Non-invasive prediction nomogram for predicting significant fibrosis in patients with metabolic-associated fatty liver disease: a cross-sectional study.

BACKGROUND AND AIM: This study aims to validate the efficacy of the conventional non-invasive score in predicting significant fibrosis in metabolic-associated fatty liver disease (MAFLD) and to develop a non-invasive prediction model for MAFLD. METHODS: This cross-sectional study was conducted among 7701 participants with MAFLD from August 2018 to December 2023. All participants were divided into a training cohort and a validation cohort. The study compared different subgroups' demographic, anthropometric, and laboratory examination indicators and conducted logistic regression analysis to assess the correlation between independent variables and liver fibrosis. Nomograms were created using the logistic regression model. The predictive values of noninvasive models and nomograms were evaluated using receiver operating characteristic (ROC) curve analysis and decision curve analysis (DCA). RESULTS: Four nomograms were developed for the quantitative analysis of significant liver fibrosis risk based on the multivariate logistic regression analysis results. The nomogram's area under ROC curves (AUC) was 0.710, 0.714, 0.748, and 0.715 in overall MAFLD, OW-MAFLD, Lean-MAFLD, and T2DM-MAFLD, respectively. The nomogram had a higher AUC in all MAFLD participants and OW-MAFLD than the other non-invasive scores. The DCA curve showed that the net benefit of each nomogram was higher than that of APRI and FIB-4. In the validation cohort, the AUCs of the nomograms were 0.722, 0.750, 0.719, and 0.705, respectively. CONCLUSION: APRI, FIB-4, and NFS performed poorly predicting significant fibrosis in patients with MAFLD. The new model demonstrated improved diagnostic accuracy and clinical applicability in identifying significant fibrosis in MAFLD.

Atmospheric turbulence effects on hollow Gaussian Schell-model array beams.

Two types of hollow array beams with circular and rectangular distributions on propagating in atmospheric turbulence are investigated and analyzed comparatively with that in free space. Analytical formulas for the cross-spectral density function of two kinds of hollow array beam propagation in linear isotropic random media are derived and used to examine the behavior of the spectral densities. It is found that such beams possess stable hollow arrays with any dimension and lobes in free space, while such distributions only maintain small distances in atmospheric turbulence and ultimately tend to a Gaussian shape due to the turbulence destroying the hollow array profiles. The effects of the turbulence parameters on the behavior of the spectral density are analyzed in depth.

Spatial correlated vortex arrays.

Spatial correlated vortex arrays may form in the same beam when a random source contains multiple helical phase structures. We introduced two types of partially coherent sources with Cartesian and polar symmetric helical phase structure and reveal the characteristics of their radiated fields, respectively. It is demonstrated that far fields generated by these families of sources carry interesting features through the joint regulation of coherence and topological charge, being lattice-like vortex patterns with adjustable dimension and shape.

Random sources with rectangular coherence.

A convenient method for modeling partially coherent sources with rectangular coherence is introduced by structuring the degree of coherence as two separable arbitrary functions with arbitrary dependence of variables. The included examples have demonstrated new opportunities of modeling random sources for beam shaping applications by coherence modulation. The first example discusses a class of rectangular sinc-correlated models generating radiating fields with self-focusing features. As a second example, we introduce a new type of partially coherent vortex beams, which has a unique feature of self-rotation around the optical axis upon propagation.

Circular polarization analyzer based on surface plasmon polariton interference.

The determination of chirality of circularly polarized light (CPL) is of great significance to the development of various optical techniques. In this paper, a miniature circular polarization analyzer (CPA) based on surface plasmon polariton (SPP) interference is proposed. The proposed CPA consists of a micron scale long sub-wavelength slit and two groups of spatially arranged periodic sub-wavelength rectangular groove pairs, which are etched in a metal layer. Under the illumination of a CPL with a given chirality, the proposed CPA is capable of forming SPP-mediated interference fringes with different periods in far field. The chirality of CPL can be directly and quantitatively differentiated by the frequency value of the far field SPP-mediated interference fringes. Different from the existing SPP-based CPAs, the proposed CPA can directly image the chirality information in far field, avoiding near-field imaging of the SPP field.

Self-focusing vortex beams.

A class of wide-stationary optical sources with a specially designed degree of coherence profile is introduced for radiating spectral densities with a vortex whose core's location and size can be controlled at a specified range. This is achieved by modeling of the source coherence state as a combination of a helicoidal separable phase and a Cartesian phase factor, depending on the separation between the $ n $th power of the radius-vectors of two points.

Propagation characteristics of a partially coherent self-shifting beam in random media.

In a recent publication [Opt. Lett.43, 4727 (2018)OPLEDP0146-959210.1364/OL.43.004727], a novel class of partially coherent sources with complex degrees of coherence was introduced. In this paper, we obtain the expression of the cross-spectral density function of the self-shifting beam generated from a light source propagating in random media. Then we calculated and simulated the behaviors of the spectral density and the spectral degree of coherence in the propagation. The results show that there will be a phenomenon of self-shifting in propagation, and the coherence of the beam is Gaussian when it is far enough from the light source. The light intensity is weakened with an increase in turbulence, while the wander of the center of the spectral density remains unchanged in different media.

Electromagnetic multi-Gaussian Schell-model vortex light sources and their radiation field properties.

A procedure for modeling the general electromagnetic Schell-model vortex light source is proposed. Based on this method, we introduce a new class of stochastic electromagnetic vortex light sources with multi-Gaussian Schell-model coherence function. The far-field statistical properties of the beams generated by such sources are studied in detail by numerical examples. Our results can be used to determine the mode structure of a new class of stochastic electromagnetic vortex light sources and of the radiation fields generated by them.

Gaussian Schell-model arrays.

We introduce a novel class of planar, quasi-homogeneous Schell-model source for producing far fields with optical lattice average intensity patterns and derive the corresponding beam conditions. The array dimension, lobes intensity profile, and periodicity of the optical lattice can be flexibly tuned by changing the correlation parameters of the source field. It is also found that, with an appropriate choice of the source parameters, the radiant intensity may possess flat-topped intensity patterns.

Source coherence-based far-field intensity filtering.

An inherent relationship between an invariant far-field beam intensity pattern and the convolution of any two legitimate degrees of coherence in the source plane is established. Two classes of random sources are introduced by modeling the source degree of coherence with the help of the convolution operation of the Gaussian Schell-model correlation function and the multi-sinc Schell-model correlation function in the polar and Cartesian symmetries. The established relationships are used to explore the far-field intensity features produced by the new sources. It is shown that the far-field intensity patterns of the novel sources have multi-sinc Schell-model transverse distributions with a Gaussian envelope, looking like the multi-sinc Schell-model beams filtered by a soft-edge Gaussian aperture. The results demonstrate the potential of coherence modulation of the source fields for far-field beam shaping applications.

Powers of the degree of coherence.

We establish conditions under which a legitimate degree of coherence of a statistically stationary beam-like field raised to a power results in a novel legitimate degree of coherence. The general results and examples relate to scalar beams having uniform and non-uniform correlations.

Products of Schell-model cross-spectral densities.

The condition under which a product of two cross-spectral densities (CSD) constitutes a valid correlation function is established. The results are obtained for the CSDs of two one-dimensional, scalar Schell-model sources, but can be readily generalized to other situations. It is shown via a number of numerical examples how new source classes of Schell-model type and the beam-like fields they radiate can be designed.

Electromagnetic sinc Schell-model beams and their statistical properties.

A class of electromagnetic sources with sinc Schell-model correlations is introduced. The conditions on source parameters guaranteeing that the source generates a physical beam are derived. The evolution behaviors of statistical properties for the electromagnetic stochastic beams generated by this new source on propagating in free space and in atmosphere turbulence are investigated with the help of the weighted superposition method and by numerical simulations. It is demonstrated that the intensity distributions of such beams exhibit unique features on propagating in free space and produce a double-layer flat-top profile of being shape-invariant in the far field. This feature makes this new beam particularly suitable for some special laser processing applications. The influences of the atmosphere turbulence with a non-Kolmogorov power spectrum on statistical properties of the new beams are analyzed in detail.