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Ultrasound modulated bioluminescence tomography (UMBLT) is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches to this problem require large numbers of optical measurements [10]. Here we propose an alternative solution for this inverse problem which requires only a single optical measurement in order to reconstruct the isotropic source. Specifically, we derive two inversion formulae based on Neumann series and Fredholm theory respectively, and prove their convergence under sufficient conditions. The resulting numerical algorithms are implemented and experimented to reconstruct both continuous and discontinuous sources in the presence of noise.
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Although cone-beam CT (CBCT) has been used to guide irradiation for pre-clinical radiotherapy(RT) research, it is limited to localize soft tissue target especially in a low imaging contrast environment. Knowledge of target shape is a fundamental need for RT. Without such information to guide radiation, normal tissue can be irradiated unnecessarily, leading to experimental uncertainties. Recognition of this need led us to develop quantitative bioluminescence tomography (QBLT), which provides strong imaging contrast to localize optical targets. We demonstrated its capability of guiding conformal RT using an orthotopic bioluminescent glioblastoma (GBM) model. With multi-projection and multi-spectral bioluminescence imaging and a novel spectral derivative method, our QBLT system is able to reconstruct GBM with localization accuracy <1mm. An optimal threshold was determined to delineate QBLT reconstructed gross target volume (GTV_{QBLT}), which provides the best overlap between the GTV_{QBLT} and CBCT contrast labeled GBM (GTV), used as the ground truth for the GBM volume. To account for the uncertainty of QBLT in target localization and volume delineation, we also innovated a margin design; a 0.5mm margin was determined and added to GTV_{QBLT} to form a planning target volume (PTV_{QBLT}), which largely improved tumor coverage from 75% (0mm margin) to 98% and the corresponding variation (n=10) of the tumor coverage was significantly reduced. Moreover, with prescribed dose 5Gy covering 95% of PTV_{QBLT}, QBLT-guided 7-field conformal RT can irradiate 99.4 pm 1.0% of GTV vs. 65.5 pm 18.5% with conventional single field irradiation (n=10). Our QBLT-guided system provides a unique opportunity for researchers to guide irradiation for soft tissue targets and increase rigorous and reproducibility of scientific discovery.
We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the minimization of a bending energy with respect to shape and density and can be considered as a one-dimensional analogue of the Canham-Helfrich model for heterogeneous biological membranes. We present a generalized Euler-Bernoulli elastica functional featuring a density-dependent stiffness coefficient. In order to treat the inherent nonconvexity of the problem we introduce an additional length scale in the model by means of a density gradient term. We derive the system of Euler-Lagrange equations and study the bifurcation structure of solutions with respect to the model parameters. Both analytical and numerical results are presented.
Quantum measurement is essential to both the foundations and practical applications of quantum information science. Among many possible models of quantum measurement, feedback measurements that dynamically update their physical structure are highly interesting due to their flexibility which enables a wide range of measurements that might otherwise be hard to implement. Here we investigate by detector tomography a measurement consisting of a displacement operation combined with photon detection followed by a real time feedback operation. We design the measurement in order to discriminate the superposition of vacuum and single photon states -- the single-rail qubit -- and find that it can discriminate the superposition states with a certainty of 96%. Such a feedback-controlled photon counter will facilitate the realization of quantum information protocols with single-rail qubits as well as the non-locality test of certain entangled states.
We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photo- and thermoacoustic tomography and Sonar, and provide artifact reduction strategies. In particular, our theorems show that it is better to arrange Sonar detectors so that the boundary of the set of detectors does not have corners and is smooth. To illustrate our results, we provide reconstructions from synthetic spherical mean data as well as from experimental photoacoustic data.
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field associated with the moving quantities from a single boundary measurement. This properties will be associated with some general class of time independent coefficients that we recover from a single Neumann boundary measurement, on some parts of the boundary, of the solution of our diffusion equation with a suitable boundary input, located on some parts of the boundary.
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