2.1.

Object Surface Acquisition

The tomograph is equipped with an extra oblique green planar laser connected with the $x$ translation stage (Fig. 2 ). A green laser has been chosen because the absorption of its light is very strong and the maximum intensity distribution remains localized near the incidence point of the mouse skin. The more critical point is the roughness of the sample surface to avoid any laser reflexion. Other techniques exist in order to scan the object surface. For example, in quality control of mechanical pieces, galvanometers can be used. Our solution by triangulation method is simplest to use and is cost effective. In Ref. 9, Schulz present a system that retrieves the 3-D surface information of the diffuse medium using a camera.

Fig. 2

Schema of the surface computation within the planar laser acquisition $xz$ plane.

At a given $x$ position, the intersection curve between the laser plane and the studied object is acquired by the top camera. The intersection is linearly distorted along the $x$ axis depending on the height of the intersection. By using the triangulation formula and provided that no region is in the shadow of the planar laser, we recover the object surface with a laser scan.

We can demonstrate the validity of this method by using a calibrated phantom. This consists of a staircase black phantom with calibrated steps of $5\text{-}\mathrm{mm}$ thickness each [Fig. 3 ]. The computed surface is presented in Fig. 3, superimposed in red over the black-and-white image of the phantom. The different slices of this surface show that each step is recovered with the right thickness, as shown in the projection given in Fig. 3. As the laser makes a $45\mathrm{deg}$ angle with the vertical, the theoretical accuracy that can be reached is given by the equivalent CCD pixel size in the object plane—i.e., 200 times $\sqrt{2}\mu \mathrm{m}$ . The error measured on the calibrated phantom is $300\mu \mathrm{m}$ , which is in accordance with the theoretical error.

Fig. 3

Staircase phantom used to validate the surface acquisition: (a) schema of the phantom, (b) calculated surface superimposed onto the phantom photograph, and (c) transversal slice of the reconstructed staircase. (Color online only.)

After a smoothing step, these errors of the surface acquisition are taken into account by the computation of the attenuation map and its use during the reconstruction process.⁷ They remain at a level sufficient for reconstruction in good conditions.

2.2.

Reconstruction Method

Here, the propagation of light modeled as a scalar field $\varphi \left(\mathbf{r}\right)$ in highly diffusive media is assumed to follow the Helmoltz equation:

Using the animal surface provided by the planar laser, we can complete the equation system with the “extrapolated boundary conditions.”⁸ The discrete form of Eq. 1 is obtained by using a finite volume method applied on an unstructured mesh that conforms to the extrapolated boundary.¹⁰

Given a $k$ map, we can compute the propagation function $G({\mathbf{r}}_1,{\mathbf{r}}_2)$ of light in the medium between any points ${\mathbf{r}}_1$ and ${\mathbf{r}}_2$ :

By modeling the laser source $\mathbf{s}$ as a Dirac delta function position at ${\mathbf{r}}_{\mathbf{s}}$ , Eqs. 1, 2 give the excitation density wave at any point $\mathbf{r}$ of the medium:

Fig. 4

Block diagram of the reconstruction algorithm. The reconstruction process is performed in two main steps: attenuation map computation detailed in the bottom dashed box, and iterative fluorescence quantity reconstruction.

We first compute the attenuation $k\left(r\right)$ map by comparison of the Green’s functions $G_{\mathit{sd}}$ to the excitation measurements ${\mathit{U}}_{\mathit{sd}}^{\mathit{exc}}$ . This first step is itself an iterative process initialized with a homogeneous map $k_0\left(r\right)$ .

Once this first step is completed, we end up with Green’s functions giving a valid description of the propagation of the light in the studied medium. The fluorescence yield can then be reconstructed from fluorescent measurements by using a classic iterative ART algorithm.¹¹ Convergence of the algorithm is achieved within 15 iterations and a relaxation parameter of 0.1.

The system is not strictly speaking underdetermined; however, it is very ill-conditioned. The regularization is obtained by stopping the iterations. The ad hoc ART iteration number has been estimated on several mice experiments.

2.3.

Filtering

A filter wheel has been added to the system. This is useful for performing multiple functional analyses on the same animal and at the same time providing the use of different fluorophores. It has already been demonstrated in single-photon emission computed tomography (SPECT) that the use of several markers can improve diagnostics.¹² For example, in optical imaging techniques, it is used to enable specific diagnosis of tumors¹³ or to validate the model of ovarian cancer used as presented in Ref. 14.

The excitation laser source wavelength is $690\mathrm{nm}$ . At present, two main fluorophores are used: Alexa 680 and Alexa 750 (Alexa Fluor Dye Series, Molecular Probes—Invitrogen). A bandpass 730AF30 filter ( $30\text{-}\mathrm{nm}$ bandpass centered at $730\mathrm{nm}$ ) makes it possible to see only Alexa 680, and a long-pass 770ALP filter (cut on at $770\mathrm{nm}$ ) makes it possible to record both fluorophores’ emission. The filters cut-on are chosen so that the filter response curve of the bandpass filter overlaps the emission curve of Alexa 680 and cuts at the very beginning of emission of Alexa 750 and so that the response curve of the long-pass filter overlaps a large part of the emission curve of Alexa 750 and cuts at the end of the emission curve of Alexa 680. The long-pass filter is separated enough from the excitation wavelength to correctly reject it and allows using any fluorophore with a fluorescence above $770\mathrm{nm}$ . Therefore, it is suitable for numerous configurations. The second (bandpass) filter was chosen to allow the demultiplexing of Alexa 750 and Alexa 680 spectra.

We measure experimentally on fluorescence reflectance imaging (FRI) images of capillary tubes containing the same quantity of fluorophore such that for Alexa 680, the ratio of the two filter’s response (bandpass filter/long-pass filter) is 3.3, and for Alexa 750, the ratio of the two filters’ response (long-pass filter/bandpass filter) is 20. These ratios indicate that Alexa 750 can be seen only by the long-pass filter and that Alexa 680 can be seen by the two filters with, however, a lower value for the long-pass filter. The FRI system [2-D illumination by a crown of LEDs on the animal’s region of interest (ROI) and records of light backscattered by the fluorescent markers on a CCD camera through a focusing lens] we used has been fully described in Ref. 15.

3.1.

Phantom Description

The phantom described in Fig. 5 (top) is used to test the separation of the two fluorophores according to the filter in use. Its bulk material is composed of a mixture of epoxy resin, titanium dioxide $\left(\mathrm{Ti}{\mathrm{O}}_2\right)$ powder for dispersers, and black ink as the absorber ( $\mu \mathrm{a}=0.2{\mathrm{cm}}^{-1}$ , ${\mu }^{\prime }s=10{\mathrm{cm}}^{-1}$ )—the absorption coefficient was measured using an absorption spectrometer during the phantom making before adding $\mathrm{Ti}{\mathrm{O}}_2$ powder. The diffusion coefficient is obtained after phantom making by fitting a transmitted optical signal through the phantom and through a range of known phantoms.

Fig. 5

Use of the filter wheel to separate two fluorophores: Alexa 680 and Alexa 750. Top: Schema of the phantom used. Bottom left: Reconstruction result with use of the high-pass filter; the two fluorophores are reconstructed, with a greater intensity for Alexa 750. Bottom right: Reconstruction result with use of the bandpass filter; only Alexa 680 is reconstructed.

It is roughly a parallelepiped, $35\mathrm{mm}$ wide, $42\mathrm{mm}$ long, and $15\mathrm{mm}$ high. Capillary tubes are placed in two of the three $3\text{-}\mathrm{mm}$ holes that are drilled in the phantom. They are separated by $2.5\mathrm{mm}$ . One of them contains Alexa 750, the other Alexa 680. The two solutions have been characterized to contain approximately $3\mathrm{pmol}$ of fluorophore. (They are prepared by diluted $3\mathrm{pmol}$ of fluorophore in a solution of Intralipid.) We use the two upper holes; the third one was used for other experiments intended to study separation in the $z$ direction.

Another test phantom is delivered with the tomograph and enables the evaluation of the machine’s stability. It has the same bulk material and the same dimensions as the phantom of Fig. 5, i.e., roughly a parallelepiped, $35\mathrm{mm}$ wide, $42\mathrm{mm}$ long, and $15\mathrm{mm}$ high. A fluorescent cylindrical inclusion (length $7\mathrm{mm}$ , diameter $2\mathrm{mm}$ ; fluorescent glass fragment), equivalent to a concentration of $15\mu \mathrm{mol}{\mathrm{L}}^{-1}$ Alexa 700, is positioned in a part of the phantom (see Fig. 6 ). The other part is homogeneous and is used to measure the $\gamma$ parameter of Eq. 1; this enables evaluating the laser stability. The technique used to validate the phantom optical properties ( $\mu a=0.2{\mathrm{cm}}^{-1}$ , ${\mu }^{\prime }s=10{\mathrm{cm}}^{-1}$ ) is the same as described earlier.

Fig. 6

Phantom used to test the repeatability and stability of the tomograph. The left part contains a fluorescent inclusion. The right part is homogeneous and is used to measure the $\gamma$ parameter of Eq. 1.

3.2.

Filtering Test

Figure 5 (bottom left) shows that, using the long-pass filter, the two fluorophores are reconstructed but with a higher contrast for Alexa 750. On the right, using the bandpass filter, only Alexa 680 is reconstructed. The two reconstructions are presented in the same colormap.

We choose here to keep the long-pass filter that equipped our system in its first version in order to be able to compare our measurements to older ones done in this first configuration.

3.3.

Repeatability

Several experiments have been performed over the fluorescent part of this phantom: five with the high-pass 770ALP filter (cut-off at $770\mathrm{nm}$ ) and six with the bandpass 730AF30 filter ( $30\text{-}\mathrm{nm}$ band-cut centered at $730\mathrm{nm}$ ). The experiments are performed the same day for each filter (one day for the bandpass filter, and one day two weeks later for the high-pass filter). The system was turned on and off two times each day. In routine use of the tomograph, one experiment is done at least once per month over the fluorescent part of the phantom, and each day over the homogeneous part.

A curve showing the values of the $\gamma$ parameter of Eq. 1 obtained on this homogeneous part is shown in Fig. 7 (top). The period covers $5\text{months}$ of tomograph use and shows a good stability of the laser.

Fig. 7

Top: Repeatability of the system showing a good stability of the $\gamma$ parameter over a $5\text{-month}$ period. Bottom: Repeatability of the experiments. The fluorescence quantity is measured in the overall reconstructed volume and is stable with the experiments.

Figure 7 (bottom) presents the reconstructed fluorescence values measured in the overall reconstructed volume for each experiment. For these experiments, the excitation sources describe a regular 7 by $7.2\mathrm{mm}$ –spaced grid $(1.4\mathrm{cm}\times 1.4\mathrm{cm})$ under the phantom. The reconstructed volume is 9 by 9 by 16 voxels. The voxel size is $2\mathrm{mm}$ by $2\mathrm{mm}$ by $1\mathrm{mm}$ .

The observed 10% drift is due to photo-bleaching of the glass inclusion. This has been studied as described in Ref. 16.

3.4.

In Vivo Mice Experiments Protocol

The global animal measurement protocol used is as follows: The animal is positioned on a heating holder free of upper glass plate or adaptation liquid. It can be gently maintained by the legs to reduce its movements. At first, the planar laser scans the animal in order to get its surface, as described earlier. Then, the animal is scanned by the near-infrared (NIR) laser. Typically, the excitation sources describe a regular 11 by $11.2\mathrm{mm}$ –spaced grid ( $2\mathrm{cm}\times 2\mathrm{cm}$ field of view) drawn in red in Fig. 8 . For each source position, the CCD camera focused at the mean thickness of a mouse (i.e., $15\mathrm{mm}$ ) first records the transmitted (excitation) images. Then a filter is inserted, and the fluorescence (emission) images are recorded.

Fig. 8

Mouse experiment: A capillary tube containing Alexa 700 is inserted in the trachea of a mouse. The mouse is maintained between two glass plates with a thickness of $15\mathrm{mm}$ . The reconstructed fluorescence is presented in superimposition over the mouse photograph. (Color online only.)

3.5.

Reproducibility with Thickness

We conducted a set of free-space in vivo experiments on female Swiss nude mice in order to compare the results to those obtained with the previous configuration of the system when the mice were maintained between two glass plates.

In the “between-plates” configuration, the mouse lies on its ventral side and is maintained between the two glass plates of the heating support. By varying the compression of a mouse, we acquired tomographic measurements for the mouse thickness ranging from $14\text{to}18\mathrm{mm}$ . Thereafter, we performed a free-space experiment where the uncompressed mouse ( $20\mathrm{mm}$ thickness) lay in its physiological position. The mouse has a capillary tube—filled with $0.4\mu \mathrm{l}$ of a solution of Intralipid and a quantity of $3.6\mathrm{pmol}$ Alexa 700—inserted in its trachea. We choose to inspect the lung area by reference to the previous study presented in Ref. 4.

The between-plates experiments are reconstructed using the previous method, which takes into account the animal area in contact with the upper glass plate given by an illumination of the animal by the lateral sides. As in this experiment, we reconstruct a capillary that is in a delimited area, and during reconstruction, we use only 10 by 8 positions (that is, 80 sources), and we consider only the detectors of the camera for which the projection is in the area in contact with the animal or in the neighboring extrapolated area. The total number of detectors (binned pixels of $500\mu \mathrm{m}$ ) of this reduced scan area is 1665. The percentage of detectors used when we use the compression plate varies from 45 to 55% of total detectors. The free-space experiment uses the surface information in order to exploit data coming from the whole animal, and we use 90% of the detectors. (100% represents all the detectors that cover the scanned area.)

Figure 8 presents the projection of the reconstructed fluorescence volume over the black-and-white photograph of the mouse for the $15\text{-}\mathrm{mm}$ -thickness between-plates experiment. We measure the reconstructed signal in a $5\mathrm{mm}\times 3\mathrm{mm}$ region of interest drawn in light green centered over the capillary tube and compare the values from one experiment to the other, as shown on Fig. 9 . This measurement done on a 2-D projection represents the sum of the fluorescence found in a $5\times 3\times 15{\mathrm{mm}}^3$ volume. The total reconstructed fluorescence is stable within 3% (deviation from “between plates” average) and, the free-space and between-plates results are in accordance. This experiment validates the free-space functionality.

Fig. 9

Results showing the good reproducibility of the experiment and the stability of the tomograph according to the animal thickness.

3.6.

Linearity with Fluorophore Quantity

In order to validate the quantification done on experiments conducted in the free-space configuration, several similar experiments have been repeated using different quantity of fluorophore inside the capillary tube. We use a range of quantity from $0.2\mathrm{pmol}\text{to}20\mathrm{pmol}$ of Alexa 700 diluted into a specific marker used for pulmonary cancerous inspection Angiolone–Alexa 700 (Fluoptics, Grenoble, France). The capillary tube is inserted in the mouse trachea, and the mouse lung area is scanned with the mouse placed in its physiological position in the free-space tomograph configuration.

We measure the reconstructed signal in a $18\mathrm{mm}\times 18\mathrm{mm}$ region of interest centered over the capillary tube. This measurement done on a 2-D projection of the $z$ slices of the reconstructed volume represents the sum of the fluorescence found in an $18\times 18\times 15{\mathrm{mm}}^3$ volume. The scale is in arbitrary units (a.u.) because the tomography gives relative values, not absolute values. In order to give absolute values, a calibration with etalon phantoms has to be done.

The curve presented in Fig. 10 shows the good linearity of the system with the fluorophore quantity inside the capillary tube (coefficient of determination $R^2$ is 0.9). The deviation from linearity ranges from 3.3% to 40%, except for two values: $13\mathrm{pmol}$ and $0.26\mathrm{pmol}$ , for which the deviation is 67% and 75%, respectively. For higher fluorophore concentrations, another phenomenon of self-absorption of the fluorophore occurs that prevent a portion of the emitted light reaching the detectors.

Fig. 10

Results showing linearity of the tomograph according to the quantity of fluorophore inside the capillary tube inserted in the mouse.

3.7.

Longitudinal Study on a Diseased Mouse

Last, we conducted an in vivo experiment on a diseased mouse in order to follow up the growth of mammary murine tumors and to validate the free-space configuration in its use for in vivo disease follow-up.

The mouse is imaged at 10, 12, and $14\text{days}$ after the primary mammary adenocarcinoma cells implantation; ${10}^6$ TSA/pc (Trichostatin A) cells in $100\mu \mathrm{l}$ phosphate-buffered saline (PBS) solution. A delay of two days between two successive measurements has been chosen because it is the time required for the animal to totally eliminate the fluorescent probe. The tumor cells are injected by the tail vein; the first organs encountered are the lungs, and the cells stay fixed there.

The mouse lies on its ventral side and is simply placed on the heating support in its physiological position in the free-space tomography configuration. The mouse is injected with a specific marker Angiolone–Alexa 700 (Fluoptics, Grenoble, France; $200\mu \mathrm{l}$ ). It has been shown that this probe targets the $\alpha \mathrm{v}\beta 3$ integrin, which is overexpressed in tumors.^{17, 18} Three hours later, the mouse is anesthetized, and the lung area is scanned with infrared light describing an 11 by $11.2\mathrm{mm}$ –spaced grid.

The superimposition of the reconstructed volumes of the mouse at days 10, 12, and 14 and of the scanned surface of the animal onto the white-light images [Fig. 11 (left)] shows the progression of the lung cancer invasion in the animal. The three reconstructed volumes are presented using the same colormap to allow comparison. The right part of Fig. 11 shows the attenuation map $k$ . The $k$ map variation with the evolution of the disease is smoother than the fluorescence variation. The slight evolution can be explained by the invasion of the tumor tissues in the lungs. This study gives similar results to the study previously carried out with the mouse maintained between plates and described in Ref. 4, and thus validates the use of the tomography in the free-space configuration for disease follow-up.

Fig. 11

Left: 3-D view of the reconstructed fluorescence quantity superimposed on the white-light image for a diseased mouse at day 10 (top), day 12 (center), and day 14 (bottom) after the tumor implantation. The increase of the fluorescence follows the development of the disease. Right: 3-D view of the attenuation map $k$ superimposed on the white-light image for a diseased mouse at day 10 (top), day 12 (center), and day 14 (bottom) after the tumor implantation. A slight modification of the map can be seen.