The Seigniory of Sark and the Duchy Of Cornwall: Similarities and Differences Including Observations on the Isles of Scilly

A unified and robust mathematical model for compressible and incompressible linear elasticity can be obtained by rephrasing the Herrmann formulation within the Hellinger-Reissner principle. This quasi-optimally converging extension of PEERS (Plane Elasticity Element with Reduced Symmetry) is called Dual-Mixed Hybrid formulation (DMH). Explicit residual-based a posteriori error estimates for DMH are introduced and are mathematically shown to be locking-free, reliable, and efficient. The estimator serves as a refinement indicator in an adaptive algorithm for effective automatic mesh generation. Numerical evidence supports that the adaptive scheme leads to optimal convergence for Lam\ue9 and Stokes benchmark problems with singularities

A Poroelastic Mixture Model of Mechanobiological Processes in Biomass Growth: Theory and Application to Tissue Engineering

In this article we propose a novel mathematical description of biomass growth that combines poroelastic theory of mixtures and cellular population models. The formulation, potentially applicable to general mechanobiological processes, is here used to study the engineered cultivation in bioreactors of articular chondrocytes, a process of Regenerative Medicine characterized by a complex interaction among spatial scales (from nanometers to centimeters), temporal scales (from seconds to weeks) and biophysical phenomena (fluid-controlled nutrient transport, delivery and consumption; mechanical deformation of a multiphase porous medium). The principal contribution of this research is the inclusion of the concept of cellular \u201cforce isotropy\u201d as one of the main factors influencing cellular activity. In this description, the induced cytoskeletal tensional states trigger signalling transduction cascades regulating functional cell behavior. This mechanims is modeled by a parameter which estimates the influence of local force isotropy by the norm of the deviatoric part of the total stress tensor. According to the value of the estimator, isotropic mechanical conditions are assumed to be the promoting factor of extracellular matrix production whereas anisotropic conditions are assumed to promote cell proliferation. The resulting mathematical formulation is a coupled system of nonlinear partial differential equations comprising: conservation laws for mass and linear momentum of the growing biomass; advection\u2013diffusion\u2013reaction laws for nutrient (oxygen) transport, delivery and consumption; and kinetic laws for cellular population dynamics. To develop a reliable computational tool for the simulation of the engineered tissue growth process the nonlinear differential problem is numerically solved by: (1) temporal semidiscretization; (2) linearization via a fixed-point map; and (3) finite element spatial approximation. The biophysical accuracy of the mechanobiological model is assessed in the analysis of a simplified 1D geometrical setting. Simulation results show that: (1) isotropic/anisotropic conditions are strongly influenced by both maximum cell specific growth rate and mechanical boundary conditions enforced at the interface between the biomass construct and the interstitial fluid; (2) experimentally measured features of cultivated articular chondrocytes, such as the early proliferation phase and the delayed extracellular matrix production, are well described by the computed spatial and temporal evolutions of cellular populations

Regularization Techniques for Inverse Problem in DOT Applications

Diffuse optical tomography (DOT) is an emerging diagnostic technique which uses near-infra-red light to investigate the optical coefficients distribution in biological tissues. The surface of the tissue is illuminated by light sources, then the outgoing light is measured by detectors placed at various locations on the surface itself. In order to reconstruct the optical coefficients, a mathematical model of light propagation is employed: such model leads to the minimization of the discrepancy between the detected data and the corresponding theoretical field. Due to severe ill-conditioning, regularization techniques are required: common procedures consider mainly \u2113 1-norm (LASSO) and \u2113 2-norm (Tikhonov) regularization. In the present work we investigate two original approaches in this context: The elastic-net regularization, previously used in machine learning problems, and the Bregman procedure. Numerical experiments are performed on synthetic 2D geometries and data, to evaluate the performance of these approaches. The results show that these techniques are indeed suitable choices for practical applications, where DOT is used as a cheap, first-level and almost real-Time screening technique for breast cancer detection

Mathematical and numerical methods for modeling drug delivery to the posterior segment of the eye

The high incidence of diseases that affect the posterior segment of the eye (PSE) - here intended as composed by sclera, choroid and retina-prompts for establishing effective and well tolerated therapies. Topical application (instillation of drops) and systemic assumption remain the most widespread drug administration routes. However, the drug achieved levels are not therapeutically sufficient therapeutic, since in the first case the drug is mainly washed away by different pathways (aqueous humor, systemic adsorption, tears) and in the second reaches the PSE target in a minimal fraction. Intravitreal injections and biodegradable episcleral implants have emerged in the last decades as alternative, more effective, administration routes. Whilst these techniques already offer significant improvements, much space is still open to research. The difficulty in delivering drugs to the PSE via the intravitreal (IV) or episcleral (EP) route resides in the several physical and dynamical barriers-including blood retinal barrier, clearance from choriocapillaries and lymphatics-which hinder the passage of the drug molecules. In combination, and in support of clinical experiments, mathematical and computational methods can be used to simulate drug concentration levels in the tissues upon IV or EP administration. In this respect, this short review gives an update of the most recent (from year 2000 to present time) developments on mathematical models for drug delivery to the PSE. We specifically focus our attention on physiological modeling works that include spatial dependency. Our review work is organized in short sections accompanied by detailed tables. We discuss descriptions of the PSE morphology, considering \u201canatomically accurate\u201d as well as reduced models and we analyze the biophysical phenomena included in the examined models. We present the numerical techniques adopted to solve the resulting systems of partial differential equations and we deal with the delicate issue of parameter choice and validation of the results. Eventually, we examine the main results and scientific achievements of the considered models. Our conclusions point out the absence of a \u201cstandard mathematical model\u201d and highlight a significant scattering of the results obtained from the different authors

Innovative biofilm inhibition and anti-microbial behavior of molybdenum sulfide nanostructures generated by microwave-assisted solvothermal route

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Standards for European training requirements in interventional neuroradiology: Guidelines by the Division of Neuroradiology/Section of Radiology European Union of Medical Specialists (UEMS), in cooperation with the Division of Interventional Radiology/UEMS, the European Society of Neuroradiology (ESNR), and the European Society of Minimally Invasive Neurological Therapy (ESMINT)

This document sets out standards for training in Interventional Neuroradiology (INR) in Europe. These standards have been developed by a working group of the European Society of Neuroradiology (ESNR) and the European Society of Minimally Invasive Neurological Therapy (ESMINT) on the initiative and under the umbrella of the Division of Neuroradiology/Section of Radiology of the European Union of Medical Specialists (UEMS)

Early red nucleus atrophy in relapse-onset multiple sclerosis

No study has investigated red nucleus (RN) atrophy in multiple sclerosis (MS) despite cerebellum and its connections are elective sites of MS-related pathology. In this study, we explore RN atrophy in early MS phases and its association with cerebellar damage (focal lesions and atrophy) and physical disability. Thirty-seven relapse-onset MS (RMS) patients having mean age of 35.6 ± 8.5 (18–56) years and mean disease duration of 1.1 ± 1.5 (0–5) years, and 36 age- and sex-matched healthy controls (HC) were studied. Cerebellar and RN lesions and volumes were analyzed on 3 T-MRI images. RMS did not differ from HC in cerebellar lobe volumes but significantly differed in both right (107.84 ± 13.95 mm3 vs. 99.37 ± 11.53 mm3, p =.019) and left (109.71 ± 14.94 mm3 vs. 100.47 ± 15.78 mm3, p =.020) RN volumes. Cerebellar white matter lesion volume (WMLV) inversely correlated with both right and left RN volumes (r = −.333, p =.004 and r = −.298, p =.010, respectively), while no correlation was detected between RN volumes and mean cortical thickness, cerebellar gray matter lesion volume, and supratentorial WMLV (right RN: r = −.147, p =.216; left RN: r = −.153, p =.196). Right, but not left, RN volume inversely correlated with midbrain WMLV (r = −.310, p =.008), while no correlation was observed between whole brainstem WMLV and either RN volumes (right RN: r = −.164, p =.164; left RN: r = −.64, p =.588). Finally, left RN volume correlated with vermis VIIb (r =.297, p =.011) and right interposed nucleus (r =.249, p =.034) volumes. We observed RN atrophy in early RMS, likely resulting from anterograde axonal degeneration starting in cerebellar and midbrain WML. RN atrophy seems a promising marker of neurodegeneration and/or cerebellar damage in RMS

On the canonical map of surfaces with q>=6

We carry out an analysis of the canonical system of a minimal complex surface of general type with irregularity q>0. Using this analysis we are able to sharpen in the case q>0 the well known Castelnuovo inequality K^2>=3p_g+q-7. Then we turn to the study of surfaces with p_g=2q-3 and no fibration onto a curve of genus >1. We prove that for q>=6 the canonical map is birational. Combining this result with the analysis of the canonical system, we also prove the inequality: K^2>=7\chi+2. This improves an earlier result of the first and second author [M.Mendes Lopes and R.Pardini, On surfaces with p_g=2q-3, Adv. in Geom. 10 (3) (2010), 549-555].Comment: Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in the special issue of Science of China Ser.A: Mathematics dedicated to him. V2:some typos have been correcte

Identification of Cell-Free Circulating MicroRNAs for the Detection of Early Breast Cancer and Molecular Subtyping

Early detection is crucial for achieving a reduction in breast cancer mortality. Analysis of circulating cell-free microRNAs present in the serum of cancer patients has emerged as a promising new noninvasive biomarker for early detection of tumors and for predicting their molecular classifications. The rationale for this study was to identify subtype-specific molecular profiles of cell-free microRNAs for early detection of breast cancer in serum. Fifty-four early-stage breast cancers with 27 age-matched controls were selected for circulating microRNAs evaluation in the serum. The 54 cases were molecularly classified (luminal A, luminal B, luminal B Her2 positive, Her-2, triple negative). NanoString platform was used for digital detection and quantitation of 800 tagged microRNA probes and comparing the overall differences in serum microRNA expression from breast cancer cases with controls. We identified the 42 most significant (P ≤ 0.05, 1.5-fold) differentially expressed circulating microRNAs in each molecular subtype for further study. Of these microRNAs, 19 were significantly differentially expressed in patients presenting with luminal A, eight in the luminal B, ten in luminal B HER 2 positive, and four in the HER2 enriched subtype. AUC is high with suitable sensitivity and specificity. For the triple negative subtype miR-25-3p had the best accuracy. Predictive analysis of the mRNA targets suggests they encode proteins involved in molecular pathways such as cell adhesion, migration, and proliferation. This study identified subtype-specific molecular profiles of cell-free microRNAs suitable for early detection of breast cancer selected by comparison to the microRNA profile in serum for female controls without apparent risk of breast cancer. This molecular profile should be validated using larger cohort studies to confirm the potential of these miRNA for future use as early detection biomarkers that could avoid unnecessary biopsy in patients with a suspicion of breast cancer.Foundation for Research Support of the State of São Paulo (FAPESP process 2015/21082-0) and Public Ministry of Labor Campinas (Research, Prevention, and Education of Occupational Cancer)