Time-resolved Fourier spectroscopy for activated optical materials

A low-cost add-on to commercial Fourier-transform spectrometers that have a continuously scanning Michelson interferometer has been developed for high-resolution, broadband, time-resolved spectroscopy. A number of innovations have been implemented to enable near-IR, visible, and UV photolumi-nescence studies. These include error correction and normalization of interferogram points to correct for laser intensity variations and missed shots, reduction of mirror-speed variations with recognition and avoidance of the timing mistakes they cause, and simple white-light-interferogram advancement optics that leave high-frequency modulation efficiency for the signal of interest unchanged in dynamically aligned systems. Application to energy-transfer phenomena in solid-state-laser media is described.     

Multi-frequency diffuse optical tomography

The performance of diffuse optical tomography (DOT) is investigated when multi-modulation frequencies are used simultaneously in the inverse problem in order to cast the forward model. The forward model used was based on the first-order Rytov approximation of the diffusion equation. Numerical measurements were generated with a finite difference approach for configurations relevant to breast optical mammography. The impact of various frequency-set characteristics was evaluated. Furthermore, the effect of sensitivity matrix preconditioning was investigated. The criteria underlying this study were based on a ‘singular value analysis’ and parameter cross-talk between absorption and scattering reconstructions. It had been shown that preconditioning the matrix was necessary to provide accurate results and an even distribution of frequencies within the larger bound. Furthermore, correlating the different criterions used demonstrated that analysis based on optimization of condition number alone was providing misleading results.     

Time-resolved diffuse optical spectroscopy: a differential absorption approach

A method is presented for the estimate of spectral changes in the absorption properties of turbid media from time-resolved diffuse optical spectroscopy. The method relies on the hypothesis of constant scattering over the wavelength range of interest, but no limitations come from the sample size and shape as the method is derived directly from the Beer-Lambert law. The effects of a moderate spectral dependence of the scattering properties and of the non-ideal instrument response function were investigated theoretically, and the results were confirmed experimentally, showing that the method can be profitably applied in cases of practical interest.     

Time-resolved optical tomography using short-pulse laser for tumor detection

Our objective is to perform a comprehensive experimental and numerical analysis of the short-pulse laser interaction with a tissue medium with the goal of tumor-cancer diagnostics. For a short-pulse laser source, the shape of the output signal is a function of the optical properties of the medium, and hence the scattered temporal optical signal helps in understanding the medium characteristics. Initially experiments are performed on tissue phantoms embedded with inhomogeneities to optimize the time-resolved optical detection scheme. Both the temporal and the spatial profiles of the scattered reflected and transmitted optical signals are compared with the numerical modeling results obtained by solving the transient radiative transport equation using the discrete ordinates technique. Next experiments are performed on in vitro rat tissue samples to characterize the interaction of light with skin layers and to validate the time-varying optical signatures with the numerical model. The numerical modeling results and the experimental measurements are in excellent agreement for the different parameters studied. The final step is to perform in vivo imaging of anesthetized rats with tumor-promoting agents injected inside skin tissues and of an anesthetized mouse with mammary tumors to demonstrate the feasibility of the technique for detecting tumors in an animal model.     

Spatially variant regularization improves diffuse optical tomography

Diffuse tomography with near-infrared light has biomedical application for imaging hemoglobin, water, lipids, cytochromes, or exogenous contrast agents and is being investigated for breast cancer diagnosis. A Newton-Raphson inversion algorithm is used for image reconstruction of tissue optical absorption and transport scattering coefficients from frequency-domain measurements of modulated phase shift and light intensity. A variant of Tikhonov regularization is examined in which radial variation is allowed in the value of the regularization parameter. This method minimizes high-frequency noise in the reconstructed image near the source-detector locations and can produce constant image resolution and contrast across the image field.     

Iterative boundary method for diffuse optical tomography

The recent application of tomographic methods to three-dimensional imaging through tissue by use of light often requires modeling of geometrically complex diffuse-nondiffuse boundaries at the tissue-air interface. We have recently investigated analytical methods to model complex boundaries by means of the Kirchhoff approximation. We generalize this approach using an analytical approximation, the N-order diffuse-reflection boundary method, which considers higher orders of interaction between surface elements in an iterative manner. We present the general performance of the method and demonstrate that it can improve the accuracy in modeling complex boundaries compared with the Kirchhoff approximation in the cases of small diffuse volumes or low absorption. Our observations are also contrasted with exact solutions. We furthermore investigate optimal implementation parameters and show that a second-order approximation is appropriate for most in vivo investigations.     

Volume image reconstruction for diffuse optical tomography

Optical tomography is a potential diagnostic method for visualizing optical properties of tissues in vivo. We present an optical tomography method that has been designed for imaging of the human testes, particularly for spectroscopic tumor differentiation. In this application we need to compute three-dimensional distributions of the optical contrast (absorption coefficient) in the tissue in real time. Thus we have given special care to elaborate an efficient inverse algorithm that takes the limitations of spatial resolution and data space point density into account. Our inverse solution is based on a linearization approach and a dedicated object space discretization. Furthermore, we introduce the concept of fuzzy voxels, which enables a reconstruction-inherent image smoothing.     

Optode positional calibration in diffuse optical tomography

Although diffuse optical tomography is a highly promising technique used to noninvasively image blood volume and oxygenation, the reconstructed data are sensitive to systemic difference between the forward model and the actual experimental conditions. In particular, small changes in optode location or in the optode-tissue coupling coefficient significantly degrade the quality of the reconstruction images. Accurate system calibration therefore is an essential part of any experimental protocol. We present a technique for simultaneously calibrating optode positions and reconstructing images that significantly improves image quality, as we demonstrate with simulations and phantom experiments.     

Pseudo-time particle filtering for diffuse optical tomography

We recast the reconstruction problem of diffuse optical tomography (DOT) in a pseudo-dynamical framework and develop a method to recover the optical parameters using particle filters, i.e., stochastic filters based on Monte Carlo simulations. In particular, we have implemented two such filters, viz., the bootstrap (BS) filter and the Gaussian-sum (GS) filter and employed them to recover optical absorption coefficient distribution from both numerically simulated and experimentally generated photon fluence data. Using either indicator functions or compactly supported continuous kernels to represent the unknown property distribution within the inhomogeneous inclusions, we have drastically reduced the number of parameters to be recovered and thus brought the overall computation time to within reasonable limits. Even though the GS filter outperformed the BS filter in terms of accuracy of reconstruction, both gave fairly accurate recovery of the height, radius, and location of the inclusions. Since the present filtering algorithms do not use derivatives, we could demonstrate accurate contrast recovery even in the middle of the object where the usual deterministic algorithms perform poorly owing to the poor sensitivity of measurement of the parameters. Consistent with the fact that the DOT recovery, being ill posed, admits multiple solutions, both the filters gave solutions that were verified to be admissible by the closeness of the data computed through them to the data used in the filtering step (either numerically simulated or experimentally generated).     

Noncontact fluorescence diffuse optical tomography of heterogeneous media

Fluorescence-enhanced diffuse optical tomography is expected to be useful to the collection of functional information from small animal models. This technique is currently limited by the extent of tissue heterogeneity and management of the shape of the animals. We propose an approach based on the reconstruction of object heterogeneity, which provides an original solution to the two problems. Three evaluation campaigns are described: the first two were performed on phantoms designed to test the reconstructions in highly heterogeneous media and noncontact geometries; the third was conducted on mice with lung tumors to test fluorescence yield reconstruction feasibility in vivo.     

Implementation of edge-preserving regularization for frequency-domain diffuse optical tomography

In this study, we first propose the use of edge-preserving regularization in optimizing an ill-conditioned problem in the reconstruction procedure for diffuse optical tomography to prevent unwanted edge smoothing, which usually degrades the attributes of images for distinguishing tumors from background tissues when using Tikhonov regularization. In the edge-preserving regularization method presented here, a potential function with edge-preserving properties is introduced as a regularized term in an objective function. With the minimization of this proposed objective function, an iterative method to solve this optimization problem is presented in which half-quadratic regularization is introduced to simplify the minimization task. Both numerical and experimental data are employed to justify the proposed technique. The reconstruction results indicate that edge-preserving regularization provides a superior performance over Tikhonov regularization.     

Model-resolution based regularization improves near infrared diffuse optical tomography

Diffuse optical tomographic imaging is known to be an ill-posed problem, and a penalty/regularization term is used in image reconstruction (inverse problem) to overcome this limitation. Two schemes that are prevalent are spatially varying (exponential) and constant (standard) regularizations/penalties. A scheme that is also spatially varying but uses the model information is introduced based on the model-resolution matrix. This scheme, along with exponential and standard regularization schemes, is evaluated objectively based on model-resolution and data-resolution matrices. This objective analysis showed that resolution characteristics are better for spatially varying penalties compared to standard regularization; and among spatially varying regularization schemes, the model-resolution based regularization fares well in providing improved data-resolution and model-resolution characteristics. The verification of the same is achieved by performing numerical experiments in reconstructing 1% noisy data involving simple two- and three-dimensional imaging domains.     

Practical fully three-dimensional reconstruction algorithms for diffuse optical tomography

We have developed an efficient fully three-dimensional (3D) reconstruction algorithm for diffuse optical tomography (DOT). The 3D DOT, a severely ill-posed problem, is tackled through a pseudodynamic (PD) approach wherein an ordinary differential equation representing the evolution of the solution on pseudotime is integrated that bypasses an explicit inversion of the associated, ill-conditioned system matrix. One of the most computationally expensive parts of the iterative DOT algorithm, the reevaluation of the Jacobian in each of the iterations, is avoided by using the adjoint-Broyden update formula to provide low rank updates to the Jacobian. In addition, wherever feasible, we have also made the algorithm efficient by integrating along the quadratic path provided by the perturbation equation containing the Hessian. These algorithms are then proven by reconstruction, using simulated and experimental data and verifying the PD results with those from the popular Gauss-Newton scheme. The major findings of this work are as follows: (i) the PD reconstructions are comparatively artifact free, providing superior absorption coefficient maps in terms of quantitative accuracy and contrast recovery; (ii) the scaling of computation time with the dimension of the measurement set is much less steep with the Jacobian update formula in place than without it; and (iii) an increase in the data dimension, even though it renders the reconstruction problem less ill conditioned and thus provides relatively artifact-free reconstructions, does not necessarily provide better contrast property recovery. For the latter, one should also take care to uniformly distribute the measurement points, avoiding regions close to the source so that the relative strength of the derivatives for measurements away from the source does not become insignificant.     

Streak camera: a multidetector for diffuse optical tomography

We describe an experimental setup for time-resolved diffuse optical tomography that uses a seven-channel light guide to transmit scattered light to a streak camera. This setup permits the simultaneous measurement of the time profiles of photons reemitted at different boundary sites of the objects studied. The instrument, its main specifications, and detector-specific data analysis before image reconstruction are described. The instrumentation was tested with phantoms simulating biological tissue, and the absorption and reduced scattering images that were obtained are discussed.     

Time-resolved Fourier transform infrared spectroscopic imaging

Fourier transform infrared (FT-IR) imaging allows simultaneous spectral characterization of large spatial areas due to its multichannel detection advantage. The acquisition of large amounts of data in the multichannel configuration results, however, in a poor temporal resolution of sequentially acquired data sets, which limits the examination of dynamic processes to processes that have characteristic time scales of the order of minutes. Here, we introduce the concept and instrumental details of a time-resolved infrared spectroscopic imaging modality that permits the examination of repetitive dynamic processes whose half-lives are of the order of milli-seconds. As an illustration of this implementation of step-scan FT-IR imaging, we examine the molecular responses to external electric-field perturbations of a microscopically heterogeneous polymer-liquid crystal composite. Analysis of the spectroscopic data using conventional univariate and generalized two-dimensional (2D) correlation methods emphasizes an additional capability for accessing of simultaneous spatial and temporal chemical measurements of molecular dynamic processes.     

Time-domain diffuse optical tomography processing by using the Mellin-Laplace transform

We investigate the use of the Mellin-Laplace transform for reconstructing optical parameters from time-resolved optical tomography in diffusive media. We present here its definition, its mathematical properties, and its sensitivity to variations of optical properties. The method was validated on two-dimensional reconstructions from simulation in the reflection geometry. We conclude that reconstructions based on the Mellin-Laplace transform are more robust to noise than the methods using first moments.     

Multispectral diffuse optical tomography with absorption and scattering spectral constraints

We present a new method to simultaneously reconstruct the images of oxyhemoglobin, deoxyhemoglobin, and water concentrations, as well as the volume fraction images of the scattering particles using continuous wave multispectral diffuse optical tomography with the absorption and scattering spectral prior constraints. In this method, the nonlinear relationship between the reduced scattering coefficient and the volume fraction and the size of the particles is linearized, allowing direct reconstruction of the volume fraction of scattering particles in tissues. The method is validated by a series of numerical simulations, phantom experiments, and in vivo clinical experiments. The initial clinical results indicate that the volume fraction of scattering particles in a malignant tumor is higher than that in a benign tumor.     

Image correction scheme applied to functional diffuse optical tomography scattering images

We have extended our investigation on the use of a linear algorithm for enhancing the accuracy of diffuse optical tomography (DOT) images, to include spatial maps of the diffusion coefficient. The results show that the corrected images are markedly improved in terms of estimated size, spatial resolution, two-object resolving power, and quantitative accuracy. These image-enhancing effects are significant at expected levels of diffusion-coefficient contrast in tissue and noise levels typical of experimental DOT data. Overall, the types and magnitudes of image-enhancing effects obtained here are qualitatively similar to those seen in previous studies on mu(a) perturbations. The implications for practical implementations of DOT time-series imaging are discussed.     

Image correction algorithm for functional three-dimensional diffuse optical tomography brain imaging

We outline a computationally efficient image correction algorithm, which we have applied to diffuse optical tomography (DOT) image time series derived from a magnetic resonance imaging (MRI)-based brain model. Results show that the algorithm increases spatial resolution, decreases spatial bias, and only modestly reduces temporal accuracy for noise levels typically seen in experiment, and produces results comparable to image reconstructions that incorporate information from MRI priors. We demonstrate that this algorithm has robust performance in the presence of noise, background heterogeneity, irregular external and internal boundaries, and error in the initial guess. However, the algorithm introduces artifacts when the absorption and scattering coefficients of the reference medium are overestimated--a situation that is easily avoided in practice. The considered algorithm offers a practical approach to improving the quality of images from time-series DOT, even without the use of MRI priors.