Fluorescence Diffuse Optical Tomography of heterogeneous
complex shape objects
L. Hervé, A. Koenig, A. Da Silva, J. Boutet, M. Berger, J.M. Dinten, P. Peltié, P. Rizo
micro Technologies for Biology and Healthcare Division,
CEA, LETI, MINATEC, Grenoble, F-38054, France
lionel.herve@cea.fr
Abstract: External shape management is challenging for fluorescence tomography. We implement the finite
differences method with arbitrary boundaries and present validations on a phantom and on a mouse with a
fluorescent tube inserted inside the lungs.
OCIS codes: (170.0170) Medical optics and biotechnology; (170.3010) Image reconstruction techniques; (170.3660) Light
propagation in tissues; (260.2510) Fluorescence
1. Introduction
Near-infrared fluorescence-enhanced Diffuse Optical Tomography (fDOT) is an emerging modality for obtaining
quantitative functional measurements. It consists in using optical excitation and measurements in order to
reconstruct the 3D distribution of a fluorescent specific marker which may be a surrogate of any biological activity.
In particular, it is shown that this technique is suitable to monitor cancer evolution in small animals.
A recurrent challenge for the fDOT technique is the management of complex geometries. Indeed, since the
forward model strongly depends on the boundary location and this latter varies for each animal experiment, it must
be recomputed for each observation and fast not to limit the throughput of the system. To date, there exist two
methods to compute forward model with an arbitrary external shape: either by using an integral term [1,2,3] to
correct an analytical expression or by using the finite element method (FEM)[4,5]. In the first case turbid medium is
supposed to have homogeneous optical properties and in the second case, the computation cost is high.
We previously reported the use of the finite differences method to manage heterogeneous media for fDOT
reconstructions. Here, to compute the forward model, we adapt the method to take into account arbitrary 3D shapes.
It is suitable for any optical properties map, any animal shape and is time-efficient. The reconstruction algorithm is
validated on a phantom and a mouse experiments performed on our laboratory made fDOT acquisition system. The
approach is being validated for the follow-up of lungs tumors of mouse models and the results will be presented at
the Biomed 2008 symposium.
2. Method
Acquisitions were performed on the non contact continuous wave optical tomography system described in [6]. It is
composed of a 690 nm laser mounted on a motorized stage, which excites the medium at its bottom side and a CCD
camera which registers the outgoing light at the top side. The excitation laser typically describes a 10 by 10 grid of 2
mm spaced points and at each of these positions, the excitation and emission signals are recorded with the CCD
camera equipped with dedicated filters. Since a typical a 2 cm by 2cm detection ROI is undersampled into 40 by 40
detection points, we have to process about 210104040=320 000 measurements per examination.
In addition to the system described in [6], a plan laser was added to scan the surface of the studied object. Since
the angle between the light plan and the vertical axis is 45°, the object surface Surf(x,y) can be restituted by
triangulation with the CCD camera mentioned above.
The light in the medium  is supposed to obey the simplified diffusion equation (1)
 2  s ( r )  k 2 ( r ) s ( r )   S s ( r )
(1)
where r is the spatial coordinates, s is the source position index, s(r) is the photon density, Ss(r) is the source term,
and k 2 (r )  3 a (r )  s (r ) is the optical property map of the light, a(r) being the attenuation coefficient and s(r)
being the scattering coefficient. The description is completed with partial current boundary conditions on d(2)


 s (r ).n   s (r )
(2)

where n is the outward normal vector to the boundary determined from Surf(x,y), and  is related to the index
mismatch at the boundary. The set of equations (1) and (2) is discretized in the finite differences way on a mesh with
a typical spacing of 2mm  2mm  1mm on the x,y and z axis. In particular, equation (2) is expressed by inserting
external points to the mesh grid and by using the extrapolated boundary condition. The obtained system is As=Ss,
thus the whole set of  is obtained by solving for the whole set of sources. To speed up the computation, the LU
decomposition is used.
As explained in [6], our reconstruction algorithm is based on the determination of k2(r) by using the
excitation measurements. Since the solution of equation (1) is nonlinearly related to k2(r), its reconstruction implies
to compute the forward model at each iteration and it justifies the need to use fast method (finite differences instead
of finite elements) to do it. Then, by using the reality-adjusted model, the fluorescence yield is computed by solving
(3) with the ART (Algebraic reconstruction technique with the relaxation parameter set to 0.1):
(3)
 s (r ) X (r )Gd (r )dr  sdm


where Gd (r ) is the Green function associated with equation (1), X(r) is the fluorescent yield map and
 sdm is the
emission measurement obtained at the detector position d for the source s. This method has already been applied on
in vivo longitudinal studies for small animals put between plates and has allowed the follow up of a growing cancer
in a mouse [7]. The total reconstruction time is about 5 minutes.
4. Validation on a phantom
A half cylinder solid phantom described in ref [6] was used to validate the non contact approach developed above
(Fig. 1). A fluorescent dot was inserted at a border of the phantom at 1.2 cm above the ground. In this experiment,
10 × 10 source positions with a 2 mm separation were considered. The CCD camera images of the phantom were
resampled to create 45 × 45 pixel images covering a 2.2 × 1.8 cm2 field of view. A nominal reconstruction mesh
composed of 12 ×12 × 26 elements with a volume element of 0.2 × 0.2 × 0.1 cm3 was used.
As explained above, the surface was scanned with a planar laser to include the description of external
boundaries of the studied object in the direct model. The obtained surface is represented in Fig 1. right and
corresponds well to the phantom geometry (the maximum height is flat and equal to the nominal value (2.5 cm), the
width of the phantom is correct).
The reconstructed fluorescence yield is presented on Fig. 1. This figure shows that the fluorescence tubes are
correctly reconstructed and are close to the expected position: the lateral position is in the alignment of the syringe
(Fig 1. left) head and recovered mean vertical position is found at 1.39 cm. As it can be seen on Fig. 1 right, the
recovered fluorescence has a vertical dispersion (4.3mm) much bigger than the lateral one (1.5mm) in accordance
with the fact that the lateral resolution of the system is much better than the vertical resolution.
50
100
150
200
250
300
350
400
450
500
100
200
300
400
500
600
Fig. 1: reconstruction of the fluorescent yield for the half cylinder phantom case. At left is presented the superimposition of the
fluorescent reconstruction with the phantom image; the black dot represents the recovered fluorescence. At right, the acquisition
of the phantom surface and the fluorescence reconstruction are presented.
4. Validation on a mouse
We conducted in vivo experiments on female Swiss nude mice in order to valid the surface acquisition of the animal
and its use in the reconstruction process. For the experiment, the mouse lies on its dorsal face over the heating
support. The surface acquisition is done over the tomography area (here lungs area) and is represented in Fig.2 (left).
We inserted a capillary tube in the mouse trachea in order to validate the reconstruction approach. The capillary
tube was filled with a solution of Intralipid and Alexa 750, 20 µM. The mouse is anesthetized and imaged over the
lungs area. The near infra-red laser describes an 11 by 11, 2 mm spaced grid under the mouse. The reconstructed
volume is about 5.8 cm3 over 9 x 10 x 16 voxels with a sampling rate of 2 mm in x and y and 1 mm in z.
Figure 3 presents the reconstructed volume superimposed over the black and white image of the mouse. The
capillary is satisfactory reconstructed in the 10 and 11 mm planes, for a 15 mm mouse thick.
Position of the fluorescent tube
Image courtesy of IAB
Fig. 2: At left, mouse surface calculated over the lungs area. In the middle, the reconstructed volume is presented alone in 3D; the
fluorescent tube is visible. At right, we present the volume superimposed over the black and white image of the mouse.
5. Conclusions
The integration of arbitrary external shape in the forward model allows animal examination without adaptation
liquid or compression plates and may increase the appealing of the fDOT technique to the biologists. We showed
that, even when the forward model is computed repeatedly and the 3D shape is taken into account, the process time
(5 minutes) does not exceed the acquisition time (10 minutes) and is no limitation to the system throughput.
The details of our formalism for the surface management and the interpolation of the boundary conditions will be
presented at the Biomed2008 symposium.
The authors would like to acknowledge J.L. Coll from INSERM U578 (Institute Albert Bonniot, Grenoble,
France) and V. Josserand from ANIMAGE (Bron, France) for having provided, prepared and carried out the mouse
experiments.
6. References
[1] R.B. Schulz, J. Ripoll, V. Ntziachristos, “Experimental Fluorescence Tomography of Tissues With Noncontact Measurements IEEE trans. on
Med. Imaging, 23(4), 492-500 (2004).
[2] J. Ripoll, R.B. Schulz, V. Ntziachristos, “Free-Space Propagation of Diffuse Light: Theory and Experiments”, Phys. Rev. Let. 91(10), 103901
(2003).
[3] J. Rippol, V. Ntziachristos “From Finite to Infinite Volumes: Removal of Boundaries in Diffuse Wave Imaging”, Phys. Rev. Let., 96, 173903
(2006).
[4] S. R. Arridge and M. Schweiger, "Photon-measurement density functions. Part 2: Finite-element-method calculations," Appl. Opt. 34, 802637 (1995)
[5] F. Fedele, J.P. Laible , M.J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography - Theory and
vectorized implementation”, Journal of Computational Physics. 187(2), pp. 597-619. 20 (2003)
[6] L. Hervé, A. Koenig, A. Da Silva, M. Berger, J. Boutet, J. M. Dinten, P. Peltié, and P. Rizo, "Noncontact fluorescence diffuse optical
tomography of heterogeneous media," Appl. Opt. 46, 4896-4906 (2007)