Semi-empirical model for diffuse reflectance from homogeneous spherical turbid media measured via small diameter detectors

The application of optical diffuse reflectance spectroscopy is impeded by the lack of exact analytical solution. Based on the results of the Monte Carlo simulation, a semi-empirical analytical expression is developed for diffuse reflectance from homogeneous spherical turbid media measured via small diameter detectors. It is valid over the typical optical property ranges for low absorption biological tissues. This solution is characterized by its simplicity and accuracy. The inversion of optical parameters of turbid media is performed using this solution. The reduced scattering coefficient can be inversely deduced from the diffuse reflectance measured via probes with various radii.     

Diffusion Calculation of Change of Back-scattered Light Beam Intensity from Turbid Medium Owing to the Existence of an Inhomogeneity

Abstract

A solution to the searchlight problem on back-scattering of a narrow pencil light from a turbid medium with an inhomogeneity is presented for semi-infinite geometry in the framework of the diffusion approximation. The inhomogeneity may be an object with a given reflection coefficient or a variation of mean scattering and absorption properties of a turbid medium. A solution to the diffusion equation for mean diffuse radiant intensity with given boundary conditions is obtained by a perturbation theory method relative to the inhomogeneity effect. The spatially limited inhomogeneity contribution to the back-scattering light intensity is expressed in terms of an inhomogeneity diffuse scattering amplitude and the probability density distribution of photon paths in depth. The theoretical results obtained are applied to the interpretation of the Cui, Kumar and Chance experiment on the change of the back-scattered light beam intensity from turbid biological tissue phantom owing to the existence of small absorbers.     

Fluorescence optical diffusion tomography

A nonlinear, Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and the diffusion coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and the emission wavelengths to reconstruct all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated by simulation and by application to experimental data from a tissue phantom containing the fluorescent agent Indocyanine Green.     

Investigation of two-layered turbid media with time-resolved reflectance

Light propagation in two-layered turbid media that have an infinitely thick second layer is investigated with time-resolved reflectance. We used a solution of the diffusion equation for this geometry to show that it is possible to derive the absorption and the reduced scattering coefficients of both layers if the relative reflectance is measured in the time domain at two distances and if the thickness of the first layer is known. Solutions of the diffusion equation for semi-infinite and homogeneous turbid media are also applied to fit the reflectance from the two-layered turbid media in the time and the frequency domains. It is found that the absorption coefficient of the second layer can be more precisely derived for matched than for mismatched boundary conditions. In the frequency domain, its determination is further improved if phase and modulation data are used instead of phase and steady-state reflectance data. Measurements of the time-resolved reflectance were performed on solid two-layered tissue phantoms that confirmed the theoretical results.     

Optimal probe geometry for near-infrared spectroscopy of biological tissue

The results of this study clarify the influence of probe geometry on spectroscopic measurements obtained from the surface of a turbid biological tissue. We show that the transition between the measurement of the predominantly backward-propagating and the predominantly forward-propagating photon fluxes is marked by the separation between the source probe and the detector probes at which the dependence of the fluence on small changes in scattering coefficient vanishes. This is the probe separation at which a variable scattering background has the least influence on the measurement of optical absorption in turbid materials. Estimates of the optimum probe spacing for typical values of absorption and scattering coefficients of soft tissue in the near-infrared spectral region (800-2500 nm) are derived from an analytical solution of the diffusion equation. The estimates were verified by Monte Carlo simulations and experiments on particle suspensions with optical properties similar to those of skin tissue.     

Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications

We present analytic solutions for fluorescent diffuse photon density waves originating from fluorophores distributed in thick turbid media. Solutions are derived for a homogeneous turbid medium containing a uniform distribution of fluorophores and for a system that is homogeneous except for the presence of a single spherical inhomogeneity Generally the inhomogeneity has fluorophore concentration, and lifetime and optical properties that differ from those of the background. The analytic solutions are verified by numerical calculations and are used to determine the fluorophore lifetime and concentration changes required for the accurate detection of inhomogeneities in biologically relevant systems. The relative sensitivities of absorption and fluorescence methods are compared.     

Fluorescent heterogeneities in turbid media: limits for detection, characterization, and comparison with absorption

The fundamental limits for detection and characterization of fluorescent (phosphorescent) inhomogeneities embedded in tissuelike highly scattering turbid media are investigated. The absorption and fluorescence contrast introduced by exogenous fluorophores are also compared. Both analyses are based on practical signal-to-noise ratio considerations. For an object with fivefold fluorophore concentration and lifetime contrast with respect to the background tissue, we find the smallest detectable fluorescent object at 3-cm depth in tissuelike turbid media to be ~0.25 cm in radius, whereas the smallest characterizable object size is ~0.75 cm in radius, given a model with 1% amplitude and 0.5 degrees phase noise. We also find that, for fluorescence extinction coefficients epsilon 相似文献   

Quantitative time-resolved fluorescence spectra of the cortical sarcoma and the adjacent normal tissue determined with an in vivo experimental method and theoretical model

In this paper, a time-resolved fluorescence spectrum method is proposed to study the difference between the cortical sarcoma and the adjacent normal tissue. This is a fluorescence-light-intensity-independent method, which makes it more reliable in the presence of interference light emitted by nonfluorescent light absorbers and scatterers. In the implementation, a model of the tumor tissue and a model of light transport in turbid media using improved Monte Carlo simulations are proposed. In this method, the time-resolved fluorescence is collected in vivo. The improved theoretical model can interpret the fluorescence lifetime measurement. The simulation results show that the decay constant of the tumor tissue spectrum is larger than that of the adjacent normal tissue because of hypoxia and hyperplasia, which fits the theoretical analysis very well.     

Excitation-and-collection geometry insensitive fluorescence imaging of tissue-simulating turbid media

We present an imaging technique for the correction of geometrical effects in fluorescence measurement of optically thick, turbid media such as human tissue. Specifically, we use the cross-polarization method to reject specular reflection and enhance the diffusive backscattering of polarized fluorescence excitation light from the turbid media. We correct the nonuniformity of the image field caused by the excitation-and-collection geometry of a fluorescence imaging system by normalizing the fluorescence image to the cross-polarized reflection image. The ratio image provides a map of relative fluorescence yield, defined as the ratio of emerging fluorescence power to incident excitation, over the surface of an imaged homogeneous turbid medium when fluorescence excitation-and-collection geometries vary in a wide range. We investigate the mechanism of ratio imaging by using Monte Carlo modeling. Our findings show that this technique could have a potential use in the detection of early cancer, which usually starts from a superficial layer of tissue, based on the contrast in the tissue fluorescence of an early lesion and of the surrounding normal tissue.     

Raman signal enhancement in deep spectroscopy of turbid media

A new, passive method for enhancing spontaneous Raman signals for the spectroscopic investigation of turbid media is presented. The main areas to benefit are transmission Raman and spatially offset Raman spectroscopy approaches for deep probing of turbid media. The enhancement, which is typically several fold, is achieved using a multilayer dielectric optical element, such as a bandpass filter, placed within the laser beam over the sample. This element prevents loss of the photons that re-emerge from the medium at the critical point where the laser beam enters the sample, the point where major photon loss occurs. This leads to a substantial increase of the coupling of laser radiation into the sample and consequently an enhanced laser photon-medium interaction process. The method utilizes the angular dependence of dielectric optical elements on impacting photon direction with its transmission spectral profile shifting to the blue with increase in the deviation of photons away from normal incidence. This feature enables it to act as a unidirectional mirror passing a semi-collimated laser beam through unhindered from one side, and at the other side, reflecting photons emerging from the sample at random directions back into it with no restrictions to the detected Raman signal. With substantial restrictions to the spectral range, the concept can also be applied to conventional backscattering Raman spectroscopy. The use of additional reflective elements around the sample to enhance the Raman signal further is also discussed. The increased signal strength yields higher signal quality, a feature important in many applications. Potential uses include sensitive noninvasive disease diagnosis in vivo, security screening, and quality control of pharmaceutical products. The concept is also applicable in an analogous manner to other types of analytical methods such as fluorescence or near-infrared (NIR) absorption spectroscopy of turbid media or it can be used to enhance the effectiveness of the coupling of laser radiation into tissue in applications such as photodynamic therapy for cancer treatment.     

Microscopic imaging through a turbid medium by use of annular objectives for angle gating

We report a new method for microscopic imaging of an object embedded in a turbid medium. The new method is based on the angle-gating mechanism achieved by the use of polarized annular objectives in the illumination and collection paths of a microscopic imaging system. A detailed experimental study is presented of the effects of the size of annular obstructions on image quality when turbid media, including polystyrene microspheres and milk suspensions, are imaged. Images of 22-mum polystyrene microspheres embedded in the turbid media show that misinterpretation can occur when circular objectives are used, because of the detection of mainly multiply scattered photons (i.e., diffusing photons). However, when annular objectives are employed, diffusing photons from a turbid medium can be efficiently suppressed; thus image contrast appears correctly, and image resolution is increased.     

Semi-analytical Monte Carlo simulation for time-resolved light propagating in multilayered turbid media

In this study, a Monte Carlo (MC) method for time-resolved light scattering from multilayered turbid media (SMCML) has been developed. This method is particularly suitable for simulating light backscattering from layered media and receiving the time-resolved signal in a finite sensor area, such as ocean detection, photomedicine and photobiology. The classical semi-analytical MC method requires the scattering events to be located in a single-layer medium. To address the multilayer problem, the energy loss mechanism of photons propagating in tissue was analyzed in this study. According to the energy contribution to the detector, only photons that contribute significantly were considered. Simulations were conducted for stochastic turbid media with different optical parameters. Temporal profiles of the echo signal were obtained with a satisfactory convergence. Compared to the classical MC method, the SMCML method can dramatically reduce the computation time by more than two orders of magnitude.     

Analytical solution of groundwater waves in unconfined aquifers with sloping boundary

A new analytical solution is derived for tide-driven groundwater waves in coastal aquifers using higher-order Boussinesq equation. The homotopy perturbation solution is derived using a virtual perturbation approach without any pre-defined physical parameters. The secular term removal is performed using a combination of parameter expansion and auxiliary term. This approach is unique compared with existing perturbation solutions. The present first-order solution compares well with the previous analytical solutions and a 2D FEFLOW solution for a steep beach slope. This is due to the fact that the higher-order Boussinesq equation captures the streamlines better than ordinary Boussinesq equation based on Dupuit’s assumption. The slope of the beach emerges as an implicit physical parameter from the solution process.     

Characterization of spatial and temporal variations in the optical properties of tissuelike media with diffuse reflectance imaging

We describe a method to characterize spatial or temporal changes in the optical properties of turbid media using diffuse reflectance images acquired under broad-beam illumination conditions. We performed experiments on liquid phantoms whose absorption (mu(a)) and reduced scattering (mu(s)') coefficients were representative of those of biological tissues in the near infrared. We found that the relative diffuse reflectance R depends on mu(a) and mu(s)' only through the ratio mu(a)/mu(s)' and that dependence can be well described with an analytical expression previously reported in the literature [S. L. Jacques, Kluwer Academic Dordrecht (1996)]. We have found that this expression for R deviates from experimental values by no more than 8% for various illumination and detection angles within the range 0 degrees-30 degrees. Therefore, this analytical expression for R holds with good approximation even if the investigated medium presents curved or irregular surfaces. Using this expression, it is possible to translate spatial or temporal changes in the relative diffuse reflectance from a turbid medium into quantitative estimates of the corresponding changes of (mu(a)/mu(s)')(1/2). In the case of media with optical properties similar to those of tissue in the near infrared, we found that the changes mu(a)/mu(s)' should occur over a volume approximately 2 mm deep and 4 mm x 4 mm wide to apply this expression.     

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

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

Monte Carlo and Multicomponent Approximation Methods for Vector Radiative Transfer by use of Effective Mueller Matrix Calculations

For single scattering in a turbid medium, the Mueller matrix is the 4 x 4 matrix that multiplies the incident Stokes vector to yield the scattered Stokes vector. This matrix contains all the information that can be obtained from an elastic-scattering system. We have extended this concept to the multiple-scattering domain where we can define an effective Mueller matrix that, when operating on any incident state of light, will yield the output state. We have calculated this matrix using two completely different computational methods and compared the results for several simple two-layer turbid systems separated by a dielectric interface. We have shown that both methods give reliable results and therefore can be used to accurately predict the scattering properties of turbid media.     

Propagation of unipolar perturbations in hysteretic media with saturation of nonlinear losses

The propagation and evolution of unipolar perturbation pulses in hysteretic media with saturation of nonlinear losses have been theoretically studied. An exact analytical solution that describes the propagation and evolution of initially triangular pulses in these media has been obtained. Numerical and graphic analyses of the obtained solution are presented.     

Effects of fiber-optic probe design and probe-to-target distance on diffuse reflectance measurements of turbid media: an experimental and computational study at 337 nm

Fiber-optic probes are widely used in optical spectroscopy of biological tissues and other turbid media. Only limited information exists, however, on the ways in which the illumination-collection geometry and the overall probe design influence the interrogation of media. We have investigated both experimentally and computationally the effect of probe-to-target distance (PTD) on the diffuse reflectance collected from an isotropically (Lambertian) scattering target and an agar-based tissue phantom. Studies were conducted with three probes characterized by either common (single-fiber) or separate (two bifurcated multifiber probes) illumination and collection channels. This study demonstrates that PTD, probe design, and tissue scattering anisotropy influence the extent of the transport of light into the medium, the light-collection efficiency, and the sampling volume of collected light. The findings can be applied toward optimization of fiber-optic probe designs for quantitative optical spectroscopy of turbid media including biological tissues.     

Fluorescence lifetime spectroscopy for pH sensing in scattering media

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

Optical cross-sectional imaging with pulse ultrasound wave assistance.

We have developed an optical cross-sectional imaging method for turbid media with the aid of a pulse ultrasound wave. Observation of deep regions in turbid media, such as tissue samples, is difficult owing to the rapid dispersion of an incoming laser beam by scattering. A pulse ultrasound wave, which is less scattered in tissues, can indicate the measuring point on the basis of the change of the optical scattering properties in a localized region. A depth-resolving capability can be achieved from the time-dependent measurement of the scattered-light intensity as the pulse ultrasound wave propagates in the sample. We verified the method by observing absorptive objects embedded in silicone rubber and by obtaining the cross-sectional image of an absorbing object surrounded by a strong scattering medium.