SignificanceAzimuth-resolved optical scattering signals obtained from cell nuclei are sensitive to changes in their internal refractive index profile. These two-dimensional signals can therefore offer significant insights into chromatin organization.AimWe aim to determine whether two-dimensional scattering signals can be used in an inverse scheme to extract the spatial correlation length ℓc and extent δn of subnuclear refractive index fluctuations to provide quantitative information on chromatin distribution.ApproachSince an analytical formulation that links azimuth-resolved signals to ℓc and δn is not feasible, we set out to assess the potential of machine learning to predict these parameters via a data-driven approach. We carry out a convolutional neural network (CNN)-based regression analysis on 198 numerically computed signals for nuclear models constructed with ℓc varying in steps of 0.1 μm between 0.4 and 1.0 μm, and δn varying in steps of 0.005 between 0.005 and 0.035. We quantify the performance of our analysis using a five-fold cross-validation technique.ResultsThe results show agreement between the true and predicted values for both ℓc and δn, with mean absolute percent errors of 8.5% and 13.5%, respectively. These errors are smaller than the minimum percent increment between successive values for respective parameters characterizing the constructed models and thus signify an extremely good prediction performance over the range of interest.ConclusionsOur results reveal that CNN-based regression can be a powerful approach for exploiting the information content of two-dimensional optical scattering signals and hence monitoring chromatin organization in a quantitative manner.
Significance: Optical scattering signals obtained from tissue constituents contain a wealth of structural information. Conventional intensity features, however, are mostly dictated by the overall morphology and mean refractive index of these constituents, making it very difficult to exclusively sense internal refractive index fluctuations.
Aim: We perform a systematic analysis to elucidate how changes in internal refractive index profile of cell nuclei can best be detected via optical scattering.
Approach: We construct stochastically inhomogeneous nuclear models and numerically simulate their azimuth-resolved scattering patterns. We then process these two-dimensional patterns with the goal of identifying features that directly point to subnuclear structure.
Results: Azimuth-dependent intensity variations over the side scattering range provide significant insights into subnuclear refractive index profile. A particular feature we refer to as contrast ratio is observed to be highly sensitive to the length scale and extent of refractive index fluctuations; further, this feature is not susceptible to changes in the overall size and mean refractive index of nuclei, thereby allowing for selective tracking of subnuclear structure that can be linked to chromatin distribution.
Conclusions: Our analysis will potentially pave the way for scattering-based assessment of chromatin reorganization that is considered to be a key hallmark of precancer progression.
We construct stochastically inhomogeneous epithelial cell models via simulation of Gaussian random fields; the extent and correlation length of subnuclear refractive index fluctuations are based on values quantified from high-resolution images of cervical tissue. We then employ the finite-difference time-domain method to simulate azimuth-resolved light scattering patterns of the constructed models. We process these two-dimensional patterns and calculate a series of Haralick features with the ultimate goal of identifying signatures that directly point to changes in subnuclear refractive index profile. Our results show that azimuthal contrast calculated over specific angular ranges is highly sensitive to the extent and correlation length of refractive index fluctuations. This metric is insensitive to changes in the overall size and mean refractive index of the constructed models, thereby allowing for selective tracking of changes in subnuclear refractive index variations.
Optical scattering provides an intrinsic contrast mechanism for the diagnosis of early precancerous changes in tissues. There have been a multitude of numerical studies targeted at delineating the relationship between cancer-related alterations in morphology and internal structure of cells and the resulting changes in their optical scattering properties. Despite these efforts, we still need to further our understanding of inherent scattering signatures that can be linked to precancer progression. As such, computational studies aimed at relating electromagnetic wave interactions to cellular and subcellular structural alterations are likely to provide a quantitative framework for a better assessment of the diagnostic content of optical signals. In this study, we aim to determine the influence of structural length-scale variations on two-dimensional light scattering properties of cells. We numerically construct cell models with different lower bounds on the size of refractive index heterogeneities and we employ the finite-difference time-domain method to compute their azimuth-resolved light scattering patterns. The results indicate that changes in length-scale variations can significantly alter the two-dimensional scattering patterns of cell models. More specifically, the degree of azimuthal asymmetry characterizing these patterns is observed to be highly dependent on the range of length-scale variations. Overall, the study described here is expected to offer useful insights into whether azimuth-resolved measurements can be explored for diagnostic purposes.
Dysplastic progression in epithelial tissues is linked to changes in morphology and internal structure of cell nuclei. These changes lead to alterations in nuclear light scattering profiles that can potentially be monitored for diagnostic purposes. Numerical tools allow for simulation of complex nuclear models and are particularly useful for quantifying the optical response of cell nuclei as dysplasia progresses. In this study, we first analyze a set of quantitative histopathology images from twenty cervical biopsy sections stained with Feulgen-thionin. Since Feulgen-thionin is stoichiometric for DNA, the images enable us to obtain detailed information on size, shape, and chromatin content of all the segmented nuclei. We use this extensive data set to construct realistic three-dimensional computational models of cervical cell nuclei that are representative of four diagnostic categories, namely normal or negative for dysplasia, mild dysplasia, moderate dysplasia, and severe dysplasia or carcinoma in situ (CIS). We then carry out finite-difference time-domain simulations to compute the light scattering response of the constructed models as a function of the polar scattering angle and the azimuthal scattering angle. The results show that these two-dimensional scattering patterns exhibit characteristic intensity ridges that change form with progression of dysplasia; pattern processing reveals that Haralick features can be used to distinguish moderately and severely dysplastic or CIS nuclei from normal and mildly dysplastic nuclei. Our numerical study also suggests that different angular ranges need to be considered separately to fully exploit the diagnostic potential of two-dimensional light scattering measurements.
Dysplastic progression is known to be associated with changes in morphology and internal structure of cells. A detailed
assessment of the influence of these changes on cellular scattering response is needed to develop and optimize optical
diagnostic techniques. In this study, we first analyzed a set of quantitative histopathologic images from cervical biopsies
and we obtained detailed information on morphometric and photometric features of segmented epithelial cell nuclei.
Morphometric parameters included average size and eccentricity of the best-fit ellipse. Photometric parameters included
optical density measures that can be related to dielectric properties and texture characteristics of the nuclei. These
features enabled us to construct realistic three-dimensional computational models of basal, parabasal, intermediate, and
superficial cell nuclei that were representative of four diagnostic categories, namely normal (or negative for dysplasia),
mild dysplasia, moderate dysplasia, and severe dysplasia or carcinoma in situ. We then employed the finite-difference
time-domain method, a popular numerical tool in electromagnetics, to compute the angle-resolved light scattering
properties of these representative models. Results indicated that a high degree of variability can characterize a given
diagnostic category, but scattering from moderately and severely dysplastic or cancerous nuclei was generally observed
to be stronger compared to scattering from normal and mildly dysplastic nuclei. Simulation results also pointed to
significant intensity level variations among different epithelial depths. This suggests that intensity changes associated
with dysplastic progression need to be analyzed in a depth-dependent manner.
Metal nanoparticles can be functionalized with biomolecules to selectively localize in precancerous tissues and can act as optical contrast enhancers for reflectance-based diagnosis of epithelial precancer. We carry out Monte Carlo (MC) simulations to analyze photon propagation through nanoparticle-labeled tissues and to reveal the importance of using a proper form of phase function for modeling purposes. We first employ modified phase functions generated with a weighting scheme that accounts for the relative scattering strengths of unlabeled tissue and nanoparticles. To present a comparative analysis, we repeat our MC simulations with simplified functions that only approximate the angular scattering properties of labeled tissues. The results obtained for common optical sensor geometries and biologically relevant labeling schemes indicate that the exact form of the phase function used as model input plays an important role in determining the reflectance response and approximating functions often prove inadequate in predicting the extent of contrast enhancement due to labeling. Detected reflectance intensities computed with different phase functions can differ up to ∼60% and such a significant deviation may even alter the perceived contrast profile. These results need to be taken into account when developing photon propagation models to assess the diagnostic potential of nanoparticle-enhanced optical measurements.
Metal nanoparticles can function as optical contrast enhancers for reflectance-based diagnosis of epithelial precancer.
We carry out Monte Carlo simulations to model photon propagation through normal tissues, unlabeled precancerous
tissues, and precancerous tissues labeled with gold nanospheres and we compute the spectral reflectance response of
these different tissue states. The results indicate that nanoparticle-induced changes in the spectral reflectance profile of
tissues depend not only on the properties of these particles but also on the source-detector geometry used. When the
source and detector fibers are oriented side by side and perpendicular to the tissue surface, the reflectance intensity of
precancerous tissue is lower compared to that of normal tissue over the entire wavelength range simulated and addition
of nanospheres enhances this negative contrast. When the fibers are tilted toward each other, the reflectance intensity of
precancerous tissue is higher compared to that of normal tissue and labeling with nanospheres causes a significant
enhancement of this positive contrast. The results also suggest that model-based spectral analysis of photon propagation
through nanoparticle-labeled tissues provides a useful framework to quantify the extent of achievable contrast
enhancement due to external labeling and to assess the diagnostic potential of nanoparticle-enhanced optical
measurements.
Monte Carlo (MC) modeling is widely used to study photon transport in tissues but is generally performed using
simplified phase functions that only approximate the angular scattering probability distribution of microscopic tissue
constituents such as cells. Finite-Difference Time-Domain (FDTD) modeling has recently provided a flexible approach
to compute scattering phase functions for realistic cell geometries. We present a computational framework that combines
MC and FDTD modeling and allows random sampling of scattering directions from cellular phase functions computed
using the FDTD method. Combined MC/FDTD simulation results indicate that the exact form of the phase function used
is an important factor in determining the modeled optical response of tissues. Subtle differences in angular scattering
probability distribution can lead to significant changes in detected reflectance intensity and the extent of these changes
depends on the specific range of scattering angles to which a given optical sensor design is most sensitive.
Monte Carlo (MC) modeling of photon transport in tissues is generally performed using simplified functions that only approximate the angular scattering properties of tissue constituents. However, such approximations may not be sufficient for fully characterizing tissue scatterers such as cells. Finite-difference time-domain (FDTD) modeling provides a flexible approach to compute realistic tissue phase functions that describe probability of scattering at different angles. We describe a computational framework that combines MC and FDTD modeling, and allows random sampling of scattering directions from FDTD phase functions. We carry out simulations to assess the influence of incorporating realistic FDTD phase functions on modeling spectroscopic reflectance signals obtained from normal and precancerous epithelial tissues. Simulations employ various fiber optic probe designs to analyze the sensitivity of different probe geometries to FDTD-generated phase functions. Combined MC/FDTD modeling results indicate that the form of the phase function used is an important factor in determining the reflectance profile of tissues, and detected reflectance intensity can change up to ~30% when a realistic FDTD phase function is used instead of an approximating function. The results presented need to be taken into account when developing photon propagation models or implementing inverse algorithms to extract optical properties from measurements.
Neoplastic progression in epithelial tissues is accompanied by structural and morphological changes in the stromal
collagen matrix. We used the Finite-Difference Time-Domain (FDTD) method, a popular computational technique for
full-vector solution of complex problems in electromagnetics, to establish a relationship between structural properties of
collagen fiber networks and light scattering, and to analyze how neoplastic changes alter stromal scattering properties.
To create realistic collagen network models, we acquired optical sections from the stroma of fresh normal and neoplastic
oral cavity biopsies using fluorescence confocal microscopy. These optical sections were then processed to construct
three-dimensional collagen networks of different sizes as FDTD model input. Image analysis revealed that volume
fraction of collagen fibers in the stroma decreases with neoplastic progression, and statistical texture features computed
suggest that fibers tend to be more disconnected in neoplastic stroma. The FDTD modeling results showed that
neoplastic fiber networks have smaller scattering cross-sections compared to normal networks of the same size, whereas
high-angle scattering probabilities tend to be higher for neoplastic networks. Characterization of stromal scattering is
expected to provide a basis to better interpret spectroscopic optical signals and to develop more reliable computational
models to describe photon propagation in epithelial tissues.
We present Monte Carlo modeling studies to provide a quantitative understanding of contrast observed in spatially resolved reflectance spectra of normal and highly dysplastic cervical tissue. Simulations have been carried out to analyze the sensitivity of spectral measurements to a range of changes in epithelial and stromal optical properties that are reported to occur as dysplasia develops and to predict reflectance spectra of normal and highly dysplastic tissue at six different source-detector separations. Simulation results provide important insights into specific contributions of different optical parameters to the overall spectral response. Predictions from simulations agree well with in vivo measurements from cervical tissue and successfully describe spectral differences observed in reflectance measurements from normal and precancerous tissue sites. Penetration depth statistics of photons detected at the six source-detector separations are also presented to reveal the sampling depth profile of the fiber-optic probe geometry simulated. The modeling studies presented provide a framework to meaningfully interpret optical signals obtained from epithelial tissues and to optimize design of optical sensors for in vivo reflectance measurements for precancer detection. Results from this study can facilitate development of analytical photon propagation models that enable inverse estimation of diagnostically relevant optical parameters from in vivo reflectance 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.
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