Harry L. Graber

MRI-guided optical tomography: prospects and computation for a new imaging method

Living tissue scatters near-infrared light randomly, can this problem be overcome to make NIR optical tomography possible? If so, it could be more accurate and less damaging than other medical imaging techniques. Computational experiments using combined MRI-optical methods show promise.

Design and implementation of dynamic near-infrared optical tomographic imaging instrumentation for simultaneous dual-breast measurements

Dynamic near-infrared optical tomographic measurement instrumentation capable of simultaneous bilateral breast imaging, having a capability of four source wavelengths and 32 source-detector fibers for each breast, is described. The system records dynamic optical data simultaneously from both breasts, while verifying proper optical fiber contact with the tissue through implementation of automatic schemes for evaluating data integrity. Factors influencing system complexity and performance are discussed, and experimental measurements are provided to demonstrate the repeatability of the instrumentation. Considerations in experimental design are presented, as well as techniques for avoiding undesirable measurement artifacts, given the high sensitivity and dynamic range (1:10(9)) of the system. We present exemplary clinical results comparing the measured physiologic response of a healthy individual and of a subject with breast cancer to a Valsalva maneuver.

Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography

Instrumentation is described that is suitable for acquiring multisource, multidetector, time-series optical data at high sampling rates (up to 150 Hz) from tissues having arbitrary geometries. The design rationale, calibration protocol, and measured performance features are given for both a currently used, CCD-camera-based instrument and a new silicon-photodiode-based system under construction. Also shown are representative images that we reconstructed from data acquired in laboratory studies using the described CCD-based instrument.

Influence of systematic errors in reference states on image quality and on stability of derived information for dc optical imaging

Optical measurements of tissue can be performed in discrete, time-averaged, and time-varying data collection modes. This information can be evaluated to yield estimates of either absolute optical coefficient values or some relative change in these values compared with a defined state. In the case of time-varying data, additional analysis can be applied to define various dynamic features. Here we have explored the accuracy with which such information can be recovered from dense scattering media using linear perturbation theory, as a function of the accuracy of the reference medium that serves as the initial guess. Within the framework of diffusion theory and a first-order solution, we have observed the following inequality regarding the sensitivity of computed measures to inaccuracy in the reference medium: Absolute measures ? relative measures > dynamic measures. In fact, the fidelity of derived dynamic measures was striking; we observed that accurate measures of dynamic behavior could be defined even if the quality of the image data from which these measures were derived was comparatively modest. In other studies we identified inaccuracy in the estimates of the reference detector values, and not to corresponding errors in the image operators, as the primary factor responsible for instability of absolute measures. The significance of these findings for practical imaging studies of tissue is discussed.

Normalized–constraint algorithm for minimizing inter–parameter crosstalk in DC optical tomography

In this report, we present a method for reducing the inter-coefficient crosstalk problem in optical tomography. The method described is an extension of a previously reported normalized difference method that evaluates relative detector values, and employs a weight matrix scaling technique together with a constrained CGD method for image reconstruction. Results from numerical and experimental studies using DC measurement data demonstrate that the approach can effectively isolate absorption and scattering heterogeneities, even for complex combinations of perturbations in optical properties. The significance of these results in light of recent theoretical findings is discussed.

Imaging of fluorescence in highly scattering media

Two one-speed radiation transport equations coupled by a dynamic equation for the distribution of fluorophore electronic states are used to model the migration of excitation photons and emitted fluorescence photons. The conditions for producing appreciable levels of fluorophore in the excited state are studied, with the conclusion that minimal saturation occurs under the conditions applicable to tissue imaging. This simplifies the derivation of the frequency response and of the imaging operator for a time-harmonic excitation source. Several factors known to influence the fluorescence response-the concentration, mean lifetime and quantum yield of the fluorophore, and the modulation frequency of the excitatory source-are examined. Optimal sensitivity conditions are obtained by analyzing the fluorescence source strength as a function of the mean lifetime and modulation frequency. The dependence of demodulation of the fluorescent signal on the above factors is also examined. In complementary studies, transport-theory-based operators for imaging fluorophore distributions in a highly scattering medium are derived. Experimental data were collected by irradiating a cylindrical phantom containing one or two fluorophore-filled balloons with continuous wave laser light. The reconstruction results show that qualitatively and quantitatively good images can be obtained, with embedded objects accurately located and the fluorophore concentration correctly determined.

A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data

In this paper, we discuss approaches our group has developed for the problem of imaging the interior of dense scattering media [1]. While our principal focus is on potential biomedical applications, we believe our methods are sufficiently general to have applications to other imaging problems as well. We begin our consideration of the imaging problem by assuming that the target medium of interest interacts with the penetrating energy source with sufficient strength to cause intense scattering. We further assume that for essentially all practical schemes, only the multiply scat- tered signal is measurable. One result of multiple scattering is that all the detected photons will have propagated above and below the plane in which the source and de- tector lie. Thus, it becomes necessary to explicitly consider volume functions whose spatial distribution will depend on the properties and geometry of the medium and on the geometry and type of illumination scheme. Measurement schemes which have been suggested include steady-state [2], ultrafast [3-5], and amplitude mod- ulated [6, 7] sources. Other schemes include holographic methods which have the potential advantages of directly yielding an image without the need for numerical reconstruction [8, 9]. In developing approaches to image reconstruction, our group has emphasized the first two of the four methods [10-16].

Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method

We present an iterative total least-squares algorithm for computing images of the interior structure of highly scattering media by using the conjugate gradient method. For imaging the dense scattering media in optical tomography, a perturbation approach has been described previously [Y. Wang et al., Proc. SPIE 1641, 58 (1992); R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87-120], which solves a perturbation equation of the form W delta x = delta I. In order to solve this equation, least-squares or regularized least-squares solvers have been used in the past to determine best fits to the measurement data delta I while assuming that the operator matrix W is accurate. In practice, errors also occur in the operator matrix. Here we propose an iterative total least-squares (ITLS) method that minimizes the errors in both weights and detector readings. Theoretically, the total least-squares (TLS) solution is given by the singular vector of the matrix [W/ delta I] associated with the smallest singular value. The proposed ITLS method obtains this solution by using a conjugate gradient method that is particularly suitable for very large matrices. Simulation results have shown that the TLS method can yield a significantly more accurate result than the least-squares method.

Luminescence optical tomography of dense scattering media.

Using a set of coupled radiation transport equations, we derive image operators for luminescence optical tomography with which it is possible to reconstruct concentration and mean lifetime distribution from information obtained from dc and time-harmonic optical sources. Weight functions and detector readings were computed from analytic solutions of the diffusion equation and from numerical solutions of the transport equation by Monte Carlo methods. Detector readings were also obtained from experiments on vessels containing a balloon filled with dye embedded in an Intralipid suspension with dye in the background. Image reconstructions were performed by the conjugate gradient descent method and the simultaneous algebraic reconstruction technique with a positivity constraint. A concentration correction was developed in which the reconstructed concentration information is used in the mean-lifetime reconstruction. The results show that the target can be accurately located in both the simulated and the experimental cases, but quantitative inaccuracies are present. Observed errors include a shadowing effect in regions that have the lowest weight within the inclusion. Application of the concentration correction can significantly improve computational efficiency and reduce error in the mean-lifetime reconstructions.

Simultaneous Low-Pass Filtering and Total Variation Denoising

This paper seeks to combine linear time-invariant (LTI) filtering and sparsity-based denoising in a principled way in order to effectively filter (denoise) a wider class of signals. LTI filtering is most suitable for signals restricted to a known frequency band, while sparsity-based denoising is suitable for signals admitting a sparse representation with respect to a known transform. However, some signals cannot be accurately categorized as either band-limited or sparse. This paper addresses the problem of filtering noisy data for the particular case where the underlying signal comprises a low-frequency component and a sparse or sparse-derivative component. A convex optimization approach is presented and two algorithms derived: one based on majorization-minimization (MM), and the other based on the alternating direction method of multipliers (ADMM). It is shown that a particular choice of discrete-time filter, namely zero-phase noncausal recursive filters for finite-length data formulated in terms of banded matrices, makes the algorithms effective and computationally efficient. The efficiency stems from the use of fast algorithms for solving banded systems of linear equations. The method is illustrated using data from a physiological-measurement technique (i.e., near infrared spectroscopic time series imaging) that in many cases yields data that is well-approximated as the sum of low-frequency, sparse or sparse-derivative, and noise components.