Fluorescence optical diffusion tomography

A nonlinear, Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and the diffusion coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and the emission wavelengths to reconstruct all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated by simulation and by application to experimental data from a tissue phantom containing the fluorescent agent Indocyanine Green.     

Imaging of fluorescent yield and lifetime from multiply scattered light reemitted from random media

The feasibility of employing fluorescent contrast agents to perform optical imaging in tissues and other scattering media has been examined through computational studies. Fluorescence lifetime and yield can give crucial information about local metabolite concentrations or environmental conditions within tissues. This information can be employed toward disease detection, diagnosis, and treatment if noninvasively quantitated from reemitted optical signals. However, the problem of inverse image reconstruction of fluorescence yield and lifetime is complicated because of the highly scattering nature of the tissue. Here a light propagation model employing the diffusion equation is used to account for the scattering of both the excitation and fluorescent light. Simulated measurements of frequency-domain parameters of fluorescent modulated ac amplitude and phase lag are used as inputs to an inverse image-reconstruction algorithm, which employs the diffusion model to predict frequency-domain measurements resulting from a modulated input at the phantom periphery. In the inverse image-reconstruction algorithm, a Newton-Raphson technique combined with a Marquardt algorithm is employed to converge on the fluorescent properties within the medium. The successful reconstruction of both the fluorescence yield and lifetime in the case of a heterogeneous fluorophore distribution within a scattering medium has been demonstrated without a priori information or without the necessity of obtaining absence images.     

Fluorescence optical diffusion tomography using multiple-frequency data

A method is presented for fluorescence optical diffusion tomography in turbid media using multiple-frequency data. The method uses a frequency-domain diffusion equation model to reconstruct the fluorescent yield and lifetime by means of a Bayesian framework and an efficient, nonlinear optimizer. The method is demonstrated by using simulations and laboratory experiments to show that reconstruction quality can be improved in certain problems through the use of more than one frequency. A broadly applicable mutual information performance metric is also presented and used to investigate the advantages of using multiple modulation frequencies compared with using only one.     

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.     

Image reconstruction scheme that combines modified Newton method and efficient initial guess estimation for optical tomography of finger joints

What we believe to be a novel 3D diffuse optical tomography scheme is developed to reconstruct images of both absorption and scattering coefficients of finger joint systems. Compared with our previous reconstruction method, the improved 3D algorithm employs both modified Newton methods and an enhanced initial value optimization scheme to recover the optical properties of highly heterogeneous media. The developed approach is tested using simulated, phantom, and in vivo measurement data. The recovered results suggest that the improved approach is able to provide quantitatively better images than our previous algorithm for optical tomography reconstruction.     

Spatially varying optical and acoustic property reconstruction using finite-element-based photoacoustic tomography

A finite-element reconstruction algorithm for simultaneous reconstruction of both optical and acoustic properties of heterogeneous media is presented. The algorithm is based on the Helmholtz-like photoacoustic wave equation in the frequency domain. A dual meshing scheme is described and an adjoint sensitivity method is adopted for efficient inverse computation. The algorithm is implemented with the second-order absorbing boundary conditions and with a multireceiving and multifrequency strategy. The algorithm is evaluated using simulated data under various practical cases including different noise levels, varied range of receiving frequency, different contrast levels between the heterogeneity and background region, and multiple targets. The effect of acoustic heterogeneity on conventional pure optical absorption reconstruction is also studied.     

Estimation of kinetic model parameters in fluorescence optical diffusion tomography

We present a technique for reconstructing the spatially dependent dynamics of a fluorescent contrast agent in turbid media. The dynamic behavior is described by linear and nonlinear parameters of a compartmental model or some other model with a deterministic functional form. The method extends our previous work in fluorescence optical diffusion tomography by parametrically reconstructing the time-dependent fluorescent yield. The reconstruction uses a Bayesian framework and parametric iterative coordinate descent optimization, which is closely related to Gauss-Seidel methods. We demonstrate the method with a simulation study.     

Image reconstruction algorithm based on the extended regularised total least squares method for electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive imaging technology that aims at the visualisation of the cross-sectional permittivity distribution of a dielectric object based on the measured capacitance data. Successful applications of ECT depend greatly on the precision and speed of the image reconstruction algorithms. ECT image reconstruction is a typical ill-posed problem, and its solution is unstable, that is, the solution is sensitive to noises in the input data. Methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. An image reconstruction algorithm based on the regularised total least squares (TLS) method that considers the errors in both the sensitivity field matrix and the capacitance data for ECT is presented. The regularised TLS method is extended using a combination robust estimation technique and an extended stabilising functional according to the ill-posed characteristics of ECT, which transforms the image reconstruction problem into an optimisation problem. In addition, the Newton algorithm is employed to solve the objective functional. Numerical simulations indicate that the algorithm is feasible and overcomes the numerical instability of ECT image reconstruction; for the cases of the reconstructed objects considered here, the spatial resolution of the reconstructed images obtained using the algorithm is enhanced; as a result, an efficient method for ECT image reconstruction is introduced.     

Confocal fluorescent imaging of tracks from heavy charged particles utilising new Al2O3:C,Mg crystals

A completely optical, non-destructive imaging of tracks in a fluorescent crystal provides a new way to detect and to assess doses from heavy charged particles and neutrons. The technique combines confocal fluorescent microscopy with a new radiation-sensitive, luminescent material based on aluminium oxide single crystals doped with carbon, magnesium and having aggregate oxygen vacancy defects (Al2O3:C,Mg). Radiation-induced colour centres in the new material have an absorption band at 620 nm and produce fluorescence at 750 nm with a high quantum yield and a short, 75 +/- 5 ns, fluorescence lifetime. Three-dimensional spatial distribution of fluorescent intensity allows one to obtain depth-dose distributions and to discriminate between high- and low-linear energy transfer radiations. Images of single tracks produced by different types of radiation have been obtained. Irradiations with a calibrated 241Am alpha source showed high efficiency for track detection. Thermal neutrons were detected using a nuclear reaction with a 6LiF radiator and production of alpha particles and tritium ions. Fast neutrons were detected using recoil protons produced in a polyethylene radiator installed in front of the crystalline detector. Three-dimensional reconstruction of a recoil proton propagating through the crystal was demonstrated.     

Penalized-likelihood image reconstruction for digital holography

Conventional numerical reconstruction for digital holography using a filter applied in the spatial-frequency domain to extract the primary image may yield suboptimal image quality because of the loss in high-frequency components and interference from other undesirable terms of a hologram. We propose a new numerical reconstruction approach using a statistical technique. This approach reconstructs the complex field of the object from the real-valued hologram intensity data. Because holographic image reconstruction is an ill-posed problem, our statistical technique is based on penalized-likelihood estimation. We develop a Poisson statistical model for this problem and derive an optimization transfer algorithm that monotonically decreases the cost function at each iteration. Simulation results show that our statistical technique has the potential to improve image quality in digital holography relative to conventional reconstruction techniques.     

Finite-element-based photoacoustic tomography: phantom and chicken bone experiments

We describe a photoacoustic image reconstruction algorithm that is based on the finite-element solution to the photoacoustic wave equation in the frequency domain. Our reconstruction approach is an iterative Newton method coupled with combined Marquardt and Tikhonov regularizations that can extract the spatial distribution of optical-absorption property in heterogeneous media. We demonstrate this algorithm by using phantom and chicken bone measurements from a circular scanning photoacoustic tomography system. The results obtained show that millimeter-sized phantom objects and chicken bones and/or joints can be clearly detected using our finite-element-based photoacoustic tomography method.     

Quantitative optical image reconstruction of turbid media by use of direct-current measurements

We present a detailed experimental study concerning quantitative optical property reconstruction of heterogeneous turbid media by use of absolute dc data only. We performed experiments by using tissuelike phantoms in both single-target and multitarget configurations in which variations in target size and optical contrast with the background were explored. Our results show that both scattering and absorption images can be reconstructed quantitatively by use of dc data only, whereas it was impossible to obtain such quantitative information in previously reported studies. We believe that this improvement is primarily a result of the realization of a novel data preprocessing/optimization scheme for accurately determining several critical parameters needed for reconstruction. The use of this data preprocessing/optimization scheme also eliminates the calibration reference measurement previously required for reconstruction. Experimental confirmation of this scheme is given in detail.     

An iterative synthetic aperture imaging algorithm with correction of diffraction effects

In this paper we present an iterative version of the synthetic aperture imaging algorithm extended synthetic aperture technique (ESAFT) proposed recently. The algorithm is based on a linear model that accounts for the distortions effects of an imaging system used for acquisition of ultrasonic data. Improved resolution (both lateral and temporal) in the reconstructed image is obtained as a result of minimizing the reconstruction mean square error. In this work, the minimization is extended to parameters that characterize expected amplitudes of each image element in the area of interest. An iterative optimization scheme is proposed, which in each step performs minimization of the reconstruction error based on the parameter matrix found in the previous step. Comparing to ESAFT, the proposed approach yields a significant improvement in resolution and a high degree of robustness with regard to initial choice of the parameter matrix. Performance of the proposed algorithm is evaluated using both real and simulated ultrasonic data.     

Absorption and scattering images of heterogeneous scattering media can be simultaneously reconstructed by use of dc data

We present a carefully designed phantom experimental study aimed to provide solid evidence that both absorption and scattering images of heterogeneous scattering media can be reconstructed independently from dc data. We also study the important absorption-scattering cross-talk issue. In this regard, we develop a simple normalizing scheme that is incorporated into our nonlinear finite-element-based reconstruction algorithm. Our results from the controlled phantom experiments show that the cross talk of an absorption object appearing in scattering images can be eliminated and that the cross talk of a scattering object appearing in absorption images can be reduced considerably. In addition, these carefully designed phantom experiments clearly suggest that both absorption and scattering images can be simultaneously recovered and quantitatively separated in highly scattering media by use of dc measurements. Finally, we discuss our results in light of recent theoretical findings on nonuniqueness for dc image reconstruction.     

A multi-stage return algorithm for solving the classical damage component of constitutive models for rocks, ceramics, and other rock-like media

Classical plasticity and damage models for porous quasi-brittle media usually suffer from mathematical defects such as non-convergence and non-uniqueness. Yield or damage functions for porous quasi-brittle media often have yield functions with contours so distorted that following those contours to the yield surface in a return algorithm can take the solution to a false elastic domain. A steepest-descent return algorithm must include iterative corrections; otherwise, the solution is non-unique because contours of any yield function are non-unique. A multi-stage algorithm has been developed to address both spurious convergence and non-uniqueness, as well as to improve efficiency. The region of pathological isosurfaces is masked by first returning the stress state to the Drucker–Prager surface circumscribing the actual yield surface. From there, steepest-descent is used to locate a point on the yield surface. This first-stage solution, which is extremely efficient because it is applied in a 2D subspace, is generally not the correct solution, but it is used to estimate the correct return direction. The first-stage solution is projected onto the estimated correct return direction in 6D stress space. Third invariant dependence and anisotropy are accommodated in this second-stage correction. The projection operation introduces errors associated with yield surface curvature, so the two-stage iteration is applied repeatedly to converge. Regions of extremely high curvature are detected and handled separately using an approximation to vertex theory. The multi-stage return is applied holding internal variables constant to produce a non-hardening solution. To account for hardening from pore collapse (or softening from damage), geometrical arguments are used to clearly illustrate the appropriate scaling of the non-hardening solution needed to obtain the hardening (or softening) solution.     

Measurement of particle-size distribution and concentration in heterogeneous turbid media with multispectral diffuse optical tomography

We present a method that is capable of extracting particle-size distribution (PSD) and concentration in heterogeneous turbid media by use of multispectral diffuse optical tomography (MSDOT). After the spectroscopic scattering images of the heterogeneous turbid media are obtained with MSDOT, the morphologic information of particles in the heterogeneities is recovered with an iterative regularized reconstruction algorithm based on Mie scattering theory when a particular form of PSD is assumed (Gaussian distribution is used in this study). The method described is tested and evaluated with both simulated and experimental data. The simulations are intended to test the sensitivity of the overall approach to noise effect. A series of phantom experiments are conducted with our newly developed ten-wavelength MSDOT system. Polystyrene microsphere suspensions contain particles of varying size from 2 to 6 microm as targets are embedded in a scattering background medium in these experiments. To achieve optimized results from experimental data, we developed a data preprocessing method for MSDOT as well as a scheme for calibrating scattering spectra. The results from both simulations and experiments show that the particle mean size and concentration can be reconstructed with acceptable accuracy, whereas the recovery of the standard deviation is sensitive to noise effect and can be as large as 86% from the experimental data.     

Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications

We present analytic solutions for fluorescent diffuse photon density waves originating from fluorophores distributed in thick turbid media. Solutions are derived for a homogeneous turbid medium containing a uniform distribution of fluorophores and for a system that is homogeneous except for the presence of a single spherical inhomogeneity Generally the inhomogeneity has fluorophore concentration, and lifetime and optical properties that differ from those of the background. The analytic solutions are verified by numerical calculations and are used to determine the fluorophore lifetime and concentration changes required for the accurate detection of inhomogeneities in biologically relevant systems. The relative sensitivities of absorption and fluorescence methods are compared.     

High-resolution colocalization of single dye molecules by fluorescence lifetime imaging microscopy

Conventional fluorescence microscopy can be used to determine the positions of objects in space when those objects are separated by distances greater than several hundred nanometers, as restricted by the diffraction limit of light. Fluorescence microscopy/spectroscopy based on fluorescence resonance energy-transfer techniques can be used to measure separation distances below approximately 10 nm. To fill the gap between these fundamental limits, we have developed an alternative technique for high-resolution colocalization of fluorescent dyes. The technique is based on fluorescence lifetime imaging. Under favorable conditions, the method can be used to distinguish, and to measure the distance between, two dye molecules that are less than 30 nm apart. To demonstrate the method, lifetime images of a mixture of Cy5 and JF9 (rhodamine derivative) molecules statistically adsorbed on a glass surface were acquired and analyzed. Since these two molecular species differ in fluorescence lifetime (for Cy5, tau(f) = 2.0 ns, and for JF9, tau(f) = 4.0 ns), it is possible to assign the contribution of fluorescence of the two dye types to each image pixel using a pattern recognition technique. Since both dye types can be excited using the same laser wavelength, the measurement is free of chromatic aberrations. The results presented demonstrate the first high-precision distance measurements between single conventional fluorescent dyes based solely on fluorescence lifetime.     

Factor graph methods for three-dimensional shape reconstruction as applied to LIDAR imaging

Two methods based on factor graphs for reconstructing the three-dimensional (3D) shape of an object from a series of two-dimensional images are presented. First, a factor graph model is developed for image segmentation to obtain silhouettes from raw images; the shape-from-silhouette technique is then applied to yield the 3D reconstruction of the object. The second method presented is a direct 3D reconstruction of the object using a factor graph model for the voxels of the reconstruction. While both methods should be applicable to a variety of input data types, they will be developed and demonstrated for a particular application involving the LIDAR imaging of a submerged target. Results from simulations and from real LIDAR data are shown that detail the performance of the methods.     

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.