Impact of model parameters on Monte Carlo simulations of backscattering Mueller matrix images of colon tissue

Discrepancy of coordinate system selection in backscattering Mueller matrix polarimetry: exploring photon coordinate system transformation invariants

In biomedical studies, Mueller matrix polarimetry is gaining increasing attention because it can comprehensively characterize polarization-related vectorial properties of the sample, which are crucial for microstructural identification and evaluation. For backscattering Mueller matrix polarimetry, there are two photon coordinate selection conventions, which can affect the following Mueller matrix parameters calculation and information acquisition quantitatively. In this study, we systematically analyze the influence of photon coordinate system selection on the backscattering Mueller matrix polarimetry. We compare the Mueller matrix elements in the right-handed-nonunitary and non-right-handed-unitary coordinate systems, and specifically deduce the changes of Mueller matrix polar decomposition, Mueller matrix Cloude decomposition and Mueller matrix transformation parameters widely used in backscattering Mueller matrix imaging as the photon coordinate system varied. Based on the theoretical analysis and phantom experiments, we provide a group of photon coordinate system transformation invariants for backscattering Mueller matrix polarimetry. The findings presented in this study give a crucial criterion of parameters selection for backscattering Mueller matrix imaging under different photon coordinate systems.

Controlling the optical pathlength in continuous-wave reflectance spectroscopy using polarization

We investigate potential improvements of continuous-wave diffuse reflectance spectroscopy within highly scattering media by employing polarization gating. Simulations are used to show the extent at which the effective optical pathlength varies in a typical scattering medium as a function of the optical wavelength, the total level of absorption, and the selected polarization channels, including elliptical and circular polarization channels. Experiments then demonstrate that a wavelength dependent polarization gating scheme may reduce the prior knowledge required to solve the problem of chromophore quantification. This is achieved by finding combinations of polarization channels which have similar effective optical pathlengths through the medium at each wavelength.

Measuring glucose concentration in a solution based on the indices of polarimetric purity

Polarization imaging is a powerful tool, which can be applied in biomedical diagnosis and many research fields. Here, we propose a new application of the indices of polarimetric purity (IPPs) composed of P1, P2, P3, to describe the glucose concentrations (GC) changes in the scattering system. The results suggest that P1 of the IPPs is a better indicator to GC in the solution than the degree of polarization (DoP) for the forward scattering detection. Meanwhile, the fitting relation among radius of scattering particle, GCs and P1 parameter has also been calculated, in which the error of inversion is no more than 4.73%. In the backscattering detection, the fitted frequency statistical histogram of the IPPs is used to measure the GCs, and their modes can represent changing trend of GCs.

Analysis of tissue microstructure with Mueller microscopy: logarithmic decomposition and Monte Carlo modeling

Significance: Definitive diagnostics of many diseases is based on the histological analysis of thin tissue cuts with optical white light microscopy. Extra information on tissue structural properties obtained with polarized light would help the pathologist to improve the accuracy of his diagnosis. <p> Aim: We report on using Mueller matrix microscopy data, logarithmic decomposition, and polarized Monte Carlo (MC) modeling for qualitative and quantitative analysis of thin tissue cuts to extract the information on tissue microstructure that is not available with a conventional white light microscopy. <p> </p> Approach: Unstained cuts of human skin equivalents were measured with a custom-built liquid-crystal-based Mueller microscope in transmission configuration. To interpret experimental data, we performed the simulations with a polarized MC algorithm for scattering anisotropic media. Several optical models of tissue (spherical scatterers within birefringent host medium, and combination of spherical and cylindrical scatterers within either isotropic or birefringent host medium) were tested. <p> </p> Results: A set of rotation invariants for the logarithmic decomposition of a Mueller matrix was derived to rule out the impact of sample orientation. These invariants were calculated for both simulated and measured Mueller matrices of the dermal layer of skin equivalents. We demonstrated that only the simulations with a model combining both spherical and cylindrical scatterers within birefringent host medium reproduced the experimental trends in optical properties of the dermal layer (linear retardance, linear dichroism, and anisotropic linear depolarization) with layer thickness. <p> </p> Conclusions: Our studies prove that Mueller polarimetry provides relevant information not only on a size of dominant scatterers (e.g., cell nuclei versus subwavelength organelles) but also on its shape (e.g., cells versus collagen fibers). The latter is directly related to the state of extracellular collagen matrix, which is often affected by early pathology. Hence, using polarimetric data can help to increase the accuracy of diagnosis. </p>

The depolarization performances of scattering systems based on the Indices of Polarimetric Purity (IPPs)

In this paper, the Indices of Polarimetric Purity (IPPs) [1-3] have been proposed to analyze the depolarization performances of mono-dispersion and poly-dispersion scattering systems. Here, we mainly investigate the influences of the particles' density, Refractive Index (RI) of the medium, incident wavelengths, the mixing ratio of bi-dispersion scattering particles and particle-size distributions of poly-dispersion scattering system on the depolarization performances for the backscattering detection. For the mono-dispersion scattering system under same incident wavelength, if the relative RI ratios (m) increase linearly, the depolarization performances of the system will first weaken and then strengthen, and of course, the incident wavelength and density of scattering particles will also influence the depolarization performances of the scattering system. For the bi-dispersion scattering system, the proportion of small particles will be negatively correlated with the depolarization property of the dispersion system, and meanwhile, the particle-size distributions will also affect the depolarization performances greatly in the poly-dispersion scattering system. The results demonstrate that the IPPs can be used to describe the depolarization performances of dispersion systems effectively.

Optical phantoms for biomedical polarimetry: a review

Calibration, quantification, and standardization of the polarimetric instrumentation, as well as interpretation and understanding of the obtained data, require the development and use of well-calibrated phantoms and standards. We reviewed the status of tissue phantoms for a variety of applications in polarimetry; more than 500 papers are considered. We divided the phantoms into five groups according to their origin (biological/nonbiological) and fundamental polarimetric properties of retardation, depolarization, and diattenuation. We found that, while biological media are generally depolarizing, retarding, and diattenuating, only one of all the phantoms reviewed incorporated all these properties, and few considered at least combined retardation and depolarization. Samples derived from biological tissue, such as tendon and muscle, remain extremely popular to quickly ascertain a polarimetric system, but do not provide quantifiable results aside from relative direction of their principal optical axis. Microspheres suspensions are the most utilized phantoms for depolarization, and combined with theoretical models can offer true quantification of depolarization or degree of polarization. There is a real paucity of birefringent phantoms despite the retardance being one of the most interesting parameters measurable with polarization techniques. Therefore, future work should be directed at generating truly reliable and repeatable phantoms for this metric determination. Diattenuating phantoms are rare and application-specific. Given that diattenuation is considered to be low in most biological tissues, the lack of such phantoms is seen as less problematic. The heterogeneity of the phantoms reviewed points to a critical need for standardization in this field. Ultimately, all research groups involved in polarimetric studies and instruments development would benefit from sharing a limited set of standardized polarimetric phantoms, as is done earlier in the round robin investigations in ellipsometry.

Characterizing the depolarization of circularly polarized light in turbid scattering media

We investigate the effectiveness of various bulk optical parameters in characterizing the degree of circular polarization (DOCP) of light diffusely reflected from scattering media. It is demonstrated that the traditional set of bulk optical parameters (namely, the scattering and absorption coefficients and the scattering asymmetry parameter) fail to characterize the observed depolarization. However, we find that there exists an additional parameter connected to the circular polarization memory phenomenon that consistently relates to observations, even in media with widely varying refractive indices and particle size distributions. This relationship is demonstrated using both Monte Carlo simulations and a new method for designing microsphere-based phantom media, which contain carefully controlled particle size distributions and depolarization characteristics.

Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radiance

Forward and adjoint Monte Carlo (MC) models of radiance are proposed for use in model-based quantitative photoacoustic tomography. A two-dimensional (2-D) radiance MC model using a harmonic angular basis is introduced and validated against analytic solutions for the radiance in heterogeneous media. A gradient-based optimization scheme is then used to recover 2-D absorption and scattering coefficients distributions from simulated photoacoustic measurements. It is shown that the functional gradients, which are a challenge to compute efficiently using MC models, can be calculated directly from the coefficients of the harmonic angular basis used in the forward and adjoint models. This work establishes a framework for transport-based quantitative photoacoustic tomography that can fully exploit emerging highly parallel computing architectures.

Anisotropic contrast optical microscope

An optical microscope is described that reveals contrast in the Mueller matrix images of a thin, transparent, or semi-transparent specimen located within an anisotropic object plane (anisotropic filter). The specimen changes the anisotropy of the filter and thereby produces contrast within the Mueller matrix images. Here we use an anisotropic filter composed of a semi-transparent, nanostructured thin film with sub-wavelength thickness placed within the object plane. The sample is illuminated as in common optical microscopy but the light is modulated in its polarization using combinations of linear polarizers and phase plate (compensator) to control and analyze the state of polarization. Direct generalized ellipsometry data analysis approaches permit extraction of fundamental Mueller matrix object plane images dispensing with the need of Fourier expansion methods. Generalized ellipsometry model approaches are used for quantitative image analyses. These images are obtained from sets of multiple images obtained under various polarizer, analyzer, and compensator settings. Up to 16 independent Mueller matrix images can be obtained, while our current setup is limited to 11 images normalized by the unpolarized intensity. We demonstrate the anisotropic contrast optical microscope by measuring lithographically defined micro-patterned anisotropic filters, and we quantify the adsorption of an organic self-assembled monolayer film onto the anisotropic filter. Comparison with an isotropic glass slide demonstrates the image enhancement obtained by our method over microscopy without the use of an anisotropic filter. In our current instrument, we estimate the limit of detection for organic volumetric mass within the object plane of ≈49 fg within ≈7 × 7 μm² object surface area. Compared to a quartz crystal microbalance with dissipation instrumentation, where contemporary limits require a total load of ≈500 pg for detection, the instrumentation demonstrated here improves sensitivity to a total mass required for detection by 4 orders of magnitude. We detail the design and operation principles of the anisotropic contrast optical microscope, and we present further applications to the detection of nanoparticles, to novel approaches for imaging chromatography and to new contrast modalities for observations on living cells.

Polarized light interaction with tissues

This tutorial-review introduces the fundamentals of polarized light interaction with biological tissues and presents some of the recent key polarization optical methods that have made possible the quantitative studies essential for biomedical diagnostics. Tissue structures and the corresponding models showing linear and circular birefringence, dichroism, and chirality are analyzed. As the basis for a quantitative description of the interaction of polarized light with tissues, the theory of polarization transfer in a random medium is used. This theory employs the modified transfer equation for Stokes parameters to predict the polarization properties of single- and multiple-scattered optical fields. The near-order of scatterers in tissues is accounted for to provide an adequate description of tissue polarization properties. Biomedical diagnostic techniques based on polarized light detection, including polarization imaging and spectroscopy, amplitude and intensity light scattering matrix measurements, and polarization-sensitive optical coherence tomography are described. Examples of biomedical applications of these techniques for early diagnostics of cataracts, detection of precancer, and prediction of skin disease are presented. The substantial reduction of light scattering multiplicity at tissue optical clearing that leads to a lesser influence of scattering on the measured intrinsic polarization properties of the tissue and allows for more precise quantification of these properties is demonstrated.

Ex vivo characterization of normal and adenocarcinoma colon samples by Mueller matrix polarimetry

Mueller matrix polarimetry along with polar decomposition algorithm was employed for the characterization of ex vivo normal and adenocarcinoma human colon tissues by polarized light in the visible spectral range (425-725 nm). Six derived polarization metrics [total diattenuation (DT ), retardance (RT ), depolarization(ΔT ), linear diattenuation (DL), retardance (δ), and depolarization (ΔL)] were compared for normal and adenocarcinoma colon tissue samples. The results show that all six polarimetric properties for adenocarcinoma samples were significantly higher as compared to the normal samples for all wavelengths. The Wilcoxon rank sum test illustrated that total retardance is a good candidate for the discrimination of normal and adenocarcinoma colon samples. Support vector machine classification for normal and adenocarcinoma based on the four polarization properties spectra (ΔT , ΔL, RT ,and δ) yielded 100% accuracy, sensitivity, and specificity, while both DTa nd DL showed 66.6%, 33.3%, and 83.3% accuracy, sensitivity, and specificity, respectively. The combination of polarization analysis and given classification methods provides a framework to distinguish the normal and cancerous tissues.

Circular polarization memory in polydisperse scattering media

We investigate the survival of circularly polarized light in random scattering media. The surprising persistence of this form of polarization has a known dependence on the size and refractive index of scattering particles, however a general description regarding polydisperse media is lacking. Through analysis of Mie theory, we present a means of calculating the magnitude of circular polarization memory in complex media, with total generality in the distribution of particle sizes and refractive indices. Quantification of this memory effect enables an alternate pathway toward recovering particle size distribution, based on measurements of diffusing circularly polarized light.

Characterizing the microstructures of biological tissues using Mueller matrix and transformed polarization parameters

Mueller matrices can be used as a powerful tool to probe qualitatively the microstructures of biological tissues. Certain transformation processes can provide new sets of parameters which are functions of the Mueller matrix elements but represent more explicitly the characteristic features of the sample. In this paper, we take the backscattering Mueller matrices of a group of tissues with distinctive structural properties. Using both experiments and Monte Carlo simulations, we demonstrate qualitatively the characteristic features of Mueller matrices corresponding to different structural and optical properties. We also calculate two sets of transformed polarization parameters using the Mueller matrix transformation (MMT) and Mueller matrix polar decomposition (MMPD) techniques. We demonstrate that the new parameters can separate the effects due to sample orientation and present quantitatively certain characteristic features of these tissues. Finally, we apply the transformed polarization parameters to the unstained human cervix cancerous tissues. Preliminary results show that the transformed polarization parameters can provide characteristic information to distinguish the cancerous and healthy tissues.

Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues

Polarization measurements allow one to enhance the imaging contrast of superficial tissues and obtain new polarization sensitive parameters for better descriptions of the micro- and macro- structural and optical properties of complex tissues. Since the majority of cancers originate in the epithelial layer, probing the morphological and pathological changes in the superficial tissues using an expended parameter set with improved contrast will assist in early clinical detection of cancers. We carry out Mueller matrix imaging on different cancerous tissues to look for cancer specific features. Using proper scattering models and Monte Carlo simulations, we examine the relationship between the microstructures of the samples, which are represented by the parameters of the scattering model and the characteristic features of the Mueller matrix. This study gives new clues on the contrast mechanisms of polarization sensitive measurements for different cancers and may provide new diagnostic techniques for clinical applications.

Ex vivo photometric and polarimetric multilayer characterization of human healthy colon by multispectral Mueller imaging

Healthy human colon samples were analyzed ex vivo with a multispectral imaging Mueller polarimeter operating from 500 to 700 nm in a backscattering configuration with diffuse light illumination impinging on the innermost tissue layer, the mucosa. The intensity and polarimetric responses were taken on whole tissues first and after progressive exfoliation of the outer layers afterwards. Moreover, these measurements were carried out with two different substrates (one bright and the other dark) successively placed beneath each sample, allowing a reasonably accurate evaluation of the contributions to the overall backscattered light by the various layers. For the shorter investigated wavelengths (500 to 550 nm) the major contribution comes from mucosa and submucosa, while for the longer wavelengths (650 to 700 nm) muscular tissue and fat also contribute significantly. The depolarization has also been studied and is found to be stronger in the red part of the spectrum, mainly due to the highly depolarizing power of the muscular and fat layers.