Novel equation to determine the hepatic triglyceride concentration in humans by MRI: diagnosis and monitoring of NAFLD in obese patients before and after bariatric surgery

Background: Non-alcoholic fatty liver disease (NAFLD) is caused by abnormal accumulation of lipids within liver cells. Its prevalence is increasing in developed countries in association with obesity, and it represents a risk factor for non-alcoholic steatohepatitis (NASH), cirrhosis and hepatocellular carcinoma. Since NAFLD is usually asymptomatic at diagnosis, new non-invasive approaches are needed to determine the hepatic lipid content in terms of diagnosis, treatment and control of disease progression. Here, we investigated the potential of magnetic resonance imaging (MRI) to quantitate and monitor the hepatic triglyceride concentration in humans. Methods: A prospective study of diagnostic accuracy was conducted among 129 consecutive adult patients (97 obesity and 32 non-obese) to compare multi-echo MRI fat fraction, grade of steatosis estimated by histopathology, and biochemical measurement of hepatic triglyceride concentration (that is, Folch value). Results: MRI fat fraction positively correlates with the grade of steatosis estimated on a 0 to 3 scale by histopathology. However, this correlation value was stronger when MRI fat fraction was linked to the Folch value, resulting in a novel equation to predict the hepatic triglyceride concentration (mg of triglycerides/g of liver tissue = 5.082 + (432.104 * multi-echo MRI fat fraction)). Validation of this formula in 31 additional patients (24 obese and 7 controls) resulted in robust correlation between the measured and estimated Folch values. Multivariate analysis showed that none of the variables investigated improves the Folch prediction capacity of the equation. Obese patients show increased steatosis compared to controls using MRI fat fraction and Folch value. Bariatric surgery improved MRI fat fraction values and the Folch value estimated in obese patients one year after surgery. Conclusions: Multi-echo MRI is an accurate approach to determine the hepatic lipid concentration by using our novel equation, representing an economic non-invasive method to diagnose and monitor steatosis in humans.

Proposal and validation of methodologies for the categorisation of continuous variables in the development of prediction models

158 p.

Validity of Resting Energy Expenditure Predictive Equations before and after an Energy-Restricted Diet Intervention in Obese Women

11 p.

About the Stabilization of a Nonlinear Perturbed Difference Equation

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

Use of generalised additive models to categorise continuous variables in clinical prediction

13 P.

The forward problem for the electromagnetic Helmholtz equation

157 p.

Ab initio study of anharmonicity in high pressure Cmca-4 metallic hydrogen

Hydrogen is the only atom for which the Schr odinger equation is solvable. Consisting only of a proton and an electron, hydrogen is the lightest element and, nevertheless, is far from being simple. Under ambient conditions, it forms diatomic molecules H2 in gas phase, but di erent temperature and pressures lead to a complex phase diagram, which is not completely known yet. Solid hydrogen was rst documented in 1899 [1] and was found to be isolating. At higher pressures, however, hydrogen can be metallized. In 1935 Wigner and Huntington predicted that the metallization pressure would be 25 GPa [2], where molecules would disociate to form a monoatomic metal, as alkali metals that lie below hydrogen in the periodic table. The prediction of the metallization pressure turned out to be wrong: metallic hydrogen has not been found yet, even under a pressure as high as 320 GPa. Nevertheless, extrapolations based on optical measurements suggest that a metallic phase may be attained at 450 GPa [3]. The interest of material scientist in metallic hydrogen can be attributed, at least to a great extent, to Ashcroft, who in 1968 suggested that such a system could be a hightemperature superconductor [4]. The temperature at which this material would exhibit a transition from a superconducting to a non-superconducting state (Tc) was estimated to be around room temperature. The implications of such a statement are very interesting in the eld of astrophysics: in planets that contain a big quantity of hydrogen and whose temperature is below Tc, superconducting hydrogen may be found, specially at the center, where the gravitational pressure is high. This might be the case of Jupiter, whose proportion of hydrogen is about 90%. There are also speculations suggesting that the high magnetic eld of Jupiter is due to persistent currents related to the superconducting phase [5]. Metallization and superconductivity of hydrogen has puzzled scientists for decades, and the community is trying to answer several questions. For instance, what is the structure of hydrogen at very high pressures? Or a more general one: what is the maximum Tc a phonon-mediated superconductor can have [6]? A great experimental e ort has been carried out pursuing metallic hydrogen and trying to answer the questions above; however, the characterization of solid phases of hydrogen is a hard task. Achieving the high pressures needed to get the sought phases requires advanced technologies. Diamond anvil cells (DAC) are commonly used devices. These devices consist of two diamonds with a tip of small area; for this reason, when a force is applied, the pressure exerted is very big. This pressure is uniaxial, but it can be turned into hydrostatic pressure using transmitting media. Nowadays, this method makes it possible to reach pressures higher than 300 GPa, but even at this pressure hydrogen does not show metallic properties. A recently developed technique that is an improvement of DAC can reach pressures as high as 600 GPa [7], so it is a promising step forward in high pressure physics. Another drawback is that the electronic density of the structures is so low that X-ray di raction patterns have low resolution. For these reasons, ab initio studies are an important source of knowledge in this eld, within their limitations. When treating hydrogen, there are many subtleties in the calculations: as the atoms are so light, the ions forming the crystalline lattice have signi cant displacements even when temperatures are very low, and even at T=0 K, due to Heisenberg's uncertainty principle. Thus, the energy corresponding to this zero-point (ZP) motion is signi cant and has to be included in an accurate determination of the most stable phase. This has been done including ZP vibrational energies within the harmonic approximation for a range of pressures and at T=0 K, giving rise to a series of structures that are stable in their respective pressure ranges [8]. Very recently, a treatment of the phases of hydrogen that includes anharmonicity in ZP energies has suggested that relative stability of the phases may change with respect to the calculations within the harmonic approximation [9]. Many of the proposed structures for solid hydrogen have been investigated. Particularly, the Cmca-4 structure, which was found to be the stable one from 385-490 GPa [8], is metallic. Calculations for this structure, within the harmonic approximation for the ionic motion, predict a Tc up to 242 K at 450 GPa [10]. Nonetheless, due to the big ionic displacements, the harmonic approximation may not su ce to describe correctly the system. The aim of this work is to apply a recently developed method to treat anharmonicity, the stochastic self-consistent harmonic approximation (SSCHA) [11], to Cmca-4 metallic hydrogen. This way, we will be able to study the e ects of anharmonicity in the phonon spectrum and to try to understand the changes it may provoque in the value of Tc. The work is structured as follows. First we present the theoretical basis of the calculations: Density Functional Theory (DFT) for the electronic calculations, phonons in the harmonic approximation and the SSCHA. Then we apply these methods to Cmca-4 hydrogen and we discuss the results obtained. In the last chapter we draw some conclusions and propose possible future work.

Prediction of Multi-Target Networks of Neuroprotective Compounds with Entropy Indices and Synthesis, Assay, and Theoretical Study of New Asymmetric 1,2-Rasagiline Carbamates

In a multi-target complex network, the links (L-ij) represent the interactions between the drug (d(i)) and the target (t(j)), characterized by different experimental measures (K-i, K-m, IC50, etc.) obtained in pharmacological assays under diverse boundary conditions (c(j)). In this work, we handle Shannon entropy measures for developing a model encompassing a multi-target network of neuroprotective/neurotoxic compounds reported in the CHEMBL database. The model predicts correctly >8300 experimental outcomes with Accuracy, Specificity, and Sensitivity above 80%-90% on training and external validation series. Indeed, the model can calculate different outcomes for >30 experimental measures in >400 different experimental protocolsin relation with >150 molecular and cellular targets on 11 different organisms (including human). Hereafter, we reported by the first time the synthesis, characterization, and experimental assays of a new series of chiral 1,2-rasagiline carbamate derivatives not reported in previous works. The experimental tests included: (1) assay in absence of neurotoxic agents; (2) in the presence of glutamate; and (3) in the presence of H2O2. Lastly, we used the new Assessing Links with Moving Averages (ALMA)-entropy model to predict possible outcomes for the new compounds in a high number of pharmacological tests not carried out experimentally.

One-dimensional potential for image-potential states on graphene

In the framework of dielectric theory, the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-potential states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by numerically solving the one-dimensional Schrodinger equation. The imagepotential state wave functions accumulate most of their probability outside the slab. We find that the random phase approximation (RPA) for the nonlocal dielectric function yields a superior description for the potential inside the slab, but a simple Fermi-Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters: the slab width and the electronic density. The theoretical calculations are compared with experimental results for the work function and image-potential states obtained by two-photon photoemission.