Determination of the optical properties of two-layer turbid media by use of a frequency-domain hybrid monte carlo diffusion model

The general two-layer inverse problem in biomedical photon migration is to estimate the absorption and scattering coefficients of each layer as well as the top-layer thickness. We attempted to solve this problem, using experimental and simulated spatially resolved frequency-domain (FD) reflectance for optical properties typical of skin overlying muscle or skin overlying fat in the near infrared. Two forward models of light propagation were used: a two-layer diffusion solution [Appl. Opt. 37, 779 (1998)] and a hybrid Monte Carlo (MC) diffusion model [Appl. Opt. 37, 7401 (1998)]. MC-simulated FD reflectance data were fitted as relative measurements to the hybrid and the pure diffusion models. It was found that the hybrid model could determine all the optical properties of the two-layer media studied to ~5%. Also, the same accuracy could be achieved by means of fitting MC-simulated cw reflectance data as absolute measurements, but fitting them as relative ones is an ill-posed problem. In contrast, two-layer diffusion could not retrieve the top-layer optical properties as accurately for FD data and was ill-posed for both relative and absolute cw data. The hybrid and the pure diffusion models were also fitted to experimental FD reflectance measurements from two-layer tissue-simulating phantoms representative of skin-on-fat and skin-on-muscle baseline optical properties. Both the hybrid and the diffusion models could determine the optical properties of the lower layer. The hybrid model demonstrated its potential to retrieve quantitatively the transport scattering coefficient of skin (the upper layer), which was not possible with the pure diffusion model. Systematic discrepancies between model and experiment may compromise the accuracy of the deduced top-layer optical properties. Identifying and eliminating such discrepancies is critical to practical application of the method.     

Measurement of the optical properties of a two-layer model of the human head using broadband near-infrared spectroscopy

We present the development of a continuous-wave method of quantifying the optical properties of a two-layered model of the human head using a broadband spectral approach. Absolute absorption and scattering properties of the upper and lower layers of phantoms with known optical properties were reconstructed from steady-state multi-distance measurements by performing differential fit analysis of the near-infrared reflectance spectrum between 700 and 1000 nm. From spectra acquired at 10, 20, and 30 mm, the concentration of a chromophore in the bottom layer was determined within an error of 10% in the presence of a 15 mm thick top layer. These results demonstrate that our method was able to determine the optical properties of the lower layer, which represents brain, with acceptable error at specific source-detector distances.     

Determination of tissue optical properties from diffuse reflectance profiles by multivariate calibration

We describe a method for determining the reduced scattering and absorption coefficients of turbid biological media from the spatially resolved diffuse reflectance. A Sugeno Fuzzy Inference System in conjunction with data preprocessing techniques is employed to perform multivariate calibration and prediction on reflectance data generated by Monte Carlo simulations. The preprocessing consists of either a principal component analysis or a new, extended curve-fitting procedure originating from diffusion theory. Prediction tests on reflectance data with absorption coefficients between 0.04 and 0.06 mm(-1) and reduced scattering coefficients between 0.45 and 0.99 mm(-1) show the root-mean-square error of this method to be 0.25% for both coefficients. With reference to practical applications, we also describe how the prediction accuracy is affected by using relative instead of absolute reflectance data, by imposing measurement noise on the reflectance data, and by changing the number and the position of detectors.     

Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium

We have examined the possibility of determining the optical properties of a two-layer medium by using a diffusion approximation radiation transport model [Appl. Opt. 37, 779 (1998)]. Continuous-wave and frequency-domain (FD) low-noise Monte Carlo (MC) data were fitted to the model. Marquardt-Levenberg and a simulated annealing algorithm were used and compared as optimization techniques. Our particular choice of optical properties for the two-layer model was consistent with skin and underlying fat in the presence of an exogenous chromophore [Appl. Opt. 37, 1958 (1998)]. The results are therefore specific to this set of optical properties. It was found that the cw diffusion solution could never be used to estimate all optical properties reliably. The combined cw and FD solutions could not be used to estimate some of the top-layer optical properties to an accuracy of better than 10%, although the absorption and the transport scattering coefficients of the bottom layer could be estimated to within 7% and 0.5%, respectively. No improvement was found from simultaneously fitting MC data at three different modulation frequencies. These results point to the need for a more accurate radiation transfer model at small source-detector separations.     

Measurement of tissue optical properties by the use of oblique-incidence optical fiber reflectometry

Fiber-optic-based oblique-incidence reflectometry is a simple and accurate method for measuring the absorption and reduced scattering coefficients mu(a) and mu?(s) of semi-infinite turbid media. Obliquely incident light produces a spatial distribution of diffuse reflectance that is not centered about the point of light entry. The amount of shift in the center of diffuse reflectance is directly related to the medium's diffusion length D. We developed a fiber-optic probe to deliver light obliquely and sample the relative profile of diffuse reflectance. Measurement in absolute units is not necessary. From the profile, it was possible to measure D, perform a curve fit for the effective attenuation coefficient mu(eff), and then calculate mu(a) and mu?(s). This method was verified with Monte Carlo simulations and tested on tissue phantoms. Our measurements of D and mu(eff) had an accuracy of approximately 5%, thus giving us 10% and 5% accuracy for mu(a) and mu?(s), respectively.     

Determination of the optical properties of a monomode optical fibre by fringes of equal chromatic order

Abstract

Multiple beam fringes of equal chromatic order are used to study the optical properties of a monomode optical fibre. The material dispersion of the core and that of the cladding of the fibre are measured. A modified single term Sellmeier dispersion formula is adopted and fitted to the experimental data. A new simple scheme of calculation is applied to reduce the interferogram. A single interferogram is sufficient to give the whole dispersion information needed across the visible spectrum.     

Equivalence of pyrheliometric and monochromatic aerosol optical depths at a single key wavelength

The atmospheric aerosol optical depth (AOD) weighted over the solar spectrum is equal to the monochromatic AOD at a certain wavelength. This key wavelength is ~0.7 mum, which is only slightly influenced by air mass and aerosol content. On the basis of this result, simple relations are proposed to predict monochromatic AOD from pyrheliometric data and vice versa. The accuracy achieved is close to ?0.01 units of AOD at ~0.7 mum, estimated from simultaneous sunphotometer data. The precision required for the estimation of the precipitable water-vapor content is approximately ?0.5 cm.     

Determination of the optical coefficients of biological tissue by neural network

A system that incorporated a laser source and a CCD camera was used to measure spatially-resolved steady-state diffuse reflectance. Monte Carlo simulations and experiments in tissue phantoms were used to train a neural network that characterizes the reflectance data on a turbid medium. The neural network was used to extract the optical properties (scattering and absorption coefficients) of biological tissue. The accuracy of the neural network was investigated and validated. Tests on tissue-simulation phantoms showed the relative errors of this technique to be 3% for the reduced scattering coefficient and 9% for the absorption coefficients. The optical properties of human skin were also measured in vivo at 633 nm. For human skin tissue it was found that our results were in good agreement with their reference values.     

Determination of optical parameters of human breast tissue from spatially resolved fluorescence: a diffusion theory model

We report the measurement of optical transport parameters of pathologically characterized malignant tissues, normal tissues, and different types of benign tumors of the human breast in the visible wavelength region. A spatially resolved steady-state diffuse fluorescence reflectance technique was used to estimate the values for the reduced-scattering coefficient (mu(s)') and the absorption coefficient (mu(a)) of human breast tissues at three wavelengths (530, 550, and 590 nm). Different breast tissues could be well differentiated from one another, and different benign tumors could also be distinguished by their measured transport parameters. A diffusion theory model was developed to describe fluorescence light energy distribution, especially its spatial variation in a turbid and multiply scattering medium such as human tissue. The validity of the model was checked with a Monte Carlo simulation and also with different tissue phantoms prepared with polystyrene microspheres as scatterers, riboflavin as fluorophores, and methylene blue as absorbers.     

Determination of optical properties of thin organic films by spectroellipsometry

Organic thin films show considerable promise for a number of bioelectronic applications, as they exhibit a wide variety of properties depending on the composition, the electronic structure and the microstructure. In this paper we discuss methods and applications of spectroellipsometry towards obtaining this type of information about thin films. Topics include methods of determining both the thickness and the dielectric properties of thin organic films and methods of determining microstructural information such as void fractions from these data. We conclude by indicating possible directions for future optical characterization work in this field. Examples are given throughout.     

Sequential estimation of optical properties of a two-layered epithelial tissue model from depth-resolved ultraviolet-visible diffuse reflectance spectra

A method for estimating the optical properties of two-layered media (such as squamous epithelial tissue) over a range of wavelengths in the ultraviolet-visible spectrum is proposed and tested with Monte Carlo modeling. The method first used a fiber-optic probe with angled illumination and the collection fibers placed at a small separation (or=1000 microm) was used to detect diffuse reflectance preferentially from the bottom layer. A second Monte Carlo-based inverse model for a two-layered medium was applied to estimate the bottom layer optical properties, as well as the top layer thickness, given that the top layer optical properties have been estimated. The results of Monte Carlo validation show that this method works well for an epithelial tissue model with a top layer thickness ranging from 200 to 500 microm. For most thicknesses within this range, the absorption coefficients were estimated to within 15% of the true values, the reduced scattering coefficients were estimated to within 20% and the top layer thicknesses were estimated to within 20%. The application of a variance reduction technique to the Monte Carlo modeling proved to be effective in improving the accuracy with which the optical properties are estimated.     

Modelling optical properties of soft tissue by fractal distribution of scatterers

Abstract

A knowledge of the local refractive index variations and size distribution of scatterers in biological tissue is required to understand the physical processes involved in light-tissue interaction. This paper describes a method for modelling the complicated soft tissue, based on the fractal approach, permitting numerical evaluation of the phase functions and four optical properties of tissue—scattering coefficient, reduced scattering coefficient, backscatter-ing coefficient, and anisotropy factor—by the use of the Mie scattering theory. A key assumption of the model is that refractive index variations caused by microscopic tissue elements can be treated as particles with size distribution according to the power law. The model parameters, such as refractive index, incident wavelength, and fractal dimension, that are likely to affect the predictions of optical properties are investigated. The results suggest that the fractal dimension used to describe how biological tissue can be approximated by particle distribution is highly dependent on how the continuous distribution is discretized. The optical properties of the tissue significantly depend on the refractive index of tissue, implying that the refractive index of the particles should be carefully chosen in the model in order accurately to predict the optical properties of the tissue concerned.     

Determination of optical coefficients of biological tissue from a single integrating-sphere

The detection of interactions between light and tissue can be used to characterize the optical properties of the tissue. The development is described of a method that determines optical coefficients of biological tissue from a single optical reflectance spectrum measured with an integrating-sphere. The experimental system incorporated a DH-2000 deuterium tungsten halogen light source, a USB4000-VIS-NIR miniature fiber optic spectrometer and an integrating-sphere. Fat emulsion and ink were used to mimic the scattering and absorbing properties of tissue in the tested sample. The measured optical reflectance spectrums with different scattering and absorbing properties were used to train a back-propagation neural network (BPNN). Then the neural network (BPNN) was used to determine the optical coefficients of biological tissue from a single optical reflectance spectrum measured with an integrating-sphere. Tests on tissue-simulation phantoms showed the relative errors of this technique to be 7% for the reduced scattering coefficient and 15% for the absorption coefficients. The optical properties of human skin were also measured in vivo.     

Fiber-optic probe for noninvasive real-time determination of tissue optical properties at multiple wavelengths

We present a compact, fast, and versatile fiber-optic probe system for real-time determination of tissue optical properties from spatially resolved continuous-wave diffuse reflectance measurements. The system collects one set of reflectance data from six source-detector distances at four arbitrary wavelengths with a maximum overall sampling rate of 100 Hz. Multivariate calibration techniques based on two-dimensional polynomial fitting are employed to extract and display the absorption and reduced scattering coefficients in real-time mode. The four wavelengths of the current configuration are 660, 785, 805, and 974 nm, respectively. Cross-validation tests on a 6 x 7 calibration matrix of Intralipid-dye phantoms showed that the mean prediction error at, e.g., 785 nm was 2.8% for the absorption coefficient and 1.3% for the reduced scattering coefficient. The errors are relative to the range of the optical properties of the phantoms at 785 nm, which were 0-0.3/cm for the absorption coefficient and 6-16/cm for the reduced scattering coefficient. Finally, we also present and discuss results from preliminary skin tissue measurements.     

Evaluation of optical properties of highly scattering media by moments of distributions of times of flight of photons

A novel method for the determination of the optical properties of tissue from time-domain measurements is presented. The data analysis is based on the evaluation of the first moment and the second centralized moment, i.e., the mean time of flight and the variance of the measured distribution of times of flight (DTOF) of photons injected by short (picosecond) laser pulses. Analytical expressions are derived for calculation of absorption and of reduced scattering coefficients from these moments by application of diffusion theory for infinite and semi-infinite homogeneous media. The proposed method was tested on experimental data obtained with phantoms, and results for absorption and reduced scattering coefficients obtained by the proposed method are compared with those obtained by fitting of the same data with analytical solutions of the diffusion equation. Furthermore, the accuracy of the moment analysis was investigated for a range of integration limits of the DTOF. The moment analysis may serve as a comparatively fast method for evaluating optical properties with sufficient accuracy and can be used, e.g., for on-line monitoring of optical properties of biological tissue.     

Clinical determination of tissue optical properties by endoscopic spatially resolved reflectometry

A noninvasive method to measure the optical properties of a diffusing and absorbing medium is described. Based on the spatially resolved measurement of diffuse reflectance at the sample surface, this method is particularly suitable for investigating the in vivo optical properties of biological tissues endoscopically in a clinical context. The sensitivity of the measurement is discussed, and two optical probes for two different clinical applications are presented. Preliminary measurements are performed on a nonbiological medium, which illustrate the possibilities of the proposed method. Finally, we report on in vivo measurements of the optical properties of the human esophageal wall at 630 nm.     

Measurement of tissue optical properties by time-resolved detection of laser-induced transient stress

We report on a technique utilizing time-resolved detection of laser-induced stress transients for the measurement of optical properties in turbid media specifically suitable for biological tissues. The method was tested initially in nonscattering absorbing media so that it could be compared with spectrophotometry. The basis of this method is provided by the conditions of temporal stress confinement in the irradiated volume where the pressure generated in tissues heated instantly by laser pulses is proportional to the absorbed laser energy density, and the exponential profile of the initial stress distribution in the irradiated volume corresponds to the z-axial distribution of the absorbed laser fluence. Planar thermoelastic waves can propagate in water-containing media with minimal distortion, and their axial profiles can be detected by an acoustic transducer with sufficient temporal resolution. The acoustic waves induced by 14-ns laser pulses in nonscattering media, turbid gels, and tissues were measured by a piezoelectric transducer with a 3-ns response time. Temporal profiles of stress transients yielded z-axial distributions of the absorbed laser energy in turbid and opaque media, provided that the speed of sound in these media was known. The absorption and effective scattering coefficients of beef liver, dog prostate, and human aortic atheroma at three wavelengths, 1064 nm (in near infrared), 532 nm (visible), and 355 nm (near UV), were deduced from laser-induced stress profiles with additional measurements of total diffuse reflectance.     

Effects of the scattering coefficient on width estimates in a two-layer tissue

Abstract

We pose the problem of estimating the width of the upper layer of a two-stratum medium using data from reflectance measurements made at the interface separating the medium from its surroundings. The lower stratum is assumed to be infinite. In this analysis both the scattering and the absorption coefficients are allowed to differ, but are assumed to be known. We also suggest a simple way to include effects of noise into the analysis.     

Determination of the macrodispersive parameters of a motion in a two-layer porous medium

Summary This paper develops a method for deriving good estimates of macrodispersive transport parameters describing the asymptotic evolution of a non-reactive chemical pollutant injected into a two-layer porous medium. These parameters are extracted from the coefficients of asymptotic time-polynomial expansions of some adequately chosen integral transforms performed upon the solution of the original transport problem.