Stokes-Darcy System, Small-Darcy-Number Behaviour and Related Interfacial Conditions

We show that the Stokes-Darcy system, which governs flows through adjacent porous and pure-fluid domains in the two-domain approach without forced filtration, can be recovered from the Helmholtz minimal dissipation principle. While the continuity of normal velocity across the interface is imposed explicitly for mass conservation, only the Beavers-Joseph-Saffman-Jones (BJSJ) interface boundary condition is imposed implicitly, and the balance of the normal-force interface boundary condition appears naturally in the variational process. This set of interface boundary conditions is well-accepted in the mathematics community. We show that these interfacial boundary conditions, at the physically important small-Darcy-number regime, are consistent with continuity of pressure across the interface condition. the tangential velocity and pressure are discontinuous in general but the discontinuity is of the order of the square root of the Darcy number. Hence these interfacial conditions are all approximately consistent in the physically important small-Darcy-number regime. the leading order dynamics in the pure fluid zone is governed by the Stokes system with the no-slip no-penetration boundary condition on the interface between the free zone and porous media at a small Darcy number. the leading order non-trivial dynamics in porous media is governed by the Darcy equation with the pressure on the interface prescribed by the pressure of the leading order Stokes flow in the pure fluid zone. Such a semi-decoupled approach has long been used by the groundwater community. Our result is the first rigorous work quantifying the error of this intuitive approach and relating different interfacial conditions

Label-free detection of exosomes from different cellular sources based on surface-enhanced Raman spectroscopy combined with machine learning models

Exosomes are significant facilitators of inter-cellular communication that can unveil cell-cell interactions, signaling pathways, regulatory mechanisms and disease diagnostics. Nonetheless, current analysis required large amount of data for exosome identification that it hampers efficient and timely mechanism study and diagnostics. Here, we used a machine-learning assisted Surface-enhanced Raman spectroscopy (SERS) method to detect exosomes derived from six distinct cell lines (HepG2, Hela, 143B, LO-2, BMSC, and H8) with small amount of data. By employing sodium borohydride-reduced silver nanoparticles and sodium borohydride solution as an aggregating agent, 100 SERS spectra of the each types of exosomes were collected and then subjected to multivariate and machine learning analysis. By integrating Principal Component Analysis with Support Vector Machine (PCA-SVM) models, our analysis achieved a high accuracy rate of 94.4% in predicting exosomes originating from various cellular sources. In comparison to other machine learning analysis, our method used small amount of SERS data to allow a simple and rapid exosome detection, which enables a timely subsequent study of cell-cell interactions, communication mechanisms, and disease mechanisms in life sciences.Comment: 5 figure

Single-port laparoscopic sacrospinous ligament suspension via the natural vaginal cavity (SvNOTES) for pelvic prolapse: The first feasibility study

ObjectiveThis study aims to investigate the feasibility and short-term efficacy of single-port laparoscopic-assisted transvaginal natural cavity endoscopic sacrospinous ligament suspensions (SvNOTES).MethodsA total of 30 patients diagnosed with anterior or/and middle pelvic organ prolapse Stages III and IV underwent natural vaginal cavity (SvNOTES), and 30 patients who underwent conventional sacrospinous ligament (SSLF) were used as a control group. The operation time, blood loss, postoperative POP-Q score, length of hospital stay, and complications were compared between the two groups.ResultsThe operation time for SvNOTE was (60 ± 13) min, which was longer than (30 ± 15) min for SSLF (P = 0.04). However, the bleeding amount in SvNOTE was 29.44 ± 2.56, significantly lower than that in the SSLF group (80 ± 10; P = 0.02), and the postoperative hospital stay in the SvNOTE group was (4 ± 2) days, longer than (3 ± 1) days in SSLF (P = 0.02). However, there were no intraoperative complications in the SvNOTE group, whereas one ureteral injury occurred in the SSLF group; in addition, the postoperative POP-Q score was significantly better in the SvNOTE group than that in the SSLF group with increasing time (P < 0.001).ConclusionCompared with SSLF, single-port laparoscopic sacrospinous ligament suspension via the natural vaginal cavity is visualized, greatly improving the success rate of sacrospinous ligament fixation, with less blood loss and fewer complications, arguably a safer and minimally invasive surgical approach

Temporal Geospatial Analysis of COVID-19 Pre-infection Determinants of Risk in South Carolina

Disparities and their geospatial patterns exist in morbidity and mortality of COVID-19 patients. When it comes to the infection rate, there is a dearth of research with respect to the disparity structure, its geospatial characteristics, and the pre-infection determinants of risk (PIDRs). This work aimed to assess the temporal–geospatial associations between PIDRs and COVID-19 infection at the county level in South Carolina. We used the spatial error model (SEM), spatial lag model (SLM), and conditional autoregressive model (CAR) as global models and the geographically weighted regression model (GWR) as a local model. The data were retrieved from multiple sources including USAFacts, U.S. Census Bureau, and the Population Estimates Program. The percentage of males and the unemployed population were positively associated with geodistributions of COVID-19 infection (p values \u3c 0.05) in global models throughout the time. The percentage of the white population and the obesity rate showed divergent spatial correlations at different times of the pandemic. GWR models fit better than global models, suggesting nonstationary correlations between a region and its neighbors. Characterized by temporal–geospatial patterns, disparities in COVID-19 infection rate and their PIDRs are different from the mortality and morbidity of COVID-19 patients. Our findings suggest the importance of prioritizing different populations and developing tailored interventions at different times of the pandemic

Regularity of the Stokes-Darcy System

We present a proof of the elliptic regularity property for the steady state Stokes-Darcy equation in a two-dimensional domain equipped with the Beavers-Joseph-Saffman-Jones (BJSJ) interface condition. Such regularity results are fundamental to the numerical analysis of various numerical methods for the Stokes-Darcy system