Intraerythrocytic pH variations during hemodialysis: A 31P NMR study

Intraerythrocytic pH variations during hemodialysis: A 31P NMR study. Before hemodialysis, patients have an intraerythrocytic pH (pHi) and an extracellular pH, measured in whole blood (pHo), which are lower than those of healthy controls. During bicarbonate hemodialysis, pHi values continuously increase, approaching a normal value at the end of the session. Concomitantly, pHo values follow similar variations. During acetate hemodialysis, pHi values exhibit a steep initial decrease, reaching a minimum after about 15 minutes. Concurrently, however, pHo values decrease only slightly. This phenomenon seems to originate in the intraerythrocytic medium and might be due to a shift in intracellular CO2/bicarbonate equilibrium. This drop in pHi exhibits interpatient variability, suggesting that the magnitude of pH decrease would be correlated with the degree of the problems observed in some patients undergoing acetate hemodialysis

Clinical efficacy, safety, and immunogenicity of a live attenuated tetravalent dengue vaccine (CYD-TDV) in Children: a systematic review with meta-analysis

BACKGROUND Dengue hemorrhagic fever is the leading cause of hospitalization and death in children living in Asia and Latin America. There is an urgent need for an effective and safe dengue vaccine to reduce morbidity and mortality in this high-risk population given the lack of dengue specific treatment at present. This review aims to determine the efficacy, safety, and immunogenicity of CYD-TDV vaccine in children. METHODS This is a systematic review including meta-analysis of randomized controlled clinical trial data from Embase, Medline, the Cochrane Library, Web of Science, and ClinicalTrials.gov. Studies that assessed CYD-TDV vaccine efficacy [(1 - RR)*100], safety (RR), and immunogenicity (weighted mean difference) in children were included in this study. Random effects model was employed to analyze patient-level data extracted from primary studies. RESULTS The overall efficacy of CYD-TDV vaccine was 54% (40-64), while serotype-specific efficacy was 77% (66-85) for DENV4, 75% (65-82) for DENV3, 50% (36-61) for DENV1, and 34% (14-49) for DENV2. 15% (-174-74) vaccine efficacy was obtained for the unknown serotype. Meta-analysis of included studies with longer follow-up time (25 months) revealed that CYD-TDV vaccine significantly increased the risk of injection site reactions (RR = 1.1: 1.04-1.17; p-value = 0.001). Immunogenicity (expressed as geometric mean titers) in descending order was 439.7 (331.7-547.7), 323 (247 - 398.7), 144.1 (117.9-170.2), and 105 (88.7-122.8) for DENV3, DENV2, DENV1, and DENV4, respectively. CONCLUSION CYD-TDV vaccine is effective and immunogenic in children overall. Reduced efficacy of CYD-TDV vaccine against DENV2 notoriously known for causing severe dengue infection and dengue outbreaks cause for serious concern. Post hoc meta-analysis of long-term follow-up data (≥25 months) from children previously vaccinated with CYD-TDV vaccine is needed to make a conclusion regarding CYD-TDV vaccine safety in children. However, CYD-TDV vaccine should be considered for use in regions where DENV2 is not endemic as currently there is no specific treatment for dengue infection

Influence of the mode of reproduction on dispersal evolution during species invasion

We consider a reaction-diffusion-reproduction equation, modeling a population which is spatially heterogeneous. The dispersion of each individuals is influenced by its phenotype. In the literature, the asymptotic propagation speed of an asexual population has already been rigorously determined. In this paper we focus on the difference between the asexual reproduction case, and the sexual reproduction case, involving a non-local term modeling the reproduction. This comparison leads to a different invasion speed according to the reproduction. After a formal analysis of both cases, leading to a heuristic of the asymptotic behaviour of the invasion fronts, we give some numerical evidence that the acceleration rate of the spatial spreading of a sexual population is slower than the acceleration rate of an asexual one. The main difficulty to get sharper results on a transient comes from the non-local sexual reproduction term

Asymptotic limit of a spatially-extended mean-field FitzHugh-Nagumo model

International audienceWe consider a spatially extended mean-field model of a FitzHugh-Nagumo neural network, with a rescaled interaction kernel. Our main purpose is to prove that its asymptotic limit in the regime of strong local interactions converges toward a system of reaction-diffusion equations taking account for theaverage quantities of the network. Our approach is based on a modulated energy argument, to compare the macroscopic quantities computed from the solution of the transport equation, and the solution of the limit system. The main difficulty, compared to the literature, lies in the need of regularity in space of the solutions of the limit system and a careful control of an internal nonlocal dissipation

Etude de modèles macroscopiques de réseaux de neurones spatialement organisés

In this thesis, we study a spatially organised neuronal network, that is the interactions between two neurons only depend on their positions. If we only consider a relatively small number of cells, the electric activity of each neuron can be modeled with the FitzHugh-Nagumo system. Yet, if we attempt to study the collective behaviour of a more sizeable assembly of neurons, we must find other models, corresponding to a larger scale of observation. Thus, the purpose of this thesis is to establish a rigourous mathematical link between the microscopic FitzHugh-Nagumo model, and macroscopic models which account for the evolution of average electrical quantities at any position in the network.The first step of our strategy consists in deriving a rigourous link between the microscopic model and an intermediary model as the number of neurons tends to infinity. We obtain a partial differential equation, which gives the evolution of the probability density of finding neurons at any time depending on their position and membrane potential. Therefore, it describes a mesoscopic scale of observation of the network.Then, we study the average electrical quantities computed from the mesoscopic model. In order to find a system of equations satisfied by these macroscopic quantities, we consider the regime of strong local interactions. To do so, we provide two different ways of rescaling. Using a relative entropy method, we find a mathematical link between the intermediary model and a reaction-diffusion system. Depending on the rescaling we choose, the diffusion term can be local or non local in space.Finally, we tackle the study of this last change of scale from a numerical analysis viewpoint. In particular, we introduce a discretization of the mesoscopic model which is asymptotic preserving in the regime of strong local interactions. Hence, we can numerically estimate rates of convergence, and we observe some dynamics of the intermediary model.Dans cette thèse, nous étudions un réseau neuronal spatialement organisé, c’est-à-dire que les interactions entre deux neurones ne dépendent que de leurs positions. Si nous ne considérons qu’un nombre relativement restreint de cellules, l’activité électrique de chaque neurone peutêtre modélisée grâce au système de FitzHugh-Nagumo. Toutefois, si nous cherchons à étudier le comportement collectif d’un groupe de neurones plus nombreux, il devient essentiel de trouver d’autres modèles, correspondant à une échelle d’observation plus grande. L’objectif decette thèse est donc d’établir un lien mathématique rigoureux entre le modèle microscopique de FitzHugh-Nagumo, et des modèles macroscopiques qui donnent l’évolution des quantités électriques moyennes à chaque position dans le réseau.La première étape de notre stratégie consiste à établir un lien rigoureux entre le modèle microscopique et un modèle intermédiaire, en faisant tendre le nombre de neurones vers l’infini. Nous obtenons une équation à dérivées partielles qui donne l’évolution de la densité de probabilité de trouver des neurones à chaque instant en fonction de leur position et de leur potentiel de membrane. Elle décrit alors une échelle mésoscopique d’observation du réseau.Ensuite, nous étudions les valeurs électriques moyennes calculées à partir du modèle mésoscopique. Afin de trouver un système d’équations satisfait par ces quantités macroscopiques, nous considérons le cas où les interactions locales entre neurones sont fortes. Pour cela, nous pro-posons deux redimensionnements possibles. En utilisant une méthode d’entropie relative, nous établissons un lien mathématique entre le modèle intermédiaire et un système de réaction-diffusion. Le terme de diffusion sera local ou non local en espace, selon le redimensionnement que nous aurons choisi.Enfin, nous attaquons l’étude de ce dernier changement d’échelle du point de vue de l’analyse numérique. En particulier, nous présentons une discrétisation du modèle mésoscopique qui préserve l’asymptotique dans le régime des interactions locales fortes. Ainsi, nous sommes capa-bles d’estimer des vitesses de convergence et d’observer des dynamiques du modèle intermédiaire

Mean-field limit of a spatially-extended FitzHugh-Nagumo neural network

International audienceWe consider a spatially-extended model for a network of interacting FitzHugh-Nagumo neurons without noise, and rigorously establish its mean-field limit towards a nonlocal kinetic equation as the number of neurons goes to infinity. Our approach is based on deterministic methods, and namely on the stability of the solutions of the kinetic equation with respect to their initial data. The main difficulty lies in the adaptation in a deterministic framework of arguments previously introduced for the mean-field limit of stochastic systems of interacting particles with a certain class of locally Lipschitz continuous interaction kernels. This result establishes a rigorous link between the microscopic and mesoscopic scales of observation of the network, which can be further used as an intermediary step to derive macroscopic models. We also propose a numerical scheme for the discretization of the solutions of the kinetic model, based on a particle method, in order to study the dynamics of its solutions, and to compare it with the microscopic model

Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions

International audienceThis paper is devoted to the numerical approximation of the spatially-extended FitzHugh-Nagumo transport equation with strong local interactions based on a particle method. In this regime, the time step can be subject to stability constraints related to the interaction kernel. To avoid this limitation, our approach is based on higher-order implicit-explicit numerical schemes. Thus, when the magnitude of the interactions becomes large, this method provides a consistent discretization of the macroscopic reaction-diffusion FitzHugh-Nagumo system. We carry out some theoretical proofs and perform several numerical experiments that establish a solid validation of the method and its underlying concepts

Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system

International audienceWe introduce a spatially extended transport kinetic FitzHugh-Nagumo model with forced local interactions and prove that its hydrodynamic limit converges towards the classical nonlocal reaction-diffusion FitzHugh-Nagumo system. Our approach is based on a relative entropy method, where the macroscopic quantities of the kinetic model are compared with the solution to the nonlocal reaction-diffusion system. This approach allows to make the rigorous link between kinetic and reaction-diffusion models