August 10, 2010 / Vol. 8, No. 8 / CHINESE OPTICS LETTERS 787
An experimental investigation on two-dimensional
shape-based diffuse optical tomography
Pingqiao Ruan (
)
1
, Feng Gao (
)
1,2∗
, Fang Yang (
DZDZDZ
)
1
, and Huijuan Zhao (
)
1,2
1
College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China
2
Tianjin Key Laboratory of Biomedical Detecting Techniques and Instruments, Tianjin 300072, China
∗
E-mail: gaofeng@tju.edu.cn
Received January 26, 2010
A two-dimensional (2D) shape-based approach of image reconstruction using a boundary element method
is developed for diffuse optical tomography (DOT). The experimental validation uses a four-channel time-
correlated single photon counting (TCSPC) system for detection and an intensity data-type for image
reconstruction. The optical and geometric parameters are simultaneously recovered using a difference
imaging scheme. Results demonstrate that the proposed DOT modality is a promising methodology of in
vivo reconstruction of the optical structures of tissues.
OCIS co des: 170.3880, 170.6960, 170.3010, 170.3660.
doi: 10.3788/COL20100808.0787.
Fluorescence molecular tomography (FMT) is a novel op-
tical imaging modality for visualizing the biochemical
events located deep inside intact living organisms with
molecule-specific fluorescent agent
[1]
. Researchers have
demonstrated that knowledge on optical properties distri-
bution in tissues significantly affects FMT
[2]
.Toprovide
optical priors for enhanced fluorescence reconstruction,
a combination of FMT and diffuse optical tomography
(DOT) is desirable.
DOT is a noninvasive medical imaging technology that
probes internal optical properties and can provide both
anatomical images and functional information of tissues.
However, due to the strong scattering nature of most tis-
sue types and relatively limited number of available noisy
data, image reconstruction in conventional voxel-based
DOT has been a severely ill-posed inverse problem
[3]
.
One way of improving this situation is to take advantage
of prior information on the probability distribution of ex-
pected parameters based on anatomical structures
[4,5]
.
The use of the anatomical structures has allowed for
the reasonable postulation of the unknown body as being
composed of a number of sub-domains of different tissues,
and the interior optical parameter values as a piecewise
constant. In this case, we can parameterize the unknowns
of the inverse problem directly in terms of a small number
of parameters describing the shape, location, and optical
properties of each region. Since unknown boundaries are
typically modeled with some parametric shape functions,
the image reconstruction can thus be cast as a shape-
based DOT issue in order to simultaneously recover the
boundary-describing parameters and optical properties
of disjoint domains
[6]
.
With the recent advancement of DOT, the shape-based
image reconstruction schemes have also been proposed.
The use of boundary element method (BEM) for shape-
based imaging in DOT has been reported
[4]
.Inthat
work, the authors recovered the shape and optical prop-
erties of an inclusion from simulated DOT data using
an alteration strategy and based on the assumption that
background values are known and exact. In this let-
ter, a two-dimensional (2D) shape-based reconstruction
scheme for steady-state DOT is validated by a cylindrical
phantom. A difference imaging scheme is used to handle
noisy measurement data, as well as to achieve more ac-
curate parameter estimation. The optical coefficients of
the background are assumed as unknown and recovered
in the reconstruction.
The diffusion approximation (DA) with Robin bound-
ary condition has been frequently used in the modeling of
light propagation for biological tissues
[4]
. Based on the
assumption on multi-domain geometries, Ω = ∪
L
=1
Ω
,
which are separated by smooth interfaces Γ
( =
2, ··· ,L), and with the piecewise constant optical prop-
erties, the steady-state formulation of the diffusion ap-
proximation was equivalent to a set of coupled Helmholtz
equations
[7]
:
∇
2
Φ
(r)−k
2
Φ
(r)=−
q
(r)
κ
, r ∈ Ω
,=1, 2, ··· ,L (1)
with boundary conditions
Φ
−1
=Φ
,κ
-1
ˆn ·∇Φ
−1
= κ
ˆn ·∇Φ
on Γ
,
cΦ
1
+2κ
1
1+R
f
1 − R
f
ˆn ·∇Φ
1
=0 on ∂Ω, (2)
where Φ
(r) is the photon density; q
(r) denotes an inte-
rior isotropic source density in domain ;thewavenum-
bers k
associated with the Helmholtz equation in each
domain has the form of k
2
= μ
a
c/κ
, c is the speed of
light in the medium, μ
a
, μ
s
,andκ
= c/[3μ
s
]arethe
absorption, reduced scattering, and diffusion coefficients,
respectively; ˆn denotes unit normal vector outward to the
boundary; and R
f
is an internal reflection factor that ac-
counts for the difference in the refractive indices between
the two sides of the most outer boundary, ∂Ω.
If the closed interfaces Γ
are sufficiently smooth, they
can be approximated by the Fourier curve. With the
shape coefficients γ
= {γ
x
n
,γ
y
n
} for the boundaries of
each inner domain defined, the parametric description of
the curve was represented by the weighted average de-
1671-7694/2010/080787-04
c
2010 Chinese Optics Letters