An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

On Seliger and Whitham`s variational principle for hydrodynamic systems from the point of view of `fictitious particles`

FAPESP, the Sao Paulo State Research Foundation[04/04611-5]

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

Statins withdrawal, vascular complications, rebound effect and similitude

Hahnemann considered the secondary action of medicines to be a law of nature and reviewed the conditions under which it occurs. It is closely related to the rebound effects observed with many modern drugs. I review the evidence of the rebound effect of statins that support the similitude principle. In view of their indications in primary and secondary prevention of cardiovascular diseases, statins are widely prescribed. Besides reducing cholesterol biosynthesis, they provide vasculoprotective effects (pleiotropic effects), including improvement of endothelial function, increased nitric oxide bioavailability, antioxidant properties, inhibition of inflammatory and thrombogenic responses, stabilisation of atherosclerotic plaques, and others. Recent studies suggest that suspension of statin treatment leads to a rebound imparing of vascular function, and increasing morbidity and mortality in patients with vascular diseases. Similarly to other classes of modern palliative drugs, this rebound effect is the same as a secondary action or vital reaction described by Samuel Hahnemann, and used in homeopathy in a therapeutic sense. Homeopathy (2010) 99, 255-262.

Rebound acid hypersecretion after withdrawal of gastric acid suppressing drugs: new evidence of similitude

Background: Homeopathy is based on the principle of similitude (similia similibus curentur) using medicines that cause effects similar to the symptoms of disease in order to stimulate the reaction of the organism. Such vital, homeostatic or paradoxical reaction of the organism is closely related to rebound effect of drugs. Method: Review of the literature concerning the rebound effects of drugs used to suppress gastric acidity, particularly proton pump inhibitors (PPIs). Results: The mechanism of action of these effects is discussed. Rebound in terms of clinical symptoms and physiological effects occur in about 40% of people taking PPIs, their timing depends on the half-life of the drug and the adaptation period of the physiological mechanisms involved. The wide use of PPIs may be linked to the rising incidence of carcinoid tumours. Conclusions: These findings support Hahnemann`s concept of secondary action of drugs. We are developing a homeopathic materia medica and repertory of modern drugs on the basis of reported rebound effects. Homeopathy (2011) 100, 148-156.

Epidemiologic and clinical survey of victims of centipede stings admitted to Hospital Vital Brazil (Sao Paulo, Brazil)

We retrospectively analyzed 98 proven cases of centipede stings admitted to Hospital Vital Brazil, Butantan Institute, Sao Paulo, Brazil, between 1990 and 2007. Most stings occurred at the metropolitan area of Sao Paulo city (n = 94, 95.9%), in the domiciles of patients (n = 67, 68.4%), and during the warm-rainy season (n = 60, 61.2%). The mean age of the victims was 32.0 +/- 18.8-years-old. Cryptops and Otostigmus genera were responsible for most cases. Around 86% of the patients sought medical care within 6 h after the sting. Both lower (56.1%) and upper limbs (41.8%) were most frequently bitten, especially the feet and hands (89.8%). The most frequent local clinical manifestations were pain (94.9%), erythema (44.9%) and edema (21.4%), and the latter was mainly observed in patients bitten by Otostigmus spp. Supportive treatment was used in only 28.6% of the patients, namely administration of local anesthesia (9.2%) and systemic analgesia (13.3%). No sequels or complications were observed in patients, and the prognostic was benign. (c) 2008 Elsevier Ltd. All rights reserved.

PRECLINICAL INVESTIGATION OF THE RETINAL BIOCOMPATIBILITY OF SIX NOVEL VITAL DYES FOR CHROMOVITRECTOMY

Purpose: To investigate the retinal biocompatibility of six novel vital dyes for chromovitrectomy. Methods: An amount of 0.05 mL of 0.5% and 0.05% light green (LG), fast green (FG), Evans blue (EB), brilliant blue (BriB), bromophenol blue (BroB), or indigo carmine (IC) was injected intravitreally in the right eye, whereas in the left eye balanced salt solution was applied for control in rabbits` eyes. Clinical examination, fluorescein angiography, histology with light microscopy, and transmission electron microscopy were performed after 1 and 7 days. Retinal cell layers were evaluated for morphologic alterations and number of cells. The electroretinographic changes were assessed at baseline, 24 hours and 7 days. Results: Fluorescein angiography disclosed hypofluorescent spots only in the 0.5% EB group. Light microscopy and transmission electron microscopy disclosed slight focal morphologic changes in eyes exposed to 0.05% IC, FG, BriB, similar to the control at 1 and 7 days. In the lower dose groups, EB, LG, and BroB caused substantial retinal alterations by light microscopy. At the higher dose, BroB and EB produced diffuse cellular edema and vacuolization within the ganglion cells, bipolar cells, and photoreceptors. FG and IC at 0.5% caused slight retinal alterations similar to balanced salt solution injection. LG at 0.5% caused diffuse vacuolization of bipolar cells after 1 and 7 days. Injection of 0.5% EB caused a significant decrease in neuroretinal cell counts in comparison to control eyes in the 7-day examination (P < 0.05). Electroretinography revealed intermittent prolonged latency and decreased amplitude in eyes injected with 0.5% EB, LG, BriB, and BroB, while at the lower dose, only LG and EB induced few functional changes. Conclusion: The progressive order of retinal biocompatibility, from safest to most toxic, was IC, FG, BriB, BroB, LG, EB.

SEM Study of Apical Morphological Alterations in Primary Teeth with Vital and Necrotic Pulps

This study evaluated, by SEM, the morphology of human primary teeth roots. Twenty-four teeth were divided into 3 groups: pulp vitality (group I) and pulp necrosis without (group II) and with apical periodontitis (group III). Roots were analyzed by the presence of periodontal ligament (PDL) fibers and resorption areas. In groups I and II, presence of PDL fibers and absence of resorption were observed in all cases (100%), while all specimens (100%) of group III showed no PDL fibers and resorption areas. In conclusion, there are morphological differences in the apical region of primary teeth with different pulpal and periapical pathologies.

Biofilm on the apical region of roots in primary teeth with vital and necrotic pulps with or without radiographically evident apical pathosis

Aim To evaluate, by scanning electron microscopy (SEM), the presence of biofilms on the external surfaces of the apical third of roots of human primary teeth with vital or necrotic pulps with and without radiographically evident periradicular pathosis. Methodology Eighteen teeth were selected: group I - normal pulp (n = 5), group II - pulp necrosis without radiographic evidence of periapical pathosis (n = 7) and group III - pulp necrosis with well-defined radiographic periapical pathosis (n = 6). After extraction, the teeth were washed with saline and immersed in 0.03 g mL(-1) trypsin solution for 20 min. The teeth were then washed in sodium cacodilate buffer and stored in receptacles containing modified Karnovsky solution. The teeth were sectioned, dehydrated in an ethanol series, critical-point dried with CO(2), sputter coated with gold and the external root surface in the apical third examined by SEM. Results In the teeth of groups I and II, the apical root surfaces were covered by collagen fibres, with no evidence of bacteria (100%). In the teeth of group III, the root apices had no collagen fibres but revealed resorptive areas containing microorganisms (cocci, bacilli, filaments and spirochetes) in all cases (100%). Conclusion Microorganisms organized as biofilms on the external root surface (extraradicular infection) were detected in primary teeth with pulp necrosis and radiographically visible periapical pathosis.

Metallopeptidase inhibitors arrest vital biological processes in the fungal pathogen Scedosporium apiospermum

P>Scedosporium apiospermum is an emerging agent of opportunistic mycoses in humans. Previously, we showed that mycelia of S. apiospermum secreted metallopeptidases which were directly linked to the destruction of key host proteins. In this study, we analysed the effect of metallopeptidase inhibitors on S. apiospermum development. As germination of inhaled conidia is a crucial event in the infectious process of S. apiospermum, we studied the morphological transformation induced by the incubation of conidia in Sabouraud-dextrose medium at 37 degrees C. After 6 h, some conidia presented a small projection resembling a germ-tube. A significant increase, around sixfold, in the germ-tube length was found after 12 h, and hyphae were exclusively observed after 24 h. Three distinct metallopeptidase inhibitors were able to arrest the transformation of conidia into hyphae in different ways; for instance, 1,10-phenanthroline (PHEN) completely blocked this process at 10 mu mol l-1, while ethylenediamine tetraacetic acid (EDTA) and ethylene glycol-bis (beta-aminoethyl ether; EGTA) only partially inhibited the differentiation at up to 10 mmol l-1. EGTA did not promote any significant reduction in the conidial growth, while PHEN and EDTA, both at 10 mmol l-1, inhibited the proliferation around 100% and 65%, respectively. The secretion of polypeptides into the extracellular environment and the metallopeptidase activity secreted by mycelia were completely inhibited by PHEN. These findings suggest that metallo-type enzymes could be potential targets for future therapeutic interventions against S. apiospermum.

Discontinuous local semiflows for Kurzweil equations leading to LaSalle`s invariance principle for differential systems with impulses at variable times

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle`s invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle`s invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. (C) 2011 Elsevier Inc. All rights reserved.

A novel bioactive glass-ceramic for treating dentin hypersensitivity

Dentin hypersensitivity (DH) is a painful response to stimulus applied to the open dentinal tubules of a vital tooth. It's a common oral condition, however, without an ideal treatment available yet. This work evaluated in vitro the effect of micron-sized particles from a novel bioactive glass-ceramic (Biosilicate) in occluding open dentinal tubules. A dentin disc model was employed to observe comparatively, using scanning electron microscopy (SEM), dentinal tubule occlusion by different products and deposition of hydroxyl carbonate apatite (HCA) on dentin surface by Biosilicate, after a single application: G1 - Dentifrice with potassium nitrate and fluoride; G2 - Two-step calcium phosphate precipitation treatment; G3 - Water-free gel containing Biosilicate particles (1%); G4 - Biosilicate particles mixed with distilled water in a 1:10 ratio; all of them after 1, 12 and 24 hours of immersion in artificial saliva. Fourier transform infrared spectroscopy (FTIR) was performed to detect HCA formation on dentin discs filled with Biosilicate after 2 minutes, 30 minutes and 12 hours of immersion in artificial saliva. SEM showed a layer of HCA formed on dentin surface after 24 hours by G4. G1, G2 and G3 promoted not total occlusion of open dentinal tubules after 24 hours. FTIR showed HCA precipitation on the dentin surface induced by Biosilicate after 30 minutes. The micron-sized particles from the bioactive glass-ceramic thus were able to induce HCA deposition in open dentinal tubules in vitro. This finding suggests that Biosilicate may provide a new option for treating DH.

Effect of nitric oxide inhibitor and donor substances on the infammatory process caused by endodontic irrigants

Nitric oxide (NO) has been considered a key molecule in infammation. OBJECTIVE: The aim of this study was to evaluate the effect of treatment with L-NAME and sodium nitroprussiate, substances that inhibit and release NO, respectively, on tissue tolerance to endodontic irrigants. MATERIAL AND METHODS: The vital dye exudation method was used in a rat subcutaneous tissue model. Injections of 2% Evans blue were administered intravenously into the dorsal penial vein of 14 male rats (200-300 g). The NO inhibitor and donor substances were injected into the subcutaneous tissue in the dorsal region, forming two groups of animals: G1 was inoculated with L-NAME and G2 with sodium nitroprussiate. Both groups received injections of the test endodontic irrigants: acetic acid, 15% citric acid, 17% EDTA-T and saline (control). After 30 min, analysis of the extravasated dye was performed by light absorption spectrophotometry (620 nm). RESULTS: There was statistically signifcant difference (p<0.05) between groups 1 and 2 for all irrigants. L-NAME produced a less intense infammatory reaction and nitroprussiate intensifed this process. CONCLUSIONS: Independently of the administration of NO inhibitors and donors, EDTA-T produced the highest irritating potential in vital tissue among the tested irrigating solutions.

Endothelial dysfunction in cardiovascular and endocrine-metabolic diseases: an update

The endothelium plays a vital role in maintaining circulatory homeostasis by the release of relaxing and contracting factors. Any change in this balance may result in a process known as endothelial dysfunction that leads to impaired control of vascular tone and contributes to the pathogenesis of some cardiovascular and endocrine/metabolic diseases. Reduced endothelium-derived nitric oxide (NO) bioavailability and increased production of thromboxane A2, prostaglandin H2 and superoxide anion in conductance and resistance arteries are commonly associated with endothelial dysfunction in hypertensive, diabetic and obese animals, resulting in reduced endothelium-dependent vasodilatation and in increased vasoconstrictor responses. In addition, recent studies have demonstrated the role of enhanced overactivation ofβ-adrenergic receptors inducing vascular cytokine production and endothelial NO synthase (eNOS) uncoupling that seem to be the mechanisms underlying endothelial dysfunction in hypertension, heart failure and in endocrine-metabolic disorders. However, some adaptive mechanisms can occur in the initial stages of hypertension, such as increased NO production by eNOS. The present review focuses on the role of NO bioavailability, eNOS uncoupling, cyclooxygenase-derived products and pro-inflammatory factors on the endothelial dysfunction that occurs in hypertension, sympathetic hyperactivity, diabetes mellitus, and obesity. These are cardiovascular and endocrine-metabolic diseases of high incidence and mortality around the world, especially in developing countries and endothelial dysfunction contributes to triggering, maintenance and worsening of these pathological situations.