Quantifying the properties of two-layer turbid media with frequency-domain diffuse reflectance

Accurately calibrated frequency domain diffuse optical spectroscopy compared against chemical analysis of porcine adipose tissue

Frequency domain diffuse optical spectroscopy (fdDOS) is a noninvasive technique to estimate tissue composition and hemodynamics. While fdDOS has been established as a valuable modality for clinical research, comparison of fdDOS with direct chemical analysis (CA) methods has yet to be reported. To compare the two approaches, we propose a procedure to confirm accurate calibration by use of liquid emulsion and solid silicone phantoms. Tissue fat (FAT) and water (H₂ O) content of two ex vivo porcine tissue samples were optically measured by fdDOS and compared to CA values. We show an average H₂ O error (fdDOS minus CA) and SD of 1.9 ± 0.2% and -0.9 ± 0.2% for the two samples. For FAT, we report a mean error of -9.3 ± 1.3% and 0.8 ± 1.3%. We also measured various body sites of a healthy human subject using fdDOS with results suggesting that accurate calibration may improve device sensitivity.

Recovery of layered tissue optical properties from spatial frequency-domain spectroscopy and a deterministic radiative transport solver

We present a method to recover absorption and reduced scattering spectra for each layer of a two-layer turbid media from spatial frequency-domain spectroscopy data. We focus on systems in which the thickness of the top layer is less than the transport mean free path   (  0.1  -  0.8l  *    )  . We utilize an analytic forward solver, based upon the N'th-order spherical harmonic expansion with Fourier decomposition   (  SHEFN  )   method in conjunction with a multistage inverse solver. We test our method with data obtained using spatial frequency-domain spectroscopy with 32 evenly spaced wavelengths within λ  =  450 to 1000 nm on six-layered tissue phantoms with distinct optical properties. We demonstrate that this approach can recover absorption and reduced scattering coefficient spectra for both layers with accuracy comparable with current Monte Carlo methods but with lower computational cost and potential flexibility to easily handle variations in parameters such as the scattering phase function or material refractive index. To our knowledge, this approach utilizes the most accurate deterministic forward solver used in such problems and can successfully recover properties from a two-layer media with superficial layer thicknesses.

Influence of nanoparticles accumulation on optical properties of human normal and cancerous liver tissue in vitro estimated by OCT

In this work, the potential use of nanoparticles as contrast agents by using spectral domain optical coherence tomography (SD-OCT) in liver tissue was demonstrated. Gold nanoparticles (average size of 25 and 70 nm), were studied in human normal and cancerous liver tissues in vitro, respectively. Each sample was monitored with SD-OCT functional imaging for 240 min. Continuous OCT monitoring showed that, after application of gold nanoparticles, the OCT signal intensities of normal liver and cancerous liver tissue both increase with time, and the larger nanoparticles tend to produce a greater signal enhancement in the same type of tissue. The results show that the values of attenuation coefficients have significant differences between normal liver tissue and cancerous liver tissue. In addition, 25 nm gold nanoparticles allow higher penetration depth than 70 nm gold nanoparticles in liver tissues.

Spectral discrimination of breast pathologies in situ using spatial frequency domain imaging

Introduction

Nationally, 25% to 50% of patients undergoing lumpectomy for local management of breast cancer require a secondary excision because of the persistence of residual tumor. Intraoperative assessment of specimen margins by frozen-section analysis is not widely adopted in breast-conserving surgery. Here, a new approach to wide-field optical imaging of breast pathology in situ was tested to determine whether the system could accurately discriminate cancer from benign tissues before routine pathological processing.

Methods

Spatial frequency domain imaging (SFDI) was used to quantify near-infrared (NIR) optical parameters at the surface of 47 lumpectomy tissue specimens. Spatial frequency and wavelength-dependent reflectance spectra were parameterized with matched simulations of light transport. Spectral images were co-registered to histopathology in adjacent, stained sections of the tissue, cut in the geometry imaged in situ. A supervised classifier and feature-selection algorithm were implemented to automate discrimination of breast pathologies and to rank the contribution of each parameter to a diagnosis.

Results

Spectral parameters distinguished all pathology subtypes with 82% accuracy and benign (fibrocystic disease, fibroadenoma) from malignant (DCIS, invasive cancer, and partially treated invasive cancer after neoadjuvant chemotherapy) pathologies with 88% accuracy, high specificity (93%), and reasonable sensitivity (79%). Although spectral absorption and scattering features were essential components of the discriminant classifier, scattering exhibited lower variance and contributed most to tissue-type separation. The scattering slope was sensitive to stromal and epithelial distributions measured with quantitative immunohistochemistry.

Conclusions

SFDI is a new quantitative imaging technique that renders a specific tissue-type diagnosis. Its combination of planar sampling and frequency-dependent depth sensing is clinically pragmatic and appropriate for breast surgical-margin assessment. This study is the first to apply SFDI to pathology discrimination in surgical breast tissues. It represents an important step toward imaging surgical specimens immediately ex vivo to reduce the high rate of secondary excisions associated with breast lumpectomy procedures.

Automatic diagnosis of melanoma using machine learning methods on a spectroscopic system

Background

Early and accurate diagnosis of melanoma, the deadliest type of skin cancer, has the potential to reduce morbidity and mortality rate. However, early diagnosis of melanoma is not trivial even for experienced dermatologists, as it needs sampling and laboratory tests which can be extremely complex and subjective. The accuracy of clinical diagnosis of melanoma is also an issue especially in distinguishing between melanoma and mole. To solve these problems, this paper presents an approach that makes non-subjective judgements based on quantitative measures for automatic diagnosis of melanoma.

Methods

Our approach involves image acquisition, image processing, feature extraction, and classification. 187 images (19 malignant melanoma and 168 benign lesions) were collected in a clinic by a spectroscopic device that combines single-scattered, polarized light spectroscopy with multiple-scattered, un-polarized light spectroscopy. After noise reduction and image normalization, features were extracted based on statistical measurements (i.e. mean, standard deviation, mean absolute deviation, L₁ norm, and L₂ norm) of image pixel intensities to characterize the pattern of melanoma. Finally, these features were fed into certain classifiers to train learning models for classification.

Results

We adopted three classifiers – artificial neural network, naïve bayes, and k-nearest neighbour to evaluate our approach separately. The naive bayes classifier achieved the best performance - 89% accuracy, 89% sensitivity and 89% specificity, which was integrated with our approach in a desktop application running on the spectroscopic system for diagnosis of melanoma.

Conclusions

Our work has two strengths. (1) We have used single scattered polarized light spectroscopy and multiple scattered unpolarized light spectroscopy to decipher the multilayered characteristics of human skin. (2) Our approach does not need image segmentation, as we directly probe tiny spots in the lesion skin and the image scans do not involve background skin. The desktop application for automatic diagnosis of melanoma can help dermatologists get a non-subjective second opinion for their diagnosis decision.

A linear gradient line source facilitates the use of diffusion models with high order approximation for efficient, accurate turbid sample optical properties recovery

In this paper, we demonstrate that a scanning MEMS mirror can be employed to create a linear gradient line source that is equivalent to a planar source. This light source setup facilitates the use of diffusion models of increased orders of approximation having closed form solution, and thus enhance the efficiency and accuracy in sample optical properties recovery. In addition, compared with a regular planar light source, the linear gradient line source occupies much less source area and has an elevated measurement efficiency. We employed a δ-P1 diffusion equation with a closed form solution and carried out a phantom study to understand the performance of this new method in determining the absorption and scattering properties of turbid samples. Moreover, our Monte Carlo simulation results indicated that this geometry had probing depths comparable to those of the conventional diffuse reflectance measurement geometry with a source-detector separation of 3 mm. We expect that this new source setup would facilitate the investigating of superficial volumes of turbid samples in the wavelength regions where tissue absorption coefficients are comparable to scattering coefficients.

Reliable recovery of the optical properties of multi-layer turbid media by iteratively using a layered diffusion model at multiple source-detector separations

Accurately determining the optical properties of multi-layer turbid media using a layered diffusion model is often a difficult task and could be an ill-posed problem. In this study, an iterative algorithm was proposed for solving such problems. This algorithm employed a layered diffusion model to calculate the optical properties of a layered sample at several source-detector separations (SDSs). The optical properties determined at various SDSs were mutually referenced to complete one round of iteration and the optical properties were gradually revised in further iterations until a set of stable optical properties was obtained. We evaluated the performance of the proposed method using frequency domain Monte Carlo simulations and found that the method could robustly recover the layered sample properties with various layer thickness and optical property settings. It is expected that this algorithm can work with photon transport models in frequency and time domain for various applications, such as determination of subcutaneous fat or muscle optical properties and monitoring the hemodynamics of muscle.

Optical characterization of two-layered turbid media for non-invasive, absolute oximetry in cerebral and extracerebral tissue

We introduce a multi-distance, frequency-domain, near-infrared spectroscopy (NIRS) method to measure the optical coefficients of two-layered media and the thickness of the top layer from diffuse reflectance measurements. This method features a direct solution based on diffusion theory and an inversion procedure based on the Levenberg-Marquardt algorithm. We have validated our method through Monte Carlo simulations, experiments on tissue-like phantoms, and measurements on the forehead of three human subjects. The Monte Carlo simulations and phantom measurements have shown that, in ideal two-layered samples, our method accurately recovers the top layer thickness (L), the absorption coefficient (µ a ) and the reduced scattering coefficient (µ' s ) of both layers with deviations that are typically less than 10% for all parameters. Our method is aimed at absolute measurements of hemoglobin concentration and saturation in cerebral and extracerebral tissue of adult human subjects, where the top layer (layer 1) represents extracerebral tissue (scalp, skull, dura mater, subarachnoid space, etc.) and the bottom layer (layer 2) represents cerebral tissue. Human subject measurements have shown a significantly greater total hemoglobin concentration in cerebral tissue (82±14 µM) with respect to extracerebral tissue (30±7 µM). By contrast, there was no significant difference between the hemoglobin saturation measured in cerebral tissue (56%±10%) and extracerebral tissue (62%±6%). To our knowledge, this is the first time that an inversion procedure in the frequency domain with six unknown parameters with no other prior knowledge is used for the retrieval of the optical coefficients and top layer thickness with high accuracy on two-layered media. Our absolute measurements of cerebral hemoglobin concentration and saturation are based on the discrimination of extracerebral and cerebral tissue layers, and they can enhance the impact of NIRS for cerebral hemodynamics and oxygenation assessment both in the research arena and clinical practice.

System analysis of spatial frequency domain imaging for quantitative mapping of surgically resected breast tissues

The feasibility of spatial frequency domain imaging (SFDI) for breast surgical margin assessment was evaluated in tissue-simulating phantoms and in fully intact lumpectomy specimens at the time of surgery. Phantom data was evaluated according to contrast-detail resolution, quantitative accuracy and model-data goodness of fit, where optical parameters were estimated by minimizing the residual sum of squares between the measured modulation amplitude and its solutions, modeled according to diffusion and scaled-Monte Carlo simulations. In contrast-detail phantoms, a 1.25-mm-diameter surface inclusion was detectable for scattering contrast >28%; a fraction of this scattering contrast (7%) was detectable for a 10 mm surface inclusion and at least 33% scattering contrast was detected up to 1.5 mm below the phantom surface, a probing depth relevant to breast surgical margin assessment. Recovered hemoglobin concentrations were insensitive to changes in scattering, except for overestimation at visible wavelengths for total hemoglobin concentrations <15  μM. The scattering amplitude increased linearly with scattering concentration, but the scattering slope depended on both the particle size and number density. Goodness of fit was comparable for the diffusion and scaled-Monte Carlo models of transport in spatially modulated, near-infrared reflectance acquired from 47 lumpectomy tissues, but recovered absorption parameters varied more linearly with expected hemoglobin concentration in liquid phantoms for the scaled-Monte Carlo forward model. SFDI could potentially reduce the high secondary excision rate associated with breast conserving surgery; its clinical translation further requires reduced image reconstruction time and smart inking strategies.

Broadband ultraviolet-visible optical property measurement in layered turbid media

The ability to accurately measure layered biological tissue optical properties (OPs) may improve understanding of spectroscopic device performance and facilitate early cancer detection. Towards these goals, we have performed theoretical and experimental evaluations of an approach for broadband measurement of absorption and reduced scattering coefficients at ultraviolet-visible wavelengths. Our technique is based on neural network (NN) inverse models trained with diffuse reflectance data from condensed Monte Carlo simulations. Experimental measurements were performed from 350 to 600 nm with a fiber-optic-based reflectance spectroscopy system. Two-layer phantoms incorporating OPs relevant to normal and dysplastic mucosal tissue and superficial layer thicknesses of 0.22 and 0.44 mm were used to assess prediction accuracy. Results showed mean OP estimation errors of 19% from the theoretical analysis and 27% from experiments. Two-step NN modeling and nonlinear spectral fitting approaches helped improve prediction accuracy. While limitations and challenges remain, the results of this study indicate that our technique can provide moderately accurate estimates of OPs in layered turbid media.

Diffuser-aided diffuse optical imaging for breast tumor: a feasibility study based on time-resolved three-dimensional Monte Carlo modeling

This study proposed diffuser-aided diffuse optical imaging (DADOI) as a new approach to improve the performance of the conventional diffuse optical tomography (DOT) approach for breast imaging. The 3-D breast model for Monte Carlo simulation is remodeled from clinical MRI image. The modified Beer-Lambert's law is adopted with the DADOI approach to substitute the complex algorithms of inverse problem for mapping of spatial distribution, and the depth information is obtained based on the time-of-flight estimation. The simulation results demonstrate that the time-resolved Monte Carlo method can be capable of performing source-detector separations analysis. The dynamics of photon migration with various source-detector separations are analyzed for the characterization of breast tissue and estimation of optode arrangement. The source-detector separations should be less than 4 cm for breast imaging in DOT system. Meanwhile, the feasibility of DADOI was manifested in this study. In the results, DADOI approach can provide better imaging contrast and faster imaging than conventional DOT measurement. The DADOI approach possesses great potential to detect the breast tumor in early stage and chemotherapy monitoring that implies a good feasibility for clinical application.

Efficient determination of the epidermal optical properties using a diffusion model-based approach: Monte Carlo studies

In our previous studies, we have shown that the diffusing probe geometry can be used in conjunction with a two-layer diffusion model to accurately recover the absorption and scattering properties of skin in vivo. By modifying the original design to the diffusing probe with planar source (DPPS) geometry, we have also demonstrated that the efficiency of the accompanying multilayer diffusion model is comparable to that of a standard semi-infinite diffusion model; thus, precise quantification of superficial tissue optical properties in real time using a diffusion model becomes possible. In this study, the performance of the DPPS diffusion model is evaluated using Monte Carlo simulations and phantom measurements. It is found that the DPPS geometry is advantageous over the conventional planar source illumination geometry in interrogating superficial volumes of samples. In addition, our simulation results have shown that the DPPS geometry is capable of accurately recovering the optical properties of 50-μm thick epidermis and could be very useful in detecting cutaneous melanoma that has a radius as small as 250 μm.

Method for depth-resolved quantitation of optical properties in layered media using spatially modulated quantitative spectroscopy

We have demonstrated that spatially modulated quantitative spectroscopy (SMoQS) is capable of extracting absolute optical properties from homogeneous tissue simulating phantoms that span both the visible and near-infrared wavelength regimes. However, biological tissue, such as skin, is highly structured, presenting challenges to quantitative spectroscopic techniques based on homogeneous models. In order to more accurately address the challenges associated with skin, we present a method for depth-resolved optical property quantitation based on a two layer model. Layered Monte Carlo simulations and layered tissue simulating phantoms are used to determine the efficacy and accuracy of SMoQS to quantify layer specific optical properties of layered media. Initial results from both the simulation and experiment show that this empirical method is capable of determining top layer thickness within tens of microns across a physiological range for skin. Layer specific chromophore concentration can be determined to <±10% the actual values, on average, whereas bulk quantitation in either visible or near infrared spectroscopic regimes significantly underestimates the layer specific chromophore concentration and can be confounded by top layer thickness.

Analysis of a diffusion-model-based approach for efficient quantification of superficial tissue properties

Previously, we reported using a diffusing probe in conjunction with a two-layer diffusion model for accurately recovering the optical properties of superficial volumes. However, the two-layer diffusion equation is computationally less efficient than a standard diffusion equation (SDE) by 3 orders of magnitude. In this Letter, we present a new approach extended from the diffusing probe geometry that enables the use of a diffusion model that has efficiency comparable to an SDE. Our Monte Carlo simulation results indicate that this new approach is not only very accurate but also sensitive to the presence of 0.5 mm(3) inhomogeneities and could be used for monitoring the early progression of skin melanoma.

Experimental and theoretical evaluation of a fiber-optic approach for optical property measurement in layered epithelial tissue

Improvements in measurement of epithelial tissue optical properties (OPs) in the ultraviolet and visible (UV-Vis) may lead to enhanced understanding of optical techniques for neoplasia detection. In this study, we investigated an approach based on fiber-optic measurement of reflectance to determine absorption and reduced scattering coefficients (μ(a) and μ(s)') in two-layer turbid media. Neural network inverse models were trained on simulation data for a wide variety of OP combinations (μ(a) = 1-22.5, μ(s)' = 5-42.5 cm(-1)). Experimental measurements of phantoms with top-layer thicknesses (D) ranging from 0.22 to 0.66 mm were performed at three UV-Vis wavelengths. OP estimation accuracy was calculated and compared to theoretical results. Mean prediction errors were strongly correlated with D and ranged widely, from 1.5 to 12.1 cm(-1). Theoretical analyses indicated the potential for improving accuracy with alternate probe geometries. Although numerous challenges remain, this initial experimental study of an unconstrained approach for fiber-optic-based OP determination in two-layer epithelial tissue indicates the potential to provide useful measurements.

Light propagation in two-layer tissues with an irregular interface

We study light propagation in a half-space composed of two homogeneous layers each having different optical properties from the other. This problem is a model for light propagation in tissues composed of a thin epithelial layer supported from below by a thick stromal layer. The interface between the two layers is irregular. Assuming that this interface is a small perturbation of a plane that is parallel to the boundary surface, we obtain an asymptotic approximation to the solution. We give a numerical method to compute this asymptotic approximation. Finally, we show how to recover this irregular interface surface from boundary measurements when the optical properties of the two layers are known.

Time-resolved diffuse optical tomography and its application to in vitro and in vivo imaging

This work reviews our research during the past several years on time-resolved (TR) near-infrared diffuse optical tomography (DOT). Following an introduction of the measuring modes, two proposed schemes of image reconstruction in TR-DOT are described: one utilizes the full TR data, and the other, referred to as the modified generalized pulse spectrum technique (GPST), uses the featured data extracted from the TR measurement. The performances of the two algorithms in quantitativeness and spatial resolution are comparatively investigated with 2-D simulated data. TR-DOT images are then presented for phantom experiments, which are obtained by using a 16-channel time-correlated single photon counting system, and the factors affecting the quantification of the reconstruction are discussed. Finally, in vitro and in vivo imaging examples are illustrated for validating the capibility of TR-DOT to provide not only the anatomical but also the physiological information of the objects.

Time-domain Green functions for diffuse light in two adjoining turbid half-spaces

Propagation of light emitted by an instantaneous source located above a plane interface between two semi-infinite turbid media is considered using the diffusion approximation. Green functions are derived for an instantaneous line source and an instantaneous point source by the method of Bellman et al. [Philos. Mag. 40, 297 (1949)], which is based on integral transforms. Both two-dimensional and three-dimensional Green functions for diffuse light have been obtained in the form of single integrals that allow for fast calculation of the specific intensity in the whole space. The influence of the optical parameters of the two media (diffusion coefficients, absorptions, and refractive indices) on the shapes of the contour lines of the specific intensity is analyzed.

Perturbation and differential Monte Carlo methods for measurement of optical properties in a layered epithelial tissue model

The use of perturbation and differential Monte Carlo (pMC/dMC) methods in conjunction with nonlinear optimization algorithms were proposed recently as a means to solve inverse photon migration problems in regionwise heterogeneous turbid media. We demonstrate the application of pMC/dMC methods for the recovery of optical properties in a two-layer extended epithelial tissue model from experimental measurements of spatially resolved diffuse reflectance. The results demonstrate that pMC/dMC methods provide a rapid and accurate approach to solve two-region inverse photon migration problems in the transport regime, that is, on spatial scales smaller than a transport mean free path and in media where optical scattering need not dominate absorption. The pMC/dMC approach is found to be effective over a broad range of absorption (50 to 400%) and scattering (70 to 130%) perturbations. The recovery of optical properties from spatially resolved diffuse reflectance measurements is examined for different sets of source-detector separation. These results provide some guidance for the design of compact fiber-based probes to determine and isolate optical properties from both epithelial and stromal layers of superficial tissues.

Analytical solution for light propagation in a two-layer tissue structure with a tilted interface for breast imaging

Reflectance measurement of breast tissue is influenced by the underlying chest wall, which is often tilted as seen by the detection probe. We develop an analytical solution of light propagation in a two-layer tissue structure with tilted interface and refractive index difference between the layers. We validate the analytical solution with Monte Carlo simulations and phantom experiments, and a good agreement is seen. The influence of varying the tilting angle of the interface on the reflectance is discussed for two types of layered structures. Further, we apply the developed analytical solution to obtain the optical properties of breast tissue and chest wall from clinical data. Inverse calculation using the developed solution applied to the data obtained from Monte Carlo simulations shows that the optical properties of both layers are obtained with higher accuracy as compared to using a simple two-layer model ignoring the interface tilt. This is expected to improve the accuracy in estimating the optical properties of breast tissue, thus enhancing the accuracy of optical tomography of breast tumors.

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=300 microm) to restrict the transport of detected light to the top layer. A Monte Carlo-based inverse model for a homogeneous medium was employed to estimate the top layer optical properties from the measured diffuse reflectance spectrum. Then a flat-tip probe with a large source-detector 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.

Investigation of light propagation models to determine the optical properties of tissue from interstitial frequency domain fluence measurements

Four models, standard diffusion approximation (SDA), single Monte Carlo (SMC), delta-P1, and isotropic similarity (ISM), are developed and evaluated as forward calculation tools in the estimation of tissue optical properties. The inverse calculation uses the ratio of the fluences and phase difference at two locations close to an intensity modulated isotropic source to recover the reduced scattering coefficient mus' and the absorption coefficient mua. Diffusion theory allows recovery of optical properties (OPs) within 5% for media with mus'mua>10. The performance of the delta-P1 model is similar to SDA, with limited enhanced accuracy. The collimation approximation may limit the use of the delta-P1 model for spherical geometry, and/or the fluence may not be accurately calculated by this model. The SMC model is the best, recovering OPs within 10% regardless of the albedo. However, the necessary restriction of the searched OPs space is inconvenient. The performance of ISM is similar to that of diffusion theory for media with mus'mua>10, and better for 1<mus'mua<10, i.e., determines absorption within 5% and reduced scattering within 20%. In practice, satisfactory estimates (within 5 to 10%) can be achieved using SDA to recover mus' and ISM to recover mua for media with mus'mua>5.

Determination of scattering volume fraction and particle size distribution in the superficial layer of a turbid medium by using diffuse reflectance spectroscopy

We have investigated the possibility of determining changes in the volume fraction of microstructure scatterers in the superficial tissue layers by using diffuse reflectance spectroscopy. To that extent we have built a two-layer optical phantom by using microparticles with various sizes in order to simulate the scattering properties of tissue microstructures. Reflectance spectral measurements were performed on a number of optical phantoms having different volume fractions of various microparticle sizes. An analytical model was developed using light-transport theory and fractal modeling approaches and was then fitted to the measured reflectance to calculate the volume fractions of the microparticles in phantoms. The results showed that we could measure changes in both the total volume fraction of the microparticles and in the overall size distribution of the microparticles with good accuracy (>80%). These results suggest the potential of using this method for measuring the volume fraction changes of tissue microstructure scatterers and applications in the detection of cancerous related morphological and structural changes.

Optical characterization of thin female breast biopsies based on the reduced scattering coefficient

One of the main goals in optical characterization of biopsies is to discern between tissue types. Usually, the theory used for deriving the optical properties of such highly scattering media is based on the diffusion approximation. However, biopsies are usually small in size compared to the transport mean free path and thus cannot be treated with standard diffusion theory. To account for this, an improved theory was developed, by the authors, that can correctly describe light propagation in small geometries (Garofalakis et al 2004 J. Opt. A: Pure Appl. Opt. 6 725-35). The theory's limit was validated by both Monte Carlo simulations and experiments performed on tissue-like phantoms, and was found to be two transport mean free paths. With the aid of this theory, we have characterized 59 samples of breast tissue including cancerous samples by retrieving their reduced scattering coefficients from time-resolved transmission data. The mean values for the reduced scattering coefficients of the normal and the tumour tissue were measured to be 9.7 +/- 2.2 cm(-1) and 10.8 +/- 1.8 cm(-1), respectively. The correlation with age was also investigated.

Light transport in two-layer tissues

We study theoretically light backscattered by tissues using the radiative transport equation. In particular we consider a two-layered medium in which a finite slab is situated on top of a half space. We solve the one-dimensional problem in which a plane wave is incident normally on the top layer and is the only source of light. The solution to this problem is obtained formally by imposing continuity between the solutions for the upper and lower layers. However, we are interested solely in probing the top layer. Assuming that the optical properties in the lower layer are known, we remove it from the problem yielding a finite slab problem by prescribing an alternate boundary condition. This boundary condition is derived using the theory of Green's functions and is exact. Hence, one needs only to solve the transport equation in a finite slab using this alternate boundary condition. We derive an asymptotic solution for the case when the slab is optically thin. We extend these results to the three-dimensional problem using Fourier transforms. These results are validated by comparisons with numerical solutions for the entire two-layered problem.

Measurement of the coagulation dynamics of bovine liver using the modified microscopic Beer-Lambert law

BACKGROUND AND OBJECTIVES

During heating, the optical properties of biological tissues change with the coagulation state. In this study, we propose a technique, which uses these changes to monitor the coagulation process during laser-induced interstitial thermotherapy (LITT).

STUDY DESIGN/MATERIALS AND METHODS

Untreated and coagulated (water bath, temperatures between 35 degrees C and 90 degrees C for 20 minutes.) samples of bovine liver tissue were examined using a Nd:YAG (lambda = 1064 nm) frequency-domain reflectance spectrometer. We determined the time integrated intensities (I(DC)) and the phase shifts (Phi) of the photon density waves after migration through the tissue. From these measured quantities, the time of flight (TOF) of the photons and the absorption coefficients of the samples were derived using the modified microscopic Beer-Lambert law.

RESULTS

The absorption coefficients of the liver samples decreased significantly with the temperature in the range between 50 degrees C and 70 degrees C. At the same time, the TOF of the investigated photos was found increased indicating an increased scattering. The coagulation dynamics could be well described using the Arrhenius formalism with the activation energy of 106 kJ/mol and the frequency factor of 1.59 x 10(13)/second.

CONCLUSIONS

Frequency-domain reflectance spectroscopy in combination with the modified microscopic Beer-Lambert (MBL) is suitable to measure heat induced changes in the absorption and scattering properties of bovine liver in vitro. The technique may be used to monitor the coagulation dynamics during local thermo-coagulation in vivo.

Determination of the optical properties of a two-layer tissue model by detecting photons migrating at progressively increasing depths

We have investigated a method for solving the inverse problem of determining the optical properties of a two-layer turbid model. The method is based on deducing the optical properties (OPs) of the top layer from the absolute spatially resolved reflectance that results from photon migration within only the top layer by use of a multivariate calibration model. Then the OPs of the bottom layer are deduced from relative frequency-domain (FD) reflectance measurements by use of the two-layer FD diffusion model. The method was validated with Monte Carlo FD reflectance profiles and experimental measurements of two-layer phantoms. The results showed that the method is useful for two-layer models with interface depths of >5 mm; the OPs were estimated, within a relatively short time (<1 min), with a mean error of <10% for the Monte Carlo reflectance profiles and with errors of <25% for the phantom measurements.

Transabdominal near infrared oximetry of hypoxic stress in fetal sheep brain in utero

The feasibility of transabdominal near-infrared (NIR) spectroscopy for detecting and quantifying fetal hypoxia in utero is demonstrated in a pregnant ewe model. A frequency domain NIR spectroscopy probe, consisting of two detectors and six sources operating at three wavelengths (675, 786, and 830 nm), was placed on the maternal abdomen directly above the fetal head. Fetal hypoxia was indirectly induced through occlusion of uterine blood flow for approximately 3 min. NIR photon diffusion measurements were made during a baseline period, during hypoxia of the fetus, and during recovery. Fetal blood samples were drawn from the fetal brachial artery and jugular veins at several time points during the cycle. Seven hypoxic cycles were induced in a total of five pregnant ewes. The NIR measurements were analyzed by using a two-layer diffusion model to deconvolve the fetal blood saturation from that of the pregnant ewe. Fetal hypoxia was detected. Good agreement was found between fetal blood saturation determined by the transabdominal NIR method and arterial and venous fetal blood saturation quantified from fetal blood samples by using a hemoximeter.

Procedure for retrieving the optical properties of a two-layered medium from time-resolved reflectance measurements

A procedure for retrieving the optical properties of a two-layered diffusive medium based on an exact analytical solution of the diffusion equation and on relative multidistance time-resolved reflectance measurements is presented. The method overcomes some limitations of previously developed procedures. Five parameters of the medium have been fitted: the absorption and the reduced scattering coefficients of both layers and the thickness of the first layer. The actual values of the parameters are correctly retrieved by the procedure. The inversion procedure does not require an initial guess for the unknown optical properties, but the starting value for the thickness of the first layer needs to be estimated with an error smaller than 50%.

Characterization of layered scattering media using polarized light measurements and neural networks

Measurements of the spatial distributions of polarized light backscattered from a two-layer scattering medium are used to train a neural network. We investigated whether the absorption coefficients and thickness of the layer can be determined when the scattering properties are known. When determining the absorption of the upper layer or the layer's thickness, polarized light measurements provide better performance than unpolarized measurements, demonstrating the sensitivity of polarized light to superficial tissue. Determination of the lower layer's absorption coefficient is not improved by polarized light measurements. Prior knowledge of the tissue under investigation is also beneficial because errors are reduced if the range of absorption or thickness is restricted.

Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method

An exact solution of the time-dependent diffusion equation for the case of a two- and a three-layered finite diffusive medium is proposed. The method is based on the decomposition of the fluence rate in a series of eigenfunctions and upon the solution of the consequent transcendental equation for the eigenvalues obtained from the boundary conditions. Comparisons among the solution of the diffusion equation and the results of Monte Carlo simulations show the correctness of the proposed model.

Models and measurements of light intensity changes during laser interstitial thermal therapy: implications for optical monitoring of the coagulation boundary location

We have developed a multi-region spherical Monte Carlo (MC) model to simulate the dynamic changes in light intensity measured during laser interstitial thermal therapy (LITT). Model predictions were validated experimentally in tissue-simulating albumen phantoms with well-characterized optical properties that vary dynamically with LITT in a way similar to tissue. For long treatments (2.5 W, approximately 1800 s), the transient light intensity changes demonstrated better qualitative agreement with a three-region MC model (with an inner layer of fully coagulated optical properties, a middle layer of partially coagulated properties and an outer region of native properties); for short treatments (4 W, approximately 240 s), better qualitative agreement was seen with a two-region MC model (with an inner layer of fully coagulated properties and outer region of native properties). These differences were attributed to differences in coagulation formation during low- and high-powered heating regimes, respectively. At the end of heating, a three-region coagulation zone was observed for both heating schemes. Quantitatively, final light intensity changes at the end of heating were compared with changes predicted by both two- and three-region MC for the same experimentally measured coagulation size and found to agree within approximately 30% for both models. The developed MC model helps lend insight into the nature of thermal coagulation events occurring for low and high power LITT irradiation schemes.

Analysis of the spatial distribution of polarized light backscattered from layered scattering media

The scattering of polarized light from a two layer scattering medium is investigated using Monte Carlo simulations. First order and normalized second order moments are used to analyze the spatial properties of the emerging light in different polarization states. Linearly and circularly polarized illumination is used to probe different depths. Absorption and layer thickness are varied and it is demonstrated that the determination of these values is aided by the inclusion of polarization information. The lateral and depth localization of light by polarization subtraction is also quantified. Potential applications of these techniques are burn depth and melanoma thickness measurements.

Reconstruction of absorber concentrations in a two-layer structure by use of multidistance time-resolved reflectance spectroscopy

The characterization of a two-layer structure was investigated by use of time-resolved reflectance over a wide spectral range. We exploited the nonlinear dependence of the measured spectra on the upper-and lower-layer properties to formulate an algorithm for the recovery of absorber concentrations in both layers. The method assumes that the spectral features of the key absorbers are known, but it does not rely on a priori knowledge of the layer thickness. Phantom tests confirmed the accuracy of the estimate of the absorber concentrations to within 10% for thickness values ranging from 0.3 to 1.2 cm. Multidistance absorption spectra from 610 to 1000 nm were obtained in vivo from the forearms of human subjects, allowing us to estimate the concentration of key tissue constituents in a two-layer approximation. Good agreement between the reconstructed spectra and the experimental data taken from two volunteers with opposite predominance of adipose and muscular tissues demonstrated the validity of this approach.

Validity of the diffusion approximation in bio-optical imaging

Accurate numerical simulations based on rigorous radiative transfer theory are used to assess the validity of the diffusion approximation that is frequently used in bio-optical imaging. These simulations show that the error is large for a non-index-matched boundary between air and tissue. This weakness of the diffusion approximation underscores the need to understand how diffusion theory can be used to extract accurate values of tissue optical properties. A validity criterion for the diffusion approximation is established on the basis of the single-scattering albedo a and the asymmetry factor g for a slab with index-matched boundaries.

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.

Recovery of optical parameters in multiple-layered diffusive media: theory and experiments

Diffuse photon density waves have lately been used both to characterize diffusive media and to locate and characterize hidden objects, such as tumors, in soft tissue. In practice, most biological media of medical interest consist of various layers with different optical properties, such as the fat layer in the breast or the different layers present in the skin. Also, most experimental setups consist of a multilayered system, where the medium to be characterized (i.e., the patient's organ) is usually bounded by optically diffusive plates. Incorrect modeling of interfaces may induce errors comparable to the weak signals obtained from tumors embedded deep in highly heterogeneous tissue and lead to significant reconstruction artifacts. To provide a means to analyze the data acquired in these configurations, the basic expressions for the reflection and transmission coefficients for diffusive-diffusive and diffusive-nondiffusive interfaces are presented. A comparison is made between a diffusive slab and an ordinary dielectric slab, thus establishing the limiting distance between the two interfaces of the slab for multiple reflections between them to be considered important. A rigorous formulation for multiple-layered (M-layered) diffusive media is put forward, and a method for solving any M-layered medium is shown. The theory presented is used to characterize a two-layered medium from transmission measurements, showing that the coefficients of scattering, mu'(s) , and absorption, mu(a) , are retrieved with great accuracy. Finally, we demonstrate the simultaneous retrieval of both mu;(s) and mu(a).