ISOGEOMETRIC OVERLAPPING ADDITIVE SCHWARZ PRECONDITIONERS IN COMPUTATIONAL ELECTROCARDIOLOGY

In this thesis we present and study overlapping additive Schwarz preconditioner for the isogeometric discretization of reaction-diffusion systems modeling the heart bioelectrical activity, known as the Bidomain and Monodomain models. The cardiac Bidomain model consists of a degenerate system of parabolic and elliptic PDE, whereas the simplified Monodomain model consists of a single parabolic equation. These models include intramural fiber rotation, anisotropic conductivity coefficients and are coupled through the reaction term with a system of ODEs, which models the ionic currents of the cellular membrane. The overlapping Schwarz preconditioner is applied with a PCG accelerator to solve the linear system arising at each time step from the isogeometric discretization in space and a semi-implicit adaptive method in time. A theoretical convergence rate analysis shows that the resulting solver is scalable, optimal in the ratio of subdomain/element size and the convergence rate improves with increasing overlap size. Numerical tests in three-dimensional ellipsoidal domains confirm the theoretical estimates and additionally show the robustness with respect to jump discontinuities of the orthotropic conductivity coefficients

LKB1 signaling is activated in CTNNB1 -mutated HCC and positively regulates β-catenin-dependent CTNNB1 -mutated HCC

International audienceCTNNB1‐mutated HCC. They were found to be well‐differentiated, almost never steatotic, and often cholestatic, with a microtrabecular or acinar growth pattern. Here, we investigated whether LKB1, which controls energy metabolism, cell polarity, and cell growth, mediates the specific phenotype of CTNNB1‐mutated HCC. The LKB1 protein was overexpressed in CTNNB1‐mutated HCC and oncogenic activation of β‐catenin in human HCC cells induced the post‐transcriptional accumulation of the LKB1 protein encoded by the LKB1 (STK11) gene. Hierarchical clustering, based on the expression of a murine hepatic liver Lkb1 (Stk11) signature in a human public dataset, identified a HCC cluster, composed of almost all the CTNNB1‐mutated HCC, that expresses a hepatic liver LKB1 program. This was confirmed by RT‐qPCR of an independent cohort of CTNNB1‐mutated HCC and the suppression of the LKB1‐related profile upon β‐catenin silencing of CTNNB1‐mutated human hepatoma cell lines. Previous studies described an epistatic relationship between LKB1 and CTNNB1 in which LKB1 acts upstream of CTNNB1. Thus, we also analyzed the consequences of Lkb1 deletion on the zonation of hepatic metabolism, known to be the hallmark of β‐catenin signaling in the liver. Lkb1 was required for the establishment of metabolic zonation in the mouse liver by positively modulating β‐catenin signaling. We identified positive reciprocal cross talk between the canonical Wnt pathway and LKB1, both in normal liver physiology and during tumorigenesis that likely participates in the amplification of the β‐catenin signaling by LKB1 and the distinctive phenotype of the CTNNB1‐mutated HCC

Isogeometric approximation of cardiac electrophysiology models on surfaces: An accuracy study with application to the human left atrium

We consider Isogeometric Analysis in the framework of the Galerkin method for the spatial approximation of cardiac electrophysiology models defined on NURBS surfaces; specifically, we perform a numerical comparison between basis functions of degree p ≥ 1 and globally C k -continuous, with k = 0 or p − 1, to find the most accurate approximation of a propagating front with the minimal number of degrees of freedom. We show that B-spline basis functions of degree p ≥ 1, which are C p−1 -continuous capture accurately the front velocity of the transmembrane potential even with moderately refined meshes; similarly, we show that, for accurate tracking of curved fronts, high-order continuous B-spline basis functions should be used. Finally, we apply Isogeometric Analysis to an idealized human left atrial geometry described by NURBS with physiologically sound fiber directions and anisotropic conductivity tensor to demonstrate that the numerical scheme retains its favorable approximation properties also in a more realistic setting

Study of the crosstalk between the Wnt/β-catenin pathway and LKB1 in hepatic physiopathology

Le foie est un organe qui exerce un rôle majeur dans le contrôle de l’homéostasie métabolique et énergétique de l’organisme en maintenant la glycémie à un taux constant. LKB1 est une sérine-thréonine kinase qui joue un rôle clef dans la physiologie cellulaire en couplant le contrôle du métabolisme au statut énergétique de la cellule. A l’aide de modèles murins ayant une délétion de LKB1 dans les hépatocytes adultes, nous avons identifié un rôle complexe pour LKB1 au sein de l’homéostasie énergétique. L’objectif de ma thèse était de caractériser ce phénotype et d’en comprendre les bases physiologiques. Nos résultats montrent une hyperglycémie à jeun chez les animaux mutants, associée à une perte de masse maigre (muscle), une accumulation du glycogène à jeun et une activation constitutive de la voie de l’insuline, qui, à long terme, conduit à une cachexie. Nos résultats suggèrent que Lkb1 hépatique exercerait un dialogue complexe avec la signalisation insuline dans le contrôle de la gluconéogenèse avec une dépendance énergétique aux acides aminés. Nous avons aussi montré qu’il existait un dialogue complexe entre LKB1 et la voie Wnt/β-caténine dans le foie. En effet, les carcinomes hépatocellulaires (CHC) mutés CTNNB1 ont des caractéristiques phénotypiques en termes de polarité et de métabolisme (absence de stéatose). Nous avons émis l’hypothèse que ce phénotype pouvait être secondaire à l’activation du gène suppresseur de tumeurs LKB1. Les mutations CTNNB1 sont en effet capable d’induire l’expression protéique de LKB1 dans les lignées hépatomateuses humaines, et les CHC mutés CTNNB1 présentent une expression protéique accrue de LKB1. De plus, dans deux modèles murins d’invalidation hépatospécifique de Lkb1, LKB1 est apparu comme requis pour l’activation du programme transcriptionnel de β-caténine mais de façon dépendante du stade de développement et du contexte nutritionnel.The liver plays a major role in the control of both metabolic and energetic homeostasis in the body by maintaining glycemia. LKB1 is a serine-threonine kinase that plays a crucial role in cell physiology by controlling cell metabolism and cell energetic status. Using murine model with LKB1 hepatospecific deletion, we identified a complex role for LKB1 in energy homeostasis. The aim of my thesis was to characterize this phenotype and to understand its physiological basis. Our results show a hyperglycemia at fasted state in mutants animals, associated with a loss of dry mass, a glycogen accumulation and a constitutive activation of insulin signaling, which leads to a cachexia at long term. Our results suggest that hepatic Lkb1 is involved in a cross talk with insulin signaling in the control of neoglucogenesis with amino acid dependence. We also showed a cross talk between LKB1 and Wnt/β-catenin signaling in the liver. Indeed, CTNNB1-mutated hepatocellular carcinoma (HCC) have phenotypic features in terms of polarity and metabolism (lack of lipid accumulation). Our hypothesis is that this phenotype would be secondary to the activation of the tumour suppressor gene LKB1. CTNNB1 mutations induce LKB1 proteic expression in human hepatoma cell lines and CTNNB1-mutated HCC show an increased proteic LKB1 expression. In two murine models of Lkb1 hepatospecific invalidation, LKB1 seems to be necessary for the activation of the β-catenin transcriptional program in a way that is dependent on developpemental state and nutritional context

Hamiltonian Cycles in Cayley Graphs of Gyrogroups

In this study, we investigate Hamiltonian cycles in the right-Cayley graphs of gyrogroups. More specifically, we give a gyrogroup version of the factor group lemma and show that some right-Cayley graphs of certain gyrogroups are Hamiltonian

An updated computational model of rabbit sinoatrial action potential to investigate the mechanisms of heart rate modulation

The cellular basis of cardiac pacemaking is still debated. Reliable computationalmodels of the sinoatrial node (SAN) action potential (AP) may help gain a deeper understanding of the phenomenon. Recently, novel models incorporating detailed Ca2+-handling dynamics have been proposed, but they fail to reproduce a number of experimental data, and more specifically effects of \u2018funny\u2019 (If ) current modifications. We therefore developed a SAN AP model, based on available experimental data, in an attempt to reproduce physiological and pharmacological heart rate modulation. Cell compartmentalization and intracellular Ca2+-handling mechanisms were formulated as in the Maltsev\u2013Lakatta model, focusing on Ca2+-cycling processes. Membrane current equations were revised on the basis of published experimental data.Modifications of the formulation of currents/pumps/exchangers to simulate If blockers, autonomic modulators and Ca2+-dependent mechanisms (ivabradine, caesium, acetylcholine, isoprenaline, BAPTA) were derived from experimental data. The model generates AP waveforms typical of rabbit SAN cells, whose parameters fall within the experimental ranges: 352 ms cycle length, 80 mV AP amplitude, 1258 mV maximum diastolic potential (MDP), 108 ms APD50, and 7.1Vs 121 maximum upstroke velocity. Rate modulation by If -blocking drugs agrees with experimental findings: 20% and 22% caesium-induced (5mM) and ivabradine-induced (3 \u3bcM) rate reductions, respectively, due to changes in diastolic depolarization (DD) slope, with no changes in either MDP or take-off potential (TOP). The model consistently reproduces the effects of autonomic modulation: 20% rate decreasewith 10 nMacetylcholine and28%increasewith 1 \u3bcMisoprenaline, again entirely due C 2012 The Authors. The Journal of Physiology C 2012 The Physiological Society DOI: 10.1113/jphysiol.2012.229435 4484 S. Severi and others J Physiol 590.18 to increase in theDDslope,with no changes in eitherMDPorTOP.Model testing of BAPTAeffects showed slowing of rate, 1226%, without cessation of beating. Our up-to-date model describes satisfactorily experimental data concerning autonomic stimulation, funny-channel blockade and inhibition of the Ca2+-related system by BAPTA, making it a useful tool for further investigation. Simulation results suggest that a detailed description of the intracellular Ca2+ fluxes is fully compatiblewith the observation that If is a major component of pacemaking and rate modulation

Generation of Mice with Hepatocyte-Specific Conditional Deletion of Notum

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