Diffuse reflectance from turbid media: an analytical model of photon migration

Using reflectometry to minimize the dependence of fluorescence intensity on optical absorption and scattering

The total diffuse reflectance RT and the effective attenuation coefficient µeff of an optically diffuse medium map uniquely onto its absorption and reduced scattering coefficients. Using this premise, we developed a methodology where RT and the slope of the logarithmic spatially resolved reflectance, a quantity related to µeff, are the inputs of a look-up table to correct the dependence of fluorescent signals on the media's optical properties. This methodology does not require an estimation of the medium's optical property, avoiding elaborate simulations and their errors to offer accurate and fast corrections. The experimental demonstration of our method yielded a mean relative error in fluorophore concentrations of less than 4% over a wide range of optical property variations. We discuss how the method developed can be employed to improve image fidelity and fluorochrome quantification in fluorescence molecular imaging clinical applications.

Influence of blood pulsation on diagnostic volume in pulse oximetry and photoplethysmography measurements

Recent advances in the development of ultra-compact semiconductor lasers and technology of printed flexible hybrid electronics have opened broad perspectives for the design of new pulse oximetry and photoplethysmography devices. Conceptual design of optical diagnostic devices requires careful selection of various technical parameters, including spectral range; polarization and intensity of incident light; actual size, geometry, and sensitivity of the detector; and mutual position of the source and detector on the surface of skin. In the current study utilizing a unified Monte Carlo computational tool, we explore the variations in diagnostic volume due to arterial blood pulsation for typical transmitted and back-scattered probing configurations in a human finger. The results of computational studies show that the variations in diagnostic volumes due to arterial pulse wave are notably (up to 45%) different in visible and near-infrared spectral ranges in both transmitted and back-scattered probing geometries. While these variations are acceptable for relative measurements in pulse oximetry and/or photoplethysmography, for absolute measurements, an alignment normalization of diagnostic volume is required and can be done by a computational approach utilized in the framework of the current study.

A technique for correction of attenuations in synchronous fluorescence spectroscopy

Synchronous fluorescence spectroscopy is an efficient technique for decoupling fluorophores which are masked in fluorescence spectroscopy due to overlapping of dominant fluorophores. By choosing appropriate offsets between excitation and emission wavelengths during signal acquisition from turbid samples, responses of individual fluorophores are highlighted as sharp peaks by using this technique. Some of the peaks may, however, still be missed due to wavelength dependent absorption and scattering effects. In this study a correction technique is used to extract such hidden signatures. The technique is validated using tissue phantoms with known concentrations of fluorophores, absorbers and scatterers. On the basis of validation studies on single and combination of two fluorophores, it is found that lower offsets display better recovery due to minimal influence of absorption by blood. Among the different offsets, 55 nm is found to be optimal for investigation of cervical precancers.

Comparative analysis of radiative transfer approaches for calculation of diffuse reflectance of plane-parallel light-scattering layers

We present an analysis of a number of different approximations for the diffuse reflectance (spherical and plane albedo) of a semi-infinite, unbounded, plane-parallel, and optically homogeneous layer. The maximally wide optical conditions (from full absorption to full scattering and from fully forward to fully backward scattering) at collimated, diffuse, and combined illumination conditions were considered. The approximations were analyzed from the point of view of their physical limitations and compared to the numerical radiative transfer solutions, whenever it was possible. The main factors impacting the spherical and plane albedo were revealed for the known and unknown scattering phase functions. The main criterion for inclusion of the models in analysis was the possibility of practical use, i.e., approximations were well parameterized and only included easily measured or estimated parameters. We give a detailed analysis of errors for different models. An algorithm for recalculation of results under combined (direct and diffuse) illumination also has been developed.

Diffuse reflectance spectroscopy as a tool to measure the absorption coefficient in skin: South African skin phototypes

In any laser skin treatment, the optical properties (absorption and scattering coefficients) are important parameters. The melanin content of skin influences the absorption of light in the skin. The spread in the values of the absorption coefficients for the South African skin phototypes are not known. A diffuse reflectance probe consisting of a ring of six light delivery fibers and a central collecting fiber was used to measure the diffused reflected light from the arms of 30 volunteers with skin phototypes I-V (on the Fitzpatrick scale). The absorption coefficient was calculated from these measurements. This real-time in vivo technique was used to determine the absorption coefficient of sun-exposed and -protected areas on the arm. The range of typical absorption coefficients for the South African skin phototypes is reported. The values for the darker South African skin types were much higher than was previously reported for darker skin phototypes. In the analysis, the contributions of the eumelanin and pheomelanin were separated, which resulted in improved curve fitting for volunteers of southern Asian ethnicity without compromising the other groups.

Retrieving skin properties from in vivo spectral reflectance measurements

A previously developed inverse method was applied to in vivo normal-hemispherical spectral reflectance measurements taken on the inner and outer forearm as well as the forehead of healthy white Caucasian and black African subjects. The inverse method was used to determine the thickness and melanin concentration in the epidermis, dermal blood volume fraction and oxygen saturation, and skin's spectral scattering coefficient. It was established that changes in melanin concentration due to racial difference and tanning, and differences in epidermal thickness and blood volume with anatomical location were detectable. The retrieved values were also consistent with independent measurements reported in the literature. The same method could be used for optical diagnosis of pathologies affecting the structure and pigmentation of human skin.

Rapid and accurate estimation of blood saturation, melanin content, and epidermis thickness from spectral diffuse reflectance

We present a method to determine chromophore concentrations, blood saturation, and epidermal thickness of human skin from diffuse reflectance spectra. Human skin was approximated as a plane-parallel slab of variable thickness supported by a semi-infinite layer corresponding to the epidermis and dermis, respectively. The absorption coefficient was modeled as a function of melanin content for the epidermis and blood content and oxygen saturation for the dermis. The scattering coefficient and refractive index of each layer were found in the literature. Diffuse reflectance spectra between 490 and 620 nm were generated using Monte Carlo simulations for a wide range of melanosome volume fraction, epidermal thickness, blood volume, and oxygen saturation. Then, an inverse method was developed to retrieve these physiologically meaningful parameters from the simulated diffuse reflectance spectra of skin. A previously developed accurate and efficient semiempirical model for diffuse reflectance of two layered media was used instead of time-consuming Monte Carlo simulations. All parameters could be estimated with relative root-mean-squared error of less than 5% for (i) melanosome volume fraction ranging from 1% to 8%, (ii) epidermal thickness from 20 to 150 mum, (iii) oxygen saturation from 25% to 100%, (iv) blood volume from 1.2% to 10%, and (v) tissue scattering coefficient typical of human skin in the visible part of the spectrum. A similar approach could be extended to other two-layer absorbing and scattering systems.

Simple and accurate expressions for diffuse reflectance of semi-infinite and two-layer absorbing and scattering media

We present computationally efficient and accurate semiempirical models of light transfer suitable for real-time diffuse reflectance spectroscopy. The models predict the diffuse reflectance of both (i) semi-infinite homogeneous and (ii) two-layer media exposed to normal and collimated light. The two-layer medium consisted of a plane-parallel slab of finite thickness over a semi-infinite layer with identical index of refraction but different absorption and scattering properties. The model accounted for absorption and anisotropic scattering, as well as for internal reflection at the medium/air interface. All media were assumed to be nonemitting, strongly forward scattering, with indices of refraction between 1.00 and 1.44 and transport single-scattering albedos between 0.50 and 0.99. First, simple analytical expressions for the diffuse reflectance of the semi-infinite and two-layer media considered were derived using the two-flux approximation. Then, parameters appearing in the analytical expression previously derived were instead fitted to match results from more accurate Monte Carlo simulations. A single semiempirical parameter was sufficient to relate the diffuse reflectance to the radiative properties and thickness of the semi-infinite and two-layer media. The present model can be used for a wide range of applications including noninvasive diagnosis of biological tissue.

Intrinsic Raman spectroscopy for quantitative biological spectroscopy part I: theory and simulations

We present a novel technique, intrinsic Raman spectroscopy (IRS), to correct turbidity-induced Raman spectral distortions, resulting in the intrinsic Raman spectrum that would be observed in the absence of scattering and absorption. We develop an expression relating the observed and intrinsic Raman spectra through diffuse reflectance using the photon migration depiction of light transport. Numerical simulations are employed to validate the theoretical results and study the dependence of this expression on sample size and elastic scattering anisotropy.

Comparison of spectral variation from spectroscopy to spectral imaging

Optical biopsy has been shown to discriminate between normal and diseased tissue with high sensitivity and specificity. Fiber-optic probe-based spectroscopy systems do not provide the necessary spatial information to guide therapy effectively, ultimately requiring a transition from probe-based spectroscopy to spectral imaging. The effect of such a transition on fluorescence and diffuse reflectance line shape is investigated. Inherent differences in spectral line shape between spectroscopy and imaging are characterized and many of these differences may be attributed to a shift in illumination-collection geometry between the two systems. Sensitivity of the line-shape disparity is characterized with respect to changes in sample absorption and scattering as well as to changes in various parameters of the fiber-optic probe design (e.g., fiber diameter, beam steering). Differences in spectral line shape are described in terms of the relative relationship between the light diffusion within the tissue and the distribution of source-detector separation distances for the probe-based and imaging illumination-collection geometries. Monte Carlo simulation is used to determine fiber configurations that minimize the line-shape disparity between the two systems. In conclusion, we predict that fiber-optic probe designs that mimic a spectral imaging geometry and spectral imaging systems designed to emulate a probe-based geometry will be difficult to implement, pointing toward a posteriori correction for illumination-collection geometry to reconcile imaging and probe-based spectral line shapes or independent evaluation of tissue discrimination accuracy for probe-based and spectral imaging systems.

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.

A review of attenuation correction techniques for tissue fluorescence

Fluorescence intensity measurements have the potential to facilitate the diagnoses of many pathological conditions. However, accurate interpretation of the measurements is complicated by the distorting effects of tissue scattering and absorption. Consequently, different techniques have been developed to attempt to compensate for these effects. This paper reviews currently available correction techniques with emphasis on clinical application and consideration given to the intrinsic accuracy and limitations of each technique.

Experimental and simulated angular profiles of fluorescence and diffuse reflectance emission from turbid media

Given the wavelength dependence of sample optical properties and the selective sampling of surface emission angles by noncontact imaging systems, differences in angular profiles due to excitation angle and optical properties can distort relative emission intensities acquired at different wavelengths. To investigate this potentiality, angular profiles of diffuse reflectance and fluorescence emission from turbid media were evaluated experimentally and by Monte Carlo simulation for a range of incident excitation angles and sample optical properties. For emission collected within the limits of a semi-infinite excitation region, normalized angular emission profiles are symmetric, roughly Lambertian, and only weakly dependent on sample optical properties for fluorescence at all excitation angles and for diffuse reflectance at small excitation angles relative to the surface normal. Fluorescence and diffuse reflectance within the emission plane orthogonal to the oblique component of the excitation also possess this symmetric form. Diffuse reflectance within the incidence plane is biased away from the excitation source for large excitation angles. The degree of bias depends on the scattering anisotropy and albedo of the sample and results from the correlation between photon directions upon entrance and emission. Given the strong dependence of the diffuse reflectance angular emission profile shape on incident excitation angle and sample optical properties, excitation and collection geometry has the potential to induce distortions within diffuse reflectance spectra unrelated to tissue characteristics.

Fluorescence depolarization in a scattering medium: effect of size parameter of a scatterer

For a monodisperse scattering medium, we investigate the dependence on scatterer size parameter for the change in anisotropy of fluorescence due to single scattering at excitation or emission wavelength. The value for the ratio of the anisotropy of fluorescence after one scattering at excitation or emission wavelength to the initial value was observed to increase with increasing value of scatterer size parameter. The effect of multiple scattering on anisotropy of fluorescence from fluorophores embedded in a scattering medium was incorporated using a photon migration model. The model was validated by experiments carried out on samples with known concentration of polystyrene microspheres as scatterers and riboflavins or reduced form of nicotinamide adenine dinucleotide as fluorophores.

Boundary conditions for light propagation in diffusive media with nonscattering regions

The diffusion approximation proves to be valid for light propagation in highly scattering media, but it breaks down in the presence of nonscattering regions. We present a compact expression of the boundary conditions for diffusive media with nonscattering regions, taking into account small-index mismatch. Results from an integral method based on the extinction theorem boundary condition are contrasted with both Monte Carlo and finite-element-method simulations, and a study of its limit of validity is presented. These procedures are illustrated by considering the case of the cerebro-spinal fluid in the brain, for which we demonstrate that for practical situations in light diffusion, these boundary conditions yield accurate results.

Imaging of fluorescence in highly scattering media

Two one-speed radiation transport equations coupled by a dynamic equation for the distribution of fluorophore electronic states are used to model the migration of excitation photons and emitted fluorescence photons. The conditions for producing appreciable levels of fluorophore in the excited state are studied, with the conclusion that minimal saturation occurs under the conditions applicable to tissue imaging. This simplifies the derivation of the frequency response and of the imaging operator for a time-harmonic excitation source. Several factors known to influence the fluorescence response-the concentration, mean lifetime and quantum yield of the fluorophore, and the modulation frequency of the excitatory source-are examined. Optimal sensitivity conditions are obtained by analyzing the fluorescence source strength as a function of the mean lifetime and modulation frequency. The dependence of demodulation of the fluorescent signal on the above factors is also examined. In complementary studies, transport-theory-based operators for imaging fluorophore distributions in a highly scattering medium are derived. Experimental data were collected by irradiating a cylindrical phantom containing one or two fluorophore-filled balloons with continuous wave laser light. The reconstruction results show that qualitatively and quantitatively good images can be obtained, with embedded objects accurately located and the fluorophore concentration correctly determined.

Convolution picture of the boundary conditions in photon migration and its implications in time-resolved optical imaging of biological tissues

To model the effect of a tissue-air boundary on time-resolved optical measurements, a convolution picture is presented based on the photon migration picture. It is demonstrated that the boundary conditions (either index matched or index mismatched) can be formulated as a spatiotemporal convolution of two terms, with the first being identical to the solution in the infinite medium and the second being independent of the original light source. The conditions under which the spatial convolution part in the second term becomes negligible are also determined thus permitting the complete separation of the two terms by use of a temporal Laplace or Fourier transformation. This result is promising, since it, suggests a method of removing the effect of the boundary conditions in the applications of time-resolved optical imaging (in both the time domain and the frequency domain) in biological tissues.

Analytical model for extracting intrinsic fluorescence in turbid media

In this paper we describe a photon migration approach for modeling fluorescence in an optically thick, turbid medium such as human tissue. In such a medium the intrinsic fluorescence spectrum of the fluorophores Φ can be distorted by the interplay of many factors, including scattering and absorption, excitation and collection geometries, and boundary conditions. The model provides an analytical relationship between the bulk fluorescence spectrum F and the diffuse reflectance spectrum R for arbitrary geometries and boundary conditions. We demonstrate that the distortion can be simply and accurately removed by measuring R from the optically thick medium over the same wavelength range and in the same manner as F. Over a wide range of tissue parameters this relationship may be written as Φα F/R(eff), with R(eff) a corrected form of the measured diffuse reflectance. The validity of this approach is demonstrated in both laboratory experiments on human aortic media and by comparison with Monte Carlo simulations and dif usion theory. Connection with a previous algorithm for extracting intrinsic fluorescence is also discussed.