The spatial distribution of small oil droplets inside a 50-mm thick soil solution was imaged with a picosecond time and spatial gated Kerr-Fourier imaging system at a signal level of approximately 10(superscript -11 of the incident illumination intensity.

A comprehensive derivation of a Fokker-Planck-type equation for the photon distribution function in a highly forward scattering medium and its exact path integral solution are presented. The solution describes the transition from the ballistic propagation regime to the diffusion-like behavior and leads to a Generalized Fermat Principle (GFP) governing the most favorable photon paths (Sigma) along and near by which the most of photons ('Fermat' photons) propagate. Examples of temporal intensity profile and 'Fermat' photons paths are presented, discussed and compared with the results of standard diffusion model.

We present theoretical and experimental work on time resolved photon migration using short pulse laser radiation. The significant information about structure of turbid tissue is carried by the early arriving photons that follow almost straight arrival and return paths to the detected object in the tissue. The diffusion approximation to the transport equation in tissue does not provide a satisfactory solution for this regime, because the earliest photons are not sufficiently randomized in media in which the phase function is highly anisotropic. We are using a path integral technique to model this regime. The experiments use a short pulse Ti:sapphire laser and streak camera to obtain time resolved photon migration data from phantom samples. Our results show that a theory based on path integral calculation agrees with experimental data better than does the diffusion approximation. The thoery based on path integral calculation agrees with experimental data better than does the diffusion approximation. The theory can be used to interpret the experimental data and obtain optical imaging through turbid media.

Experimental time-resolved data was used for direct reconstruction of images of laboratory phantoms in highly scattering media. Using different time zones of the temporal profiles, computed images were calculated by solving a one-step linear perturbation equation derived from transport theory. In nearly all cases tested, high quality reconstructions were obtained even for highly undermined problems.

Optical Coherence Tomography (OCT) is a new technique that is used to obtain cross- sectional images of highly scattering tissue. OCT has been applied to image both architectural and cellular morphologic structures in clinically relevant in vitro human tissues, including the human epiglottis and full-thickness skin. The performance of OCT at 850 nm and 1300 nm is compared. In addition, high numerical aperture OCT enhanced confocal microscopy have potential for non-invasive in vivo diagnosis.

Performing imaging in the wavelength region of 1 to 1.3 micrometers is attractive because the scattering coefficient is up to a factor of 2 less in this wavelength region than at wavelengths commonly used near 800 nm. While hemoglobin absorption cannot be used for contrast at the longer wavelengths, the requirements for contrast are reduced, and other contrast sources are available. Higher numbers of photons may be used for imaging in this longer wavelength region. Longer wavelength imaging is challenging because the detectors operating beyond 1 micrometers , we have developed upconverting time gates that upconvert images from longer wavelengths (1-1.3 micrometers ) to wavelengths below 1 micrometers where good detectors exist.

Temporal profiles of transmitted and backscattered pulses from a three layered random medium were measured. Using wave-diffusion telegraphic equation and best fitting algorithms, the properties of the middle layer of slightly different optical parameters from the surrounding media were determined. The thickness and the transport mean free path were found using the transmitted pulses while the location and the aborption length of the layer were found using the backscattered pulses.

Scattering coefficients of two turbid media with the particle size varying from 0.45 micrometers to 10 micrometers have been measured from three time regions: ballistic, ballistic and snake, and steady state using a picosecond Kerr-Fourier imaging system. In all cases, the measured time- resolved scattering coefficients were found to be larger than the cw scattering coefficients.

The resolution of transillumination images is improved by time gating. Theoretically, the point spread function can be made as small as desired by shortening sufficiently the time gate. This assertion does not imply that any small object can be made visible by shortening the time gate. Indeed the noise is a limiting factor to detect objects embedded in scattering medium. The noise has been measured experimentally as a function of the time gate. Experiments have been performed on formaldehyde fixed breast tissues (10 mm thick) with a pulsed Ti:sapphire source (200 fs pulses), detected by an ultrafast diode (the resolution of the measuring system is 40 ps). Any biological tissue, even without object such as tumors or haemorrhages, has heterogeneities, the contribution of which can be considered as a noise, called the anatomical noise. The results show that in our experimental conditions, this anatomical noise is predominant on the noise due to the measuring system, at the exception of very small time gate; and it decreases as the time gate increases. This noise will limit the spatial resolution achievable by time gated transillumination.

We present an analytical perturbation analysis to study the sensitivity of diffusive photon flux to the addition of a small spherical defect object in turbid multiple scattering media such as human tissue. As a first simple application of this perturbation theory, we derive analytically the photon migration path distribution function for both the infinite medium and the semi- infinite medium geometries. This allows one to write down analytical expressions of the shape and size of the so-called 'banana' region in which the photon migration paths are concentrated. We then derive analytically the sensitivity of detected photon flux densities to the inclusion of a small spherical defect in a turbid tissue medium, for both continuous wave (cw) and frequency modulation conditions, and arbitrary contrast between the optical parameters of the defect sphere and those of the surrounding medium.

We present a formal, microscopic, solution of the radiative transfer problem for an inhomogeneous background. The inhomogeneity is described by a local change in the complex, dielectric autocorrelation function. For the homogeneous background we consider a dielectric autocorrelation function arising from a colloidal suspension of small dielectric spheres. This autocorrelation function can be determined from measurement of the angle-resolved, specific light intensity for photons in the vicinity of R propagating in direction k. Given the nature of the homogeneous background, angle-resolved light intensity measurements may be used to determine the size, shape, and internal structure of the inhomogeneity. In principle, this method improves the resolution of optical tomography to the scale of several optical wavelengths in contrast to methods based on the diffusion approximation which have a resolution on the scale of several transport mean free paths. Angle-resolved, multiple scattering tomography may be useful for the characterization of near-surface tumors.

This paper describes a convenient and quick method to determine the reduced scattering coefficient (mu) _s' and absorption coefficient (mu) _a by fitting a theoretical equation to a measured profile R_m(t). It is based on two new principles; one is to adjust (mu) _s' so as to make a new function f(t) be linear and the other is to use a special function (alpha) t + (beta) + (gamma) /t for quick determination of (mu) _s¹. Test results of the new method are given for several samples.

The photon diffusion equation is frequently used to describe the photon migration in random media like living tissues. The equation of transfer; an integro-differential equation that can hardly be solved directly. The conventional derivation of the diffusion equation gives the diffusion coefficient by using both the reduced scattering coefficient and absorption coefficient. Also the equation is believed to be valid only for cases of small absorption coefficient compared with the scattering coefficient. From recent numerical simulations, it was found that the conventional diffusion coefficient led to a large error in the early time after the impulse incidence, and it was also suggested that the diffusion coefficient given only by the reduced scattering coefficient would produce better results. In this report, the photon diffusion equation for homogeneous and inhomogeneous media is derived with a strict procedure, and the resulting diffusion coefficient is found to be determined only by the reduced scattering coefficient independently of the absorption coefficient involved. This derivation is valid independent of whether the absorption coefficient is sufficiently small or not. The solution of the fluence rate is obtained therefrom in a power series of the attenuation coefficient under a general condition. The solution in case of slowly changing absorption coefficient is also obtained in terms of an attenuation factor relative to the solution when the medium is free from the absorption. Some examples of the latter solution are given.

Standard Monte Carlo methods used in photon diffusion score absorbed photons or statistical weight deposited within voxels comprising a mesh. An alternative approach to a stochastic description is considered for rapid surface flux calculations and finite medias. Matrix elements are assigned to a spatial lattice whose function is to score vector intersections of scattered photons making transitions into either the forward or back solid angle half spaces. These complete matrix elements can be related to the directional fluxes within the lattice space. This model differentiates between ballistic, quasi-ballistic, and highly diffuse photon contributions, and effectively models the subsurface generation of a scattered light flux from a ballistic source. The connection between a path integral and diffusion is illustrated. Flux perturbations can be effectively illustrated for tissue-tumor-tissue and for 3 layer systems with strong absorption in one or more layers. For conditions where the diffusion theory has difficulties such as strong absorption, highly collimated sources, small finite volumes, and subsurface regions, the computation time of the algorithm is rapid with good accuracy and compliments other description of photon diffusion. The model has the potential to do computations relevant to photodynamic therapy (PDT) and analysis of laser beam interaction with tissues.

We develop a perturbation theory for diffuse light transport in random media that is applicable to objects with different scattering and absorption than the surrounding medium. The effect of an object with increased absorption is a simple depletion of the surrounding light field. An object with increased scattering causes a similar depletion that can be interpreted as scattering induced absorption. Additionally, a sharp transition of the scattering coefficient at the surface causes a dipole-like surface induced back scattering of light in the direction of the source. In an example we show that the first order 'Born' approximation fails for too strong perturbations, but that an iterative algorithm to calculate higher order approximations can still yield accurate results.

An optical-fiber-coupled, elastic-scatter spectrometer has proven effective in discriminating between malignant and nonmalignant tissue in the human bladder and gastrointestinal tract. The system injects broadband light into the tissue with an optical fiber and spectrally analyzes the returning light collected by an adjacent fiber. The collected photons have experienced multiple scattering events and therefore arrive at the analysis fiber after traveling varied paths. The diameter of the source fiber is comparable to its separation from the collection fiber. The diffusion model is inappropriate for this geometry; therefore, Monte Carlo simulations are used. In addition, the size of the scattering sites in tissue are expected to be of the same order as the excitation wavelengths, and Mie theory is expected to provide the best description of the scattering and extinction. We will present and compare the results of simulations and measurements of the elastic scatter signal for suspensions of latex spheres in hemoglobin solutions of varying concentrations.

Reconstructed images in optical CT by using temporally extrapolated absorbance method (TEAM) are presented. In order to evaluate the system we made optical phantoms with absorbing material, scattering material, and solvents. We reconstructed images by FBP with the new concept on the optical density by the TEAM. TEAM was superior to other methods in S/N ratio and spatial resolution.

Near IR time resolved spectroscopy has been studied for quantitative determination of absorbance in highly scattering medium such as tissue. When a very narrow optical pulse is incedent into a scattering medium, the detected pulse through the medium broadens and the temporal profile is closely related to the optical property of the scattering medium. The photon migration in highly scattering medium can be described with the diffusion theory. Thus the optical property of the scattering medium can be determined by analyzing the shape of the detected tamporal profile with the diffusion equation. We have developed the time resolved spectroscopy (TRS) system based on a time correlated single photon counting technique for data acquisition and diffusion theory for data analysis. Pulsed laser diodes with two different wavelengths are used as light sources in the system. The system size is compact and it can be moved around a laboratory or hospital easily. We demonstrated its use in vivo experiments. As a result, we were able to accurately determine absorber concentrations in a highly scattering medium and the result of these in vivo experiments indicate possible use of the system for quantitative clinical studies.

We investigate the relationship between the apparent absorption coefficient and actual absorption coefficient inside the vessels. This analytical formula predicts that the apparent absorption coefficient measured on a biological organ is a volume-weighted sum of the absorption coefficients of different absorbing components. Further, we present some apparent absorption coefficients measured in vivo in animals and humans and show that ignoring the background absorption can lead to significant errors in oxygenation determination.

Absorption coefficient measurements of strongly scattering homogeneous media have been performed using time-resolved transmittance of 100 fs pulse through a slab and cylindrical phantoms containing scattering particles suspended in weakly absorbing media. The scattering and absorption coefficients, (mu) _s and (mu) _a, were selected so that the optical properties of the media were similar to those of biological tissues in the near-infrared wavelength range. Measured curves of time-resolved transmittance of the pulse through the media were used to estimate the (mu) _a and reduced scattering coefficient, (mu) '_s, of the media. The experiments were made at two different wavelengths, 784 nm and 810 nm. Estimated (mu) _a and (mu) '_s were in good agreement with those measured in a nonscattering case by means of spectrophotometer and calculated by using the Mie theory.

Near-infrared spectroscopy is increasingly being used for monitoring cerebral oxygenation and haemodynamics. One current concern is the effect of the cerebrospinal fluid upon the distribution of light in the head. There are difficulties in modeling clear layers in scattering systems. The Monte Carlo model should handle clear regions accurately, but is too slow to be used for realistic geometries. The diffusion equation can be solved quickly for realistic geometries, but is only valid in scattering regions. In this paper we describe experiments carried out on a solid slab phantom to investigate the effect of clear regions. These experiments were used to examine the accuracy with which the different models described propagation through a clear layer inside a scattering object. We found that the presence of a clear layer had a significant effect upon the light distribution, which was modeled correctly by Monto Carlo techniques, but not by diffusion theory.

Determination of the optical pathlength of light in tissue is important to quantitate NIRS data. However, the inhomogeneity of the illuminated tissues increases the difficulty of determining the relevant optical pathlength in the tissue. For instance, in the head, the contribution of the tissues overlying the brain to the total optical pathlength cannot be ignored in the monitoring of cerebral oxygenation with NIRS. In this study, time-of-flight measurements of an inhomogeneous phantom are carried out in the laboratory to examine the contribution of the overlying tissue to the optical pathlength. The phantom consists of two homogeneous components, the boundaries of which are two concentric cylinders. The TPSF is measured with a picosecond laser and a streak camera, and the change of TPSF with the distance between source and detection fibers is examined. The experimental TPSF and mean time of flight are compared with the results of a Monto Carlo simulation and a finite element model based on the diffusion equation. A comparison of the accuracy of prediction of the pathlength by each model is presented as a function of the spacing between source and detection fibers. The intensity photon measurement density functions in each of the cylinders were estimated from the Monte Carlo simulations. The results provide estimates for the amount of the NIRS signal arising from overlying tissues in the head.

A time-resolved imaging technique has been used to obtain 2D near-IR images of a solid phantom with optical properties very similar to those of breast tissue. The phantom consisted of a highly scattering plastic slab, 54 mm thick, containing four small cylindrical blocks of contrasting optical properties. Imaging involved translating a beam of pulses in two dimensions across the surface of the phantom while recording the temporal distribution of the transmitted light at the opposite surface with a streak camera. The entire imaging process was performed automatically under computer control. Images generated using the earliest arriving light improved the visibility of the embedded cylinders compared to continuous light transillumination, but those images corresponding to flight times less than around 700ps were severly degraded due to a lack of detected photons. This degradation was partially overcome while still achieving a significant gain in contrast and resolution by comparison of the data to a photon transport model of the temporal distributions and using the model predictions as high signal-to-noise versions of the original data. All the embedded cylinders were revealed with sub-centimeter resolution.

An instrument has been designed that should allow the measurement of the temporal point spread function (TPSF) of tissue by a cross-correlation technique using an avalanche photodiode (APD) detector. Although not having the temporal resolution of a streak camera, the system is small, rugged, portable, and relatively inexpensive. A laser producing a stream of ultra-short (few ps) pulses of light is used to interrogate the tissue. The scattered light is detected on a small area APD, the gain of which can be rapidly changed, by modulation of the applied DC bias voltage. The gain of the photodiode is usually low, but for a time period of the order of a few hundred picoseconds, the gain is increased. A lock-in amplifier measures the output of the photodiode and displays the difference between the output in the two gain states. Hence the photodiode is made to sample only a small section of the TPSF. A variable time-delay mechanism in the system, allows any section of the TPSF to be sampled, therefore allowing measurement of the whole TPSF. The novel method of generating the modulation voltage for the APD, which uses microwave techniques, means that it is possible to use an electronic phase shifting network, rather than the more commonly used mechanical time-delay mechanism. In principle, this means that the system should be very rugged and reliable, as there are no moving parts. The light source used during the system development is a large mode-locked Ti:sapphire laser, however by replacing this with a picosecond pulsed laser diode, a compact and portable instrument can be built, capable of being used at the bedside.

We discuss algorithms for solving the image reconstruction problem in photon diffusion imaging. Experimental verification including an absorption image of a bovine brain at one centimeter resolution is provided.

Light absorption in heterogeneous media is investigated by optoacoustic method both theortetically and experimentally. Methods to study light absorption in opaque and turbid media, containing absorbing particles, are discussed. The resolution of the order of 10 microns is realized over the ultrasonic frequency range up to 100 MHz. Optoacoustic method allows one to determine light absorption distribution with the resolution of several microns. These possibilities are demonstrated experimentally for absorbing particles in transparent (water), homogeneously absorbing (cupric chloride solution in water), and turbid (milk) media. The distributions of light absorption in continuously inhomogeneous media (magnetic liquids) are investigated.

The temporal behavior of light diffusing through dense random media has been shown to provide information on the time-dependent density fluctuations within the media. For homogeneous fluctuating media, such as dense colloids, the magnitude of these fluctuations is obtained from the temporal intensity autocorrelation of an emerging speckle. In this contribution, we present experimental measurements of heterogeneous fluctuating media, i.e. turbid random media with spatially heterogeneous static and dynamic components, and we demonstrate that low resolution images of such media may be derived from position-dependent temporal autocorrelation measurements. Our analysis is based on a diffusion approximation for the correlation transport equation. The method should enable experimentors to distinguish different dynamical regions within turbid media.

Steady-state (SS) optical measurements are simpler and less expensive than frequency-domain (FD) measurements. So why bother with FD? This paper illustrates the advantage obtained by FD vs. SS, using computer simulated experiments. A single shperical object is placed in the center of our model for the human prostate. The object is given a range of sized and values for its incremental absorption ((Delta) (mu) _a) above the background medium (bloodless prostate), with the condition that the optical volume (equals object volume X (Delta) (mu) _a) remains constant. Simulations of SS measurements and FD measurements using a 3 GHz modulation frequency were conducted and two measurements simulated: the frequency difference ((Delta) P equals phase with object--phase without object) and the relative amplitude (A/A₀ equals amplitude with object/amplitude without object). The results show that A/A₀ at SS and 3 GHz are very similar in their response to the object size, and the (Delta) P at 3 GHz offered important additional information.

The diffusion approximation to the photon transport equation is the simplest model for photon migration. The applicability of the diffusion approximation, however, is limited. For example, it is strictly valid only when the absorption coefficient is small compared to the scattering coefficient and the source modulation frequency is small compared to the scattering rate. In this contribution we establish the theoretical range of validity of the diffusion approximation, review a frequency-dependent solution of the transport equation within the P₃ approximation, and establish the significance of the P₃ solution using Monte Carlo computer simulations. We find that the P₃ approximation, in most cases, permits a more accurate determination of the optical properties of highly absorbing media as well as from data obtained at modulation frequencies greater than 3 GHz. Interestingly, for highly anisotropic scattering (g equals 0.9), we find that diffusion theory and the P₃ approximation predict approximately the same values for the reduced scattering coefficient.

In this study, we investigate the influence of layered tissue structures on the phase-resolved reflectance. As a particular example, we consider the affect of the skin, skull, and meninges on noninvasive blood oxygenation determination of the brain. In this case, it's important to know how accurate one can measure the absorption coefficient of the brain through the enclosing layers of different tissues. Experiments were performed on layered gelatin tissue phantoms and the results compared to diffusion theory. It is shown that when a high absorbing medium is placed on top of a low absorbing medium, the absorption coefficient of the lower layer is accessible. In the inverse case, where a low absorbing medium is placed on top of a high absorbing medium, the absorption coefficient of the underlying medium can only be determined if the differences in the absorption coefficient are small, or the top layer is very thin. Investigations on almost absorption and scattering free layers, like the cerebral fluid filled arachnoid, reveal that the determination of the absorption coefficient is barely affected by these kinds of structures.

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.

We have developed a high-bandwidth frequency-domain photon migration (FDPM) instrument which capable of noninvasively determining the optical properties of biological tissues in near- real-time. This portable, inexpensive, diode-based instrument is unique in the sense that we employ direct diode laser modulation avalanche photodiode detection. Diffusion models were used to extract the optical properties (absorption and transport scattering coefficients) of tissue-simulating solution from the 300 kHz to 1 GHz photon density wave data.

Tissue fluorescence, whether from endogenous or exogenous probes, provides an opportunity for interrogation on the basis of structure and function. However to date, there has been little understanding of the localization of signal origin of fluorescence signals re-emitted from tissues. Previously, we have shown using finite element computations that the origin or re- emitted fluorescence signal depends upon the lifetime of the optical probe. The signal arising from long-lived phosphorescent probes may predominately come from the tissue-air interface rather than from deep within the tissue. Therefore, the use of short-lived optical probes may be desirable for fluorescence spectroscopy and as contrast agents for biomedical optical lived probes embedded within scattering media. Our results show that upon proper referencing of frequency-domain measurements, lifetime measurements can be made in the presence of uniform and nonuniform distribution of optical probes. The implications for biomedical optical imaging on the basis of probe lifetime are discussed.

In frequency-domain photon migration (FDPM), two factors make high modulation frequencies desirable. First, with frequencies as high as a few GHz, the phase lag versus frequency plot has sufficient curvature to yield both the scattering and absorption coefficients of the tissue under examination. Second, because of increased attenuation, high frequency photon density waves probe smaller volumes, an asset in small volume in vivo or in vitro studies. This trend toward higher modulation frequencies has led us to re-examine the derivation of the standard diffusion equation (SDE) from the Boltzman transport equation. We find that a second-order time-derivative term, ordinarily neglected in the derivation, can be significant above 1 GHz for some biological tissue. The revised diffusion equation, including the second-order time-derivative, is often termed the P1 equation. We compare the dispersion relation of the P1 equation with that of the SDE. The P1 phase velocity is slower than that predicted by the SDE; in fact, the SDE phase velocity is unbounded with increasing modulation frequency, while the P1 phase velocity approaches c/sqrt(3) is attained only at modulation frequencies with periods shorter than the mean time between scatterings of a photon, a frequency regime that probes the medium beyond the applicability of diffusion theory. Finally we caution that values for optical properties deduced from FDPM data at high frequencies using the SDE can be in error by 30% or more.

We present an analytic solution to the amplitude and phase distributions of photon density waves in strongly scattering, spherically symmetric, two-layer media containing a spherical object. The normal mode series method is employed to solve the inhomogeneous Helmholtz equation in spherical coordinates, with suitable boundary conditions. By comparing the total field on the surface of the outer layer when the object is present to when it is absent, we evaluate the potential sensitivity of an optical imaging system to inhomogeneities in absorption and scattering. For four types of background media which are different in their absorption and scattering properties, we determine: i) the modulation frequency that achieves an optimal compromise between signal detection reliability and sensitivity to the presence of object; ii) the minimum detectable object radius, iii) the smallest detectable change in its absorption coefficient and iv) scattering coefficient for a fixed object size. A discussion of the qualitative and quantitative findings is given.

We consider the problem of imaging the optical absorption of a highly-scattering medium probed by diffusing waves. We present a path integral formulation of this inverse scattering problem that is used to obtain explicit inversion formulas for diffusion imaging.

In this work we compare the Born and Rytov approximations for frequency-domain diffusing wave tomography. We confirm that the Rytov approximation gives a more accurate reconstruction of the absorptive properties. In addition, the natural separation of amplitude and phase within the Rytov approximation presents the possibility for image reconstruction algorithms which use either the phase shift or the amplitude decay of the diffusive waves. We demonstrate this effect, and apply these algorithms to simultaneously reconstruct the scattering and absorption properties of heterogeneous turbid media.

A fast iterative imaging algorithm has been developed to examine the potential of diffuse optical tomography (DOT) for clinical imaging. Forward calculations using diffusion theory were used to generate light fluence distributions within highly scattering media such as tissue. A 3D multigrid finite difference algorithm has been employed to solve the complex diffusion equation in the frequency-domain for irregular objects with spatially varying absorption and scattering coefficients. An iteractive inversion scheme has been used to solve for the distribution of interaction coefficients from tomographic measurements of the phase and amplitude of the AC photon density at the surface of the object. The time required to calculate images can be minimized using the multigrid finite difference forward solution along with a Newton-Raphson steepest descent inversion algorithm. The potential of DOT was evaluated using theoretical 3D test objects with various absorption and scattering inhomogeneities from which the phase and amplitude data were calculated from both finite difference and Monte Carlo simulations. Estimates of the resolution and contrast were calculated in order to assess the detectability of biological targets, such as tumors, blood volume changes, or blood oxygenation changes. The 3D nature of these calculations should be beneficial for optimized iterative reconstruction.

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.

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 studies are directed towards the development of a pulsed laser based optoacoustic technique to visualize absorbed light distribution in irradiated tissues. Optoacoustic technique utilizes the time-resolved detection of laser-induced stress transients to visualize absorbed laser fluence distribution in opaque and heterogeneous tissues. The acoustic signal induced under confined stress conditions of irradiation by an Nd:YAG laser pulse displays Z-axial light distribution and may be used for imaging the tissue layers where a temperature-rise of about 1 degree(s)C is achieved. Scanning of the acoustic transducer along the tissue surface line by line until entire surface of interest is tested, permits reconstruction of a 3D optoacoustic image of the irradiated tissue. Z-axial resolution of optoacoustic imaging is defined as a product of the temporal resolution of piezoelectric transducer and the speed of sound in tissues. Lateral (radial) resolution of optoacoustic images is a funtion of piezoelectric detector diameter, the diameter of laser-induced acoustic wave, and a depth of optoacoustic probing (acoustic diffraction factor). The role of various parameters, such as tissue optical properties, tissue thickness, laser beam diameter, and diameter of piezoelectric element, were evaluated for imaging resolution in lateral direction. The results of our studies demonstrated that a broad- band acoustic transducer may become a useful tool for in vivo diagnostic imaging and feed- back information during clinical laser procedures. First in vivo measurements were performed and found to be in agreement with tissue histology. This study is a very first step in the basic design of optoacoustic tomographic technology for light absorbing tissues.

Several concepts have been proposed to improve the spatial resolution of near infrared (NIR) tomography, e.g. CW illumination with spatial collimation, deconvolution, Fourier plane filtering, impulse illumination with temporal discrimination, frequency modulated illumination with amplitude- and phase-sensitive detection,...Another point of major importance is that, for a given technique, the image obtained is due to a specific combination of the local variations of the diffusion and absorption coefficients. This second aspect has been studied much less systematically. Incoherent light transport in tissues can be modeled by the radiative transfer equation. The diffusion approximation is applicable to 'thick enough' tissue and is very useful by the simple analytic solutions it provides. If sources and boundary conditions are treated carefully, the validity of this approximation is already good at modest values of the source- detector distance--except at very early times. We use the diffusion approximation and a perturbation approach. For CW illumination, we quantitatively evaluate the image of a small 'defect' imbedded in a homogeneous tissue, as a function of the characteristics of the defect (position, volume, variations of diffusion, and absorption) and of the geometry (wide or narrow light beam, thickness of the tissue, position of the detector). We show how these results could be used to optimize the discrimination of NIR imaging techniques.

The performance of reconstruction algorithms for near-IR optical tomography depends critically on the accuracy of the forward model used to evaluate the closeness of a given solution to that most consistent with the data (Maximum A-Posteriori criterion). Statistical photon noise can be accounted for theoretically, but there are also problems with inaccurate geometry, refractive index mismatching, and boundary effects. Sensitivity to such effects depends extensively on what measures are being used (time-varying intensity, integrated intensity, mean time, etc.). Although reconstructions have been obtained with a variety of data measures, including noise, they are often derived under strict assumptions about the accuracy of the model. In this paper we discuss the robustness of data measures and image reconstruction in the presence of model inaccuracies. In particular we consider robustness with respect to geometric errors in the modeling of the support of the solution and to the initial estimates for the starting solution vector.

We introduce photon measurement density functions (PMDF) as a generalization of photon sampling volumes in near-IR transillumination of scattering tissue. For a given source-detector pair, the PMDF identifies the regions within the tissue contributing to the measurement signal. The knowledge of these regions of sensitivity is important for both spectroscopic applications where the penetration depth of the probing light must be known, and for imaging applications where the PMDF can be used to select the measurement types best suited for the reconstruction of a given tissue parameter. We have developed analytical models which allows to calculate PMDFs for certain geometries and a variety of measurement types in 3D, and a finite element model (FEM) which can be applied to arbitrarily complex and inhomogeneous 2D cases. As an example, we present calculations performed on a FEM mesh generated from an MRI image of a human head.

Models of light propagation in tissue fall into two general categories: stochastic such as Monte Carlo, or Random Walk, or deterministic, such as the diffusion approximation. The former attempts to model the discrete, particle, nature of light, and inherently includes noise via the random numbers used to generate steps. The latter models the continuous, wave nature of light via a partial differential equation. Considerable effort has gone into showing that the mean of a deterministic model equates to, and the mean of a stochastic model converges to, the mean of experimental data. Efficiency considerations lead to a Monte Carlo model that has reduced variance in the sense that sample mean more quickly converges to the expectation value. When considering image reconstruction problems it is vital to be able to predict the standard errors of data from any given measure. Unfortunately, variance reduction Monte Carlo models greatly underestimate the standard errors, and 'analog' Monte Carlo methods that give correct estimates are very inefficient. In this paper we derive standard error estimations from a deterministic model that is very much faster, and demostrate the equivalence of these estimates with stochastic methods. The application of reliable error-estimates to image reconstruction is shown.

As mathematical model for the light propagation in highly scattering media, the diffusion equation for the photon density is used. The solution of the forward problem obtained by the finite element method (FEM) is compared with the analytical solution in a rectangle homogeneous domain. The application of a numerical method as the FEM allows to take into account different geometries and various embedded objects. For the inverse imaging problem two reconstruction methods are introduced acting as iterative algorithms based on the FEM forward model. As cost function the l₂-norm of output flux differences for a selected combination of times, detector, and source positions is used. The effectiveness of the image reconstruction method is demonstrated by some instructive examples.

This paper presents a new algorithm for solving the perturbation equation of the form W(Delta) x equals (Delta) I encountered in optical tomographic image reconstruction. The methods we developed previously are all based on the least squares formulation, which finds a solution that best fits the measurement (Delta) x while assuming the weight matrix W is accurate. In imaging problems, usually errors also occur in the weight matrix W. In this paper, we propose an iterative total least squares (ITLS) method which 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 associated with the minimal singular value. The proposed ITLS method obtains this solution using a conjugate gradient method which is particularly suitable for very large matrices. Experimental results have shown that the TLS method can yield a significantly more accurate result than the LS method when the perturbation equation is overdetermined.

The quality of the answer computed by an image reconstruction algorithm could significantly depend on certain details of the data collection and analysis procedures. We describe some of the decisions that must be made during both of these steps, e.g. the geometry, number, and locations of both sources and detectors, selection of a set of time windows or modulation frequencies, and whether to process the data in a simultaneous or sequential manner. Because no set of choices is self-evidently optimal, we chose to use one comprehensive set of internal light intensity distributions and detector reading, both computed from Monte Carlo simulations, as a standard for tests of different varieties of image reconstruction algorithms applied to different subsets of detector readings. The reference medium in all cases was a densely scattering homogeneous, infinitely long cylinder. The three targets consisted of the same cylinder with the addition of either a single black absorbing rod on the axis, a single black absorbing rod parallel to the axis, or thirteen black absorbing rods distributed in the form of an 'X'. Time-resolved detector responses and internal collision densities were computed directly, and from these, time-independent and frequency domain data were subsequently calculated. Images were recontructed using algebraic algorithms that solve a system of linear perturbation equations that are valid only for sufficiently weak perturbations of the reference medium. Results shown compare images obtained using data from different domains and different sets of source locations. The quality of the one-absorber images is very good to excellent. The quality of the images of the thirteen-absorber target, for which the weak perturbation premise is very strongly voilated, is only fair. Sources of random and systematic errors are identified, and the effects of both types is discussed.

We present results examining the dependence of image quality for imaging in dense scattering media as influenced by the choice of parameters pertaining to the physical measurement and factors influencing the efficiency of the computation. The former includes the density of the weight matrix as affected by the target volume, view angle, and source condition. The latter includes the density of the weight matrix and type of algorithm used. These were examined by solving a one-step linear perturbation equation derived from the transport equation using three different algorithms: POCS, CGD, and SART algorithms with contraints. THe above were explored by evaluating four different 3D cylindrical phantom media: a homogeneous medium, an media containing a single black rod on the axis, a single black rod parallel to the axis, and thirteen black rods arrayed in the shape of an 'X'. Solutions to the forward problem were computed using Monte Carlo methods for an impulse source, from which was calculated time- independent and time harmonic detector responses. The influence of target volume on image quality and computational efficiency was studied by computing solution to three types of reconstructions: 1) 3D reconstruction, which considered each voxel individually, 2) 2D reconstruction, which assumed that symmetry along the cylinder axis was know a proiri, 3) 2D limited reconstruction, which assumed that only those voxels in the plane of the detectors contribute information to the detecot readings. The effect of view angle was explored by comparing computed images obtained from a single source, whose position was varied, as well as for the type of tomographic measurement scheme used (i.e., radial scan versus transaxial scan). The former condition was also examined for the dependence of the above on choice of source condition [ i.e., cw (2D reconstructions) versus time-harmonic (2D limited reconstructions) source]. The efficiency of the computational effort was explored, principally, by conducting a weight matrix 'threshold titration' study. This involved computing the ratio of each matrix element to the maximum element of its row and setting this to zero if the ratio was less than a preselected threshold. Results obtained showed that all three types of reconstructions provided good image quality. The 3D reconstruction outperformed the other two reconstructions. The time required for 2D and 2D limited reconstruction is much less (< 10%) than that for the 3D reconstruction. The 'threshold titration' study shows that artifacts were present when the threshold was 5% or higher, and no significant differences of image quality were observed when the thresholds were less tha 1%, in which case 38% (21,849 of 57,600) of the total weight elements were set to zero. Restricting the view angle produced degradation in image quality, but, in all cases, clearly recognizable images were obtained.

A novel algorithm for imaging of small abnormalities hidden in the highly scattering media is developed. Frequency modulated signal is used as the data for the inverse problem solution. Two major novelties of this method are: (i) 'focusing' idea, by which one images 'suspected' areas only, and (ii) rather weak dependence of the method from the initial guess, which might be rather far from the background media. Numerical experiments with synthetic data are presented.

Recent work aimed at providing an absolute measurement of tissue haemoglobin saturation and a new instrument development, the spatially resolved spectrometer (SRS), are discussed. The theoretical basis of operation of this device and its hardware implementation are described and the results of validation studies on tissue simulating phantoms are presented as are preliminary measurements on human volunteers and observations on patients undergoing neurosurgery. In its present form the instrument appears to produce absolute haemoglobin saturation values for resting human skeletal muscle and the normally perfused human head which are rather low based on physiological expectations. However, we obtained a tight correlation between the saturation values measured by the SRS instrument and those obtained from blood-gas analysis of samples drawn from a jugular bulb catheter in one neurosurgery subject during clamping of the right carotid arteries.

We present a new data reduction algorithm to quantify absorption and reduced scattering coefficients of living tissues. The method requires source-detector separations larger than 2 cm and provides a simple, economic way to characterize tissue optical properties in the range of 600-900 nm and blood oxygenation. The results show that blood oxygenation in tissue can be quantified simply and accurately with this method for diffusing steady-state light, provided a suitable base-line calibration is available.

The principle of frequency modulated continuous wave radar (FMCW) has been applied to optical frequencies. By tuning the wavelength of a semiconductor laser with time, high resolution imaging in scattering media is possible. The spatial resolution depends mainly on the tuning range of the laser. Several tuning principles to be used in optical FMCW are discussed. As a coherent detection scheme with small bandwidth is used, low noise and high dynamic range are expected. The basic theory is outlined and experimental results are presented. Nonlinear tuning characteristics that degrade the resolution are discussed and interferometric methods enhancing system characteristics are proposed.

The absorption and the reduced scattering coefficients of living tissues were obtained from measurements of time-resolved reflectance at near-IR wavelengths. The inversion procedure was based on the temporal spread function for a semi-infinite medium given by the diffusion approximation. Measurements showed significant variations between the optical parameters measured on different organs and different volunteers. The single scattering properties (extinction coefficient and scattering function at small forward scattering angles) of bovine and swine brain were obtained from transmissometric measurements on thin slices of tissues. Large differences between the optical properites of white and grey matter were observed, whereas minor differences were found between bovine and swine samples.

A simple and quick approach was invented to measure optical properties of tissue-like turbid media. A laser beam with oblique incidence to the medium causes the center of the diffuse reflectance that is several transport mean free paths away from the incident point to shift from the point of incedence. The amount of shift is used to compute the reduced scattering coefficient by a simple formula. This formula is a function of the refractive index of the turbid medium divided by that of the incident medium and the angle of incidence off the surface normal for a semi-infinite turbid medium having a much smaller absorption coefficient than the reduced scattering coefficient. For a turbid medium having a comparable absorption coefficient with the reduced scattering coefficient, a revision to the above formula was made. The slope of the diffuse reflectance can be used to compute the penetration depth. Both the computation of the reduced scattering coefficient and penetration depth are based on simple and quick algorithms. the validity condition of the algorithms for slabs of turbid media are studied. This technique has potential for noninvasive, in vivo, real-time diagnosis of disease or monitoring of treatments.

Hysterectomy is the most common major operation performed in the United States with dysfunctional uterine bleeding as one of the major indications. The clinical needs for simple and safe endometrial destruction are essential. Photodynamic therapy (PDT) may offer a simple and cost effective solution for the treatment of dysfunctional uterine bleeding. The dosimetry is discussed for the case of topical application of photosensitizer. This technique might be the method of preference because undesired side effects such as skin photosensitization that is typical for systemically injected photosensitizers, can be avoided. Effective PDT requires a sufficient amount of light delivered to the targeted tissue in a reasonable period of time. A trifurcated optical applicator consisting of three cylindrical diffusing fibers has been constructed, and this applicator can deliver a typical required optical dose of about 50-100 J/cm² to the full depth of the endometrium for an exposure time of 10-20 minutes.

The concept of ultrasonic tagging of light is investigated as a possible modality for imaging human tissue with nonionizing radiation. Experiments were performed to detect the presence of ultrasonically tagged light in an optically scattering medium. Experiments with a doubled Nd:YAG laser incident on a tank filled with water and varying concentrations of 3 micrometers diameter latex microspheres showed that the doppler phase modulation due to Brownian motion as well as a phase modulation due to the presence of focused CW ultrasound were both observable using heterodyne detection of the scattered light. The experimental apparatus is described and data are presented for the detected ultrasonically modulated signal level versus particle concentration.

A high resolution light imaging system has been developed utilizing an HeNe (628 nm, 32 mW) and a receiver with post collimation mounted on an x, y table to scan the object. The image can be either recorded on a film or stored in a computer for display on a terminal. Tests show that the system in the regular mode is capable of detecting the spine and soft tissues in anesthetized mice, and of transilluminating fully an adult skull bone with a resolution for details better than one third mm. In teeth, all regular carious lesions, including incipient lesions larger than one third of a mm, can be seen in front or in the back of the tooth, none of which could be detected by dental x-ray systems. Applying a new high resolution mode, the resolution can be increased in teeth to less than 0.1 mm. Some difficulty still exists in detecting small lesions on occlusal or approximal surfaces.

A breadboard NIR sensor system has been developed based on the novel Psuedo-Random Modulation/Resolution Enhancement Technique (PRM/RET) and using a medium power diode laser system. The breadboard sensor system has been used to measure the photon migration in a phantom model consisting of milk and additive inks. The result clearly demostrates the unique capability of the PRM/RET sensor system for high-resolution time-resolved spectroscopic measurement with a nanosecond resolution which is currently limited by the digitizer bandwidth. The data obtained from this experiment was analyzed to retrieve the optical parameters of the phantom quantitatively. Based on the performance of the breadboard system, a prototype system configuration is being designed to obtain over a few GHz bandwidth and a few tens of psec precision which will be applied for the simple and accurate retrieval of the cerebral optical properties.

Diffusion approximation (first-order) and Monte Carlo methods have been widely used in modeling light propagation tissues. Diffusion theory can provide a reasonably accurate description of light distributions in regions some distance from boundaries and sources, whereas Monte Carlo methods can give a more accurate solution without these limitations, but are computationally time-consuming. A higher-order diffusion approximation of light propagation in 2D tissue geometries using a finite element method is presented in this paper. We demonstrate that higher-order diffusion approximation can provide more accurate solutions than the usual first-order diffusion model yet is still much lower in computational cost than Monte Carlo simulation. Two benchmark problems are tested. The first one which consists of a rectangular geometry has an exact analytical solution and confirms our higher-order diffusion model implementation. The second test problem is an optically homogeneous, 2D cylindrical geometry and the computed solutions are compared with measrued data along the boundary of a tissue-like liquid phantom. The agreement is found to be promising and potentially more accurate than the conventional first-order diffusion equation approximation.

We demonstrate successful image reconstruction based on experimental data obtained with a cw HeNe laser system in a laboratory phantom having two optically distinct regions. The experimental system which presently supplies intensity only measurements exploits a tomographic type of data collection scheme that provides information from which a spatially variable optical diffusion coefficient map is deduced. Different types of boundary constraints have been considered and the images produced indicate that the zero average intensity boundary constraint results in better imaging quality. While the cw optical system used in these experiments is crude, and the physical phantom imaged is highly idealized, the results suggest that tomographic data collection coupled to a finite element image formation algorithm offers a potentially powerful approach for biologically based optical imaging.

Reflectance and fluorescence spectroscopy are successfully used for skin disease diagnostics. Human skin optical parameters are defined by its turbid, scattering properties with nonuniform absorption and fluorescence chromophores distribution, its multilayered structure, and variability under different physiological and pathological conditions. Theoretical modeling of light propagation in skin could improve the understanding of these condition and may be useful in the interpretation of in vivo reflectance and autofluorescence (AF) spectra. Laser application in medical optical tomography, tissue spectroscopy, and phototherapy stimulates the development of optical and mathematical light-tissue interaction models allowing to account the specific features of laser beam and tissue inhomogeneities. This paper presents the version of a Monte Carlo method for simulating of optical radiation propagation in biotissue and highly scattering media, allowing for 3D geometry of a medium. The simulation is based on use of Green's function of medium response to single external pulse. The process of radiation propagation is studied in the area with given boundary conditions, taking into account the processes of reflection and refraction at the boundaries of layers inside the medium under study. Results of Monte Carlo simulation were compared with experimental investigations and demonstrated good agreement.

Based on the computerized microscope 'Diamorph', originally designed to provide morphodensitometric parameters of cells and tissues via image processing, we have elaborated a unified appraoch enabling to perform both structural and functional diagnostics of blood cells. The structural diagnostics consists of the registration of the stationary erythrocyte profile while the functional diagnostics is related to the dynamic flow parameters in a glass capillary. This approach has been tested on samples of blood drawn from patients previously subjected to low-energy ionizing radiation.

We present results for real-time holographic imaging in the medical imaging window (approximately 650 to 1000 nm) using photorefractive media. By recording holograms of a USAF test chart using a Ti:sapphire laser, we have selected the coherent)mostly ballistic) light and formed an image through a scattering medium which simulates biological tissue. The advantage of this approach is that a 2D image may be acquired in 'real time', i.e. without scanning. This will permit electronic signal processing and averaging, which may be used to reduce the deleterious effects of speckle. If the holograom is written with ultrashort pulses, then time-gated imaging is possible. This may be used to provide depth information by recording the 'time of flight' of the image light. We have recorded such holograms with picosecond pulses and present time-gated image data.

Laser doppler probing of moving matter is an effective noninvasive technique for velocity field profiling. For this, quality laser doppler anemometers (LDA) are widely used for the diagnostics of spatially distributed flows. When applied to transparent media, high spatial resolution of the LDA is attainable by forming very small probe volumes at the focus of the probing laser beam(s). In highly scattering media, such as biological tissues, laser radiation propagates in the course of multiple scattering events. As no focusing is possible, the shape, size, and location of the probe volume appear uncertain. In our study on Monte Carlo computer simulated experiments we sought to reveal spatial patterns in LDA doppler spectrum formation. We applied a model of semi-infinite turbid medium to simulate experiments with biological materials at the backscattering detection mode. The medium contained similar light scattering particles, a certain portion of those regarded as moving. The scattering properties of the particles were chosen roughly similar to those of red blood cells.

Principal component analysis (PCA) is used to analyze the components of variable concentration (chromophores) from near IR spectroscopy measurement. Up until now, this method was only used in some special cases when the singular vectors of the measurement data matrix clearly resemble the component spectra or some simple combinations (e.g. sum or difference) of the spectra. In this paper, we find and derive a generally applicable theoretical relationship between the singular vectors and the component spectra. With this relationship, PCA becomes a powerful tool to detect how many and also which chromophores contribute to the observed attenuation changes measured by NIRS. Based on this relationship, a method is proposed to estimate the components of variable concentration from the data matrix by means of a principal component analysis and canonical correlation analysis (CCA). This method, which detects the chromophores of variable concentrations by analyzing numerically the canonical correlations, is more accurate and more generally applicable. Some results of the ananlysis are given.

A linear perturbation model for reconstructing images of absorption ((Sigma) _a) and scattering ((Sigma) _s) cross sections of a highly scattering medium is presented. Two factors limiting the accuracy of image reconstructed from linear perturbation models are described. These are the self-shadowing effect of a single perturbation and the mutual coupling effect of two perturbations. A relaxation method to numerically solve the diffusion equation for a slab geometry and to compute the flux of diffuse light crossing both surfaces of an initially nonabsorbing ((Sigma) _s equals 1.0, (Sigma) _a equals 0.00 slab, as the (Sigma) _a in one or two cells of the medium is increased. When a single voxel was perturbed, it was found that: 1) for all voxel locations considered, a plot of change in light flux versus change in (Sigma) _a deviates significantly from a straight line when the additional (Sigma) _a exceeds approximately 0.1; 2) the rate at which the flux perturbation approaches its limiting value as (Sigma) _a increases is independent of the detector location; 3) with the exception of voxels in the immediate vicinity of the source, the rate at which the flux perturbation approaches its limiting value as (Sigma) _a increases is independent of the location of the perturbed voxel. When two voxels were perturbed simultaneously, it was found that: 1) the distance separating two voxels is the most important determinant of the maximal mutual coupling effect they can have; 2) the maximal mutual coupling effect falls rapidly as the distance between two voxels increases; 3) if both perturbed voxels are lie in the same layer (i.e., depth), the rate at which the mutual coupling effect approaches its limiting value as the (Sigma) _a perturbations increase is independent of the detector locations; 4) when the perturbed voxels are in different layers, there is a small but significant difference between the effects of mutual coupling on the diffuse transmission and on the diffuse reflectance. Low- order rational functions are sufficient for modeling both the self-shadowing and mutual coupling effects. Methods for modifying image reconstruction algorithms to incorporate corrections for these two effects are discussed.

This study reports on results of our efforts to improve the efficiency and stability of previously developed reconstruction algorithms for optical diffusion tomography. The previous studies, which applied regularization and a priori contraints to iterative methods--POCS, CGD, and SART algorithms--showed that in most cases, good quality reconstructions of simply structured media were achievalbe using a perturbation model. The CGD method, which is the most efficient of the three algorithms, was, however, in some instances not able to produce good quality images because of the difficulty in applying range constraints, which can cause divergence. In this study, a scheme is proposed to detect this gradient vector is reset and the CGD reconstruction is restarted using the previous reconstruction as the initial value. In gradient vector is reset and the CGD reconstruction is restarted using the previous reconstruction as the initial value. In addition, a rescaling technique, which rescaled the weight matrix to make it more uniform and less ill-conditioned, is also used to suppress numerical errors and accelerate convergence. Two criteria, rescaling the maximum of each column to 1 and rescaling the average of each column to 1, were applied and compared to results without rescaling. The results show that, with properly imposed constraints, good quality images can be obtained using the CGD method. The convergence speed is much slower when constraints are imposed, but still comparable to the POCS and SART algorithms, The rescaling technique produces more stable and more accurate reconstructions, and speeds up the reconstruction significantly for all three algorithms.

Samples of erythrocyte suspensions in normal and pathological whole blood in Couette flow with thickness of 1 mm have been studied by laser backscattering technique. This method allows us to analyze the kinetics of the disruption of large and small aggregates and to reveal the effects of growth of aggregates in shear flow followed by the quick sedimentation and migration of erythrocytes to the axis of the flow in case of pathological blood. Reproducible low-frequency oscillations of the photocurrent measured at the output of the photodetector of light backscattered from different sites in the flow have been registered. These oscillations appeared at shear rates from 30 to 70 sec^-1. Their frequency was proportional to the shear rate or the frequncy of rotation of the inner cylinder. It is possible that these oscillations are the manifestation of Taylor vortexes. In the given experimental geometry and shear rates the Taylor number is lower than the value of the Taylor number for simple fluids.

The novel method for the imaging of highly scattering objects is proposed. The method is based on the measurements of two-frequency correlations of scattered radiation.

On tissue scattering parameters, determination illustrating sensitivity and dynamic range of frequency-domain method using a mode-locked Nd:YAG laser and modulated injection GaAs laser were performed. For microwave range, both methods in application tissue and water- milk mixtures, latex investigation comparable results were obtained.

A homemade static light scattering set-up has been used to study scattering of spherical polystyrene particles (polyballs) and bacterial strains. The polyballs are of different sizes and of spherical shape. Bacterial strains are thin rods and of different sizes. Unpolarized, linearly polarized, and circularly polarized light is used in our studies. The relation between size, shape, and the state of polarization of the incident light on scattering is studied experimentally. The polarization ratio and the scattering ratio are determined for the macromolecules.

The permeability of tumor blood vessels to contrast agents (Gd chelates) has formed the basis for MRI breast tumor identification. It is also believed that angiogenesis starts before further tumor growth. Here we report tumor detection and localization using the fluorescence of Indocyanine Green (ICG). ICG fluorescence is excited by CW NIR laser light with a central wavelength of 830 nm is recored as a function of time. Differential fluorescence signals were observed after a low-dose intraveneous injection of ICG aqueous solution in rat model experiments. The difference between the fluorescence signal from the tumor side and the fluorescence signal from the control side is detectable even when the tumor is very small. During the tumor exponential growth phase, the ratio of these two signals is approximately 2.5; the ratio of the initial ICG clearance velocity in the tumor leg to that in the control leg is about 3. New investigations on human subjects with breast tumors, or reoccurrence after breast tumors were removed, are underway, and preliminary differential fluorescence signals have been observed.

By transilluminating human tissue in vivo in the visible and near-IR regions, specific information can be obtained in utilizing both the scattering and the absorbing properties of light. Different compositions of fatty, fibrous, glandular, and muscular tissues are associated with different optical parameters (reduced scattering and absorption coefficients). To characterize human breast tissue in vivo, measurements were carried out in a clinical environment. Thus the tissues, which showed a variety of pathalogical alteration, where measured in patients with different age, different breast size, in varying locations in the breast. The results indicate that other characteristics beyond the pure detection of the amount of blood in the neovascular network, in particular the volume concentrations of water and fat, seem to be important for the discrimination. In order to quantify this observation, an analytical model was developed that takes the volume percentages of fat and water, the concentration and oxygenation of hemoglobin, and the relevant optical coefficients into account. The in vivo spectra could be fitted in all cases. Typical results will be discussed and preliminary statistical correlations presented.

The detection of small amounts of indocyanine green (ICG) in small volumes would suggest its potential use in the detection of early breast tumors. While phased array has already shown its ability to sharply localize small amounts of ICG in the picomole region, the question has arisen, what would be the comparable sensitivity of continous light systems for the same purpose? If this were a comparable sensitivity, the advantages of the simplest of opto- electronic systems and the use of light intensity not limited to those available under FDA regulations for laser diodes could be realized. In this research work, we investigate two methods of enhancing the contrast agent between diseased and healthy tissue using low frequency amplitude modulated light sources. The first method exploits the symmetry between the left and right breast and the second exploits the cylindrical symmetry of the breast. Both effect are enhanced by the use of an injected contrast agent (ICG). Based on the theory and model study, several human subjects cases were studied in the Hospital of the University of Pennsylvania. The results show that the peak signal can get about 60 seconds after ICG injection through the vein and then will take few minutes to get back to the baseline. The half decay time and maximum (Delta) OD are dependent of the characteristics of the breast tissue.

Optical determinations of tissue temperature by near-infrared (NIR) spectroscopy provides the basis for measuring localized changes in tissue metabolism associated with congnition, mechanical work, inflammation, or malignancy. Absorbance changes in NIR spectra of tissue water are shown to correlate with tissue sample temperature. Digital tissue transmission spectra of samples 1-5 mm thick of bovine and avain muscles were obtained over temperatures ranging from 17 to 45C. Reflectance spectra were obtained from blocks of porcine muscle over the temperature range 14 to 46C. Multilinear regression analysis of the correlation between absorbance or reflectance and tissue temperature demonstrated that each O-H bond onvertone spectral region (960, 1200, 1450, and 1920 nm) has a high correlation with tissue temperature. Transmission results gave standard error of the estimates (SEE) and standard error of prediction (SEP) from cross-validation analysis of 0.02 to 0.12C for SEE and 0.04 to 0.12C for SEP. Reflectance results gave SEEs of 0.06 to 0.24C. Combinations of O-H vibrational modes of water give rise to NIR absorbance in solution and tissue. The spectra show a regular shift to shorter wavelength absorbance as temperature increases. Such shifts may be due to decreasing hydrogen-bonding with increasing temperature. These studies have established that the temperature dependent changes in water NIR spectra can be utilized to evaluate tissue temperature with precision and accuracy.

Disorders of mitochondrial metabolism are manifest by inordinate fatigue, weakness, as well as severe neuromuscular disorders. Diagnosis has required pathologic findings on muscle biopsy and identification of biochemical defects in mitochondrial respiration. NIRS, a noninvasive optical technique, permits the quantitative measurement of changes in blood volume and tissue oxygenation in vivo, at rest, during exercise, and post-exercise recovery. The dual wavelength spectrophotometer consists of an optic probe with 2 lights appropriate for red light emission. Interference filters select the wavelengths, 760 to 850 nm, appropriate to the broad bands of hemoglobin, in conjunction with silicon detectors sensitive to this infrared spectrum. In all normal test subjects, the blood volume tracing demonstrated a decreased blood volume normally seen in exercising muscle. The increase of absorbance at 760 nm, with respect to absorbance at 850 nm, reflects deoxygenation of hemoglobin and occurred promptly at the start of exercise. At the end of exercise, oxygenation returned to baseline accompanied by hyperemia. Four patients with known disorders of mitochondrial metabolism demonstrated a paradoxical oxygenation during exercise that returned to baseline at the end of exercise. Increased oxygen supplied by a normal cardiopulmonary response to exercise is not utilized and results in a pardoxical oxygenation during exercise. This simple, noninvasive technique permits an accurate measurement of oxygen utilization in the exercising limb and is a useful clinical tool in screening patients for disorders of mitochondrial metabolism.

We have computed optical images of the female breast based on analysis of tomographic data obtained from simulated time-independent optical measurements of anatomically accurate maps derived from segmented 3D magnetic resonance (MR) images. Images were segmented according to the measured MR contrast levels for fat and parenchymal tissue from T1 weighted acquisitions. Computed images were obtained from analysis of solutions to the forward problem for breasts containing 'added pathologies', representing tumors, to breasts lacking these inclusions. Both breast size and its optical properties have been examined in tissue. In each case, two small simulated tumors were 'added' to the background issue. Values of absorption and scattering coefficients of the tumors have been examined that are both greater and less than the surrounding tissue. Detector responses and the required imaging operators were computed by numerically solving the diffusion equation for inhomogeneous media. Detectors were distributed uniformly, in a circular fashion, around the breast in a plane positioned parallel and half-way between the chest wall and the nipple. A total of 20 sources were used, and for each 20 detectors. Reconstructed images were obtained by solving a linear perturbation equation derived from transport theory. Three algorithms were tested to solve the perturbation equation and include, the methods of conjugate gradient decent (CGD), projection onto convex sets (POCS), and simultaneous algebraic reconstruction technique (SART). Results obtained showed that in each case, high quality reconstructions were obtained. The computed images correctly resolved and identified the spatial position of the two tumors. Additional studies showed that computed images were stable to large systematic errors in the imaging operators and to added noise. Further, examination of the computed detector readings indicate that images of tissue up to approximately 10 cm in thickness should be possible. The results reported are the first to demonstrate that high quality images of small added inclusions can be obtained from anatomically accurate models of thick tissues having arbitrary boundaries based on the analysis of diffusely sscattered light.

Phase maps of optical wave fields are found to consist primarily of phase saddles strung between phase singularities (vortices). Phase extrema (maxima or minima) appear to be absent in the phase fields of laser beams, and are relatively rare in the phase fields of speckle patterns. Theoretical models are presented that help explian this unexpected result. The relationship between stationary points of phase and stationary points of amplitude is also considered.

Infrared vibration spectroscopy appears to be a more powerful technique for diagnosis than visible or UV spectroscopy. Advantages of IR spectra include: 1) vibrational motion has a smaller tissue absorption coefficient than electronic motion, 2) scattering of infrared radiation has a lower cross section than visible or UV light, (these two facts allow deeper penetration of IR radiation) and 3) vibration spectra provide a better fingerprint of chemical groups present in cells than the unresolved broad electronic spectrum of biological molecules. In the present work, Fourier-transform IR spectroscopy was used to compare cultured human fibroblast and malignant fibrosarcoma cells. Significant differences were observed by comparing the spectra of the normal cells with that of the cancer cells. the PO₂ symmetric stretching mode at 1082cm^-1 in the cancer cell is reduced in intensity. These observations are similar to those reported previously by Wong et al in comparing the IR spectra of pairs of normal and cancerous cells from the colon and cervix. However, the observed increase in the relative intensity of the symmetric to antisymmetric CH₃ bending mode are only found in fibrosarcoma and basal cell carcinoma. The decrease in intensity of the CH₂ bending mode relative to that of CH₃ mode was observed only for fibrosarcoma cells. This finding with paired human fibroblast and fibrosarcoma cells suggests that fatty acid chains or side chains of protein in the cancer cells are partially degraded leading to more terminal carbon. It is also possible that changes in the environment upon carcinogenesis induces a change in the relative absorption cross sections for the CH₃ and CH₂ bending vibrations.

Based on the Rayleigh-Gans-Debye thin shell approximation, a fast Fourier cosine transform method was developed to retrieve vesicle size distributions directly from the light scattering measurement. The method was tested numerically mainly on the scattering data generated by the exact Mie solution for isotropic vesicles. Monomodal and bimodal Gaussian distributions were used to represent vesicles with radii ranging from 0.05 micrometers to 0.5 micrometers . The recovered distributions were in good aggreement with the original distributions. Peak positions were recovered within 10% of the original ones, even when 20% random error was added to the simulated data. Noise tolerance of this method was much higher for large vesicles than for small vesicles. The effect of the refractive index of the medium was also investigated using the simulated data. To study the effect of the optical anisotropy of the membrane on the recovery, the exact Mie solution for anisotropic hollow spheres was used to simulate scattered intensity data. The recovered distributions in this case were slightly shifted towards small radii from the original ones.

An accuracy analysis is made of currently used near infrared spectroscopy (NIRS) algorithms, based on the Beer-Lambert law, for quantification of chromophore concentration changes in neonatal brain. In particular, the regression method and chromophores considered, as well as the influence of the wavelength-dependent extinction coefficients, on the accuracy of the computed concetration changes of Hb, HbO₂, and Cytaa₃ is investigated. The total least squares method, which considers errors in the specific extinction coefficients as well, is able to double the accuracy (compared to least squares), when appropriate weights, derived from the error variances, are added and enough wavelength measurements (> 100) are available. Furthermore, the influence of the number of wavelenghts used, as well as the importance of the choice of the wavelength sebset, is studied. It is shown that the accuracy significantly increases, up to 10 wavelengths. Additionally, optimizing the condition number of the extinction coefficient matrix allows to select small wavelength subsets that clearly outperform presently used sets in accuracy for all computed concentration changes. Finally, the influence of the chromphores, such as H₂O is shown. H₂O may only be included in the model when enough wavelengths (> 100) are used for NIRS measurement or when the chosen subset minimizes the condition number of the corresponding extinction coefficient matrix.

The effect of inhomogeneities within a highly scattering medium on the reflectance and on the transmittance was studied both with numerical simulations and with measurements on phantoms. A slab of diffusing medium with optical properties similar to those of a compressed breast was condidered. With an elementary Monto Carlo code the temporal point spread functions corresponding to photons emerging at different distances from the thin collimated light source were evaluated. For some detector positions, the coordinates of all the scattering points for each received photon were stored. Numerical simulations were carried out first for a homogeneous medium, requiring a few days for calculations. Using the stored trajectories it was possible to obtain in a short time, the corresponding temporal point spread functions when an absorbing inhomogeneity was considered within the slab. It was possible to obtain the temporal point spread function for many different positions, sizes, and shapes of the inhomogeneity inside the diffusing medium. The accuracy of the numerical results was checked by a comparison to experimental results obtained from measurements on suspensions of calibrated spheres having known optical properties. Measurements were carried out both with a picosecond system and with a continuous wave system.

We measured the time-dependent optical point-spread-function of light which has traversed a turbid, multiply scattering medium. We used a coherently amplified raman polarization (CARP)-gate system which had 250 femtosecond temporal and submillimeter spatial resolution. We find that resolutions better than the theoretically predicted diffusion limited value are achievable for samples longer than 90 scattering lengths when the anisotropy parameter g is greater than 0.995. Experimental results can be fit adequately with a model based on the isotropic-scattering solution to the transport equation in an infinite, turbid solid, characterized by a rescaled scattering length l_r.

We study the optical detection of absorptive tumors in turbid tissues, using a random-walk model to describe the migration of photons in the tissue. We consider time-resolved transillumination measurements in slab-like tissues, and calculate the tranmsmitted intensity with and without the inclusion. The ratio of these quantities, defined as the measure of the detectability, is studied as a function of the inclusion size and absorption coefficient. The detectability is found to depend only on the difference between the absorptivities of the abnormality and the surrounding tissue. The nonmonotonic behavior in time of this ratio corresponds to the three different types of photon trajectories in the tissue, and its extremum points provide information which can be used to determine the optimal time window for best detection.

The possibility is considered for revealing and identifying pathology through the spatially distributed low amplitude dynamic optical contrasts, which reflect the physiological dynamics of the living tissue. A simple conventional CCD-based system and software for optical image sequence processing are described. Examples of the application of this approach for breast imaging diagnostics are demonstrated. Problems of description and analysis of living tissue integral spatio-temporal patterns are discussed.

In the process of inflammation, leukocytes must travel from the intraluminal space of the capillary to the interstitial space in order to reach the site of the inflammation. The two major populations of mature human leukocytes based on the morphology are the polymorphonuclear leukocytes (PMN), and mononuclear leukocytes (MNL). Previous research on PMNs and MNLs at the Biomedical Engineering and Science Institute of Drexel University have shown that their migration can be markedly enhanced by excitation with electric and magnetic fields. This presentation demonstrates that the migration of PMNs under excitation of photons is enhanced in the red light region of (lambda) equals 660 nm and inhibited in the green light region of (lambda) equals 565 nm. There is an intensity threshold at which red light enhances migration and an intensity threshold at which green light inhibits migration. In these experiments the Boyden technique was used with the distance of the cell migration through a cellulose filter measured in terms of the leading edge. The comparison of the relative value of the distance to cell migration under a light to cell migration without a light stimulus was recorded as a cytokinetic index, K.I.. K.I. is a measure of the cytokinesis which is the progress of the cell movement in which the migration is enhanced by substances in the cell environment irrespective of a concentration gradient. The cytotactic index is a measure of cytotaxis which is the directional movement along a chemical gradient formed by a chemotactic factor. A Russian pulsed commercial laser biostimulator in the near infrared wavelength above an intensity threshold enhances PMN migration. Intermittent green and red stimulators below the intensity threshold markedly influence the cytokinetic index of PMNs while above the intensity threshold, this influence is deminished.

The presence of glucose in an aqueous solution increases its refractive index and therefore has an influence upon the scattering properties of particles suspended in solution. The subsequent effect upon light transport in multiple scattering, tissue simulating phantoms is demonstrated experimentally in a slab geometry and theoretically by applying diffusion theory. As the glucose-induced scattering changes are small, any possible application for noninvasive glucose monitoring in diabetic parients has to rely on an accurate separation of scattering and absorption changes. In phangom studies, it is shown that optional measurements in the frequency domain allow this separation. Furthermore, preliminary experiments suggest that this method can be applied in vivo. It was found that changing the blood flow in tissue, the effect on the scattering coefficient is small.

Time-resolved absorption spectra were measured in the near-IR wavelength range from 700 to 900 nm with rat heads in vivo under various respiratory conditions, based on our time- resolved microscopic Beer-Lambert law. The spectra were expressed in absolute absorption per unit optical path (cm^-1). Applying a regression analysis to the spectra, we obtained absolute concentrations of HbO₂ and Hb in the rat head. These values agreed with those measured in direct assay analysis, and the feasibility of our time-resolved photometry for quantitation of chromophores in living tissue was demonstrated. This fact supports our assumption that light absorption in a scattering media such as living tissues in independent of the scattering. Based on this study, we constructed a portable system for clinical applications. The system employs three diode lasers of different wavelengths for generating picosecond light pulses and high speed PMT for a time-correlated single photon counting method. The system performance shows its applicability to quantitative monitoring of oxygen metabolism in living tissues.

Medical optical imaging (MOI) and spectroscopy (MOS) use light emitted into opaque tissues in order to determine the interior structure and chemical content. These optical techniques have been developed in an attempt to prospectively identify impending brain injuries before they become irreversible, thus allowing injury to be avoided or minimized. Optical imaging and spectroscopy center around the simple idea that light passes through the body in small amounts, and emerges bearing clues about tissues through which it passed. Images can be reconstructed from such data, and this is the basis of optical tomography. We have used a time-of-flight system reported earlier to monitor oxygenation and image hemorrahage in neonatal brain. This chapter summarizes our early results.

Absorption and reduced scattering coefficients at 715 and 825 nm as well as hemoglobin saturation and content of the forehead and the forearm were measured by a 110 MHz frequency-domain multisource instrument. The absolute data obtained by the frequency- domain spectrometer were compared with oxygenation changes measured by a continuous wave instrument during quadriceps ischemia and postural changes. These preliminary results indicate that portable frequency-domain instruments could be very helpful to investigate brain and muscle pathophysiology.

A new nonperturbative method for studying diffuse photon imaging using frequency domain continous (CW) near-infrared (NIR) light source is developed. In solving the forward problem, this new method is in principle more accurate than the simple perturbation theory. Based on this method, a new image reconstruction algorithm is developed for the inverse problem. A test of this new imaging algorithm is provided by reconstructing images of cylindrical inclusions in uniform turbid media of cross-sectional sizes comparable to realistic human brains and breasts. Preliminary images obtained represent quite well the dimensions of the actual cylindrical object cross sections, with a spatial resolution of around 0.5 cm.

In response to the conference organizer's request, I am presenting a summary of the current status of medical optical imaging and spectroscopy. This is a topic which is advancing rapidly and on which there have been a number of conferences recently, and yet there has not been presented an overview of the field and some idea of what the advantages and disadvantages of the photon diffusion technology may be. Thus, this paper emphasizes diffusion waves for spectroscopy and imaging deep within the tissue and, at the same time, for providing specificity information of both absorption and scattering. In achieving this goal, I will not be able to cite all of the advantages of technologies that view the superficial layers of skin, retina, etc., on the one hand, nor those that measure the photons that have been scattered minimally on the transit between input and output. One of the main reasons for this is that specificity of the optical methods requires all of the information available: absorption and scattering of intrinsic signals naturally in the tissue, and of extrinsic signal due to contrast agents that have been artificially lodged in strategic tissue volumes. Since this paper is essentially the transcript of a lecture, it is not proposed as a topic review and does not contain full-scale bibliographic references, some of which may be found in a recent review elsewhere. This paper highlights what we all might accomplish in order to bring to bear with maximal effectiveness the optical method for altering the outcome of medical problems. I have not emphasized the mathematics of photon diffusion so well represented by the papers of this symposium volume. The achievable goals of the optical methods are to speed detection, improve diagnosis, guide therapy, and what appears in the minds of most, contribute to the improvement of medical economics. In order to fulfill these objectives, we will in the end have to demonstrate by lengthy and expensive clinical studies that the medical devices we develop are really what we think they are as determined by accepted procedures for clinical studies. This is a difficult and expensive route and one track along which many technologies will 'fall by the wayside'. However, our technology is maturing: we are obtaining numbers for important medical problems. It is indeed difficult to make these kinds of contributions; medical devices are not new. The choice of methods is manifold and the niches or windows of opportunity are circumscribed.