Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states

Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter.

An infrared reflection-absorption spectroscopic (IRRAS) study of the interaction of lipid A and lipopolysaccharide Re with endotoxin-binding proteins.

Lipopolysaccharides (LPS, endotoxins) are main constituents of the outer membranes of Gram-negative bacteria, with the 'endotoxic principle' lipid A anchoring LPS into the membrane. When LPS is removed from the bacteria by the action of the immune system or simply by cell dividing, it may interact strongly with immunocompetent cells such as mononuclear cells. This interaction may lead, depending on the LPS concentration, to beneficial (at low) or pathophysiological (at high concentrations) reactions, the latter frequently causing the septic shock syndrome. There is a variety of endogenous LPS-binding proteins. To this class belong lactoferrin (LF) and hemoglobin (Hb), which have been shown to suppress and enhance the LPS-induced cytokine secretion in mononuclear cells, respectively. To elucidate the interaction mechanisms of endotoxins with these proteins, we have investigated in an infrared reflection-absorption spectroscopy (IRRAS) study the interaction of LPS or lipid A monolayers at the air/water interface with LF and Hb proteins, injected into the aqueous subphase. The data are clearly indicative of completely different interaction mechanisms of the endotoxins with the proteins, with the LF acting only at the LPS backbone, whereas Hb incorporates into the lipid monolayer. These data allow an understanding of the different reactivities in the biomedicinal systems.

Population pharmacokinetics and clinical response for artemether-lumefantrine in pregnant and nonpregnant women with uncomplicated Plasmodium falciparum malaria in Tanzania.

Artemether-lumefantrine (AL) is the first-line treatment for uncomplicated malaria in the second and third trimesters of pregnancy. Its efficacy during pregnancy has recently been challenged due to altered pharmacokinetic (PK) properties in this vulnerable group. The aim of this study was to determine the PK profile of AL in pregnant and nonpregnant women and assess their therapeutic outcome. Thirty-three pregnant women and 22 nonpregnant women with malaria were treated with AL (80/480 mg) twice daily for 3 days. All patients provided five venous plasma samples for drug quantification at random times over 7 days. Inter- and intraindividual variability was assessed, and the effects of covariates were quantified using a nonlinear mixed-effects modeling approach (NONMEM). A one-compartment model with first-order absorption and elimination with linear metabolism from drug to metabolite fitted the data best for both arthemether (AM) and lumefantrine (LF) and their metabolites. Pregnancy status and diarrhea showed a significant influence on LF PK. The relative bioavailability of lumefantrine and its metabolism rate into desmethyl-lumefantrine were, respectively, 34% lower and 78% higher in pregnant women than in nonpregnant patients. The overall PCR-uncorrected treatment failure rates were 18% in pregnant women and 5% in nonpregnant women (odds ratio [OR] = 4.04; P value of 0.22). A high median day 7 lumefantrine concentration was significantly associated with adequate clinical and parasitological response (P = 0.03). The observed reduction in the relative bioavailability of lumefantrine in pregnant women may explain the higher treatment failure in this group, mostly due to lower posttreatment prophylaxis. Hence, a modified treatment regimen of malaria in pregnancy should be considered.

On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher-Kolmogorov-Petrovskii-Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

Population pharmacokinetics of mefloquine, piperaquine and artemether-lumefantrine in Cambodian and Tanzanian malaria patients.

BACKGROUND: Inter-individual variability in plasma concentration-time profiles might contribute to differences in anti-malarial treatment response. This study investigated the pharmacokinetics of three different forms of artemisinin combination therapy (ACT) in Tanzania and Cambodia to quantify and identify potential sources of variability. METHODS: Drug concentrations were measured in 143 patients in Tanzania (artemether, dihydroartemisinin, lumefantrine and desbutyl-lumefantrine), and in 63 (artesunate, dihydroartemisinin and mefloquine) and 60 (dihydroartemisinin and piperaquine) patients in Cambodia. Inter- and intra-individual variabilities in the pharmacokinetic parameters were assessed and the contribution of demographic and other covariates was quantified using a nonlinear mixed-effects modelling approach (NONMEM®). RESULTS: A one-compartment model with first-order absorption from the gastrointestinal tract fitted the data for all drugs except piperaquine (two-compartment). Inter-individual variability in concentration exposure was about 40% and 12% for mefloquine. From all the covariates tested, only body weight (for all antimalarials) and concomitant treatment (for artemether only) showed a significant influence on these drugs' pharmacokinetic profiles. Artesunate and dihydroartemisinin could not be studied in the Cambodian patients due to insufficient data-points. Modeled lumefantrine kinetics showed that the target day 7 concentrations may not be achieved in a substantial proportion of patients. CONCLUSION: The marked variability in the disposition of different forms of ACT remained largely unexplained by the available covariates. Dosing on body weight appears justified. The concomitance of unregulated drug use (residual levels found on admission) and sub-optimal exposure (variability) could generate low plasma levels that contribute to selecting for drug-resistant parasites.

Population pharmacokinetic-pharmacodynamic modelling of angiotensin receptor blockade in healthy volunteers.

OBJECTIVE: To compare the pharmacokinetic and pharmacodynamic characteristics of angiotensin II receptor antagonists as a therapeutic class. DESIGN: Population pharmacokinetic-pharmacodynamic modelling study. METHODS: The data of 14 phase I studies with 10 different drugs were analysed. A common population pharmacokinetic model (two compartments, mixed zero- and first-order absorption, two metabolite compartments) was applied to the 2685 drug and 900 metabolite concentration measurements. A standard nonlinear mixed effect modelling approach was used to estimate the drug-specific parameters and their variabilities. Similarly, a pharmacodynamic model was applied to the 7360 effect measurements, i.e. the decrease of peak blood pressure response to intravenous angiotensin challenge recorded by finger photoplethysmography. The concentration of drug and metabolite in an effect compartment was assumed to translate into receptor blockade [maximum effect (Emax) model with first-order link]. RESULTS: A general pharmacokinetic-pharmacodynamic (PK-PD) model for angiotensin antagonism in healthy individuals was successfully built up for the 10 drugs studied. Representatives of this class share different pharmacokinetic and pharmacodynamic profiles. Their effects on blood pressure are dose-dependent, but the time course of the effect varies between the drugs. CONCLUSIONS: The characterisation of PK-PD relationships for these drugs gives the opportunity to optimise therapeutic regimens and to suggest dosage adjustments in specific conditions. Such a model can be used to further refine the use of this class of drugs.

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

Ab initio absorption spectrum of NiO combining molecular dynamics with the embedded cluster approach in a discrete reaction field

We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the material model. By means ofcomplete active space self-consistent field second-order perturbation theory (CASPT2) calculations on embedded clusters extracted from the resulting trajectory, we describe localized spectroscopic phenomena on NiO with an efficient treatment of electron correlation. The inclusion of thermal motion into the theoretical description allowsus to study electronic transitions that, otherwise, would be dipole forbidden in the ideal structure and results in a natural reproduction of the band broadening. Moreover, we improved the embedded cluster model by incorporating self-consistently at the complete active space self-consistent field (CASSCF) level a discrete (or direct) reaction field (DRF) in the cluster surroundings. The DRF approach offers an efficient treatment ofelectric response effects of the crystalline embedding to the electronic transitions localized in the cluster. We offer accurate theoretical estimates of the absorption spectrum and the density of states around the Fermi level of NiO, and a comprehensive explanation of the source of the broadening and the relaxation of the charge transferstates due to the adaptation of the environment

Plasma and cerebrospinal fluid population pharmacokinetics of temozolomide in malignant glioma patients

RESUME : Objectif: Le glioblastome multiforme (GBM) est la tumeur cérébrale maligne la plus agressive qui conduit au décès de la majorité des patients moins d'une année après le diagnostic. La plupart des agents chimiothérapeutiques actuellement disponibles ne traversent pas la barrière hémato¬encéphalique et ne peuvent par conséquent pas être utilisés pour ce type de tumeur. Le Temozolomide (TMZ) est un nouvel agent alkylant récemment développé pour le traitement des gliomes malins. A ce jour, très peu d'informations sont disponibles sur la pénétration intra-cérébrale de cet agent. Au cours d'une étude pilote de phase II menée auprès de 64 patients atteints de GBM, l'administration précoce de TMZ combinée à une radiothérapie standard (RT) afin d'intervenir au plus tôt dans l'évolution de la maladie, a permis de prolonger la survie de ces patients, résultat qui pu être confirmé par la suite lors de l'étude randomisée de phase III. L'objectif de cette étude a été de déterminer les paramètres pharmacocinétique du TMZ dans le plasma et le liquide céphalo-rachidien (LCR), d'évaluer l'influence de certains facteurs individuels (âge, sexe, surface corporelle, fonction rénale/hépatique, co-médications, RT concomitante) sur ces différents paramètres, et enfin d'explorer la relation existant entre l'exposition au TMZ et certains marqueurs cliniques d'efficacité et de toxicité. Matériel et Méthode: Les concentrations de TMZ ont été mesurées par chromatographie liquide à haute performance (HPLC) dans le plasma et le LCR de 35 patients atteints de GBM nouvellement diagnostiqués (étude pilote) ou de gliomes malins en récidive (étude récidive). L'analyse pharmacocinétique de population a été réalisée à l'aide du programme NONMEM. L'exposition systémique et cérébrale, définie par les AUC (Area Under the time-concentration Curve) dans le plasma et le LCR, a été estimée pour chaque patient et corrélée à la toxicité, la survie ainsi que la survie sans progression tumorale. Résultats: Un modèle à 1 compartiment avec une cinétique d'absorption et de transfert Kplasma -> LCR de ordre a été retenu afin de décrire le profil pharmacocinétique du TMZ. Les valeurs moyennes de population ont été de 10 L/h pour la clairance, de 30.3 L pour le volume de distribution, de 2.1 h pour la 1/2 vie d'élimination, de 5.78 hE-1 pour la constante d'absorption, de 7.2 10E4 hE-1 pour Kplasma->LCR et de 0.76 hE-1 pour KLCR plasma. La surface corporelle a montré une influence significative sur la clairance et le volume de distribution, alors que le sexe influence la clairance uniquement. L'AUC mesurée dans le LCR représente ~20% de celle du plasma et une augmentation de 15% de Kplasma->LCR a été observée lors du traitement concomitant de radiochimiothérapie. Conclusions: Cette étude est la première analyse pharmacocinétique effectuée chez l'homme permettant de quantifier la pénétration intra-cérébrale du TMZ. Le rapport AUC LCR/AUC Plasma a été de 20%. Le degré d'exposition systémique et cérébral au TMZ ne semble pas être un meilleur facteur prédictif de la survie ou de la tolérance au produit que ne l'est la dose cumulée seule. ABSTRACT Purpose: Scarce information is available on the brain penetration of temozolomide (TMZ), although this novel methylating agent is mainly used for the treatment of ma¬lignant brain tumors. The purpose was to assess TNIZ phar¬macokinetics in plasma and cerebrospinal fluid (CSF) along with its inter-individual variability, to characterize covari¬ates and to explore relationships between systemic or cere¬bral drug exposure and clinical outcomes. Experimental Design: TMZ levels were measured by high-performance liquid chromatography in plasma and CSF samples from 35 patients with newly diagnosed or recurrent malignant gliomas. The population pharmacoki¬netic analysis was performed with nonlinear mixed-effect modeling software. Drug exposure, defined by the area un¬der the concentration-time curve (AUC) in plasma and CSF, was estimated for each patient and correlated with toxicity, survival, and progression-free survival. Results: A three-compartment model with first-order absorption and transfer rates between plasma and CSF described the data appropriately. Oral clearance was 10 liter/h; volume of distribution (VD), 30.3 liters; absorption constant rate, 5.8 hE-1; elimination half-time, 2.1 h; transfer rate from plasma to CSF (Kplasma->CSF), 7.2 x 10E-4hE-1 and the backwards rate, 0.76hE-1. Body surface area signifi¬cantly influenced both clearance and VD, and clearance was sex dependent. The AU CSF corresponded to 20% of the AUCplasma. A trend toward an increased K plasma->CSF of 15% was observed in case of concomitant radiochemo-therapy. No significant correlations between AUC in plasma or CSF and toxicity, survival, or progression-free survival were apparent after deduction of dose-effect. Conclusions: This is the first human pharmacokinetic study on TMZ to quantify CSF penetration. The AUC CSF/ AUC plasma ratio was 20%. Systemic or cerebral exposures are not better predictors than the cumulative dose alone for both efficacy and safety.

Fault diagnosis by refining the parameter uncertainty space of nonlinear dynamic systems

This paper deals with fault detection and isolation problems for nonlinear dynamic systems. Both problems are stated as constraint satisfaction problems (CSP) and solved using consistency techniques. The main contribution is the isolation method based on consistency techniques and uncertainty space refining of interval parameters. The major advantage of this method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements, and model errors. Interval calculations bring independence from the assumption of monotony considered by several approaches for fault isolation which are based on observers. An application to a well known alcoholic fermentation process model is presented

Constraint satisfaction techniques under uncertain conditions for fault diagnosis in nonlinear dynamic systems

The speed of fault isolation is crucial for the design and reconfiguration of fault tolerant control (FTC). In this paper the fault isolation problem is stated as a constraint satisfaction problem (CSP) and solved using constraint propagation techniques. The proposed method is based on constraint satisfaction techniques and uncertainty space refining of interval parameters. In comparison with other approaches based on adaptive observers, the major advantage of the presented method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements and model errors and without the monotonicity assumption. In order to illustrate the proposed approach, a case study of a nonlinear dynamic system is presented

Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: umbrella motion in NH3

A general reduced dimensionality finite field nuclear relaxation method for calculating vibrational nonlinear optical properties of molecules with large contributions due to anharmonic motions is introduced. In an initial application to the umbrella (inversion) motion of NH3 it is found that difficulties associated with a conventional single well treatment are overcome and that the particular definition of the inversion coordinate is not important. Future applications are described

Field-induced coordinates for the determination of dynamic vibrational nonlinear optical properties

Three conjugated organic molecules that span a range of polarity and valence-bond/charge transfer characteristics were studied. It was found that dispersion can be insignificant, and that adequate treatment can be achieved with frequency-dependent field-induced vibrational coordinates (FD-FICs)