Class Notes for Math 921/922: Real Analysis, Instructor Mikil Foss

Topics include: Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon- Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration, Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon-Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration.

Avaliação anatômica e tomografica das estruturas abdominais do Alouatta guariba clamitans (Bugio-Ruivo – Cabrera,1940)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Artroplastia total híbrida nacional em cães Portadores de displasia coxofemoral

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Análise da locomoção e estudos por imagens em porcos com sindactilia

Pós-graduação em Biotecnologia Animal - FMVZ

Isotopic, trace element and nutrient characterization of coastal waters from Ubatuba inner shelf area, south-eastern Brazil

Stable isotopes, tritium, radium isotopes, radon, trace elements and nutrients data were collected during two sampling campaigns in the Ubatuba coastal area (south-eastern Brazil) with the aim of investigating submarine groundwater discharge (SGD) in the region. The isotopic composition (delta D, delta(18)O, (3)H) of submarine waters was characterised by significant variability and heavy isotope enrichment. The stable isotopes and tritium data showed good separation of groundwater and seawater groups. The contribution of groundwater in submarine waters varied from a few % to 17%. Spatial distribution of (222)Rn activity concentration in surface seawater revealed changes between 50 and 200 Bq m(-3) which were in opposite relationship with observed salinities. Time series measurements of (222)Rn activity concentration in Flamengo Bay (from 1 to 5 kBq m(-3)), obtained by in situ underwater gamma-spectrometry showed a negative correlation between the (222)Rn activity concentration and tide/salinity. This may be caused by sea level changes as tide effects induce variations of hydraulic gradients, which increase (222)Rn concentration during lower sea level, and opposite, during high tides where the (222)Rn activity concentration is smaller. The estimated SGD fluxes varied during 22-26 November between 8 and 40 cm d(-1), with an average value of 21 cm d(-1) (the unit is cm(3)/cm(2) per day). The radium isotopes and nutrient data showed scattered distributions with offshore distance and salinity. which implies that in a complex coast with many small bays and islands, the area has been influenced by local currents and groundwater-seawater mixing. SGD in the Ubatuba area is fed by coastal contaminated groundwater and re-circulated seawater (with small admixtures of groundwater). which claims for potential environmental concern with implications on the management of freshwater resources in the region. (C) 2007 Elsevier Ltd. All rights reserved.

Predicting dysthyroid optic neuropathy using computed tomography volumetric analyses of orbital structures

OBJECTIVE: To evaluate the ability of orbital apex crowding volume measurements calculated with multidetector-computed tomography to detect dysthyroid optic neuropathy. METHODS: Ninety-three patients with Graves' orbitopathy were studied prospectively. All of the patients underwent a complete neuro-ophthalmic examination and computed tomography scanning. Volumetric measurements were calculated from axial and coronal contiguous sections using a dedicated workstation. Orbital fat and muscle volume were estimated on the basis of their attenuation values (in Hounsfield units) using measurements from the anterior orbital rim to the optic foramen. Two indexes of orbital muscle crowding were calculated: i) the volumetric crowding index, which is the ratio between soft tissue (mainly extraocular muscles) and orbital fat volume and is based on axial scans of the entire orbit; and ii) the volumetric orbital apex crowding index, which is the ratio between the extraocular muscles and orbital fat volume and is based on coronal scans of the orbital apex. Two groups of orbits (with and without dysthyroid optic neuropathy) were compared. RESULTS: One hundred and two orbits of 61 patients with Graves' orbitopathy met the inclusion criteria and were analyzed. Forty-one orbits were diagnosed with Graves' orbitopathy, and 61 orbits did not have optic neuropathy. The two groups of orbits differed significantly with regard to both of the volumetric indexes (p<0.001). Although both indexes had good discrimination ability, the volumetric orbital apex crowding index yielded the best results with 92% sensitivity, 86% specificity, 81%/94% positive/negative predictive value and 88% accuracy at a cutoff of 4.14. CONCLUSION: This study found that the orbital volumetric crowding index was a more effective predictor of dysthyroid optic neuropathy than previously described computed tomography indexes were.

Diltiazem como alternativa ao betabloqueador na angiotomografia de artérias coronárias

FUNDAMENTO: A redução da frequência cardíaca (FC) na angiografia por tomografia das artérias coronarianas (ATCCor) é fundamental para a qualidade de imagem. A eficácia dos bloqueadores de cálcio como alternativas para pacientes com contraindicações aos betabloqueadores não foi definida. OBJETIVOS: Comparar a eficácia na redução da FC e variabilidade RR do metoprolol e diltiazem na ATCCor. MÉTODOS: Estudo prospectivo, randomizado, aberto, incluiu pacientes com indicação clínica de ATCCor, em ritmo sinusal, com FC>70bpm e sem uso de agentes que interferissem com a FC. Cinquenta pacientes foram randomizados para grupos: metoprolol IV 5-15 mg ou até FC≤60 bpm(M), e diltiazem IV 0,25-0,60mg/kg ou até FC≤60 bpm (D). Pressão arterial (PA) e FC foram aferidas na condição basal, 1min, 3min e 5min após agentes, na aquisição e após ATCCor. RESULTADOS: A redução da FC em valores absolutos foi maior no grupo M que no grupo D (1, 3, 5min, aquisição e pós-exame). A redução percentual da FC foi significativamente maior no grupo M apenas no 1 min e 3 min após início dos agentes. Não houve diferença no 5 min, durante a aquisição e após exame. A variabilidade RR percentual do grupo D foi estatisticamente menor do que a do grupo M durante a aquisição (variabilidade RR/ FC média da aquisição). Um único caso de BAV, 2:1 Mobitz I, revertido espontaneamente ocorreu (grupo D). CONCLUSÃO: Concluímos que o diltiazem é uma alternativa eficaz e segura aos betabloqueadores na redução da FC na realização de angiografia por tomografia computadorizada das artérias coronarianas. (Arq Bras Cardiol. 2012; [online].ahead print, PP.0-0)

De Novo Thrombotic Microangiopathy After Kidney Transplantation: Clinical Features, Treatment, and Long-Term Patient and Graft Survival

Introduction. Posttransplant thrombotic microangiopathy (TMA)/hemolytic uremic syndrome (HUS) can occur as a recurrent or de novo disease. Methods. A retrospective single-center observational study was applied in order to examine the incidence and outcomes of de novo TMA/HUS among transplantations performed between 2000 and 2010. Recurrent HUS or antibody-mediated rejections were excluded. Results. Seventeen (1.1%) among 1549 kidney transplant recipients fulfilled criteria for de novo TMA. The mean follow-up was 572 days (range, 69-1769). Maintenance immunosuppression was prednisone, tacrolimus (TAC), and mycophenolic acid in 14 (82%) patients. Mean age at onset was 40 +/- 15 years, and serum creatinine was 6.1 +/- 4.1 mg/dL. TMA occurred at a median of 25 days (range, 1-1755) after transplantation. Nine (53%) patients developed TMA within 1 month of transplantation and only 12% after 1 year. Clinical features were anemia (hemoglobin < 10 g/dL) in 9 (53%) patients, thrombocytopenia in 7 (41%), and increased lactate dehydrogenase in 12 (70%). Decreased haptoglobin was observed in 64% and schistocytes in 35%. Calcineurin inhibitor (CM) withdrawal or reduction was the first step in the management of 10/15 (66%) patients, and 6 (35%) received fresh frozen plasma (FFP) and/or plasmapheresis. TAC was successfully reintroduced in six patients after a median of 17 days. Eight (47%) patients needed dialytic support after TMA diagnosis and 75% remained on dialysis. At 4 years of follow-up, death-censored graft survival was worse for TMA group (43.0% versus 85.6%, log-rank = 0.001; hazard ratio = 3.74) and there was no difference in patient survival (53.1% versus 82.2%, log-rank = 0.24). Conclusion. De novo TMA after kidney transplantation is a rare but severe condition with poor graft outcomes. This syndrome may not be fully manifested, and clinical suspicion is essential for early diagnosis and treatment, based mainly in CM withdrawal and FFP infusions and/or plasmapheresis.

Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

Nerve fiber layer in glaucomatous hemifield loss: a case-control study with time- and spectral-domain optical coherence tomography

Purpose: To evaluate the retinal nerve fiber layer measurements with time-domain (TD) and spectral-domain (SD) optical coherence tomography (OCT), and to test the diagnostic ability of both technologies in glaucomatous patients with asymmetric visual hemifield loss. Methods: 36 patients with primary open-angle glaucoma with visual field loss in one hemifield (affected) and absent loss in the other (non-affected), and 36 age-matched healthy controls had the study eye imaged with Stratus-OCT (Carl Zeiss Meditec Inc., Dublin, California, USA) and 3 D OCT-1000 (Topcon, Tokyo, Japan). Peripapillary retinal nerve fiber layer measurements and normative classification were recorded. Total deviation values were averaged in each hemifield (hemifield mean deviation) for each subject. Visual field and retinal nerve fiber layer "asymmetry indexes" were calculated as the ratio between affected versus non-affected hemifields and corresponding hemiretinas. Results: Retinal nerve fiber layer measurements in non-affected hemifields (mean [SD] 87.0 [17.1] mu m and 84.3 [20.2] mu m, for TD and SD-OCT, respectively) were thinner than in controls (119.0 [12.2] mu m and 117.0 [17.7] mu m, P<0.001). The optical coherence tomography normative database classified 42% and 67% of hemiretinas corresponding to non-affected hemifields as abnormal in TD and SD-OCT, respectively (P=0.01). Retinal nerve fiber layer measurements were consistently thicker with TD compared to SD-OCT. Retinal nerve fiber layer thickness asymmetry index was similar in TD (0.76 [0.17]) and SD-OCT (0.79 [0.12]) and significantly greater than the visual field asymmetry index (0.36 [0.20], P<0.001). Conclusions: Normal hemifields of glaucoma patients had thinner retinal nerve fiber layer than healthy eyes, as measured by TD and SD-OCT. Retinal nerve fiber layer measurements were thicker with TD than SD-OCT. SD-OCT detected abnormal retinal nerve fiber layer thickness more often than TD-OCT.

Visual impairment in children with spastic cerebral palsy measured by psychophysical and electrophysiological grating acuity tests

Background: This study measured grating visual acuity in 173 children between 6-48 months of age who had different types of spastic cerebral palsy (CP). Method: Behavioural acuity was measured with the Teller Acuity Cards (TAC) using a staircase psychophysical procedure. Electrophysiological visual acuity was estimated using the sweep VEP (sVEP). Results: The percentage of children outside the superior tolerance limits was 44 of 63 (69%) and 50 of 55 (91%) of tetraplegic, 36 of 56 (64%) and 42 of 53 (79%) of diplegic, 10 of 48 (21%) and 12 of 40 (30%) of hemiplegic for sVEP and TAC, respectively. For the sVEP, the greater visual acuity deficit found in the tetraplegic group was significantly different from that of the hemiplegic group (p < 0.001). In the TAC procedure the mean visual acuity deficits of the tetraplegic and diplegic groups were significantly different from that of hemiplegic group (p < 0.001). The differences between sVEP and TAC means of visual acuity difference were statistically significant for the tetraplegic (p < 0.001), diplegic (p < 0.001), and hemiplegic group (p = 0.004). Discussion: Better visual acuities were obtained in both procedures for hemiplegic children compared to diplegic or tetraplegic. Tetraplegic and diplegic children showed greater discrepancies between the TAC and sVEP results. Inter-ocular acuity difference was more frequent in sVEP measurements. Conclusions: Electrophysiologically measured visual acuity is better than behavioural visual acuity in children with CP.

ESPECTRA: Searching the Bipolar Spectrum in Eating Disorder patients

Abstract Background Bipolar Disorder (BD) is a chronic, recurrent and highly prevalent illness. Despite the need for correct diagnosis to allow proper treatment, studies have shown that reaching a diagnosis can take up to ten years due to the lack of recognition of the broader presentations of BD. Frequent comorbidities with other psychiatric disorders are a major cause of misdiagnosis and warrant thorough evaluation. Methods/Design ESPECTRA (Occurrence of Bipolar Spectrum Disorders in Eating Disorder Patients) is a single-site cross-sectional study involving a comparison group, designed to evaluate the prevalence of bipolar spectrum in an eating disorder sample. Women aged 18-45 years will be evaluated using the SCID-P and Zurich criteria for diagnosis and the HAM-D, YOUNG, SCI-MOODS, HCL-32, BIS-11, BSQ, WHOQoL and EAS instruments for rating symptoms and measuring clinical correlates. Discussion The classificatory systems in psychiatry are based on categorical models that have been criticized for simplifying the diagnosis and leading to an increase in comorbidities. Some dimensional approaches have been proposed aimed at improving the validity and reliability of psychiatric disorder assessments, especially in conditions with high rates of comorbidity such as BD and Eating Disorder (ED). The Bipolar Spectrum (BS) remains under-recognized in clinical practice and its definition is not well established in current diagnostic guidelines. Broader evaluation of psychiatric disorders combining categorical and dimensional views could contribute to a more realistic understanding of comorbidities and help toward establishing a prognosis.

Prevalence of apical periodontitis detected in cone beam CT images of a Brazilian subpopulation

Objectives The aim of this study was to determine the prevalence of apical periodontitis (AP) detected in cone beam CT (CBCT) images from a database. Methods CBCT images of 300 Brazilian patients were assessed. AP images were measured in three dimensions. Age, gender, number and location of total teeth in each patient were considered. AP location was considered according to tooth groups. The extent of AP was determined by the largest diameter in any of the three dimensions. Percentages and the X2 test were used for statistical analysis. Results AP was found in 51.4% of the patients and in 3.4% of the teeth. Higher prevalence of AP was found in 60- to 69-year-olds (73.1%) and in mandibular molars (5.9%) (p < 0.05). Inadequate endodontic treatment presented higher prevalence of AP (78.1%). Conclusions AP can be frequently found in CBCT examinations. The presence of AP has a significant association with patients' age, and tooth type and condition. CBCT databases are useful for cross-sectional studies about AP prevalence in a population.

Clinical, tomographic aspects and relevance of torus palatinus: case report of two sisters

Despite the nomenclature suggested to be a tumor, torus palatinus (TP) is an overgrowth of the bone in the palatal region and represents an anatomic variation. Its prevalence varies among the population studied and its etiology is still unclear; however, it seems to be a multifactorial disorder with genetics and environmental involvement. Surgical removal of the TP is indicated in the following circumstances: (1) deglutition and speech impairment, (2) cancer phobia, (3) traumatized mucosa over the torus, and (4) prosthetic reasons. The aim of this case report is describe cases that occurred in two sisters, emphasizing the genetic etiology of this anatomic variation. In addition, intra-oral exam and computed tomography scan (axial, coronal and sagittal view) provided a detailed assessment of the TP and elimination of other possible diagnoses, furthermore allowed a better analyzes of the anatomic relation with adjacentes structures. No surgical removal was indicated for both cases.

Neurovascular anatomical variations in the anterior palate observed on CBCT images

Objective: This study aimed to assess the presence of additional foramina and canals in the anterior palate region, through cone beam computed tomography (CBCT) images, describing their location, direction, and diameter. Materials & Methods: CBCT exams of 178 subjects displaying the anterior maxilla were included and the following parameters were registered: gender; age group; presence of additional foramina in the anterior palate (AFP) with at least 1 mm in diameter; location and diameter of AFP; and direction of bony canals associated with AFP. Results: Twenty-eight patients (15.7%) presented AFP and in total 34 additional foramina were registered. No statistical differences between patients with or without AFP were found for gender or age. The average diameter of AFP was 1.4 mm (range from 1 to 1.9 mm). Their location was variable, with most of the cases occurring in the alveolar process near the incisors or canines (n = 27). In 18 cases, AFP was associated with bony canals with upward or oblique direction toward the anterior nasal cavity floor. In 14 cases, the canal presented as a direct extension of the canalis sinuosus, in an upward direction laterally to the nasal cavity aperture. In two cases, the canal was observed adjacent to the incisive and joined the nasopalatine canal superiorly. Discussion: CBCT images have a crucial role in the recognition of anatomical variations by allowing detailed tridimensional evaluations. Additional foramina and canals in the anterior region of the upper jaw are relatively frequent. Practitioners should be aware and trained to identify these variations. Conclusions: Over 15% of the population studied had additional foramina in the anterior palate, between 1 mm and 1.9 mm wide, with variable locations. In most cases the canals associated with these foramina either presented as a direct extension of the canalis sinuosus, or coursed towards the nasal cavity floor.