Patologia óssea do insuficiente renal crónico: desafio clínico-biológico ; Caracterização da osteodistrofia renal e efeitos da biocompatibilidade de membranas de hemodiálise, na remodelação óssea

Resumo: Os resultados das nossas investigações, apresentadas ao longo desta dissertação,contribuíram para a otimização do diagnóstico invasivo e não invasivo da osteodistrofia renal e permitiram evidenciar a relevância, para a expressão clínica e histológica da ODR, de algumas articularidades específicas da população hemodialisada, nomeadamente: a utilização de membranas de hemodiálise mais biocompatíveis e com elevada permeabilidade, o recurso a técnicas de hemodiafiltração com otimização da capacidade convectiva, as limitações dos marcadores bioquímicos de remodelação óssea ou a insuficiência / deficiência em vitamina D nativa (bem como os resultados da suplementação com esta vitamina). Testámos, pela primeira vez em doentes hemodialisados, novos marcadores da formação e reabsorção óssea, que validámos mediante a comparação com os resultados da histomorfometria óssea. No seu conjunto, e de forma integrada, as nossas investigações permitiram-nos: - Evidenciar a diminuição da expressão do recetor da PTH/PTHrP na cartilagem de crescimento, num modelo animal de IRC, o que explica, pelo menos em parte, o atraso de crescimento observado nesta patologia, bem como a diminuição da resposta à ação da PTH; - Demonstrar as vantagens da determinação da isoforma óssea da fosfatase alcalina, em relação à fosfatase alcalina total, no diagnóstico diferencial entre baixa e elevada remodelação óssea; - Utilizar, pela primeira vez em hemodialisados, a piridinolina e a desoxipiridinolina no diagnóstico da reabsorção óssea. Este foi o primeiro marcador sérico específico da atividade osteoclástica, utilizado com sucesso em doentes anúricos em hemodiálise. Evidenciámos uma excelente correlação destes dois marcadores bioquímicos com a superfície osteoclástica e com o número de osteoclastos/mm2;- Demonstrar as acentuadas limitações de outros marcadores da formação e reabsorção óssea (nomeadamente a osteocalcina, o propeptido carboxiterminal do procolagénio tipo I-PICP, e o Telopeptido do colagénio tipo I – ICTP) com base nas correlações entre os doseamentos séricos ou plasmáticos destes marcadores e a biópsia óssea com avaliação histomorfométrica; -Evidenciar as limitações induzidas pela sobrecarga alumínica na interpretação dos níveis séricos dos marcadores não invasivos da remodelação óssea;-Testar a eficácia e segurança da utilização de “microdoses” de desferroxamina na terapêutica da intoxicação alumínica, em doentes com acentuada exposição a este metal;-Demonstrar que os doentes hemodialisados cronicamente com dialisadores de poliacrilonitrilo (membranas de alta permeabilidade),apresentavam menor ativação osteoblástica e osteoclástica, que os doentes dialisados com membranas de cuprofano(baixa permeabilidade), sendo os níveis de iPTH semelhantes em ambos os grupos estudados. Estes resultados apontam para uma menor ativação da remodelação óssea quando se utilizam membranas de hemodiálise mais biocompatíveis e/ou de maior permeabilidade, o que se poderá relacionar com a ultrafiltração de mediadores da ativação celular ou com a menor ativação dos mecanismos estimuladores da remodelação óssea, por parte destas membranas. Entre os mediadores da remodelação óssea que demonstrámos serem relevantes e estarem aumentados no soro de hemodialisados com membranas de baixo fluxo, contam-se a beta-2-microglobulina (2-M) e algumas citoquinas, com ação estimuladora das linhagens celulares envolvidas na remodelação óssea. Demonstrámos igualmente uma correlação positiva dos níveis séricos de 2-M com os níveis séricos da osteocalcina, da isoenzima óssea da fosfatase alcalina (marcadores da formação óssea) e com os níveis séricos da piridinolina (marcador da reabsorção óssea). Os níveis séricos de 2-M correlacionaram-se ainda, de forma negativa, com o volume osteoide (matriz óssea não calcificada). Nestes doentes hemodialisados, demonstrámos a presença de níveis séricos aumentados da interleucina-1, do antagonista do recetor da interleucina-1, da interleucina-6 e do recetor solúvel da interleucina-6. Salientamos as relações inversas que observámos, por um lado entre os níveis de antagonista do recetor da interleucina-1 e a superfície osteoblástica, e por outro lado entre o rácio do recetor da interleucina-6 / interleucina-6 (IL6-r/IL6) e a superfície osteoclástica. De acordo com estes nossos resultados originais, entendemos que a interferência nos níveis circulantes e na ativação local destes mediadores poderá justificar, em grande parte, o aumento da prevalência de doença óssea adinâmica, descrita por nós e por outros grupos. Evidenciámos uma elevadíssima prevalência de doença adinâmica (>50% dos doentes), numa população de hemodialisados sem exposição prévia ao alumínio, tratados de acordo com os K/DOQI “guidelines” e que ao longo de um ano mantiveram níveis séricos de cálcio e de fósforo controlados. Consequentemente, os doentes tratados de forma otimizada apresentaram uma prevalência surpreendentemente elevada de doença adinâmica. Os nossos resultados (classificados com o grau de evidência máxima pelos peritos KDIGO) contribuíram para dar suporte à grande diferença nos guidelines K/DOQI (2003) e KDIGO (2009) no que respeita aos valores alvo da PTH. Estamos conscientes que de que o facto de termos uma percentagem tão elevada de doença óssea adinâmica nas nossas populações de hemodialisados, bem como a demonstração de que alguns doentes com valores de PTH intacta (2ª geração) de cerca de 600 pg/ml tinham doença óssea adinâmica, condicionaram os novos objetivos KDIGO para a PTH. Os nossos resultados suportam, em nossa opinião, a adequação e vantagem da utilização dos critérios da KDIGO em vez dos KDOQI. Tendo em conta que os primeiros definem objetivos para a PTH entre 2 e 9 vezes o limite superior do normal e não se comprometem com valores alvo absolutos e rígidos (definidos previamente nos KDOQI entre 150 e 300 pg/mL), esta nova abordagem parece-nos mais correta.Na nossa investigação clínica, caracterizámos ainda a população hemodialisada portuguesa no que respeita aos níveis séricos de calcidiol, identificando a população com suficiência, insuficiência ou deficiência em vitamina D3. Documentámos uma acentuada prevalência de insuficiência e mesmo de deficiência nesta vitamina, numa vasta população de hemodialisados, a qual, muito provavelmente, reflete de forma fidedigna, o que se pode observar na restante população de doentes portugueses IRC em estádio 5d (em diálise). Descrevemos, pela primeira vez em doentes hemodialisados, uma associação entre deficiência em calcidiol e a presença de fatores de risco cardiovascular (que têm sido identificados nos doentes urémicos). A nossa investigação conduziu-nos a resultados originais, ao identificar os níveis baixos de 25(OH)vitamina D3 como um provável fator de risco cardiovascular em hemodialisados, visto que a deficiência nesta vitamina se associou, de forma muito significativa, ao aumento da prevalência de calcificações vasculares, a inflamação, a pressão de pulso mais elevada, a hipertrofia ventricular esquerda, a insuficiência cardíaca e a níveis séricos aumentados de “BNP-Brain natriuretic peptide”. Finalmente, numa avaliação prospetiva, de intervenção terapêutica, corrigimos a insuficiência ou deficiência em 25(OH)vitamina D3 e demonstrámos que essa correção se associou a uma redução dos fatores de risco cardiovascular. Esta última intervenção foi totalmente inovadora, visto ser a primeira avaliação prospetiva da evolução dos fatores de risco cardiovasculares, em função da suplementação com vitamina D nativa, em doentes hemodialisados. Em resumo, pensamos que os resultados das nossas investigações, acima sumarizadas e apresentadas ao longo dos diversos capítulos desta dissertação,contribuiram para uma nova perspetiva da osteodistrofia renal e para recolocar o foco da atenção dos nefrologistas no tecido ósseo e no eixo paratormona – vitamina D – remodelação óssea. Este eixo surje claramente envolvido em múltiplos processos fisiopatológicos, que suportam a elevada morbilidade e mortalidade (nomeadamente de causa cardiovascular) observada nos doentes urémicos.---------ABSTRACT: The results of our research, presented throughout this thesis, contributed towards the optimisation of the invasive and non-invasive diagnosis of renal osteodystrophy. They have also highlighted the importance, to the clinical and histological expression of the ODR, of some specific characteristics of the haemodialysis population, including: the use of biocompatible high permeability haemodialysis membranes, the use of haemodiafiltration techniques with convection enhancement, as well as the limitations of biochemical markers of bone turnover or native vitamin D insufficiency/deficiency (along with the supplementation results of this vitamin). New bone formation and resorption markers, which were validated by comparison with the results of bone histomorphometry, have been tested for the first time on haemodialysis patients.As a whole, and in an integrated approach, our research enabled us to: - Show the decrease of the PTH/PTHrP receptor expression in cartilage growth, used on an IRC animal model, which explains, to some extent, not only the delayed growth observed in this pathology, but also the slow response to PTH. - Point out the advantages of the determination of bone isoform of alkaline phosphatase, in relation to the total alkaline phosphatase, in the differential diagnosis between low and high-bone turnover.- Use pyridinoline and deoxypyridinoline in the diagnosis of bone resorption for the first time on haemodialysis patients. This was the first specific serum market of the osteoclastic activity, which was successfully used on anuric patients undergoing haemodialysis treatment. We also observed an excellent correlation of these biochemical markers with the osteoclastic surface and the number of osteoclasts/mm2. - Demonstrate the sharp limitations of other markers of bone formation and resorption (namely osteocalcin, carboxyterminal propeptide of type I-PICP procollagen and telopeptide of type I-ICTP collagen) based on correlations between these markers’ serum or plasma assays and bone biopsy with histomorphometric assessment.-Show the limitations induced by aluminium overload in the interpretation of serum levels of bone remodelling non-invasive markers.-Test the efficacy and the safety of the use of deferoxamine “microdoses” for treatment of aluminium overload among patients with high levels of serum aluminium. - Demonstrate that patients with chronic haemodialysis dialysers of polyacrylonitrile (high permeability membranes) show a lower osteoblastic and osteoclastic activation than those undergoing dialysis with cuprofan membranes (low permeability), being the iPTH levels similar in both groups of patients. These findings point towards a lower activation of bone remodelling when using more biocompatible dialysis membranes and/or of higher permeability, which may relate to the ultrafiltration of cell activation mediators or to the lower activation of the stimulating mechanisms of bone remodelling, regarding the membranes. Beta-2-microglobulin (2-M) and some cytokines that play a role/participate in bone remodelling are among the bone remodelling mediators, which we demonstrated to be relevant and to be increased in the serum of haemodialysis with low flow membranes. We also proved that there is a positive correlation of serum 2-M levels not only with serum osteocalcin levels, of the bone isoenzyme of alkaline phosphatase (bone forming markers), but also with levels of serum pyridinoline (bone resorption marker).Serum 2-M levels correlate negatively with the volume of osteoid (uncalcified bone matrix). We also demonstrated the presence of elevated serum levels of interleukin-1,interleukin-1 receptor antagonist, interleukin-6 and soluble interleukin-6 receptor in haemodialysis patients. We stress the inverse relationship which we observed on one hand between the interleukin-1 receptor antagonist levels and the osteoblastic surface and on the other between the ratio of interleukin-6 receptor / interleukin-6 (IL6-r/IL6) and the osteoblastic surface. According to these unique findings, we believe that the interference in the circulating levels and in the local activation of these mediators may partly explain the rising prevalence of adynamic bone disease. A high prevalence of adynamic disease has also been observed in a haemodialysis population (>50% of patients) with no previous exposure to aluminium. The patients were treated according to K/DOQI guidelines and maintained controlled serum calcium and phosphorus levels over one year. As a result, the patients who received optimised treatment showed a surprisingly high prevalence of adynamic disease. Our results, which were ranked with the highest degree of evidence by KDIGO experts, contributed to the great difference regarding the target values of PTH in the K/DOQI (2003) and KDIGO (2009) guidelines. We are aware that the finding of such a high percentage of adynamic bone disease in our haemodialysis population, as well as the evidence that some patients with intact PTH values (2nd generation) of 600 pg/ml suffered from adynamic bone disease, have hindered, the new KDIGO objectives to PTH.In our opinion, our results support the suitability and the advantage of using KDIGO criteria instead of KDOQI. This seems to be the right approach when taking into consideration that KDIGO sets objectives to PTH between 2 and 9 times the normal upper limit and does not compromise with the rigid and absolute target values (between 150 and 300 pg/mL) previously defined by KDOQI. In our clinical research, the Portuguese haemodialysis population was characterised in terms of serum clacidiol levels and identified as having vitamin D3 sufficiency, insufficiency or deficiency. It was also recorded the prevalence of severe vitamin D3 insufficiency and even deficiency in a large haemodialysis population, which most likely provides a reliable picture of the rest of the population in IRC Portuguese patients with 5d stage (undergoing dialysis). We described for the first time in aemosialysis patients an association between calcidiol deficiency and the presence of ardiovascular risk factors, (which have been identified on uraemic patients).Our research led us to unique findings by having identified the low levels of 25(OH) vitamin D3 as a likely cardiovascular risk factor in patients undergoing haemodialysis treatment, given that deficiency in this vitamin has been significantly associated not only with a rise in the prevalence of vascular calcifications, but also inflammation, left ventricular hypertrophy, high pulse pressure and high serum BNPBrain natriuretic peptide levels. Finally, based on a prospective assessment of therapeutic intervention, 25(OH)vitamin D3 insufficiency or deficiency was corrected and we were able to demonstrate that this same correction was associated with a reduction in cardiovascular risk factors. This was a forward-looking intervention regarding the supplementation of native vitamin D in haemodialysis patients, since it was the first prospective assessment of the evolution of cardiovascular risk factors. In short, the results of our research, summarised above and presented throughout the various chapters of this thesis, contributed towards a new perspective of the renal osteodystrophy and also to draw the nephrologists’ attention to the bone tissue and to the axis PTH – vitamin D – bone remodelling. This axis appears clearly involved in multiple physiopathological processes, which support the high morbidity and mortality rate, (particularly of cardiovascular causes), observed in uraemic patients.

Thermal conditions affecting heat transfer in FDM/FFE: a contribution towards the numerical modelling of the process

The performance of parts produced by Free Form Extrusion (FFE), an increasingly popular additive manufacturing technique, depends mainly on their dimensional accuracy, surface quality and mechanical performance. These attributes are strongly influenced by the evolution of the filament temperature and deformation during deposition and solidification. Consequently, the availability of adequate process modelling software would offer a powerful tool to support efficient process set-up and optimisation. This work examines the contribution to the overall heat transfer of various thermal phenomena developing during the manufacturing sequence, including convection and radiation with the environment, conduction with support and between adjacent filaments, radiation between adjacent filaments and convection with entrapped air. The magnitude of the mechanical deformation is also studied. Once this exercise is completed, it is possible to select the material properties, process variables and thermal phenomena that should be taken in for effective numerical modelling of FFE.

Tunnel engineering – influence of the type and the quantity of measurements in the back analysis of geomechanical parameters

The monitoring data collected during tunnel excavation can be used in inverse analysis procedures in order to identify more realistic geomechanical parameters that can increase the knowledge about the interested formations. These more realistic parameters can be used in real time to adapt the project to the real structure in situ behaviour. However, monitoring plans are normally designed for safety assessment and not especially for the purpose of inverse analysis. In fact, there is a lack of knowledge about what types and quantity of measurements are needed to succeed in identifying the parameters of interest. Also, the optimisation algorithm chosen for the identification procedure may be important for this matter. In this work, this problem is addressed using a theoretical case with which a thorough parametric study was carried out using two optimisation algorithms based on different calculation paradigms, namely a conventional gradient-based algorithm and an evolution strategy algorithm. Calculations were carried for different sets of parameters to identify several combinations of types and amount of monitoring data. The results clearly show the high importance of the available monitoring data and the chosen algorithm for the success rate of the inverse analysis process.

The role of IFNγ in higher brain function: in health and under chronic stress

Tese de Doutoramento em Ciências da Saúde

FISHji: new ImageJ macros for the quantification of fluorescence in epifluorescence images

Fluorescence in situ hybridization (FISH) is based on the use of fluorescent staining dyes, however, the signal intensity of the images obtained by microscopy is seldom quantified with accuracy by the researcher. The development of innovative digital image processing programs and tools has been trying to overcome this problem, however, the determination of fluorescent intensity in microscopy images still has issues due to the lack of precision in the results and the complexity of existing software. This work presents FISHji, a set of new ImageJ methods for automated quantification of fluorescence in images obtained by epifluorescence microscopy. To validate the methods, results obtained by FISHji were compared with results obtained by flow cytometry. The mean correlation between FISHji and flow cytometry was high and significant, showing that the imaging methods are able to accurately assess the signal intensity of fluorescence images. FISHji are available for non-commercial use at http://paginas.fe.up.pt/nazevedo/.

Multikriterielle, optimale Planung von Verteilungsnetzen im liberalisierten Energiemarkt unter Verwendung von spieltheoretischen Verfahren

Power network planning, liberalisation, optimisation, game theory, distribution network, dispersed generation, modelling, simulation, energy market

Modellierungsansatz und Kennzahlensystem für die Optimierung von Wertschöpfungsprozessen

Value-added process, Prcess optimisation, imultaneous Endineering, Concurrent Engineering, Process Factors, Procecc modelling

Single period Markowitz portfolio selection, performance gauging and duality: a variation on Luenberger's shortage function

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

Artificial diets for the production of natural enemies (predators and parasitoids) of greenhouse pest insects

The aim of this contract was to finalise in vitro rearing on artificial diets of entomophagous insects useful to control insect pests mainly in greenhouses through an analytical and rational approach. The work focuses on the development and optimisation of artificial diets for one coccinellid (Harmonia axyridis), two heteropteran predators (Orius laevigatus, Dicyphus tamaninii), and a braconid parasitoid of aphids (Aphidius ervi). The definition of the artificial diets was based on biochemical analyses of their natural food (aphids) or substitution food for the predators (Ephestia kuehniella eggs). Reliable quality control parameters of the entomophages produced were used in order to adjust dietary composition and formulation of the different diets tested.

Efficient knowledge retrieval to calibrate input variables in forest fire prediction

Forest fires are a serious threat to humans and nature from an ecological, social and economic point of view. Predicting their behaviour by simulation still delivers unreliable results and remains a challenging task. Latest approaches try to calibrate input variables, often tainted with imprecision, using optimisation techniques like Genetic Algorithms. To converge faster towards fitter solutions, the GA is guided with knowledge obtained from historical or synthetical fires. We developed a robust and efficient knowledge storage and retrieval method. Nearest neighbour search is applied to find the fire configuration from knowledge base most similar to the current configuration. Therefore, a distance measure was elaborated and implemented in several ways. Experiments show the performance of the different implementations regarding occupied storage and retrieval time with overly satisfactory results.

Marine biotoxins in the Catalan littoral: could biosensors be integrated into monitoring programmes?

Aquest article descriu els sensors enzimàtics i immunosensors electroquímics que s’han desenvolupat als nostres grups per a la detecció de la biotoxina marina àcid okadaic (OA), i discuteix la possibilitat d’integrar-los en programes de seguiment. Els sensors enzimàtics per a OA que es presenten es basen en la inhibició de la proteïna fosfatasa (PP2A) per aquesta toxina i la mesura electroquímica de l’activitat enzimàtica mitjançant l’ús de substrats enzimàtics apropiats, electroquímicament actius després de la seva desfosforació per l’enzim. Els immunosensors electroquímics descrits en aquest article es basen en un enzimoimmunoassaig sobre fase sòlida competitiu indirecte (ciELISA), amb fosfatasa alcalina (ALP) o peroxidasa (HRP) com a marcatges, i un sistema de reciclatge enzimàtic amb diaforasa (DI). Els biosensors presentats aquí s’han aplicat a l’anàlisi de dinoflagel·lats, musclos i ostres. Les validacions preliminars amb assaigs colorimètrics i LC-MS/MS han demostrat la possibilitat d’utilitzar les bioeines desenvolupades per al cribratge preliminar de biotoxines marines en mostres de camp o de cultiu, que ofereixen informació complementària a la cromatografia. En conclusió, tot i que encara cal optimitzar alguns paràmetres experimentals, la integració dels biosensors a programes de seguiment és viable i podria proporcionar avantatges respecte a altres tècniques analítiques pel que fa al temps d’anàlisi, la simplicitat, la selectivitat, la sensibilitat, el fet de poder ser d’un sol ús i l’efectivitat de cost. This article describes the electrochemical enzyme sensors and immunosensors that have been developed by our groups for the detection of marine biotoxin okadaic acid (OA), and discusses the possibility of integrating them into monitoring programmes. The enzyme sensors for OA reported herein are based on the inhibition of immobilised protein phosphatase 2A (PP2A) by this toxin and the electrochemical measurement of the enzyme activity through the use of appropriate enzyme substrates, which are electrochemically active after dephosphorylation by the enzyme. The electrochemical immunosensors described in this article are based on a competitive indirect Enzyme- Linked ImmunoSorbent Assay (ciELISA), using alkaline phosphatase (ALP) or horseradish peroxidase (HRP) as labels, and an enzymatic recycling system with diaphorase (DI). The biosensors presented herein have been applied to the analysis of dinoflagellates, mussels and oysters. Preliminary validations with colorimetric assays and LC-MS/MS have demonstrated the possibility of using the developed biotools for the preliminary screening of marine biotoxins in field or cultured samples, offering complementary information to chromatography. In conclusion, although optimisation of some experimental parameters is still required, the integration of biosensors into monitoring programmes is viable and may provide advantages over other analytical techniques in terms of analysis time, simplicity, selectivity, sensitivity, disposability of electrodes and cost effectiveness.

Biologics in rheumatoid arthritis - recommendations for Swiss practice.

The new paradigm of therapy in rheumatoid arthritis is to aim toward early and complete remission, using a larger use of conventional DMARDs and biologic agents. The present recommendations were established through a consensus to help practitioners in their daily use of those agents, to reflect the current "best practice" in Switzerland.

Agent based simulation to optimise emergency departments

Nowadays, many of the health care systems are large and complex environments and quite dynamic, specifically Emergency Departments, EDs. It is opened and working 24 hours per day throughout the year with limited resources, whereas it is overcrowded. Thus, is mandatory to simulate EDs to improve qualitatively and quantitatively their performance. This improvement can be achieved modelling and simulating EDs using Agent-Based Model, ABM and optimising many different staff scenarios. This work optimises the staff configuration of an ED. In order to do optimisation, objective functions to minimise or maximise have to be set. One of those objective functions is to find the best or optimum staff configuration that minimise patient waiting time. The staff configuration comprises: doctors, triage nurses, and admissions, the amount and sort of them. Staff configuration is a combinatorial problem, that can take a lot of time to be solved. HPC is used to run the experiments, and encouraging results were obtained. However, even with the basic ED used in this work the search space is very large, thus, when the problem size increases, it is going to need more resources of processing in order to obtain results in an acceptable time.

Le management de juridiction : analyse comparative de l'organisation et du fonctionnement managérial de cinq juridictions du pouvoir judiciaire à Genève

Cette étude comparative analyse le management au sein de cinq juridictions du pouvoir judiciaire genevois. Elle s'intéresse en particulier au président et au greffier de juridiction, qui, dans ces structures, sont investis de cette mission, et se fonde sur une conception actualisée du cycle traditionnel de management. Comment fonctionnent et s'organisent les juridictions du point de vue managérial ? Comment les managers se répartissent-ils leur rôle et leurs responsabilités ? Quelles sont les pratiques managériales utilisées, et comment sont-elles perçues par les collaborateurs et les managers ? Cet ouvrage a pour objectif de répondre à ces questions et de formuler une série de recommandations visant l'optimisation du management juridictionnel au sein du pouvoir judiciaire à Genève.

A study on the expressive power of some fragments of the modal µ-Calculus

Résumé Le μ-calcul est une extension de la logique modale par des opérateurs de point fixe. Dans ce travail nous étudions la complexité de certains fragments de cette logique selon deux points de vue, différents mais étroitement liés: l'un syntaxique (ou combinatoire) et l'autre topologique. Du point de vue syn¬taxique, les propriétés définissables dans ce formalisme sont classifiées selon la complexité combinatoire des formules de cette logique, c'est-à-dire selon le nombre d'alternances des opérateurs de point fixe. Comparer deux ensembles de modèles revient ainsi à comparer la complexité syntaxique des formules as¬sociées. Du point de vue topologique, les propriétés définissables dans cette logique sont comparées à l'aide de réductions continues ou selon leurs positions dans la hiérarchie de Borel ou dans celle projective. Dans la première partie de ce travail nous adoptons le point de vue syntax¬ique afin d'étudier le comportement du μ-calcul sur des classes restreintes de modèles. En particulier nous montrons que: (1) sur la classe des modèles symétriques et transitifs le μ-calcul est aussi expressif que la logique modale; (2) sur la classe des modèles transitifs, toute propriété définissable par une formule du μ-calcul est définissable par une formule sans alternance de points fixes, (3) sur la classe des modèles réflexifs, il y a pour tout η une propriété qui ne peut être définie que par une formule du μ-calcul ayant au moins η alternances de points fixes, (4) sur la classe des modèles bien fondés et transitifs le μ-calcul est aussi expressif que la logique modale. Le fait que le μ-calcul soit aussi expressif que la logique modale sur la classe des modèles bien fondés et transitifs est bien connu. Ce résultat est en ef¬fet la conséquence d'un théorème de point fixe prouvé indépendamment par De Jongh et Sambin au milieu des années 70. La preuve que nous donnons de l'effondrement de l'expressivité du μ-calcul sur cette classe de modèles est néanmoins indépendante de ce résultat. Par la suite, nous étendons le langage du μ-calcul en permettant aux opérateurs de point fixe de lier des occurrences négatives de variables libres. En montrant alors que ce formalisme est aussi ex¬pressif que le fragment modal, nous sommes en mesure de fournir une nouvelle preuve du théorème d'unicité des point fixes de Bernardi, De Jongh et Sambin et une preuve constructive du théorème d'existence de De Jongh et Sambin. RÉSUMÉ Pour ce qui concerne les modèles transitifs, du point de vue topologique cette fois, nous prouvons que la logique modale correspond au fragment borélien du μ-calcul sur cette classe des systèmes de transition. Autrement dit, nous vérifions que toute propriété définissable des modèles transitifs qui, du point de vue topologique, est une propriété borélienne, est nécessairement une propriété modale, et inversement. Cette caractérisation du fragment modal découle du fait que nous sommes en mesure de montrer que, modulo EF-bisimulation, un ensemble d'arbres est définissable dans la logique temporelle Ε F si et seulement il est borélien. Puisqu'il est possible de montrer que ces deux propriétés coïncident avec une caractérisation effective de la définissabilité dans la logique Ε F dans le cas des arbres à branchement fini donnée par Bojanczyk et Idziaszek [24], nous obtenons comme corollaire leur décidabilité. Dans une deuxième partie, nous étudions la complexité topologique d'un sous-fragment du fragment sans alternance de points fixes du μ-calcul. Nous montrons qu'un ensemble d'arbres est définissable par une formule de ce frag¬ment ayant au moins η alternances si et seulement si cette propriété se trouve au moins au n-ième niveau de la hiérarchie de Borel. Autrement dit, nous vérifions que pour ce fragment du μ-calcul, les points de vue topologique et combina- toire coïncident. De plus, nous décrivons une procédure effective capable de calculer pour toute propriété définissable dans ce langage sa position dans la hiérarchie de Borel, et donc le nombre d'alternances de points fixes nécessaires à la définir. Nous nous intéressons ensuite à la classification des ensembles d'arbres par réduction continue, et donnons une description effective de l'ordre de Wadge de la classe des ensembles d'arbres définissables dans le formalisme considéré. En particulier, la hiérarchie que nous obtenons a une hauteur (ωω)ω. Nous complétons ces résultats en décrivant un algorithme permettant de calculer la position dans cette hiérarchie de toute propriété définissable.