Polarized light transport in refractive weak scattering media.

This paper is devoted to modeling of the light transport in refractive and weak scattering media by means of the vector radiative transfer equation. In refractive media polarization of light depends not only on the law of scattering but also on the refractive index distribution and can change along curved light trajectories according to the Rytov law of the polarization ellipse rotation. Results of numerical simulations are presented in the form of CCD camera images, which is how data are acquired in tomographic imaging experiments.

Light transport in refractive turbid media.

Light scattering in refractive media can be used for visualization of caustics and singularities of wavefronts of the incident radiation. Its modeling requires solving the radiative transfer equation. Numerical solution of the radiative transfer equation in turbid media with a spatially varying refractive index is presented and discussed in this paper. The approach is based on the self-consistent approximation of the radiative transfer equation and results in a relatively inexpensive and robust numerical algorithm. Simulations are presented for several cases including a weakly scattering medium with varying refractive index and a refractive weakly scattering medium with embedded highly scattering objects.

Metal artefact reduction in digital tomosynthesis using component decomposition.

We propose a technique for metal artefact reduction in digital tomosynthesis reconstruction. Although the problem was addressed earlier in the literature, we suggest another approach, which is, in our opinion, simpler, and easier to implement. It is a two-stage algorithm. At the first stage, attenuation images are segmented by decomposing their intensity distributions into gaussian-like components. Statistical information contained in each component is used for pixel classification. Components corresponding to metallic objects are identified, and a pixel threshold value separating regions occupied by metal objects from the rest of the image is found. Based on this value, at the second stage, a smooth mapping of image intensity is applied. This makes dense regions transparent, resulting in the artefact reduction in reconstruction. The methodology is demonstrated by several examples.

Tomographic imaging with polarized light.

We report three-dimensional tomographic reconstruction of optical parameters for the mesoscopic light scattering regime from experimentally obtained datasets by using polarized light. We present a numerically inexpensive approximation to the radiative transfer equation governing the polarized light transport. This approximation is employed in the reconstruction algorithm, which computes two optical parameters by using parallel and perpendicular polarizations of transmitted light. Datasets were obtained by imaging a scattering phantom embedding highly absorbing inclusions. Reconstruction results are presented and discussed.

Fluorescence lifetime optical tomography in weakly scattering media in the presence of highly scattering inclusions.

We consider the problem of fluorescence lifetime optical tomographic imaging in a weakly scattering medium in the presence of highly scattering inclusions. We suggest an approximation to the radiative transfer equation, which results from the assumption that the transport coefficient of the scattering media differs by an order of magnitude for weakly and highly scattering regions. The image reconstruction algorithm is based on the variational framework and employs angularly selective intensity measurements. We present numerical simulation of light scattering in a weakly scattering medium that embeds highly scattering objects. Our reconstruction algorithm is verified by recovering optical and fluorescent parameters from numerically simulated datasets.

Förster resonance energy transfer imaging in vivo with approximated radiative transfer equation.

We describe a new light transport model, which was applied to three-dimensional lifetime imaging of Förster resonance energy transfer in mice in vivo. The model is an approximation to the radiative transfer equation and combines light diffusion and ray optics. This approximation is well adopted to wide-field time-gated intensity-based data acquisition. Reconstructed image data are presented and compared with results obtained by using the telegraph equation approximation. The new approach provides improved recovery of absorption and scattering parameters while returning similar values for the fluorescence parameters.

Accuracy of the independent atom approximation in digital tomosynthesis Monte Carlo simulations.

Monte Carlo (MC) codes serve as the gold standard simulation tool during design and optimisation of x-ray imaging systems. Such simulations often model Rayleigh scattering based on the Independent Atom Approximation Model (IAM). This model neglects the low range molecular interference (MI) effects of non-crystalline materials such as human tissues. Previous work has found discrepancies in the simulated images of planar x-ray images between IAM and MI models. However, insignificant differences were found for computed tomography (CT) reconstructions. In this work we present Geant4 MC simulations of a flat panel source digital tomosynthesis (DT) system for human extremities. Results show that with a 1:9 scatter to primary ratio (SPR) in the x-ray projections, the DT reconstructions are insensitive to the differences of the IAM and MI models. Therefore, MC codes that use the IAM model are sufficient for the study of DT systems. That is because DT algorithms have a larger effect on image quality than the few percent change in the noise due to a physical model and noise suppression methods make this change even less important. Dependency of this conclusion on SPR must be considered in other DT modalities where SPR might be larger.

3D chest tomosynthesis using a stationary flat panel source array and a stationary detector: a Monte Carlo proof of concept.

3D imaging modalities such as computed tomography and digital tomosynthesis typically scan the patient from different angles with a lengthy mechanical movement of a single x-ray tube. Therefore, millions of 3D scans per year require expensive mechanisms to support a heavy x-ray source and have to compensate for machine vibrations and patient movements. However, recent developments in cold-cathode field emission technology allow the creation of compact, stationary arrays of emitters. Adaptix Ltd has developed a novel, low-cost, square array of such emitters and demonstrated 3D digital tomosynthesis of human extremities and small animals. The use of cold-cathode field emitters also makes the system compact and lightweight. This paper presents Monte Carlo simulations of a concept upgrade of the Adaptix system from the current 60 kVp to 90 kVp and 120 kVp which are better suited for chest imaging. Between 90 kVp and 120 kVp, 3D image quality appears insensitive to voltage and at 90 kVp the photon yield is reduced by 40%-50% while effective dose declines by 14%. A square array of emitters can adequately illuminate a subject for tomosynthesis from a shorter source-to-image distance, thereby reducing the required input power, and offsetting the 28%-50% more input power that is required for operation at 90 kVp. This modelling suggests that lightweight, stationary cold-cathode x-ray source arrays could be used for chest tomosynthesis at a lower voltage, with less dose and without sacrificing image quality. This will reduce weight, size and cost, enabling 3D imaging to be brought to the bedside.

Fast image reconstruction in fluorescence optical tomography using data compression.

We present a method for fast reconstruction in fluorescence optical tomography with very large data sets. In recent reports, CCD cameras at multiple positions have been used to collect optical measurements, producing more than 10(7) data samples. This makes storage of the full system Jacobian infeasible, and so data are usually subsampled. The method reported here allows use of the full data set, via image compression methods, and explicit construction of the (small) Jacobian, meaning optimal inversion methods can be applied, and thus leading to very fast reconstruction.

Meshless reconstruction technique for digital tomosynthesis.

A novel meshless reconstruction algorithm for digital tomosynthesis (DT) is presented and assessed against experimental data. The algorithm does not require a three-dimensional grid or mesh allocation and performs a slice-by-slice reconstruction where each slice position can be chosen at runtime. The methodology is based on the filtered backprojection algorithm adapted to DT. However, in the traditional approach the backprojection comes first and the filtering follows. Because the backprojection requires ray tracing, in our case it is replaced with an equivalent image mapping procedure. The idea to swap the filtering and backprojection had been introduced earlier for computerized tomography (CT). Here we use this idea but develop it differently. Contrary to CT imaging, where the source and detector are rotated, in DT the subject and the flat panel detector are fixed in space. This imaging geometry allows reconstruction in planes parallel to the flat panel detector, which results in a significant simplification of the filter of backprojection algorithm. Moreover, the algorithm is not memory demanding and can be used with very large datasets. Two versions of the meshless algorithm are presented. One of them is based on convolution type filtering, while another uses filtering in the Fourier domain. Both versions are assessed and compared against the cone beam algorithm.

Three-dimensional imaging of Förster resonance energy transfer in heterogeneous turbid media by tomographic fluorescent lifetime imaging.

We report a three-dimensional time-resolved tomographic imaging technique for localizing protein-protein interaction and protein conformational changes in turbid media based on Förster resonant energy-transfer read out using fluorescence lifetime. This application of "tomoFRET" employs an inverse scattering algorithm utilizing the diffusion approximation to the radiative-transfer equation applied to a large tomographic data set of time-gated images. The approach is demonstrated by imaging a highly scattering cylindrical phantom within which are two thin wells containing cytosol preparations of HEK293 cells expressing TN-L15, a cytosolic genetically encoded calcium Förster resonant energy-transfer sensor. A 10 mM calcium chloride solution was added to one of the wells, inducing a protein conformation change upon binding to TN-L15, resulting in Förster resonant energy transfer and a corresponding decrease in the donor fluorescence lifetime. We successfully reconstruct spatially resolved maps of the resulting fluorescence lifetime distribution as well as of the quantum efficiency, absorption, and scattering coefficients.

Combined reconstruction of fluorescent and optical parameters using time-resolved data.

We present an algorithm for simultaneous reconstruction of optical parameters, quantum yield, and lifetime in turbid media with embedded fluorescent inclusions. This algorithm is designed in the Fourier domain as an iterative solution of a system of differential equations of the Helmholtz type and does not involve full ill-conditioned matrix computations. The approach is based on allowing the unknown optical parameters, quantum yield, and lifetime to depend on the Fourier spectral parameter. The algorithm was applied to a time-gated experimental data set acquired by imaging a highly scattering cylindrical phantom concealing small fluorescent tubes. Relatively accurate reconstruction demonstrates the potential of the method.

Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging.

A novel adaptive mesh technique in the Fourier domain is introduced for problems in fluorescence lifetime imaging. A dynamical adaptation of the three-dimensional scheme based on the finite volume formulation reduces computational time and balances the ill-posed nature of the inverse problem. Light propagation in the medium is modeled by the telegraph equation, while the lifetime reconstruction algorithm is derived from the Fredholm integral equation of the first kind. Stability and computational efficiency of the method are demonstrated by image reconstruction of two spherical fluorescent objects embedded in a tissue phantom.

Optical Tomography in weakly scattering media in the presence of highly scattering inclusions.

We consider the problem of optical tomographic imaging in a weakly scattering medium in the presence of highly scattering inclusions. The approach is based on the assumption that the transport coefficient of the scattering media differs by an order of magnitude for weakly and highly scattering regions. This situation is common for optical imaging of live objects such an embryo. We present an approximation to the radiative transfer equation, which can be applied to this type of scattering case. Our approach was verified by reconstruction of two optical parameters from numerically simulated datasets.

Angularly selective mesoscopic tomography.

We report three-dimensional tomographic reconstruction of optical parameters for the mesoscopic light-scattering regime from experimentally obtained datasets by employing angularly selective data acquisition. The approach is based on the assumption that the transport coefficient of a scattering medium differs by an order of magnitude for weakly and highly scattering regions. Datasets were obtained by imaging a weakly scattering phantom, which embeds a highly scattering cylinder of two to three photons' mean path length in diameter containing light-absorbing inclusions. Reconstruction results are presented and discussed.

In vivo fluorescence lifetime tomography of a FRET probe expressed in mouse.

Förster resonance energy transfer (FRET) is a powerful biological tool for reading out cell signaling processes. In vivo use of FRET is challenging because of the scattering properties of bulk tissue. By combining diffuse fluorescence tomography with fluorescence lifetime imaging (FLIM), implemented using wide-field time-gated detection of fluorescence excited by ultrashort laser pulses in a tomographic imaging system and applying inverse scattering algorithms, we can reconstruct the three dimensional spatial localization of fluorescence quantum efficiency and lifetime. We demonstrate in vivo spatial mapping of FRET between genetically expressed fluorescent proteins in live mice read out using FLIM. Following transfection by electroporation, mouse hind leg muscles were imaged in vivo and the emission of free donor (eGFP) in the presence of free acceptor (mCherry) could be clearly distinguished from the fluorescence of the donor when directly linked to the acceptor in a tandem (eGFP-mCherry) FRET construct.

Fluorescence lifetime optical tomography with Discontinuous Galerkin discretisation scheme.

We develop discontinuous Galerkin framework for solving direct and inverse problems in fluorescence diffusion optical tomography in turbid media. We show the advantages and the disadvantages of this method by comparing it with previously developed framework based on the finite volume discretization. The reconstruction algorithm was used with time-gated experimental dataset acquired by imaging a highly scattering cylindrical phantom concealing small fluorescent tubes. Optical parameters, quantum yield and lifetime were simultaneously reconstructed. Reconstruction results are presented and discussed.

Adjoint time domain method for fluorescent imaging in turbid media.

Application of adjoint time domain methods to the inverse problem in 3D fluorescence imaging is a novel approach. We demonstrate the feasibility of this approach experimentally on the basis of a time gating technique completely in the time domain by using a small number of time windows. The evolution of the fluorescence energy density function inside a highly scattering cylinder was reconstructed together with optical parameters. Reconstructed energy density was used in localizing two fluorescent tubes. Relatively accurate reconstruction demonstrates the effectiveness and the potential of the proposed technique.

Tomographic bioluminescence imaging with varying boundary conditions.

Three-dimensional bioluminescence imaging is an emerging technique that can be used to monitor molecular events in intact living systems. The inverse problem of 3D bioluminescence imaging does not have a unique solution because it requires reconstruction of a 3D source function from a 2D one. A novel approach that addresses this problem with the aid of a simple experimental setup and solves the uniqueness problem of the solution for a monochromatic measurement set is suggested here. The approach is verified numerically by reconstructing bioluminescent objects of various shapes embedded inside highly scattering media, such as biologiçal tissue.

Fluorescence lifetime imaging by using time-gated data acquisition.

The use of the time gating technique for lifetime reconstruction in the Fourier domain is a novel technique. Time gating provides sufficient data points in the time domain for reliable application of the Fourier transform, which is essential for the time deconvolution of the system of the integral equations employed in the reconstruction. The Fourier domain telegraph equation is employed to model the light transport, which allows a sufficiently broad interval of frequencies to be covered. Reconstructed images contain enough information needed for recovering the lifetime distribution in a sample for any given frequency within the megahertz-gigahertz band. The use of this technique is essential for recovering time-dependent information in fluorescence imaging. This technique was applied in reconstruction of the lifetime distribution of four tubes filled with Rhodamine 6G embedded inside a highly scattering slab. Relatively accurate fluorescence lifetime reconstruction demonstrates the effectiveness and the potential of the proposed technique.