2.1.1.

FDOT system

The FDOT system used in this study is based on our optical data acquisition platform described previously in Ref. 22 with slight modifications (Fig. 1 ). The main specifications of the constituents are recapitulated here for completeness. We use a continuous-wave $785\text{-}\mathrm{nm}$ laser diode (HL7851G, Opnext, Tokyo, Japan) housed inside a laser diode mounting module (TCLDM9, Thorlabs, Newton, New Jersey) with an integrated aspheric focusing lens. The mounting module is connected to a temperature controller and a laser diode driver (LDC205C and TED200C, Thorlabs, Newton, New Jersey). We implemented a scanning laser using a galvo scanner, which consists of a pair of perpendicularly positioned galvanometers each equipped with a high-reflectance mirror (6230H, Cambridge Technology, Lexington, Massachusetts) [Fig. 1b]. This galvo scanner directs the laser beam in a raster pattern in small steps and creates a discrete 2-D grid of illumination source positions across the surface of the animal.

Fig. 1

(a) Experimental setup and schematic drawings of (b) the galvo scanner and (c) the rotation stage: 1, the CCD camera; 2, the lens; 3, the white-light LED; 4, the filter wheel; 5, the rotation stage; 6, the galvo scanner; and 7, the laser diode assembly.

The photodetector is a CCD camera (Imager QE, LaVision, Goettingen, Germany) equipped with a large-aperture lens (AF Nikkor $50\mathrm{mm}$ $f∕1.8\mathrm{D}$ , Nikon, Melville, New York). The cooled CCD chip $(-12°\mathrm{C})$ has an array of $1376\times 1040\text{pixels}$ ( $6.45\text{-}\mu \mathrm{m}$ isotropic pixel size). A filter wheel is mounted in front of the camera, which houses 785- and $830\text{-}\mathrm{nm}$ bandpass interference filters with a $10\text{-}\mathrm{nm}$ passband (CVI Laser, Albuquerque, New Mexico). A white light-emitting diode (LED) light source equipped with a ground glass diffuser (LIU004 and DG20-120, Thorlabs, Newton, New Jersey) is mounted above the camera lens so that the exact surface of the animal can be reconstructed optically (algorithm detailed later).

We developed a motorized rotation stage to vertically suspend the animal on the imaging platform [Fig. 1c], which uses two stepper motors to simultaneously rotate the upper and lower torso of the animal to achieve nonobstructed panoramic optical sampling. The stepper motors (Excitron, Boulder, Colorado) have a minimum step size of $0.9\mathrm{deg}$ and an angular position error of $<0.1\mathrm{deg}$ . The laser and the camera are arranged in a transillumination configuration. The laser beam impinging the animal surface is $\sim 15\mathrm{deg}$ from the optical axis of the camera lens to avoid glare (due to scattering and reflections) within the field of view (FOV) of the camera.

The activation of the CCD camera, the actuation of the rotation stage and the galvo scanner is controlled using our own LabVIEW program (version 8.5, National Instruments, Austin, Texas) and auxiliary electronic devices. The entire FDOT system was shrouded by light blocking/absorbing material during optical data acquisition.

2.1.2.

Micro-CT system

A dual-imaging-chain micro-CT system, consisting of two perpendicularly configured x-ray tube/detector pairs, as previously described in Ref. 23, is used to a acquire anatomical micro-CT data. The system has two Varian A197 x-ray tubes with dual focal spots (0.6 and $1.0\mathrm{mm}$ ). The tubes are designed for angiographic studies with high instantaneous flux and total heat capacity, and are powered by two Epsilon High-Frequency X-ray generators (EMD Technologies, Quebec, Canada). The system has two identical XDI-VHR 2 detectors (Photonic Science, East Sussex, United Kingdom) using ${\mathrm{Gd}}_2{\mathrm{O}}_2\mathrm{S}$ phosphor with a pixel size of $22\mu \mathrm{m}$ , an input taper size of $110\mathrm{mm}$ , and an image matrix of $4008\times 2672$ . Both detectors allow on-chip binning of up to $8\times 8\text{pixels}$ and subarea readout, and subsequently can achieve a temporal resolution as high as $100\mathrm{ms}$ .

2.2.1.

Animal preparation

All animal studies were approved by the Duke University Institutional Animal Care and Use Committee. Animal experiments were conducted on nude mouse (Nu/Nu, $33.6\mathrm{g}$ , male) cadavers to limit the complexity of animal support. At $24\mathrm{h}$ before imaging, the animal received an injection of liposomal blood-pool contrast agent²⁴ for micro-CT, delivered via the tail vein with a dose of $14\mathrm{ml}∕\mathrm{kg}$ . Before imaging began, the animal was euthanized by injecting a lethal dose of the mixture of sodium pentobarbital $(100\mathrm{mg}∕\mathrm{kg})$ and butorphanol tartrate $(2\mathrm{mg}∕\mathrm{kg})$ , after which a glass capillary ( $2.4\mathrm{mm}$ in inner diameter and $50\mathrm{mm}$ in length) was inserted into the chest cavity via a midline ventral incision on the neck, leaving approximately $15\mathrm{mm}$ of the capillary outside. A fluorescent inclusion in the animal was created by filling this glass capillary with $18.4\mu \mathrm{M}$ indocyanine green (ICG) solution (in deionized water). Care was taken to ensure that the glass capillary was between the heart and the spine to simulate the worst-case scenario in animal FDOT studies. Sutures were used on the incision to fix the capillary to the skin.

After surgery, the animal was vertically positioned in the rotation stage by attaching its fore and hind limbs to the top and bottom bars mounted to the stepper motors, respectively [Fig. 1c]. The angular acceleration and deceleration of the stepper motors were empirically set to ensure smooth rotation without deforming the posture of the animal during the experiment.

The ICG solution was prepared while the surgical procedures were being performed on the animal; it was kept in a dark container until the animal was positioned on the rotation stage; and was injected into the glass capillary just before optical data acquisition began. The time interval between solution preparation and the end of fluorescence acquisition is $30\text{to}60\min$ .

2.2.2.

Optical data acquisition

In this study, our region of interest (ROI) was set at the portion of the chest cavity around the heart, in which the fluorescent inclusion is surrounded by the heart, lungs, ribs, and spine. Note that the surgical procedures on the animal did not affect the optical measurement because the incision and the suture were outside the ROI (on the neck), and that we performed dissection on the animal after the experiment and found no blood clog in the chest. The focal plane of the camera was set at the midpoint between the rotation center and the proximal surface (with respect to the camera) of the animal. Panoramic data acquisition was achieved by incrementally rotating the animal $360\mathrm{deg}$ . For each acquisition angle, the laser scanned vertically for 5 points spanning $\sim 6\mathrm{mm}$ , along a line largely centered at the middle of the thoracic vertebrae. For each laser scanning position, the CCD camera was activated to acquire a fluorescence CCD image (with the $830\text{-}\mathrm{nm}$ filter) for an exposure time of $4\mathrm{s}$ . After the galvo scanner completed a scan and resumed its initial state, the animal was turned a small angle by the rotation stage, followed by another round of laser scan and data acquisition. This process was repeated until the phantom returned to its initial angular position. In this study, we used an angular step size of $9\mathrm{deg}$ , resulting in a total of 40 acquisition angles. Afterward, the acquisition procedure detailed previously for the fluorescence data was repeated at the excitation wavelength (with the $785\text{-}\mathrm{nm}$ bandpass filter) to acquire the excitation data. Each of the fluorescence and excitation data acquisitions took approximately $15\min$ to finish. The number of detectors is 28 per angle per source position. As a result, the full dataset consists of 200 sources, 1120 detectors, and 5600 fluorescence measurements.

To properly model the forward problem, the exact 3-D geometry of the animal surface is necessary. In this study, the surface was obtained using an optical method. After fluorescence and excitation data acquisition, we used the white LED light source to illuminate the animal surface and acquire a reflectance CCD image at each angular position without any filter (camera exposure time $20\mathrm{ms}$ ).

The last step in optical data acquisition was to calibrate the exact positions of the laser impinging on the animal surface. After the rotation stage was removed for micro-CT imaging, a planar translucent/attenuating calibration target made from Garolite (off the shelf) was placed in the focal plane of the camera lens. The surface of the target facing the camera was marked with evenly spaced horizontal and vertical lines with premeasured distances. The raster pattern of the laser was repeated, while the camera acquired an image at each scanning position, during which a neutral density filter was used to protect the CCD from excessive light. Together with the optically reconstructed animal surface, these optical calibration images were used to localize the exact illumination source positions in the forward model (algorithm described later).

2.2.3.

Micro-CT imaging

After acquiring the optical data, the rotation stage (with the animal still attached) and its peripherals were transported to the nearby x-ray laboratory for micro-CT imaging without disturbing the animal. In this study, only a single imaging chain was used for micro-CT imaging ( $80\mathrm{kVp}$ , $160\mathrm{mA}$ , $10\mathrm{ms}$ exposure, and 220 projections over $198\mathrm{deg}$ of rotation). A geometric calibration procedure was performed afterward, which enabled computation of the projection matrices required for reconstruction using our lab-developed x-ray calibration phantom.²⁵ A cone-beam reconstruction was applied on the projection images to form a ${\left(512\right)}^3$ matrix with an isotropic voxel size of $88\mu \mathrm{m}$ . Reconstruction used a Feldkamp algorithm with Parker weighting,^{26, 27} which was implemented in a commercial software package Cobra EXXIM (EXXIM Computing, Livermore, California). Note that in our lab-developed micro-CT system, we typically use half-scan-angle reconstruction scanning, i.e., an arc of $180\mathrm{deg}$ plus the fan angle ( $7\mathrm{deg}$ for our system). This is preferred to a full $360\text{-}\mathrm{deg}$ rotation for in vivo studies because the tubes and wires carrying anesthesia gas and physiologic monitoring signals are coupled to the animal vertically from above or bottom and a half scan angle rotation creates less tension to the auxiliaries than a full rotation. Nonetheless, the half scan angle does not affect the image quality in micro-CT reconstruction, because of the specific algorithm used for reconstruction.²⁷

2.3.1.

Optical surface reconstruction

The highly diffusive white LED light source is mounted just above the camera lens [shown in Fig. 1a] and is relatively far away from the animal $(\sim 30\mathrm{cm})$ compared to the dimensions of the animal $(\sim 2\times 4\mathrm{cm})$ within the camera FOV. As a result, we can consider the white-light CCD images as front-illuminated by a parallel light source. These white-light images are segmented using thresholding and are subsequently converted to binary images. These binary images contain the profiles of the animal at different acquisition angles and are equivalent to the back-illuminated parallel projection images. The relation between a 3-D volume and its 2-D projections is well modeled by the Radon transform.²⁸ For computational efficiency, these binary images were downsampled by a factor of 4 before further processing, resulting in an isotropic in-plane resolution of $0.182\mathrm{mm}$ . Because the rotation center of the animal does not necessarily coincide with the center of camera FOV, each binary image is corrected for its horizontal displacement. Such correction is achieved by comparing each pair of images acquired at the opposite angular positions and finding a displacement so that these two images closest mirror each other in terms of the smallest root mean square (rms) difference. For each horizontal line in this series of corrected binary images, we apply an inverse Radon transform followed by thresholding (at 95% level) to produce a binary 2-D axial slice containing the contour of the animal surface. The 3-D surface contour is obtained by stacking all axial slices ( $0.182\text{-}\mathrm{mm}$ 3-D isotropic resolution), as shown in Fig. 2 . The source and detector positions relative to the animal surface are also shown in Fig. 2 (marked by the double-arrow near the chest). This optically reconstructed animal surface is the geometrical basis for fluorescence image reconstruction and coregistration with anatomical micro-CT data.

Fig. 2

The 3-D surface contour of the animal (central) reconstructed from the white-light reflectance images from multiple acquisition angles (peripheral) using an inverse Radon transform. The area marked by a double-arrow on the surface contour represents the source and detector positions (shown as red and blue markers respectively), which define the ROI $(22⩽z⩽30\mathrm{mm})$ in reconstruction. (Color online only.)

2.3.2.

Source/detector localization

With the 3-D surface contour and the optical calibration images available, the positions of the illumination sources on the animal surface can be computed from the origin and the direction of the impinging laser beam. The laser beam emitted from the laser diode is directed by the first reflector ( $x$ scan) and followed by the second reflector ( $y$ scan) before it impinges on the animal surface. The origin of the impinging laser beam is therefore located at the center of the $y$ scan reflector, and is known from geometrical measurement. The optical calibration images give an accurate position of the laser beam impinging the calibration target, from which the angle of each imaging laser beam is computed. The 3-D positions of the illumination sources are given by the intersection of the impinging lasers with the optically reconstructed animal surface. In this study, we used the FOV of the CCD camera to define the global coordinate system. The length unit of this coordinate system is the spatial resolution of the camera at the calibration target (i.e., in the camera focal plane), which is given by dividing the known grid spacing on the target by the number of voxels between corresponding lines on the grid. In our configuration, the spatial resolution of the CCD camera at its focal plane is $45.5\mu \mathrm{m}∕\text{pixel}$ (isotropic).

Since the CCD is essentially a matrix of photodetectors, one can choose the specific locations on the CCD image as the detector positions after data acquisition. We specified a 2-D array of fixed locations in a CCD image ( $4\times 7$ points covering an area of $5.25\times 9.42\mathrm{mm}$ horizontally and vertically, respectively) so that the ROI (the chest cavity around the heart) was adequately covered, which was applied to all acquisition angles. These detector positions chosen in the CCD images were mapped onto the animal surface using the same method as in localizing the source positions, except that the origin of the detector vector was set at the center of the surface of the camera lens. The measured fluorescence signal amplitude is the averaged intensity over a cluster of $7\times 7\text{pixels}$ around a detector position, which corresponds to a rectangular area of $0.273\times 0.273\mathrm{mm}$ in the focal plane.

2.3.3.

Structural priors

In this study, we used an atlas mouse anatomy to assist FDOT reconstruction because integration of a second imaging modality, such as CT or MRI, typically significantly increases the complexity of experimental designs for most animal studies. This atlas anatomy was derived from a time-gated high-resolution 4-D MRI data of mice,²⁹ known as MOBY. In this paper, we refer to the anatomical structures derived from this digital atlas, which is a generalized representation of the mouse anatomy, as the MOBY anatomy.

The MOBY anatomy has different resolution and orientation from those of our optical imaging. Another difference between the MOBY and the actual anatomy is the posture of the animal during imaging. In the MOBY anatomy, the animal was lying prone, while in our optical imaging, the animal was upright. Nonetheless, comparisons between our micro-CT and the MOBY images show that the differences are mostly in the curvature of the neck and the position of the head, which is out of our ROI. As a result, we take only the MOBY anatomy that contains the chest cavity and model the differences as a rigid coordinate system transformation and anisotropic scaling. Specifically, we first adjusted the orientation of the MOBY anatomy so that its principle axes coincided with those of the optically reconstructed 3-D surface. Second, we manually adjusted the origin of the MOBY anatomy in three dimensions and the scales of its three principle axes iteratively: for the $z$ axis (vertical) adjustment, the collarbones and the lower-end ribs in the MOBY anatomy matched the corresponding points in the optical surface, which were inherently registered to the highly visible landmarks in the white-light CCD image; and for the $x$ and $y$ axes (in the horizontal plane), the relative size of the MOBY anatomy to the optical surface matched that measured in the micro-CT images.

Among all structures in the MOBY anatomy, we retained the following as a trade-off between anatomical accuracy and modeling simplicity: the muscle, bone (rib and spine), heart, lung, and liver. We adopted the method detailed in Ref. 30 to compute the absorption and diffusion coefficients of different types of tissue at the excitation and fluorescence wavelengths (785 and $830\mathrm{nm}$ ). The specific values of the optical properties are listed in Table 1 .

Table 1

Optical properties, namely, the absorption coefficient μa , the reduced scattering coefficient μs′ and the index of refraction n , of each type of tissue at the excitation and the fluorescence wavelengths (785 and 830nm , respectively).

To evaluate the improvement of imaging quality as a result of the MOBY anatomy, we also created a homogeneous medium for comparison, which was a replica of the medium with MOBY anatomy, except that all types of tissue were assigned the same optical properties as that of the muscle.

2.3.4.

Image reconstruction

Because of the large number of measurement channels, image reconstruction methods based on Monte Carlo simulations cannot be used without significant computing resources.³¹ And because of the complexity of the mouse anatomy, analytical methods are also not applicable. The finite element method (FEM) can be applied to an arbitrarily complex geometry and has proven to be effective in diffuse optical tomography, e.g., as demonstrated in Refs. 12, 32, 33, 34, 35. Therefore, image reconstruction in this study was carried out using an FEM software package for near-IR fluorescence and spectral tomography, known ³⁶ as NIRFAST, which uses the diffusion equation in the frequency domain as the forward problem solver (modeling light propagation in the medium), and uses a Tikhonov regularization method to iteratively solve the inverse problem (obtaining the fluorescence yield). The Tikhonov regularization parameter is dynamically defined as the ratio of the variances of the measurement and optical properties. In addition, this software package was developed on the scientific programming platform MATLAB (The MathWorks, Natick, Massachusetts), which fits naturally with our existing data processing tools. Because a continuous-wave light source was used in this study, we specified a very low modulation frequency of ${10}^{-6}\mathrm{Hz}$ in NIRFAST.

The hybrid geometry of the animal created from the optical surface and the MOBY anatomy was downsampled to a resolution of ${\left(1\mathrm{mm}\right)}^3$ and converted to a tetrahedral mesh using a MATLAB routine for the 3-D Delaunay triangulation method, which is based on the Quickhull algorithm.³⁷ The mesh contains 10,220 nodes and 57,917 elements within a reconstruction boundary of $24\times 22\times 28\mathrm{mm}$ . Using our lab-developed computer program, fluorescence/excitation signals, source/detector positions, along with the mesh data were subsequently converted from MATLAB internal data structures to formatted text files that could be read by NIRFAST.

2.3.5.

Data coregistration

The reconstruction result from the FDOT data (a 3-D matrix of fluorescence yield) must be coregistered with the anatomical micro-CT images to verify the reconstruction and compute the appropriate figures of merit. Coregistration of the FDOT and CT results was achieved via the optically reconstructed animal surface.

The FDOT result from the FEM reconstruction software is represented in a 3-D mesh (tetrahedral grid with variable size), while the CT data are represented in a 3-D matrix (cubic grid with constant size). We took a series of nine axial slices with an interval of $1\mathrm{mm}$ along the $z$ axis using a built-in interpolation tool of NIRFAST. These slices cover the entire ROI in our FDOT reconstruction, which is dictated by the coverage of the source/detector positions. This series of slices form a 3-D matrix (isotropic in-plane resolution but anisotropic in three dimensions), and will be referred to as the NIRFAST matrix in this paper. Each of these slices was subsequently thresholded at 50% of its maximum value to create a 2-D full width at half maximum (FWHM) plot, and normalized by its in-plane maximum for clearer visualization. These FWHM plots are hereafter referred to as the FWHM matrix.

The coregistration of the FWHM matrix and micro-CT images was realized using a visualization software package Amira (version 5.2, Visage Imaging, Berlin, Germany). First, the NIRFAST matrix, which clearly shows the animal surface contour, was registered to the optically reconstructed surface by scaling the $x$ and $y$ axes of the former. The $z$ axis of the NIRFAST matrix was scaled by the inverse of the interslice distance in the micro-CT data. These two data sets match each other almost perfectly because the animal geometry used in reconstruction was based on the optical surface. The slight mismatch was the result of mesh generation and data interpolation. The FWHM matrix was registered to the optical surface using the same scaling parameters.

Next, the optical surface was rotated, translated, and scaled to match the animal surface constructed from the micro-CT data. This transformation has $6\text{degrees}$ of freedom (3 in translation, 2 in rotation, and 1 in scaling) because both data sets have isotropic resolution. The optical surface was matched to the micro-CT surface by manually adjusting the preceding six transformation parameters.

The same transformation parameters found in the preceding were applied to the FWHM matrix, which had been registered to the optical surface, to achieve the final coregistration of the fluorescence reconstruction result ( $\sim 1\mathrm{mm}$ resolution) and the high-resolution anatomical images from micro-CT ( $88\mu \mathrm{m}$ resolution).