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

AAPM Task Group Report 311: Guidance for performance evaluation of fluorescence-guided surgery systems

The last decade has seen a large growth in fluorescence-guided surgery (FGS) imaging and interventions. With the increasing number of clinical specialties implementing FGS, the range of systems with radically different physical designs, image processing approaches, and performance requirements is expanding. This variety of systems makes it nearly impossible to specify uniform performance goals, yet at the same time, utilization of different devices in new clinical procedures and trials indicates some need for common knowledge bases and a quality assessment paradigm to ensure that effective translation and use occurs. It is feasible to identify key fundamental image quality characteristics and corresponding objective test methods that should be determined such that there are consistent conventions across a variety of FGS devices. This report outlines test methods, tissue simulating phantoms and suggested guidelines, as well as personnel needs and professional knowledge bases that can be established. This report frames the issues with guidance and feedback from related societies and agencies having vested interest in the outcome, coming from an independent scientific group formed from academics and international federal agencies for the establishment of these professional guidelines.

Development of a custom optical imaging system for non-invasive monitoring and delineation of lower limb varicose veins using hyperspectral imaging and quantitative phase analysis

BACKGROUND

Varicose veins (VV) are a prevalent chronic venous disorder, particularly affecting women of childbearing age. This condition is associated with significant complications, including pain, discomfort, leg cramps, ulceration, reduced quality of life, absenteeism, and even mortality. This study aims to develop a custom non-invasive, non-contact optical imaging system combined with magnitude and phase image calculation to monitor and visualize varicose veins and their tributaries using hyperspectral imaging and quantitative phase analysis with a k-means clustering algorithm.

RESULTS

Ten volunteers participated in the optical imaging system study. They were exposed to a polychromatic light source spanning the wavelength range of 400 nm-950 nm. The diffuse reflection spectra for varicose veins exhibited a peak at 530 nm, while leg veins showed a peak at 780 nm. Hyperspectral images obtained at these specific wavelengths were normalized in order to homogenize the spectral signatures of each pixel (converting the hyperspectral image to 8 bit RGB image) and filtered using a moving average filter. Subsequently, the varicose veins and leg veins were delineated and detected using quantitative phase analysis and a k-means clustering algorithm.

CONCLUSION

In conclusion, the custom optical imaging system, utilizing hyperspectral imaging and the associated clustering algorithm, provides detailed information regarding the spatial distribution of varicose veins. This information can assist vascular physicians in facilitating easier diagnosis and treatment planning.

Quality Assessment of Fruits and Vegetables Based on Spatially Resolved Spectroscopy: A Review

Damage occurs easily and is difficult to find inside fruits and vegetables during transportation or storage, which not only brings losses to fruit and vegetable distributors, but also reduces the satisfaction of consumers. Spatially resolved spectroscopy (SRS) is able to detect the quality attributes of fruits and vegetables at different depths, which is of great significance to the quality classification and defect detection of horticultural products. This paper is aimed at reviewing the applications of spatially resolved spectroscopy for measuring the quality attributes of fruits and vegetables in detail. The principle of light transfer in biological tissues, diffusion approximation theory and methodologies are introduced, and different configuration designs for spatially resolved spectroscopy are compared and analyzed. Besides, spatially resolved spectroscopy applications based on two aspects for assessing the quality of fruits and vegetables are summarized. Finally, the problems encountered in previous studies are discussed, and future development trends are presented. It can be concluded that spatially resolved spectroscopy demonstrates great application potential in the field of fruit and vegetable quality attribute evaluation. However, due to the limitation of equipment configurations and data processing speed, the application of spatially resolved spectroscopy in real-time online detection is still a challenge.

Estimation of bulk optical properties of turbid media from hyperspectral scatter imaging measurements: metamodeling approach

In many research areas and application domains, the bulk optical properties of biological materials are of great interest. Unfortunately, these properties cannot be obtained easily for complex turbid media. In this study, a metamodeling approach has been proposed and applied for the fast and accurate estimation of the bulk optical properties from contactless and non-destructive hyperspectral scatter imaging (HSI) measurements. A set of liquid optical phantoms, based on intralipid, methylene blue and water, were prepared and the Vis/NIR bulk optical properties were characterized with a double integrating sphere and unscattered transmittance setup. Accordingly, the phantoms were measured with the HSI technique and metamodels were constructed, relating the Vis/NIR reflectance images to the reference bulk optical properties of the samples. The independent inverse validation showed good prediction performance for the absorption coefficient and the reduced scattering coefficient, with R(2)(p) values of 0.980 and 0.998, and RMSE(P) values of 0.032 cm(-1) and 0.197 cm(-1) respectively. The results clearly support the potential of this approach for fast and accurate estimation of the bulk optical properties of turbid media from contactless HSI measurements.

Robust estimation of cerebral hemodynamics in neonates using multilayered diffusion model for normal and oblique incidences

The diffusion approximation is useful for many optical diagnostics modalities, such as near-infrared spectroscopy. However, the simple normal incidence, semi-infinite layer model may prove lacking in estimation of deep-tissue optical properties such as required for monitoring cerebral hemodynamics, especially in neonates. To answer this need, we present an analytical multilayered, oblique incidence diffusion model. Initially, the model equations are derived in vector-matrix form to facilitate fast and simple computation. Then, the spatiotemporal reflectance predicted by the model for a complex neonate head is compared with time-resolved Monte Carlo (TRMC) simulations under a wide range of physiologically feasible parameters. The high accuracy of the multilayer model is demonstrated in that the deviation from TRMC simulations is only a few percent even under the toughest conditions. We then turn to solve the inverse problem and estimate the oxygen saturation of deep brain tissues based on the temporal and spatial behaviors of the reflectance. Results indicate that temporal features of the reflectance are more sensitive to deep-layer optical parameters. The accuracy of estimation is shown to be more accurate and robust than the commonly used single-layer diffusion model. Finally, the limitations of such approaches are discussed thoroughly.

Convolution model of the diffuse reflectance for layered tissues

We present an explicit model for the diffuse reflectance due to a collimated beam of light incident normally on layered tissues. This model is derived using the corrected diffusion approximation applied to a layered medium, and it takes the form of a convolution with an explicit kernel and the incident beam profile. This model corrects the standard diffusion approximation over all source-detector separation distances provided the beam is sufficiently wide compared to the scattering mean free path. We validate this model through comparison with Monte Carlo simulations. Then we use this model to estimate the optical properties of an epithelial layer from Monte Carlo simulation data. Using measurements at small source-detector separations and this model, we are able to estimate the absorption coefficient, scattering coefficient, and anisotropy factor of epithelial tissues efficiently with reasonable accuracy.

Metamodeling approach for efficient estimation of optical properties of turbid media from spatially resolved diffuse reflectance measurements

A metamodeling approach is introduced and applied to efficiently estimate the bulk optical properties of turbid media from spatially resolved spectroscopy (SRS) measurements. The model has been trained on a set of liquid phantoms covering a wide range of optical properties representative for food and agricultural products and was successfully validated in forward and inverse mode on phantoms not used for training the model. With relative prediction errors of 10% for the estimated bulk optical properties the potential of this metamodeling approach for the estimation of the optical properties of turbid media from spatially resolved spectroscopy measurements has been demonstrated.

Three-dimensional Neumann-series approach to model light transport in nonuniform media

We present the implementation, validation, and performance of a three-dimensional (3D) Neumann-series approach to model photon propagation in nonuniform media using the radiative transport equation (RTE). The RTE is implemented for nonuniform scattering media in a spherical harmonic basis for a diffuse-optical-imaging setup. The method is parallelizable and implemented on a computing system consisting of NVIDIA Tesla C2050 graphics processing units (GPUs). The GPU implementation provides a speedup of up to two orders of magnitude over non-GPU implementation, which leads to good computational efficiency for the Neumann-series method. The results using the method are compared with the results obtained using the Monte Carlo simulations for various small-geometry phantoms, and good agreement is observed. We observe that the Neumann-series approach gives accurate results in many cases where the diffusion approximation is not accurate.

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.

Spatial frequency domain spectroscopy of two layer media

Monitoring of tissue blood volume and oxygen saturation using biomedical optics techniques has the potential to inform the assessment of tissue health, healing, and dysfunction. These quantities are typically estimated from the contribution of oxyhemoglobin and deoxyhemoglobin to the absorption spectrum of the dermis. However, estimation of blood related absorption in superficial tissue such as the skin can be confounded by the strong absorption of melanin in the epidermis. Furthermore, epidermal thickness and pigmentation varies with anatomic location, race, gender, and degree of disease progression. This study describes a technique for decoupling the effect of melanin absorption in the epidermis from blood absorption in the dermis for a large range of skin types and thicknesses. An artificial neural network was used to map input optical properties to spatial frequency domain diffuse reflectance of two layer media. Then, iterative fitting was used to determine the optical properties from simulated spatial frequency domain diffuse reflectance. Additionally, an artificial neural network was trained to directly map spatial frequency domain reflectance to sets of optical properties of a two layer medium, thus bypassing the need for iteration. In both cases, the optical thickness of the epidermis and absorption and reduced scattering coefficients of the dermis were determined independently. The accuracy and efficiency of the iterative fitting approach was compared with the direct neural network inversion.

Reflected light intensity profile of two-layer tissues: phantom experiments

Experimental measurements of the reflected light intensity from two-layer phantoms are presented. We report, for the first time, an experimental observation of a typical reflected light intensity behavior for the two-layer structure characterized by two different slopes in the reflected light profile of the irradiated tissue. The point in which the first slope changes to the second slope, named as the crossover point, depends on the upper layer thickness as well as on the ratio between the absorption coefficients of the two layers. Since similar experiments from one-layer phantoms present a monotonic decay behavior, the existence and the location of the crossover point can be used as a diagnostic fingerprint for two-layer tissue structures. This pertains to two layers with greater absorptivity in the upper layer, which is the typical biological case in tissues like skin.

Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling

Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.

Artifact reduction method in ultrasound-guided diffuse optical tomography using exogenous contrast agents

In diffuse optical tomography (DOT), a typical perturbation approach requires two sets of measurements obtained at the lesion breast (lesion or target site) and a contra-lateral location of the normal breast (reference site) for image reconstruction. For patients who have a small amount of breast tissue, the chest-wall underneath the breast tissue at both sites affects the imaging results. In this group of patients, the perturbation, which is the difference between measurements obtained at the lesion and reference sites, may include the information of background mismatch which can generate artifacts or affect the reconstructed quantitative absorption coefficient of the lesion. Also, for patients who have a single breast due to prior surgery, the contra-lateral reference is not available. To improve the DOT performance or overcome its limitation, we introduced a new method based on an exogenous contrast agent and demonstrate its performance using animal models. Co-registered ultrasound was used to guide the lesion localization. The results have shown that artifacts caused by background mismatch can be reduced significantly by using this new method.

Simple two-layer reflectance model for biological tissue applications: lower absorbing layer

A simple two-layer tissue reflectance model is described. This work is a continuation of our investigations on modeling reflectance from two-layered tissues that we recently initiated. In the present article, we describe a variation of a two-layer model that assumes a lower absorbing and scattering layer and an upper scattering-only layer. This two-layer configuration is a realistic model for biological tissues in the visible and near-IR spectral ranges, where the upper layer may be an epithelial layer and the lower layer is a vascularized stroma layer. Application of the model yields estimates for tissue parameters, such as the thickness of the upper layer or the absorption properties of the lower layer. These parameters are of great interest for the noninvasive study of a wide range of epithelial biological tissues. The validity range and accuracy of the model are tested on tissue phantoms in both the forward and inverse modes of application.

Optical tomography method that accounts for tilted chest wall in breast imaging

The chest wall underneath breast tissue distorts light reflection measurements, especially measurements obtained from distant source-detector pairs. For patients with a chest wall located at a shallower depth, the chest-wall effect needs to be considered in the image reconstruction procedure. Following our previous studies, this work systemically evaluates the performance of a two-layer model-based reconstruction using the finite element method, and compares it with the performance of the semi-infinite model. The results obtained from simulations and phantom experiments show that the two-layer model improves the light quantification of the targets. The improvements are attributed to improved background estimation and more accurate weight matrix calculation using a two-layer model compared to the semi-infinite model. Fitted two-layer background optical properties obtained from a group of ten patients with chest walls located less than 2 cm deep are more representative of breast tissue and chest-wall optical properties.

Diffuse Optics for Tissue Monitoring and Tomography

This review describes the diffusion model for light transport in tissues and the medical applications of diffuse light. Diffuse optics is particularly useful for measurement of tissue hemodynamics, wherein quantitative assessment of oxy- and deoxy-hemoglobin concentrations and blood flow are desired. The theoretical basis for near-infrared or diffuse optical spectroscopy (NIRS or DOS, respectively) is developed, and the basic elements of diffuse optical tomography (DOT) are outlined. We also discuss diffuse correlation spectroscopy (DCS), a technique whereby temporal correlation functions of diffusing light are transported through tissue and are used to measure blood flow. Essential instrumentation is described, and representative brain and breast functional imaging and monitoring results illustrate the workings of these new tissue diagnostics.

Light diffusion in a turbid cylinder. II. Layered case

This paper is the second of two dealing with light diffusion in a turbid cylinder. The diffusion equation was solved for an N-layered finite cylinder. Solutions are given in the steady-state, frequency, and time domains for a point beam incident at an arbitrary position of the first layer and for a circular flat beam incident at the middle of the cylinder top. For special cases the solutions were compared to other solutions of the diffusion equation showing excellent agreement. In addition, the derived solutions were validated by comparison with Monte Carlo simulations. In the time domain we also derived a fast solution ( approximately 10ms) for the case of equal reduced scattering coefficients and refractive indices in all layers.

Light diffusion in N-layered turbid media: steady-state domain

We deal with light diffusion in N-layered turbid media. The steady-state diffusion equation is solved for N-layered turbid media having a finite or an infinitely thick N'th layer. Different refractive indices are considered in the layers. The Fourier transform formalism is applied to derive analytical solutions of the fluence rate in Fourier space. The inverse Fourier transform is calculated using four different methods to test their performance and accuracy. Further, to avoid numerical errors, approximate formulas in Fourier space are derived. Fast solutions for calculation of the spatially resolved reflectance and transmittance from the N-layered turbid media ( approximately 10 ms) with small relative differences (<10(-7)) are found. Additionally, the solutions of the diffusion equation are compared to Monte Carlo simulations for turbid media having up to 20 layers.

Simple two-layer reflectance model for biological tissue applications

A two-layer tissue diffuse reflectance model is described. The model is based on a simple one-layer model that we have recently developed and successfully applied to the analysis of in vivo skin reflectance. The model, which is specifically designed for use with a fiber optic probe, has as its main features simplicity and ease of application, and it is capable of estimating the thickness and the absorption coefficient of a superficial absorbing and scattering layer. Both of these parameters are of great interest for the noninvasive study of epithelial biological tissues. The validity range and accuracy of the model are tested on tissue phantoms in both the forward and inverse modes of application.

Robust multiparameter method of evaluating the optical and thermal properties of a layered tissue structure using photothermal radiometry

The thermal and optical properties of multilayered dental tissue structure, the result of the surface-grown prismless layer on enamel, were evaluated simultaneously using multiparameter fits of photothermal radiometry frequency responses. The photothermal field generated in a tooth sample with near-infrared laser excitation was described using a coupled diffuse-photon-density and thermal wave model. The optical (absorption and scattering) coefficients and thermal parameters (spectrally averaged infrared emissivity, thermal diffusivity and conductivity) of each layer, as well as the thickness of the upper prismless enamel layer, were fitted using a multiparameter simplex downhill minimization algorithm. The results show that the proposed fitting approach can increase robustness of the multiparameter estimation of tissue properties in the case of ill-defined multiparameter fits, which are unavoidable in in vivo tissue evaluation. The described method can readily be used for noninvasive in vitro or in vivo characterization of a wide range of layered biological tissues.

Image reconstruction method for a two-layer tissue structure accounts for chest-wall effects in breast imaging

We develop a new tomographic imaging reconstruction algorithm for a two-layer tissue structure. Simulations and phantom experiments show more accurate reconstruction of target optical properties compared with those results obtained from a semi-infinite tissue model for layered structures. This improvement is mainly attributed to the more accurate estimation of background optical properties and more accurate estimation of weight matrix for imaging reconstruction by considering the light propagation effect in the second layer. Clinical results of breast lesions are also presented to demonstrate the utility of this new imaging algorithm.

Localization of adipose tissue embedded biliary tree vessels by use of near-infrared diffuse photon propagation models: a computational feasibility study

Biliary tree structures are embedded in adipose tissue and, therefore, cannot be visualized directly by the surgeon during cholecystectomy operations. This can lead to inadvertent injuries with serious complications for the patient. Computational studies were performed to assess the feasibility of noninvasively localizing these structures from spectrally resolved near-infrared reflectance measurements. Methodologies were developed for vessel localization, both on the adipose tissue surface and depthwise, by use of semi-infinite and two-layer models of diffuse photon propagation in tissues, respectively. The simulation results, along with some preliminary experimental measurements on tissue-simulating phantoms, prove the feasibility of these methods and show promise for their future clinical application.

The physics, biophysics and technology of photodynamic therapy

Photodynamic therapy (PDT) uses light-activated drugs to treat diseases ranging from cancer to age-related macular degeneration and antibiotic-resistant infections. This paper reviews the current status of PDT with an emphasis on the contributions of physics, biophysics and technology, and the challenges remaining in the optimization and adoption of this treatment modality. A theme of the review is the complexity of PDT dosimetry due to the dynamic nature of the three essential components -- light, photosensitizer and oxygen. Considerable progress has been made in understanding the problem and in developing instruments to measure all three, so that optimization of individual PDT treatments is becoming a feasible target. The final section of the review introduces some new frontiers of research including low dose rate (metronomic) PDT, two-photon PDT, activatable PDT molecular beacons and nanoparticle-based PDT.

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-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.

Influence of fiber optic probe geometry on the applicability of inverse models of tissue reflectance spectroscopy: computational models and experimental measurements

Accurate recovery of tissue optical properties from in vivo spectral measurements is crucial for improving the clinical utility of optical spectroscopic techniques. The performance of inversion algorithms can be optimized for the specific fiber optic probe illumination-collection geometry. A diffusion-theory-based inversion method has been developed for the extraction of tissue optical properties from the shape of normalized tissue diffusion reflectance spectra, specifically tuned for a fiber probe that comprises seven hexagonally close-packed fibers. The central fiber of the probe goes to the spectrometer as the detecting fiber, and the surrounding six outer fibers are connected to the white-light source as illumination fibers. The accuracy of the diffusion-based inversion algorithm has been systematically assessed against Monte Carlo (MC) simulation as a function of probe geometry and tissue optical property combinations. By use of this algorithm, the spectral absorption and scattering coefficients of normal and cancerous tissue are efficiently retrieved. Although there are significant differences between the diffusion approximation and the MC simulation at short source-detector (SD) separations, we show that with our algorithm the tissue optical properties are well retrieved within the SD separation of 0.5-3 mm that is compatible with endoscopic specifications. The presented inversion method is computationally efficient for eventual real-time in vivo tissue diagnostics application.

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.

Estimating optical properties in layered tissues by use of the Born approximation of the radiative transport equation

We use the Born approximation of the radiative transport equation to recover simultaneously the absorption and scattering coefficients in a single layer of a two-layer tissue sample from reflectance data. This method reduces the estimation of both optical properties to a single linear, least-squares problem. It is valid over length scales smaller than a transport mean free path and hence is useful for epithelial tissue layers. We demonstrate the accuracy of this method by using spatially resolved reflectance data computed with Monte Carlo simulations.

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.

The use of spatially resolved fluorescence and reflectance to determine interface depth in layered fluorophore distributions

The possibility of using spatially resolved fluorescence and reflectance measurements to recover tissue optical properties, fluorophore concentration and the thickness of a superficial layer in a two-layer geometry was investigated. A diffusion theory model was used to fit reflectance and fluorescence data generated using Monte Carlo simulations or experimentally obtained using tissue-simulating phantoms. Initial analysis fitting diffusion theory generated data suggested that it should be possible to recover all parameters from a single set of spatially resolved fluorescence and reflectance measurements. However, when Monte Carlo or experimental data were fitted the results were less impressive. Overall, it was shown that there is a strong coupling between interface depth, fluorophore concentration and tissue absorption, especially at larger depths. The recovery of all input parameters from a single set of spatially resolved measurements was limited to interface depths less than 3 mm, which is a reasonable range for measuring fluorophore in skin. When the tissue optical properties and fluorophore concentrations were known, then the interface depth could be monitored with good accuracy in simulated serial measurements. These results may also point to deficiencies in the diffusion theory model that introduce significant errors in the fitted results.

Analytical model to describe fluorescence spectra of normal and preneoplastic epithelial tissue: comparison with Monte Carlo simulations and clinical measurements

Fluorescence spectroscopy has shown promise for the detection of precancerous changes in vivo. The epithelial and stromal layers of tissue have very different optical properties; the albedo is relatively low in the epithelium and approaches one in the stroma. As precancer develops, the optical properties of the epithelium and stroma are altered in markedly different ways: epithelial scattering and fluorescence increase, and stromal scattering and fluorescence decrease. We present an analytical model of the fluorescence spectrum of a two-layer medium such as epithelial tissue. Our hypothesis is that accounting for the two different tissue layers will provide increased diagnostic information when used to analyze tissue fluorescence spectra measured in vivo. The Beer-Lambert law is used to describe light propagation in the epithelial layer, while light propagation in the highly scattering stromal layer is described with diffusion theory. Predictions of the analytical model are compared to results from Monte Carlo simulations of light propagation under a range of optical properties reported for normal and precancerous epithelial tissue. In all cases, the mean square error between the Monte Carlo simulations and the analytical model are within 15%. Finally, model predictions are compared to fluorescence spectra of normal and precancerous cervical tissue measured in vivo; the lineshape of fluorescence agrees well in both cases, and the decrease in fluorescence intensity from normal to precancerous tissue is correctly predicted to within 5%. Future work will explore the use of this model to extract information about changes in epithelial and stromal optical properties from clinical measurements and the diagnostic value of these parameters.

Green functions for diffuse photon-density waves generated by a line source in two nonabsorbing turbid media in contact

Diffuse photon-density waves generated by an instantaneous line source that is parallel to the interface between two semi-infinite turbid media are studied by use of the diffusion approximation. For two nonabsorbing media the Green functions for diffuse light are obtained based on the Green functions for temperature fields that were derived with the Cagniard-de Hoop method. The boundary conditions for diffuse light take into account the discontinuity in the specific intensity at the interface between two media with different refractive indices. The results of the calculations of the specific intensities and the gradient lines for different sets of parameters are presented.

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.

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.

Characterization of dysplastic tissue morphology and biochemistry in Barrett's esophagus using diffuse reflectance and light scattering spectroscopy

LSS and DRS are techniques that provide diagnostically useful information based on changes in the intensity of backscattered light that has experienced either a single or multiple scattering events. These changes can be detected effectively using statistical and model-based algorithms. In addition to providing a means to detect the presence of dysplasia noninvasively, the latter approach yields potentially significant insights into the processes that are involved in the development of dysplasia in BE. Because DRS and LSS provide complementary information to each other and to other spectroscopic modalities, such as fluorescence, it is possible that a combination of all these techniques will ultimately provide a highly accurate real-time method for detecting BE dysplasia. Extending point spectroscopic measurements to imaging of the esophagus will be challenging, but continuous progess in the development of powerful light sources, sensitive detectors, and micro-optical elements should allow this method to become a reality in the near future.

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.

Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness

A dual wavelength time-resolved reflectance system was developed for monitoring haemoglobin saturation noninvasively. At each wavelength, the time-resolved reflectance data were fitted to a diffusion model of light propagation in a homogeneous, semi-infinite medium to yield the absolute scattering and absorption coefficients. The absorption coefficients were then used to calculate haemoglobin saturation. A two-layer phantom containing human erythrocytes in a scattering solution in the bottom layer was used to study system performance under more realistic conditions. The top layer was chosen to simulate either skin or fat and the oxygenation of the bottom layer, which corresponded to muscle, was controlled. The thickness of the fat layer was varied from 1.5 to 10 mm to investigate the effects of increasing the top layer thickness. These results, obtained with the simple diffusion model, were compared with simultaneous measurements of oxygenation made directly in the bottom layer. Errors in estimating haemoglobin saturation with this method ranged from 5-11% depending on the thickness of the top layer and its optical properties.

Analytical approximate solutions of the time-domain diffusion equation in layered slabs

Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.

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).

Non-invasive determination of muscle blood flow in the extremities from laser Doppler spectra

We investigate theoretically the non-invasive determination of blood flow in muscles of the extremities using laser Doppler measurements. Laser Doppler spectra are calculated using Monte Carlo simulations and solutions of the correlation diffusion equation. The extremities are modelled as a two-layered turbid medium. The first layer represents the skin and subcutaneous fat layer and the second layer the muscle. It is shown that the absolute root-mean-square velocity of the blood in the muscle layer can be accurately derived in many practical cases if the laser Doppler spectra are measured at a distance which is sufficiently far from the source, and if the optical properties of the muscle are simultaneously determined.

A diffusion theory model of spatially resolved fluorescence from depth-dependent fluorophore concentrations

A photon diffusion model has been developed to calculate the steady-state spatially resolved fluorescence from pencil beam excitation in layered tissue. The model allows the calculation of both the excitation reflectance and the fluorescence escape for an arbitrary continuous depth distribution of tissue optical properties and fluorophore concentration. The validity of this model was verified by comparison with Monte Carlo simulations and experimental measurements using phantoms with tissue-like optical properties. The potential usefulness of the spatially resolved fluorescence was explored using the model and simulations of realistic drug distributions. It was shown that using this technique it may be possible to quantify the diffusion of a topically administered drug into the skin, or the photobleaching of a sensitizer during photodynamic therapy.

Broadband absorption spectroscopy in turbid media by combined frequency-domain and steady-state methods

A technique for measuring broadband near-infrared absorption spectra of turbid media that uses a combination of frequency-domain (FD) and steady-state (SS) reflectance methods is presented. Most of the wavelength coverage is provided by a white-light SS measurement, whereas the FD data are acquired at a few selected wavelengths. Coefficients of absorption (mu(a)) and reduced scattering (mu(s)') derived from the FD data are used to calibrate the intensity of the SS measurements and to estimate mu(s)' at all wavelengths in the spectral window of interest. After these steps are performed, one can determine mu(a) by comparing the SS reflectance values with the predictions of diffusion theory, wavelength by wavelength. Absorption spectra of a turbid phantom and of human breast tissue in vivo, derived with the combined SSFD technique, agree well with expected reference values. All measurements can be performed at a single source-detector separation distance, reducing the variations in sampling volume that exist in multidistance methods. The technique uses relatively inexpensive light sources and detectors and is easily implemented on an existing multiwavelength FD system.

Tissue oxygen saturation measured by near infrared spectrophotometry correlates with arterial oxygen saturation during induced oxygenation changes in neonates

The aim of this study was to compare quantitatively the changes in tissue oxygen saturation (TOS), determined by two algorithms (TOSc and TOSa) based on near-infrared spectrophotometry, to the changes in arterial oxygen saturation (SaO2) measured by pulse oximetry. TOSc is an algorithm derived by the manufacturer (Critikon) based on a modified Beer-Lambert law; TOSa, our own algorithm, uses the diffusion approximation of light transport for the semi-infinite boundary condition. Slow changes of more than 3% in SaO2 were carried out in 20 mechanically ventilated neonates by altering the inspired oxygen fraction. For each change the regression lines of TOSc versus SaO2, TOSa versus SaO2 and TOSc versus TOSa were calculatcd. For each infant the mcan slope, intercept and r2 of these lines were determined. In 18 preterm infants we obtained median 9.5 (range one to 13) measurements corresponding to a total of 166 measurements. The mean SaO2 was 91.6 (SD 2.3)%, TOSc was 64.7 (SD 7.2)% and TOSa was 71.4 (SD 11.0)%. Changes in TOSc and TOSa were strongly correlated to changes in SaO2 (r2 = 0.86 and r2 = 0.87). TOSc considerably but systematically underestimated the size of the change: delta TOSc = 0.49 delta SaO2. TOSa quantified changes reasonably correctly: delta TOSa = 0.90 delta SaO2. Changes in TOSc and TOSa were highly correlated (r2 = 0.98). These results are promising, but the large inter-individual variation requires further work.

Anisotropy of light propagation in human skin

Using spatially resolved, steady state diffuse reflectometry, a directional dependence was found in the propagation of visible and near infrared light through human skin in vivo. The skin's reduced scattering coefficient mu(s)' varies by up to a factor of two between different directions of propagation at the same position. This anisotropy is believed to be caused by the preferential orientation of collagen fibres in the dermis, as described by Langer's skin tension lines. Monte Carlo simulations that examine the effect of partial collagen fibre orientation support this hypothesis. The observation has consequences for non-invasive diagnostic methods relying on skin optical properties, and it could be used non-invasively to determine the direction of lines of cleavage in order to minimize scars due to surgical incisions.