Les questions <EM>"Qu'est-ce qu'une preuve?"</EM> et <EM>"Quand deux preuves sont-elles identiques?"</EM> sont fondamentales pour la théorie de la preuve. Mais pour la logique classique propositionnelle --- la logique la plus répandue --- nous n'avons pas encore de réponse satisfaisante. C'est embarrassant non seulement pour la théorie de la preuve, mais aussi pour l'informatique, où la logique classique joue un rôle majeur dans le raisonnement automatique et dans la programmation logique. De même, l'architecture des processeurs est fondée sur la logique classique. Tous les domaines dans lesquels la recherche de preuve est employée peuvent bénéficier d'une meilleure compréhension de la notion de preuve en logique classique, et le célèbre problème NP-vs-coNP peut être réduit à la question de savoir s'il existe une preuve courte (c'est-à-dire, de taille polynomiale) pour chaque tautologie booléenne. Normalement, les preuves sont étudiées comme des objets syntaxiques au sein de systèmes déductifs (par exemple, les tableaux, le calcul des séquents, la résolution, ...). Ici, nous prenons le point de vue que ces objets syntaxiques (également connus sous le nom d'arbres de preuve) doivent être considérés comme des représentations concrètes des objets abstraits que sont les preuves, et qu'un tel objet abstrait peut être représenté par un arbre en résolution ou dans le calcul des séquents. Le thème principal de ce travail est d'améliorer notre compréhension des objets abstraits que sont les preuves, et cela se fera sous trois angles différents, étudiés dans les trois parties de ce mémoire: l'algèbre abstraite (chapitre 2), la combinatoire (chapitres 3 et 4), et la complexité (chapitre 5).

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Les systèmes cholinergique et dopaminergique jouent un rôle prépondérant dans les fonctions cognitives. Ce rôle est exercé principalement grâce à leur action modulatrice de l’activité des neurones pyramidaux du cortex préfrontal. L’interaction pharmacologique entre ces systèmes est bien documentée mais les études de leurs interactions neuroanatomiques sont rares, étant donné qu’ils sont impliqués dans une transmission diffuse plutôt que synaptique. Ce travail de thèse visait à développer une expertise pour analyser ce type de transmission diffuse en microscopie confocale. Nous avons étudié les relations de microproximité entre ces différents systèmes dans le cortex préfrontal médian (mPFC) de rats et souris. En particulier, la densité des varicosités axonales en passant a été quantifiée dans les segments des fibres cholinergiques et dopaminergiques à une distance mutuelle de moins de 3 µm ou à moins de 3 µm des somas de cellules pyramidales. Cette microproximité était considérée comme une zone d’interaction probable entre les éléments neuronaux. La quantification était effectuée après triple-marquage par immunofluorescence et acquisition des images de 1 µm par microscopie confocale. Afin d’étudier la plasticité de ces relations de microproximité, cette analyse a été effectuée dans des conditions témoins, après une activation du mPFC et dans un modèle de schizophrénie par déplétion des neurones cholinergiques du noyau accumbens. Les résultats démontrent que 1. Les fibres cholinergiques interagissent avec des fibres dopaminergiques et ce sur les mêmes neurones pyramidaux de la couche V du mPFC. Ce résultat suggère différents apports des systèmes cholinergique et dopaminergique dans l’intégration effectuée par une même cellule pyramidale. 2. La densité des varicosités en passant cholinergiques et dopaminergiques sur des segments de fibre en microproximité réciproque est plus élevée comparé aux segments plus distants les uns des autres. Ce résultat suggère un enrichissement du nombre de varicosités axonales dans les zones d’interaction. 3. La densité des varicosités en passant sur des segments de fibre cholinergique en microproximité de cellules pyramidales, immunoúactives pour c-Fos après une stimulation visuelle et une stimulation électrique des noyaux cholinergiques projetant au mPFC est plus élevée que la densité des varicosités de segments en microproximité de cellules pyramidales non-activées. Ce résultat suggère un enrichissement des varicosités axonales dépendant de l’activité neuronale locale au niveau de la zone d'interaction avec d'autres éléments neuronaux. 4. La densité des varicosités en passant des fibres dopaminergiques a été significativement diminuée dans le mPFC de rats ayant subi une déplétion cholinergique dans le noyau accumbens, comparée aux témoins. Ces résultats supportent des interrelations entre la plasticité structurelle des varicosités dopaminergiques et le fonctionnement cortical. L’ensemble des donneès démontre une plasticité de la densité locale des varicosités axonales en fonction de l’activité neuronale locale. Cet enrichissement activité-dépendant contribue vraisemblablement au maintien d’une interaction neurochimique entre deux éléments neuronaux. / The cognitive functions of the rat medial prefrontal cortex (mPFC) are modulated by ascending modulatory systems such as the cholinergic and dopaminergic afferent systems. However, despite the well-documented pharmacological interactions between the cholinergic and dopaminergic afferents and pyramidal cells in the PFC, there is only scarce neuroanatomical data on the reciprocal interrelationships between these neuronal elements in the mPFC. This might be due to the diffuse rather than synaptic transmission mode of intercellular communication of the cholinergic system in the mPFC. For these reasons, the neuroanatomical relationships between the cholinergic and dopaminergic systems and pyramidal cells in the mPFC are examined, with an emphasis on the local density of the cholinergic and dopaminergic axon varicosities. To analyze the plasticity of these interrelationships, the two systems were examined in condition of increased neuronal activity in the mPFC, or of decrease dopaminergic activity in a model of schizophrenia. The microproximity relationships between cholinergic and dopaminergic fibers as well as with pyramidal cells were studied in the mPFC of rats and mice. In particular, the number of axon varicosities in cholinergic and dopaminergic fiber segments within 3 µm from each other or from pyramidal cells were quantified. This microproximity was considered as a possible interaction zone between two neuronal elements. Quantification was performed using triple immunofluorescence labeling and acquisition of 1 µm optic sections using confocal microscopy. To assess the plasticity of these relationships, the analysis has been performed in control condition as well as after a cortical activation or a decreased dopaminergic input in a schizophrenia model. Our results demonstrate a neuroanatomical convergence of cholinergic and dopaminergic fibers on the same pyramidal cell from layer V (output) of mPFC, suggestinggests the integration of different types of inputs by the same pyramidal cell, which may be transmitted to subcortical areas to execute prefrontal cognitive control. Close apposition between cholinergic and dopaminergic fibers could also be seen in the mPFC. There was an increase of the density of cholinergic and dopaminergic en passant varicosities on those fiber segments within microproximity of each other, compared to those outside the reciprocal microproximity, supporting functional importance of the close apposition between those two ascending neuromodulatory systems into the mPFC. There was enrichment of cholinergic en passant varicosities on the fiber segments within microproximity of c-Fos activated pyramidal cells in the mPFC of visually and HDB electrically stimulated rats, indicating association between axonal varicosity density and the local neuronal activity. There was decrease of dopaminergic en passant varicosities in the mPFC of rats with ChAT depletion in the N.Acc., compared to controls. This evidence supports the association between dopaminergic axonal varicosities and relevant neuronal activity in a complex neuronal network. This thesis shows that the density of cholinergic and dopaminergic axonal varicosity density in the mPFC is influenced by and contributes to the relevant local neuronal activity from the interactions of different transmitter systems. Such interactions of different systems in a complex and intricate prefrontal neuronal network endeavour to maintain the delicate balance for cognitive processes.

The entorhinal cortex (EC) in the medial temporal lobe plays a critical role in memory formation and is implicated in several neurological diseases including temporal lobe epilepsy and Alzheimer’s disease. Despite the known importance of this brain region, little is known about the normal bioelectrical activity patterns of the EC in awake, behaving primates. In order to develop effective therapies for diseases affecting the EC, we must first understand its normal properties. To contribute to our understanding of the EC, I monitored the activity of individual neurons and populations of neurons in the EC of rhesus macaque monkeys during free-viewing of photographs using electrophysiological techniques. The results of these experiments help to explain how primates can form memories of, and navigate through, the visual world. These experiments revealed neurons in the EC that represent visual space with triangular grid receptive fields and other neurons that prefer to fire near image borders. These properties are similar to those previously described in the rodent EC, but here the neuronal responses relate to viewing of remote space as opposed to representing the physical location of the animal. The representation of visual space may be aided by another EC neuron type that was discovered, free-viewing saccade direction cells, neurons that signaled the direction of upcoming saccades. Such a signal could be used by other cells to prepare to fire according to the future gaze location. Many of these spatially-responsive neurons also represented memory for images, suggesting that they may be useful for associating items with their locations. I also examined the neuronal circuitry of recognition memory for visual stimuli in the EC, and I found that population synchronization within the gamma-band (30-140 Hz) in superficial layers of the EC was modulated by stimulus novelty, while the strength of memory formation modulated gamma-band synchronization in the deep layers and in layer III. Furthermore, the strength of connectivity in the gamma-band between different layers was correlated with the strength of memory formation, with deep to superficial power transfer being correlated with stronger memory formation and superficial to deep transfer correlated with weaker memory formation. These findings support several previous investigations of hippocampal-entorhinal connectivity in the rodent and advance our understanding of the functional circuitry of the medial temporal lobe memory system. Finally, I explored the design of a device that could be used to investigate properties of brain tissue in vitro, potentially aiding in the development of treatments for disorders of the EC and other brain structures. We designed, fabricated, and validated a novel device for long-term maintenance of thick brain slices and 3-dimensional dissociated cell cultures on a perforated multi-electrode array. To date, most electrical recordings of thick tissue preparations have been performed by manually inserting electrode arrays. This work demonstrates a simple and effective solution to this problem by building a culture perfusion chamber around a planar perforated multi-electrode array. By making use of interstitial perfusion, the device maintained the thickness of tissue constructs and improved cellular survival as demonstrated by increased firing rates of perfused slices and 3-D cultures, compared to unperfused controls. To the best of our knowledge, this is the first thick tissue culture device to combine forced interstitial perfusion for long-term tissue maintenance and an integrated multi-electrode array for electrical recording and stimulation.

甲基安非他命是一種被廣泛濫用的非法神經興奮劑，而且使用之後常伴隨著精神疾病的發生，動物研究也顯示，施打甲基安非他命所引起的神經毒性不僅會造成多巴胺神經元及血清素神經元的損傷，也引起認知功能和社交行為的缺失，同時對於產生迷幻作用的5-HT2A受體作用劑的行為反應增強。N,N,N-trimethylglycine (TMG)和N,N-dimethylglycine (DMG)是甘胺酸的甲基化衍生物，由於這兩種藥物具有治療神經系統疾病的潛力，因此本研究的目的為評估TMG及DMG是否可以預防或改善小鼠在甲基安非他命的暴露下所導致的行為缺失包括新位置辨識測試，新物體辨識測試，社交行為互動測試以及使用5-HT2A受體作用劑DOI 誘導小鼠頭部抽搐(head twitch )的行為。實驗方式為腹腔注射給予雄性ICR小鼠甲基安非他命，一天注射四劑（4 × 5mg/kg），每劑間隔兩小時。實驗一，小鼠在暴露甲基安非他命，先確認行為改變後，給予腹腔注射TMG及DMG (10或30 mg/kg)連續七天，評估TMG及DMG的治療效果。實驗二在施打每劑甲基安非他命30分鐘前給予TMG及DMG (100 mg/kg)，七天後進行行為評估，實驗三，評估TMG及DMG個別及混合劑量的治療效果，小鼠給予甲基安非他命之後，先確認行為改變，再給予腹腔注射TMG及DMG (20、5+5或是10+10 mg/kg) 連續七天，七天後進行行為測試。實驗四，檢測TMG及DMG的治療效果是否藉由活化NMDA受體glycine binding site，小鼠給予甲基安非他命七天之後，腹腔注射TMG及DMG (20 mg/kg)並在給予TMG及DMG前30分鐘給予glycine binding site 拮抗劑7-chlorokynurenic acid (7-CK) (1 mg/kg)，連續給藥七天，七天後進行行為評估。實驗結果發現連續給予七天TMG及DMG在個別劑量及混合劑量中都能夠恢復甲基安非他命所造成的認知功能缺損，社交退縮和降低由DOI 誘導小鼠頭部抽搐行為表現，以及在紋狀體中酪氨酸羥化酶的蛋白質表達減少情況。而前給予7-CK則阻斷TMG及DMG對甲基安非他命所造成的認知功能缺損，社交退縮的改善作用，但是對TMG及DMG對DOI 誘導小鼠頭部抽搐的行為的改善作用影響較小，顯示TMG及DMG可能都是經由活化NMDA 受體的glycine binding site改善甲基安非他命所造成的認知功能缺損，社交退縮，這些發現表示，TMG及DMG具有治療甲基安非他命成癮者所造成的精神分裂等異常症狀的潛力。 / Methamphetamine (METH) is a widely abused illicit psychostimulant. METH use is commonly associated with psychosis. A neurotoxic regimen of METH, which damages the dopaminergic and serotonergic neurons, causes cognitive dysfunction, social interaction deficits, and supersensitivity to hallucinogen in mice. N,N,N-trimethylglycine (TMG) and N,N-dimethylglycine (DMG) are methyl derivatives of amino acid glycine and naturally occur as intermediate metabolites in choline-to-glycine metabolism. Growing evidence shows that both compounds have potential to treat some neurological disorders. The aim of this study was to examine the protective and therapeutic effects of TMG and DMG on METH-induced behavioral aberrations. The novel location recognition test (NLRT), the novel objective recognition test (NORT), the social interaction and the hallucinogenic 2, 5-dimethoxy-4-iodoamphetamine (DOI)-induced head twitch response were evaluated. Male ICR mice received one day drug treatment with four injections of METH (4 × 5 mg/kg, i.p.) or saline at 2h interval. First, TMG or DMG (10 or 30 mg/kg, i.p.) were separately administered once daily for seven consecutive days after the behavioral impairment was confirmed in METH-treated mice. Seven days after final injection of TMG and DMG, the behavioral tests were monitored. Secondly, the preveting effects of TMG and DMG were examined by TMG and DMG (100 mg/kg, i.p.) pretreatment, 30 min prior to each dose of METH. Third, the lower dose (20 mg/kg) and combined effects of TMG and DMG (5+5 or 10+10 mg/kg i.p.) were evaluated. Fourth, in order to determine if the improving effects of TMG and DMG are mediated by NMDA receptor glycine binding site, the glycine binding site antagonist 7-CK (1 mg/kg, i.p.) was administered 30 min prior to each dose of TMG and DMG (20 mg/kg, i.p.), TMG and DMG dose-dependently improved, but not prevented the METH-induced cognition deficits, social withdrawal and hypersensitivity to hallucinogen with additional effect. Pretreatment of 7-CK, reversed the improving effects of TMG and DMG on behavioral deficits after METH exposure, yet had minor effect on hypersensitivity to hallucinogen. These results demonstrate that TMG and DMG might activate the glycine binding site of NMDA receptor to improve METH-induced cognition deficits and social withdrawal. TMG and DMG may be the novel therapeutic agents for psychiatric disorders related to METH abuse.

[Truncated abstract] An elevated total plasma homocysteine concentration (tHcy) is associated with an increased risk of myocardial infarction and ischemic stroke. Folic acid, vitamin B6 and B12 supplements significantly reduce tHcy even in people who are not overtly vitamin deficient. If homocysteine is a causal risk factor for atherothrombotic events, treatment with B-vitamins might prove a simple and cost-effective means to reduce cardiovascular risk. However, it remains unclear whether elevated tHcy causes atherosclerosis or is simply a risk marker. To prove that homocysteine is a modifiable risk factor for cardiovascular disease it is necessary to show that lowering tHcy reduces vascular risk. The aim of this study was to determine whether long-term homocysteine-lowering with B-vitamins would improve vascular structure and function in people with a history of stroke. This study was a cross-sectional sub-study of the Vitamins TO Prevent Stroke trial (VITATOPS), a multi-centre, randomised, double-blind, placebo-controlled clinical trial designed to test the efficacy and safety of B-vitamins (folic acid 2mg, vitamin B6 25mg and vitamin B12 0.5mg) in the prevention of vascular events in patients with a recent history of stroke or transient ischemic attack. 173 VITATOPS participants were recruited for the current study. Age, sex, stroke type, medications, cardiovascular risk factors and smoking history were recorded and blood pressure, height, weight, waist and hip girth were measured in all subjects at least two years after randomisation. ... After a mean treatment period of 3.9 ± 0.9 years, the subjects randomised to vitamin treatment had significantly lower tHcy than the subjects randomised to placebo (7.9mol/L, 95%CI 7.5, 8.4 versus 11.8mol/L, 95%CI 10.9, 12.8; p<0.001). There were no significant differences between groups in CIMT (0.84 ± 0.17mm vitamins versus 0.83 ± 0.18mm placebo; p=0.74) or FMD (median of 4.0%, IQR 0.9, 7.2, vitamins versus 3.0%, IQR 0.6, 6.6 placebo; p=0.48). Pooled estimates from the meta-analyses showed that B-vitamin treatment reduces CIMT by 0.10mm (95%CI –0.20, -0.01mm) and increases FMD by 1.4%, (95%CI 0.7, 2.2), although these estimates may have been influenced by positive publication bias. The improvement in FMD was significant in studies of less than eight weeks duration but not in studies with longer treatment periods. The association between tHcy and CIMT and FMD was eliminated by adjustment for renal function and long-term B-vitamin treatment did not alter the strong linear relationship between tHcy and cystatin C. Lowering tHcy did not alter arterial wall inflammation assessed by 18FDG-PET, although small subject numbers meant we were unable to exclude a minor treatment effect. Long-term homocysteine-lowering with B-vitamin treatment did not improve CIMT or FMD or reduce arterial wall inflammation in people with a history of stroke. The relationship between tHcy and these markers of vascular risk was eliminated by adjustment for renal function. Our data are consistent with the hypothesis that elevated tHcy is a risk marker for cardiovascular disease rather than a modifiable causal risk factor.

The aim of this study is to use an intermedial theory to analyse and contextualize embodiment and violence in the Chinese author Mo Yan’s Life and Death Are Wearing Me Out. I use Jørgen Bruhn’s mediality model, introduced in The Intermediality of Narrative Literature: Medialities Matter (2016), to analyse medial phenomena such as intra- and intermediality in the novel. Bruhn’s model mainly covers relations between several media and within a single medium. The focus of this study lies on the blending of different media within the novel. My hypothesis is that the depiction of embodied violence in the novel is a literary strategy, based on cognitive functions and Chinese oral traditions to communicate historical events, as well as through an intermedial depiction of those events, a way to avoid censorship. Of particular importance to this study are medial phenomena connected to visualization of memories, and intermediality as discipline a voice between media texts, to establish how a literary text through narrative techniques can create an illusion of cinematic blending. I see this as an illustration of the historical hierarchical struggle between art forms. This is a broader perspective on literary depiction in Mo Yan’s novel than generally can be found in interpretations originating in a Western discourse. The result of my study shows that medial phenomena such as inter- and intramediality are woven into a narrative theme of remembrance of historical political events. Such memories are communicated through depictions of embodied violence, as well as the impact of trauma on anonymous bodies reminiscent of cinematic techniques, heightened by the metafictive voice of Mo Yan within the novel. It is a perspective that is also accentuated through auditory and visual elements that recall the ability of audio-visual media techniques to create identification with exposed bodies through close-up depictions of body and violence. Hence, Mo Yan has constructed a grid of medial phenomena in the novel through which he is able to convey historical processes without risking censorship.

Représenter un objet géométrique complexe par un ensemble de primitives simples est une tâche souvent fondamentale, que ce soit pour la reconstruction et la réparation de données, ou encore pour faciliter la visualisation ou la manipulation des données. Le choix de la ou les primitives, ainsi que celui de la méthode d'approximation, impactent fortement les propriétés de la représentation de forme qui sera obtenue.Dans cette thèse, nous utilisons les boules comme seule primitive. Nous prenons ainsi un grand soin à décrire les unions finies de boules et leur structure. Pour cela, nous nous reposons sur les faisceaux de boules. En particulier, nous aboutissons à une description valide en toute dimension, sans hypothèse de position générale. En chemin, nous obtenons également plusieurs résultats portant sur les tests d'inclusion locale et globale dans une union de boules.Nous proposons également une nouvelle méthode d'approximation par union finie de boules, l'approximation par boules à (delta,epsilon)-près. Cette approche contraint l'union de boules à couvrir un sous-ensemble de la forme d'origine (précisément, un epsilon-érodé), tout en étant contenu dans un sur-ensemble de la forme (un delta-dilaté). En nous appuyant sur nos précédents résultats portant sur les unions de boules, nous démontrons plusieurs propriétés de ces approximations. Nous verrons ainsi que calculer une approximation par boules à (delta,epsilon)-près qui soit de cardinal minimum est un problème NP-complet. Pour des formes simples dans le plan, nous présentons un algorithme polynomial en temps et en espace qui permet de calculer ces approximations de cardinal minimum. Nous concluons par une généralisation de notre méthode d'approximation pour une plus large variété de sous-ensembles et sur-ensembles. / Describing a complex geometric shape with a set of simple primitives is often a fundamental task for shape reconstruction, visualization, analysis and manipulation. The type of primitives, as well as the choice of approximation scheme, both greatly impact the properties of the resulting shape representation.In this PhD, we focus on balls as primitives. Using pencils of balls, we carefully describe finite unions of balls and their structure. In particular, our description holds in all dimension without assuming general position. On our way, we also establish various results and tools to test local and global inclusions within these unions.We also propose a new approximation scheme by union of balls, the (delta,epsilon)-ball approximation. This scheme constrains the approximation to cover a core subset of the original shape (specifically, an epsilon-erosion), while being contained within a superset of the shape (a delta-dilation). Using our earlier results regarding finite unions of balls, we prove several properties of these approximations. We show that computing a cardinal minimum (delta,epsilon)-ball approximation is an NP-complete problem. For simple planar shapes however, we present a polynomial time and space algorithm that outputs a cardinal minimum approximation. We then conclude by generalizing the approximation scheme to a wider range of core subsets and bounding supersets.

[pt] O Envelope de Retas Médias - ERM consiste da união de três conjuntos invariantes afins: o Affine Envelope Symmetry Set - AESS; o Mid-Parallel Tangents Locus - MPTL; e a Evoluta Afim - EA. O ERM de curvas planas convexas é um assunto que tem sido muito explorado. Porém, não existe na literatura nenhum estudo do ERM para superfícies. Por isso, o objetivo principal desta tese é generalizar o ERM de curvas convexas para superfícies convexas. Para tanto, dividimos a tese em duas partes. A primeira consiste de uma revisão sobre a geometria afim de curvas planas e do estudo do ERM com uma nova abordagem. Na segunda parte realizamos uma breve introdução da geometria afim de hipersuperfícies e a generalização do ERM. Na generalização do ERM, trabalhamos com superfícies, definimos os planos médios e estudamos o que denominamos Envelope de Planos Médios -EPM. Provamos que, o EPM assim como o ERM, é formado por três conjuntos invariantes afins: a Superfície de Centros de 3 mais 3-Cônicas - SC3C; o Mid-Parallel Tangents Surface -MPTS; e a Evoluta de Curvas Médias - ECM. / [en] The Envelope of Mid-Lines - EML consists of the union of three affine invariant sets: the Affine Envelope Symmetry Set - AESS; the Mid-Parallel Tangents Locus - MPTL; and the Affine Evolute. The EML of convex planar curves is a subject that has been very explored. However, there is no study in the literature of the EML for surfaces. Therefore, the main objective of this thesis is to generalize the EML of convex curves to convex surfaces. We divide the writing into two parts. The first part consists of a study of the EML with a new approach. In the second part we consider the EML for surfaces, that we call Envelope of Mid-Planes - EMP. We prove that, the EMP, like the EML, is formed by three affine invariant sets: the Centers of 3 plus 3-Conics Surface - C3CS; the Mid-Parallel Tangents Surface -MPTS; and the Medial Curves Evolute - MCE.

A atresia biliar (AB) é uma colangiopatia de etiologia indeterminada que leva à necessidade de transplante hepático, mesmo com a realização da Portoenterostomia em tempo hábil. O espessamento da camada média da artéria hepática sugere o envolvimento de um distúrbio angiogênico. Este estudo objetivou avaliar a expressão imunoistoquímica do VEGF A e seus receptores nas estruturas hepatobiliares de pacientes com AB. Nós avaliamos, por método semiquantitativo, a positividade do VEGF A, VEGFR1 e VEGFR2 em biópsia de fígados obtidas por ocasião da Portoenterostomia de crianças com AB (n=52),com (n=14) e sem (n=38) malformação extra-hepáticas. Seviram como controles, pacientes com colestase intra-hepática (CI)\ (n=7). A positividade do VEGFA foi também avaliada em explantes (n=33) e porta hepatis (n=16) de pacientes com AB. Avaliamos morfometricamente as variáveis positividade de CK7 (PCK7) em biópsia de pacientes com AB e a relação espessura da camada média arterial/ diâmetro luminal (REMD) em ramos da artéria hepática de pacientes com AB e de pacientes com CI. Nós encontramos que a positividade do VEGF A foi maior em pacientes com AB por ocasião da Portoenterostomia (p=0, 006) que nos outros grupos, enquanto que nos explantes, a positividade de VEGF A foi maior no parênquima (P<0.001). A positividade do VEGFR2 em ducto biliares e hepatócitos foi menor em pacientes com AB que nos casos de CI (P=0.023 e P=0.011, respectivamente). Maior positividade de CK7 ocorreu em pacientes com artérias e estruturas biliares positivas para VEGF A (P<0.001 e P=0.040, respectivamente). Nos pacientes com AB por ocasião da Portoenterostomia a positividade do VEGF A em estruturas biliares, artérias e hepatócitos correlacionou-se com PCK7 (P=0.031, P=0.031 e P=0.032, respectivamente). O VEGF A foi expresso no porta hepatis de pacientes com AB em artérias e em ductos biliares, principalmente nos pacientes sem malformações extra-hepáticas (P=0.013). A positividade do VEGF A associou-se com a maior REMD (P=0.016 e P=0.044, respectivamente). Nossos achados sugerem que a colangiopatia isquêmica, agravada pela proliferação biliar, ocorre na AB por ocasião da Portoenterostomia, começando no porta hepatis. O espessamento da camada média arterial está associada à expressão do VEGF A. / In Biliary atresia (BA) a cholangiopathy of elusive etiology leads to the need of liver transplantation regardless of timely performance of Portoenterostomy; hepatic arterial medial thickening suggests involvement of a disturbed angiogenesis. This study aimed to evaluate the immunohistochemical expression of VEGF A and its receptors in hepatobiliary structures in BA. We semiquantitatively analyzed the positivity rate of VEGF A, VEGF-R1 and -R2 in liver biopsies obtained at Portoenterostomy from infants with BA (n=52), with (n=14) and without (n=38) extrahepatic malformations. Controls were infants with intrahepatic cholestasis (IC, n=7). VEGF A positivity was also evaluated in explants (n=33) and at porta hepatis (n=16) from patients with BA. We morphometrically assessed the variables percentage of CK-7 positivity (PCK7) in biopsies from patients with BA, and the ratio medial layer thickness/luminal diameter (RMED) in hepatic arterial branches from infants with BA and IC. We found that arterial VEGF A positivity was higher in patients with BA at the time of Portoenterostomy (P=0.006) than in other groups, while explants’parenchyma presented the highest VEGF A positivity (P<0.001). Biliary and hepatocytic VEGFR2 positivity was lower in BA than IC (P=0.023 and P=0.011, respectively). Higher PCK7 occurred in arterial and biliary VEGF A-positive patients (P<0.001 and P=0.040, respectively). Biliary, arterial and hepatocytic VEGF A positivity in BA at Portoenterostomy was correlated with PCK7 (P=0.031, P=0.031 and P=0.032, respectively). VEGF A was expressed at porta hepatis from BA patients in arteries, and, in bile ducts mainly in patients without extrahepatic malformations (P=0.013). Biliary and arterial VEGF A positivity was associated with higher RMED (P=0.016 and P=0.044, respectively). Our findings suggest that an ischemic cholangiopathy, aggravated by biliary proliferation, exists in BA at the time of Portoenterostomy, beginning at porta hepatis. Medial layer thickening is associated with VEGF A expression.