Numerical Bifurcation Analysis of PDEs From Lattice Boltzmann Model Simulations: a Parsimonious Machine Learning Approach

We address a three-tier data-driven approach for the numerical solution of the inverse problem in Partial Differential Equations (PDEs) and for their numerical bifurcation analysis from spatio-temporal data produced by Lattice Boltzmann model simulations using machine learning. In the first step, we exploit manifold learning and in particular parsimonious Diffusion Maps using leave-one-out cross-validation (LOOCV) to both identify the intrinsic dimension of the manifold where the emergent dynamics evolve and for feature selection over the parameter space. In the second step, based on the selected features, we learn the right-hand-side of the effective PDEs using two machine learning schemes, namely shallow Feedforward Neural Networks (FNNs) with two hidden layers and single-layer Random Projection Networks (RPNNs), which basis functions are constructed using an appropriate random sampling approach. Finally, based on the learned black-box PDE model, we construct the corresponding bifurcation diagram, thus exploiting the numerical bifurcation analysis toolkit. For our illustrations, we implemented the proposed method to perform numerical bifurcation analysis of the 1D FitzHugh-Nagumo PDEs from data generated by D1Q3 Lattice Boltzmann simulations. The proposed method was quite effective in terms of numerical accuracy regarding the construction of the coarse-scale bifurcation diagram. Furthermore, the proposed RPNN scheme was ∼ 20 to 30 times less costly regarding the training phase than the traditional shallow FNNs, thus arising as a promising alternative to deep learning for the data-driven numerical solution of the inverse problem for high-dimensional PDEs

Thresholds of ENDOGLIN expression in endothelial cells explains vascular etiology in Hereditary Hemorrhagic Telangiectasia type 1

Hereditary Hemorrhagic Telangiectasia type 1 (HHT1) is an autosomal dominant inherited disease characterized by arteriovenous malformations and hemorrhage. HHT1 is caused by mutations in ENDOGLIN, which encodes an ancillary receptor for Transforming Growth Factor-beta/Bone Morphogenetic Protein-9 expressed in all vascular endothelial cells. Haploinsufficiency is widely accepted as the underlying mechanism for HHT1. However, it remains intriguing that only some, but not all, vascular beds are affected, as these causal gene mutations are present in vasculature throughout the body. Here, we have examined the endoglin expression levels in the blood vessels of multiple organs in mice and in humans. We found a positive correlation between low basal levels of endoglin and the general prevalence of clinical manifestations in selected organs. Endoglin was found to be particularly low in the skin, the earliest site of vascular lesions in HHT1, and even undetectable in the arteries and capillaries of heterozygous endoglin mice. Endoglin levels did not appear to be associated with organ-specific vascular functions. Instead, our data revealed a critical endoglin threshold compatible with the haploinsufficiency model, below which endothelial cells independent of their tissue of origin exhibited abnormal responses to Vascular Endothelial Growth Factor. Our results support the development of drugs promoting endoglin expression as potentially protective.Stem cells & developmental biolog

A new ghost cell/level set method for moving boundary problems:application to tumor growth

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth

Design of MRI Structured Spiking Neural Networks and Learning Algorithms for Personalized Modelling, Analysis, and Prediction of EEG Signals

Abstract This paper proposes a novel method and algorithms for the design of MRI structured personalized 3D spiking neural network models (MRI-SNN) for a better analysis, modeling, and prediction of EEG signals. It proposes a novel gradient-descent learning algorithm integrated with a spike-time-dependent-plasticity algorithm. The models capture informative personal patterns of interaction between EEG channels, contrary to single EEG signal modeling methods or to spike-based approaches which do not use personal MRI data to pre-structure a model. The proposed models can not only learn and model accurately measured EEG data, but they can also predict signals at 3D model locations that correspond to non-monitored brain areas, e.g. other EEG channels, from where data has not been collected. This is the first study in this respect. As an illustration of the method, personalized MRI-SNN models are created and tested on EEG data from two subjects. The models result in better prediction accuracy and a better understanding of the personalized EEG signals than traditional methods due to the MRI and EEG information integration. The models are interpretable and facilitate a better understanding of related brain processes. This approach can be applied for personalized modeling, analysis, and prediction of EEG signals across brain studies such as the study and prediction of epilepsy, peri-perceptual brain activities, brain-computer interfaces, and others

Pharmacological assessment of ibuprofen arginate on platelet aggregation and colon cancer cell killing

This work was funded in part by grants from the Wellcome Trust (0852551Z108/Z, to J.A.M.) and British Heart Foundation (FS/16/1/31699, to NSK). SM is a recipient of a PhD award from the King of Saud University, AT is a recipient of a MRC PhD studentship

An iron-based beverage, HydroFerrate fluid (MRN-100), alleviates oxidative stress in murine lymphocytes in vitro

BackgroundSeveral studies have examined the correlation between iron oxidation and H2O2 degradation. The present study was carried out to examine the protective effects of MRN-100 against stress-induced apoptosis in murine splenic cells in vitro. MRN-100, or HydroFerrate fluid, is an iron-based beverage composed of bivalent and trivalent ferrates.MethodsSplenic lymphocytes from mice were cultured in the presence or absence of MRN-100 for 2 hrs and were subsequently exposed to hydrogen peroxide (H2O2) at a concentration of 25 μM for 14 hrs. Percent cell death was examined by flow cytometry and trypan blue exclusion. The effect of MRN-100 on Bcl-2 and Bax protein levels was determined by Western blot.ResultsResults show, as expected, that culture of splenic cells with H2O2 alone results in a significant increase in cell death (apoptosis) as compared to control (CM) cells. In contrast, pre-treatment of cells with MRN-100 followed by H2O2 treatment results in significantly reduced levels of apoptosis. In addition, MRN-100 partially prevents H2O2-induced down-regulation of the anti-apoptotic molecule Bcl-2 and upregulation of the pro-apoptotic molecule Bax.ConclusionOur findings suggest that MRN-100 may offer a protective effect against oxidative stress-induced apoptosis in lymphocytes

Nutritional considerations during prolonged exposure to a confined, hyperbaric, hyperoxic environment: Recommendations for saturation divers

Saturation diving is an occupation that involves prolonged exposure to a confined, hyperoxic, hyperbaric environment. The unique and extreme environment is thought to result in disruption to physiological and metabolic homeostasis, which may impact human health and performance. Appropriate nutritional intake has the potential to alleviate and/or support many of these physiological and metabolic concerns, whilst enhancing health and performance in saturation divers. Therefore, the purpose of this review is to identify the physiological and practical challenges of saturation diving and consequently provide evidence-based nutritional recommendations for saturation divers to promote health and performance within this challenging environment. Saturation diving has a high-energy demand, with an energy intake of between 44 and 52 kcal/kg body mass per day recommended, dependent on intensity and duration of underwater activity. The macronutrient composition of dietary intake is in accordance with the current Institute of Medicine guidelines at 45-65 % and 20-35 % of total energy intake for carbohydrate and fat intake, respectively. A minimum daily protein intake of 1.3 g/kg body mass is recommended to facilitate body composition maintenance. Macronutrient intake between individuals should, however, be dictated by personal preference to support the attainment of an energy balance. A varied diet high in fruit and vegetables is highly recommended for the provision of sufficient micronutrients to support physiological processes, such as vitamin B12 and folate intake to facilitate red blood cell production. Antioxidants, such as vitamin C and E, are also recommended to reduce oxidised molecules, e.g. free radicals, whilst selenium and zinc intake may be beneficial to reinforce endogenous antioxidant reserves. In addition, tailored hydration and carbohydrate fueling strategies for underwater work are also advised

Poorly controlled type 2 diabetes is accompanied by significant morphological and ultrastructural changes in both erythrocytes and in thrombin-generated fibrin: implications for diagnostics

We have noted in previous work, in a variety of inflammatory diseases, where iron dysregulation occurs, a strong tendency for erythrocytes to lose their normal discoid shape and to adopt a skewed morphology (as judged by their axial ratios in the light microscope and by their ultrastructure in the SEM). Similarly, the polymerization of fibrinogen, as induced in vitro by added thrombin, leads not to the common ‘spaghetti-like’ structures but to dense matted deposits. Type 2 diabetes is a known inflammatory disease. In the present work, we found that the axial ratio of the erythrocytes of poorly controlled (as suggested by increased HbA1c levels) type 2 diabetics was significantly increased, and that their fibrin morphologies were again highly aberrant. As judged by scanning electron microscopy and in the atomic force microscope, these could be reversed, to some degree, by the addition of the iron chelators deferoxamine (DFO) or deferasirox (DFX). As well as their demonstrated diagnostic significance, these morphological indicators may have prognostic value.Biotechnology and Biological Sciences Research Council (grant BB/L025752/1) as well as the National Research Foundation (NRF) of South Africa.http://www.cardiab.com/hb201

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference