Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations

We present a finite-element-based algorithm for reconstruction of fluorescence lifetime and yield in turbid media, using frequency-domain data. The algorithm is based on a set of coupled diffusion equations that describe the propagation of both excitation and fluorescent emission light in multiply scattering media. Centered on Newton's iterative method, we implemented our algorithm by using a synthesized scheme of Marquardt and Tikhonov regularizations. A low-pass spatial filter is also incorporated into the algorithm for enhancing image reconstruction. Simulation studies using both noise-free and noisy data have been performed with the nonzero photon density boundary conditions. Our results suggest that quantitative images can be produced in terms of fluorescent lifetime and yield values and location, size, and shape of heterogeneities within a circular background region.     

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.     

Three-dimensional unconstrained and constrained image-reconstruction techniques applied to fluorescence, frequency-domain photon migration

The development of near-infrared (NIR) optical imaging for biomedical optical imaging is hampered by the computational intensiveness of large-scale three-dimensional (3-D) image reconstruction and the potential lack of endogenous contrast for detection of relevant tissue features. In this contribution the inverse optical imaging problem is formulated in three dimensions in a noncompressive geometry as a simple-bound constrained minimization problem in order to recover the interior fluorescence properties of exogenous contrast agent from frequency-domain photon migration measurements at the boundary. The solution of the forward optical diffusion problem for the frustum shape containing fluorescence inclusions of 10:1 contrast is accomplished by use of the Galerkin finite-element formulation. The inverse approach employs the truncated Newton method with trust region and a modification of automatic reverse differentiation to speed the computation of the optimization problem. The image-reconstruction results confirm that the constrained minimization may offer a more logical approach for the 3-D optical imaging problem than unconstrained optimization.     

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.     

Experimental verification of a theory for the time-resolved fluorescence spectroscopy of thick tissues

Fluorescence spectroscopy provides potential contrast enhancement for near-infrared tissue imaging and physiologically correlated spectroscopy. We present a fluorescence photon migration model and test its quantitative predictive capabilities with a frequency-domain measurement that involves a homogeneous multiple-scattering tissue phantom (with optical properties similar to those of tissue in the near infrared) that contains a fluorophore (rhodamine B). After demonstrating the validity of the model, we explore its ability to recover the fluorophore's spectral properties from within the multiple-scattering medium. The absolute quantum yield and the lifetime of the fluorophore are measured to within a few percent of the values measured independently in the absence of scattering. Both measurements are accomplished without the use of reference fluorophores. In addition, the model accurately predicts the fluorescence emission spectrum in the scattering medium. Implications of these absolute measurements of lifetime, quantum yield, concentration, and emission spectrum from within multiple-scattering media are discussed.     

Active constrained truncated Newton method for simple-bound optical tomography

In the past, nonlinear unconstrained optimization of the optical imaging problem has focused on Newton-Raphson techniques. Besides requiring expensive computation of the Jacobian, the unconstrained minimization with Tikhonov regularization can pose significant storage problems for large-scale reconstructions, involving a large number of unknowns necessary for realization of optical imaging. We formulate the inverse optical imaging problem as both simple-bound constrained and unconstrained minimization problems in order to illustrate the reduction in computational time and storage associated with constrained image reconstructions. The forward simulator of excitation and generated fluorescence, consisting of the Galerkin finite-element formulation, is used in an inverse algorithm to find the spatial distribution of absorption and lifetime that minimizes the difference between predicted and synthetic frequency-domain measurements. The inverse approach employs the truncated Newton method with trust region and a modification of automatic reverse differentiation to speed the computation of the optimization problem. The reconstruction results confirm that the physically based, constrained minimization with efficient optimization schemes may offer a more logical approach to the large-scale optical imaging problem than unconstrained minimization with regularization.     

Dynamically adaptive mesh refinement technique for image reconstruction in optical tomography

A novel adaptive mesh technique is introduced for problems of image reconstruction in luminescence optical tomography. 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. The arbitrary shape of the bounding surface is handled by an additional refinement of computational cells on the boundary. Dynamical shrinking of the search volume is introduced to improve computational performance and accuracy while locating the luminescence target. Light propagation in the medium is modeled by the telegraph equation, and the image-reconstruction algorithm is derived from the Fredholm integral equation of the first kind. Stability and computational efficiency of the introduced method are demonstrated for image reconstruction of one and two spherical luminescent objects embedded within a breastlike tissue phantom. Experimental measurements are simulated by the solution of the forward problem on a grid of 5x5 light guides attached to the surface of the phantom.     

Near-infrared fluorescence contrast-enhanced imaging with area illumination and area detection: the forward imaging problem

Fluorescence frequency-domain photon migration measurements were acquired from tissue phantoms, each containing a fluorescent target, by means of area illumination and area detection on the same surface and for the first time, to our knowledge, compared with predictions computed with a numerical solution to the coupled photon diffusion equations. We accomplished area illumination and area detection using a planar, intensity-modulated excitation light source and a gain-modulated intensified charge-coupled device camera, respectively. A 1-ml vessel containing 1-microm solution of Indocyanine Green in 1% Liposyn was immersed 1 cm deep in each 512-ml tissue phantom. For most tissue phantoms, the background surrounding the 1-ml target was composed of Liposyn solution containing Indocyanine Green or 3,3'-Diethylthiatricarbocyanine Iodide such that the target-to-background ratio of fluorescence yield was > or = 10:1. Measurements of fluorescence modulation amplitude and phase were predicted with a mean error ranging from 10.1% to 13.6% and 0.56 degrees to 1.72 degrees, respectively. These numbers are similar to those obtained by use of single-pixel frequency-domain photon migration techniques and validate the potential use of area illumination and area detection for biomedical imaging of tissues. Results also demonstrate that target-to-background ratios of fluorescence yield and fluorescence lifetime significantly affect target detectability.     

Fluorescence-lifetime determination in tissues or other scattering media from measurement of excitation and emission kinetics

Measurements of nanosecond and subnanosecond fluorescence lifetimes are restricted to dilute, nonscattering systems since excitation and emission photon times of flight significantly affect measured fluorescent decay kinetics. We provide the theoretical rationale for frequency-domain measurements of phase-shift and amplitude demodulation made at excitation and emission wavelengths for direct determination of lifetimes in tissues and other scattering media. We confirm our analytical expressions using standard laser dyes such as 3,3'-diethylthiatricarbocyanine iodide, IR- 125, and IR- 140 in polystyrene suspensions with similar scattering properties as tissues. Our results have significant implication for lifetime-based spectroscopy in tissues and other scattering media.     

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.     

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.     

Biomedical optical tomography using dynamic parameterization and bayesian conditioning on photon migration measurements

Stochastic reconstruction techniques are developed for mapping the interior optical properties of tissues from exterior frequency-domain photon migration measurements at the air-tissue interface. Parameter fields of absorption cross section, fluorescence lifetime, and quantum efficiency are accurately reconstructed from simulated noisy measurements of phase shift and amplitude modulation by use of a recursive, Bayesian, minimum-variance estimator known as the approximate extended Kalman filter. Parameter field updates are followed by data-driven zonation to improve the accuracy, stability, and computational efficiency of the method by moving the system from an underdetermined toward an overdetermined set of equations. These methods were originally developed by Eppstein and Dougherty [Water Resources Res. 32, 3321 (1996)] for applications in geohydrology. Estimates are constrained to within feasible ranges by modeling of parameters as beta-distributed random variables. No arbitrary smoothing, regularization, or interpolation is required. Results are compared with those determined by use of Newton-Raphson-based inversions. The speed and accuracy of these preliminary Bayesian reconstructions suggest the near-future application of this inversion technology to three-dimensional biomedical imaging with frequency-domain photon migration.     

Simultaneous mapping of absorption and scattering coefficients from a three-dimensional model of time-resolved optical tomography

A Newton-Raphson inversion algorithm has been extended for simultaneous absorption and scattering reconstruction of fully three-dimensional (3D) diffuse optical tomographic imaging from time-resolved measurements. The proposed algorithm is derived from the efficient computation of the Jacobian matrix of the forward model and uses either the algebraic reconstruction technique or truncated singular-value decomposition as the linear inversion tool. Its validation was examined with numerically simulated data from 3-D finite-element discretization models of tissuelike phantoms, with several combinations of geometric and optical properties, as well as two commonly used source-detector configurations. Our results show that the fully 3-D image reconstruction of an object can be achieved with reasonable quality when volumetric light propagation in tissues is considered, and temporal information from the measurements can be effectively employed. Also, we investigated the conditions under which 3-D issues could be approximately addressed with two-dimensional reconstruction algorithms and further demonstrated that these conditions are seldom predictable or attainable in practice. Thus the application of 3-D algorithms to realistic situations is necessary.     

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.     

Fluorescence lifetime spectroscopy for pH sensing in scattering media

Fluorescence lifetime spectroscopy in the presence of tissuelike scattering is demonstrated from measurements of phase and modulation ratio as a function of modulation frequency using a pH-sensitive dye, Carboxy Seminaphthofluorescein-1 (C-SNAFL-1). From the optical diffusion equation describing the propagation and generation of fluorescence within solutions of 0.5 microM C-SNAFL-1 containing 2.0% (by volume) of Intralipid as a scatterer, the values of the average lifetime of C-SNAFL-1 were determined as the solution pH varied between 5 and 9. Average lifetime values were found to match those measured using traditional phase-modulation measurement in nonscattering media. Furthermore, the robustness of the spectroscopic technique was demonstrated by conducting lifetime measurements at varying scatterer concentrations (1.5-3.0 vol % Intralipid). These results confirm the approach for analytical sensing in scattering media via fluorescence lifetime kinetics in order to track changes in analyte concentrations.     

High-resolution imaging in a deep turbid medium based on an ultrasound-switchable fluorescence technique

The spatial resolution of fluorescence imaging techniques in deep optically turbid media such as tissues is limited by photon diffusion. To break the diffusion limit and achieve high-resolution and deep-tissue fluorescence imaging, a fundamentally different method was demonstrated based on a concept of ultrasound-switchable fluorescence. The results showed that a small fluorescent tube with a diameter of ～180?μm at a depth of ～20?mm in an optical scattering medium ([Formula: see text] and [Formula: see text] cm(-1)) can be clearly imaged with a size of ～260?μm. The depth-to-resolution ratio is shown to be about one order of magnitude better than other deep-tissue fluorescence imaging techniques.     

Three-dimensional fluorescence enhanced optical tomography using referenced frequency-domain photon migration measurements at emission and excitation wavelengths

The ultimate success of near-infrared optical tomography rests on the precise measurement of light propagation within tissues or random media, the accurate prediction of these measurements from a light propagation model, and an efficient three-dimensional solution of the inverse imaging problem. To date, optical tomography algorithms have focused on frequency-domain photon migration (FDPM) measurements of phase-delay and amplitude attenuation, which are reported relative to the incident light, even though phase-delay and amplitude of incident light are nearly impossible to measure directly. In this contribution, we examine referenced, fluorescence-enhanced frequency-domain photon migration measured at excitation and/or emission wavelengths and report on a measurement strategy to minimize measurement and calibration error for efficient coupling of data to a distorted Born iterative imaging algorithm. We examine three referencing approaches and develop associated inversion algorithms for (1) normalizing detected emission FDPM data to the predicted emission wave arising from a homogeneous medium, (2) referencing detected emission FDPM data to that detected at a reference point, and (3) referencing detected emission FDPM data to detected excitation FDPM data detected at a reference point. Our results show the latter approach to be practical while reducing the nonlinearity of the inverse problem. Finally, in light of our results, we demonstrate the method for eliminating the influence of source strength and instrument functions for effective fluorescence-enhanced optical tomography using FDPM.     

Image reconstruction by backprojection from frequency-domain optical measurements in highly scattering media

The reconstruction of the location and optical properties of objects in turbid media requires the solution of the inverse problem. Iterative solutions to this problem can require large amounts of computing time and may not converge to a unique solution. Instead, we propose a fast, simple method for approximately solving this problem in which calculated effective absorption and reduced scattering coefficients are backprojected to create an image of the objects. We reconstructed images of objects with centimeter dimensions embedded in a diffusive medium with optical characteristics similar to those of human tissue. Data were collected by a frequency-domain spectrometer operating at 120 MHz with a laser diode light source emitting at 793 nm. Intensity and phase of the incident photon density wave were collected from linear scans at different projection angles. Although the positions of the objects are correctly identified by the reconstructed images, the optical parameters of the objects are recovered only qualitatively.     

Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements

Optical imaging and localization of objects inside a highly scattering medium, such as a tumor in the breast, is a challenging problem with many practical applications. Conventional imaging methods generally provide only two-dimensional (2-D) images of limited spatial resolution with little diagnostic ability. Here we present an inversion algorithm that uses time-resolved transillumination measurements in the form of a sequence of picosecond-duration intensity patterns of transmitted ultrashort light pulses to reconstruct three-dimensional (3-D) images of an absorbing object located inside a slab of a highly scattering medium. The experimental arrangement used a 3-mm-diameter collimated beam of 800-nm, 150-fs, 1-kHz repetition rate light pulses from a Ti:sapphire laser and amplifier system to illuminate one side of the slab sample. An ultrafast gated intensified camera system that provides a minimum FWHM gate width of 80 ps recorded the 2-D intensity patterns of the light transmitted through the opposite side of the slab. The gate position was varied in steps of 100 ps over a 5-ns range to obtain a sequence of 2-D transmitted light intensity patterns of both less-scattered and multiple-scattered light for image reconstruction. The inversion algorithm is based on the diffusion approximation of the radiative transfer theory for photon transport in a turbid medium. It uses a Green s function perturbative approach under the Rytov approximation and combines a 2-D matrix inversion with a one-dimensional Fourier-transform inversion to achieve speedy 3-D image reconstruction. In addition to the lateral position, the method provides information about the axial position of the object as well, whereas the 2-D reconstruction methods yield only lateral position.     

Fluorescence spectroscopy of tissue: recovery of intrinsic fluorescence from measured fluorescence

We present a method for recovering the intrinsic fluorescence coefficient, defined as the product of the fluorophore absorption coefficient and the fluorescence energy yield, of an optically thick, homogeneous, turbid medium from a surface measurement of fluorescence and from knowledge of medium optical properties. The measured fluorescence signal is related to the intrinsic fluorescence coefficient by an optical property dependent path-length factor. A simple expression was developed for the path-length factor, which characterizes the penetration of excitation light and the escape of fluorescence from the medium. Experiments with fluorescent tissue phantoms demonstrated that intrinsic fluorescence line shape could be recovered and that fluorophore concentration could be estimated within ±15%, over a wide range of optical properties.