Turbulent nature of refractive-index variations in biological tissue

Image contrast reduction mechanism in full-field optical coherence tomography

Correct interpretation of image contrast obtained with full-field optical coherence tomography (FFOCT) technique is required for accurate medical diagnosis applications. In this work, first, the characteristics of microscopic structures of tissue that generate the contrast in en-face tomographic image obtained with FFOCT are discussed. Then an overview is given of the parameters that affect image contrast. Finally, the contrast correction factor for correct image interpretation and the contrast limits to practical FFOCT systems are outlined.

Fractal propagation method enables realistic optical microscopy simulations in biological tissues

Current simulation methods for light transport in biological media have limited efficiency and realism when applied to three-dimensional microscopic light transport in biological tissues with refractive heterogeneities. We describe here a technique which combines a beam propagation method valid for modeling light transport in media with weak variations in refractive index, with a fractal model of refractive index turbulence. In contrast to standard simulation methods, this fractal propagation method (FPM) is able to accurately and efficiently simulate the diffraction effects of focused beams, as well as the microscopic heterogeneities present in tissue that result in scattering, refractive beam steering, and the aberration of beam foci. We validate the technique and the relationship between the FPM model parameters and conventional optical parameters used to describe tissues, and also demonstrate the method's flexibility and robustness by examining the steering and distortion of Gaussian and Bessel beams in tissue with comparison to experimental data. We show that the FPM has utility for the accurate investigation and optimization of optical microscopy methods such as light-sheet, confocal, and nonlinear microscopy.

Bridging Three Orders of Magnitude: Multiple Scattered Waves Sense Fractal Microscopic Structures via Dispersion

Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5  μm in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.

Imaging Cells in Flow Cytometer Using Spatial-Temporal Transformation

Flow cytometers measure fluorescence and light scattering and analyze multiple physical characteristics of a large population of single cells as cells flow in a fluid stream through an excitation light beam. Although flow cytometers have massive statistical power due to their single cell resolution and high throughput, they produce no information about cell morphology or spatial resolution offered by microscopy, which is a much wanted feature missing in almost all flow cytometers. In this paper, we invent a method of spatial-temporal transformation to provide flow cytometers with cell imaging capabilities. The method uses mathematical algorithms and a spatial filter as the only hardware needed to give flow cytometers imaging capabilities. Instead of CCDs or any megapixel cameras found in any imaging systems, we obtain high quality image of fast moving cells in a flow cytometer using PMT detectors, thus obtaining high throughput in manners fully compatible with existing cytometers. To prove the concept, we demonstrate cell imaging for cells travelling at a velocity of 0.2 m/s in a microfluidic channel, corresponding to a throughput of approximately 1,000 cells per second.

Model-based analysis on the influence of spatial frequency selection in spatial frequency domain imaging

Frequency variation in spatial frequency domain imaging is a powerful tool for adjusting the penetration depth of the imaging signal and the parameter sensitivity toward absorption and diffusive and subdiffusive scattering. Through our computational analysis, using an analytical solution of the radiative transfer equation, we add quantitation to this tool by linking the different spatial frequency regimes to their relative information content and to their absolute depth sensitivity. Special focus is placed on high spatial frequencies by analysis of the phase function parameter γ and its significance and ambiguity in describing subdiffusive scattering.

Fourier spectrum analysis of full-field optical coherence tomography for tissue imaging

We propose a model of the full-field optical coherence tomography (FFOCT) technique for tissue imaging, in which the fractal model of the spatial correlation function of the refractive index of tissue is employed to approximate tissue structure. The results may be helpful for correctly interpreting en face tomographic images obtained with FFOCT.

Validation of quantitative attenuation and backscattering coefficient measurements by optical coherence tomography in the concentration-dependent and multiple scattering regime

Optical coherence tomography (OCT) has the potential to quantitatively measure optical properties of tissue such as the attenuation coefficient and backscattering coefficient. However, to obtain reliable values for strong scattering tissues, accurate consideration of the effects of multiple scattering and the nonlinear relation between the scattering coefficient and scatterer concentration (concentration-dependent scattering) is required. We present a comprehensive model for the OCT signal in which we quantitatively account for both effects, as well as our system parameters (confocal point spread function and sensitivity roll-off). We verify our model with experimental data from controlled phantoms of monodisperse silica beads (scattering coefficients between 1 and 30  mm(−1) and scattering anisotropy between 0.4 and 0.9). The optical properties of the phantoms are calculated using Mie theory combined with the Percus–Yevick structure factor to account for concentration-dependent scattering. We demonstrate excellent agreement between the OCT attenuation and backscattering coefficient predicted by our model and experimentally derived values. We conclude that this model enables us to accurately model OCT-derived parameters (i.e., attenuation and backscattering coefficients) in the concentration-dependent and multiple scattering regime for spherical monodisperse samples.

Subdiffusion reflectance spectroscopy to measure tissue ultrastructure and microvasculature: model and inverse algorithm

Reflectance measurements acquired from within the subdiffusion regime (i.e., lengthscales smaller than a transport mean free path) retain much of the original information about the shape of the scattering phase function. Given this sensitivity, many models of subdiffusion regime light propagation have focused on parametrizing the optical signal through various optical and empirical parameters. We argue, however, that a more useful and universal way to characterize such measurements is to focus instead on the fundamental physical properties, which give rise to the optical signal. This work presents the methodologies that used to model and extract tissue ultrastructural and microvascular properties from spatially resolved subdiffusion reflectance spectroscopy measurements. We demonstrate this approach using ex-vivo rat tissue samples measured by enhanced backscattering spectroscopy.

Monte Carlo model of the depolarization of backscattered linearly polarized light in the sub-diffusion regime

We present a predictive model of the depolarization ratio of backscattered linearly polarized light from spatially continuous refractive index media that is applicable to the sub-diffusion regime of light scattering. Using Monte Carlo simulations, we derived a simple relationship between the depolarization ratio and both the sample optical properties and illumination-collection geometry. Our model was validated on tissue simulating phantoms and found to be in good agreement. We further show the utility of this model by demonstrating its use for measuring the depolarization length from biological tissue in vivo. We expect our results to aid in the interpretation of the depolarization ratio from sub-diffusive reflectance measurements.

Spatially resolved optical and ultrastructural properties of colorectal and pancreatic field carcinogenesis observed by inverse spectroscopic optical coherence tomography

Field carcinogenesis is the initial stage of cancer progression. Understanding field carcinogenesis is valuable for both cancer biology and clinical medicine. Here, we used inverse spectroscopic optical coherence tomography to study colorectal cancer (CRC) and pancreatic cancer (PC) field carcinogenesis. Depth-resolved optical and ultrastructural properties of the mucosa were quantified from histologically normal rectal biopsies from patients with and without colon adenomas (n=85) as well as from histologically normal peri-ampullary duodenal biopsies from patients with and without PC (n=22). Changes in the epithelium and stroma in CRC field carcinogenesis were separately quantified. In both compartments, optical and ultra-structural alterations were consistent. Optical alterations included lower backscattering (μb) and reduced scattering (μs') coefficients and higher anisotropy factor g. Ultrastructurally pronounced alterations were observed at length scales up to ∼450  nm, with the shape of the mass density correlation function having a higher shape factor D, thus implying a shift to larger length scales. Similar alterations were found in the PC field carcinogenesis despite the difference in genetic pathways and etiologies. We further verified that the chromatin clumping in epithelial cells and collagen cross-linking caused D to increase in vitro and could be among the mechanisms responsible for the observed changes in epithelium and stroma, respectively.

Numerical investigation of two-dimensional light scattering patterns of cervical cell nuclei to map dysplastic changes at different epithelial depths

We use an extensive set of quantitative histopathology data to construct realistic three-dimensional models of normal and dysplastic cervical cell nuclei at different epithelial depths. We then employ the finite-difference time-domain method to numerically simulate the light scattering response of these representative models as a function of the polar and azimuthal scattering angles. The results indicate that intensity and shape metrics computed from two-dimensional scattering patterns can be used to distinguish between different diagnostic categories. Our numerical study also suggests that different epithelial layers and angular ranges need to be considered separately to fully exploit the diagnostic potential of two-dimensional light scattering measurements.

Rare-earth-doped biological composites as in vivo shortwave infrared reporters

The extension of in vivo optical imaging for disease screening and image-guided surgical interventions requires brightly-emitting, tissue-specific materials that optically transmit through living tissue and can be imaged with portable systems that display data in real-time. Recent work suggests that a new window across the short wavelength infrared region can improve in vivo imaging sensitivity over near infrared light. Here we report on the first evidence of multispectral, real-time short wavelength infrared imaging offering anatomical resolution using brightly-emitting rare-earth nanomaterials and demonstrate their applicability toward disease-targeted imaging. Inorganic-protein nanocomposites of rare-earth nanomaterials with human serum albumin facilitated systemic biodistribution of the rare-earth nanomaterials resulting in the increased accumulation and retention in tumor tissue that was visualized by the localized enhancement of infrared signal intensity. Our findings lay the groundwork for a new generation of versatile, biomedical nanomaterials that can advance disease monitoring based on a pioneering infrared imaging technique.

Ultrastructural alterations in field carcinogenesis measured by enhanced backscattering spectroscopy

Optical characterization of biological tissue in field carcinogenesis offers a method with which to study the mechanisms behind early cancer development and the potential to perform clinical diagnosis. Previously, low-coherence enhanced backscattering spectroscopy (LEBS) has demonstrated the ability to discriminate between normal and diseased organs based on measurements of histologically normal-appearing tissue in the field of colorectal (CRC) and pancreatic (PC) cancers. Here, we implement the more comprehensive enhanced backscattering (EBS) spectroscopy to better understand the structural and optical changes which lead to the previous findings. EBS provides high-resolution measurement of the spatial reflectance profile P(rs) between 30 microns and 2.7 mm, where information about nanoscale mass density fluctuations in the mucosa can be quantified. A demonstration of the length-scales at which P(rs) is optimally altered in CRC and PC field carcinogenesis is given and subsequently these changes are related to the tissue's structural composition. Three main conclusions are made. First, the most significant changes in P(rs) occur at short length-scales corresponding to the superficial mucosal layer. Second, these changes are predominantly attributable to a reduction in the presence of subdiffractional structures. Third, similar trends are seen for both cancer types, suggesting a common progression of structural alterations in each.

Utilizing confocal microscopy to measure refractive index of articular cartilage

This study proposes a method for measuring the refractive index of articular cartilage within a thin and small specimen slice. The cartilage specimen, with a thickness of about 50 μm, was put next to a thin film of immersion oil of similar thickness. Both the articular cartilage and immersion oil were scanned along the depth direction using a confocal microscope. The refractive index mismatch between the cartilage and the immersion oil induced a slight axial deformation in the confocal images of the cartilage specimen that was accurately measured by a subpixel edge-detection-based technique. A theoretical model was built to quantify the focal shift of confocal microscopy caused by the refractive index mismatch. With the quantitative deformations of cartilage images and the quantified function of focal shift, the refractive index of articular cartilage was accurately interpolated. At 561 nm, 0.1 MPa and 20 °C, the overall refractive index of the six cartilage plugs was 1.3975 ± 0.0156. The overall coefficient of variation of all cartilage specimens was 0.68%, which indicated the high repeatability of our method. The verification experiments using distilled water showed a minimal relative error of 0.02%.

Can OCT be sensitive to nanoscale structural alterations in biological tissue?

Exploration of nanoscale tissue structures is crucial in understanding biological processes. Although novel optical microscopy methods have been developed to probe cellular features beyond the diffraction limit, nanometer-scale quantification remains still inaccessible for in situ tissue. Here we demonstrate that, without actually resolving specific geometrical feature, OCT can be sensitive to tissue structural properties at the nanometer length scale. The statistical mass-density distribution in tissue is quantified by its autocorrelation function modeled by the Whittle-Mateŕn functional family. By measuring the wavelength-dependent backscattering coefficient μb(λ) and the scattering coefficient μs, we introduce a technique called inverse spectroscopic OCT (ISOCT) to quantify the mass-density correlation function. We find that the length scale of sensitivity of ISOCT ranges from ~30 to ~450 nm. Although these sub-diffractional length scales are below the spatial resolution of OCT and therefore not resolvable, they are nonetheless detectable. The sub-diffractional sensitivity is validated by 1) numerical simulations; 2) tissue phantom studies; and 3) ex vivo colon tissue measurements cross-validated by scanning electron microscopy (SEM). Finally, the 3D imaging capability of ISOCT is demonstrated with ex vivo rat buccal and human colon samples.

Nanoplatform-based optical contrast enhancement in epithelial tissues: quantitative analysis via Monte Carlo simulations and implications on precancer diagnostics

This paper presents a comprehensive computational analysis of the spectral optical response of epithelial tissues labeled with gold nanoparticles. Monte Carlo modeling is employed to simulate nanoparticle-induced changes in reflectance signals and to assess whether labeling can generate sufficient exogenous contrast that can better pinpoint precancer progression. Simulation results suggest that the observed contrast profile is highly dependent on a series of factors including the labeling scheme, optical sensor geometry, and wavelength. It is evident, however, that selection of an optimal labeling and sensing strategy can lead to a significant enhancement of the inherent positive or negative contrast and can improve the diagnostic potential of optical measurements.

Probing multifractality in tissue refractive index: prospects for precancer detection

Multiresolution analysis on the spatial refractive index inhomogeneities in the epithelium and connective tissue regions of a human cervix reveals a clear signature of multifractality. Importantly, the derived multifractal parameters, namely, the generalized Hurst exponent and the width of the singularity spectrum, derived via multifractal detrended fluctuation analysis, shows interesting differences between tissues having different grades of precancers. The refractive-index fluctuations are found to be more anticorrelated, and the strength of multifractality is observed to be considerably stronger in the higher grades of precancers. These observations on the multifractal nature of tissue refractive-index variations may prove to be valuable for developing light-scattering approaches for noninvasive diagnosis of precancer and early-stage cancer.

Improved Fourier-based characterization of intracellular fractal features

A novel Fourier-based image analysis method for measuring fractal features is presented which can significantly reduce artifacts due to non-fractal edge effects. The technique is broadly applicable to the quantitative characterization of internal morphology (texture) of image features with well-defined borders. In this study, we explore the capacity of this method for quantitative assessment of intracellular fractal morphology of mitochondrial networks in images of normal and diseased (precancerous) epithelial tissues. Using a combination of simulated fractal images and endogenous two-photon excited fluorescence (TPEF) microscopy, our method is shown to more accurately characterize the exponent of the high-frequency power spectral density (PSD) of these images in the presence of artifacts that arise due to cellular and nuclear borders.

Applying a new computational method for biological tissue optics based on the time-dependent two-dimensional radiative transfer equation

Optical tomography is a medical imaging technique based on light propagation in the near infrared (NIR) part of the spectrum. We present a new way of predicting the short-pulsed NIR light propagation using a time-dependent two-dimensional-global radiative transfer equation in an absorbing and strongly anisotropically scattering medium. A cell-vertex finite-volume method is proposed for the discretization of the spatial domain. The closure relation based on the exponential scheme and linear interpolations was applied for the first time in the context of time-dependent radiative heat transfer problems. Details are given about the application of the original method on unstructured triangular meshes. The angular space (4πSr) is uniformly subdivided into discrete directions and a finite-differences discretization of the time domain is used. Numerical simulations for media with physical properties analogous to healthy and metastatic human liver subjected to a collimated short-pulsed NIR light are presented and discussed. As expected, discrepancies between the two kinds of tissues were found. In particular, the level of light flux was found to be weaker (inside the medium and at boundaries) in the healthy medium than in the metastatic one.

Scattering-phase theorem: anomalous diffraction by forward-peaked scattering media

The scattering-phase theorem states that the values of scattering and reduced scattering coefficients of the bulk random media are proportional to the variance of the phase and the variance of the phase gradient, respectively, of the phase map of light passing through one thin slice of the medium. We report a new derivation of the scattering phase theorem and provide the correct form of the relation between the variance of phase gradient and the reduced scattering coefficient. We show the scattering-phase theorem is the consequence of anomalous diffraction by a thin slice of forward-peaked scattering media. A new set of scattering-phase relations with relaxed requirement on the thickness of the slice are provided. The condition for the scattering-phase theorem to be valid is discussed and illustrated with simulated data. The scattering-phase theorem is then applied to determine the scattering coefficient μs, the reduced scattering coefficient μ's, and the anisotropy factor g for polystyrene sphere and Intralipid-20% suspensions with excellent accuracy from quantitative phase imaging of respective thin slices. The spatially-resolved μs, μ's and g maps obtained via such a scattering-phase relationship may find general applications in the characterization of the optical property of homogeneous and heterogeneous random media.

Differing self-similarity in light scattering spectra: a potential tool for pre-cancer detection

The fluctuations in the elastic light scattering spectra of normal and dysplastic human cervical tissues analyzed through wavelet transform based techniques reveal clear signatures of self-similar behavior in the spectral fluctuations. The values of the scaling exponent observed for these tissues indicate the differences in the self-similarity for dysplastic tissues and their normal counterparts. The strong dependence of the elastic light scattering on the size distribution of the scatterers manifests in the angular variation of the scaling exponent. Interestingly, the spectral fluctuations in both these tissues showed multi-fractality (non-stationarity in fluctuations), the degree of multi-fractality being marginally higher in the case of dysplastic tissues. These findings using the multi-resolution analysis capability of the discrete wavelet transform can contribute to the recent surge in the exploration for non-invasive optical tools for pre-cancer detection.

Automated biochemical, morphological, and organizational assessment of precancerous changes from endogenous two-photon fluorescence images

Background

Multi-photon fluorescence microscopy techniques allow for non-invasive interrogation of live samples in their native environment. These methods are particularly appealing for identifying pre-cancers because they are sensitive to the early changes that occur on the microscopic scale and can provide additional information not available using conventional screening techniques.

Methodology/Principal Findings

In this study, we developed novel automated approaches, which can be employed for the real-time analysis of two-photon fluorescence images, to non-invasively discriminate between normal and pre-cancerous/HPV-immortalized engineered tissues by concurrently assessing metabolic activity, morphology, organization, and keratin localization. Specifically, we found that the metabolic activity was significantly enhanced and more uniform throughout the depths of the HPV-immortalized epithelia, based on our extraction of the NADH and FAD fluorescence contributions. Furthermore, we were able to separate the keratin contribution from metabolic enzymes to improve the redox estimates and to use the keratin localization as a means to discriminate between tissue types. To assess morphology and organization, Fourier-based, power spectral density (PSD) approaches were employed. The nuclear size distribution throughout the epithelial depths was quantified by evaluating the variance of the corresponding spatial frequencies, which was found to be greater in the normal tissue compared to the HPV-immortalized tissues. The PSD was also used to calculate the Hurst parameter to identify the level of organization in the tissues, assuming a fractal model for the fluorescence intensity fluctuations within a field. We found the range of organization was greater in the normal tissue and closely related to the level of differentiation.

Conclusions/Significance

A wealth of complementary morphological, biochemical and organizational tissue parameters can be extracted from high resolution images that are acquired based entirely on endogenous sources of contrast. They are promising diagnostic parameters for the non-invasive identification of early cancerous changes and could improve significantly diagnosis and treatment for numerous patients.

Determination of spatial correlation functions of refractive index of living tissue

We present what to our knowledge the first method of determination of spatial correlation functions of refractive index fluctuations of living tissues by Fourier domain optical coherence tomography (FDOCT). Based on the second-order statistical description of the random characteristic of living tissue, a formula which clearly relates the spectral electrical power from the detector to the Fourier spectrum of the refractive index correlation function is given. The method is characterized by its capability of noninvasive measurements in vivo. It has the potential of allowing quantitative discrimination between different tissue types or the same tissue at different pathological states by determining their Fourier components of spatial correlation functions of refractive index.

Stem cell differentiation indicated by noninvasive photonic characterization and fractal analysis of subcellular architecture

We hypothesised that global structural changes in stem cells would manifest with differentiation, and that these changes would be observable with light scattering microscopy. Analysed with a fractal dimension formalism, we observed significant structural changes in differentiating human mesenchymal stem cells within one day after induction, earlier than could be detected by gene expression profiling. Moreover, light scattering microscopy is entirely non-perturbative, so the same sample could be monitored throughout the differentiation process. We explored one possible mechanism, chromatin remodelling, to account for the changes we observed. Correlating with the staining of HP1α, a heterochromatin protein, we applied novel microscopy methods and fractal analysis to monitor the plastic dynamics of chromatin within stem cell nuclei. We showed that the level of chromatin condensation changed during differentiation, and provide one possible explanation for the changes seen with the light scattering method. These results lend physical insight into stem cell differentiation while providing physics-based methods for non-invasive detection of the differentiation process.

Quantitative Carré differential interference contrast microscopy to assess phase and amplitude

We present a method of using an unmodified differential interference contrast microscope to acquire quantitative information on scatter and absorption of thin tissue samples. A simple calibration process is discussed that uses a standard optical wedge. Subsequently, we present a phase-stepping procedure for acquiring phase gradient information exclusive of absorption effects. The procedure results in two-dimensional maps of the local angular (polar and azimuthal) ray deviation. We demonstrate the calibration process, discuss details of the phase-stepping algorithm, and present representative results for a porcine skin sample.

Measurement of optical scattering properties with low-coherence enhanced backscattering spectroscopy

Low-coherence enhanced backscattering (LEBS) is a depth selective technique that allows noninvasive characterization of turbid media such as biological tissue. LEBS provides a spectral measurement of the tissue reflectance distribution as a function of distance between incident and reflected ray pairs through the use of partial spatial coherence broadband illumination. We present LEBS as a new depth-selective technique to measure optical properties of tissue in situ. Because LEBS enables measurements of reflectance due to initial scattering events, LEBS is sensitive to the shape of the phase function in addition to the reduced scattering coefficient (μ(s) (*)). We introduce a simulation of LEBS that implements a two parameter phase function based on the Whittle-Matérn refractive index correlation function model. We show that the LEBS enhancement factor (E) primarily depends on μ(s) (*), the normalized spectral dependence of E (S(n)) depends on one of the two parameters of the phase function that also defines the functional type of the refractive index correlation function (m), and the LEBS peak width depends on both the anisotropy factor (g) and m. Three inverse models for calculating these optical properties are described and the calculations are validated with an experimental measurement from a tissue phantom.

Quantification of nanoscale density fluctuations by electron microscopy: probing cellular alterations in early carcinogenesis

Most cancers are curable if they are diagnosed and treated at an early stage. Recent studies suggest that nanoarchitectural changes occur within cells during early carcinogenesis and that such changes precede microscopically evident tissue alterations. It follows that the ability to comprehensively interrogate cell nanoarchitecture (e.g., macromolecular complexes, DNA, RNA, proteins and lipid membranes) could be critical to the diagnosis of early carcinogenesis. We present a study of the nanoscale mass-density fluctuations of biological tissues by quantifying their degree of disorder at the nanoscale. Transmission electron microscopy images of human tissues are used to construct corresponding effective disordered optical lattices. The properties of nanoscale disorder are then studied by statistical analysis of the inverse participation ratio (IPR) of the spatially localized eigenfunctions of these optical lattices at the nanoscale. Our results show an increase in the disorder of human colonic epithelial cells in subjects harboring early stages of colon neoplasia. Furthermore, our findings strongly suggest that increased nanoscale disorder correlates with the degree of tumorigenicity. Therefore, the IPR technique provides a practicable tool for the detection of nanoarchitectural alterations in the earliest stages of carcinogenesis. Potential applications of the technique for early cancer screening and detection are also discussed.

Noninvasive identification of subcellular organization and nuclear morphology features associated with leukemic cells using light-scattering spectroscopy

Leukemia is the most common and deadly cancer among children and one of the most prevalent cancers among adults. Improvements in its diagnosis and monitoring of leukemic patients could have a significant impact in their long-term treatment. We demonstrate that light-scattering spectroscopy (LSS)-based approaches could serve as a tool to achieve this goal. Specifically, we characterize the light scattering properties of leukemic (NALM-6) cells and compare them to those of normal lymphocytes and granulocytes in the 440-710 nm range, over ±4 deg about the exact backscattering direction. We find that the LSS spectra are well described by an inverse power-law wavelength dependence, with a power exponent insensitive to the scattering angle but significantly higher for leukemic cells than for normal leukocytes. This is consistent with differences in the subcellular morphology of these cells, detected in differential interference contrast images. Furthermore, the residual light-scattering signal, extracted after subtracting the inverse power-law fit from the data, can be analyzed assuming a Gaussian distribution of spherical scatterers using Mie theory. This analysis yields scatterer sizes that are consistent with the diameters of cell nuclei and allows the detection of the larger nuclei of NALM-6 cells compared to those of lymphocytes and granulocytes.

Quantification of nanoscale density fluctuations using electron microscopy: Light-localization properties of biological cells

We report a study of the nanoscale mass-density fluctuations of heterogeneous optical dielectric media, including nanomaterials and biological cells, by quantifying their nanoscale light-localization properties. Transmission electron microscope images of the media are used to construct corresponding effective disordered optical lattices. Light-localization properties are studied by the statistical analysis of the inverse participation ratio (IPR) of the localized eigenfunctions of these optical lattices at the nanoscale. We validated IPR analysis using nanomaterials as models of disordered systems fabricated from dielectric nanoparticles. As an example, we then applied such analysis to distinguish between cells with different degrees of aggressive malignancy.

Quantitatively characterizing fluctuations of dielectric susceptibility of tissue with Fourier domain optical coherence tomography

A new model of Fourier domain optical coherence tomography (FDOCT) is proposed, valid within the first Born approximation, which takes the fluctuations of the dielectric susceptibility of tissue into account. It is shown that the spectral electrical power at the detector in the FDOCT system is proportional to the Fourier component of the spatial correlation function of the dielectric susceptibility of the tissue, proportional to the squares of the spectrum of the incident light field and the amplitude reflectance of the reference mirror. One possible application of the obtained result is to use the measured spectral data of the spatial correlation function of the dielectric susceptibility to quantitatively characterize properties of tissue.

Intrinsic optical biomarkers associated with the invasive potential of tumor cells in engineered tissue models

This report assesses the ability of intrinsic two-photon excited fluorescence (TPEF) and second harmonic generation (SHG) imaging to characterize features associated with the motility and invasive potential of epithelial tumor cells engineered in tissues. Distinct patterns of organization are found both within the cells and the matrix that depend on the adhesive properties of the cells as well as factors attributed to adjacent fibroblasts. TPEF images are analyzed using automated algorithms that reveal unique features in subcellular organization and cell spacing that correlate with the invasive potential. We expect that such features have significant diagnostic potential for basic in vitro studies that aim to improve our understanding of cancer development or response to treatments, and, ultimately can be applied in prognostic evaluation.

Physical interpretation of the phase function related parameter γ studied with a fractal distribution of spherical scatterers

The optical properties within limited volumes of diffusive media can be probed by carrying spatially-resolved measurements of diffused light at short source-detector separation (typically one scattering mean free path). At such distance, analytical models only relying on the absorption and reduced scattering coefficients fail at correctly predicting reflectance and it was demonstrated that adding a third optical coefficient γ improves the description of light propagation conditions near the source. In an attempt to relate the γ coefficient to physical properties of turbid media, this paper uses a fractal distribution law for modeling scatterers' sizes distributions and investigates numerically and experimentally how γ is related to the fractal power α. The results indicate that within the range of γ typically encountered in biological samples, this coefficient is approximately linearly correlated with α.

Light scattering and morphology of the lymphocyte as applied to flow cytometry for distinguishing healthy and infected individuals

A simple optical model of single lymphocytes with smooth and nonsmooth surfaces has been developed for healthy and infected individuals. The model can be used for rapid (in the real-time scale) solution of the inverse light-scattering problem on the basis of optical data measured by label-free flow cytometry. Light scattering patterns have been calculated for the model developed. It has been shown that the smooth and nonsmooth cells can be resolved using the intensities of the sideward- and backward-scattered light. We have found by calculations and validated by the flow cytometer experiments that intensity distributions for the cells of lymphocyte populations can be used as a preliminary signatures of some virus infections. Potential biomedical applications of the findings for label-free flow cytometry detection of individuals infected with viruses of hepatitis B or C and some others viruses are presented.

Depth-resolved imaging and detection of micro-retroreflectors within biological tissue using Optical Coherence Tomography

A new approach to in vivo biosensor design is introduced, based on the use of an implantable micron-sized retroreflector-based platform and non-invasive imaging of its surface reflectivity by Optical Coherence Tomography (OCT). The possibility of using OCT for the depth-resolved imaging and detection of micro-retroreflectors in highly turbid media, including tissue, is demonstrated. The maximum imaging depth for the detection of the micro-retroreflector-based platform within the surrounding media was found to be 0.91 mm for porcine tissue and 1.65 mm for whole milk. With further development, it may be possible to utilize OCT and micro-retroreflectors as a tool for continuous monitoring of analytes in the subcutaneous tissue.

Square law between spatial frequency of spatial correlation function of scattering potential of tissue and spectrum of scattered light

The significance of beam condition for scattered light from random tissue is analyzed for a practical optical imaging system with a finite numerical aperture. It is shown that in the transmitted illumination case, the information carrying part of the spectrum of the scattered light is proportional to the square of the spatial frequency of the spatial correlation function of the scattering potential of the medium. The result may be helpful in interpreting images obtained with microscopes in biological studies.

Spectral changes of the light produced by scattering from tissue

The effect of the two-point spatial correlation function of human tissue on the spectrum of scattered light is considered within the accuracy of the first Born approximation. An expression for the maximum of the spectrum of the scattered light at various scattering angles is derived. It is shown that for most biological tissues the spectrum of the backscattered light is centered at a higher frequency with respect to the incident spectrum.

Investigating the spectral characteristics of backscattering from heterogeneous spherical nuclei using broadband finite-difference time-domain simulations

Reflectance spectra measured from epithelial tissue have been used to extract size distribution and refractive index of cell nuclei for noninvasive detection of precancerous changes. Despite many in vitro and in vivo experimental results, the underlying mechanism of sizing nuclei based on modeling nuclei as homogeneous spheres and fitting the measured data with Mie theory has not been fully explored. We describe the implementation of a three-dimensional finite-difference time-domain (FDTD) simulation tool using a Gaussian pulse as the light source to investigate the wavelength-dependent characteristics of backscattered light from a nuclear model consisting of a nucleolus and clumps of chromatin embedded in homogeneous nucleoplasm. The results show that small-sized heterogeneities within the nuclei generate about five times higher backscattering than homogeneous spheres. More interestingly, backscattering spectra from heterogeneous spherical nuclei show periodic oscillations similar to those from homogeneous spheres, leading to high accuracy of estimating the nuclear diameter by comparison with Mie theory. In addition to the application in light scattering spectroscopy, the reported FDTD method could be adapted to study the relations between measured spectral data and nuclear structures in other optical imaging and spectroscopic techniques for in vivo diagnosis.

Detecting precancerous lesions in the hamster cheek pouch using spectroscopic white-light optical coherence tomography to assess nuclear morphology via spectral oscillations

We have developed a novel dual-window approach for spectroscopic optical coherence tomography (OCT) measurements and applied it to probe nuclear morphology in tissue samples drawn from the hamster cheek pouch carcinogenesis model. The dual-window approach enables high spectral and depth resolution simultaneously, allowing detection of spectral oscillations, which we isolate to determine the structure of cell nuclei in the basal layer of the epithelium. The measurements were executed with our parallel frequency domain OCT system, which uses light from a thermal source, providing high bandwidth and access to the visible portion of the spectrum. The structural measurements show a highly statistically significant difference between untreated (normal) and treated (hyperplastic/dysplastic) tissues, indicating the potential utility of this approach as a diagnostic method.

Amplitude and phase of tightly focused laser beams in turbid media

A framework is developed that combines electric field Monte Carlo simulations of random scattering with an angular-spectrum representation of diffraction theory to determine the amplitude and phase characteristics of tightly focused laser beams in turbid media. For planar sample geometries, the scattering-induced coherence loss of wave vectors at larger angles is shown to be the primary mechanism for broadening the focal volume. This approach for evaluating the formation of the focal volume in turbid media is of direct relevance to the imaging properties of nonlinear coherent microscopy, which rely on both the amplitude and phase of the focused fields.

Nonscalar elastic light scattering from continuous random media in the Born approximation

A three-parameter model based on the Whittle-Matérn correlation family is used to describe continuous random refractive-index fluctuations. The differential scattering cross section is derived from the index correlation function using nonscalar scattering formulas within the Born approximation. Parameters such as scattering coefficient, anisotropy factor, and spectral dependence are derived from the differential scattering cross section for this general class of functions.

Light scattering spectroscopy of human skin in vivo

We present an in vivo study of the reduced scattering coefficient of normal skin and of common melanocytic nevi in Caucasian subjects. The spectral shape of the reduced scattering coefficient is described well by a power-law dependence on the wavelength, in accordance with previous studies of light scattering by biological tissues. We investigate statistical variations in the scattering spectrum slope and also identify an inherent correlation between scattering intensity and scattering spectral slope, observed mainly in normal skin. In addition, we do not find any significant differences between the scattering properties of normal skin and common melanocytic nevi. Finally, we also provide a short review of previously published studies reporting on the light scattering properties of human skin both in vivo and in vitro.

Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis

We present a light scattering study using angle-resolved low coherence interferometry (a/LCI) to assess nuclear morphology and subcellular structure within MCF-7 cells at several time points after treatment with chemotherapeutic agents. Although the nuclear diameter and eccentricity are not observed to change, the light scattering signal reveals a change in the organization of subcellular structures that we interpret using fractal dimension (FD). The FD of subcellular structures in cells treated with paclitaxel and doxorubicin is observed to increase significantly compared with that of control cells as early as 1.5 and 3 hours after application, respectively. The FD is then found to decrease slightly at 6 hours postapplication for both agents only to increase again from 12 to 24 hours posttreatment when the observations ceased. The changes in structure appear over two time scales, suggesting that multiple mechanisms are evident in these early apoptotic stages. Indeed, quantitative image analysis of fluorescence micrographs of cells undergoing apoptosis verifies that the FD of 4',6-diamidino-2-phenylindole-stained nuclear structures does not change significantly in cells until 12 hours after treatment, whereas that of MitoTracker stained mitochondria is seen to modulate as early as 3 hours after treatment. In contrast, cells receiving an increased dose of paclitaxel that induced G(2)-M arrest, but not apoptosis, only exhibited the early change in subcellular structure but did not show the later change associated with changes in nuclear substructure. These results suggest that a/LCI may have utility in detecting early apoptotic events for both clinical and basic science applications.

Binary phase masking for optical interrogation of matters in turbid media

For optically interrogating substances overlaid by turbid media, a method of wavefront manipulation by means of binary phase masking is proposed. Through altering the degree of mode matching between the fields reaching the collection optics and the field distribution of the propagation mode of single-mode waveguides, the proposed method can be used to suppress the collection of short-range light originated near the collection optics while permitting unimpeded collection of light originated from sites substantially behind turbid media. General description of the principles is accompanied by a numerical modeling. A group of binary phase masks, mutually orthogonal, are introduced for practical applications.

Comparative evaluation of two simple diffuse reflectance models for biological tissue applications

We present a comparative evaluation of two simple diffuse reflectance models for biological tissue applications. One model is based on a widely accepted and used in biomedical optics implementation of diffusion theory, and the other one is based on a semiempirical approach derived from basic physical principles. We test the models on tissue phantoms and on human skin, utilizing a standard six-around-one optical fiber probe for light delivery and collection. We show that both models are suitable for use with an optical fiber probe and illustrate the potential, applicability, and validity range of the models.