Microwave spectrometry for the Evaluation of the structural integrity of metallic stents

Purpose: To assess the feasibility of a method based on microwave spectrometry to detect structural distortions of metallic stents in open air conditions and envisage the prospects of this approach toward possible medical applicability for the evaluation of implanted stents. Methods: Microwave absorbance spectra between 2.0 and 18.0 GHz were acquired in open air for the characterization of a set of commercial stents using a specifically design setup. Rotating each sample over 360º, 2D absorbance diagrams were generated as a function of frequency and rotation angle. To check our approach for detecting changes in stent length (fracture) and diameter (recoil), two specific tests were performed in open air. Finally, with a few adjustments, this same system provides 2D absorbance diagrams of stents immersed in a water-based phantom, this time over a bandwidth ranging from 0.2 to 1.8 GHz. Results: The authors show that metallic stents exhibit characteristic resonant frequencies in their microwave absorbance spectra in open air which depend on their length and, as a result, may reflect the occurrence of structural distortions. These resonances can be understood considering that such devices behave like dipole antennas in terms of microwave scattering. From fracture tests, the authors infer that microwave spectrometry provides signs of presence of Type I to Type IV stent fractures and allows in particular a quantitative evaluation of Type III and Type IV fractures. Recoil tests show that microwave spectrometry seems able to provide some quantitative assessment of diametrical shrinkage, but only if it involves longitudinal shortening. Finally, the authors observe that the resonant frequencies of stents placed inside the phantom shift down with respect to the corresponding open air frequencies, as it should be expected considering the increase of dielectric permittivity from air to water. Conclusions: The evaluation of stent resonant frequencies provided by microwave spectrometry allows detection and some quantitative assessment of stent fracture and recoil in open air conditions. Resonances of stents immersed in water can be also detected and their characteristic frequencies are in good agreement with theoretical estimates. Although these are promising results, further verifica tion in a more relevant phantom is required in order to foresee the real potential of this approach.

ESCCAR international congress on Rickettsia and other intracellular bacteria.

The European Society for the study of Chlamydia, Coxiella, Anaplasma and Rickettsia (ESCCAR) held his triennial international meeting in Lausanne. This meeting gathered 165 scientists from 28 countries and all 5 continents, allowing efficient networking and major scientific exchanges. Topics covered include molecular and cellular microbiology, genomics, as well as epidemiology, veterinary and human medicine. Several breakthroughs have been revealed at the meeting, such as (i) the presence of CRISPR (the "prokaryotic immune system") in chlamydiae, (ii) an Anaplasma effector involved in host chromatin remodelling, (iii) the polarity of the type III secretion system of chlamydiae during the entry process revealed by cryo-electron tomography. Moreover, the ESCCAR meeting was a unique opportunity to be exposed to cutting-edge science and to listen to comprehensive talks on current hot topics.

Redox Signaling by the RNA Polymerase III TFIIB-Related Factor Brf2.

TFIIB-related factor 2 (Brf2) is a member of the family of TFIIB-like core transcription factors. Brf2 recruits RNA polymerase (Pol) III to type III gene-external promoters, including the U6 spliceosomal RNA and selenocysteine tRNA genes. Found only in vertebrates, Brf2 has been linked to tumorigenesis but the underlying mechanisms remain elusive. We have solved crystal structures of a human Brf2-TBP complex bound to natural promoters, obtaining a detailed view of the molecular interactions occurring at Brf2-dependent Pol III promoters and highlighting the general structural and functional conservation of human Pol II and Pol III pre-initiation complexes. Surprisingly, our structural and functional studies unravel a Brf2 redox-sensing module capable of specifically regulating Pol III transcriptional output in living cells. Furthermore, we establish Brf2 as a central redox-sensing transcription factor involved in the oxidative stress pathway and provide a mechanistic model for Brf2 genetic activation in lung and breast cancer.

CHARACTERIZING THE MECHANISM OF QUETIAPINE DISTRIBUTION IN LIPID-CORE NANOCAPSULES PSEUDO-PHASES USING A VALIDATED LC/UV METHOD

Quetiapine is an atypical antipsychotic used to treat schizophrenia. However, despite great interest for its chronic therapeutic use, quetiapine has some important side effects such as weight gain induction. The development of a quetiapine nanocarrier can potentially target the drug into central nervous system, resulting in a reduction of systemic side effects and improved patient treatment. In the present work, a simple liquid chromatography/ultraviolet detection (LC/UV) analytical method was developed and validated for quantification of total quetiapine content in lipid core nanocapsules as well as for determination of incorporation efficiency. An algorithm proposed by Oliveira et al. (2012) was applied to characterize the distribution of quetiapine in the pseudo-phases of the nanocarrier, leading to a better understanding of the quetiapine nanoparticles produced. The analytical methodology developed was specific, linear in the range of 0.5 to 100 µg mL−1 (r2 > 0,99), and accurate and precise (R.S.D < ±5%). The absolute recovery of quetiapine from the nanoparticles was approximately 98% with an incorporation efficiency of approximately 96%. The results indicated that quetiapine was present in a type III distribution according to the algorithm, and was mainly located in the core of the nanoparticle because of its logD in the formulation pH (6.86 ± 0.4).

Spectrophotometric study of iron oxidation in the iron(II)/thiocyanate/acetone system and some analytical applications

The possibility of using thiocyanate to determine iron(II) and/or iron(III) in water-acetone mixture has been re-examined as part of a systematic and comparative study involving metallic complexes of pseudohalide ligands. Some parameters that affect the complete oxidation of the ferrous cations, their subsequent complexation and the system stability have been studied to optimize the experimental conditions. Our results show the viability and potentiality of this simply methodology as an alternative analytical procedure to determine iron cations with high sensitivity, precision and accuracy. Studies on the calibration, stability, precision, and effect of various different ions have been carried out by using absorbance values measured at 480 nm. The analytical curve for the total iron determination obeys Beer's law (r = 0.9993), showing a higher sensitivity (molar absorptivity of 2.10x10(4) L cm-1 mol-1) when compared with other traditional systems (ligands) or even with the "similar" azide ion [1.53x10(4) L cm-1 mol-1, for iron-III/azide complexes, in 70% (v/v) tetrahydrofuran/water, at 396 nm]. Under such optimized experimental conditions, it is possible to determine iron in the concentration range from 0.5 to 2 ppm (15-65% T for older equipments, quartz cells of 1.00 cm). Analytical applications have been tested for some different materials (iron ores), also including pharmaceutical products for anemia, and results were compared with atomic absorption determinations. Very good agreement was obtained with these two different techniques, showing the potential of the present experimental conditions for the total iron spectrophotometric determinations (errors < 5%). The possibility of iron speciation was made evident by using another specific and auxiliary method for iron(II) or (III).

Analyses of the development and glycoproteins present in the ovarian follicles of Poecilia vivipara (Cyprinodontiformes, Poeciliidae)

The morphofunctional aspects of oogenesis of Poecilia vivipara were studied aiming to understand the reproductive biology and development of species with internal fertilization, particularly those belonging to the family Poeciliidae. The stages of gonadal maturation and follicular development were characterized using mesoscopic, histological, histochemical, and lectin cytochemical analyses. Through mesoscopic evaluation the ovarian development was classified in six phases of development: immature, in maturation I, in maturation II, mature I, mature II, and post-spawn. Based on microscopic examination of the ovaries, we identified the presence of oocytes types I and II during the previtellogenic phase and types III, IV, and V during the vitellogenic phase. As oogenesis proceeded the oocyte cytosol increased in volume and presented increased cytoplasmic granule accumulation, characterizing vitellogenesis. The zona radiata (ZR) increased in thickness and complexity, and the follicular epithelium, which was initially thin and consisting of pavimentous cells, in type III oocytes exhibited cubic simple cells. The histochemical and cytochemical analyses revealed alterations in the composition of the molecular structures that form the ovarian follicle throughout the gonadal development. Our study demonstrated differences in the female reproductive system among fish species with internal and external fertilization and we suggest P. vivipara can be used as experimental model to test environmental toxicity.

The effect of down-regulation of Smad3 by RNAi on hepatic stellate cells and a carbon tetrachloride-induced rat model of hepatic fibrosis

Searching for effective Smad3 gene-based gene therapies for hepatic fibrosis, we constructed siRNA expression plasmids targeting the rat Smad3 gene and then delivered these plasmids into hepatic stellate cells (HSCs). The effect of siRNAs on the mRNA levels of Smad2, Smad3, Smad4, and collagens I-α1, III-α1 and IV-α1 (Colα1, Col3α1, Col4α1, respectively) was determined by RT-PCR. Eighty adult male Sprague-Dawley rats were randomly divided into three groups. Twice a week for 8 weeks, the untreated hepatic fibrosis model (N = 30) and the treated group (N = 20) were injected subcutaneously with 40% (v/v) carbon tetrachloride (CCl4)-olive oil (3 mL/kg), and the normal control group (N = 30) was injected with olive oil (3 mL/kg). In the 4th week, the treated rats were injected subcutaneously with liposome-encapsulated plasmids (150 µg/kg) into the right liver lobe under general anesthesia once every 2 weeks, and the untreated rats were injected with the same volume of buffer. At the end of the 6th and 8th weeks, liver tissue and sera were collected. Pathological changes were assessed by a semi-quantitative scoring system (SSS), and a radioimmunoassay was used to establish a serum liver fibrosis index (type III procollagen, type IV collagen, laminin, and hyaluronic acid). The mRNA expression levels of the above cited genes were reduced in the HSCs transfected with the siRNA expression plasmids. Moreover, in the treated group, fibrosis evaluated by the SSS was significantly reduced (P < 0.05) and the serum indices were greatly improved (P < 0.01). These results suggest that Smad3 siRNA expression plasmids have an anti-fibrotic effect.

Problème centre-foyer et application

Dans ce mémoire, nous étudions le problème centre-foyer sur un système polynomial. Nous développons ainsi deux mécanismes permettant de conclure qu’un point singulier monodromique dans ce système non-linéaire polynomial est un centre. Le premier mécanisme est la méthode de Darboux. Cette méthode utilise des courbes algébriques invariantes dans la construction d’une intégrale première. La deuxième méthode analyse la réversibilité algébrique ou analytique du système. Un système possédant une singularité monodromique et étant algébriquement ou analytiquement réversible à ce point sera nécessairement un centre. Comme application, dans le dernier chapitre, nous considérons le modèle de Gauss généralisé avec récolte de proies.

Rôle de Paa dans la pathogénicité des Escherichia coli attachants et effaçants (AEEC)

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Role of CD4+ T cells in the regulation of the immune response against encapsulated Group B Streptococcus

Le Streptocoque de groupe B (GBS) est un important agent d’infection invasive pouvant mener à la mort et demeure la cause principale de septicémie néonatale à ce jour. Neuf sérotypes ont été officiellement décrits basés sur la composition de la capsule polysaccharidique (CPS). Parmi ces sérotypes, le type III est considéré le plus virulent et fréquemment associé aux maladies invasives graves, telle que la méningite. Malgré que plusieurs recherches aient été effectuées au niveau des interactions entre GBS type III et les cellules du système immunitaire innées, aucune information n’est disponible sur la régulation de la réponse immunitaire adaptative dirigée contre ce dernier. Notamment, le rôle de cellules T CD4+ dans l’immuno-pathogenèse de l’infection causée par GBS n’a jamais été étudié. Dans cet étude, trois différents modèles murins d’infection ont été développé pour évaluer l’activation et la modulation des cellules T CD4+ répondantes au GBS de type III : ex vivo, in vivo, et in vitro. Les résultats d’infections ex vivo démontrent que les splénocytes totaux répondent à l’infection en produisant des cytokines de type-1 pro-inflammatoires. Une forte production d’IL-10 accompagne cette cascade inflammatoire, probablement dans l’effort de l’hôte de maintenir l’homéostasie. Les résultats démontrent aussi que les cellules T sont activement recrutées par les cellules répondantes du système inné en produisant des facteurs chimiotactiques, tels que CXCL9, CXCL10, et CCL3. Plus spécifiquement, les résultats obtenus à partir des cellules isolées T CD4+ provenant des infections ex vivo ou in vivo démontrent que ces cellules participent à la production d’IFN-γ et de TNF-α ainsi que d’IL-2, suggérant un profil d’activation Th1. Les cellules isolées T CD4+ n’étaient pas des contributeurs majeurs d’IL-10. Ceci indique que cette cytokine immuno-régulatrice est principalement produite par les cellules de l’immunité innée de la rate de souris infectées. Le profil Th1 des cellules T CD4+ a été confirmé en utilisant un modèle in vitro. Nos résultats démontrent aussi que la CPS de GBS a une role immuno-modulateur dans le développement de la réponse Th1. En résumé, cette étude adresse pour la première fois, la contribution des cellules T CD4+ dans la production d’IFN-γ lors d’une infection à GBS et donc, dans le développement d’une réponse de type Th1. Ces résultats renforcent d’avantage le rôle central de cette cytokine pour un control efficace des infections causées par ce pathogène.

The study of RNA tertiary interactions in tRNA structure and function

Le rôle des deux paires de bases universelles inverse Hoogsteen U : A ( RHUAs ) présentent chez les ARNt standards , une dans la boucle T et l'autre dans le noyau de la forme en L , a été étudiée. Pour chacun des RHUAs , un criblage génétique spécialisé in vivo chez les bactéries , le système suppresseur ambre ( pour l'étude de la RHUA dans la boucle T ) et le système d'ARNt de la sélénocystéine ( tRNASec ) ( pour l'étude de la RHUA dans le noyau ) , ont été utilisé pour générer des variants fonctionnels à partir de multiples librairies combinatoires . Ces variants ont ensuite été séquencé et soumis à une analyse systématique qui comprend la modélisation informatique et un type d'analyse phylogénétique. Les résultats du système suppresseur ambre ont montré un ensemble de variants fonctionnels qui ne nécessitent pas le motif RHUA dans la boucle T et qui ont remplacé la méthode standard de l'interaction entre les boucles D et T avec une double hélice interboucle , ILDH . D'autres études ont abouti à la détermination d'un modèle In silico de l'alternative à la norme standard de la boucle T, sous le nom de type III . Les résultats du système tRNASec ont révélé que pour cette ARNt exceptionnel, l'absence de RHUA ( dans le noyau ) assure une flexibilité accrue qui est spécifiquement nécessaire pour la fonction de tRNASec . Ainsi, les ARNt standards , à la différence de tRNASec , avec la présence universelle de RHUA dans le noyau , a été naturellement sélectionnée pour être rigide . Pris ensemble, la RHUA joue un rôle essentiel dans la stabilisation des interactions tertiaires.

Influence du microbiote intestinal sur le métabolisme et la virulence des Escherichia coli entérohémorragiques

Les Escherichia coli entérohémorragiques (EHEC) représentent un problème majeur de santé publique dans les pays développés. Les EHEC sont régulièrement responsables de toxi-infections alimentaires graves chez l’humain et causent des colites hémorragiques et le symptôme hémolytique et urémique, mortel chez les enfants en bas âge. Les EHEC les plus virulents appartiennent au sérotype O157:H7 et le bovin constitue leur réservoir naturel. À ce jour il n’existe aucun traitement pour éviter l’apparition des symptômes liés à une infection à EHEC. Par conséquent, il est important d’augmenter nos connaissances sur les mécanismes employés par le pathogène pour réguler sa virulence et coloniser efficacement la niche intestinale. Dans un premier temps, l’adaptation de la souche EHEC O157:H7 EDL933 à l’activité métabolique du microbiote intestinal a été étudiée au niveau transcriptionnel. Pour se faire, EDL933 a été cultivée dans les contenus caecaux de rats axéniques (milieu GFC) et dans ceux provenant de rats colonisés par le microbiote intestinal humain (milieu HMC). Le HMC est un milieu cécal conditionné in vivo par le microbiote. Dans le HMC par rapport au GFC, EDL933 change drastiquement de profile métabolique en réponse à l’activité du microbiote et cela se traduit par une diminution de l’expression des voies de la glycolyse et une activation des voies de l’anaplérose (voies métaboliques dont le rôle est d’approvisionner le cycle TCA en intermédiaires métaboliques). Ces résultats, couplés avec une analyse métabolomique ciblée sur plusieurs composés, ont révélé la carence en nutriments rencontrée par le pathogène dans le HMC et les stratégies métaboliques utilisées pour s’adapter au microbiote intestinal. De plus, l’expression des gènes de virulence incluant les gènes du locus d’effacement des entérocytes (LEE) codant pour le système de sécrétion de type III sont réprimés dans le HMC par rapport au GFC indiquant la capacité du microbiote intestinal à réprimer la virulence des EHEC. L’influence de plusieurs composés intestinaux présents dans les contenus caecaux de rats sur l’expression des gènes de virulence d’EDL933 a ensuite été étudiée. Ces résultats ont démontré que deux composés, l’acide N-acétylneuraminique (Neu5Ac) et le N-acétylglucosamine (GlcNAc) répriment l’expression des gènes du LEE. La répression induite par ces composés s’effectue via NagC, le senseur du GlcNAc-6-P intracellulaire et le régulateur du catabolisme du GlcNAc et du galactose chez E. coli. NagC est un régulateur transcriptionnel inactivé en présence de GlcNAc-6-P qui dérive du catabolisme du Neu5Ac et du transport GlcNAc. Ce travail nous a permis d’identifier NagC comme un activateur des gènes du LEE et de mettre à jour un nouveau mécanisme qui permet la synchronisation de la virulence avec le métabolisme chez les EHEC O157:H7. La concentration du Neu5Ac et du GlcNAc est augmentée in vivo chez le rat par le symbiote humain Bacteroides thetaiotaomicron, indiquant la capacité de certaines espèces du microbiote intestinal à relâcher les composés répresseurs de la virulence des pathogènes. Ce travail a permis l’identification des adaptations métaboliques des EHEC O157:H7 en réponse au microbiote intestinal ainsi que la découverte d’un nouveau mécanisme de régulation de la virulence en réponse au métabolisme. Ces données peuvent contribuer à l’élaboration de nouvelles approches visant à limiter les infections à EHEC.

Characterization and virulence potential of phenotypically diverse Aeromonas veronii isolates recovered from moribund freshwater ornamental fishes of Kerala, India

In the present study, we investigated the involvement of Aeromonas spp. in eliciting disease outbreaks in freshwater ornamental fishes across the state of Kerala, India. We investigated three incidences of disease, in which the moribund fishes exhibited clinical signs such as haemorrhagic septicemia (in gouramy, Trichogaster sp.), dropsy (in Oscar, Astronotus ocellatus) and tail rot/fin rot (in gold fish, Carassius carassius). Pure cultures (n = 20 from each fish; 60 in total) of Aeromonas spp. were recovered from the abdominal fluid as well as from internal organs of affected fishes, although they could not be identified to species level because of the variations in their phenotypic characters. The molecular fingerprinting of the isolates using Enterobacterial Repetitive Intergenic Consensus PCR proved the genetic diversity of the isolates from the three sites. The phylogenetic trees constructed using concatenated sequences (using 16S rRNA, gyrA, gyrB and rpoD genes) indicated that they were related to Aeromonas veronii. They exhibited marked cytotoxic and haemolytic activity, which were responsible for the pathogenic potential of the isolates. The isolates possessed multiple virulence genes such as enterotoxins (act and alt), haemolytic toxins (aerA and hlyA), genes involved in type III secretion system (ascV, aexT and ascF–ascG), glycerophospholipid-cholesterol acyltransferase (gcat) and a type IV pilus (tapA) gene, as determined by PCR. Virulence of representative isolates to goldfish was also tested, and we found LD50 values of 104.07–105.35 cfu/fish. Furthermore, the organisms could be recovered as pure cultures from the lesions as well as from the internal organs.

Factores asociados a infección de fracturas abiertas de extremidades por accidentes de tránsito. Bogotá, 2012-2013

Los traumatismos por accidentes de tránsito, constituyen un problema de salud pública, a nivel mundial. Las lesiones más frecuentes son las fracturas de extremidades (84.3%). Las fracturas tienen un elevado riesgo de presentar infecciones, secuelas e incapacidades permanentes. Objetivo : Determinar si los factores asociados con la patología (lugar de fractura, clasificación de fractura, comorbilidades del paciente) y/o los factores relacionados con la atención médica (uso de profilaxis antibiótica diferente al protocolo institucional, tiempo prolongado para remisión, demoras en manejo quirúrgico) se asocian a mayor probabilidad de presentar infección de fracturas abiertas, en población mayor a 15 años, atendidos por accidente de tránsito, en una clínica de Bogotá de tercer nivel especializada en atención de SOAT, durante el período Octubre de 2012 a Octubre de 2013. Metodología: Estudio de casos y controles no apareado, relación 1:3, conformado por 43 casos (fracturas abiertas infectadas) y 129 controles (fracturas abiertas no infectadas). Resultados: La edad media de los casos fue de 39.42 +/- 16.82 años (med=36 años) y la edad media de los controles fue de 33.15 +/- 11.78 años (med=30 años). El 83.7% de los casos y el 78.3% de los controles corresponden al sexo masculino. Predominaron los accidentes en motocicleta en el 81.4% de los casos y el 86% de los controles. En el análisis bivariado se encuentra que la edad mayor a 50 años (p=0.042), una clasificación de la fractura grado IIIB o IIIC (p=0.02), cumplimiento del protocolo antibiótico institucional según el grado de fractura (p=0.014) y un tiempo mayor a 24 horas desde el momento del accidente al centro especializado en trauma (p=0.035) se asociaron significativamente con infección de la fractura abierta. En el análisis multivariado se encuentra únicamente que la clasificación de la fractura grado IIIB o IIIC se asocia con infección de la fractura OR 2.6 IC95% (1.187 – 5.781) (p=0.017). La duración de hospitalización fue mayor en los casos (32.37+/- 22.92 días, med=26 días) que en los controles (8.81 +/- 7.52 días, med=6 días) (p<0.001). El promedio de lavados quirúrgicos fue mayor en los casos (4.85±4.1, med=4.0) que en el grupo control (1.94±1.26, med=2) (p<0.001). Conclusiones: La infección posterior a una fractura abierta, implica costos elevados de atención con hospitalizaciones prolongadas y mayor frecuencia de intervenciones quirúrgicas como se evidencia en el presente estudio. Se debe fortalecer el sistema de remisión y contra remisión para acortar los tiempos de inicio de manejo especializado de los pacientes con fracturas abiertas. Se debe incentivar dentro de las instituciones, el cumplimiento de protocolos de profilaxis antibiótica según el grado de la fractura para disminuir el riesgo de complicación infecciosa.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.