Mueller matrix analysis of a biologically sourced engineered tissue construct as polarimetric phantom.

Significance: The polarimetric properties of biological tissues are often difficult to ascertain independent of their complex structural and organizational features. Conventional polarimetric tissue phantoms have well-characterized optical properties but are overly simplified. We demonstrate that an innovative, biologically sourced, engineered tissue construct better recapitulates the desired structural and polarimetric properties of native collagenous tissues, with the added benefit of potential tunability of the polarimetric response. We bridge the gap between non-biological polarimetric phantoms and native tissues. Aim: We aim to evaluate a synthesized tissue construct for its effectiveness as a phantom that mimics the polarimetric properties in typical collagenous tissues. Approach: We use a fibroblast-derived, ring-shaped engineered tissue construct as an innovative tissue phantom for polarimetric imaging. We perform polarimetry measurements and subsequent analysis using the Mueller matrix decomposition and Mueller matrix transformation methods. Scalar polarimetric parameters of the engineered tissue are analyzed at different time points for both a control group and for those treated with the transforming growth factor ( TGF ) - ß 1 . Second-harmonic generation (SHG) imaging and three-dimensional collagen fiber organization analysis are also applied. Results: We identify linear retardance and circular depolarization as the parameters that are most sensitive to the tissue culture time and the addition of TGF - ß 1 . Aside from a statistically significant increase over time, the behavior of linear retardance and circular depolarization indicates that the addition of TGF - ß 1 accelerates the growth of the engineered tissue, which is consistent with expectations. We also find through SHG images that collagen fiber organization becomes more aligned over time but is not susceptible to the addition of TGF - ß 1 . Conclusions: The engineered tissue construct exhibits changes in polarimetric properties, especially linear retardance and circular depolarization, over culture time and under TGF - ß 1 treatments. This tissue construct has the potential to act as a controlled modular optical phantom for polarimetric-based methods.

A note on the Hill-Ogden generalised strains.

This brief contribution provides an overview of the Hill-Ogden generalised strain tensors, and some considerations on their representation in generalised (curvilinear) coordinates, in a fully covariant formalism that is adaptable to a more general theory on Riemannian manifolds. These strains may be naturally defined with covariant components or naturally defined with contravariant components. Each of these two macro-families is best suited to a specific geometrical context.

Characterization and classification of ductal carcinoma tissue using four channel based stokes-mueller polarimetry and machine learning.

Interaction of polarized light with healthy and abnormal regions of tissue reveals structural information associated with its pathological condition. Even a slight variation in structural alignment can induce a change in polarization property, which can play a crucial role in the early detection of abnormal tissue morphology. We propose a transmission-based Stokes-Mueller microscope for quantitative analysis of the microstructural properties of the tissue specimen. The Stokes-Mueller based polarization microscopy provides significant structural information of tissue through various polarization parameters such as degree of polarization (DOP), degree of linear polarization (DOLP), and degree of circular polarization (DOCP), anisotropy (r) and Mueller decomposition parameters such as diattenuation, retardance and depolarization. Further, by applying a suitable image processing technique such as Machine learning (ML) output images were analysed effectively. The support vector machine image classification model achieved 95.78% validation accuracy and 94.81% testing accuracy with polarization parameter dataset. The study's findings demonstrate the potential of Stokes-Mueller polarimetry in tissue characterization and diagnosis, providing a valuable tool for biomedical applications.

Mueller matrix-based characterization of cervical tissue sections: a quantitative comparison of polar and differential decomposition methods.

Significance: Quantitative optical polarimetry has received considerable recent attention owing to its potential for being an efficient diagnosis and characterizing tool with potential applications in biomedical research and various other disciplines. In this regard, it is crucial to validate various Mueller matrix (MM) decomposition methods, which are utilized to extract and quantify the intrinsic individual polarization anisotropy properties of various complex optical media. Aim: To quantitatively compare the performance of both polar and differential MM decomposition methods for probing the structural and morphological changes in complex optical media through analyzing their intrinsic individual polarization parameters, which are extracted using the respective decomposition algorithms. We also intend to utilize the decomposition-derived anisotropy parameters to distinguish among the cervical tissues with different grades of cervical intraepithelial neoplasia (CIN) and to characterize the healing efficiency of an organic crystal. Approach: Polarization MM of the cervical tissues with different grades of CIN and the different stages of the self-healing crystal are recorded with a home-built MM imaging setup in the transmission detection geometry with a spatial resolution of ≈400 nm. The measured MMs are then processed with both the polar and differential MM decomposition methods to extract the individual polarization parameters of the respective samples. The derived polarization parameters are further analyzed to validate and compare the performance of both the MM decomposition methods for probing and characterizing the structural changes in the respective investigated optical media through their decomposition-derived intrinsic individual polarization properties. Results: Pronounced differences in the decomposed-derived polarization anisotropy parameters are observed for cervical tissue sections with different grades of CIN. While a significant increase in the depolarization parameter (Δ) is obtained with the increment of CIN stages for both the polar [Δ=0.32 for CIN grade one (CIN-I) and Δ=0.53 for CIN grade two (CIN-II))] and differential (Δ=0.35 for CIN-I and Δ=0.56 for CIN-II) decomposition methods, a trend reversal is seen for the linear diattenuation parameter (dL), indicating the structural distortion in the cervical morphology due to the CIN disease. More importantly, with the differential decomposition algorithm, the magnitude of the derived dL parameter decreases from 0.26 to 0.19 with the progression of CIN, which was not being probed by the polar decomposition method. Conclusion: Our results demonstrate that the differential decomposition of MM holds certain advantages over the polar decomposition method to characterize and probe the structural changes in the cervical tissues with different grades of CIN. Although the quantified individual polarization parameters obtained through both the MM decomposition methods can be used as useful metrics to characterize various optical media, in case of complex turbid media such as biological tissues, incorporation of the differential decomposition technique may yield more efficient information. Also, the study highlights the utilization of MM polarimetry with an appropriate decomposition technique as an efficient diagnostic and characterizing tool in the realm of biomedical clinical research, and various other disciplines.

Research on IMU Calibration Model Based on Polar Decomposition.

As an important deterministic error of the inertial measurement unit (IMU), the installation error has a serious impact on the navigation accuracy of the strapdown inertial navigation system (SINS). The impact becomes more severe in a highly dynamic application environment. This paper proposes a new IMU calibration model based on polar decomposition. Using the new model, the installation error is decomposed into a nonorthogonal error and a misalignment error. The compensation of the IMU calibration model is decomposed into two steps. First, the nonorthogonal error is compensated, and then the misalignment error is compensated. Based on the proposed IMU calibration model, we used a three-axis turntable to calibrate three sets of strapdown inertial navigation systems (SINS). The experimental results show that the misalignment errors are larger than the nonorthogonal errors. Based on the experimental results, this paper proposes a new method to simplify the installation error. This simplified method defines the installation error matrix as an antisymmetric matrix composed of three misalignment errors. The navigation errors caused by the proposed simplified calibration model are compared with the navigation errors caused by the traditional simplified calibration model. The 48-h navigation experiment results show that the proposed simplified calibration model is superior to the traditional simplified calibration model in attitude accuracy, velocity accuracy, and position accuracy.

Polarimetric comparison of fresh and frozen skeletal muscle tissues of goat.

Optical properties can provide rich information about morphology and structure of tissues. Fresh and frozen muscle tissue samples of goat are investigated using imaging polarimetry to understand its structural nature. The outcomes demonstrate that the muscle tissues lose, to some extent, their integrity and organization on freezing. The fresh tissues offer very small circular retardance as compared to frozen samples. However, linear retardance is the main contributor in fresh muscle samples. Ultimately, linear and circular retardance can be used to differentiate fresh and frozen tissues. These investigations illustrate the capabilities of optical polarimetry for the characterization of muscle tissue structures. Specifically, the structure of biological tissue samples can be differentiated using real-time, cost effective and non-invasive optical polarimetry in the field of meat industry and biomedical diagnosis.

Deformable image registration for tissues with large displacements.

Image registration for internal organs and soft tissues is considered extremely challenging due to organ shifts and tissue deformation caused by patients' movements such as respiration and repositioning. In our previous work, we proposed a fast registration method for deformable tissues with small rotations. We extend our method to deformable registration of soft tissues with large displacements. We analyzed the deformation field of the liver by decomposing the deformation into shift, rotation, and pure deformation components and concluded that in many clinical cases, the liver deformation contains large rotations and small deformations. This analysis justified the use of linear elastic theory in our image registration method. We also proposed a region-based neuro-fuzzy transformation model to seamlessly stitch together local affine and local rigid models in different regions. We have performed the experiments on a liver MRI image set and showed the effectiveness of the proposed registration method. We have also compared the performance of the proposed method with the previous method on tissues with large rotations and showed that the proposed method outperformed the previous method when dealing with the combination of pure deformation and large rotations. Validation results show that we can achieve a target registration error of [Formula: see text] and an average centerline distance error of [Formula: see text]. The proposed technique has the potential to significantly improve registration capabilities and the quality of intraoperative image guidance. To the best of our knowledge, this is the first time that the complex displacement of the liver is explicitly separated into local pure deformation and rigid motion.

Orthogonal Matrix Retrieval In Cryo-Electron Microscopy.

In single particle reconstruction (SPR) from cryo-electron microscopy (EM), the 3D structure of a molecule needs to be determined from its 2D projection images taken at unknown viewing directions. Zvi Kam showed already in 1980 that the autocorrelation function of the 3D molecule over the rotation group SO(3) can be estimated from 2D projection images whose viewing directions are uniformly distributed over the sphere. The autocorrelation function determines the expansion coefficients of the 3D molecule in spherical harmonics up to an orthogonal matrix of size (2l + 1) × (2l + 1) for each l = 0,1,2,…. In this paper we show how techniques for solving the phase retrieval problem in X-ray crystallography can be modified for the cryo-EM setup for retrieving the missing orthogonal matrices. Specifically, we present two new approaches that we term Orthogonal Extension and Orthogonal Replacement, in which the main algorithmic components are the singular value decomposition and semidefinite programming. We demonstrate the utility of these approaches through numerical experiments on simulated data.