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.

We present an analytical solution for the scattering of diffuse photon density waves from an infinite circular, cylindrical inhomogeneity embedded in a homogeneous highly scattering turbid medium. The analytical solution, based on the diffusion approximation of the Boltzmann transport equation, represents the contribution of the cylindrical inhomogeneity as a series of modified Bessel functions integrated from zero to infinity and weighted by different angular dependencies. This series is truncated at the desired precision, similar to the Mie theory. We introduce new boundary conditions that account for specular reflections at the interface between the background medium and the cylindrical inhomogeneity. These new boundary conditions allow the separate recovery of the index of refraction of an object from its absorption and reduced scattering coefficients. The analytical solution is compared with data obtained experimentally to evaluate the predictive capability of the model. Optical properties of known cylindrical objects are recovered accurately. However, as the radius of the cylinder decreases, the required measurement signal-to-noise ratiorapidly increases. Because of the new boundary conditions, an upperlimit can be placed on the recovered size of cylindrical objects with radii below 0.3 cm if they have a substantially different index of refraction from that of the background medium.

Optical inhomogeneities embedded in a turbid medium are characterized not only by their absorption and reduced scattering coefficients, but also by their index of refraction relative to the background medium. Although in diffusion theory it is impossible to separate the index of refraction from the absorption and reduced scattering coefficients in an infinite homogeneous medium, application of boundary conditions for an inhomogeneity adds enough information to separately determine these optical properties. A mismatched index of refraction affects diffuse photon propagation in two ways: photons travel at a different speed inside the inhomogeneity, and photons entering and leaving the inhomogeneity are influenced by Fresnel reflections at the surface of the object. We have integrated these two effects into the analytical solution to the diffusion equation for a cylinder in an infinite medium. Theoretical results are compared with experimental data, and the effect of index of refraction mismatch is evaluated for different combinations of optical properties.

To study the behavior of cerebral physiological parameters and to further the understanding of the functional magnetic resonance imaging (fMRI) blood-oxygen-level-dependent (BOLD) effect, multisource frequency-domain near-infrared and BOLD fMRI signals were recorded simultaneously during motor functional activation in humans. From the near-infrared data information was obtained on the changes in cerebral blood volume and oxygenation. To relate our observations to changes in cerebral blood flow the well-known "balloon" model was employed. Our data showed that the deoxyhemoglobin concentration is the major factor determining the time course of the BOLD signal. The increase in cerebral blood oxygenation during functional activation is due to an increase in the velocity of blood flow, and occurs without significant swelling of the blood vessels.

Tissue glucose levels affect the refractive index of the extracellular fluid. The difference in refractive index between the extracellular fluid and the cellular components plays a role in determining the reduced scattering coefficient (micro(s)') of tissue. Hence a physical correlation may exist between the reduced scattering coefficient and glucose concentration. We have designed and constructed a frequency-domain near-infrared tissue spectrometer capable of measuring the reduced scattering coefficient of tissue with enough precision to detect changes in glucose levels in the physiological and pathological range.

The reconstruction of scattering and absorption inhomogeneities in tissues generally involves the solution of the inverse scattering problem. This is a computationally intesive task that cannot be easily performed during image acquisition. Instead, we obtain approximate spatial maps of absorption and scattering coefficients using a back-projection algorithm, similar in principle to that used in computerized tomography. Given the nonlinear nature of light propagation in tissue, we expect that this approach can only give a first approximation solution of the reconstruction problem. Our preliminary results indicate that relatively accurate maps are rapidly obtained. We have reconstructed, to a first approximation, the optical parameters and positions of scattering and partially absorbing objects. Our back-projection approach employs frequency-domain methods using a light emitting diode as the light source (100 MHz modulation frequency, peak wavelength 715 nm). Data is collected from multiple linear scans of the investigated area at different projection angles, as in computerized tomography.

Our research is aimed at the development of a frequency-domain instrument for conducting non-invasive, real-time, near-infrared, optical tomography of tissue in vivo. Our goal is to reconstruct a spatial map of the optical properties of a strongly scattering medium in a semi-infinite-geometry sampling configuration. Specifically, we focus our attention on the absorption coefficient ((mu) a ) and the reduced scattering coefficient ((mu) s ') of the medium. We have developed a frequency-domain measurement protocol (which we call precalibrated), which permits one to recover the values of (mu) a and (mu) s ' of a uniform tissue-like phantom from a measurement at a single source-detector separation and a single modulation frequency. It requires a preliminary reference measurement on a calibration sample of known optical properties before the measurement on the investigated sample. This approach is in principle rigorous only in macroscopically homogeneous media. We have verified that the equations valid for uniform media can still be applied to yield qualitative information on the optical nature of the inhomogeneity if the effect of macroscopic inhomogeneities on the measured phase and intensity is not too large. In vitro measurements on turbid media containing scattering and absorbing homogeneities, with optical properties very similar to the background medium, gave encouraging results. We plan to implement this measurement protocol in a multisource, multidetector instrument for optical tomography.

Near-IR optical tomography is thwarted by the highly scattering nature of light propagation in tissue. We propose a weighted back-projection method to produce a spatial map of an optical parameter which characterized the investigated medium. We have studied the problem of the choice of the back-projection weight function for the absorption coefficient ((mu) a ) and for the reduced scattering coefficient ((mu) s ') of tissuelike phantoms. Working in frequency-domain optical imaging, we have initially approached the problem of quantifying the effect caused by a small absorbing defect embedded in the medium on the measured DC intensity, AC amplitude, and phase. The collection of DC, AC, and phase changes during a 1 mm step raster scan of the absorbing defect provides information on the photon path distributions and, in general, on the probed spatial region when DC, AC, and phase are, respectively, the measured parameters. We report experimentally determined weight functions for (mu) a and (mu) s '. They indicate that absorption and scattering maps can significantly differ in terms of resolution.

Near infrared optical imaging is emerging as a potentially important imaging modality, because it offers real time data access, portability, cost-effectiveness, and the relatively safe use of non-ionizing radiation. Reconstruction of images by optical tomography is complicated by the diffusive character of light propagation in optically heterogeneous tissue. The spatial volume element probed by the light path between the light source and optical detector is rather wide and depends on a variety of experimental and instrumental factors. We have published an optical image of the hand in air based on photon density wave distribution characteristics, using both steady-state (intensity) and frequency-domain (phase and modulation)1 experimental conditions. Since then, we have developed new instrumentation, better measurement protocols, some reconstruction algorithms and a more complete theoretical understanding of photon diffusion in both homogeneous and heterogeneous media. We have now performed frequency-domain measurements (at a modulation frequency of 160 MHz with 760 nm near infrared light) with the hand immersed in a scattering fluid (the infinite geometry arrangement). The advantages of our current approach include the spectroscopic resolution of physiologically interesting tissue regions, greater spatial resolution, the generation of absorption and reduced scattering coefficient maps of the image, rapid data acquisition, real time simultaneous display of the experimental parameters and calculated optical parameters and the possibility of obtaining some tomographic reconstruction.