Modeling ionic flow between small targets: insights from diffusion and electro-diffusion theory

The flow of ions through permeable channels causes voltage drop in physiological nanodomains such as synapses, dendrites and dendritic spines, and other protrusions. How the voltage changes around channels in these nanodomains has remained poorly studied. We focus this book chapter on summarizing recent efforts in computing the steady-state current, voltage and ionic concentration distributions based on the Poisson-Nernst-Planck equations as a model of electro-diffusion. We first consider the spatial distribution of an uncharged particle density and derive asymptotic formulas for the concentration difference by solving the Laplace's equation with mixed boundary conditions. We study a constant particles injection rate modeled by a Neumann flux condition at a channel represented by a small boundary target, while the injected particles can exit at one or several narrow patches. We then discuss the case of two species (positive and negative charges) and take into account motions due to both concentration and electrochemical gradients. The voltage resulting from charge interactions is calculated by solving the Poisson's equation. We show how deep an influx diffusion propagates inside a nanodomain, for populations of both uncharged and charged particles. We estimate the concentration and voltage changes in relations with geometrical parameters and quantify the impact of membrane curvature.Comment: 17 pages, 8 figures, 1 tabl

Global electro-thermal modelling and circuit-type simulation of SiC Mosfet power devices in short-circuit operation for critical system analysis

International audienceThe purpose of this paper is to present, for the first time, a global transient electrothermal model and simulation results of commercially recent silicon carbide (SiC) power MOSFET devices. The developed models aim is faithfully transposing specifically experimental short-circuit (SC) behaviour of the studied components, ready-to-use for the analysis of an inverter-leg malfunctioning. After extensive experimentation, a thermal model of the SiC die allows to develop models of gate-leakage current and drain-source current during SC. After verifying the robustness of the proposed models, an original circuit-type with an easy implementation is performed using a commercial circuit simulation tool

Activation du système rénine-angiotensine pulmonaire et remodelage pulmonaire dans l'insuffisance cardiaque chronique

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal

Narrow escape in composite domains forming heterogeneous networks

Cellular networks are often composed of thin tubules connecting much larger node compartments. These structures serve for active or diffusion transport of proteins. Examples are glial networks in the brain, the endoplasmic reticulum in cells or dendritic spines located on dendrites. In this latter case, a large ball forming the head is connected by a narrow passage. In all cases, how the transport of molecules, ions or proteins is regulated determines the time scale of chemical reactions or signal transduction. In the present study, based on modeling diffusion in three dimensions, we compute the mean time for a Brownian particle to reach a narrow target inside such a composite network made of tubules connected to spherical nodes. We derive asymptotic formulas by solving a mixed Neumann-Dirichlet boundary value problem with small Dirichlet part. We first consider the case of a network domain organized in a 2-D lattice structure that consists of spherical ball compartments connected via narrow cylindrical passages. When there is a single target we derive a matrix equation for each Mean First Passage Time (MFPT) averaged over each spherical compartment. We then consider a composite domain consisting of a spherical head-like domain connected to a large cylinder via a narrow cylindrical neck. For Brownian particles starting within the narrow neck, we derive formulas for the MFPT to reach a target on the spherical head. When diffusing particles can be absorbed upon hitting additional absorbing boundaries of the large cylinder, we compute the probability and conditional MFPT to reach a target. We compare these formulas with numerical solutions of the mixed boundary value problem and with Brownian simulations. To conclude, the present analysis reveals that the mean arrival time, driven by diffusion in heterogeneous networks, is controlled by the target and narrow passage sizes.Comment: 33 pages and 13 figure

Serosurvey for viruses associated with reproductive failure in newly introduced gilts and in multiparous sows in Belgian sow herds

A serosurvey for viruses associated with reproductive disorders was conducted in 25 conventional Belgian farms. Serum antibody titers for porcine reproductive and respiratory syndrome virus (PRRSV), porcine circovirus type 2 (PCV2), porcine parvovirus (PPV), porcine enteroviruses (PEV) and swine influenza viruses (SIV) were determined in gilts and sows. All the animals were seropositive for PCV2 and >95% were seropositive for all 4 embryopathogenic PEV serotypes. Consequently, special preventive measures appear to be unnecessary for these viruses. In I farm, non-vaccinated gilts were found to run a risk of developing PPV-induced reproductive disorders. Vaccination against PPV could exclude this risk. In 10 farms, gilts seronegative for one or more specific SIV subtypes were introduced into a herd that had previously been infected with the same subtypes. Vaccination of gilts against SIV may prevent reproductive disorders in gilts and respiratory problems in their offspring. In I farm, newly purchased gilts that were possibly shedding PRRSV were introduced into a PRRSV seronegative sow herd. Serological screening prior to purchase or vaccination of the sows could have resolved this dangerous situation

Sur un modèle d'érythropoïèse comportant un taux de mortalité dynamique

Ce mémoire concerne la modélisation mathématique de l’érythropoïèse, à savoir le processus de production des érythrocytes (ou globules rouges) et sa régulation par l’érythropoïétine, une hormone de contrôle. Nous proposons une extension d’un modèle d’érythropoïèse tenant compte du vieillissement des cellules matures. D’abord, nous considérons un modèle structuré en maturité avec condition limite mouvante, dont la dynamique est capturée par des équations d’advection. Biologiquement, la condition limite mouvante signifie que la durée de vie maximale varie afin qu’il y ait toujours un flux constant de cellules éliminées. Par la suite, des hypothèses sur la biologie sont introduites pour simplifier ce modèle et le ramener à un système de trois équations différentielles à retard pour la population totale, la concentration d’hormones ainsi que la durée de vie maximale. Un système alternatif composé de deux équations avec deux retards constants est obtenu en supposant que la durée de vie maximale soit fixe. Enfin, un nouveau modèle est introduit, lequel comporte un taux de mortalité augmentant exponentiellement en fonction du niveau de maturité des érythrocytes. Une analyse de stabilité linéaire permet de détecter des bifurcations de Hopf simple et double émergeant des variations du gain dans la boucle de feedback et de paramètres associés à la fonction de survie. Des simulations numériques suggèrent aussi une perte de stabilité causée par des interactions entre deux modes linéaires et l’existence d’un tore de dimension deux dans l’espace de phase autour de la solution stationnaire.This thesis addresses erythropoiesis mathematical modeling, which is the process of erythrocytes production and its regulation by erythropeitin. We propose an erythropoiesis model extension which includes aging of mature cells. First, we consider an age-structured model with moving boundary condition, whose dynamics are represented by advection equations. Biologically, the moving boundary condition means that the maximal lifespan varies to account for a constant degraded cells flux. Then, hypotheses are introduced to simplify and transform the model into a system of three delay differential equations for the total population, the hormone concentration and the maximal lifespan. An alternative model composed of two equations with two constant delays is obtained by supposing that the maximal lifespan is constant. Finally, a new model is introduced, which includes an exponential death rate depending on erythrocytes maturity level. A linear stability analysis allows to detect simple and double Hopf bifurcations emerging from variations of the gain in the feedback loop and from parameters associated to the survival function. Numerical simulations also suggest a loss of stability caused by interactions between two linear modes and the existence of a two dimensional torus in the phase space close to the stationary solution