Improvement of Fluorescence Tomography
Reconstructions with Higher Order Born Approximation of
Diffuse Photon Density Waves
Lionel Hervé, Anabela Da Silva, Anne Koenig, Jean-Marc Dinten, Jérôme Boutet, Michel Berger,
Isabelle Texier, Philippe Peltié, Philippe Rizo.
LETI-CEA Recherche Technologique, 17 rue des martyrs 38054 Grenoble cedex 9 France
lionel.herve@cea.fr
Abstract: We present the results of a fluorescence tomography experiment which shows that
the quality of the fluorescence reconstruction is improved when the forward model is corrected
from the optical properties variations of the probed medium.
OCIS codes : (170.0170)Medical optics and biotechnology; (170.3010) Image reconstruction techniques; (170.3660) Light
propagation in tissues; (260.2510) Fluorescence.
1. Introduction
Fluorescence tomography modality is envisioned to be an economical functional quantitative measure and could
benefit to the pharmacological industry for experiments on small animal. It consists in injecting cancer specific
fluorescence marker and reconstructing the fluorescence by using the fluorescence tomography technique. The
reconstructed fluorescence can be used as a marker of the cancer activity to evaluate the efficiency of treatments.
Currently, the technique is limited by the large heterogeneities of biological tissues which create artefacts on the
reconstruction and reduce the quality of the subsequent analysis. Here, we describe how we take these
heterogeneities into account and show the efficiency of our method through a phantom experimental validation.
2. Experimental setup – Phantom geometry
Fluorescence tomography experiments consist in illuminating a highly scattering medium with near infrared light
(excitation wavelength) and measuring the transmitted light at two wavelengths (at the excitation and the
fluorescence wavelengths) thanks to the use of filters placed in front of the camera (Fig 1).
CCD Camera
Filter
cylindrical-shaped box
Turbid medium
6mm
15mm
Fluorescence tank
6.5mm
1.5mm
positions for the excitation laser
Fig 1- Geometry of a fluorescence tomography experiment
Our light source is a continuous laser (690nm, 26 mW, Powertechnology) beam coupled into a multimode optical
fibre and focused by a lens to a single spot underside the studied medium. The fibre and the lens are driven by two
motorized translation stages (Newport) that allow XY scanning of the specimen over a distance of 100 x 100 mm.
At each step of the laser spot, light is collected from the specimen and imaged onto the cooled CCD camera
(Hamamatsu 12 bits Orca-ER chosen for its high sensitivity in the NIR and working in 2x2 binning) using a 25 mm
f/l objective. Fluorescence filtering is achieved through a couple of filters (Schott high pass RG9 and Schott narrow
bandpass) mounted in front of the objective.
For this experiment, we position a cylindrical tank (interior dimensions: diameter=6 mm, height=6.5mm) filled
with 1mol/L of Alexa750 fluorophore positioned at 1.5mm from the bottom of a cylindrical-shaped box
(diameter=110 mm) filled up with a scattering liquid (mixture of water, black India ink as the absorber and intralipid
(Fresenius Kabi) as the scattering medium).
The laser source describes a 7 by 7, 3mm sampled grid. A 2.42.4cm2 region of interest is extracted from the
CCD camera images and resampled to create a 3333 pixels images.
3. Theory
Our goal is to solve the following equation [1][2]:  s (rd ) 
fl

V
G (rs , r ). X (r ).G (r , rd )dr , where the unknown
X represents the fluorescence map of the medium, rs is the position of the source indexed by s, rd is the position of
the detector indexed by d, V is the reconstruction volume,  s ( rd ) is the fluorescence signal detected at rd when
fl
the source s is used and G(r,r’) describes the transmission of the light from location r to location r’. Its discretized
version is:
U sdfl  m1 Gsm .Gmd . X m
M
(1)
where U sd =  s ( rd ) and M represents the number of mesh elements. In the same way, the excitation photon wave
fl
fl
follows the equation:  s ( rd )  G ( rs , rd ) which discretized equation is:
exc
U sdexc  Gsd
(2)
In reference [3], the authors demonstrate that the resolution of the Eq 3.1, ratio of (1) over (2) is very robust
since the use of analytical functions G0 obtained for a homogeneous medium (denoted by the superscript 0) leads to
accurate reconstructions in the experiments conducted on heterogeneous media. Thus, the utilization of Eq 3.2 is the
way used currently to take into account heterogeneities of the medium for fluorescence tomography reconstructions.
0
0
U sdfl
M Gsm .Gmd

m1 G 0 .X m
U sdexc
sd
(3.1)
U sdfl
M G .G
 m1 sm md . X m
exc
Gsd
U sd
(3.2)
(3)
In this paper, we show that the use of G functions adapted to the inhomogeneous medium (Eq 3.2) allows better
reconstruction of the fluorescence map.
The calculation of the transfer functions Gs for an inhomogeneous medium follows the mathematical
derivations detailed in the reference [4]. Gs are deduced from the difference U sd  U sd between the
exc
0 exc
measurements and U sd
parameters

0
a
0 exc
which is the measure we would have for a homogeneous medium with known optical
and  ' (respectively the homogeneous absorption and reduced scattering coefficients). It can be
0
s
obtained by repeating the experiment described in part 2 without the fluorescent cylindrical reservoir or by using, as
0 exc
we did, an analytical forward model U sd
  .Gsd0 where the parameter which depends on the source power, is
calibrated.
4. Results
The grid for the attenuation and fluorescence reconstruction is a 141415 mesh. We first reconstruct the
attenuation map of the medium along with the G functions corrected from the medium attenuation variations. Fig. 2left represents horizontal sections of the computed attenuation map versus increasing z values. It shows the presence
of a cylindrical region of low attenuation (here represented as white) at 2.5mm<z<9.5mm, explained by the fact that
no ink was added in the fluorescent solution.
We then reconstruct the fluorescence map by solving Eq 3.1 or Eq. 3.2 (20 iterations of ART (algebraic
reconstruction technique), relaxation=0.01). Fig 2-middle shows the 3D fluorescence map reconstructed. Fig 2-right
shows a section of the reconstruction volume at z=0,45cm. We computed the z-mean value and the standard
deviation according to the directions of the distribution of the reconstructed fluorescence map in order to quantify
the accuracy of the position and the shape of the reconstructions. These figures are given in the of Fig 3 which
shows the reconstruction with corrected G functions (Eq 3.2) is closer to the expected values than non corrected
reconstruction (Eq 3.1) especially when the z resolution is considered. Vertical profiles of the two distributions in
the axis of the fluorophore tank are also given on Fig 3 which shows the z-localization and z-resolution are better
when the reconstruction is performed with corrected transfer functions.
Z1 = 0.05 cm
Z1 = 0.05 cm
Z2 = 0.15 cm
Z3 = 0.25 cm
Z4 = 0.35 cm
Z5 = 0.45 cm
Z6 = 0.55 cm
Z7 = 0.65 cm
Z8 = 0.75 cm
Z9 = 0.85 cm
Z10 = 0.95 cm
Z11 = 1.05 cm
Z12 = 1.15 cm
Z13 = 1.25 cm
Z14 = 1.35 cm
Z15 = 1.45 cm
Z5 = 0.45 cm
Z9 = 0.85 cm
-0.01
0
Z
Z
Z
0.01
Fig 2 Attenuation map of the medium. High values of the parameter correspond to low attenuation (Left). 3D representation of the
reconstructed fluorescence map, with the position of the sources (x) and the position of a plane of the meshes (.) (middle). Extraction
of the median section of the fluorescence zone (right)
Z13 = 1.25 cm
0,007
Mean(Z)
4.9mm
With
Correction
(Eq 3.2)
4.8mm
Without
Correction
(Eq 3.1)
5.0mm
Standard deviation(X)
1.5mm
1.7mm
1.9mm
Standard deviation(Y)
1.5cm
1.8mm
2.0mm
Standard deviation(Z)
1.9mm
2.3mm
3.0mm
With correction
Without correction
0,006
fluorescence intensity (a.u.)
Expected
values
0,005
0,004
0,003
0,002
0,001
Position of the
fluorophore
0
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
-0,001
z position (mm)
Fig 3. Analysis of the fluorescence map distribution and vertical profiles obtained by the reconstructions with or without
corrected G functions
5. Conclusion
To obtain more accurate fluorescence tomography reconstruction, we recommend the use of G functions corrected
from variations of the optical properties of the studied object.
6. References
[1] M. S. Patterson and B. W. Pogue, “Mathematical model for time-resolved and frequency-domain fluorescence spectroscopy in biological
tissues,” Appl. Opt. 33, 1963–1974 (1994)
[2] M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, "Fluorescence lifetime imaging in turbid media", Optics Letters, Vol. 21,
no. 2, 158-160 (1996)
[3] A. Soubret, J. Rippoll, V. Ntziachristos, “Accuracy of Fluorescent Tomography in the Presence of Heterogeneities: Study of the Normalized
Born Ratio”, IEEE Trans. on med imag. 24, no 10, 1377-86 (2005)
[4] E. Scherleitner, B.G. Zagar, “Optical Tomography Imaging Based on Higher Order Born Approximation of Diffuse Photon Density Waves”,
IEEE Trans. on instrum. and meas. 54, no 4, 1607-11 (2005)
Z