Fluorescence tomography seeks to image an inaccessible fluorophore distribution inside an object like a small
animal by injecting light at the boundary and measuring the light emitted by the fluorophore. Optical parameters
(e.g. the conversion efficiency or the fluorescence life-time) of certain fluorophores depend on physiologically
interesting quantities like the pH value or the oxygen concentration in the tissue, which allows functional rather
than just anatomical imaging.
To reconstruct the concentration and the life-time from the boundary measurements, a nonlinear inverse
problem has to be solved. It is, however, difficult to estimate the uncertainty of the reconstructed parameters in
case of iterative algorithms and a large number of degrees of freedom. Uncertainties in fluorescence tomography
applications arise from model inaccuracies, discretization errors, data noise and a priori errors. Thus, a Markov
chain Monte Carlo method (MCMC) was used to consider all these uncertainty factors exploiting Bayesian
formulation of conditional probabilities.
A 2-D simulation experiment was carried out for a circular object with two inclusions. Both inclusions had
a 2-D Gaussian distribution of the concentration and constant life-time inside of a representative area of the
inclusion. Forward calculations were done with the diffusion approximation of Boltzmann's transport equation.
The reconstruction results show that the percent estimation error of the lifetime parameter is by a factor of
approximately 10 lower than that of the concentration. This finding suggests that lifetime imaging may provide
more accurate information than concentration imaging only.
The results must be interpreted with caution, however, because the chosen simulation setup represents a
special case and a more detailed analysis remains to be done in future to clarify if the findings can be generalized.
Fluorescence tomography aims at the reconstruction of the concentration and life-time of fluorescent inclusions
from boundary measurements of light emitted. The underlying ill-posed problem is often solved with gradient
descent of Gauss-Newton methods, for example. Unfortunately, these approaches don't allow to assess the
quality of the reconstruction (e.g. the variance and covariance of the parameters) and also require the tuning of
We intend to mitigate this drawback by the application of topological derivatives and Markov-chain Monte-Carlo (MCMC) methods for solving the inverse problem. This submission focuses on the topological derivative,
which is used for the initialization of the MCMC code. The basic idea is to probe every location inside the
domain with an infinitely small fluorescent ball and to estimate the effect of such a perturbation on the residual,
which is the difference of the theoretically predicted data to the true measurement. Obviously, the reconstructed
inclusions should be placed at locations for which the topological derivative is significantly negative, i.e. where
the residual decreases.
Previous results show that usual first-order approximations deteriorates for probe inclusions close to the
boundary. This seems to be a particular feature of certain inverse problems such as fluorescence tomography or
electrical impedance tomography. Fortunately this flaw may be corrected using a few higher-order terms which
may be explicitly determined With this extension the topological derivative can be utilized as a one-step method
for the determination of the number of inclusions and their approximate locations. This outcome is used as
initialization for the MCMC algorithm.
Fluorescence tomography excites a fluorophore inside a sample by light sources on the surface. From boundary measurements of the fluorescent light, the distribution of the fluorophore is reconstructed. The optode placement determines the quality of the reconstructions in terms of, e.g., resolution and contrast-to-noise ratio. We address the adaptation of the measurement setup. The redundancy of the measurements is chosen as a quality criterion for the optodes and is computed from the Jacobian of the mathematical formulation of light propagation. The algorithm finds a subset with minimum redundancy in the measurements from a feasible pool of optodes. This allows biasing the design in order to favor reconstruction results inside a given region. Two different variations of the algorithm, based on geometric and arithmetic averaging, are compared. Both deliver similar optode configurations. The arithmetic averaging is slightly more stable, whereas the geometric averaging approach shows a better conditioning of the sensitivity matrix and mathematically corresponds more closely with entropy optimization. Adapted illumination and detector patterns are presented for an initial set of 96 optodes placed on a cylinder with focusing on different regions. Examples for the attenuation of fluorophore signals from regions outside the focus are given.
With the increasing importance of molecular imaging fluorescence based methods are continuously gaining impact.
In fluorescence optical tomography excitation light is injected into the tissue where the fluorophore converts
it to radiation of another wavelength. From the emitted light reaching the boundary the 3-D distribution of the
fluorophore is reconstructed. This paper aims at finding the optimal spatial distribution of optodes in order to
keep their number (hardware costs) low while gaining maximum information from the target object.
The implemented algorithm starts with an arbitrary pool of feasible optodes. The optimal subset is searched
by minimizing the mutual information between the different measurements. This goal is reached by subsequently
removing those sources and detectors which add the least independent information until a stopping criterion is
Mutual information is estimated by calculating the inner products between the rows of the sensitivity matrix
i.e. the first derivative of the forward mapping with respect to the optical parameters to be reconstructed. We
assembled this matrix with a finite element implementation of the diffusion approximation of light propagation
in scattering tissues. When starting with an initial pool of 96 optodes regularly spaced on a cylindrical surface
and focusing on different target regions within the cylinder, the algorithm always converged towards physically
reasonable optimal sets. Optimal source/detector patterns are be presented graphically and numerically.