Determination of optical scattering properties in turbid media using Mueller matrix imaging

A need exists for the continued development of diagnostic tools and methods capable of distinguishing and characterizing slight differences in the optical properties of tissues. We present a method to estimate the scattering coefficient contribution as a function of particle size in complex mixtures of polystyrene spheres. The experimental method we used is a Mueller matrix imaging approach. The Mueller matrix encodes the polarization-dependent properties of the sample and describes how a given sample will transform an incident light polarization state. A partial least-squares approach is used to form a model around a set of Mueller matrix image-based measurements to accurately predict the individual scattering coefficient contributions in phantoms containing 0.2, 0.5, 1, and 2 microm-diameter polystyrene spheres. The results show individual scattering coefficient contribution errors as low as 0.1585 cm(-1) can be achieved. In addition, it is shown how the scattering type (i.e., Rayleigh and Mie) is encoded within the Mueller matrix. Such methods may eventually lead to the development of improved diagnostic tools capable of characterizing and distinguishing between tissue abnormalities, such as superficial cancerous lesions from their benign counterparts.     

Broadband absorption spectroscopy of turbid media using a dual step steady-state method

We present a method for the determination of the absorption coefficient of turbid media in a broad wavelength range with high spectral resolution using a dual step method. First, the reduced scattering coefficient is determined for a few wavelengths with spatially resolved reflectance measurements. The reduced scattering coefficient for the intermediate wavelengths is interpolated by fitting a power law. Second, the absorption coefficient is obtained from measurements of the total reflectance using the a priori knowledge of the reduced scattering coefficient. By applying a white light source and a spectrometer to measure the total reflectance, the absorption coefficient is determined with a high spectral resolution. The methodology is verified by comparing the absorption coefficients determined by the spatially resolved reflectance measurements with those obtained by the dual step method. The influence of an unknown refractive index and phase function on the determination of the optical properties is investigated. In addition, the optical properties of Intralipid/ink phantoms and the fat layer of porcine rind were determined. The absorption coefficient of the investigated phantoms varying by four orders of magnitude could be determined with an average error of less than 10%.     

Numerical simulation of light propagation and scattering in turbid biological media.

This article considers the processes of light propagation and scattering in biological tissues. The results obtained made it possible to estimate basic signal parameters and their dependence on various optical parameters with respect to the laser Doppler flowmeter and laser Doppler microscope. We also developed a new method to determine the indicatrix asymmetry of single and multiple light scattering by a suspension of oriented spheroidal particles that simulated erythrocytes in a shear flow. It was found that the angular dependence of the asymmetry index provides infonnation on the shape and orientation of particles. In addition, we obtained single scattering indicatrices, which may improve the accuracy of computer simulation of light scattering by blood.     

Scattering coefficient determination in turbid media with backscattered polarized light

A simple empirical method is presented to determine the scattering coefficient mu' s from backscattered polarized images of turbid media. It uses the ratio, pixel by pixel, of two images that are the second and the first backscattered Stokes parameter images Q and I, respectively. Taking this image ratio, then integrating it over the azimuth angle, we get a function depending on the distance from the light entrance point. This function has a maximum. Using Monte Carlo simulations, for a fixed reduced scattering coefficient mu s and for an anisotropy factor g varying between 0 and 0.8, it is found a linear relationship between the scattering coefficient mu s and the inverse of the maximum position of this function.     

Photon migration in turbid media with anisotropic optical properties

We analyse properties of photon migration in reflectance measurements made on a semi-infinite medium bounded by a plane, in which optical parameters may vary in directions neither parallel to, nor perpendicular to the bounding plane. Our aim in doing this is to develop the formulae necessary to deduce parameters of directionality from both time-gated and continuous wave measurements. The mathematical development is based on a diffusion picture, in which the bounding plane is regarded as being totally absorbing so that all photons reaching the surface contribute to the reflectance.     

Performance of isotropic light dosimetry probes based on scattering bulbs in turbid media

In a previous paper the calibration of an isotropic light detector in clear media was described and validated. However, in most applications the detector is used to measure light distribution in turbid (scattering) media, that is, in tissues or tissue equivalent optical phantoms. Despite its small diameter (typically 0.8 mm), inserting the detector in a turbid medium may perturb the light distribution and change the fluence rate at the point of measurement. In the present paper we estimate the error in the fluence rate measured by a detector in turbid media after calibration in a clear medium (air), using an optical phantom and detector bulbs of different optical properties. The experimental results are compared with calculations using the diffusion approximation to the transport equation in a spherical geometry. From measurements in optical phantoms and the results of the calculations it appears that introduction of the detector into a water-based turbid medium with refractive index, absorption- and scattering coefficients different from those of the detector bulb may require corrections to the detector response of up to 10-15%, in order to obtain the true fluence rate in that medium. The diffusion model is used to explore the detector response in a number of tissues of interest in photodynamic therapy, using tissue optical properties from the literature. Based on these model calculations it is estimated that in real tissues the fluence rate measured by the detector is up to 3% below the true value.     

Diffusion coefficient for photon transport in turbid media

Light propagation in a turbid medium is considered using the linear transport equation. The existence of a diffusion length is proved for the Henyey-Greenstein scattering kernel for all absorption ratios. Numerical methods are given that allow accurate computation of the diffusion coefficient quite easily.     

Fiber dispersion in time domain measurements compromising the accuracy of determination of optical properties of strongly scattering media

Limitations in the accuracy of measurements of optical properties (absorption and scattering coefficients) of strongly scattering media that are due to temporal dispersion inside the detection fibers of a time-of-flight setup were investigated for a tissue-like phantom. It is shown that the absorption and reduced scattering coefficients may be overestimated by up to 90% (depending on length and numerical aperture of the fibers) if the instrumental response measurements for the setup are performed by direct illumination of the tip of the detection fibers with collimated short laser pulses. However, the accuracy can be improved significantly if a thin layer of scattering media is used in front of the detection fibers during the response measurements. The relevance of the investigated dispersion effects is discussed with respect to frequency-domain measurements as well.     

Determination of optical properties in heterogeneous turbid media using a cylindrical diffusing fiber

For interstitial photodynamic therapy (PDT), cylindrical diffusing fibers (CDFs) are often used to deliver light. This study examines the feasibility and accuracy of using CDFs to characterize the absorption (μ(a)) and reduced scattering (μ'(s)) coefficients of heterogeneous turbid media. Measurements were performed in tissue-simulating phantoms with μ(a)?between 0.1 and 1?cm(-1)?and μ'(s) between 3 and 10?cm(-1)?with CDFs 2 to 4?cm in length. Optical properties were determined by fitting the measured light fluence rate profiles at a fixed distance from the CDF axis using a heterogeneous kernel model in which the cylindrical diffusing fiber is treated as a series of point sources. The resulting optical properties were compared with independent measurement using a point source method. In a homogenous medium, we are able to determine the absorption coefficient μ(a)?using a value of μ'(s) determined a priori (uniform fit) or μ'(s) obtained by fitting (variable fit) with standard (maximum) deviations of 6% (18%) and 18% (44%), respectively. However, the CDF method is found to be insensitive to variations in μ'(s), thus requiring a complementary method such as using a point source for determination of μ'(s). The error for determining μ(a)?decreases in very heterogeneous turbid media because of the local absorption extremes. The data acquisition time for obtaining the one-dimensional optical properties distribution is less than 8?s. This method can result in dramatically improved accuracy of light fluence rate calculation for CDFs for prostate PDT in vivo when the same model and geometry is used for forward calculations using the extrapolated tissue optical properties.     

Spectroscopic method for determination of the absorption coefficient in brain tissue

I use Monte Carlo simulations and phantom measurements to characterize a probe with adjacent optical fibres for diffuse reflectance spectroscopy during stereotactic surgery in the brain. Simulations and measurements have been fitted to a modified Beer-Lambert model for light transport in order to be able to quantify chromophore content based on clinically measured spectra in brain tissue. It was found that it is important to take the impact of the light absorption into account when calculating the apparent optical path length, lp, for the photons in order to get good estimates of the absorption coefficient, μa. The optical path length was found to be well fitted to the equation lp=a+b ln(Is)+c ln(μa)+d ln(Is)ln(μa), where Is is the reflected light intensity for scattering alone (i.e., zero absorption). Although coefficients a-d calculated in this study are specific to the probe used here, the general form of the equation should be applicable to similar probes.     

Determination of optical properties of turbid media using pulsed photothermal radiometry.

Pulsed photothermal radiometry (PPTR) measures blackbody radiation emitted by a sample after absorption of an optical pulse. Three techniques for obtaining the absorption coefficient of absorbing-only, semi-infinite samples are examined and shown to give comparable results. An analytic theory for the time dependence of the PPTR signal in semi-infinite scattering and absorbing media has been derived and tested in a series of controlled gel phantoms. This theory, based on the diffusion approximation of the radiative transport equation, is shown to model the time course of the detected signal accurately. Furthermore, when the incident fluence is known, the theory can be used in a non-linear, two-parameter fitting algorithm to determine the absorption and reduced scattering coefficients of a turbid sample with an accuracy of 10-15% for transport albedos ranging from 0.42-0.88.     

New bacterial absorption method for determination of hepatitis A IgM and IgA antibodies

Antibodies against hepatitis A virus (anti-HAV) can be determined by a commercially available radioimmunoassay (RIA) (HavabTM, Abbott). To discriminate between recent and past hepatitis A infection this RIA was used in combination with absorption with protein A-containing staphylococci. However, nonabsorbable anti-HAV was repeatedly detected in late-convalescent sera using this methods. The nature of these antibodies was studied in serum samples from 12 such patients. In all patients, the late-convalescent sera contained no IgM class anti-HAV as judged by sucrose density gradient centrifugation. The restricted specificity of staphylococcal protein A explains the lack of absorption. Some recently described streptococcal strains capable of binding all IgG subclasses (including IgG3) as well as both IgA subclasses were, therefore, added to the staphylococci. Absorption studies using these strains indicated that the previously nonabsorbable anti-HAV in these 12 patients was mainly of the IgA class. A bacterial mixture including IgA-binding streptococci seems preferable to routine determination of IgM anti-HAV in acute hepatitis A diagnosis. The results also indicate that IgA anti-HAV in serum can persist for more than two years after a hepatitis A infection.     

Radiative transport in the delta-P1 approximation for semi-infinite turbid media

We have developed an analytic solution for spatially resolved diffuse reflectance within the deltaP1 approximation to the radiative transport equation for a semi-infinite homogeneous turbid medium. We evaluate the performance of this solution by comparing its predictions with those provided by Monte Carlo simulations and the standard diffusion approximation. We demonstrate that the delta-P1 approximation provides accurate estimates for spatially resolved diffuse reflectance in both low and high scattering media. We also develop a multi-stage nonlinear optimization algorithm in which the radiative transport estimates provided by the delta-P1 approximation are used to recover the optical absorption (microa), reduced scattering (micros'), and single-scattering asymmetry coefficients (g1) of liquid and solid phantoms from experimental measurements of spatially resolved diffuse reflectance. Specifically, the delta-P1 approximation can be used to recover microa, micros', and g1 with errors within +/- 22%, +/- 18%, and +/- 17%, respectively, for both intralipid-based and siloxane-based tissue phantoms. These phantoms span the optical property range 4 < (micros' /microa) < 117. Using these same measurements, application of the standard diffusion approximation resulted in the recovery of microa and micros' with errors o f +/- 29% and +/- 25%, respectively. Collectively, these results demonstrate that the delta-P1 approximation provides accurate radiative transport estimates that can be used to determine accurately the optical properties of biological tissues, particularly in spectral regions where tissue may display moderate/low ratios of reduced scattering to absorption (micros'/microa).     

Consequences of scattering for spectral imaging of turbid biologic tissue

Spectral imaging permits two-dimensional mapping of the backscattering properties of biological systems. Such mapping requires broadband illumination of the entire area of interest. However, imaging of turbid biological media under these conditions often involves mean photon path lengths that exceed the pixel size. Using a numerical Monte Carlo model, we have studied the effects of photon scattering in a hemoglobin-bearing model system. We find that photon migration and the resulting wavelength-dependent optical coupling between pixels can complicate the analysis of imaging spectroscopy data. In fact, the wavelength dependence of photon trajectories also alters the distribution of photon exit angles at the tissue surface. We therefore find that the finite optical field of view of an imaging spectrometer can affect the measured spectra in the absence of chromatic aberrations.     

Monte-Carlo-based model for the extraction of intrinsic fluorescence from turbid media

A Monte-Carlo-based model of fluorescence is developed that is capable of extracting the intrinsic fluorescence properties of tissue, which are independent of the absorption and scattering properties of tissue. This model is flexible in its applicability to different illumination-collection geometries and is also valid for a wide range of optical properties, representative of tissue in the UV-visible spectrum. This is potentially useful in a variety of biomedical applications, including cancer diagnostics and monitoring the physiological response to therapy. The model is validated using phantoms composed of hemoglobin (absorber), polystyrene spheres (scatterer), and furan-2 (fluorophore). It is found that this model is able to retrieve the intrinsic fluorescence spectra of the tissue phantoms and recover the intrinsic fluorescence intensity of furan within the phantoms to within a mean error of less than 10%.     

Changes in scattering and absorption properties of esthetic filling materials after aging

OBJECTIVES: Assuming that color changes after aging are related to changes in translucency of materials, the purpose of the present study was to determine the correlation between the changes in color and the changes in scattering and absorption properties after accelerated aging with representative dental esthetic restorative materials: glass ionomer, resin-modified glass ionomer, compomer, and resin composite. METHODS: Color was measured according to the CIELAB color scale in the transmittance and reflectance modes and used to calculate changes in color (deltaE*(ab)), color coordinates (deltaL*, delta a*, and delta b*), translucency parameter (deltaTP), scattering coefficient (deltaS), absorption coefficient (deltaK), and light reflectivity (deltaRI) after accelerated aging. Simple correlations between each pair of the changes in optical values were calculated, and multiple regression analysis was used to determine the parameters influencing the changes in color and color coordinates (p = 0.05). RESULTS: In the resin composite and compomer, deltaS, deltaK, and deltaRI values were approximately zero, whereas deltaS was as high as 8.9 in the glass ionomer. For most comparisons, correlation coefficient (r) was between 0.700 and 0.997. DeltaL* was found to have a major influence on color changes, and deltaS, deltaTP, and deltaRI influenced deltaL*. Therefore, changes in scattering and absorption properties, after aging, were closely correlated with changes in color and color coordinates, especially in glass ionomer-based filling materials.     

Experimental spectro-angular mapping of light distribution in turbid media

We present a new approach to the analysis of radiance in turbid media. The approach combines data from spectral, angular and spatial domains in a form of spectro-angular maps. Mapping provides a unique way to visualize details of light distribution in turbid media and allows tracking changes with distance. Information content of experimental spectro-angular maps is verified by a direct comparison with simulated data when an analytical solution of the radiative transfer equation is used. The findings deepen our understanding of the light distribution in a homogenous turbid medium and provide a first step toward applying the spectro-angular mapping as a diagnostic tool for tissue characterization.     

Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media

We present a novel tomographer for three-dimensional reconstructions of fluorochromes in diffuse media. Photon detection is based on charge-coupled device technology that allows the implementation of a large parallel array of detection channels with high sensitivity. Using this instrument we studied the response and detection limits of near-infrared fluorochromes in diffuse media as a function of light intensity and for a wide range of biologically relevant concentrations. We further examined the resolution of the scanner and the reconstruction linearity achieved. We demonstrate that the instrument attains better than 3 mm resolution, is linear within more than two orders of magnitude of fluorochrome concentration, and can detect fluorescent objects at femto-mole quantities in small animal-like geometries. These measurements delineate detection and reconstruction characteristics associated with imaging of novel classes of fluorescent probes developed for in vivo molecular and functional probing of tissues.