Test bars immersed in thick intralipid solution have been imaged with sub-millimeter spatial resolution using a time and spatial gated Kerr-Fourier imaging system. Image contrast has been measured as a function of the Fourier aperture.

A 2.5 mm thin fat strip embedded in the middle of a 4 cm thick chicken breast tissue is located using ultrafast time-resolved transillumination.

Near-infrared spectroscopy (NIRS) and near-infrared optical imaging (NIRI) are two medical techniques under development, respectively offering the ability to use light to noninvasively quantitate metabolite concentration and to image structure within the human body. Due to the dual effects of scattering and absorbance, quantitative measurement using NIRS and reconstruction of deep-tissue structure using NIRI have been problematic. Significant advances have occurred, however, over the past few years that have brought these measurements closer to reality. In this paper, we present several of the areas in which our laboratory has made progress, and discuss the relevance of these contributions in the light of work by other laboratories. With regard to NIR spectroscopy, it now appears both practical and necessary to take into account the length of the paths taken by light in order to derive deep-tissue estimates of pigment concentrations such as hemoglobin. With regard to NIR imaging, path corrected approaches offer improved resolution, and have been used successfully by our group and others to image phantoms, animals, and now humans. Different simplifications have been used in order to accomplish separately spectroscopy and imaging, but it is hoped that a common method will allow combination of the two techniques in order to achieve spatially resolved quantitative optical measurements.

A study has been performed of the image contrast produced by small spheres embedded in a homogenous highly scattering medium. The scattering medium consisted of a suspension of uniform latex microspheres, and the spheres situated at various depths in the medium were either transparent or totally opaque. The imaging technique involved measuring and discriminating between the flight times of transmitted photons. The principal components of the imaging system are a picosecond laser and a streak camera. A beam of pulses was translated in two dimensions across a vertical surface of the medium while the camera measured the temporal distribution of light collected from a point on the opposite surface. Images are presented which were generated using transmitted light integrated over steadily increasing periods of time. The contrast produced by each type of sphere was evaluated as a function of the period of time over which the transmitted light was integrated.

We describe a new technique called femtosecond transillumination optical coherence tomography which combines femtosecond pulses, coherent heterodyne detection, and fiber- optic confocal imaging to achieve time-gated and spatially resolved imaging through diffusive biological tissue. Images of absorbing objects embedded in scattering biological media are demonstrated by selecting either the earliest arriving unscattered ballistic component or the least scattered portion of the diffuse transmitted light. Time and spatially resolved analysis of photon migration through model scattering systems is used to establish fundamental limits for this class of time-gated and spatially resolved optical imaging techniques, and to evaluate their potential biomedical applications in early tumor diagnosis.

We describe the use of various nonlinear interactions based on stimulated Raman scattering for time gated imaging and their application to imaging through turbid media. Results are presented showing images obtained through solutions of non dairy creamer with attenuation of e^-33 and 100 micrometers resolution, and through 6 mm of raw chicken meat, and 12 mm of human abdominal fat.

We have measured time-resolved transmittance of ps laser pulses through scattering suspensions of thickness d employing time-correlated single photon counting. When absorption is neglected time-resolved transmittance and its Fourier transform can be expressed in terms of scaled variables, i.e. time (Theta) and angular frequency (Omega) , respectively. We have complemented our investigations on resolution by imaging translucent and absorbing objects embedded in animal tissue in vitro. Objects below the resolution limit, i.e. bars with cross sections 6 mm by 3 mm were detected at the center position of tissue being 4 cm thick. This was achieved by selecting sufficiently short initial time intervals, corresponding to fractions f < 0.1, enhancing contrast considerably in this way.

Numerical and experimental results of a study carried out to investigate the capabilities of the time gating technique to enhance images of biological tissues are reported. In particular we have investigated the confocal scanning configuration. The experimental results were obtained by using a picosecond laser and a streak camera system. The numerical results were obtained by using Monte Carlo simulations. Both elementary and semianalytic Monte Carlo methods were used. The numerical results showed that by using the time gating technique the contrast can be significantly increased when a short gating time is used. The measured time resolved spread functions were in general good agreement with numerical results. However, the experimental results showed that with our experimental setup it is difficult to measure with sufficient accuracy the small energy received during a short gating time when the slab of tissue is larger than 1 cm.

Comparative measurements were undertaken in the imaging of oblique structures in scattering media. First, an experimental set-up is described for an optically switched ps-radar. Hereby, laser pulses with duration of 3 ps are used to illuminate the object and an optically switched Kerr-gate which is selecting the light pulses scattered by the object (blood-vessel-phantom). The power of the set-up is demonstrated by the identification of this phantom embedded in several kinds of human tissue. The depth of observation was found in the range of 2 mm to 5 mm. Second, the coherence imaging (CI) is a new technique for non-invasive cross-sectional imaging of biological structure based on low coherence interferometry. In a modified Mach- Zehnder-Interferometer we positioned a phantom (tray with intralipid solution with test structure inside). The transmitted photons were optically modulated. These marked `coherent photons' were detected during an on-dimensional scan through the test structure in the scattering media.

Various characteristics of photon diffusion process in biological tissues are examined for the following geometries: (1) a semi-infinite homogeneous medium, (2) a homogeneous slab with thickness d equals 10 mm, and (3) an infinite host medium containing an inclusion object of different optical properties, using a Monte Carlo (MC) simulation technique. Our simulation results are compared with both the diffusion theory and a discrete lattice model (when applicable). We discuss the applicability of using MC simulations as a means to characterize absorbing objects in realistic biological tissue systems.

The effects of discrete absorbing and scattering objects on light propagation characteristics in random media were examined. Light propagation in the inhomogeneous medium was modeled using a finite difference representation of the time-dependent diffusion equation. Time- resolved experiments were conducted in brain-simulating phantoms containing objects of various sizes and optical properties. The validity of the model was assessed by comparing the experimental pulse to that predicted by the model.

The temporal profiles of ultrashort laser pulses propagating in random scattering media were measured inside and outside the media and analyzed using the diffusion theory. The scattered pulse profiles measured inside the random media were found to be described by the photon density instead of the photon flux. In contrast, the scattered pulse profiles emitted from the surface of the media were found to be described by either the photon density or the photon flux. These results can be consistently explained by the diffuse intensity of transport theory.

Both diffusion theory and similarity relations for light reflectance by semi-infinite turbid media have been analyzed by comparing their computational results with Monte Carlo simulation results. Since a large number of photon packets are traced, the variance of the Monte Carlo simulation results is small enough to reveal the detailed defects of diffusion theories and similarity relations. We have demonstrated that both diffusion theory and similarity relations provide very accurate results when the photon sources are isotropic and one transport mean free path below the turbid medium surface or deeper. This analysis has led to a hybrid model of Monte Carlo simulation and diffusion theory, which combines the accuracy advantage of Monte Carlo simulation and the speed advantage of diffusion theory. The similarity relations are used for the transition from the Monte Carlo simulation to the diffusion theory.

Finite element (FEM) predictions of the solution to the forward imaging problem are presented. In this study, the forward imaging problem consisted of predicting time-dependent photon migration measurements from information regarding the presence, location, geometry, and optical properties of a single heterogeneity obscured within a uniform, homogeneous random medium. FEM solutions which predict time-domain measurements of emitted light, I(t), suggest that the successful use of these measurements in an inverse imaging algorithm may be limited in the range of heterogeneity volumes and optical properties by factors such as the source/detector geometry. Two dimensional plots of fluence rate, (Phi) (p,t), illustrate the physical basis of photon migration as described by particle, photon density wave, and optical wave transport theories. FEM solutions which predict frequency-domain measurements of phase-shift, (Theta) (f), and modulation, M(f) illustrate the physical basis of interfering photon density wave measurements for detection and localization of a single absorber.

In order to investigate the applicability of Monte-Carlo simulations for (Doppler) light scattering in tissue, two upscaled experimental models were constructed. The models consisted of thin layers, either water or gelatin, with scatterers, which can be moved relative to each other. Measurements and simulations of the scattered intensity and the Doppler frequency moments are in rather good agreement.

By using both picosecond time-resolved spectroscopy and Monte Carlo simulations, we studied photon migration in a cylindrical phantom. Fan beam style source-receiver geometry was considered. The influence of inhomogeneities inside the phantom on impulse response of short incident light was studied considering a black body located at various positions inside the scattering medium. Applicability of time gating technique to the fan beam geometry for enhancement of image resolution was also examined.

Quantitation of near infrared spectroscopic (NIRS) data requires an accurate knowledge of the effective optical pathlengths within the various components of an inhomogeneous scattering medium. For instance, in the monitoring of cerebral oxygenation by NIRS, the contribution of the overlying tissues such as the skin and the skull to the total optical pathlength must be known. To elucidate this problem a Monte Carlo model of light transport through a heterogeneous scattering and absorbing medium has been developed in which the boundaries of the heterogeneous media are concentric spheres. The inside medium represents brain tissue and the outside medium represent skin and skull. The Monte Carlo model uses an anisotropic scattering phase function and values for absorption coefficient ((mu) _a) and scattering coefficient ((mu) _s) in each medium that are based upon experimentally measured data. The model follows paths of photons from an input point to their exit on the medium boundary and calculates the total optical pathlength (the differential pathlength DP) and the pathlength in each medium. An analytical proof of the applicability of the Modified Beer-Lambert Law in a heterogeneous medium is also presented and the possible contribution of the overlying tissues of the head to the total NIRS signal is discussed.

Prediction of light distribution in random medium is still an unsolved problem. Although the Monte Carlo method can deal with medium with inhomogeneous and anisotropic optical properties, the long calculating time makes it hard to be applied clinically. This paper presents a block method, by which the target medium is divided into many small cubic blocks. The absorptances and transmittances of these small cubes are pre-calculated by the Monte Carlo method. The light propagation in the random medium is simulated by calculating the light transmission between these small cubes. With this method, the distribution of light absorption in target medium can be determined within one minute even in a personal computer. As an example, the distribution of light absorption in a tumor surrounded by normal tissue is shown.

Time-resolved spectroscopy is expected to be developed for imaging of buried absorbers inside strongly scattering media. It is required to know the temporal behaviors of the reflectance and/or transmittance produced by the propagation of light impulse incident on scattering and absorbing media. The Monte Carlo method (MC) is the most frequently used numerical method, but its computation time is considerably long to obtain the results with a satisfactory accuracy. A faster numerical method is required for analysis of temporal profiles of reflectance and transmittance through random media with complicated configurations. One of the methods to solve the photon diffusion equation numerically is finite element method (FEM). This paper reports the FEM results of temporal profiles of transmittance of light impulse through scattering slabs and cylinders. Time courses of transmittances through homogeneously scattering and absorbing slabs are obtained by FEM and compared with those by MC. The results of cylinders with homogeneous scattering and inhomogeneous absorption coefficients are also presented. Temporal variations of the cross-sectional profiles of the fluence rate generated by impulse incident on a surface are shown by contour plotting, and the effect of the location and size of the localized absorbing volume on the transmittances are discussed.

We present a finite element (FE) model for calculation of photon propagation in highly scattering tissues. The model can either be used for time domain measurements, where the temporal distribution of transmitted light after an ultra short input pulse is measured, or for frequency domain measurements, where the input is a frequency modulated light source, and the phase shift and modulation depth between the input and output signal are measured. The FE model is used on inhomogeneous objects to investigate the effect of scattering and absorbing inhomogeneities on boundary measurements in both the time and frequency domain. The time and frequency versions are validated by comparing the results with data from analytical calculations and from a Monte-Carlo model. By comparing data from a two- dimensional and a three-dimensional FE model we derive a conversion factor for integrated intensity and mean time of flight that will permit the reconstruction of 3D data from a cylinder using a 2D FE model. The reconstruction is demonstrated on data generated with the FE forward model.

A Monte-Carlo simulation of photon transport through biological tissues has been developed to predict the quality of time resolved images of the breast by transillumination. The smallest diameter of a detectable carcinoma located in the breast has been computed. The simulation has been compared with analytical results of the multiple scattering theory and then with experimental results from streak camera measurements. The validity of the simulation has been thus assessed. The simulation suggests that time resolved imaging of biological tissues is possible and invaluable in the near infrared by transillumination. The enhancement of the transfer function by the introduction of time resolved detection is verified and the limitative contribution of the noise at short gating times has been investigated. The estimated diameter of the smallest detectable sphere is derived from the image quality index theory and its value is around 4 mm for a 40 mm thick breast slab. The simulated images of an absorbing object (approximating the carcinoma) within a homogeneous medium (approximating the surrounding tissue) show a significant improvement of the image with short gating times.

In reflectance pulse oximetry the ratio R/IR between the red and infrared intensity fluctuations, as measured at the skin surface, is used to estimate the arterial oxygen saturation. This ratio is influenced by light propagation in tissue, as measurements at several distances between light sources and detectors simultaneously show that R/IR depends on this distance. In the present study the influence of the estimated tissue properties on R/IR and its distance dependence are investigated by means of Monte Carlo simulations, a method to vary the optical properties without the need for a new Monte Carlo simulation. A three wavelength model has been introduced, because of secondary emission of the red LED. The influence of water absorption has been taken into account. The simulation results depend on the chosen optical properties. Results of R/IR for S_aO₂ equals 98% with properties from in vivo experiments agree much better with the measured values than the predictions based on in vitro data available in literature. The results show that the condensed Monte Carlo simulation is a valuable tool to gain insight in the principles of reflectance pulse oximetry: The model, assuming a homogeneous distribution of pulsations, is able to describe the experimental results for pulse sizes, R/IR and its distance dependence very well.

Characteristics of a system of interest can be analyzed by studying the system response to a particular input. NIR spectroscopy frequently uses an impulse (time resolved spectroscopy, TRS) and a sinusoidally modulated wave input (phase modulated spectroscopy, PMS). In this paper, we describe the theoretical principle of phase change in PMS measurement due to the heterogeneity. The phase change in a dynamic system is studied experimentally by using an experimental model and simple physiological systems.

We describe a simple method for measuring the differential pathlength of photons in a scattering medium utilizing the absorption features of water. The method allows quantification of chromophore concentration changes measured by near infrared spectroscopy without the need for time- or frequency-resolved measurements. We present the results of validation experiments performed on tissue phantoms and in-vivo comparisons between the differential path estimates yielded by water absorption and time-resolved measurements. We discus the accuracy of the differential path estimates provided by both the 975 nm and the 840 nm water features, finding that while the 840 nm feature is measured with lower accuracy for a given light flux, it is intrinsically a more accurate differential path estimator.

Optical techniques represent a valuable tool for analysis of turbid media. Recent development has emphasized dynamic measurements where either ultrashort laser pulses or high frequency amplitude modulated laser light are launched into the medium. The properties of the transmitted light range from quasi-coherent in media with limited scattering to the almost randomized incoherent behavior in strongly turbid media. The present discussion considers the influence of a boundary between a heavily scattering medium with an almost isotropic diffuse light distribution and a non-scattering medium. This case can be approximated in terms of well established solutions of the diffusion equation. It is further demonstrated that the somewhat composite mathematical expressions can be interpreted in a very simple, intuitive manner. This type of approximation is, of course, of limited validity in the surface layer itself. However, the simplicity of this approximation might make it a valuable tool for several applications.

Quantitative determination of chromophore concentrations by near infrared spectroscopy (NIRS) is possible by using the differential pathlength of the detected light, measured noninvasively as the mean time delay of the impulse response function of the tissue. Experimentally this information in the time domain is also available in the frequency domain by intensity modulating the input light and sweeping the modulation frequency between zero and infinity. We describe an intensity modulated optical spectrometer which differs from previously described systems in using four different wavelengths, a wideband modulation frequency (1 MHz to 500 MHz), and the simultaneous measurement of three parameters the dc intensity, ac amplitude, and the phase shift. The measured dc intensity in conjunction with the ac phase shift data allows changes in absorption coefficient (and hence chromophore concentration) to be determined more accurately by correcting for real time path length variations. The ac phase shift in combination with the ac modulation depth theoretically allows for the absolute measurement of tissue absorption and scattering coefficient. Preliminary performance figures for the system suggest values of rms noise of 0.0006 OD, 0.0011 rad and 0.0008% for the measured attenuation, ac phase shift and modulation depth. Using a phantom of fixed geometry with known scattering and absorption properties, the ability of the system to reproduce the information content of the impulse response function for a homogeneous phantom is investigated.

In this study, the (mu) _s' (scattering constant) and the (mu) _a (absorption constant) of rat liver mitochondria were measured by time resolved spectroscopy (TRS) with a newly innovated medium matching method. Freshly isolated rat liver mitochondria were placed inside a pouch and submerged in an intralipid emulsion. Two sets of various concentrations of intralipid emulsion, one with different concentrations of intralipid and no ink and another with various concentrations of ink and a fixed intralipid concentration, were scanned for matching the (mu) _s' and the (mu) _a of the mitochondria. Two states of the mitochondria were scanned: the resting state (orthodox state, or state 4) and the active state (condensed state, or state 3). During the active state of the mitochondria, the active respiration of the mitochondria was initiated by the addition of either calcium chloride or ADP/succinate/P_i. Comparisons of the (mu) _s' and the (mu) _a were made of mitochondria at different states.

Much of the experimental work reported on the applications of near infrared spectroscopy and imaging for therapeutic purposes has been performed on multifarious tissue simulating materials, which often have unreproducible optical properties. To facilitate the quantitative testing of spectroscopy equipment, stable, reproducible phantoms which replicate the optical properties of tissue are needed. This paper describes one such phantom. The base material is a clear, non polymerized liquid polyester resin, which forms a solid on addition of a catalyst. The polyester has a low intrinsic absorption coefficient for infrared light and is nonscattering. Before the resin is set, measured quantities of scattering particle suspensions and absorbing dyes can be added. The scattering phase function of these particles has been measured, and the mean cosine of the scattering angle, g, calculated. Knowing this, by varying the concentration of scattering particles a range of materials with known transport scattering coefficients can be produced. By varying the concentration and mix of dyes, the absorption coefficient of the resin can be easily controlled. The resin can be easily machined or cast into arbitrary shapes, with regions of differing optical properties. Once set, the polyester is stable, in terms of both physical and optical properties.

In a recent optical study two dimensional intensity patterns of light irradiated into suspensions of mitochondria were investigated. We designed our experimental model in such a way that the concentration of scattering particles was similar to concentrations found in tissues of humans and mammals. Earlier measurements performed in isolated and hemoglobin-free perfused rat liver and heart revealed that tissue spectra were strongly altered by light scattering when functional states of the two organs e.g. tissue oxygenation were changed. Based upon Mie's theory as well as our observations in perfused organs we concluded that an important factor able to induce sizeable changes in light scattering under physiological or pathophysiological conditions could be alterations in size of subcellular particles. The classical Mie theory which yields for single multipole scattering shows an increase in forward and backward scattering as a function of particle radius. E.g. when particle size is increased from a radius of 0.1 to 2 micrometers forward scattering is augmented by a factor of 273,000 while backward scattering attains a value of 13,900. Measurements of angular light distribution obtained in mitochondrial suspensions revealed first evidence that multiple multipole scattering increases backward scattering while forward scattering becomes diminished when particle size is enlarged.

In a recent optical study two dimensional intensity patterns of light irradiated into suspensions of mitochondria were investigated. We designed our experimental model in such a way that the concentration of scattering particles was similar to concentrations found in tissues of humans and mammals. Earlier measurements performed in isolated and hemoglobin-free perfused rat liver and heart revealed that tissue spectra were strongly altered by light scattering when functional states of the two organs e.g. tissll on the measurements was investigated analytically and with Monte-Carlo simulations.

Recently, researchers have used phase modulation of photons (PMP) at near infrared wavelengths to assess in vivo tissue blood perfusion. The incident light intensity is amplitude modulated in the megahertz to gigahertz range and the phase shift is measured at the detector for the photon waves that have migrated through biological tissue. The obtained phase shift is related to the pathlength for the detected photons. In the past, the models for this process have not considered the effect upon phase produced by inhomogeneities within the in vivo tissue. The phase shift is a function of the distribution of the optical properties within the medium. We used a simple experimental model to investigate the effect upon phase shift of the location for optical changes. A mathematical model has been developed to describe this effect. The results demonstrate that a measured phase shift depends upon the location at which the optical properties are changed, as well as upon the magnitude of change in the optical properties. In vivo tissue is inhomogeneous so that its optical properties are also inhomogeneous. It is therefore important to consider the optical property distribution of the in vivo tissue when assessing blood perfusion using phase modulation measurements.

We describe the use of diffuse light in homogeneous media to determine the dynamic properties of small scattering particles. A novel interferometric technique is used to measure average displacements of freely diffusing particles over times of just 20 nsec. Another experiment on an industrially significant dispersion provides insight into the process of gel formation.

The time-resolved reflectance of photons from a homogeneous tissue was modeled using a Monte Carlo simulation. The data was then converted by fast Fourier transform (FFT) into the frequency domain. In the frequency domain, the phase, (Phi) , and modulation, M, of collected light from a frequency-modulated light source was determined. A comparison of Monte Carlo and diffusion theory was made for various separation distances between the source and collector on the tissue surface. The results showed that Monte Carlo and diffusion theory agreed in the time domain only for times larger than 500 ps after injection of an impulse of photons. In the frequency domain, Monte Carlo and diffusion theory agreed only if the probe separation, r, was at least 2 cm apart for (mu) _s' equals (mu) _s(1 - g) equals 5 cm^-1, or in dimension less units r(mu) _s' > 10. The effect of buried absorbed is also tested in the time and frequency domains. A semi-infinite volume of absorber is placed at 0, 3 mm, 6 mm, or (infinity) from the surface of a nonabsorbing tissue. The presence of a deep absorber on the time and frequency domain data show that attenuation of longer pathlength photons causes the phase of collected photons to reduce and the modulation of collected photons to increase. Both effects are indicative of the net shorter pathlength of the ensemble of collected photons.

In most of the optical methods proposed for imaging an absorbing object embedded in a turbid medium, data is collected using a single source and detector scanned mechanically across the surface of the medium. In this study we exploited destructive interference of diffusive photon- density waves originating from two sources to localize one absorbing (or fluorescent) object in a scattering medium. A frequency-domain instrument is described for scanning several laser- beam spots across the surface of a turbid medium using 1D (or 2D) acousto-optical deflectors and detecting the signals with a gated, intensified CCD camera at a modulation frequency of 246 MHz. The localization of multiple objects arranged in the form of a spatial grating was investigated theoretically with an analytic model by combining the magnitude and phase of the signals detected from the objects. A novel grating pattern comprising several destructively interfering lines, which acts as spatial frequency filter, is discussed. The results were compared with those obtained using a single-source/single-detector scanning configuration. We show that the FWHM (full-width half-maximum) of the signal detected using the single- source/single-detector configuration establishes a limiting spatial scale over which multiple objects can be resolved. Beyond this limit the resolution can only be increased under severe penalty of contrast and signal loss.

We perform experiments which confirm the existence of diffuse photon density waves in homogeneous diffusive media and show that these waves obey some simple principles of optics. In particular, experiments are done to show that Snell's law holds for waves moving across a boundary between media of different diffusional indices of refraction. Other experiments are performed which investigate the scattering of these waves from spherical objects, and simple models are presented to explain these results. Finally we demonstrate that it is possible to excite a fluorescent object with a diffuse photon density wave, creating a transduced diffuse photon density wave with a different wavelength. In summary we discuss the implications of these results for medical imaging.

In this paper, basic principles of in- and anti-phased array in the localization of a heterogeneity in a scattering continuum are discussed. Various geometric configuration of multi-source placements, initial phase, and sinusoidal ac amplitude modulation are introduced. Phase and light intensity profiles in the plane of interest were computed analytically for a homogeneous scattering medium. Changes in the phase and the ac intensity with respect to the position of absorbers were also simulated by using a probabilistic numerical solution, the B-W-K technique.

This paper describes in-phase and anti-phase interferences effects that can exhibit deep amplitude nulls and sharp phase transitions. In order to broaden the range of the amplitude null and phase transition, a series of light sources are arrayed in one, two, or three dimensions with an appropriate detection system located in the null plane of each array. The system is expected to be ideal for locating a small absorption/scattering discontinuities in a relatively homogenous scatterer such as human breast. The techniques of scanning are mechanical and electrical, or by as yet untested optical elements.

We have developed an iterative reconstruction algorithm for TOAST, based on a finite element method (FEM) forward model that is fast and very flexible. The algorithm can be used at present with either non-time-resolved and/or time-resolved data, and can reconstruct either (mu) _a and/or (mu) _s parameters. An equivalent version can be formulated in terms of phase shift and modulation frequency. The basis of the algorithm is to attempt to find the minimum error norm between the measured data and the forward model acting on the trial solution, by a `classical' non-linear search in the distribution of the (mu) _a and (mu) _s parameters. In principle any search strategy could be used, but the advantage of our approach is that it employs analytical results for the gradient change (partial)M/(partial)(mu) , where M is the measurement. A number of factors influence the performance of the algorithm -- sampling density of the data and solution, noise in the data, accuracy of the model, and appropriate usage of a priori information. It appears that the presence of local minima of the error norm surface cannot be ignored. This paper presents an analysis of the performance of the algorithm on data generated from the FEM model, and from an independent Monte-Carlo model.

Results of experimental studies are presented based on steady-state optical tomographic measurements performed at 720 nm on tissue-like media having cylindrical geometry and a thickness equivalent to an uncompressed female breast. Experimental data were evaluated using a linear perturbation equation, previously described, derived from the transport equation. Results obtained demonstrate that high-resolution (< 1 mm edge detection) images are recoverable of small-diameter objects buried at depths not visible from the surface.

The idea of diffuse tomography has been recently introduced as a way of modeling an imaging problem using photons with very low energy. In this paper, we discuss how to use `Pluecker relations' to simplify the general equations. Using Pluecker relations, we are now able to reduce the original system of equations to a pair of equations before we run out of computing power.

Pulse propagation is measured in a highly scattering medium and the photon mean free path is measured for different densities of scatterers. We analyze the effect of detector orientation relative to the light source, which is a probe of the anisotropy of the photon current. We compare pulse transmission in an effectively infinite geometry to pulse transmission in a backscattering experiment. We determine the boundary condition at the interface between the scattering medium and the free medium. This consists of linear combinations of absorbing and reflecting conditions.

A genetic algorithm based approach is employed in the inverse problem of reconstructing the interior of a diffusing medium. Diffusion of optical energy in a scattering medium is simulated by a relaxation scheme. The genetic algorithm uses an error measure to successively modify an initial set of solutions yielding new generations of improved solutions. The error measure, which determines the relative merit of a particular solution, is determined by comparing the data obtained by simulating diffusion through the solution with those for the unknown medium. Unlike conventional iterative schemes, successive generations of solutions are generated through a directed parallel search in the solution space without any knowledge of the derivative of the error surface. The parallel search mechanism alleviates the problem of getting trapped in local minima. Results of experiments performed on two-dimensional planar media are presented along with suggestions for hybrid approaches that incorporate other reconstruction schemes.

Diffusion theory has been a useful and frequently applied analytical method to study the transport of light in random media. The diffusion equation requires unphysical boundary conditions. This is reflected in the fact that the diffusion solution must differ from the exact solution in a boundary region a few mean free paths thick. Exact transport theory indicates that for particle diffusion the true boundary is to be replaced by an extrapolated boundary 0.71 transport mean free paths outside of it. This is the number that has universally been used in treating light diffusion, although it is sometimes neglected because it is often a very short distance. However, because there is reflection at the boundary due to mismatch in the index of refraction, the extrapolation distance for diffusion of light is longer than that for particles, and this must be taken into account. The correction is large, even for modest indices of refraction. We show here that the appropriate boundary condition is given in terms of an extrapolation distance and tabulate this quantity as a function of relative scattering probability and index of refraction of the medium.

High frequency, intensity-modulated light waves are attenuated and phase-shifted by the absorption and scattering properties of highly scattering media, such as tissue. The simultaneous measurement of the average light intensity, modulation amplitude, and phase- shift at a fixed distance from a sinusoidally modulated light source, permits a quantitative determination of the absolute values of the absorption and scattering coefficients from a frequency-domain scan. Our studies have established the range of modulation frequencies that give the highest sensitivity to changes of the optical parameters in model systems. We have measured the optical absorption spectra of dyes suspended in highly scattering media. These spectra match those found in non-scattering media. This frequency-domain approach provides a simple method to perform quantitative spectroscopy in highly scattering media.

Measurements of time-dependent photon migration appear to provide more information for biomedical optical image reconstruction than continuous wave measurements. Yet the ultimate success of photon migration imaging (PMI) for biomedical optical tomography depends upon developing a method which can rapidly measure `time-of-flight' information, and, in near-real time, extract important information required for image reconstruction. Image reconstruction requires information to (1) detect, (2) locate the position and volume, and (3) characterize the optical properties of an optical heterogeneity that would otherwise be obscured by tissue-like scattering. In this presentation, we report PMI `images' of an obscured absorber obtained from two-dimensional time-dependent photon migration measurements which arise from single point source illumination of a scattering medium with modulated light. These PMI `images' along with a theoretical basis for PMI, suggest the potential to rapidly detect and locate the three- dimensional position of an absorber from two-dimensional frequency-domain measurements of phase, (Theta) ((rho) ,f), and modulation, M((rho) ,f). Independent single-pixel measurements and Monte Carlo simulations of (Theta) ((rho) ,f) and M((rho) ,f) confirm the PMI `images' and the hypothesis for PMI.

We studied the ability to detect small absorbing objects embedded in a highly scattering medium. Absorbing spheres of varying size, from 0.8 mm to 6.8 mm radius, submerged in a solution of highly scattering, low absorbing liquid: skim milk, were studied in a trans- illumination geometry. Groups of more than one sphere and a single circular disk, with radius identical to that of one of the spheres, were also studied. Single linear raster scans in the plane of the sphere, with the spheres centered between the source and detector, were made. Data was taken in the frequency-domain, yielding profiles of the objects in each of the three measurable quantities: dc intensity, phase, and modulation. The diffraction pattern form the sphere differed from that of the disk, demonstrating a volume effect associated with photon diffusion. The diffraction pattern of multiple spheres differed from that of single spheres.

A rigorous technique using a Monte Carlo model has been developed to determine the optical properties of biological tissue from goniometer and integrating sphere measurements. Using these techniques, the wavelength dependence of the phase function, g-value, absorption coefficient, scattering and reduced scattering coefficient were determined for postmortem neonate and adult human brain tissue over the wavelength range of 500 to 1000 nm. Single scattering phase functions as a function of wavelength have been measured using a goniometer system and optically thin tissue slices. Spectra for the absorption and scattering coefficients have been determined from a set of integrating sphere measurements, using a white light source and a CCD spectrometer. The integrating sphere data were analyzed using a novel Monte Carlo inversion technique, which makes use of the measured phase functions and which takes into account the effects of sample geometry and the angular dependence of specular reflection. This method overcomes some of the problems and shortfalls of the analytical techniques which employ Kubelka Munk or diffusion theory. The reduced scattering coefficients for all types of brain tissue showed a linear decrease with increasing wavelength. The wavelength dependence of the scattering coefficient and the phase function is shown to be considerable, and cannot be neglected.

Pathlength can be evaluated by measuring the time taken from a picosecond (psec) near infrared (IR) laser pulse to cross tissue. Differential pathlength factor (DPF) is calculated by dividing the mean pathlength by the inter-fiber distance. Data on DPF variability on humans are scarce. We investigated the forehead and forearm DPF in resting conditions and dynamically during brain hypoxic hypoxia, muscle ischemia and voluntary isometric exercise. At 3 cm inter optode spacing DPF at 800 nm was 4.3 +/- 0.2 (n equals 14, mean +/- SD) on the forearm, and 6.5 +/- 0.5 (n equals 8) on the forehead. Brain, muscle, and breast DPF values were almost constant over the inter optode spacing 2.5 - 4 cm. DPF was roughly constant in the central region of forehead. DPF drastically decreased under the fronto- temporal junction for the presence of muscle in the optical field. DPF decreased 5 - 10% during forearm ischemia with and without maximal voluntary contraction and during brain hypoxic hypoxia.

A non-invasive, near-infrared tissue spectrophotometer has been previously described. The device utilizes the differential absorption characteristics of oxy-hemoglobin (HbO₂) and deoxy-hemoglobin (Hb) at 760 and 850 nm to indicate localized changes in tissue oxygenation. The present study was undertaken to examine the relative magnitude of vastus lateralis deoxygenation in highly-trained cyclists at maximal effort. A ramp exercise to exhaustion was immediately followed by a cuff ischemia to elicit a maximal Hb signal. All of the subjects exhibited further deoxygenation upon cuff ischemia; determined to be 63%, 69%, 72%, and 56% of maximal Hb signal. This suggests that there was incomplete depletion of oxygen supply in the vastus lateralis muscles of these subjects at exhaustion.

The diffusive reflectance intensity of skin in the near-infrared range is shown to be greatly influenced by its water content, similar to the way in which hemoglobin content affects the skin color in the visible range. The different behavior of water and hemoglobin at selected wavelengths might allow us to distinguish changes in fluid balance. The simplicity and high sensitivity of an optical method show a promising way of identifying a slight change in water content in soft tissue. The understanding of how the skin reflectance spectrum responds to the change in blood and water content will be the basis of a simplified multi-wavelength monitoring instrument.

NIR time resolved spectroscopy (TRS) is one of the most feasible methods which can be used for the characterization of biological systems, due to its non-invasive nature and safety features in measurement. Breast cancer is the leading cause of death in women ages 40 - 44 and accounts for 32% of all cancer diagnosis in women. The occurrence rate is as high as one out of nine women in the USA. Breast cancer is the most common form of cancer and the second leading cause of cancer death in North America. Therefore, it is natural for researchers in the field of NIR spectroscopy to have strong interest in optical properties of normal and abnormal breast tissue. One of the main interests of NIR spectroscopy in breast cancer is the localization of the tumor. Another important feature is to characterize an anomaly non- invasively since more than 75% of mammographical anomalies are found to be benign. This could reduce the anxiety that the patients would have, as well as lower the clinical expense for the biopsy and operation (approximately $4,000 per a case).

A new technique called Ultrasound Tagging of Light (UTL) for imaging breast tissue is described. In this approach, photon localization in turbid tissue is achieved by cross- modulating a laser beam with focussed, pulsed ultrasound. Light which passes through the ultrasound focal spot is `tagged' with the frequency of the ultrasound pulse. The experimental system uses an Argon-Ion laser, a single PIN photodetector, and a 1 MHz fixed-focus pulsed ultrasound transducer. The utility of UTL as a photon localization technique in scattering media is examined using tissue phantoms consisting of gelatin and intralipid. In a separate study, in vivo optical reflectance spectrophotometry was performed on human breast tumors implanted intramuscularly and subcutaneously in nineteen nude mice. The validity of applying a quadruple wavelength breast cancer discrimination metric (developed using breast biopsy specimens) to the in vivo condition was tested. A scatter diagram for the in vivo model tumors based on this metric is presented using as the `normal' controls the hands and fingers of volunteers. Tumors at different growth stages were studied; these tumors ranged in size from a few millimeters to two centimeters. It is expected that when coupled with a suitable photon localization technique like UTL, spectral discrimination methods like this one will prove useful in the detection of breast cancer by non-ionizing means.

Determining the relationship between light absorption and chromophore concentration in brain is complicated by photon scattering, which makes it difficult to determine pathlength. In the current study we apply newly developed phase modulation (PMS) and time-resolved (TRS) spectrometers to determine tissue scattering, pathlength and brain vascular hemoglobin saturation (BVH). PMS measurements were made from both frontal cortices of 36 adults using light guides separated by 4 cm and tightly placed against the forehead. TRS measurements were done with a 5 cm probe separation. For the PMS measurements, changes in phase shift were detected at 754 and 816 nm wavelengths. For TRS, the wavelength was 670 nm in all subjects, and some subjects had additional measurements made at a wavelength of 820 nm. Scattering and the extrapolated pathlength in the absence of hemoglobin were determined from the TRS data. This information was combined with the PMS data to determine BVH. The coefficient variation for the calculated saturation was only 0.04. This suggests both scattering and pathlength have significant intersubject variability and need to be explicitly determined for appropriate calculation of hemoglobin saturation.

A procedure is described which is based on the imaging of scattered photons in human tissue. This is demonstrated in diagnostic of the maxillary. When an applicator radiation (NIR) is brought into the nasopharynx the photons transmit through the maxillary. In dependence of the optical parameters of the tissue ((mu) _a, (mu) _s, g) a part of the photons reach the ground of the Orbita, they are scattered there and detected with a CCD-camera which is positioned in front of the maxillary. During disease of the maxillary the optical parameters are changing drastically. The detected part of scattered photons are in correlation with these changes. These changes are demonstrated in IRD-pictures. The IRF is a modification of the IRD. A `light source' is produced in the tissue structure, i.e. during fluorescence angiography through adequate excitation of these markers with laser light. In dependence of the optical parameters of the tissue layers structure relevant scattered light is detectable. With a CCD- camera two dimensional pictures are detected with use of special filter components.