MARS: a mouse atlas registration system based on a planar x-ray projector and an optical camera

As shown in figure 1(a), the MARS is composed of a top-view planar x-ray projector and a side-view optical camera. Unlike tomographic CT systems, the MARS is stationary. Only one single x-ray projection and one optical photo need to be taken for the subject; therefore the acquisition time is only a few seconds. Figure 1(b) demonstrates the hardware components of the MARS. The whole system is enclosed in a steel box of 305 × 254 × 125 mm³ for x-ray shielding. A miniature x-ray tube (MAGNUM® 40 kV x-ray source, Moxtek Inc., UT, USA) is placed 238 mm above the center of the mouse field of view (FOV), and the x-ray detector (RedEye™ 200 Remote Sensor, Rad-icon Imaging Corp. CA, USA) with 98 × 96 mm² imaging area is placed 45 mm under the FOV center. The distances of the x-ray source and detector are designed to capture the main body (from nose to the root of the tail) of a medium sized (∼25 g) laboratory mouse. To eliminate the very low-energy x-rays which mostly contribute to soft tissue dose, a 1 mm thick aluminum filter is placed on top of the collimator. The x-ray tube configuration is set at 40 kVp, 100 µA and 3 s exposures. The voltage and current used here are much lower than those used for a commercial micro-CT system, and the single-view x-ray projection delivers significantly less radiation than a fully tomographic CT (e.g. about 1/450 of the dose delivered by a CT scan of 70 kVp, 500 µA for 10 min).

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For the optical part, a webcam (Firefly® MV, Point Grey Research Inc., BC, Canada) with a 5 mm focal length lens is placed 185 mm laterally to the right side of the FOV center. The camera exposure time is set to 200 ms and LED backlights with a thin piece of light diffuser are positioned on the left side of the mouse. The backlight highlights the body silhouette during the photo acquisition.

Figure 1(c) shows the MARS box in operation. A multi-modality animal imaging chamber similar to that used in previous work (Suckow et al 2009) with anesthesia and heating support is used for the image acquisition. The chamber also maintains the subjects in a regularized posture, i.e. with stretched limbs and prone position. For imaging, the mouse chamber first enters the MARS box, the x-ray projection is acquired for 3 s, followed by a snapshot from the optical camera. Figure 1(c) also shows that the MARS box is combined with the PETbox4 system (Gu et al 2011), a bench-top preclinical PET scanner developed by our group. For combined imaging, the MARS box is simply positioned in front of the PETbox4, with collinear openings that allow the imaging chamber with the mouse subject to move freely between the two systems. Combined PETbox4/MARS images are shown in the results.

Both the x-ray projector and optical camera were calibrated as pinhole systems. The geometric parameters of the pinhole systems were calibrated with a planar checkerboard (figure 2(a)) visible to both the x-ray and the optical camera. The checkerboard was designed as a 7 × 7 square pattern and the dimension of each square was 6 × 6 mm². The PCB production technique was used to etch the checkerboard pattern of copper onto the substrate. The geometric parameters to be calibrated included intrinsic and extrinsic parameters. The intrinsic parameters included the focal length, principal point, image skew and distortions of each pinhole system. The extrinsic parameters included the translation and rotation of each pinhole system with respect to the world coordinate system. To calibrate the intrinsic parameters, multiple (10–20) random positions and orientations of the checkerboard were captured separately by each system. Figure 2(b) demonstrates a result of the intrinsic parameter calibration, where the barrel distortion of the side-view photo is eliminated after taking into account the intrinsic distortion (for the top-view x-ray there is no appreciable image distortion). To calibrate the extrinsic parameters, the checkerboard was positioned at an oblique angle so that both systems could image it simultaneously. The common coordinate space of the two systems was determined based on this oblique checkerboard position (figure 2(c)), with the origin defined at the upper-left corner of the checkerboard (facing the operator), the x- and y-axes defined parallel with the checkerboard edges, and the z-axis defined perpendicular to the checkerboard plane. The Camera Calibration Toolbox for Matlab® was used to calculate the intrinsic and extrinsic parameters based on the multiple x-ray and optical checkerboard images. The toolbox requires the checkerboard size and the square number as inputs, while no information on checkerboard positions was required. The user needs to manually specify the four corners of the checkerboard in each image, then the method will automatically search for the corners of each individual square and compute the optimal intrinsic and extrinsic parameters that match the square corners. For details of the calibration method used by the toolbox, we refer the readers to Zhang (1999) and Heikkila and Silven (1997). To define the common coordinate space (i.e. the world coordinate space), the angle and position of the checkerboard do not need to be unique, because the world coordinate system is only a connection between the atlas coordinates and the projection coordinates. Moreover, since the MARS is designed to be combined with molecular imaging systems, it is necessary to co-register the MARS world coordinate system with the molecular imaging system. For the specific application of this paper, we co-register the MARS with the PETbox4 scanner using four ²²Na point sources that were fixed in the imaging chamber. The point sources were imaged with both MARS and PETbox4, and the source positions in both MARS and CT images were manually specified. The 3D coordinates of the point sources in MARS space were calculated by back-projecting the 2D coordinates into 3D, and then the 3D rigid transformation (including translation and rotation) between the two point sets (MARS and CT) was calculated.

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The x-ray image (figure 3(a)) and the optical photo (figure 3(d)) are preprocessed before atlas registration. The perspective and barrel distortions of the acquired images are corrected using the geometric calibration parameters. Moreover, since the mouse is imaged along with the chamber, we need to eliminate the chamber from both the x-ray and optical images. An additional x-ray projection of the empty chamber (figure 3(b)) is acquired and eliminated from the subject x-ray image. Let I_mc be the x-ray image of the mouse and chamber, I_c be the x-ray image of the empty chamber and I_d be the dark current image of the x-ray detector. The chamber-eliminated image of the mouse I_m (figure 3(c)) can be calculated as I_m = (I_mc − I_d)/(I_c − I_d). In the side-view backlit optical photo, lower parts of the mouse body are blocked by the chamber, leaving only the back region and upper head visible to the camera. Therefore, a rectangular region (figure 3(d)) enclosing the visible body part is used for atlas registration. An automatic thresholding method (Bersen 1986) is applied to the selected region to extract the body silhouette (figure 3(e)). The acquisition of the empty chamber x-ray and the manual determination of the optical rectangular region must be performed only once for each MARS gantry, since the position of the chamber is always fixed to the gantry, similar to previous work by our group (Chow et al 2006).

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The limited mouse area visible in the side-view photo reduces the completeness of the acquired data, making direct application of the atlas registration method described in our previous simulation study (Wang et al 2010) unfeasible. To solve this problem, we constructed a statistical mouse atlas based on multiple training subjects, and fit the atlas to the incomplete data using the techniques of SSM and CGM. Since this method is similar to the approach that we used for CT-based atlas registration, here we only briefly introduce this method and refer the readers to Wang et al (2012) for more details.

The statistical mouse atlas was trained with 83 organ-labeled micro-CT images selected from the database at the Crump Institute for molecular imaging, UCLA (Stout et al 2005). The training subjects include three most frequently used strains (Nude, BC57 and severe-combined immunodeficient (SCID)), with body weights ranging from 15 to 30 g. The liver contrast agent Fenestra™ (ART, Quebec, Canada) was injected intra-venously into the training subjects to provide better CT contrast of abdominal soft tissues. Major organs, including the skin, skeleton, lungs, heart, brain, liver, spleen and kidneys, were segmented from these training CT images. Triangular meshes of the segmented organs were generated and the SSM was constructed as the point distribution model of the mesh vertices:

$$\begin{equation} S = \bar S + Vb, \end{equation} \tag{ 1 }$$

where S is a shape instance of the model and $\bar S$ is the mean shape. The shape is represented as a vector that lines up the coordinates of all the mesh vertices. V is the matrix of the shape variation modes, which are obtained using the principal component analysis of the mesh vertices, and b represents the shape coefficients that control the linear combination of the variation modes. By optimizing the value of b, the shape model can be fited to the individual subject images, which in our case are the x-ray image and side-view silhouette.

To register the atlas with the MARS images, a hierarchical approach is used (as shown in figure 4), i.e. the organs with high x-ray contrasts are registered first, and then the low x-ray contrast organs are mapped according to the registered high contrast organs.

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To register the high contrast organs, a SSM, namely SSM₁, is constructed for the skin, skeleton and lungs. For initialization, the mean shape of SSM₁ is roughly positioned at the subject location of the MARS gantry. This initialization needs to be performed only once for a fixed gantry. The deformation of SSM₁ is described by the vector T = [l, b], where l is a nine-element 3D linear transformation, including three translations, three rotations and three anisotropic scaling factors; b is the shape coefficient of SSM₁, which contains 24 principal components that represent 95% of the training set variations. The initial values of l and b are set to identity transform and 0, respectively. The registration is executed iteratively. For each iteration, the virtual x-ray projection and side-view silhouette of the atlas are generated using the fast mesh projection method (Wang et al 2010), based on the geometric calibration parameters of the x-ray projector and the optical camera, respectively. The similarity (f_X) between the atlas x-ray projection and the individual x-ray projection is measured with mutual information (Wells et al 1996), and the similarity (f_S) between the atlas silhouette and the individual silhouette captured by the optical camera is measured with 1-Kappa, where Kappa is the Kappa statistics (Klein and Staring 2011) that measures the overlapping ratio between two binary regions. The combined similarity between the deformed atlas and the individual subject is calculated as f = f_X + f_S. Here we use equal weights for f_X and f_S because they are considered equally important for the registration. Although the x-ray provides more anatomical information than the optical silhouette, the side-view silhouette also implies the lateral curvature of the spine, which is important for defining the 3D spine curvature. The Powell method (Powell 1964) is used to obtain the optimal value of T (i.e. T* in figure 4) that minimizes the value of f. A multi-resolution scheme is used to accelerate the registration and to avoid convergence to local minima. Three resolution levels are used, and the down-sampling ratios of the three levels are 4, 2 and 1.

After the high contrast organs are registered, the brain mesh borrowed from the Digimouse atlas (Dogdas et al 2007) is mapped with the 3D thin-plate-spline interpolation, using the skull vertices as the control points. To map the heart, liver, spleen and kidneys, a SSM, namely SSM₂, is constructed for those organs. The anatomical correlation between SSM₁ and SSM₂ is learned from the training set using the CGM. Given the shape coefficients of SSM₁ fitted to the individual subject, the CGM is used to predict the shape coefficients of SSM₂, so that SSM₂ is also fitted to the individual subject.

The accuracy of the mouse atlas registration was evaluated by comparing the registered atlas with the segmented micro-CT images of five test subjects. The test subjects included three commonly used strains (Nude, SCID and BC57s) and covered the weight range of 18–33 g. The subjects were injected with minimal dose of Fenestra™ LC (Suckow and Stout 2008) to maintain reasonable CT contrast without undermining the spine contrast in the MARS x-ray projection images. For each subject, the MARS scan was acquired first, and then the imaging chamber with the mouse subject was transferred to a micro-CT system (microCAT II, Siemens Preclinical Solutions, Knoxville, TN, USA) for a tomographic CT scan. During both MARS and CT scans, the subjects were kept anesthetized in the chamber to minimize posture changes. Based on the reconstructed CT images, major organs were manually segmented by a human expert. To establish the transformation from the CT coordinate space to the MARS coordinate space, the skin mesh of the segmented CT was mapped into the MARS space by a linear matrix M, which represents the translation and rotation in 3D space. The values of translation and rotation were manually fine-tuned until the top-view and side-view projections of the skin mesh matched well with the body outlines in the MARS images. Finally the inverse of M was used to map the registered atlas into the CT space, and the overlapping ratios between the atlas organs and the segmented CT organs were measured using the Dice coefficient,

$$\begin{equation} {\rm Dice} = 2\frac{{\big| {{\rm R}_{\rm A} \cap {\rm R}_{\rm S} } \big|}}{{\big| {{\rm R}_{\rm A} } \big| + \big| {{\rm R}_{\rm S} } \big|}}, \end{equation} \tag{ 2 }$$

where R_A and R_S represent the organ region of the registered atlas and the expert segmentation, respectively (| · | denotes the number of voxels and ∩ means the overlapping between two regions). The Dice coefficient has the value range of [0, 1], where 1 corresponds to complete overlapping and 0 corresponds to no overlapping.

To measure the accuracy of registered organ volume, the recovery coefficient of organ volume (RC_vlm) was used,

$$\begin{equation} {\rm RC}_{{\rm vlm}} = \frac{{V_{\rm A} }}{{V_{\rm S} }}, \end{equation} \tag{ 3 }$$

where V_A and V_S are the organ volumes of the registered atlas and the expert segmentation, respectively.

The surface distances between the registered atlas organs and the expert segmented organs were measured by the averaged surface distance (ASD),

$$\begin{equation} {\rm ASD} = \frac{1}{2}\left( {\frac{1}{{n_{\rm A} }}\sum\limits_{i = 0}^{n_{\rm A} } {d_i} + \frac{1}{{n_{\rm S} }}\sum\limits_{j = 0}^{n_{\rm S} } {d_j } } \right), \end{equation} \tag{ 4 }$$

where n_A and n_S are the numbers of vertices in the surface meshes of the registered atlas and the expert segmentation, respectively. d_i is the minimum distance from the ith vertex of the atlas surface to all the vertices of the expert segmentation surface and d_j is the minimum distance from the jth vertex of the expert segmentation surface to all the vertices of the atlas surface. Based on this definition, smaller ASD means better registration accuracy.

Table 1 reports the Dice coefficients of the major organs of the five test subjects. The strain and weight information of the animal is also listed. As reflected from the Dice results, the first subject had the best overall accuracy, while the second subject had the worst overall accuracy. Larger organs such as the whole body, the brain and the liver generally have better registration accuracy, while smaller or long-shape organs such as the spleen or skeleton normally have poorer registration accuracy. For visual illustration, the registration results of the best (subject 1), average (subject 4) and worst accuracies (subject 2) are shown in figure 5. Organ outlines of the registered atlas are projected onto the x-ray and optical images. The low contrast organs are not projected since it is impossible to visually compare these organs with the atlas projections in the MARS images.

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Table 2 reports the RC_vlm of the major organs of the five test subjects. Unlike the Dice coefficients, the RC_vlm does not present an obvious subject-dependent distribution. The mean RC_vlm of all the organs falls into the range of [0.9, 1.3], which means reasonably good estimations of the organ volumes. In terms of standard deviation, the whole body and the brain demonstrate smallest deviations (0.04 and 0.06, respectively) across the test subjects, while the spleen has the largest deviation (0.35).

Table 3 reports the ASDs of the major organs of the five test subjects. For all the organs, the mean ASD falls into the range of [0.83, 1.35], meaning the registration accuracy is around 1 mm. Similar to the Dice coefficient results, subject 2 showed worst (largest) ASDs for most organs. It can also be seen that the spleen and the skeleton do not have much worse (larger) mean ASDs than the other organs, which are different from the Dice results. Such a finding suggests that the spleen and the skeleton have got reasonably close registration, but their curved shapes led to imperfect volumetric overlapping ratios.

The atlas registration accuracy of this study was also compared with two previous studies, i.e. our previous simulation study that compares different combinations of the non-tomographic imaging devices (Wang et al 2010) and the study that registered the statistical mouse atlas with fully in tomographic CT images (Wang et al 2012). The purpose selecting these two studies was to determine whether the performance of the MARS agrees well with the simulation design, and also to compare the MARS-based atlas registration with a fully tomographic CT-based atlas registration. Figure 6 illustrates the comparison of the means and standard deviations of the organ Dice coefficients. It can be seen that the MARS performance of this study is within the statistical margin of error of the simulation design. For some of the organs, such as the lungs, the spleen and the kidneys, this study has slightly better mean Dice coefficients than the simulation study, while for the rest of the organs the simulation study is better. For the 'CT registration' study the Dice coefficients of the whole body, skeleton and brain were not available, since that study only focused on the trunk region. However, for the available organs, it is obvious that the mean values of the CT-based registration are larger than those of the MARS-based registration. This finding illustrates the tradeoff between accuracy of atlas registration and system complexity, cost and radiation dose by using a simpler imaging system than fully tomographic CT.

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The registration algorithm was programmed with C++, and took 3–4 min for each subject on a desktop PC with 3.05 GHz CPU and 6 GB RAM, using a single CPU thread.

As introduced in section 2.1, the MARS can be easily combined with a molecular imaging system, such as the PETbox4 tomograph. Figure 7 shows an example of a registered atlas overlaid with the PETbox4 image. A 30 g mouse was injected with ∼50 µCi [¹⁸F]FDG 1 h before the scan. The registered atlas was converted to a volumetric image by filling the organ meshes with pseudo CT Hounsfield values (as shown in figures 7(a) and (b)). The volume rendering of the registered atlas overlaid with the PET signal is shown in figure 7(c). With the combined PET/MARS images, the atlas not only provides anatomical reference for the PET image, it also offers initial organ regions for quantifying the PET organ uptakes, but an evaluation of this is out of the scope of this paper.

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