Plexiglas cubes containing FM
The FM were composed of four sources of germanium68 (74 kBq; diameter, 1 mm; and length, 0.5 mm; Isotop Product Laboratories, Valencia, CA, USA) originally designed for PETCT coregistration, included in the center of four Plexiglas cubes of 1 × 1 × 1 cm. A spot of 2 mm diameter was drawn with standard white liquid corrector (TippEx®, Bic, Clichy, France) on top of each Plexiglas cube, exactly above the ^{68}Ge sources. The cubes were then glued permanently to a custom made transparent Plexiglas mouse supporting plate at four corners close to the position of the mouse on the plate (Figure 1A).
Animal experiments
Animal experiments were performed under an animal use and care protocol approved by the animal ethics committee and conducted in accordance with Directive 2010/63/EU of the European Parliament. Six female nude mice (body weight of approximately 25 g) were obtained from Elevage Janvier (Le Genest Saint Isle, France) and received a subcutaneous injection in the flank of 10^{6} PC12multiple endocrine neoplasis syndrome type 2A (MEN2A) cells [20]. The mice were anesthetized by continuous gaseous anesthesia (1–2% isoflurane in O_{2}) and imaged sequentially by fDOT and PET. The nearinfrared (NIR) fluorescent dye Sentidye® (20 nmol; Fluoptics, Grenoble, France) was injected 3 h before starting the fDOT acquisition at a volume of 100 μL. FDG (7,400 kBq in 100 μL; Flucis, IBA, France) was administered 1 h before the PET scan. Each mouse underwent a 20min fDOT acquisition followed by a 30min PET acquisition. The anesthetized mice were transferred from the fDOT to PET scanner by means of the mouse supporting plate, while great care was taken to avoid movement of the animal in regard to its support. The contact of the ventral side of a nude mouse with the Plexiglas surface of the mouse holder is sticky enough to ensure that the mouse is not moving when transferred between scanners located at the same room.
Acquisition of the optical images
Images were acquired in the 3D optical imager TomoFluo3D (Cyberstar, Grenoble, France) [7]. To obtain the position of the FM, two optical images covering both the subject and the FM were acquired with the mouse placed in prone position: (1) a planar white light image recorded from a camera snapshot yielding the x and y coordinates (Figure 1B), and (2) an image of the 3D surface of the animal, acquired by rapid consecutive camera shootings during axial scanning with an inclined green planar laser of the TomoFluo3D, yielding the z coordinates (Figure 1C). One image was recorded for each laser position during laser scanning of the animal in the axial direction, and all images were then combined into a single image [7]. A surface image of the animal was then reconstructed from the intersection curve between the surface of the animal and the surface of the supporting plate by triangulation [7].
The fDOT image was obtained by a 20min scan of a defined volume of interest covering the tumor using excitation by a 680nm laser on the anterior side of the animal [7] and recording with a CCD camera fixed above its dorsal side. The scanning grid consisted of 7 × 6 sources in steps of 2 mm, and the detection area was 15 × 13 mm^{2}. A 2 × 2 binning was applied, and the mesh volume corresponding to the detection area was mathematically discretized in voxels of 0.67 × 0.67 × 1 mm^{3} size to build the reconstruction mesh volume. Finally, the inverse problem of the tomographic reconstruction was solved with the algebraic reconstruction technique [7].
PET image acquisition
A 30min scan was acquired in a Focus 220 MicroPET scanner (Siemens, Knoxville, TN, USA). Image acquisition and reconstruction used the MicroPET Manager Software (SiemensConcorde Microsystems) based on a filtered backprojection algorithm. The attenuation correction was based on the segmentation of the emission map [21]; the dimensions of reconstruction volumes were 256 × 256 × 95 with a voxel size of 0.475 × 0.475 × 0.796 mm^{3}. The counts were decaycorrected and expressed in Bq/cm^{3}.
Image coregistration
As the three optical images (white light image, surface image and fDOT reconstruction) were acquired in the same spatial referential, the transformation matrix between the fDOT image and the white light image T
_{
fDOT−photo
} is calculated using the intrinsic parameters of fDOT. Hence, the T
_{
fDOTPET
} transformation matrix for fDOT to PET coregistration is a product of T
_{
fDOTphoto
} and T
_{
photoPET
}:
{T}_{fDOTPET}={T}_{fDOTphoto}\times {T}_{photoPET}
(1)
The coregistration (T
_{
photoPET
}) method was processed in four steps:

1.
Detection of the optical planar (x, y) FM coordinates.
The TippEx® spot drawn on the top of each Plexiglas cube helped visualize the planar position of the FM in optical images. Four squareshaped regions of detection (ROD) were assigned onto predetermined positions in the planar white light image (Figure 1B). Each ROD had a size of 6 × 6 mm, corresponding to 30 × 30 pixels in the concatenated mouse photograph, i.e., three times larger than the TippEx® spots' dimensions in order to obey the NyquistShannon sampling theorem [22] while avoiding parasite signals from the mouse body. The first step consisted in the automatic detection of the x and y coordinates of the FM based on the maximal intensity inside the corresponding RODs (Figure 1B). Three image preprocessing steps were then performed successively: (1) filtering with a 3 × 3 median filter that eliminated most of the noise present in the RODs, (2) highpass thresholding of image pixel intensities at a threshold value of 90 % of the maximum intensity and (3) application of a Deriche's recursive Gaussian filter [23] in order to center the gradient intensity change in the images of the TippEx® spots. Following these three steps, the coordinates of the local maximum intensity in each ROD coincided with the center of the FM signal given by the TippEx® spots in the planar white light image and assigned positions (x
_{opt}, y
_{opt}) of the FM.

2.
Detection of the optical altitude (z) FM coordinates.
Since the optical surface image (Figure 1C) and the planar white light image are concatenated in the same orientation and the same pixel size, the (x, y) coordinates in both images correspond directly. The intensity values of the optical surface image representing the distance between the upper surface of the FM and the supporting plate were measured at position x
_{opt}, y
_{opt} to yield the z 0_{opt} value of the upper surface of the FM. Altogether, the combination of the optical surface image and the planar white light image allowed assigning full 3D coordinates (x
_{opt}, y
_{opt}, z 0_{opt}) to each FM in the optical image.

3.
Detection of PET FM coordinates.
Four 3D RODs of 9 mm^{3} (dimensions three times larger than the dimension of FM signal in PET image) were defined in the PET volume image (Figure 1E). Following completion of the same image preprocessing steps as for the detection of the optical planar coordinates, the local maximum was detected in each ROD to yield the coordinates (x
_{PET}, y
_{PET}, z
_{PET}) of the FM in the PET volume image. Since the optical and PET signals from the FM do not coincide in the z dimension (i.e., the optical signal is on top of the Plexiglas cube, and the PET signal inserted inside the cube), a distance dz was added to account for translation in the z direction after the calculation of the rigid transformation matrix between the optical and PET image.

4.
Transformation from the mouse photograph to the PET volume.
A rigid transformation with translation and rotation was applied to coregister the optical and PET coordinates of the FM. With Po = {Po
_{1}, Po
_{2}, Po
_{3}, Po
_{4}} and Pp = {Pp
_{1}, Pp
_{2}, Pp
_{3}, Pp
_{4}} being the four FM positions in the optical and the PET volume images, respectively, the translation T and rotation R were defined as Equation 2:
Pp=R\ast \mathbf{P}\mathbf{o}+\mathbf{T}
(2)
The algorithm to compute the transformation R, T used the singular value decomposition (SVD) [24] approach to find the least square error criterion (Equation 3),
\sum _{i=1}^{N}E=\sum _{i=1}^{N}{\left\leftPpi\left(RPoi+T\right)\right\right}^{2}\text{,}\phantom{\rule{0.25em}{0ex}}\left(\text{where}N=4\text{is the number of FM}\text{.}\right)
(3)
The point sets {Pp
_{
i
}} and {Po
_{
i
}} were imposed the same centroid for calculating rotation:
\begin{array}{l}\overline{Pp}=\frac{1}{N}\sum _{i=1}^{N}P{p}_{i}\phantom{\rule{2em}{0ex}}\widehat{P}{p}_{i}=P{p}_{i}\overline{Pp}\\ \overline{Po}=\frac{1}{N}\sum _{i=1}^{N}P{o}_{i}\phantom{\rule{2em}{0ex}}\widehat{P}{o}_{i}=P{o}_{i}\overline{Po}\end{array}
(4)
Rewriting and reducing Equation 3:
\begin{array}{c}\phantom{\rule{3.8em}{0ex}}\sum _{i=1}^{n}E=\sum _{i=1}^{N}{\left\left\widehat{P}{p}_{i}\widehat{R}\phantom{\rule{0.12em}{0ex}}\widehat{P}{o}_{i}\right\right}^{2}\\ =\sum _{i=1}^{N}\left(\widehat{P}{p}_{i}^{T}\phantom{\rule{0.12em}{0ex}}\widehat{P}{p}_{i}+\widehat{P}{o}_{i}^{T}\phantom{\rule{0.12em}{0ex}}\widehat{P}{o}_{i}2\widehat{P}{p}_{i}^{T}\phantom{\rule{0.12em}{0ex}}\widehat{R}\phantom{\rule{0.12em}{0ex}}\widehat{P}{o}_{i}\right)\end{array}
(5)
Transformation was expressed as Equation 6:
\widehat{T}=\overline{Pp}\widehat{R}\phantom{\rule{0.12em}{0ex}}\overline{Po}
(6)
The \widehat{R}, \widehat{T} is the optimal transformation that maps the set {Pp
_{
i
}} to the {Po
_{
i
}}. Equation 5, also known as the orthogonal Procrustes problem [24, 25], is minimal when the last term is maximal.
The optical images, being proportionally larger than the PET image due (1) to the difference in the pixel size between the optical planar image (0.21 × 0.21 mm) and the PET image (0.47 × 0.47 mm), and (2) to the parallax induced by the camera detecting the TippEx® spots from the upper surface of the cube, a scaling factor was applied by calculating the average distance of the points in the x and y axes between the two modalities as (do
_{
x
}
, do
_{
y
}) and (dp
_{
x
}
, dp
_{
y
}):
\begin{array}{c}d{o}_{x}=\left[\left(P{o}_{2}\left(x\right)P{o}_{1}\left(x\right)\right)+\left(P{o}_{4}\left(x\right)P{o}_{3}\left(x\right)\right)\right]/2\\ d{p}_{x}=\left[\left(P{p}_{2}\left(x\right)P{p}_{1}\left(x\right)\right)+\left(P{p}_{4}\left(x\right)P{p}_{3}\left(x\right)\right)\right]/2\\ d{o}_{y}=\left[\left(P{o}_{3}\left(y\right)P{o}_{1}\left(y\right)\right)+\left(P{o}_{4}\left(y\right)P{o}_{2}\left(y\right)\right)\right]/2\\ d{p}_{x}=\left[\left(P{p}_{3}\left(x\right)P{p}_{1}\left(x\right)\right)+\left(P{p}_{4}\left(x\right)P{p}_{2}\left(x\right)\right)\right]/2\end{array}
(7)
A 2 × 2 scaling matrix was then built:
S=\left[\begin{array}{ccc}\hfill {S}_{x}\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill {S}_{y}\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill {s}_{z}\hfill \end{array}\right]
(8)
where Sx=\frac{d{o}_{x}}{d{p}_{x}}, Sy=\frac{d{o}_{y}}{d{p}_{y}} and S z = 1 (i.e., no scaling in the z direction).
After correcting for distance dz, the final transformation matrix T
_{
photoPET
} for the optical photograph to the PET volume was:
{T}_{photo\u2013PET}=\left[\begin{array}{cccc}\hfill \widehat{R}{S}_{11}\hfill & \hfill \widehat{R}{S}_{12}\hfill & \hfill \widehat{R}{S}_{13}\hfill & \hfill \widehat{T}x\hfill \\ \hfill \widehat{R}{S}_{21}\hfill & \hfill \widehat{R}{S}_{22}\hfill & \hfill \widehat{R}{S}_{23}\hfill & \hfill \widehat{T}y\hfill \\ \hfill \widehat{R}{S}_{31}\hfill & \hfill \widehat{R}{S}_{32}\hfill & \hfill \widehat{R}{S}_{33}\hfill & \hfill \widehat{T}z\hfill \end{array}\right]
(9)
where RS are the rotation matrix elements R multiplied by the scaling matrix elements S of Equation 8.
Applying the matrix in Equation 9 to the optical photography (Figure 1F) aligned the 3D PET image (Figure 1G) to yield the coregistered bimodal image shown in Figure 1H.
The barycenterbased method
The barycenterbased method [13–18] calculates average location of body's mass weighted in space. The barycenter was calculated as the center of mass B of a system (i.e., all voxels within the RODs) defined as the average of their positions ri, weighted by their mass mi:
B=\frac{\sum {m}_{i}{r}_{i}}{\sum {m}_{i}}
(10)
For the mouse photograph, as the barycenter was calculated in two dimensions, the left upper corner of each ROD was taken as origin, and the vector r
_{
i
} corresponded to the relative position from this origin to each pixel within the ROD. The signal intensity of each pixel inside the ROD gave the value of m
_{
i
}. For the PET image, the barycenter was calculated in 3D, and the position of the first voxel (left upper in coronal view and first section in the z direction) of the 3D ROD was taken as the origin. The position of each voxel relative to this point was taken as r
_{
i
} and the value of each voxel as m
_{
i
}. The barycenter calculated for each ROD represented the FM's position.