. According to the listed features and the small changes of the heart location in the slice sequence, the normalized standard snake deforming algorithm [42,43] was employed here. The snake curve x(s) = [x1 (s), x2 (s)] defined on the interval [0, 1] moves through the image to minimize the energy function shown as 1 2 1 2 (α x (s) + β x (s) ) + κEext (x(s)) ds Esnake = (1) 2 0 The minimization of Esnake for a snake is done by solving the Eq. (2), αx (s) − βx (s) − ∇Eext (x(s)) = 0
(2)
where x (s) and x (s) denote the first and second derivatives of x(s) with respect to s; Eext (x(s)) is the external energy function derived from the characteristics of the image. x (s) and x (s) denote the second and fourth derivatives of x(s) with respect to s, separately; ∇ is the gradient operator. The solution to Eq. (2) can be obtained in an iterative way. The left parameters were summarized as follows:
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α (elasticity) → weighting parameter which controls the snake’s tension; β (rigidity) → weighting parameter that control the snake’s rigidity; κ (external force) → a weight that determines the strength of the external force; γ (viscosity)→ the step size of each iteration, controls the deformation speed of the curve; n → the number of iterations.
Firstly, one initial contour f needs to be set for the whole heart segmentation. The choice of the f was important and was manually defined here. The slice where the f located should own a large area of the heart, which was normally the middle slice of the heart. It would promise the f large enough to contain all the heart in every slice, due to the normalized standard snake deforming algorithm could only shrink from the initial contour. In addition, the f should avoid including any sternums and ribs around heart, which would deteriorate the segmentation results. Full heart segmentation was accomplished as follow. As the heart is located in the thorax, the slices which included lung would contain the heart. Therefore, the slices which would be processed were chosen in advance automatically. Then the initial contour f was manually depicted in the middle slice of the heart. The f was used as the initial contour for every slice of the heart sequence above the middle slice; for the rest slices, the previous contour was taken as initial contour for the current slice. The parameters used in the algorithm were set as: α = 3; β = 0; κ = 0.6; γ = 1; n = 20, which were determined experimentally. 2.2.3. Segmentation of liver and spleen Be different with the bone structures, lung and heart, the liver and spleen have their own characteristics, thus they need other proper segmentation methods. First of all, the slices which contained spleen and liver were automatically acquired with physiological knowledge that they located in the abdomen. Then, an appropriate intensity transformation was made to enhance the contrast as the preprocessing of the slices in which the bone structures, lung and heart were removed. A marker-controlled watershed algorithm with boundary curvature ratio based merging criterion [44] was adopted to the preprocessed slices. The number of regions used in the algorithm was set to be 20 and morphological filter size was 3 × 3. These parameters were defined by repeated experiments to maintain detailed information of liver and spleen with faster merging procedure. A threshold method was then used to identify the spleen from these segmented regions. Considering spleen had the best contrast in every preprocessed slice at this time point, the maximum intensity of each slice was chosen. Then the minimum of them was defined as the threshold S for spleen segmentation. At last, a six-connected neighborhood was used to identify the spleen volume that is the largest to delete the class of the liver lobes and some noise point of which intensities were similar to spleen. As for the liver, S was its upper limit of threshold and the lower limit was estimated based on the CT number of mouse liver. Similar to the processing of spleen, a six-connected neighborhood was also used to identify the liver volume that is the largest to eliminate the interference around the sternum and ribs caused by beam hardening. 2.2.4. Validation of the image segmentation The segmented results were compared to the reference datasets acquired by a senior mouse anatomy expert to evaluate the segmentation results. Tanimoto coefficient (or Jaccard coefficient), one of the most popular criterion to evaluate the accuracy of image segmentation, was adopted here. It was defined as 100 ×
|X ∩ Y | |X ∪ Y |
(3)
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Wherein, X and Y are the segmented dataset and the reference dataset, respectively. The coefficient measured the similarity of X and Y is given in percentage between 0 and 100. The value of 100 represents the perfect segmentation while the value of 0 indicates X and Y do not overlap at all. In combination with Tanimoto coefficient, the relative volume difference (RVD) is also measured for distinguishing over- or under-segmentation. RVD is also given in percentage and is defined as follows: |X| − |Y | 100 × (4) |Y | The positive value of RVD indicates over-segmentation while the negative for under-segmentation. 2.3. FMT guided by segmentation results of micro-CT Segmentation of micro-CT data to identify different organs and structures could be used for FMT reconstruction in two ways as follows: in the forward problem, it can allow assigning more accurate absorption and reduced scattering coefficients in the initial guess based on the segmented regions; in the inverse problem, it provides constraints to ease the ill-posedness [22]. In FMT, the diffusion equation couple, which is approximation of radiation transfer equation, is employed to describe the excitation light and fluorescence propagating in the tissues [45] ∇ · [Dx (r)∇Φx (r)] − μax (r)Φx (r) = −S(r)
(5)
∇ · [Dm (r)∇Φm (r)] − μam (r)Φm (r) = −Φx (r)ημaf (r)
(6)
where, subscripts x and m represent the excitation and emission field, respectively. D(r) = 1/3(μs (r)+ μa (r)) is the diffusion coefficient. μs (r) and μa (r) are the reduced scattering coefficient and absorption coefficient, respectively; Φ(r) denotes the photon density; and ημaf (r) is the fluorescence yield. S(r) represents the isotropic source. Besides, the Robin boundary conditions are applied to solve the diffusion equation. In order to introduce the structural priors, finite element method (FEM) was used to model the Eqs (5) and (6) [46] with MATLAB (Mathwork, U.S.) routine. In the inverse problem, we used Newton-Raphson method to minimize the least-squares function [5]: 2
χ (ημaf ) =
Ns Nd
F 2 (φm ij − φij )
(7)
i=1 j=1
Where Ns and Nd denote the number of the sources and the detectors, respectively. φm ij is the measured F density, while φij is the calculated density with FEM. The fluorescence yield vector is updated with the equation:
−1 T Δημaf = J T J + λI J Δφ (8) F where J is the Jacobian matrix derived with adjoint method [4]. Δφij = φm ij − φij is the error vector between the calculated and measured density. λ is the regularization factor. In our research, Laplace regularization was used to introduce the priors in the inversion [6]. Therefore, the λ could be expressed as: ⎧ node i and node j are in the same region ⎨ −1/N node i and node j are in the different regions λ= 0 (9) ⎩ 1 i=j
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Fig. 2. Contrast-enhanced images from transaxial (a) and (b), coronal (c) and sagittal (d) slices of the same mice at 9 hours post-injection. The heart, lung, liver, spleen and abdominal aorta are well visualized. Reconstruction voxel size was 130 × 130 × 130 µm3 .
where N is the node number in one segmented region of micro-CT images. We used two transaxial segmented images of the mouse, which could be seen in Figs 4(a) and 5(a), to demonstrate the utility of the segmentation. Also two tumors with biomarkers were supposed to be in the lung and spleen with diameter of 1.6 mm, respectively. And the fluorescence yield of the biomarker was appointed to be 0.01 mm−1 . Then 12 sources and 36 detectors were used in the simulation, and the simulated fluorescence measured was added with the 2% Gauss noise. According to the segmented results, the image of Figs 4 (a) and 5(a) were meshed with 3187 nodes and 6203 elements into four regions, respectively. The meshed results and the setting of the sources (circles) and detectors (rectangular) could be seen in Figs 4(b) and 5(b). The segmented tissues, including bone, heart, lung, liver, spleen and the other tissues which were all treated as muscle could be assigned the optical parameters with the results in the previous researches [47]. Due to the excitation and emission wavelength of the biomarker we used is about 750 and 780 nm [35], respectively, the μam and μax both adopted the absorption coefficient parameters listed in the Table 1. Image reconstruction was applied with the approach described before. The reconstruction without priors was also carried out for comparison. In the comparison study, the tissues were regarded as homogeneous with the optical parameters of muscle. 3. Results 3.1. Small animal imaging Transaxial (a) and (b), coronal (c) and sagittal (d) contrast-enhanced images of an anesthetized mouse were shown in Fig. 2. The effective radiation dose was estimated to be about 150 mGy, about 2% of the
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µa (mm−1 ) 0.0267 0.0388 0.0840 0.1598 0.1598 0.0275
µs (mm−1 ) 1.9956 0.2795 2.0056 0.5780 0.5780 0.7756
Fig. 3. 3D visualization of the heart, lung, liver, spleen segmentation in place with the representation of bone structures including ribs, spine, cartilage, sternums and scapula. (Colours are visible in the online version of the article; http://dx.doi.org/ 10.3233/XST-140425)
LD50/30 for small rodent [48]. Usage of blood-pool contrast agent improved the contrast performance of soft tissues significantly. As can be seen in Fig. 2, the heart and abdominal aorta were well visualized and the liver and spleen were also defined. 3.2. Image segmentation and validation The lung, bone structures, liver and spleen were segmented automatically while heart was defined semi-automatically. Take the slices shown in Fig. 2(a) and (b) for example, the contours of liver, spleen and bone structures were depicted in the original slice as indicated in Figs 4(a) and 5(a). Figure 3 gives a 3D visualization of the heart, lung, liver, spleen segmentation in place with the representation of bone structures. Thirty segmented slices were chosen randomly and analyzed compared with the reference images, each of which was repeated five times. The Tanimoto coefficient was measured to be 91.28 ± 5.78 and RVD was 0.27 ± 3.15 which suggested our method results in slight over-segmentation. This is partially due to the blood vessels, including inferior vena cava and abdominal aorta in the liver, were contained in the region of liver, for its intensity is very similar to the liver parenchyma. Similar to the vascular in liver, the bronchus and vascular in the lung were also treated as lung tissue which could be seen in Figs 4(a)
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Table 2 Results of FMT simulation guided by priors segmented from micro-CT Thorax Abdomen
Error Position Concentration Position Concentration
Without priors 1.36 mm 198.0% 0.52 mm 49.8%
With priors 0.14 mm 40.3% 0.10 mm 10.8%
Improvement 89.7% 79.6% 80.8% 78.3%
Fig. 4. Thesegmented and reconstructed results of one thoraxslice. (a) Transaxial image of thorax with the segmented contour. (b) Sources and detectors in FMT and meshed result according to the segmented contour in (a),the red rectangles and the green circles present the sources and the detectors, respectively. (c) Reconstructed fluorophore concentration maps without the guidance of priors in a transaxial image of thorax. (d) Reconstructed fluorophore concentration maps when the priors were utilized in a transaxial image of thorax. White circles in (c) and (d) indicate the actual shape and position of the fluorophore. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/XST-140425)
and 5(a), respectively. We have not removed the blood vessels or bronchus for the consideration that the segmented data are used for guiding and constraining the FMT whose resolution is far lower than micro-CT. 3.3. FMT guided by segmentation results of micro-CT The reconstructed images of the fluorophore without and with priors could be found in (c) and (d) of Figs 4 and 5, respectively. The position and the concentration of the reconstructed fluorophore were calculated to investigate the improvement quantitatively. The position of the fluorophore was calculated with the mass center of the image. And the maximum of the reconstruction image was regarded as the concentration. In the image of thorax shown in Fig. 4(c) and (d), the errors of the position and concentration were 1.36 mm and 198.0% without priors while they reduced to 0.14 mm and 40.3% after the priors were introduced, thus gave declines by 89.7% and 79.6%, separately. Whereas in the image of
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Fig. 5. The segmented and reconstructed results of one abdomen slice. (a) Transaxial image of abdomen with the segmented contour. (b) Source and detectors in FMT and meshed result according to the segmented contour in (a), the red rectangles and the green circles present the sources and the detectors, respectively. (c) Reconstructed fluorophore concentration maps without the guidance of priors in a transaxial image of abdomen. (d) Reconstructed fluorophore concentration maps when the priors were utilized in a transaxial image of abdomen. White circles in (c) and (d) indicate the actual shape and position of the fluorophore. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/XST-140425)
abdomen in Fig. 5(c) and (d), the error of the position and concentration respectively reduced from 0.52 mm and 49.8% to 0.10 mm and 10.8%, which could also be expressed as the improvement of 80.8% and 78.3%. Results of the two cases, which also could be seen in Table 2, indicated that the segmented structural priors from micro-CT have made FMT reconstruction more accurate both in localization and quantification. 4. Discussion In this paper, we propose a framework to extract structural priors from the rotating object micro-CT for improving FMT reconstruction. With the assistance of blood-pool contrast agent, micro-CT could provide relatively clear boundaries of mouse organs. Some image segmentation approaches were employed to get the tissues separately. The FMT simulation results exhibited the improvement of reconstruction image quality after the application of segmented priors. The parameters used in the segmentation algorithm are critical for the quality of segmentation, therefore they need be chosen for optimization. In heart segmentation, the initial contour f of the heart should be depicted carefully, because the normalized standard snake deforming algorithm is normally sensitive to the initial conditions. In addition, due to a little different contrast enhancement results of heart, liver and spleen in different mice under the same experimental conditions, the parameters described in the segmentation maybe need slight adjustment.
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The Tanimoto coefficient was measured to be 91.28 ± 5.78 which indicated the segmented dataset overlap well with the reference dataset. And the RVD of 0.27 ± 3.15 showed there exited a little oversegmentation as expected, because some great vessels were not eliminated, for example inferior vena cava was treated as liver parenchyma. We have not segmented the vessels for the reasons as follows. The spatial resolution of FMT is usually no better than 1 mm, much lower than the spatial resolution of micro-CT which is tens of microns. Therefore, finer segmentation may leads to subtle improvement of the reconstruction results. Furthermore, the segmented areas of vessels are so small, which could make the meshing with FEM more complicated and reconstruction much time-consuming. Although micro-CT could not provide the optical properties of organs directly, the optical parameters could be estimated by adopting the previous results. And the mismatch of the optical parameters in forward problem still could improve the performance of the FMT [12]. In our simulation study, the disturbance of the optical properties of the tissue induced by the contrast agent was not involved. However, it should be taken into account when small animal imaging is performed. We measured the optical properties of the contrast agent with a spectrophotomete (Lambda 950, PerkinElmer, U.S.). The absorption coefficient is 0.36 mm−1 , and the reduced scattering coefficient is 8.43 mm−1 , at the wavelength of 780 nm. Consequently, the optical properties of the organs which are enhanced with the contrast agent may be changed. Nevertheless, because the micro-CT could measure the distribution of the contrast agent in the mice quantitatively, it would be easy to evaluate the changes of the optical properties of the organs. Taking the spleen for example, the iodine concentration reaches up to5.77 mg/ml and the corresponding absorption coefficient and reduced scattering coefficient is 0.0438 mm−1 and 0.973 mm−1 , respectively. The results have demonstrated the utility of our scheme of extracting structural priors from micro-CT. However, the scheme needs the blood-pool contrast agent and this makes the experiments inconvenient. As a matter of fact, in a longitudinal study, we only need to scan the mouse with the contrast agent once and obtain the segmented anatomic dataset using our proposed scheme. Then the follow-up experiments without contrast agent may be well segmented with relatively simple image registration method based on the acquired dataset rather than the general atlas. The reasons are as follows: there are no individual differences in image registration for it is the same mouse in all scans; the posture is similar, so the variations of organs are small both in shape and position. The segmentation of the tissues of the mouse in a longitudinal study will be achieved in our future studies. Acknowledgment This work was supported by the National Key Technology R&D Program of China (Grant No. 2012BAI23B02) and Specific International Scientific Cooperation (Grant No. 2010DFR30820). References [1] [2] [3] [4] [5]
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