Fluorescence Optical Tomography in Cylindrical
Geometry for Small Animal Multimodality Tomographer
A. da Silva , M. Leabad, J.-M. Dinten, Ph. Peltié, Ph. Rizo
LETI-CEA Recherche Technologique 17 rue des Martyrs, 38054 Grenoble Cedex 9, France
anabela.dasilva@cea.fr
Abstract : A small animal tomographer dedicated to co-registration of fluorescence optical signal
and X-rays measurements is under development. An exact analytical solution to the diffusion
equation used for modelling the optical forward problem has been established.
2006 Optical Society of America
OCIS codes: (170.5280) Photon Migration; (170.3010) Image Reconstruction Techniques; (170.3880) Medical and
Biological Imaging
1. Introduction
In the last few years, numerous groups [1-2] have validated the potential of near-infrared fluorescence-enhanced
Diffuse Optical Tomography (fDOT) as a mean for image reconstruction of the bio-distribution of fluorescent
markers. By tagging regions of interest with target-specific fluorescing molecular probes, this technique enables
estimation of three-dimensional (3D) locations and geometries of targeted areas, such as tumors. A variety of these
new “smart” probes are currently being developed [3]. In order to complete and to get the best benefit of small
animal examinations, there is an increasing need of multimodality imaging instruments. The purpose of such
systems is to offer the possibility to get, in vivo, both anatomical and functional information. Moreover, anatomical
measurements can also be used as a regularization factor in order to get the reconstructions of the biodistribution of
fluorochromes more accurate and to speed up the treatment.
X-rays radiography has been chosen as the anatomical imaging modality because of the accuracy of the
anatomical information it provides and its versatility. Fig. 1 shows how radiographic measurements can provide,
throughout dual energy processing, accurate information on mice skeleton. Moreover, X-rays can provide 3D
anatomical information through Computed Tomography (CT).
Fig. 1: Radiography of a mouse: a combination of high and low energy X-ray images (left) allows the recovery of both the
skeleton (bones image) and soft tissues (right).
This paper is dedicated to the presentation of the optical imaging system. The cylindrical geometry has been
naturally chosen as a compromise: i) this geometry is suitable with X-rays cone beam CT of the whole animal body;
ii) by immersing the animal in an index matching fluid, an analytical solution to the optical forward problem can be
derived and introduced in a reconstruction scheme.
The second part of this paper is devoted to the description of the model used for the resolution of the forward
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problem, and the general principle of the reconstruction technique (inverse problem). Then details on the
instrumentation and on the phantom experiments are provided. Finally, we conclude.
2. Description of the model
Fig. 2: Schematic and notations used (left), Photograph (center) and schematic (right) of the experimental setup
A finite cylinder with radius a and height l (Fig. 2) is considered. Its absorption coefficient is supposed to be  a and
diffusion coefficient D. An exact analytical solution to the diffusion equation used for modeling the optical forward
problem has been established. For this geometry, we proceeded by analogy with the classical solutions to the
equations of heat conduction in solids. According to the recommendations found in Ref. [4], and , by analogy with
the problem of conduction of heat in solids [5-6], an analytical solution to the diffusion equation, for a finite
cylindrical diffusing medium, has been established:

1 
m z
m z'   I n (rq m )
I n aqm K n r ' q m   K n aqm I n r ' q m cos n(   ' )
G cyl ( , r, r' ) 
sin
sin

Dl  m 1
l
l n   I n (aq m )


with
q m  k 02  m 2 2 l 2 and

k 02   a D  i c n D , Kn and In are respectively the first and second kind
modified Bessel functions of nth order. The solution for the fluorescence signal can then be expressed, in Continuous
Wave (CW) mode, as follows:
 fl rs , rd  
G
cyl
(1 , rs , r )  (r )Gcyl (2 , r , rd )dr
Volume
β is the conversion factor of the excitation light at a point r into fluorescence light. The volume of the cylinder is
then meshed into N voxels and the problem becomes a matrix inversion problem solved by a classical
reconstruction algorithm ( the Algebraic Reconstruction Technique has been chosen [7]).
3. Experiments
The optical system (Fig. 2) is basically composed with a laser beam for excitation of the fluorochromes, and a CCD
camera coupled with a chromatic filter for the fluorescence detection. The animal is placed inside a transparent tube
filled with an index matching fluid. In order to perform multiple views of fluorescence data acquisitions, the
cylinder is fixed to a rotating stage. The excitation beam is brought to the cylinder via two mirrors mounted on
translation plates allowing alignment and a translation vertical scan. The optical data acquisitions are performed
with a high sensitivity CCD camera (Hamamatsu). In complement to the optical system, a X-ray generator and a Xray detector have been placed perpendicularly to the optical chain.
The first validation experiments have been performed on a phantom consisting of a cylindrical transparent
plastic tube (Fig. 3a), filled with intralipid 0.5% (corresponding to a reduced scattering coefficient μs’ ~ 6 cm-1) and
India Black ink for absorption (μa ~ 0.1 cm-1). Two capillary tubes (Ø ~ 1 mm), filled with Cy5 fluorochromes (100
M) have been inserted inside (Fig. 3b). For this experiment, 120 different sources positions have been considered
(10 different rotation angles X 12 vertical translations). An image of one fluorescent data acquisition is presented on
Fig. 3c.
We first started by simulating the experiment by taking into account the actual geometry (actual sources,
detectors and fluorochromes positions) and perform the reconstruction on those noiseless synthetic data. Then, once
the reconstruction parameters fixed, the focus is made on reconstructions obtained from the experiments (Fig. 4).
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a)
b)
c)
Fig. 3: a) Cylindrical phantom without (left) and with (right) diffusing medium; b) Detailed scheme of the positioning of
the capillary tubes; c) Fluorescence signal collected through the chromatic filter via the CCD camera, for a given source
position.
Fig. 4: Example of experimental data reconstructions
Fig. 4 shows an example of reconstruction obtained with the optical system. Additional measurements have been
performed, with higher excitation wavelength, and with different fluorescent dyes.
4. Conclusion
An instrument, dedicated to coregistration of optical and X ray measurements, has been developed. The optical
reconstruction software is currently beeing validated: the first reconstructions obtained on both synthetic and
experimental data are satisfying. Experimental measurements, at different wavelengths, on cylindrical phantoms
with different fluorescent inclusions geometries have been also performed as a validation and will be presented at
BIOMED 2006 conference. The cylindrical analytical approach has been compared to a Finite Element Method
approach: analytical approach brings a significant gain of computing time. In our futur work, the anatomical
information brought by the X ray data will be exploited and introduced in the reconstruction scheme.
REFERENCES
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